url
stringlengths 16
775
| text
stringlengths 100
1.02M
| date
timestamp[s] | metadata
stringlengths 1.07k
1.1k
|
|---|---|---|---|
https://phys.libretexts.org?title=TextBooks_%26_TextMaps/University_Physics_TextMaps/Map:_University_Physics_(OpenStax)/Map:_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/7:_Quantum_Mechanics/7.A:_Quantum_Mechanics_(Answers) | Skip to main content
$$\require{cancel}$$
# 7.A: Quantum Mechanics (Answers)
## Check Your Understanding
7.1. $$\displaystyle (3+4i)(3−4i)=9−16i^2=25$$
7.2. $$\displaystyle A=\sqrt{2/L}$$
7.3. $$\displaystyle (1/2−1/π)/2=9%$$
7.4. $$\displaystyle 4.1×10^{−8}eV; 1.1×10^{−5}nm$$
7.5. $$\displaystyle 0.5mω^2x^2ψ(x)∗ψ(x)$$
7.6. None. The first function has a discontinuity; the second function is double-valued; and the third function diverges so is not normalizable.
7.7. a. 9.1%;
b. 25%
7.8. a. 295 N/m;
b. 0.277 eV
7.9. $$\displaystyle ⟨x⟩=0$$
7.10. $$\displaystyle L_{proton}/L_{electron}=\sqrt{m_e/m_p}=2.3%$$
## Conceptual Questions
1. $$\displaystyle 1/\sqrt{L}$$, where $$\displaystyle L=length$$; 1/L, where $$\displaystyle L=length$$
3. The wave function does not correspond directly to any measured quantity. It is a tool for predicting the values of physical quantities.
5. The average value of the physical quantity for a large number of particles with the same wave function.
7. Yes, if its position is completely unknown. Yes, if its momentum is completely unknown.
9. No. According to the uncertainty principle, if the uncertainty on the particle’s position is small, the uncertainty on its momentum is large. Similarly, if the uncertainty on the particle’s position is large, the uncertainty on its momentum is small.
11. No, it means that predictions about the particle (expressed in terms of probabilities) are time-independent.
13. No, because the probability of the particle existing in a narrow (infinitesimally small) interval at the discontinuity is undefined.
15. No. For an infinite square well, the spacing between energy levels increases with the quantum number n. The smallest energy measured corresponds to the transition from n = 2 to 1, which is three times the ground state energy. The largest energy measured corresponds to a transition from $$\displaystyle n=∞$$ to 1, which is infinity. (Note: Even particles with extremely large energies remain bound to an infinite square well—they can never “escape”)
17. No. This energy corresponds to $$\displaystyle n=0.25$$, but n must be an integer.
19. Because the smallest allowed value of the quantum number n for a simple harmonic oscillator is 0. No, because quantum mechanics and classical mechanics agree only in the limit of large nn.
21. Yes, within the constraints of the uncertainty principle. If the oscillating particle is localized, the momentum and therefore energy of the oscillator are distributed.
23. doubling the barrier width
25. No, the restoring force on the particle at the walls of an infinite square well is infinity.
## Problems
27. $$\displaystyle ∣ψ(x)∣^2sin^2ωt$$
29. (a) and (e), can be normalized
31. a. $$\displaystyle A=\sqrt{2α/π}$$;
b. $$\displaystyle probability=29.3%$$;
c. $$\displaystyle ⟨x⟩=0⟨x⟩=0$$;
d. $$\displaystyle ⟨p⟩=0$$;
e. $$\displaystyle ⟨K⟩=α^2ℏ^2/2m$$
33. a. $$\displaystyle Δp≥2.11×10^{−34}N⋅s$$;
b. $$\displaystyle Δv≥6.31×10^{−8}m$$;
c. $$\displaystyle Δv/\sqrt{k_BT/m_α}=5.94×10^{−11}$$
35. $$\displaystyle Δτ≥1.6×10^{−25}s$$
37. a. $$\displaystyle Δf≥1.59MHz$$;
b. $$\displaystyle Δω/ω_0=3.135×10^{−9}$$
39. Carrying out the derivatives yields $$\displaystyle k^2=\frac{ω^2}{c^2}$$.
41. Carrying out the derivatives (as above) for the sine function gives a cosine on the right side the equation, so the equality fails. The same occurs for the cosine solution.
43. $$\displaystyle E=ℏ^2k^2/2m$$
45. $$\displaystyle ℏ^2k^2ℏ$$; The particle has definite momentum and therefore definite momentum squared.
47. 9.4 eV, 64%
49. 0.38 nm
51. 1.82 MeV
53. 24.7 nm
55. $$\displaystyle 6.03Å$$
57. a.
The wave functions for the n=1 through n=5 states of the electron in an infinite square well are shown. Each function is displaced vertically by its energy, measured in meV. The n=1 state is the first half wave of the sine function. The n=2 function is the first full wave of the sine function. The n=3 function is the first one and a half waves of the sine function. The n=4 function is the first two waves of the sine function. The n=5 function is the first two and a half waves of the sine function. ;
b. $$\displaystyle λ_{5→3}=12.9nm,λ_{3→1}=25.8nm,λ_{4→3}=29.4nm$$
59. proof
61. $$\displaystyle 6.662×10^{14}Hz$$
63. $$\displaystyle n≈2.037×10^{30}$$
65. $$\displaystyle ⟨x⟩=0.5mω^2⟨x^2⟩=ℏω/4$$; $$\displaystyle ⟨K⟩=⟨E⟩−⟨U⟩=ℏω/4$$
67. proof
69. A complex function of the form, $$\displaystyle Ae^{iϕ}$$, satisfies Schrӧdinger’s time-independent equation. The operators for kinetic and total energy are linear, so any linear combination of such wave functions is also a valid solution to Schrӧdinger’s equation. Therefore, we conclude that Equation 7.68 satisfies Equation 7.61, and Equation 7.69 satisfies Equation 7.63.
71. a. 4.21%;
b. 0.84%;
c. 0.06%
73. a. 0.13%;
b. close to 0%
75. 0.38 nm
## Additional Problems
77. proof
79. a. 4.0 %;
b. 1.4 %;
c. 4.0%;
d. 1.4%
81. a. $$\displaystyle t=mL^2/h=2.15×10^{26}years$$;
b. $$\displaystyle E_1=1.46×10^{−66}J,K=0.4J$$
83. proof
85. 1.2 N/m
87. 0
## Challenge Problems
89. 19.2µm;11.5µm19.2µm;11.5µm
91. 3.92%
93. proof
### Contributors
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2018-05-21T03:02:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8582653999328613, "perplexity": 1367.989296684728}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863923.6/warc/CC-MAIN-20180521023747-20180521043747-00215.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_I_-_Mechanics%2C_Sound%2C_Oscillations%2C_and_Waves_(OpenStax)/17%3A_Sound/17.5%3A_Sources_of_Musical_Sound | $$\require{cancel}$$
# 17.5: Sources of Musical Sound
Skills to Develop
• Describe the resonant frequencies in instruments that can be modeled as a tube with symmetrical boundary conditions
• Describe the resonant frequencies in instruments that can be modeled as a tube with anti-symmetrical boundary conditions
Some musical instruments, such as woodwinds, brass, and pipe organs, can be modeled as tubes with symmetrical boundary conditions, that is, either open at both ends or closed at both ends (Figure 17.24). Other instruments can be modeled as tubes with anti-symmetrical boundary conditions, such as a tube with one end open and the other end closed (Figure 17.25).
Figure $$\PageIndex{1}$$: Some musical instruments can be modeled as a pipe open at both ends.
Figure $$\PageIndex{2}$$: Some musical instruments can be modeled as a pipe closed at one end.
Resonant frequencies are produced by longitudinal waves that travel down the tubes and interfere with the reflected waves traveling in the opposite direction. A pipe organ is manufactured with various tubes of fixed lengths to produce different frequencies. The waves are the result of compressed air allowed to expand in the tubes. Even in open tubes, some reflection occurs due to the constraints of the sides of the tubes and the atmospheric pressure outside the open tube.
The antinodes do not occur at the opening of the tube, but rather depend on the radius of the tube. The waves do not fully expand until they are outside the open end of a tube, and for a thin-walled tube, an end correction should be added. This end correction is approximately 0.6 times the radius of the tube and should be added to the length of the tube.
Players of instruments such as the flute or oboe vary the length of the tube by opening and closing finger holes. On a trombone, you change the tube length by using a sliding tube. Bugles have a fixed length and can produce only a limited range of frequencies.
The fundamental and overtones can be present simultaneously in a variety of combinations. For example, middle C on a trumpet sounds distinctively different from middle C on a clarinet, although both instruments are modified versions of a tube closed at one end. The fundamental frequency is the same (and usually the most intense), but the overtones and their mix of intensities are different and subject to shading by the musician. This mix is what gives various musical instruments (and human voices) their distinctive characteristics, whether they have air columns, strings, sounding boxes, or drumheads. In fact, much of our speech is determined by shaping the cavity formed by the throat and mouth, and positioning the tongue to adjust the fundamental and combination of overtones. For example, simple resonant cavities can be made to resonate with the sound of the vowels (Figure 17.26). In boys at puberty, the larynx grows and the shape of the resonant cavity changes, giving rise to the difference in predominant frequencies in speech between men and women.
Figure $$\PageIndex{3}$$: The throat and mouth form an air column closed at one end that resonates in response to vibrations in the voice box. The spectrum of overtones and their intensities vary with mouth shaping and tongue position to form different sounds. The voice box can be replaced with a mechanical vibrator, and understandable speech is still possible. Variations in basic shapes make different voices recognizable.
Example 17.6
## Finding the Length of a Tube with a 128-Hz Fundamental
(a) What length should a tube closed at one end have on a day when the air temperature is 22.0 °C if its fundamental frequency is to be 128 Hz (C below middle C)? (b) What is the frequency of its fourth overtone?
## Strategy
The length L can be found from the relationship fn = $$n \frac{v}{4L}$$, but we first need to find the speed of sound v.
## Solution
1. Identify knowns: The fundamental frequency is 128 Hz, and the air temperature is 22.0 °C. Use fn = $$n \frac{v}{4L}$$ to find the fundamental frequency (n = 1), $$f_{1} = \frac{v}{4L} \ldotp$$Solve this equation for length, $$L = \frac{v}{4f_{1}} \ldotp$$Find the speed of sound using v = (331 m/s)$$\sqrt{\frac{T}{273\; K}}$$,$$v = (331\; m/s) \sqrt{\frac{295\; K}{273\; K}} = 344\; m/s \ldotp$$Enter the values of the speed of sound and frequency into the expression for L.$$L = \frac{v}{4f_{1}} = \frac{344\; m/s}{4(128\; Hz)} =0.672\; m$$
2. Identify knowns: The first overtone has n = 3, the second overtone has n = 5, the third overtone has n = 7, and the fourth overtone has n = 9. Enter the value for the fourth overtone into fn = $$n \frac{v}{4L}$$, $$f_{9} = 9 \frac{v}{4L} = 9 f_{1} = 1.15\; kHz \ldotp$$
## Significance
Many wind instruments are modified tubes that have finger holes, valves, and other devices for changing the length of the resonating air column and hence, the frequency of the note played. Horns producing very low frequencies require tubes so long that they are coiled into loops. An example is the tuba. Whether an overtone occurs in a simple tube or a musical instrument depends on how it is stimulated to vibrate and the details of its shape. The trombone, for example, does not produce its fundamental frequency and only makes overtones.
If you have two tubes with the same fundamental frequency, but one is open at both ends and the other is closed at one end, they would sound different when played because they have different overtones. Middle C, for example, would sound richer played on an open tube, because it has even multiples of the fundamental as well as odd. A closed tube has only odd multiples.
# Resonance
Resonance occurs in many different systems, including strings, air columns, and atoms. As we discussed in earlier chapters, resonance is the driven or forced oscillation of a system at its natural frequency. At resonance, energy is transferred rapidly to the oscillating system, and the amplitude of its oscillations grows until the system can no longer be described by Hooke’s law. An example of this is the distorted sound intentionally produced in certain types of rock music.
Wind instruments use resonance in air columns to amplify tones made by lips or vibrating reeds. Other instruments also use air resonance in clever ways to amplify sound. Figure 17.27 shows a violin and a guitar, both of which have sounding boxes but with different shapes, resulting in different overtone structures. The vibrating string creates a sound that resonates in the sounding box, greatly amplifying the sound and creating overtones that give the instrument its characteristic timbre. The more complex the shape of the sounding box, the greater its ability to resonate over a wide range of frequencies. The marimba, like the one shown in Figure 17.28, uses pots or gourds below the wooden slats to amplify their tones. The resonance of the pot can be adjusted by adding water.
Figure $$\PageIndex{4}$$: String instruments such as (a) violins and (b) guitars use resonance in their sounding boxes to amplify and enrich the sound created by their vibrating strings. The bridge and supports couple the string vibrations to the sounding boxes and air within. (credit a: modification of work by Feliciano Guimares; credit b: modification of work by Steve Snodgrass)
Figure $$\PageIndex{5}$$: Resonance has been used in musical instruments since prehistoric times. This marimba uses gourds as resonance chambers to amplify its sound. (credit: “APC Events”/Flickr)
We have emphasized sound applications in our discussions of resonance and standing waves, but these ideas apply to any system that has wave characteristics. Vibrating strings, for example, are actually resonating and have fundamentals and overtones similar to those for air columns. More subtle are the resonances in atoms due to the wave character of their electrons. Their orbitals can be viewed as standing waves, which have a fundamental (ground state) and overtones (excited states). It is fascinating that wave characteristics apply to such a wide range of physical systems.
# Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-06-17T11:20:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5456523299217224, "perplexity": 1069.1934888378187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998473.44/warc/CC-MAIN-20190617103006-20190617125006-00301.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Asteiglitz.kenneth | ## Steiglitz, Kenneth
Compute Distance To:
Author ID: steiglitz.kenneth Published as: Steiglitz, Kenneth; Steiglitz, K.; Steiglitz, Ken Homepage: https://www.cs.princeton.edu/~ken/ External Links: MGP · Wikidata · dblp · GND · IdRef
Documents Indexed: 59 Publications since 1965, including 3 Books 1 Further Contribution Co-Authors: 40 Co-Authors with 55 Joint Publications 1,149 Co-Co-Authors
all top 5
### Co-Authors
4 single-authored 6 Papadimitriou, Christos Harilaos 6 Squier, Richard K. 4 Bruno, John L. 4 Dickinson, Bradley W. 4 Honig, Michael L. 3 Kohler, Walter H. 3 Toueg, Sam 2 Bernstein, Arthur J. 2 Chin, Francis Y. L. 2 Dikaiakos, Marios D. 2 Iwano, Kazuo 2 Jakubowski, Mariusz H. 2 Kugelmass, Steven D. 2 Liu, Bede 2 Masry, Elias 2 Rogers, Anne 2 Ullman, Jeffrey David 2 Vergis, Anastasios 1 Aho, Alfred Vaino 1 Balakrishnan, Venkataramanan 1 Boyd, Stephen Poythress 1 Cappello, Peter R. 1 Coffman, Edward Grady jun. 1 Elkind, Edith 1 Gopinath, B. 1 Graham, Ronald Lewis 1 Henderson, Peter B. 1 Hopcroft, John Edward H. 1 Kodek, Dusan M. 1 Krone, Martin J. 1 Lawrence, J. P. III 1 Mirzaian, Andranik 1 Niedringhaus, William P. 1 Norman, Stephen A. 1 Park, James K. 1 Rantapaa, Erik 1 Rogers, Elizabeth A. 1 Sahai, Amit 1 Schwartz, Stuart C. 1 Sethi, Ravi 1 Sha, Edwin Hsing-Mean 1 Shapiro, Daniel G. 1 Thurston, William Paul
all top 5
### Serials
7 IEEE Transactions on Information Theory 5 Complex Systems 4 SIAM Journal on Computing 4 IEEE Transactions on Acoustics, Speech, and Signal Processing 3 IEEE Transactions on Computers 3 Journal of the Association for Computing Machinery 2 IEEE Transactions on Communications 2 Networks 2 Operations Research 2 International Journal of Control, I. Series 1 Information Processing Letters 1 Journal of Computational Physics 1 Journal of the Franklin Institute 1 Bulletin of Mathematical Biology 1 IEEE Transactions on Automatic Control 1 IEEE Transactions on Circuits and Systems 1 Information and Control 1 Management Science 1 Mathematics and Computers in Simulation 1 Mathematical Programming 1 Physica D 1 SIAM Journal on Applied Mathematics 1 Computational Economics 1 Multiple-Valued Logic 1 Parallel Algorithms and Applications 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling
all top 5
### Fields
32 Computer science (68-XX) 16 Operations research, mathematical programming (90-XX) 16 Information and communication theory, circuits (94-XX) 10 Numerical analysis (65-XX) 5 Systems theory; control (93-XX) 4 Combinatorics (05-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Approximations and expansions (41-XX) 1 Field theory and polynomials (12-XX) 1 Associative rings and algebras (16-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX)
### Citations contained in zbMATH Open
38 Publications have been cited 1,202 times in 1,179 Documents Cited by Year
Combinatorial optimization: algorithms and complexity. Zbl 0503.90060
1982
Combinatorial optimization: algorithms and complexity. Corr. repr. of the 1982 original. Zbl 0944.90066
1998
Soliton-like behavior in automata. Zbl 0604.68061
Park, James K.; Steiglitz, Kenneth; Thurston, William P.
1986
Evaluating polynomials at fixed sets of points. Zbl 0326.65027
Aho, A. V.; Steiglitz, K.; Ullman, J. D.
1975
Some examples of difficult traveling salesman problems. Zbl 0383.90105
1978
Eigenvectors and functions of the discrete Fourier transform. Zbl 0563.65022
1982
Frugality in path auctions. Zbl 1318.91092
Elkind, Edith; Sahai, Amit; Steiglitz, Ken
2004
The complexity of analog computation. Zbl 0594.68040
Vergis, Anastasios; Steiglitz, Kenneth; Dickinson, Bradley
1986
On the complexity of local search for the traveling salesman problem. Zbl 0381.68043
1977
Characterization and theoretical comparison of branch-and-bound algorithms for permutation problems. Zbl 0279.68035
Kohler, Walter H.; Steiglitz, Kenneth
1974
Exact. approximate, and guaranteed accuracy algorithms for the flow-shop problem n/2/F/F. Zbl 0313.68030
Kohler, Walter H.; Steiglitz, Kenneth
1975
Heuristic-programming solution of a flowshop-scheduling problem. Zbl 0279.90021
Krone, Martin J.; Steiglitz, Kenneth
1974
The equivalence of digital and analog signal processing. Zbl 0202.50604
Steiglitz, K.
1965
Combinatorial optimization. Algorithms and complexity. (Kombinatornaya optimizatsiya. Algoritmy i slozhnost’). Transl. from the English. Zbl 0598.90067
1985
Computing with solitons: A review and prospectus. Zbl 1007.68063
Jakubowski, Mariusz H.; Steiglitz, Ken; Squier, Richard
2001
Randomized pattern search. Zbl 0234.65064
Lawrence, J. P. III; Steiglitz, Kenneth
1972
Some complexity results for the traveling salesman problem. Zbl 0369.90060
1976
Phase unwrapping by factorization. Zbl 0565.65027
1982
A semiring on convex polygons and zero-sum cycle problems. Zbl 0711.68095
Iwano, Kazuo; Steiglitz, Kenneth
1990
When can solitons compute? Zbl 0883.68097
Jakubowski, Mariusz H.; Steiglitz, Ken; Squier, Richard K.
1996
On system identification from noise-obscured input and output measurements. Zbl 0199.49202
Rogers, E. A.; Steiglitz, K.
1970
The identification and control of unknown linear discrete systems. Zbl 0218.93020
Schwartz, S. C.; Steiglitz, K.
1971
Series expansion of wide-sense stationary random processes. Zbl 0239.60038
Masry, Elias; Liu, Bede; Steiglitz, Kenneth
1968
Simulating the madness of crowds: Price bubbles in an auction-mediated robot market. Zbl 0912.90090
Steiglitz, Ken; Shapiro, Daniel
1998
Transmission of an analog signal over a fixed bit-rate channel. Zbl 0141.35304
Steiglitz, K.
1966
Some complexity issues in digital signal processing. Zbl 0578.68035
Cappello, Peter R.; Steiglitz, Kenneth
1984
The design of small-diameter networks by local search. Zbl 0409.94037
Toueg, Sam; Steiglitz, Kenneth
1979
Some complexity results in the design of deadlock-free packet switching networks. Zbl 0468.68048
Toueg, Sam; Steiglitz, Kenneth
1981
An $$O(N^2)$$ algorithm for partial fraction expansion. Zbl 0346.65011
Chin, Francis Y.; Steiglitz, Kenneth
1977
The expression of algorithms by charts. Zbl 0242.68017
Bruno, J.; Steiglitz, K.
1972
Programmable parallel arithmetic in cellular automata using a particle model. Zbl 0939.68718
Squier, Richard K.; Steiglitz, Ken
1994
Mathematical foundations of signal processing. Zbl 0835.94002
Steiglitz, Kenneth
1993
Optimal binary coding of ordered numbers. Zbl 0137.13603
Steiglitz, K.; Bernstein, A. J.
1965
A problem in single-machine sequencing with nonlinear delay costs. Zbl 0345.90021
Henderson, Peter B.; Steiglitz, Kenneth
1976
Some experiments with the pathological linear programs of N. Zadeh. Zbl 0388.90043
Niedringhaus, William P.; Steiglitz, Kenneth
1978
Encoding of analog signals for binary symmetric channels. Zbl 0199.21703
Bernstein, A. J.; Steiglitz, K.; Hopcroft, J. E.
1966
Rational transform approximation via the Laguerre spectrum. Zbl 0229.65096
Steiglitz, Kenneth
1965
Pairwise competition and the replicator equation. Zbl 1334.92357
Morgan, John; Steiglitz, Ken
2003
Frugality in path auctions. Zbl 1318.91092
Elkind, Edith; Sahai, Amit; Steiglitz, Ken
2004
Pairwise competition and the replicator equation. Zbl 1334.92357
Morgan, John; Steiglitz, Ken
2003
Computing with solitons: A review and prospectus. Zbl 1007.68063
Jakubowski, Mariusz H.; Steiglitz, Ken; Squier, Richard
2001
Combinatorial optimization: algorithms and complexity. Corr. repr. of the 1982 original. Zbl 0944.90066
1998
Simulating the madness of crowds: Price bubbles in an auction-mediated robot market. Zbl 0912.90090
Steiglitz, Ken; Shapiro, Daniel
1998
When can solitons compute? Zbl 0883.68097
Jakubowski, Mariusz H.; Steiglitz, Ken; Squier, Richard K.
1996
Programmable parallel arithmetic in cellular automata using a particle model. Zbl 0939.68718
Squier, Richard K.; Steiglitz, Ken
1994
Mathematical foundations of signal processing. Zbl 0835.94002
Steiglitz, Kenneth
1993
A semiring on convex polygons and zero-sum cycle problems. Zbl 0711.68095
Iwano, Kazuo; Steiglitz, Kenneth
1990
Soliton-like behavior in automata. Zbl 0604.68061
Park, James K.; Steiglitz, Kenneth; Thurston, William P.
1986
The complexity of analog computation. Zbl 0594.68040
Vergis, Anastasios; Steiglitz, Kenneth; Dickinson, Bradley
1986
Combinatorial optimization. Algorithms and complexity. (Kombinatornaya optimizatsiya. Algoritmy i slozhnost’). Transl. from the English. Zbl 0598.90067
1985
Some complexity issues in digital signal processing. Zbl 0578.68035
Cappello, Peter R.; Steiglitz, Kenneth
1984
Combinatorial optimization: algorithms and complexity. Zbl 0503.90060
1982
Eigenvectors and functions of the discrete Fourier transform. Zbl 0563.65022
1982
Phase unwrapping by factorization. Zbl 0565.65027
1982
Some complexity results in the design of deadlock-free packet switching networks. Zbl 0468.68048
Toueg, Sam; Steiglitz, Kenneth
1981
The design of small-diameter networks by local search. Zbl 0409.94037
Toueg, Sam; Steiglitz, Kenneth
1979
Some examples of difficult traveling salesman problems. Zbl 0383.90105
1978
Some experiments with the pathological linear programs of N. Zadeh. Zbl 0388.90043
Niedringhaus, William P.; Steiglitz, Kenneth
1978
On the complexity of local search for the traveling salesman problem. Zbl 0381.68043
1977
An $$O(N^2)$$ algorithm for partial fraction expansion. Zbl 0346.65011
Chin, Francis Y.; Steiglitz, Kenneth
1977
Some complexity results for the traveling salesman problem. Zbl 0369.90060
1976
A problem in single-machine sequencing with nonlinear delay costs. Zbl 0345.90021
Henderson, Peter B.; Steiglitz, Kenneth
1976
Evaluating polynomials at fixed sets of points. Zbl 0326.65027
Aho, A. V.; Steiglitz, K.; Ullman, J. D.
1975
Exact. approximate, and guaranteed accuracy algorithms for the flow-shop problem n/2/F/F. Zbl 0313.68030
Kohler, Walter H.; Steiglitz, Kenneth
1975
Characterization and theoretical comparison of branch-and-bound algorithms for permutation problems. Zbl 0279.68035
Kohler, Walter H.; Steiglitz, Kenneth
1974
Heuristic-programming solution of a flowshop-scheduling problem. Zbl 0279.90021
Krone, Martin J.; Steiglitz, Kenneth
1974
Randomized pattern search. Zbl 0234.65064
Lawrence, J. P. III; Steiglitz, Kenneth
1972
The expression of algorithms by charts. Zbl 0242.68017
Bruno, J.; Steiglitz, K.
1972
The identification and control of unknown linear discrete systems. Zbl 0218.93020
Schwartz, S. C.; Steiglitz, K.
1971
On system identification from noise-obscured input and output measurements. Zbl 0199.49202
Rogers, E. A.; Steiglitz, K.
1970
Series expansion of wide-sense stationary random processes. Zbl 0239.60038
Masry, Elias; Liu, Bede; Steiglitz, Kenneth
1968
Transmission of an analog signal over a fixed bit-rate channel. Zbl 0141.35304
Steiglitz, K.
1966
Encoding of analog signals for binary symmetric channels. Zbl 0199.21703
Bernstein, A. J.; Steiglitz, K.; Hopcroft, J. E.
1966
The equivalence of digital and analog signal processing. Zbl 0202.50604
Steiglitz, K.
1965
Optimal binary coding of ordered numbers. Zbl 0137.13603
Steiglitz, K.; Bernstein, A. J.
1965
Rational transform approximation via the Laguerre spectrum. Zbl 0229.65096
Steiglitz, Kenneth
1965
all top 5
### Cited by 2,064 Authors
19 Papadimitriou, Christos Harilaos 12 Kasperski, Adam 11 Bertsekas, Dimitri Panteli 10 Steiner, George 10 Zieliński, Paweł 8 Butkovič, Peter 8 Pan, Victor Yakovlevich 7 Cheng, Tai-Chiu Edwin 6 Aarts, Emile Hubertus Leonardus 6 Averbakh, Igor 6 Ibaraki, Toshihide 6 Li, Jianping 6 Li, Shuguang 6 Pesch, Erwin 6 Punnen, Abraham P. 6 Schost, Éric 6 Yannakakis, Mihalis 6 Ye, Yinyu 5 Adamatzky, Andrew I. 5 Barketau, Maksim S. 5 Berman, Oded 5 Bostan, Alin 5 Brucker, Peter J. 5 Gutin, Gregory Z. 5 Hall, Nicholas G. 5 Hao, Jin-Kao 5 Jacobson, Sheldon H. 5 Katoh, Naoki 5 Liu, Yanpei 5 Orlin, James B. 5 Pardalos, Panos M. 5 Paschos, Vangelis Th. 5 Shabtay, Dvir 4 Adler, Ilan 4 Atakishiev, Natig M. 4 Castanon, David A. 4 Crama, Yves 4 Fotakis, Dimitris A. 4 Hochbaum, Dorit S. 4 Ji, Min 4 Jiao, Licheng 4 Kalantari, Bahman 4 Kern, Walter 4 Roos, Cornelis 4 Sergienko, Ivan Vasylyovych 4 Shang, Ronghua 4 Terlaky, Tamás 4 Tovey, Craig A. 4 Vavasis, Stephen A. 4 Vazirani, Vijay V. 4 Ventre, Carmine 4 Yang, Dar-Li 4 Yang, Suh-Jenq 3 Ahuja, Ravindra K. 3 Alexopoulos, Christos 3 Anstreicher, Kurt M. 3 Arkin, Esther M. 3 Armstrong, Derek E. 3 Avis, David M. 3 Barvinok, Alexander I. 3 Blum, Christian 3 Cardoso, Domingos Moreira 3 Cechlárová, Katarína 3 DasGupta, Bhaskar 3 de la Puente, Maria Jesus 3 Demange, Marc 3 Durak-Ata, Lutfiye 3 Feo, Thomas A. 3 Finger, Marcelo 3 Fuchssteiner, Benno 3 Goerigk, Marc 3 Golden, Bruce L. 3 Greco, Gianluigi 3 Grigoriev, Alexander 3 Gu, Jun 3 Gutjahr, Walter J. 3 Hurink, Johann L. 3 Jurisch, Bernd 3 Khuller, Samir 3 Körner, Frank 3 Kravtsov, Mikhail Konstantinovich 3 Lichen, Junran 3 Murota, Kazuo 3 Panishev, A. V. 3 Prokopyev, Oleg Alexan 3 Raman, Venkatesh 3 Ritter, Gunter 3 Rosenbaum, Paul Richard 3 Serbes, Ahmet 3 Shafransky, Yakov M. 3 Tale, Prafullkumar 3 Tatti, Nikolaj 3 Toth, Paolo 3 Tseng, Paul 3 Tsitsiklis, John N. 3 Vaidya, Pravin M. 3 Werner, Frank 3 Yellen, Jay E. 3 Zhang, Jianzhong 2 Al-Khayyal, Faiz A. ...and 1,964 more Authors
all top 5
### Cited in 260 Serials
92 European Journal of Operational Research 66 Discrete Applied Mathematics 52 Theoretical Computer Science 46 Computers & Operations Research 40 Mathematical Programming. Series A. Series B 34 Annals of Operations Research 30 Information Processing Letters 30 Operations Research Letters 28 Linear Algebra and its Applications 23 Networks 22 Journal of Computer and System Sciences 20 Algorithmica 15 Cybernetics and Systems Analysis 14 Artificial Intelligence 14 Journal of Global Optimization 13 Journal of Combinatorial Optimization 12 Information Sciences 11 Journal of Complexity 11 Computational Optimization and Applications 11 Optimization Letters 10 Pattern Recognition 9 Computers & Mathematics with Applications 9 Mathematical Programming 9 Physica D 8 Applied Mathematics and Computation 8 SIAM Journal on Algebraic and Discrete Methods 8 Optimization 8 Journal of Symbolic Computation 8 Annals of Mathematics and Artificial Intelligence 8 Mathematical Problems in Engineering 7 Automatica 7 Journal of Scheduling 6 OR Spektrum 6 International Journal of Approximate Reasoning 6 Automation and Remote Control 6 Journal of Heuristics 6 Optimization Methods & Software 6 Natural Computing 6 Discrete Optimization 5 Acta Informatica 5 Discrete Mathematics 5 International Journal of Control 5 Asia-Pacific Journal of Operational Research 5 Mathematical and Computer Modelling 5 Machine Learning 5 Games and Economic Behavior 5 Applied Mathematical Modelling 5 Computational Statistics and Data Analysis 5 Journal of Computer and Systems Sciences International 5 Constraints 5 Prikladnaya Diskretnaya Matematika 4 Journal of the Franklin Institute 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Physics 4 Journal of Statistical Physics 4 Computing 4 Journal of Optimization Theory and Applications 4 Naval Research Logistics 4 Statistica Neerlandica 4 Cybernetics 4 Information and Computation 4 Applied Mathematics Letters 4 Neural Computation 4 Computational Geometry 4 ZOR. Zeitschrift für Operations Research 4 Mathematical Methods of Operations Research 4 Data Mining and Knowledge Discovery 4 RAIRO. Operations Research 3 Chaos, Solitons and Fractals 3 BIT 3 Fuzzy Sets and Systems 3 The Journal of Symbolic Logic 3 Mathematics and Computers in Simulation 3 Mathematical Systems Theory 3 Opsearch 3 Advances in Applied Mathematics 3 Systems & Control Letters 3 Mathematical Social Sciences 3 Combinatorica 3 Circuits, Systems, and Signal Processing 3 International Journal of Production Research 3 Discrete & Computational Geometry 3 Journal of Automated Reasoning 3 Signal Processing 3 Random Structures & Algorithms 3 Zeitschrift für Operations Research. Serie A: Theorie 3 Distributed Computing 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Applied and Computational Harmonic Analysis 3 Journal of Nonlinear Mathematical Physics 3 4OR 3 Journal of Discrete Algorithms 3 Mathematical Programming Computation 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of General Systems 2 Mathematical Notes 2 Physica A 2 Theoretical and Mathematical Physics 2 The Annals of Statistics 2 International Journal of Computer & Information Sciences ...and 160 more Serials
all top 5
### Cited in 50 Fields
688 Operations research, mathematical programming (90-XX) 455 Computer science (68-XX) 143 Combinatorics (05-XX) 125 Numerical analysis (65-XX) 74 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 50 Statistics (62-XX) 41 Information and communication theory, circuits (94-XX) 35 Systems theory; control (93-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 26 Biology and other natural sciences (92-XX) 21 Mathematical logic and foundations (03-XX) 20 Convex and discrete geometry (52-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Probability theory and stochastic processes (60-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 12 Quantum theory (81-XX) 10 Number theory (11-XX) 10 Field theory and polynomials (12-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Algebraic geometry (14-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 6 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 5 Group theory and generalizations (20-XX) 5 Difference and functional equations (39-XX) 5 Geometry (51-XX) 4 Commutative algebra (13-XX) 4 Measure and integration (28-XX) 4 Partial differential equations (35-XX) 4 Abstract harmonic analysis (43-XX) 4 Operator theory (47-XX) 3 Integral transforms, operational calculus (44-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Ordinary differential equations (34-XX) 2 Astronomy and astrophysics (85-XX) 1 General algebraic systems (08-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-05-24T12:17:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4612042009830475, "perplexity": 9347.407135283946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662572800.59/warc/CC-MAIN-20220524110236-20220524140236-00077.warc.gz"} |
https://www.lanl.gov/science-innovation/science-programs/office-of-science-programs/high-energy-physics/theoretical-physics-2qfy18.php | # Theoretical Physics Quarterly Progress Reports
Investigating the field of high energy physics through experiments that strengthen our fundamental understanding of matter, energy, space, and time.
# Los Alamos HEP Theory Quarterly Report FY2018-Q2
Daniele Alves, Tanmoy Bhattacharya, Michael L. Graesser, Rajan Gupta, Michael S. Warren
The primary areas of activity of the theory group are in physics beyond the Standard Model, cosmology, dark matter, lattice quantum chromodynamics, neutrinos, the fundamentals of quantum field theory and gravity, and particle astrophysics. The questions pursued by this group relate to deep mysteries in our understanding of Nature at the level of the the Standard Model and beyond. The main tools we use are quantum field theory and General Relativity.
## Lattice QCD
The Los Alamos Lattice QCD team and their collaborators are carrying out precision studies investigating signatures of new physics at the TeV scale, Novel CP violating operator's contribution to nEDM, elucidating the structure of the nucleon, and understanding QCD at finite temperature. Progress during this quarter on these projects is described below. The team spent considerable time working on Quantum Information and Computing and are PI/members of four proposals responding to the DOE call "Quantum Information Science Enabled Discovery For High Energy Physics" was developed and submitted.
### Nucleon charges and form-factors
Extensive additional simulations of isovector and flavor-diagonal charges gA, gS and gT from the 2+1+1-flavor clover-on-HISQ calculations were completed, including the analysis of the very time consuming second physical mass HISQ ensemble with lattice size ${96}^{3}×192$ at 0.06 fm on cluster and GPU computers at Los Alamos and using ERCAP allocations at NERSC. The final analysis of nucleon charges, electric, magnetic and axial vector form factors using up to 3-state fits for both the 2+1+1-flavor clover-on-HISQ and 2+1-flavor clover on clover lattice QCD formulations is almost complete and five manuscripts describing the results are in final draft form. Preliminary results, presented by Rajan Gupta and Yong-Chull Jang at Lattice 2017, have been published as part of the conference proceedings. First results for the axial vector form factors from 2+1+1-flavor clover-on-HISQ have been published in PhysRevD.96.114503.
### Matrix elements of novel CP violating operators and nEDM
Calculations of the matrix elements of the quark chromo electric dipole moment operator (cEDM) and mixing with the pseudoscalar operator are ongoing. The formalism for these calculations and new numerical techniques are being developed. Status of results was presented at Lattice 2017 by Boram Yoon in a plenary talk titled "neutron electric moment on the lattice". The gradient flow method for controlling the mixing and renormalizing issues for the cEDM operator is being investigated.
### Disconnected diagrams
The matrix elements of iso-scalar and flavor diagonal operators are needed for the analysis of a number of interesting qualities such as the nucleon electric dipole moment, the nucleon sigma term and the strangeness content of the proton, and the interaction of dark matter with nucleons. These matrix elements get contributions from disconnected diagrams, that are computationally challenging to compute with high precision. Bhattacharya, Gupta and Yoon worked on the draft manuscript describing the results of extensive simulations carried out over the last three years for publication. In these calculations they analyze the chiral and continuum extrapolation for the flavor diagonal charges for the first time. They are continuing to collaborate with Gambhir, Orginos and Stathopoulos at William and Mary to develop a new method based on deflation and hierarchical probing to speed up the calculation of disconnected diagrams.
Relevant References:
arXiv:1611.01193
### Transverse Momentum Distribution Functions
Results for the Sivers and Boer-Mulders shift, the transversity and the generalized worm-gear shift for two different fermion discretization schemes were finalized and published in PRD [arXiv:1706.03406]. New simulations, in collaboration with the Regensburg group, have been initiated.
### Behavior of QCD at finite temperature
Investigated the properties of QCD at finite temperature, including the nature of the transition, the equation of state and the fluctuations of conserved charges (electric charge, strangeness, baryon number) around the transition temperature (140–160 MeV) as part of the HOTQCD collaboration. The five publications have over 2100 citations.
## Dark Matter and LHC Physics
Graesser is revisiting the topological dark matter scenario and generalizing it in several directions. He is collaborating with J. Osinski, a University of New Mexico graduate student visiting Los Alamos for 6 months on a DOE Office of Science Graduate Student Research Award. They are exploring how the predictions for the relic dark matter density in such a scenario depends on the cosmological history prior to Big Bang Nucleosynthesis. A draft is in preparation for posting to the arXiv.
He is also continuing his work with Tuhin Roy (TATA) and Arun Thalapillil (Pune) on improving the sensitivity of the LHC to new TeV-scale physics scenarios.
## Neutrinoless double beta decay
During this quarter Graesser has been revisiting the contribution of Majorana neutrinos to the neutrinoless double beta decay process, using chiral effective field theory. He and collaborators (Cirigliano, Dekens, de Vries, Mereghetti, Pastore, van Kolck) posted a preprint ``A new leading contribution to neutrinoless double beta decay”, arXiv:1802.10097, which has been accepted for publication in Physical Review Letters. In this paper, the authors identify a new contact operator involving 4 nucleons - i.e., short range - which occurs at the same order as the neutrino potential induced by Majorana neutrinos. The evidence is based on renormalization and using chiral symmetry to relate this process to other isospin breaking observables involving two nucleons. This effect had been missed in all previous computations. The authors speculate on the impact this new contribution will have on nuclear matrix elements of relevance to experimental searches.
Graesser and collaborators (Cirigliano, Dekens, de Vries, Mereghetti) have developed a "master decay" formula that computes the neutrinoless double decay process induced by Majorana neutrinos, as well as any other Beyond the Standard Model physics described at low energies by dimension-7 and/or dimension-9 Delta L=2 violating operators. This master formula is derived using chiral effective field theory, and includes all leading order effects. This formula supersedes all previous formulae for NDBD 0+ -> 0+ transitions, as it includes a rigorous derivation of all leading order chiral dynamics (leading order perturbative and non-perturbative renormalization effects), all relevant low-energy constants (known and unknown), a larger set of gauge invariant operators, and includes all possible interferences in the amplitude. It can be used to match to specific lepton number violating models, a point illustrated by matching the effective theory to the left-right symmetric model. A paper is in preparation.
## MeV Axions and New Physics at the GeV Scale
Daniele S. M. Alves has worked on the following topics: (1) phenomenology of the QCD axion in the MeV mass range, and associated new physics at the GeV scale; (2) phenomenology of sterile neutrinos with BSM interactions, including a "sterile neutrino MSW effect", and associated implications for short baseline anomalies; and (3) generalizations of Tensor Networks and Entanglement Renormalization methods to continuous field theories. A proposal responding to the DOE call "Quantum Information Science Enabled Discovery For High Energy Physics" was developed and submitted.
Relevant References:
arXiv:1710.03764
Contacts | Media | Calendar | 2022-09-24T22:04:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6085859537124634, "perplexity": 1958.7816682457883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030333541.98/warc/CC-MAIN-20220924213650-20220925003650-00503.warc.gz"} |
https://mooseframework.inl.gov/modules/tensor_mechanics/systems.html | ## BCs
• Tensor Mechanics App
• ADPressureApplies a pressure on a given boundary in a given direction
• CoupledPressureBCApplies a pressure from a variable on a given boundary in a given direction
• DashpotBC
• DisplacementAboutAxisImplements a boundary condition that enforces rotationaldisplacement around an axis on a boundary
• InteractionIntegralBenchmarkBC
• PenaltyInclinedNoDisplacementBCPenalty Enforcement of an inclined boundary condition
• PresetAccelerationPrescribe acceleration on a given boundary in a given direction
• PresetDisplacementPrescribe the displacement on a given boundary in a given direction.
• PresetVelocity
• PressureApplies a pressure on a given boundary in a given direction
• StickyBCImposes the boundary condition if exceeds the bounds provided
• CavityPressure
• CoupledPressure
• InclinedNoDisplacementBC
• Pressure
## ICs
• Tensor Mechanics App
• VolumeWeightedWeibullInitialize a variable with randomly generated numbers following a volume-weighted Weibull distribution
## Kernels
• Tensor Mechanics App
• ADGravityApply gravity. Value is in units of acceleration.
• ADStressDivergenceRSphericalTensorsCalculate stress divergence for a spherically symmetric 1D problem in polar coordinates.
• ADStressDivergenceRZTensorsCalculate stress divergence for an axisymmetric problem in cylindrical coordinates.
• ADStressDivergenceTensorsStress divergence kernel with automatic differentiation for the Cartesian coordinate system
• CosseratStressDivergenceTensorsStress divergence kernel for the Cartesian coordinate system
• DynamicStressDivergenceTensorsResidual due to stress related Rayleigh damping and HHT time integration terms
• GeneralizedPlaneStrainOffDiagGeneralized Plane Strain kernel to provide contribution of the out-of-plane strain to other kernels
• GravityApply gravity. Value is in units of acceleration.
• InertialForceCalculates the residual for the interial force () and the contribution of mass dependent Rayleigh damping and HHT time integration scheme ($\eta \cdot M \cdot ((1+\alpha)velq2-\alpha \cdot vel-old)$)
• InertialForceBeamCalculates the residual for the interial force/moment and the contribution of mass dependent Rayleigh damping and HHT time integration scheme.
• InertialTorqueKernel for interial torque: density * displacement x acceleration
• MomentBalancing
• OutOfPlanePressureApply pressure in the out-of-plane direction in 2D plane stress or generalized plane strain models
• PhaseFieldFractureMechanicsOffDiagStress divergence kernel for phase-field fracture: Computes off diagonal damage dependent Jacobian components. To be used with StressDivergenceTensors or DynamicStressDivergenceTensors.
• PlasticHeatEnergyPlastic heat energy density = coeff * stress * plastic_strain_rate
• PoroMechanicsCouplingAdds , where the subscript is the component.
• StressDivergenceBeamQuasi-static and dynamic stress divergence kernel for Beam element
• StressDivergenceRSphericalTensorsCalculate stress divergence for a spherically symmetric 1D problem in polar coordinates.
• StressDivergenceRZTensorsCalculate stress divergence for an axisymmetric problem in cylindrical coordinates.
• StressDivergenceTensorsStress divergence kernel for the Cartesian coordinate system
• StressDivergenceTensorsTrussKernel for truss element
• WeakPlaneStressPlane stress kernel to provide out-of-plane strain contribution
• DynamicTensorMechanics
• PoroMechanics
• TensorMechanics
### Kernels/PoroMechanics
• Tensor Mechanics App
• PoroMechanicsActionSet up stress divergence kernels with coordinate system aware logic
## Modules
### Modules/TensorMechanics
#### Modules/TensorMechanics/LineElementMaster
• Tensor Mechanics App
• CommonLineElementActionSets up variables, stress divergence kernels and materials required for a static analysis with beam or truss elements. Also sets up aux variables, aux kernels, and consistent or nodal inertia kernels for dynamic analysis with beam elements.
• LineElementActionSets up variables, stress divergence kernels and materials required for a static analysis with beam or truss elements. Also sets up aux variables, aux kernels, and consistent or nodal inertia kernels for dynamic analysis with beam elements.
## NodalKernels
• Tensor Mechanics App
• NodalGravityComputes the gravitational force for a given nodal mass.
• NodalRotationalInertiaCalculates the inertial torques and inertia proportional damping corresponding to the nodal rotational inertia.
• NodalTranslationalInertiaComputes the interial forces and mass proportional damping terms corresponding to nodal mass.
## Postprocessors
• Tensor Mechanics App
• CavityPressurePostprocessorInterfaces with the CavityPressureUserObject to store the initial number of moles of a gas contained within an internal volume.
• CrackFrontData
• InteractionIntegralComputes the interaction integral for fracture
• JIntegralCalculates the J-integral at a specified point along the crack front
• Mass
• MaterialTensorIntegralThis postprocessor computes an element integral of a component of a material tensor as specified by the user-supplied indices
• MaterialTimeStepPostprocessorThis postprocessor estimates a timestep that reduces the increment change in a material property below a given threshold.
• MixedModeEquivalentKComputes the mixed-mode stress intensity factor given the , , and stress intensity factors
• TorqueReactionTorqueReaction calculates the torque in 2D and 3Dabout a user-specified axis of rotation centeredat a user-specied origin. | 2019-05-23T13:13:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.799920916557312, "perplexity": 11998.79233138713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257244.16/warc/CC-MAIN-20190523123835-20190523145835-00412.warc.gz"} |
https://indico.fnal.gov/event/13106/contributions/17445/ | 2017 JINA-CEE Frontiers in Nuclear Astrophysics
Feb 7 – 9, 2017
US/Eastern timezone
The First (α,xn) reaction in inverse kinematics study with the HabaNERO detector at NSCL
Feb 7, 2017, 4:45 PM
1h 15m
111 N Grand Ave, Lansing, MI 48933
Poster [Main Conference]
Speaker
Dr Sunghoon (Tony) Ahn (JINA/NSCL)
Description
(α,xn) reactions have been identified as the main production mechanism of Z=38-47 abundances in neutrino driven winds during core-collapse supernovae scenario. Recent sensitivity studies showed that uncertainties in (α,xn) reaction rates directly affect calculated abundances in the neutrinodriven wind models with an impact that is comparable to that from astrophysical uncertainties. Current reaction rate uncertainties are relatively large since there is almost no acknowledgement of experimental data for (α,xn) cross sections involved in the nucleosynthesis calculation. We have developed the Heavy ion Accelerated Beam induced (Alpha,Neutron) Emission Ratio Observer (HabaNERO) for the measurement of relevant (α,xn) reaction cross sections in the theoretical study, including 75Ga(α,xn). The HabaNERO is a neutron long counter system which consists of 44 BF3 and 36 3He gas-filled proportional tubes oriented in rings along the beam axis embedded in a polyethylene matrix. The configuration of the tubes in the matrix was optimized to obtain a high average neutron detection efficiency as constant as possible in the neutron range En = 0.1-19.5 MeV that corresponds to the neutron energies of interest. We have performed the detector commissioning using mono-energetic neutron beams at Edward Accelerator Laboratory, Ohio University, as well as a 75Ga(α,xn) cross section measurement at the National Superconducting Cyclotron Laboratory. We will present the detector development and the first experiment of (α,xn) reaction in inverse kinematics with 75Ga radioactive ion beams and our new detector.
Primary author
Dr Sunghoon (Tony) Ahn (JINA/NSCL)
Presentation materials
There are no materials yet. | 2022-12-03T20:20:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8420961499214172, "perplexity": 7747.466708601389}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710936.10/warc/CC-MAIN-20221203175958-20221203205958-00767.warc.gz"} |
https://lammps.sandia.gov/doc/compute_bond_local.html | compute bond/local command
Syntax
compute ID group-ID bond/local value1 value2 ...
• ID, group-ID are documented in compute command
• bond/local = style name of this compute command
• one or more values may be appended
• value = dist or engpot or force or engvib or engrot or engtrans or omega or velvib
dist = bond distance
engpot = bond potential energy
force = bond force
engvib = bond kinetic energy of vibration
engrot = bond kinetic energy of rotation
engtrans = bond kinetic energy of translation
omega = magnitude of bond angular velocity
velvib = vibrational velocity along the bond length
Examples
compute 1 all bond/local engpot
compute 1 all bond/local dist engpot force
Description
Define a computation that calculates properties of individual bond interactions. The number of datums generated, aggregated across all processors, equals the number of bonds in the system, modified by the group parameter as explained below.
The value dist is the current length of the bond.
The value engpot is the potential energy for the bond, based on the current separation of the pair of atoms in the bond.
The value force is the magnitude of the force acting between the pair of atoms in the bond.
The remaining properties are all computed for motion of the two atoms relative to the center of mass (COM) velocity of the 2 atoms in the bond.
The value engvib is the vibrational kinetic energy of the two atoms in the bond, which is simply 1/2 m1 v1^2 + 1/2 m2 v2^2, where v1 and v2 are the magnitude of the velocity of the 2 atoms along the bond direction, after the COM velocity has been subtracted from each.
The value engrot is the rotationsl kinetic energy of the two atoms in the bond, which is simply 1/2 m1 v1^2 + 1/2 m2 v2^2, where v1 and v2 are the magnitude of the velocity of the 2 atoms perpendicular to the bond direction, after the COM velocity has been subtracted from each.
The value engtrans is the translational kinetic energy associated with the motion of the COM of the system itself, namely 1/2 (m1+m2) Vcm^2 where Vcm = magnitude of the velocity of the COM.
Note that these 3 kinetic energy terms are simply a partitioning of the summed kinetic energy of the 2 atoms themselves. I.e. total KE = 1/2 m1 v1^2 + 1/2 m2 v2^2 = engvib + engrot + engtrans, where v1,v2 are the magnitude of the velocities of the 2 atoms, without any adjustment for the COM velocity.
The value omega is the magnitude of the angular velocity of the two atoms around their COM position.
The value velvib is the magnitude of the relative velocity of the two atoms in the bond towards each other. A negative value means the 2 atoms are moving toward each other; a positive value means they are moving apart.
Note that all these properties are computed for the pair of atoms in a bond, whether the 2 atoms represent a simple diatomic molecule, or are part of some larger molecule.
The local data stored by this command is generated by looping over all the atoms owned on a processor and their bonds. A bond will only be included if both atoms in the bond are in the specified compute group. Any bonds that have been broken (see the bond_style command) by setting their bond type to 0 are not included. Bonds that have been turned off (see the fix shake or delete_bonds commands) by setting their bond type negative are written into the file, but their energy will be 0.0.
Note that as atoms migrate from processor to processor, there will be no consistent ordering of the entries within the local vector or array from one timestep to the next. The only consistency that is guaranteed is that the ordering on a particular timestep will be the same for local vectors or arrays generated by other compute commands. For example, bond output from the compute property/local command can be combined with data from this command and output by the dump local command in a consistent way.
Here is an example of how to do this:
compute 1 all property/local btype batom1 batom2
compute 2 all bond/local dist engpot
dump 1 all local 1000 tmp.dump index c_1[*] c_2[*]
Output info:
This compute calculates a local vector or local array depending on the number of keywords. The length of the vector or number of rows in the array is the number of bonds. If a single keyword is specified, a local vector is produced. If two or more keywords are specified, a local array is produced where the number of columns = the number of keywords. The vector or array can be accessed by any command that uses local values from a compute as input. See this section for an overview of LAMMPS output options.
The output for dist will be in distance units. The output for velvib will be in velocity units. The output for omega will be in velocity/distance units. The output for engtrans, engvib, engrot, and engpot will be in energy units. The output for force will be in force units.
none | 2018-07-17T15:19:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.517588198184967, "perplexity": 1268.0160883576223}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589752.56/warc/CC-MAIN-20180717144908-20180717164908-00478.warc.gz"} |
https://www.allaboutcircuits.com/worksheets/inverting-and-noninverting-opamp-voltage-amplifier-circuits | # Inverting and Noninverting OpAmp Voltage Amplifier Circuits
## Analog Integrated Circuits
• #### Question 1
Don’t just sit there! Build something!!
Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.
You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuit-building exercises, follow these steps:
1. Carefully measure and record all component values prior to circuit construction.
2. Draw the schematic diagram for the circuit to be analyzed.
3. Carefully build this circuit on a breadboard or other convenient medium.
4. Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.
5. Mathematically analyze the circuit, solving for all voltage and current values.
6. Carefully measure all voltages and currents, to verify the accuracy of your analysis.
7. If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully re-calculate the values and re-measure.
Avoid using the model 741 op-amp, unless you want to challenge your circuit design skills. There are more versatile op-amp models commonly available for the beginner. I recommend the LM324 for DC and low-frequency AC circuits, and the TL082 for AC projects involving audio or higher frequencies.
As usual, avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading”. I recommend resistor values between 1 kΩ and 100 kΩ.
One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.
Reveal answer
• #### Question 2
Write the transfer function (input/output equation) for an operational amplifier with an open-loop voltage gain of 100,000, and the inverting input connected directly to its output terminal. In other words, write an equation describing the output voltage of this op-amp (Vout) for any given input voltage at the non-inverting input (Vin(+)):
Then, once you have an equation written, solve for the over-all voltage gain $$(A_v = \frac{V_{out}}{V_{in(+)}})$$ of this amplifier circuit, and calculate the output voltage for a non-inverting input voltage of 6 volts.
Reveal answer
• #### Question 3
Write the transfer function (input/output equation) for an operational amplifier with an open-loop voltage gain of 100,000, and the inverting input connected to a voltage divider on its output terminal (so the inverting input receives exactly one-half the output voltage). In other words, write an equation describing the output voltage of this op-amp (Vout) for any given input voltage at the non-inverting input (Vin(+)):
Then, once you have an equation written, solve for the output voltage if the non-inverting input voltage is -2.4 volts.
Reveal answer
• #### Question 4
Generators used in battery-charging systems must be regulated so as to not overcharge the battery(ies) they are connected to. Here is a crude, relay-based voltage regulator for a DC generator:
Simple electromechanical relay circuits such as this one were very common in automotive electrical systems during the 1950’s, 1960’s, and 1970’s. The fundamental principle upon which their operation is based is called negative feedback: where a system takes action to oppose any change in a certain variable. In this case, the variable is generator output voltage. Explain how the relay works to prevent the generator from overcharging the battery with excessive voltage.
Reveal answer
• #### Question 5
A mechanic has an idea for upgrading the electrical system in an automobile originally designed for 6 volt operation. He wants to upgrade the 6 volt headlights, starter motor, battery, etc, to 12 volts, but wishes to retain the original 6-volt generator and regulator. Shown here is the original 6-volt electrical system:
The mechanic’s plan is to replace all the 6-volt loads with 12-volt loads, and use two 6-volt batteries connected in series, with the original (6-volt) regulator sensing voltage across only one of those batteries:
Explain how this system is supposed to work. Do you think the mechanic’s plan is practical, or are there any problems with it?
Reveal answer
• #### Question 6
Calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and as a figure in units of decibels (dB). Also, write a general equation for calculating the voltage gain of such an amplifier, given the resistor values of R1 and R2:
Reveal answer
• #### Question 7
Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and as a figure in units of decibels (dB):
Reveal answer
• #### Question 8
Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and as a figure in units of decibels (dB):
Reveal answer
• #### Question 9
Determine both the input and output voltage in this circuit:
Reveal answer
• #### Question 10
What would have to be altered in this circuit to increase its overall voltage gain?
Reveal answer
• #### Question 11
The equation for voltage gain (AV) in a typical non-inverting, single-ended opamp circuit is as follows:
AV = R1 R2 1
Where,
R1 is the feedback resistor (connecting the output to the inverting input)
R2 is the other resistor (connecting the inverting input to ground)
Suppose we wished to change the voltage gain in the following circuit from 5 to 6.8, but only had the freedom to alter the resistance of R2:
Algebraically manipulate the gain equation to solve for R2, then determine the necessary value of R2 in this circuit to give it a voltage gain of 6.8.
Reveal answer
• #### Question 12
Calculate the necessary resistor value (R1) in this circuit to give it a voltage gain of 30:
Reveal answer
• #### Question 13
Calculate the necessary resistor value (R1) in this circuit to give it a voltage gain of 10.5:
Reveal answer
• #### Question 14
Predict how the operation of this operational amplifier circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
Resistor R1 fails open:
Solder bridge (short) across resistor R1:
Resistor R2 fails open:
Solder bridge (short) across resistor R2:
Broken wire between R1/R2 junction and inverting opamp input:
For each of these conditions, explain why the resulting effects will occur.
Reveal answer
• #### Question 15
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels), then calculate the overall voltage gain:
Reveal answer
• #### Question 16
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels), then calculate the overall voltage gain:
Reveal answer
• #### Question 17
How much effect will a change in the op-amp’s open-loop voltage gain have on the overall voltage gain of a negative-feedback circuit such as this?
If the open-loop gain of this operational amplifier were to change from 100,000 to 200,000, for example, how big of an effect would it have on the voltage gain as measured from the non-inverting input to the output?
Reveal answer
• #### Question 18
Suppose a technician is checking the operation of the following electronic circuit:
She decides to measure the voltage on either side of resistor R1 with reference to ground, and obtains these readings:
On the top side of R1, the voltage with reference to ground is -5.04 volts. On the bottom side of R1, the voltage with reference to ground is -1.87 volts. The color code of resistor R1 is Yellow, Violet, Orange, Gold. From this information, determine the following:
Voltage across R1 (between top to bottom):
Polarity ( and -) of voltage across R1:
Current (magnitude) through R1:
Direction of current through R1:
Additionally, explain how this technician would make each one of these determinations. What rules or laws of electric circuits would she apply?
Reveal answer
• #### Question 19
Trace the directions for all currents in this circuit, and calculate the values for voltage at the output (Vout) and at test point 1 (VTP1) for several values of input voltage (Vin):
Vin VTP1 Vout 0.0 V 0.4 V 1.2 V 3.4 V 7.1 V 10.8 V
Then, from the table of calculated values, determine the voltage gain (AV) for this amplifier circuit.
Reveal answer
• #### Question 20
Calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and as a figure in units of decibels (dB). Also, write a general equation for calculating the voltage gain of such an amplifier, given the resistor values of R1 and R2:
Reveal answer
• #### Question 21
Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and as a figure in units of decibels (dB):
Reveal answer
• #### Question 22
Determine both the input and output voltage in this circuit:
Reveal answer
• #### Question 23
The equation for voltage gain (AV) in a typical inverting, single-ended opamp circuit is as follows:
AV = R1 R2
Where,
R1 is the feedback resistor (connecting the output to the inverting input)
R2 is the other resistor (connecting the inverting input to voltage signal input terminal)
Suppose we wished to change the voltage gain in the following circuit from 3.5 to 4.9, but only had the freedom to alter the resistance of R2:
Algebraically manipulate the gain equation to solve for R2, then determine the necessary value of R2 in this circuit to give it a voltage gain of 4.9.
Reveal answer
• #### Question 24
Calculate the necessary resistor value (R1) in this circuit to give it a voltage gain of 15:
Reveal answer
• #### Question 25
Calculate the necessary resistor value (R1) in this circuit to give it a voltage gain of 7.5:
Reveal answer
• #### Question 26
Predict how the operation of this operational amplifier circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
Resistor R1 fails open:
Solder bridge (short) across resistor R1:
Resistor R2 fails open:
Solder bridge (short) across resistor R2:
Broken wire between R1/R2 junction and inverting opamp input:
For each of these conditions, explain why the resulting effects will occur.
Reveal answer
• #### Question 27
There is something wrong with this amplifier circuit. Note the relative amplitudes of the input and output signals as measured by an oscilloscope:
This circuit used to function perfectly, but then began to malfunction in this manner: producing a “clipped” output waveform of excessive amplitude. Determine the approximate amplitude that the output voltage waveform should be for the component values given in this circuit, and then identify possible causes of the problem and also elements of the circuit that you know cannot be at fault.
Reveal answer
• #### Question 28
Calculate the output voltage of this op-amp circuit (using negative feedback):
Also, calculate the DC voltage gain of this circuit.
Reveal answer
• #### Question 29
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels), then calculate the overall voltage gain:
Reveal answer
• #### Question 30
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels), then calculate the overall voltage gain:
Reveal answer
• #### Question 31
What possible benefit is there to adding a voltage buffer to the front end of an inverting amplifier, as shown in the following schematic?
Reveal answer
• #### Question 32
Operational amplifier circuits employing negative feedback are sometimes referred to as “electronic levers,” because their voltage gains may be understood through the mechanical analogy of a lever. Explain this analogy in your own words, identifying how the lengths and fulcrum location of a lever relate to the component values of an op-amp circuit:
Reveal answer
• #### Question 33
Compare and contrast inverting versus non-inverting amplifier circuits constructed using operational amplifiers:
How do these two general forms of opamp circuit compare, especially in regard to input impedance and the range of voltage gain adjustment?
Reveal answer
• #### Question 34
Predict how the input impedance (Zin) of this inverting operational amplifier circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
Resistor R1 fails open:
Solder bridge (short) across resistor R1:
Resistor R2 fails open:
Solder bridge (short) across resistor R2:
Broken wire between R1/R2 junction and inverting opamp input:
Operational amplifier loses power:
For each of these conditions, explain why the input impedance changes as it does.
Reveal answer
• #### Question 35
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels), then calculate the overall voltage gain:
Reveal answer
• #### Question 36
Shown here are two different voltage amplifier circuits with the same voltage gain. Which of them has greater input impedance, and why? Try to give as specific an answer for each circuit’s input impedance as possible.
Reveal answer
• #### Question 37
A simple “follower” circuit that boosts the current-output ability of this non-inverting amplifier circuit is a set of bipolar junction transistors, connected together in a “push-pull” fashion like this:
However, if connected exactly as shown, there will be a significant voltage error introduced to the opamp’s output. No longer will the final output voltage (measured across the load) be an exact 3:1 multiple of the input voltage, due to the 0.7 volts dropped by the transistor in active mode:
There is a very simple way to completely eliminate this error, without adding any additional components. Modify the circuit accordingly.
Reveal answer
• #### Question 38
A student wishes to build a variable-gain amplifier circuit using an operational amplifier and a potentiometer. The purpose of this circuit is to act as an audio amplifier for a small speaker, so he can listen to the output of a digital audio player without having to use headphones:
Before building the project in a finalized form, the student prototypes it on a solderless breadboard to make sure it functions as intended. And it is a good thing he decided to do this before wasting time on a final version, because it sounds terrible!
When playing a song, the student can hear sound through the headphones, but it is terribly distorted. Taking the circuit to his instructor for help, the instructor suggests the following additions:
After adding these components, the circuit works great. Now, music may be heard through the speaker with no noticeable distortion.
Explain what functions the extra components perform, and why the circuit did not work as originally built.
Reveal answer
• #### Question 39
There is something wrong with this amplifier circuit. Despite an audio signal of normal amplitude detected at test point 1 (TP1), there is no output measured at the Äudio signal out” jack:
Next, you decide to check for the presence of a good signal at test point 3 (TP3). There, you find 0 volts AC and DC no matter where the volume control is set.
From this information, formulate a plan for troubleshooting this circuit, answering the following questions:
What type of signal would you expect to measure at TP3?
What would be your next step in troubleshooting this circuit?
Are there any elements of this circuit you know to be working properly?
What do you suppose would be the most likely failure, assuming this circuit once worked just fine and suddenly stopped working all on it’s own?
Reveal answer
• #### Question 40
The junction between the two resistors and the inverting input of the operational amplifier is often referred to as a virtual ground, the voltage between it and ground being (almost) zero over a wide range of circuit conditions:
If the operational amplifier is driven into saturation, though, the “virtual ground” will no longer be at ground potential. Explain why this is, and what condition(s) may cause this to happen.
Hint: analyze all currents and voltage drops in the following circuit, assuming an opamp with the ability to swing its output voltage rail-to-rail.
Reveal answer
• #### Question 41
The same problem of input bias current affecting the precision of opamp voltage buffer circuits also affects non-inverting opamp voltage amplifier circuits:
To fix this problem in the voltage buffer circuit, we added a “compensating” resistor:
To fix the same problem in the non non-inverting voltage amplifier circuit, we must carefully choose resistors R1 and R2 so that their parallel equivalent equals the source resistance:
R1 || R2 = Rsource
Of course, we must also be sure the values of R1 and R2 are such that the voltage gain of the circuit is what we want it to be.
Determine values for R1 and R2 to give a voltage gain of 7 while compensating for a source resistance of 1.45 kΩ.
Reveal answer
### Related Content
• Share
Published under the terms and conditions of the Creative Commons Attribution License
0 Comments | 2021-04-21T02:22:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4494921863079071, "perplexity": 2316.0374016588244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00491.warc.gz"} |
http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=mat&rak=0707-8 | Turkish Journal
of
Mathematics
[email protected]
# Turkish Journal of Mathematics
On maximum principle and existence of positive weak solutions for n\times n nonlinear elliptic systems involving degenerated p-Laplacian operators
H. M. SERAG, S. A. KHAFAGY
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr City
(11884), Cairo-EGYPT
e-mail: [email protected], [email protected].
Abstract: We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -DP,pui=\sumj=1naij(x)|uj|p-2uj+fi(x,u1,u2, ... ,un) in W, ui=0,\ i=1,2,. n on \partial W \} where the degenerated p-Laplacian defined as D P,pu=div [P(x)|\nabla u|p-2\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using sub-super solutions method''.
Key Words: Maximum principle, existence of positive weak solution, nonlinear elliptic system, degenerated p-Laplacian.
Turk. J. Math., 34, (2010), 59-72.
Full text: pdf
Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1. | 2013-06-19T17:44:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8698557615280151, "perplexity": 4477.468144150656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368709000375/warc/CC-MAIN-20130516125640-00080-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://wiki.cosmos.esa.int/planckpla/index.php?title=HFI/LFI_joint_data_processing&oldid=7165 | # HFI/LFI joint data processing
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
The goal is to obtain various catalogues, identify the different astrophysical components whose superposition leads to the observed sky, and provides a statistical characterisation of the , in particular through a likelihood code (of a particular theoretical $C(\ell)$ given Planck data). | 2018-03-22T11:46:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.713098406791687, "perplexity": 6260.660467355609}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647883.57/warc/CC-MAIN-20180322112241-20180322132241-00783.warc.gz"} |
https://www.ecb.europa.eu/pub/economic-bulletin/articles/2018/html/ecb.ebart201804_01.da.html | SØGEMULIGHEDER
Hjem Medier Explainers Forskning & Offentliggørelser Statistik Pengepolitik €uroen Betalinger & Markeder Kariere & Job
Forslag
Sortér efter
Findes ikke på dansk
Foreign direct investment and its drivers: a global and EU perspective
Prepared by Federico Carril-Caccia and Elena Pavlova
Published as part of the ECB Economic Bulletin, Issue 4/2018.
The relevance of foreign direct investment (FDI) as a source of economic activity has increased rapidly over the last decade. Between 2000 and 2016 the share of FDI stock in global GDP increased from 22% to 35%. Following a decline during the Great Recession, mergers and acquisitions (M&As), the most dynamic component of FDI, have recovered, reaching a record value of USD 1.2 trillion in the first quarter of 2018. The intensification of FDI activity has important implications for both origin and destination countries in terms of, for example, economic growth, productivity, wages and employment. Moreover, the expansion of multinational enterprises (MNEs) has been accompanied by the creation of complex cross-border production chains, which also has important implications.
This article presents several findings regarding the main developments in and determinants of FDI over the past decade, at both global and EU level. Since the beginning of the 2000s there has been a gradual shift in the global FDI landscape, with emerging market economies (EMEs) gaining in prominence both as a source of and as a destination for such investment. EMEs have attracted a growing share of FDI flows, reaching more than 50% of the world’s total inward FDI in 2013. In addition, FDI flows are dominated by a relatively small number of M&As. In 2016 M&As with a value in excess of USD 1 billion accounted for only 1% of all FDI projects, but they generated 55% of total FDI flows. Moreover, evidence suggests that FDI and exports are not competing but complementary strategies for serving foreign markets. Finally, since 2008 EU countries are no longer the world’s main FDI investors and recipients. Nevertheless, econometric analysis shows that belonging to the EU dramatically boosts FDI flows in member countries.
1 Introduction
The last decade has witnessed a surge in FDI. Between 2000 and 2016, FDI stocks grew from 22% of world GDP to 35%. FDI, which is defined as a situation where a firm owns at least 10% of a company located in a different country,[1] is carried out by MNEs, which invest abroad either through greenfield investments (GIs), i.e. the setting-up of subsidiaries abroad, or through M&As.[2]
FDI has the potential to bring several benefits to the recipient country. The arrival of MNEs in a country can foster efficiency through increased competition. It can also produce positive productivity spillovers as MNEs integrate domestic firms into their production processes through forward and backward linkages. In addition, MNEs tend to make new technology available and provide access to new markets, improving the training and qualifications of the local workforce and increasing wages and employment. The extent of these positive outcomes will depend partly on the host country’s absorptive capacity.[3] For EU countries, existing evidence confirms the positive impact of FDI.[4]
Traditionally, advanced economies have played a major role as both the source and destination of FDI. Until the beginning of the Great Recession, almost 90% of outward FDI (OFDI) flows came from advanced economies. EU countries were particularly prominent, as their share in world OFDI was nearly 50%. At the same time, the EU and other advanced economies attracted between 60% and 70% of total inward FDI (IFDI) flows.
Since 2008 there has been a dramatic change in the global FDI landscape. OFDI and IFDI from and into EMEs have started to gain in importance. By 2014 EMEs represented 41% and 56% of global OFDI and IFDI respectively, while the EU’s share of OFDI and IFDI had shrunk to only 15% and 18% respectively.
This article provides an overview of the main FDI trends and drivers. Section 2 outlines some fundamental developments. Section 3 focuses on determinants of FDI. Section 4 addresses the relationship between FDI and exports, i.e. whether they are complementary or substitutes. Finally, Section 5 analyses the FDI performance of euro area and non-euro area EU countries over time, including the benefits of EU/euro area membership when it comes to attracting IFDI.
2 Key developments in global FDI
Over the last two decades the global map of inward and outward FDI has changed significantly. FDI has traditionally originated from advanced economies, which were also the main destination (see Chart 1). Since the early 2000s, the importance of EMEs as a destination for FDI has gradually increased. In 2013, for the first time, EMEs attracted more than 50% of global IFDI.[5]
Over the last 16 years, EMEs have also progressively increased in importance as a source of FDI. As illustrated in Chart 2, the share of FDI originating from EMEs started to increase at the beginning of the 2000s. After 2008 the rate of growth of FDI from EMEs accelerated, and in 2014 EMEs accounted for 41% of total OFDI[6].
In the EU and other advanced economies, M&As play a prominent role in total IFDI flows. Between 2003 and 2016, an increasing share of IFDI in the EU and other advanced economies was accounted for by M&As.[7] As shown in Chart 3, in both country groups M&As made up around 80% of total IFDI flows in 2016. Although M&As have also increased in importance in EMEs, IFDI in those countries is still dominated by GIs. In 2016 GIs accounted for around 80% of IFDI into EMEs. In the case of OFDI, a similar trend is observed. For the EU and other advanced economies, M&As had become the preferred mode of outward investment by 2016, while for EMEs GIs remained predominant. At the global level, in the period 2003‑2016 EMEs provided the destination for 62.7% of total GI and 19.3% of M&A investment. In terms of OFDI, the EU and other advanced economies accounted for 72% of GI and 82.4% of M&A investment.
The services sector has become the main target for foreign acquisitions. The sectoral distribution of IFDI was fairly constant in the period 2003‑16. During this period, 70% of international M&As were in the services sector, followed by manufacturing (24%) and the primary sector (6%). In the case of GIs, the distribution between services and manufacturing was more even (50.4% and 48.2% respectively), while the primary sector lagged far behind (1.4%).[8]
3 The structural determinants of FDI
MNEs can engage in FDI activities for a number of strategic reasons (using local platforms to enhance market penetration, absorbing or transferring new technologies, gaining access to resources or control of competitors, reducing production costs, etc.). A firm’s internationalisation usually depends on three basic preconditions: (i) high productivity, as only the most productive firms have the capacity to invest abroad; (ii) the existence of firm-specific advantages which are not easily transferable to third parties and are at the core of the firm’s output; and (iii) a relatively strong market position in the home country.[9] The determinants of FDI can in turn be grouped in the following way: (i) ownership, which allows a firm to best exploit its competitive advantages abroad; (ii) location, which involves exploiting locational advantages across the globe (e.g. supply of labour or natural resources); and (iii) internalisation, whereby a firm internalises foreign markets for the use or generation of assets. Accordingly, FDI is driven by four main factors: (i) markets; (ii) assets; (iii) natural resources; and (iv) efficiency seeking.[10]
First, by investing abroad, companies may seek access to promising new markets. From this perspective, inward FDI should tend to be positively correlated with the size of the host country economy and its market potential in terms of economic growth.[11]
Second, asset-seeking FDI is driven by access to new, complementary resources and capabilities. This type of investment is motivated by a firm’s desire to improve or expand its existing technologies, managerial skills or labour force. It is often directed towards advanced countries.[12] In the EU, technological progress has been among the main drivers of IFDI.[13] Conversely, in the case of EMEs, a positive correlation between technological intensity and IFDI is not expected.
Third, FDI flows may also be driven by the desire for access to natural resources. This type of FDI is more likely to be directed towards EMEs which have abundant natural resources. However, large natural resource endowments can also deter IFDI into EMEs owing to what is known as the “natural resource curse”, i.e. the negative long-term impact of large natural resources on a country’s development (e.g. in terms of economic growth, institutional quality or capital allocation), which may hamper its capacity to attract FDI.[14] This outcome, however, is neither universal nor unavoidable, but affects certain countries under certain conditions, such as high dependence of exports and fiscal revenues on resource wealth, low saving rates, highly volatile resource revenues, and crowding-out of other activities.
Fourth, efficiency-seeking FDI is mainly driven by lower labour costs and higher productivity. In the case of labour costs, existing evidence in the literature is far from conclusive.[15] This type of investment is generally expected to be directed towards EMEs with large supplies of cheap labour (e.g. China and Vietnam) for the development of low value added economic activities.[16]
Research confirms the important role played by institutional quality in determining IFDI.[17] Low institutional quality implies a higher cost of doing business and higher transaction costs.[18] MNEs are likely to avoid countries with high instability, as it can imply sudden changes in the legal framework and a higher risk of expropriation.[19] Similarly, they tend to avoid countries with high levels of corruption and bureaucracy, as they imply a direct extra cost of doing business.[20] On the other hand, compliance with the rule of law and private property rights are valued positively by MNEs. Similarly, ease of doing business (e.g. in terms of access to finance, trade regulation and the number of steps needed to start a business) is another significant driver of inward FDI.[21]
Finally, macroeconomic stability is another relevant driver of inward FDI. The absence of large swings in inflation and exchange rates in a host country is a localisation advantage that can attract FDI by lowering risks related to the expected value of assets and profits generated abroad.
Emerging countries’ MNEs (EMNEs) have specific motivations when investing abroad. EMNEs differ from advanced economies’ MNEs in that they tend to be characterised by a lack of ownership advantages and international experience and are subject to low institutional quality at home.[22] In addition, they also differ as regards the prominent role still played by state-owned MNEs in emerging economies. For EMNEs, therefore, investing abroad is aimed first and foremost at becoming globally competitive by filling their competitiveness gap.[23] Thus, EMNEs seek to acquire technology and managerial skills and to access highly qualified labour – all factors that are scarce in their home country or would be costly to develop internally. Another distinctive characteristic of EMNEs is that, especially where natural resources are concerned, they appear to be more willing to operate in host countries with low institutional quality than MNEs from advanced economies.[24] Box 1 provides an overview of the activities of the largest MNEs originating from both advanced and emerging economies in terms of their economic performance, capital intensity and overall economic relevance.
The internationalisation of EMNEs is affected by the policies of their national governments, which are often pursued via state-owned enterprises. China is a prime example. Government initiatives such as the “Go Global” policy, the “One Belt One Road” initiative and “China Manufacturing 2025” are fostering and shaping Chinese corporate investment abroad.[25]
Box 1 MNEs and their investment deals
Prepared by Federico Carril-Caccia and Elena Pavlova
Based on real economy indicators, such as foreign activity, the biggest MNEs still originate predominantly from large, advanced economies and the manufacturing sector, although EMNEs and the services sector are growing in importance. According to UNCTAD’s 2015 ranking of the world’s 100 largest MNEs, only eight were EMNEs. Moreover, 62 came from just four countries: the United States (21 companies), the United Kingdom (17), Germany (13) and Japan (11). More than half of these MNEs operate in the following sectors: motor vehicles; mining, quarrying and petroleum; pharmaceuticals; electricity, gas and water; petroleum refining; and, within the services sector, telecommunications. Of the ten largest MNEs by market capitalisation in 2016, half were in the information and communications technology (ICT) sector.[26]
The world’s largest MNEs according to the UNCTAD classification play a prominent role in terms of employment, sales and assets in the host countries in which they operate. The foreign activities of these firms are impressive even when compared with some nation states: the top company in terms of employment abroad has 800,000 employees, which is larger than Estonia’s total labour force; the foreign sales volume of one of the most prominent automotive corporations (USD 190 billion) is equivalent to the annual GDP of countries like Greece and Portugal; and the foreign assets held by the largest oil company (USD 290 billion) are close to the annual GDP of economies such as Ireland and Colombia. Similarly, the market capitalisation of one of the most prominent ICT corporations (2016: around USD 600 billion) is on a par with the GDP of Argentina.[27]
Comparing the 92 biggest MNEs from advanced economies with the 100 biggest EMNEs, on average the former recorded 4% higher sales per employee than the latter in 2015. In addition, the capital/labour ratio of advanced economies’ MNEs was 31% higher, and the relative importance of their economic activity abroad, as measured by the foreign activity index,[28] was 26% higher (see Chart A).
Total global FDI is dominated by a relatively small number of very large deals. In 2016 – the last year for which complete data are available – nearly 21,000 FDI projects took place, with a volume of almost USD 1.8 trillion. Out of these projects, 215 M&A deals accounted for 55% of the total volume. In terms of the number of M&A projects worth more than USD 1 billion, the main investors were the United States (18.6%), China (15.4%) and the United Kingdom (8.4%), while the main recipients were the United States (33%), the United Kingdom (11.2%) and Germany (4.7%). Interestingly, about 58% of these very large deals occurred in the services sector.[29]
4 FDI and exports: substitutes or complementary?
When serving a foreign market, FDI and exports have traditionally been seen as substitutes. The underlying idea is that an MNE might prefer to invest abroad rather than export from home in order to forestall the risk of its technological advantage being lost to competitors[30] and to avoid costs such as transportation costs, tariffs and anti-dumping measures[31] (“horizontal FDI”). Through horizontal FDI a firm can exploit its know-how and technological capabilities without them being appropriated by third parties, as might more easily happen through the functioning of supply chains.
In reality, MNEs often complement their exports by owning subsidiaries abroad. This has led to MNEs having an increasing share of world trade.[32] In addition, existing evidence in the literature suggests that there is a positive correlation between a country’s capacity to attract FDI and its level of trade openness.[33] This raises the question of which types of FDI are positively correlated with trade openness and exports from the source to the host country.
First, by means of vertical FDI, MNEs distribute and optimise their production across borders. Headquarters and subsidiaries perform specific economic activities, rather than broad ones, and the different productive sites are linked via trade (i.e. imports and exports).[34] This type of investment is efficiency-seeking in nature: MNEs exploit different characteristics across countries in order to minimise costs. As a result, global production processes become more fragmented as firms locate their production and source their inputs across national borders.
Second, FDI can also serve as a tool for enhancing the market penetration of exports. Export-supporting FDI refers to MNEs’ investment in the wholesale and retail sector.[35] Under this model, the MNE sets up a subsidiary in a foreign country in order to import and distribute its goods or services. In this case, unlike in the case of horizontal FDI, bilateral exports of final goods and FDI are positively correlated.
Third, MNEs also invest abroad in order to supply the host country and third countries directly with their products. “Export-platform FDI” is aimed at serving regions in a way which can either complement or substitute exports.[36] This investment strategy, which is typically directed at countries belonging to a common market, will be pursued if the production costs in the home market and trade costs of serving a given foreign market together are higher than the costs of producing and exporting from a third country. This type of investment does not necessarily entail the replication of the firm’s entire economic activity abroad, as trade in intermediates and services will probably take place between the firm’s headquarters and its foreign subsidiaries, thereby contributing to the functioning of global value chains.
Trade liberalisation policies are expected to affect each of the aforementioned types of FDI – horizontal, vertical, export-supporting and export-platform – in different ways. They are likely to hamper horizontal FDI, as they reduce trade costs and thus reduce the incentive to produce in foreign markets instead of exporting. Bilateral trade liberalisation involving “deep” trade agreements (e.g. including non‑trade provisions on investment and competition, legal and institutional provisions, and economic collaboration) tends to facilitate vertical and export‑supporting FDI. The profitability of both strategies increases as trade costs fall. For export-platform FDI, the relationship is more ambiguous, as its nature can vary from being purely horizontal to being similar to export-supporting FDI. Nevertheless, it will always seek to serve not only one country but a whole region.
Box 2 focuses on the relationship between M&As and the value added that is embedded in exports. The results obtained show a complementarity between M&As and exports from the source to the host country, mostly owing to export‑supporting FDI.
Box 2 The relationship between M&As and the value added embedded in exports
Prepared by Federico Carril-Caccia and Elena Pavlova
To investigate the relationship between M&As and exports, an augmented gravity model is estimated. This model sheds light on how M&A investments from source country i to host country j are affected by different measures of export flows from i to j. We estimate the following equation:[37]
In this way, this model takes into account the economic size of the source and destination countries ( $G D P s u m$), their capital intensity difference ( $d i f f G D P p c$), whether they share a currency ( $c u r r e n c y$), the existence of a preferential trade agreement ( $P T A$) or a bilateral investment treaty and the institutional quality in the home and host countries ( $r u l e l a w$).[38] The variable of interest is $e x p o r t s$, which denotes the extent to which variation in exports from the source to the host country in a given year affects M&As. Under the substitution hypothesis (i.e. horizontal FDI), a negative correlation is expected, while a positive correlation would imply complementarity between M&As and exports (i.e. vertical FDI or export-supporting FDI).
This analysis is based on a bilateral M&A database from Thomson Reuters, which is combined with the World Input-Output Database (WIOD). The dataset covers the period 2000‑14 and 41 source and destination countries, representing more than 80% of world trade, M&As and GDP during the period. The M&A database allows the number of M&A projects and their value to be studied separately, with the former referring to the capacity to create new bilateral relationships and the latter to the capital flow. The WIOD database allows exports of final and intermediate goods to be considered separately, as well as the value added embedded in them. Thus, the domestic value added embedded in final and intermediate goods exports, the domestic value added which returns home via final and intermediate exports, and the foreign value added embedded in final and intermediate goods exports[39] are considered separately in the analysis. By using the value added embedded in exports, as opposed to gross exports, it is possible to account for the domestic and foreign inputs used for exporting. Moreover, the issue of double counting of exports and imports is avoided.[40]
The estimation results in Table A show that M&As are mainly export-supporting and, to a significant extent, vertical. Exports of final goods, irrespective of the domestic or foreign value added embedded in them, have a positive impact on the number of M&A projects and their value. This finding suggests that M&As are mostly export-supporting. By contrast, overall exports in intermediate goods do not have any effect on either the number of projects or their value. However, in terms of the number of projects, domestic value added in exports which returns home via final and intermediate imports processed abroad does have a positive impact. All in all, this last result provides some evidence of vertical FDI being positively correlated with the exporting of intermediate goods which are processed abroad before returning home.
5 Foreign direct investment in the EU and the euro area
The process of economic, monetary and institutional integration in the EU has been a key driver of FDI. As shown by the analysis in Box 3, joining the EU and the euro area is estimated to have boosted bilateral FDI flows among members by sizeable amounts.
Restrictions on inward FDI across the EU are, on average, lower than in OECD countries. While they are not homogeneous across EU Member States, the restrictions on inward FDI in the EU are, with only two exceptions, lower than the OECD average. According to Chart 4, which shows IFDI regulatory restrictions in 2016, all EU countries apart from Austria and Poland have lower restrictions than the OECD average. However, while countries like Luxembourg, Slovenia and Portugal have virtually no restrictions, Austria, Poland, Sweden, Italy, Slovakia and France are significantly above the EU average. At sectoral level, EU Member States have almost no restrictions on FDI in the manufacturing sector, while restrictions in the primary sector are generally larger than in the services sector.
The EU’s weight in global IFDI decreased after 2007, but has rebounded somewhat since 2015. Although, on average, EU restrictions on IFDI are significantly below both the OECD and the non-OECD average, the combined share of EU Member States in global IFDI declined significantly in the period 2008‑14, before partially recovering. Chart 1 illustrates the distribution of world IFDI across three country clusters: the EU (including intra-EU IFDI), other advanced economies and EMEs. Before 2008 EU countries were the main recipients of global FDI. On average, between 2000 and 2007, EU countries attracted 43.1% of the world’s FDI, while other advanced economies attracted 23.8% and EMEs 33%. By contrast, in the period 2008‑16 there was a significant shift in the distribution of FDI in favour of EMEs and to the detriment of the EU. In this period the EU attracted, on average, only 26.7% of the world’s FDI, while 25.2% went to other advanced economies and 48.1% went to EMEs.
The Great Recession triggered by the financial crisis of 2007‑08 has adversely affected the EU’s capacity to attract FDI. As Chart 5 shows, between 2000 and 2015, IFDI was more volatile in non-euro area EU countries than in the euro area. Accordingly, the drop in IFDI into the EU owing to the crisis has been more marked in non-euro area EU countries. The gradual decline in IFDI into euro area economies has been driven mainly by the drop in FDI from non-euro area EU countries and by the euro crisis in 2012. Meanwhile, for non-euro area EU countries, there has been a significant decline in IFDI received from all EU Member States since 2008.
Since 2007 the EU’s position as a source of FDI within the region has also been in decline. For euro area countries, other euro area countries continue to be the main source of FDI, but their weight gradually decreased during the first years of the Great Recession. In addition, intra-euro area FDI plunged in 2012 (see Chart 5). For non-euro area EU economies this trend has been even more severe: in 2008 euro area countries accounted for 70% of total IFDI into non-euro area EU countries, but by 2014 that share had fallen to 50%.
Like the rest of the world, the EU has been witnessing a surge in new investors. Chart 5 shows that the share of FDI from EMEs has significantly increased since 2008 (especially in the euro area), with the top three investors being China, Singapore and Brazil. FDI from EMEs into the EU is mostly driven by a desire to access EU markets and to acquire technologies and brands.[41]
In line with the global trend, EU countries are increasingly investing in EMEs. Outward FDI from EU Member States presents a similar pattern to IFDI. As Chart 6 shows, OFDI from the euro area has been less volatile than OFDI from non-euro area EU countries. While the total volume of OFDI flows from the euro area remained stable during the period 2008‑15, for non-euro area EU countries there was an appreciable slowdown. At the same time, both euro area and non-euro area EU countries have significantly shifted the destination of their OFDI in favour of EMEs. This trend can be explained by the sovereign debt crisis, increased economic uncertainty and the low economic growth suffered by most EU countries until recently. In this context, EU MNEs partly reduced their investments abroad and partly re-directed their investments towards fast-growing EMEs with high market potential. Many EU MNEs reduced their investments abroad, particularly in the case of non-euro area EU countries, whose share of OFDI flows to other EU members declined to only 13% in the period 2012‑15. Nevertheless, as the economic recovery strengthens, intra-EU FDI is likely to recover.
The latest challenge that the EU is facing is the United Kingdom’s upcoming departure from the EU (Brexit). While the impact of Brexit is uncertain, most studies have estimated a reduction in FDI into the United Kingdom of between 12% and 28%.[42] Indeed, Brexit could significantly increase the cost of accessing the EU Single Market from the United Kingdom, making the country less attractive for foreign investors. In addition, changes in regulation that might take place in the United Kingdom after exiting the EU could make doing business in the United Kingdom more costly for EU MNEs.
Box 3 The impact of EU and euro area integration on FDI flows
Prepared by Federico Carril-Caccia and Elena Pavlova
The economic impact of regional integration in Europe has been widely addressed in the literature. The main focus has been on the impact on trade, but some studies have also given insights into how the EU and, in particular, the euro area have affected FDI among their members. These studies[43] tend to show significant growth in FDI among EU Member States. As regards EU membership, the estimated increase in FDI ranges between 28 and 83 percentage points, while the incremental effect of euro area membership ranges between 21 and 44 percentage points. However, these studies consider different periods and different sets of countries, so they are not fully comparable and they measure the impact of EU accession and euro adoption for different countries.
In order to overcome these issues, we use a bilateral FDI flows database covering the period 1985‑2012 for 34 host countries and 70 source countries.[44] The countries and time period covered mean that we take into account the accession of 17 countries into the EU and the whole process of Economic and Monetary Union (EMU). We estimate the following equation:[45]
where $F D I$ represents the FDI flows from one country to another. With this model we take into account the demand and supply sides ( $G D P s u m$), the capital intensity difference between a pair of countries ( $d i f f G D P p c$), whether countries have signed a preferential trade agreement ( $P T A$) or a bilateral investment treaty ( $B I T$), the economic size similarity ( $S I M I$) and the difference in human capital endowment between the source and host country ( $d i f f H C$). Moreover, the equation controls for the real exchange rate ( $r e e r$) and a set of institutional indicators to account for institutional quality.[46] Our variables of interest are $E U i j t$, which is a dummy that takes the value 1 in year t whenever a pair of countries are EU members, $E A i j t$, which is a dummy that takes the value 1 in year t whenever a pair of countries belong to the euro area, and , which is a dummy that takes the value 1 in year t whenever the destination country is an EU member.[47]
The results indicate that, on average, joining the EU increased inward FDI flows from other EU countries by 43.9%, but did not have a significant impact on a country’s capacity to attract FDI from non-EU countries. On average, adopting the euro increased FDI from other euro area members by 73.7%. Thus, the additional effect of belonging to the common currency area can be estimated at around 20%.[48] Indeed, the EU reduced the cost of doing business across the borders between its members, and the euro area stimulated cross-border capital flows among its members, as exchange and liquidity risk were eliminated.[49] The results also indicate that membership of the EU and the euro area partially mitigated the negative trend in IFDI after the Great Recession that was highlighted in the previous section.
6 Conclusions
The prominence of FDI has increased significantly over the past 16 years, rising from 22% to 35% of world GDP. FDI has traditionally originated from advanced economies, but two important developments have occurred since the Great Recession:
• EMEs have gained in weight both as recipients and as sources of global FDI. Since 2013 EMEs have managed to attract more than 50% of total inward FDI and have provided nearly 30% of total outward FDI.
• At the same time, the share of IFDI flowing into and OFDI flowing from advanced economies, in particular the EU, has been gradually decreasing.
FDI is carried out by the most productive firms in source countries via M&As and GI. The relevance of each type of investment varies depending on the source and destination countries concerned and the sector towards which it is directed. FDI flows are largely driven by relatively few deals. More specifically:
• Looking at IFDI, M&As are the main mode of entry into EU countries and other advanced economies, while GI is the most common form of IFDI in EMEs. Regarding OFDI, M&As and GI are similar in importance for the EU and other advanced economies, whereas GI is the preferred form of FDI for EMEs. Nearly 70% of M&As are directed towards the services sector, while GIs are evenly distributed between manufacturing and services.
• The largest MNEs tend to come from advanced economies. Some are so large in terms of sales, assets and number of employees that they are comparable in size to the GDP and labour force of entire countries. Total FDI is driven largely by a small number of very large M&A deals. In 2016 very large M&As accounted for only 1% of the world’s FDI projects, but 55% of total FDI flows. The majority of these deals focused on the acquisition of firms in the services sector.
FDI has the potential to produce several positive effects on host economies. Market‑seeking FDI is channelled towards catching-up economies with market potential, whereas asset-seeking FDI is aimed at securing access to new or complementary capabilities for MNEs. Natural resource-seeking FDI is directed towards EMEs, but large natural resource endowments in a host country can also deter FDI under certain circumstances. Efficiency-seeking FDI is mainly driven by low labour costs. High institutional quality, ease of doing business and macroeconomic stability can help attract FDI, as these factors reduce the adverse risks associated with investment. Finally, M&As are mainly complementary to trade, rather than a substitute for it.
Turning to Europe, EU and euro area membership has fostered FDI among members. EU countries have, on average, fewer restrictions on FDI than the rest of the world. Since the Great Recession, however, the EU is no longer the world’s main FDI investor and recipient and its share has gradually declined. However, the decline in IFDI and OFDI has been more marked for non-euro area EU countries than for euro area countries. The latter have continued to receive sizeable IFDI flows, stemming mainly from other advanced economies outside of the EU.
1. See Balance of Payments and International Investment Position Manual, Sixth Edition (BPM6), International Monetary Fund, 2009.
2. GI is motivated by the desire of MNEs to exploit their competitive advantage abroad. This mode of investment is based on pursuing economic activities that are very similar and complementary to those already developed by the parent company. M&As concern the acquisition of at least 10% of the shares in an existing firm. M&As are driven by the following objectives: (i) increasing market share by acquiring competitors; (ii) exploiting synergies between the investing and target companies (e.g. in terms of technology); and (iii) internalising host country-specific assets of the target company (e.g. market share or institutional knowledge). See Davies, R.B., Desbordes, R. and Ray, A., “Greenfield versus Merger & Acquisition FDI: Same Wine, Different Bottles?”, UCD Centre for Economic Research Working Paper Series, WP15/03, University College Dublin School of Economics, 2015; and Nocke, V. and Yeaple, S.R., “Cross-border mergers and acquisitions vs. greenfield foreign direct investment: The role of firm heterogeneity”, Journal of International Economics, Vol. 72(2), 2007, pp. 336‑365.
3. See Blomström, M. and Kokko, A., “Multinational Corporations and Spillovers”, Journal of Economic Surveys, Vol. 12(3), 1998, pp. 247‑277.
4. See, for example, Ashraf, A., Herzer, D. and Nunnenkamp, P., “The Effects of Greenfield FDI and Cross‐border M&As on Total Factor Productivity”, The World Economy, Vol. 39(11), 2016, pp. 1728‑1755; Bertrand, O., “Effects of foreign acquisitions on R&D activity: Evidence from firm-level data for France”, Research Policy, Vol. 38(6), 2009, pp. 1021‑1031; Bloom, N., Sadun, R. and Van Reenen, J., “Americans Do IT Better: US Multinationals and the Productivity Miracle”, American Economic Review, Vol. 102(1), 2012, pp. 167‑201; Dachs, B. and Peters, B., “Innovation, employment growth, and foreign ownership of firms: A European perspective”, Research Policy, Vol. 43(1), 2014, pp. 214‑232; and Girma, S. and Görg, H., “Evaluating the foreign ownership wage premium using a difference-in-differences matching approach”, Journal of International Economics, Vol. 72(1), 2007, pp. 97‑112.
5. Data on FDI flows in this section are taken from the United Nations Conference on Trade and Development (UNCTAD). The period covered is 1970‑2016.
6. One might expect total IFDI and total OFDI in Charts 1 and 2 to be equal. However, owing to statistical differences, mainly as a consequence of slightly different definitions across countries, there are discrepancies between the two series.
7. Owing to limitations in the availability of M&A and GI statistics, we only describe the period 2003‑16.
8. Statistics are based on the total number of FDI projects (GIs and M&As) that took place during the period 2003‑16. Data are taken from UNCTAD (2017), op. cit., annex tables 16 and 23.
9. See Helpman, E., Melitz, M.J. and Yeaple, S.R., “Export Versus FDI with Heterogeneous Firms”, American Economic Review, Vol. 94(1), 2004, pp. 300‑316; Hymer, S.H., The International Operations of National Firms: A Study of Direct Foreign Investment, MIT Press, 1976; and Love, J.H., “Technology sourcing versus technology exploitation: an analysis of US foreign direct investment flows”, Applied Economics, Vol. 35(15), 2003, pp. 1667‑1678.
10. See Dunning, J.H., “The Eclectic Paradigm of International Production: A Restatement and Some Possible Extensions”, Journal of International Business Studies, Vol. 19(1), 1988, pp. 1‑31.
11. See Blonigen, B.A., “A Review of the Empirical Literature on FDI Determinants”, Atlantic Economic Journal, Vol. 33(4), 2005, pp. 383‑403; Davies et al. (2015), op. cit.; and Nielsen, B.B., Asmussen, C.G. and Weatherall, C.D., “The location choice of foreign direct investments: Empirical evidence and methodological challenges”, Journal of World Business, Vol. 52(1), 2017, pp. 62‑82.
12. See Amighini, A.A., Rabellotti, R. and Sanfilippo, M., “Do Chinese state-owned and private enterprises differ in their internationalization strategies?”, China Economic Review, Vol. 27, 2013, pp. 312‑325.
13. See Villaverde, J. and Maza, A., “The determinants of inward foreign direct investment: Evidence from the European regions”, International Business Review, Vol. 24(2), 2015, pp. 209‑223. The authors define technological progress in terms of R&D investment, R&D personnel, the technology intensity of the sector and human capital.
14. See Asiedu, E., “Foreign direct investment, natural resources and institutions”, IGC Working Papers, International Growth Centre, March 2013.
15. See Nielsen et al. (2017), op. cit.
16. See Buckley, P.J., Clegg, L.J., Cross, A.R., Liu, X., Voss, H. and Zheng, P., “The determinants of Chinese outward foreign direct investment”, Journal of International Business Studies, Vol. 38(4), 2007, pp. 499‑518.
17. See Blonigen (2005), op. cit. and Nielsen et al. (2017), op. cit.
18. See Dunning, J.H., “Internationalizing Porter’s Diamond”, MIR: Management International Review, Vol. 33, 1993, pp. 7‑15.
19. See Bénassy‐Quéré, A., Maylis, C. and Thierry, M., “Institutional Determinants of Foreign Direct Investment”, The World Economy, Vol. 30(5), 2007, pp. 764‑782.
20. See Wei, S.-J., “How Taxing is Corruption on International Investors?”, The Review of Economics and Statistics, Vol. 82(1), 2000, pp. 1‑11.
21. See Carril-Caccia, F., Ghali, S., Milgram Baleix, J., Paniagua, J. and Zitouna, H., “FDI in MENA: Impact of political and trade liberalisation process”, Femise Research Papers, FEM41‑07, Forum Euroméditerranéen des Instituts de Sciences Économiques, 2018; and Corcoran, A. and Gillanders, R., “Foreign direct investment and the ease of doing business”, Review of World Economics, Vol. 151(1), 2015, pp. 103‑126.
22. See Buckley et al. (2007), op. cit.
23. See Amal, M., Baffour Awuah, G., Raboch, H. and Andersson, S., “Differences and similarities of the internationalization processes of multinational companies from developed and emerging countries”, European Business Review, Vol. 25(5), 2013, pp. 411‑428.
24. See Buckley et al. (2007), op. cit.
25. See Huang, Y., “Understanding China’s Belt & Road Initiative: Motivation, framework and assessment”, China Economic Review, Vol. 40, 2016, pp. 314‑321; Wuttke, J., “The Dark Side of China’s Economic Rise”, Global Policy, Vol. 8(S4), 2017, pp. 62‑70; and Buckley et al. (2007), op. cit.
26. See Gray, A., “These are the world’s 10 biggest corporate giants”, World Economic Forum, 2017.
27. See Gray (2017), op. cit.
28. The foreign activity index is calculated on the basis of MNEs’ share of employees abroad, as well as foreign assets and foreign sales.
29. Statistics are based on UNCTAD (2017), op. cit., annex table 17.
30. See Dunning (1988), op. cit.
31. See Blonigen (2005), op. cit.
32. See Antràs, P. and Yeaple, S.R., “Multinational Firms and the Structure of International Trade”, Handbook of International Economics, Vol. 4, 2014, pp. 55‑130.
33. Trade openness is defined as the ratio of total trade to GDP. See Chakrabarti, A., “The Determinants of Foreign Direct Investments: Sensitivity Analyses of Cross‐Country Regressions”, Kyklos, Vol. 54(1), 2001, pp. 89‑114.
34. See Hanson, G.H., Mataloni Jr, R.J. and Slaughter, M.J., “Vertical Production Networks in Multinational Firms”, The Review of Economics and Statistics, Vol. 87(4), 2005, pp. 664‑678.
35. See Krautheim, S., “Export‐supporting FDI”, Canadian Journal of Economics/Revue canadienne d'économique, Vol. 46(4), 2013, pp. 1571‑1605.
36. See Ekholm, K., Forslid, R. and Markusen, J.R., “Export‐platform foreign direct investment”, Journal of the European Economic Association, Vol. 5(4), 2007, pp. 776‑795.
37. The estimator used is the Poisson Pseudo Maximum Likelihood (PPML). See Santos Silva, J.M.C. and Tenreyro, S., “The Log of Gravity”, The Review of Economics and Statistics, Vol. 88(4), 2006, pp. 641‑658.
38. In addition, the model includes country-pair fixed effects to take into account all time-invariant transaction costs across pairs of countries (e.g. distance) and year fixed effects to account for global macroeconomic trends.
39. The value added in exports is decomposed in accordance with Wang, Z., Wei, S.J. and Zhu, K., “Quantifying International Production Sharing at the Bilateral and Sector Levels”, NBER Working Papers, No 19677, 2013. See also the article entitled “The impact of global value chains on the macroeconomic analysis of the euro area”, Economic Bulletin, Issue 8, ECB, 2017.
40. Cross-border trade statistics partially double count trade flows, as a portion of exports consists of imported inputs and some exported output is later reimported into the country of origin. As the origin of the value added is not accounted for in gross trade statistics, the domestic and foreign economic activity embedded in exports and imports respectively may be overestimated. In addition, any analysis based on gross trade data may overestimate the importance of some trading partners and underestimate the importance of others.
41. See, for example, Blomkvist, K. and Drogendijk, R., “Chinese outward foreign direct investments in Europe”, European Journal of International Management, Vol. 10(3), 2016, pp. 343‑358; Carril-Caccia, F. and Milgram Baleix, J., “From Beijing to Madrid: Profiles of Chinese investors in Spain”, Universia Business Review, Vol. 51, 2016, pp. 112‑129; and Giuliani, E., Gorgoni, S., Günther, C. and Rabellotti, R., “Emerging versus advanced country MNEs investing in Europe: A typology of subsidiary global-local connections”, International Business Review, Vol. 23(4), 2015, pp. 680‑691.
42. See, for example, Dhingra, S., Ottaviano, G., Sampson, T. and Van Reenen, J., “The Impact of Brexit on Foreign Investment in the UK”, CEP Brexit Analysis, No 3, Centre for Economic Performance, London School of Economics, 2016; Bruno, R., Campos, N., Estrin, S. and Tian, M., “Technical Appendix to ‘The Impact of Brexit on Foreign Investment in the UK’ – Gravitating towards Europe: An Econometric Analysis of the FDI Effects of EU Membership”, Centre for Economic Performance, London School of Economics, 2016; and HM Treasury, “HM Treasury analysis: the long-term economic impact of EU membership and the alternatives”, report presented to the UK Parliament by the Chancellor of the Exchequer, 2016.
43. See, for example, Brouwer, J., Paap, R. and Viaene, J.-M., “The trade and FDI effects of EMU enlargement”, Journal of International Money and Finance, Vol. 27(2), 2008, pp. 188‑208; De Sousa, J. and Lochard, J., “Does the Single Currency Affect Foreign Direct Investment?”, The Scandinavian Journal of Economics, Vol. 113(3), 2011, pp. 553‑578; Flam, H. and Nordström, H., “The euro and Single Market impact on trade and FDI”, manuscript, Institute for International Economic Studies, Stockholm University, 2007; Dhingra et al. (2016), op. cit.; and HM Treasury (2016), op. cit.
44. Data are taken from OECD BMD3 FDI statistics.
45. Based on the Poisson Pseudo Maximum Likelihood estimator – see Santos Silva and Tenreyro (2006), op. cit.
46. Indicators of institutional quality include investment protection ( , government stability ( $g o v s t a b j t$) and the enforcement of law ( $l a w j t$).
47. In addition, the model includes country-pair and year fixed effects to take into account all time-invariant transaction costs across pairs of countries (e.g. distance) and global macroeconomic trends.
48. The additional growth in FDI among euro area members is calculated using the following formula: . See Coeurdacier, N., De Santis, R.A. and Aviat, A., “Cross-border mergers and acquisitions and European integration”, Economic Policy, Vol. 24(57), 2009, pp. 56‑106.
49. See Rodriguez Palenzuela, D., Dees, S. and the Saving and Investment Task Force, “Savings and investment behaviour in the euro area”, Occasional Paper Series, No 167, ECB, January 2016. | 2023-02-04T06:59:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 18, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31262221932411194, "perplexity": 5806.633880589704}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500094.26/warc/CC-MAIN-20230204044030-20230204074030-00371.warc.gz"} |
https://gssc.esa.int/navipedia/index.php?title=Sidereal_Time&oldid=11651 | If you wish to contribute or participate in the discussions about articles you are invited to join Navipedia as a registered user
# Sidereal Time
Jump to navigation Jump to search
Fundamentals
Title Sidereal Time
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011
The reference is the Vernal Equinox, or the Aries point, which is defined as the intersection between the equator and the ecliptic plane [footnotes 1]. Two types of Aries point can be considered depending on which equator plane is considered (i.e, the mean equator or the true equator).
Figure 1: Mean and True equinox.
According to the previous definitions, four classes of sidereal times are introduced:
• Local "Apparent" Sidereal Time (LAST)($\Theta$): is the hour angle of the "true" Aries point (from local meridian) [footnotes 5].
• Greenwich "Apparent" Sidereal Time (GAST)($\Theta_{_G}$): is the hour angle of "true" Aries point, from Greenwich meridian.
• Local Mean Sidereal Time (LMST)($\theta$): the same that LAST with the mean equinox.
• Greenwich Mean Sidereal Time (GMST)($\theta_{_G}$): the same that GAST with the mean equinox.
The Figure 2 summaries these four sidereal times.
Figure 2: Different sidereal Times (from [Seeber, 1993]) [1]
GAST and GMST are given by equations (3) and (4) in CEP to ITRF, respectively. Local and Greenwich Sidereal Times differ by the longitude $\displaystyle \lambda$ of the local meridian. The difference between Apparent and Mean Sidereal Times is called Equation of Equinoxes (where $\displaystyle \alpha_E$ is given by equation (7) in CEP to ITRF):
$\begin{array}{lcl} GMST\,-\,LMST\,=\,GAST\,-\,LAST\,=\,\lambda \\ GMST\,-\,GAST\,=\,LMST\,-\,LAST\,=\,\alpha_E \end{array} \qquad \mbox{(1)}$
## Notes
1. ^ Ecliptic: Apparent circular path of the sun on the celestial sphere during the course of a year. The plane of the ecliptic is inclined an angle of about 23$^{o}$26$^{'}$ with respect to the celestial equator, see equation (5) in ICRF to CEP.
2. ^ Actually, the mean ecliptic. Like earth rotation pole, Ecliptic pole suffers a Precession and Nutation effect due to the perturbation of moon and major planets on earth orbit. Nevertheless its amplitude is 50 times shorter than the earth rotation pole and, at the level of accuracy required here, we will not distinguish between mean or true ecliptic.
3. ^ This equator is defined as the plane that contains the Geocenter and is orthogonal to the instantaneous daily rotation axis.
4. ^ Due to the accuracies needed, it is enough to compute the true Aries point using mean Ecliptic plane. We will refer to this plane always as "the ecliptic", without distinguishing between the mean or the true one.
5. ^ Apparent in Astronomy refers to what is seen from an Ideal earth's centre, without atmosphere and rotation. With these conditions the effects of light refraction, light aberration and parallax has been suppressed.
## References
1. ^ [Seeber, 1993] Seeber, G., 1993. Satellite Geodesy: Foundations, Methods, and Applications. Walter de Gruyter & Co., Berlin, Germany. | 2019-05-25T10:17:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.770886242389679, "perplexity": 2987.3946047498434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257939.82/warc/CC-MAIN-20190525084658-20190525110658-00430.warc.gz"} |
https://zbmath.org/authors/chern.shiing-shen | ## Chern, Shiing-Shen
Compute Distance To:
Author ID: chern.shiing-shen Published as: Chern, Shiing-shen; Chern, Shiing-Shen; Chern, S. S.; Chern, S.-S.; Chern, Shiingshen; Chern, Shiing Shen; Chern, Shing-Shen; Chern, S.-s.; Chern, Shiing S. more...less Further Spellings: Chen, Xingshen; Chén Xǐngshēn; 陳省身 External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef Awards: Wolf Prize (1983) · Wolf Prize (1984) · Shaw Prize (2004)
Documents Indexed: 236 Publications since 1935, including 26 Books 20 Contributions as Editor · 9 Further Contributions Biographic References: 33 Publications Co-Authors: 75 Co-Authors with 83 Joint Publications 1,306 Co-Co-Authors
all top 5
### Co-Authors
142 single-authored 7 Bao, David 7 Griffiths, Phillip Augustus 7 Shen, Zhongmin 5 Blaschke, Wilhelm 5 Burau, Rolf Werner 5 Leichtweiss, Kurt 5 Müller, Hans Robert 5 Santaló, Luis Antonio 5 Strubecker, Karl Georg 4 Wolfson, Jon Gordon 3 Bott, Raoul Harry 3 Bryant, Robert L. 3 Cartan, Élie 3 Cecil, Thomas E. 3 Cheng, Shiu-Yuen 3 Finikov, Sergeĭ Pavlovich 3 Hirzebruch, Friedrich 3 Kobayashi, Shoshichi 3 Osserman, Robert 3 Saldin, D. K. 3 Smale, Steve 2 Batra, Romesh C. 2 Cesari, Lamberto 2 Goldberg, Vladislav V. 2 Harp, G. R. 2 Hsiung, Chuan-Chih 2 Ji, Lizhen 2 Ji, Shanyu 2 Kuiper, Nicolaas Hendrik 2 Lashof, Richard K. 2 Morse, Marton 2 Moser, Jürgen K. 2 Simons, James 2 Spanier, Edwin Henry 2 Tenenblat, Keti 2 Yien, Chih-Ta 1 Abbott, James C. 1 Abhyankar, Shreeram Shankar 1 Allan, Vicki H. 1 Arcoumanis, C. 1 Arupathi, R. 1 Benz, Walter 1 Bliss, Gilbert Ames 1 Boothby, William M. 1 Borel, Armand 1 Bou, D. 1 Cartier, Pierre 1 Chandrasekharan, Komaravolu 1 Chen, Weihuan 1 Chevalley, Claude 1 Chi, Minyou 1 Chow, Wei-Liang 1 Cowen, Michael J. 1 Davis, Martin David 1 Davis, Philip J. 1 do Carmo, Manfredo Perdigão 1 Dohm, Volker 1 Ehrenpreis, Leon 1 Fu, Lei 1 Fuchs, Wolfgang H. J. 1 Gardner, Robert Brown 1 Garoff, Stephen 1 Goldberg, Samuel I. 1 Goldschmidt, Hubert Leopold 1 Griffith, Phillip A. 1 Grunsky, Helmut 1 Haberfield, C. M. 1 Hain, Richard M. 1 Hale-La Salle 1 Hamilton, Richard S. 1 Hano, J. 1 Hardy, Godfrey Harold 1 Hartman, Philip 1 Henkin, Leon Albert 1 Hersh, Reuben 1 Hopf, Heinz 1 1 Hu, Sze-Tsen 1 Igusa, Jun-ichi 1 Iyanaga, Shokichi 1 Jackson, Dunham 1 Jou, Yuh-Lin 1 Kac, Mark 1 Kailath, Thomas 1 Kölzow, Dietrich 1 Korevaar, Jacob 1 Kostant, Bertram 1 Lanczos, Cornelius 1 Lang, Serge 1 Lax, Peter David 1 Leichtweiß, K. 1 Levine, Harold I. 1 Levinson, Norman 1 Li, Peter 1 Liao, Shantao 1 Mac Lane, Leslie Saunders 1 McShane, Edward James 1 Megson, Graham M. 1 Moore, Calvin C. 1 Müller, Hans Robert ...and 30 more Co-Authors
all top 5
### Serials
16 Annals of Mathematics. Second Series 8 Proceedings of the National Academy of Sciences of the United States of America 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 American Journal of Mathematics 7 Bulletin of the American Mathematical Society 5 Proceedings of Symposia in Pure Mathematics 4 Bulletin des Sciences Mathématiques. Deuxième Série 4 Notices of the American Mathematical Society 4 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 4 Mathematical Sciences Research Institute Publications 3 Acta Mechanica 3 Computer Physics Communications 3 Mathematische Annalen 3 Mechanics Research Communications 3 Proceedings of the American Mathematical Society 3 Advances in Mathematics 3 Journal of Mathematics and Mechanics 3 Springer Collected Works in Mathematics 2 International Journal of Modern Physics B 2 American Mathematical Monthly 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Acta Mathematica 2 Commentarii Mathematici Helvetici 2 Duke Mathematical Journal 2 Journal of Differential Geometry 2 Transactions of the American Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 International Journal of Production Research 2 L’Enseignement Mathématique. 2e Série 2 Bollettino della Unione Matematica Italiana. Series II 2 Lecture Notes in Mathematics 2 Nankai Tracts in Mathematics 2 Acta. Pontificia Academia Scientarum 2 Surveys of Modern Mathematics 2 Universitext 1 Modern Physics Letters A 1 Applicable Analysis 1 Computers and Electrical Engineering 1 Computers and Structures 1 Houston Journal of Mathematics 1 International Journal of Mechanical Sciences 1 International Journal of Solids and Structures 1 Journal d’Analyse Mathématique 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Rocky Mountain Journal of Mathematics 1 The Mathematical Intelligencer 1 Algebra Universalis 1 Annales Polonici Mathematici 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Archiv der Mathematik 1 Inventiones Mathematicae 1 The Journal of the Indian Mathematical Society. New Series 1 Manuscripta Mathematica 1 Mathematica Scandinavica 1 Michigan Mathematical Journal 1 Studies in Applied Mathematics 1 Roczniki Polskiego Towarzystwa Matematycznego. Seria II. Wiadomości Matematyczne 1 International Journal of Mathematics 1 FGCS. Future Generation Computer Systems 1 IEEE Transactions on Signal Processing 1 Journal of Dynamic Systems, Measurement and Control 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Physics of Fluids 1 The Asian Journal of Mathematics 1 Stochastic Environmental Research and Risk Assessment 1 Fuzzy Optimization and Decision Making 1 Journal of the Society for Industrial & Applied Mathematics 1 Scripta Mathematica 1 L’Enseignement Mathématique 1 Sankhyā 1 Contemporary Mathematics 1 Graduate Texts in Mathematics 1 Princeton Mathematical Series 1 Series on University Mathematics 1 Mathematical Medley 1 Anais da Academia Brasileira de Ciências 1 Journal of the Chinese Mathematical Society 1 Science Record 1 World Scientific Series in 20th Century Physics
all top 5
### Fields
114 Differential geometry (53-XX) 37 History and biography (01-XX) 16 Manifolds and cell complexes (57-XX) 16 Global analysis, analysis on manifolds (58-XX) 15 Several complex variables and analytic spaces (32-XX) 14 General and overarching topics; collections (00-XX) 12 Algebraic geometry (14-XX) 11 Mechanics of deformable solids (74-XX) 10 Partial differential equations (35-XX) 8 Algebraic topology (55-XX) 5 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Operations research, mathematical programming (90-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)
### Citations contained in zbMATH Open
178 Publications have been cited 4,495 times in 3,775 Documents Cited by Year
An introduction to Riemann-Finsler geometry. Zbl 0954.53001
Bao, D.; Chern, S.-S.; Shen, Z.
2000
Real hypersurfaces in complex manifolds. Zbl 0302.32015
Chern, S. S.; Moser, Jürgen K.
1975
Characteristic forms and geometric invariants. Zbl 0283.53036
Chern, Shiing-shen; Simons, James
1974
Minimal submanifolds of a sphere with second fundamental form of constant length. Zbl 0216.44001
Chern, S. S.; do Carmo, Manfredo Perdigão; Kobayashi, S.
1970
Exterior differential systems. Zbl 0726.58002
Bryant, Robert L.; Chern, S. S.; Gardner, Robert B.; Goldschmidt, Hubert L.; Griffiths, P. A.
1991
Existence and uniqueness theorem for uncertain differential equations. Zbl 1196.34005
Chen, X.; Liu, B.
2010
Riemann-Finsler geometry. Zbl 1085.53066
Chern, Shiing-Shen; Shen, Zhongmin
2005
A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Zbl 0060.38103
Chern, Shiing-Shen
1944
Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic section. Zbl 0148.31906
Bott, Raoul; Chern, Shiing-shen
1965
On the total curvature of immersed manifolds. Zbl 0078.13901
Chern, Shiing-Shen; Lashof, Richard K.
1957
Minimal surfaces by moving frames. Zbl 0521.53050
Chern, Shiing-shen; Wolfson, Jon Gordon
1983
On the curvatura integra in a Riemannian manifold. Zbl 0060.38104
Chern, Shiing-shen
1945
Lectures on differential geometry. Zbl 0940.53001
Chern, S. S.; Chen, W. H.; Lam, K. S.
1999
Complete minimal surfaces in Euclidean $$n$$-spaces. Zbl 0172.22802
Chern, Shiing-shen; Osserman, R.
1967
Harmonic maps of the two-sphere into a complex Grassmann manifold. II. Zbl 0627.58017
Chern, Shiing-Shen; Wolfson, Jon G.
1987
Characteristic classes of Hermitian manifolds. Zbl 0060.41416
Chern, Shiing-Shen
1946
Pseudospherical surfaces and evolution equations. Zbl 0605.35080
Chern, S. S.; Tenenblat, K.
1986
The geometry of $$G$$-structures. Zbl 0136.17804
Chern, Shiing-shen
1966
Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space. Zbl 0052.17601
Chern, Shiing-shen; Kuiper, Nicolaas H.
1952
Some cohomology classes in principal fiber bundles and their application to Riemannian geometry. Zbl 0209.25401
Chern, S. S.; Simons, J.
1971
Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern. 2nd ed. Zbl 0669.53001
Hopf, Heinz
1989
On the index of a fibered manifold. Zbl 0083.17801
Chern, Shiing-Shen; Hirzebruch, Friedrich; Serre, Jean-Pierre
1957
Finsler geometry is just Riemannian geometry without the quadratic restriction. Zbl 1044.53512
Chern, Shiing-Shen
1996
On curvature and characteristic classes of a Riemann manifold. Zbl 0066.17003
Chern, Shiing-Shen
1955
On the total curvature of immersed manifolds. II. Zbl 0095.35803
Chern, Shiing-shen; Lashof, Richard K.
1958
Complex manifolds without potential theory. Zbl 0158.33002
Chern, Shiing-shen
1967
Intrinsic norms on a complex manifold. Zbl 0202.11603
Chern, S. S.; Levine, H. I.; Nirenberg, Louis
1969
Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed. Zbl 0444.32004
Chern, Shiing-shen
1979
On the curvatures of a piece of hypersurface in Euclidean space. Zbl 0147.20901
Chern, Shiing-shen
1965
Topics in differential geometry. Zbl 0054.06801
Chern, Shiing-shen
1951
An elementary proof of the existence of isothermal parameters on a surface. Zbl 0066.15402
Chern, Shiing-Shen
1955
An analogue of Bäcklund’s theorem in affine geometry. Zbl 0407.53002
Chern, Shing-Shen; Terng, Chuu-Lian
1980
Some new characterizations of the Euclidean sphere. Zbl 0063.00833
Chern, Shiing-Shen
1945
On Riemannian metrics adapted to three-dimensional contact manifolds. Zbl 0561.53039
Chern, S. S.; Hamilton, R. S.
1985
On the multiplication in the characteristic ring of a sphere bundle. Zbl 0033.40202
Chern, Shiing-shen
1948
On the volume decreasing property of a class of real harmonic mappings. Zbl 0303.53049
Chern, Shiing-shen; Goldberg, Samuel I.
1975
Abel’s theorem and webs. Zbl 0386.14002
Chern, S. S.; Griffiths, Phillip
1978
Sur la géométrie d’un système d’équations différentielles du second ordre. JFM 65.1419.01
Chern, S.-S.
1939
Complex analytical mappings of Riemann surfaces. I. Zbl 0103.30104
Chern, Shiing-shen
1960
On special $$W$$-surfaces. Zbl 0067.13801
Chern, Shiing-Shen
1955
Pseudo Riemannian geometry and the Gauss-Bonnet formula. Zbl 0113.37001
Chern, Shiing-shen
1963
Web geometry. Zbl 0483.53013
Chern, Shiing-Shen
1982
Lie groups and KdV equations. Zbl 0408.35074
Chern, Shiing-shen; Peng, Chia-kuei
1979
On the kinematic formula in integral geometry. Zbl 0142.20704
Chern, Shiing-shen
1966
A theorem on orientable surfaces in four-dimensional space. Zbl 0043.38403
Chern, Shiing-shen; Spanier, Edwin H.
1951
On the minimal immersions of the two-sphere in a space of constant curvature. Zbl 0217.47601
Chern, S.-s.
1970
The geometry of the differential equation $$y''' = F(x, y, y', y'')$$. JFM 66.0879.02
Chern, S. S.
1940
Einstein hypersurfaces in a Kählerian manifold of constant holomorphic curvature. Zbl 0168.19505
Chern, Shiing-shen
1967
A note on the Gauss-Bonnet theorem for Finsler spaces. Zbl 0849.53046
Bao, David; Chern, S. S.
1996
On the kinematic formula in the Euclidean space of $$n$$ dimensions. Zbl 0046.16101
Chern, Shiing-Shen
1952
The integrated form of the first main theorem for complex analytic mappings in several complex variables. Zbl 0142.04802
Chern, Shiing-shen
1960
Simple proofs of two theorems on minimal surfaces. Zbl 0175.18603
Chern, Shiing-shen
1969
Topologische Fragen der Differentialgeometrie. LXII. Eine Invariantentheorie der Dreigewebe aus $$r$$-dimensionalen Mannigfaltigkeiten im $$\mathbb{R}_{2r}$$. Zbl 0013.41802
Chern, Shiing-Shen
1936
On a notable connection in Finsler geometry. Zbl 0787.53018
Bao, David; Chern, S. S.
1993
On the projective structure of a real hypersurface in $$C_{n+1}$$. Zbl 0305.53019
Chern, Shiing-Shen
1975
Integral formulas for hypersurfaces in Euclidean space and their applications to uniqueness theorems. Zbl 0090.12802
Chern, Shiing-shen
1959
On a generalization of Kaehler geometry. Zbl 0078.14103
Chern, Shiing-shen
1957
Tautness and Lie sphere geometry. Zbl 0635.53029
Cecil, Thomas E.; Chern, Shiing-Shen
1987
Pseudogroupes continus infinis. Zbl 0053.01604
Chern, Shiing-Shen
1953
On holomorphic mappings of hermitian manifolds of the same dimension. Zbl 0184.31202
Chern, Shiing-shen
1968
Élie Cartan and his mathematical work. Zbl 0046.00304
Chern, Shiing-shen; Chevalley, Claude
1952
Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space. Zbl 0049.23402
Chern, Shiing-shen; Kuiper, Nicolaas H.
1952
On the characteristic classes of complex sphere bundles and algebraic varieties. Zbl 0051.14301
Chern, Shiing-shen
1953
A sampler of Riemann-Finsler geometry. Zbl 1054.53001
2004
Riemannian geometry in an orthogonal frame. From lectures delivered by Élie Cartan at the Sorbonne 1926–27. With a preface to the Russian edition by S. P. Finikov. Translated from the 1960 Russian edition by Vladislav V. Goldberg and with a foreword by S. S. Chern. Zbl 1025.53002
Cartan, Élie
2001
Dupin submanifolds in Lie sphere geometry. Zbl 0678.53003
Cecil, Thomas E.; Chern, Shiing-Shen
1989
On integral geometry in Klein spaces. JFM 68.0462.02
Chern, S. S.
1942
Deformation of surfaces preserving principal curvatures. Zbl 0566.53002
Chern, Shiing-shen
1985
On the Riemann mapping theorem. Zbl 0872.32016
Chern, Shiing-Shen; Ji, Shanyu
1996
Differentiable manifolds. Zbl 0099.37402
Chern, Shiing-shen
1959
An inequality for the rank of a web and webs of maximum rank. Zbl 0402.57001
Chern, Shiing-Shen; Griffiths, Phillip A.
1978
Differential geometry; its past and its future. Zbl 0232.53001
Chern, Shiing-shen
1971
Minimal surfaces in an Euclidean space of $$n$$ dimensions. Zbl 0136.16701
Chern, Shiing-shen
1965
Wave propagation under curvature effects in a heterogeneous medium. Zbl 0878.35009
Chen, X.; Namah, G.
1997
Curves and surfaces in Euclidean space. Zbl 0683.53002
Chern, S. S.
1989
Geometrical interpretation of the sinh-Gordon equation. Zbl 0497.53056
Chern, Shiing-Shen
1981
On isothermic coordinates. Zbl 0056.40206
Chern, Shiing-shen; Hartman, Philip; Wintner, Aurel
1954
On the Euclidean connections in a Finsler space. Zbl 0060.39210
Chern, Shiing-shen
1943
Some new viewpoints in differential geometry in the large. Zbl 0063.00834
Chern, Shiing-Shen
1946
Scientific report on the Second Summer Institute. Several complex variables. Part II: Complex manifolds. Zbl 0074.30301
Chern, Shiing-shen
1956
On minimal spheres in the four-sphere. Zbl 0212.26402
Chern, S.-S.
1970
The geometry of the differential equation $$y'''=f(x,y,y',y'')$$. Zbl 0024.19801
Chern, Shiing-Shen
1940
Riemannian geometry as a special case of Finsler geometry. Zbl 0868.53051
Chern, Shiing-shen
1996
Meromorphic vector fields and characteristic numbers. Zbl 0265.32013
Chern, Shiing-Shen
1973
Exterior differential systems. Zbl 0516.58003
Bryant, Robert L.; Chern, Shiing-shen; Griffiths, Phillip A.
1982
La géométrie des sous-variétés d’un espace euclidean à plusieurs dimensions. Zbl 0064.17504
Chern, Shiing-Shen
1955
On integral geometry in Klein spaces. Zbl 0147.22303
Chern, Shiing-shen
1942
Topologische Fragen der Differentialgeometrie. LXII: Eine Invariantentheorie der Dreigewebe aus $$r$$-dimensionalen Mannigfaltigkeiten im $$R_{2r}$$. JFM 62.0829.03
Chern, S.-S.
1936
Sur la géométrie d’une équation différentielle du troisieme ordre. Zbl 0016.16401
Chern, Shiing-shen
1937
Sur la géométrie d’un système d’équations différentielles du second ordre. Zbl 0023.07701
Chern, Shiing-Shen
1939
On the characteristic classes of Riemannian manifolds. Zbl 0034.25002
Chern, Shiing-Shen
1947
Laplace transforms of a class of higher dimensional varieties in a projective space of $$n$$ dimensions. Zbl 0063.00831
Chern, Shiing-shen
1944
Some formulas related to complex transgression. Zbl 0203.54202
Bott, Raoul; Chern, S. S.
1970
Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). Revised printing of the second edition 1979. Zbl 1101.32301
Chern, Shiing-Shen
1995
On the isometry of compact submanifolds in Euclidean space. Zbl 0124.37501
Chern, Shiing-shen; Hsiung, C.
1963
Projective geometry and Riemann’s mapping problem. Zbl 0843.32013
Chern, Shiing-Shen; Ji, Shanyu
1995
Corrections and addenda to our paper: Abel’s theorem and webs. Zbl 0474.14003
Chern, S. S.; Griffiths, P.
1981
Foliations on a surface of constant curvature and the modified Korteweg- de Vries equations. Zbl 0483.53019
Chern, Shiing-Shen; Tenenblat, Keti
1981
On surfaces of constant mean curvature in a three-dimensional space of constant curvature. Zbl 0521.53006
Chern, Shiing-shen
1983
Topological questions of differential geometry. LX: Enumerations of webs. (Topologische Fragen der Differentialgeometrie. LX: Abzählungen für Gewebe.) Zbl 0011.13202
Chern, Shiing-Shen
1935
Existence and uniqueness theorem for uncertain differential equations. Zbl 1196.34005
Chen, X.; Liu, B.
2010
Multistage scenario-based interval-stochastic programming for planning water resources allocation. Zbl 1418.90183
Li, Y. P.; Huang, G. H.; Chen, X.
2009
Finite-size scaling of the correlation length in anisotropic systems. Zbl 1142.82333
Chen, X. S.; Zhang, H. Y.
2007
Chern’s work in geometry. Zbl 1125.53001
Yau, Shing-Tung
2006
On multiscale significance of Rice’s normality structure. Zbl 1192.74009
Yang, Q.; Chen, X.; Zhou, W. Y.
2006
A novel DCT-based algorithm for computing the modulated complex lapped transform. Zbl 1374.94695
Chen, X.; Dai, Q.
2006
Riemann-Finsler geometry. Zbl 1085.53066
Chern, Shiing-Shen; Shen, Zhongmin
2005
A sampler of Riemann-Finsler geometry. Zbl 1054.53001
2004
Chen, X.; Kim, K. S.
2003
The effects of thin and ultrathin liquid films on dynamic wetting. Zbl 1186.76101
Chen, X.; Ramé, E.; Garoff, S.
2003
Riemannian geometry in an orthogonal frame. From lectures delivered by Élie Cartan at the Sorbonne 1926–27. With a preface to the Russian edition by S. P. Finikov. Translated from the 1960 Russian edition by Vladislav V. Goldberg and with a foreword by S. S. Chern. Zbl 1025.53002
Cartan, Élie
2001
Riemannian geometry in an orthogonal frame. From lectures delivered by Élie Cartan at the Sorbonne 1926–27. With a preface to the Russian edition by S. P. Finikov. Translated from the 1960 Russian edition by Vladislav V. Goldberg and with a foreword by S. S. Chern. Zbl 1009.53003
Cartan, Élie
2001
Wolf prize in mathematics. Vol. 2. Zbl 1030.01001
2001
Riemannian geometry in an orthogonal frame. From lectures delivered by Élie Cartan at the Sorbonne 1926–27. With a preface to the Russian edition by S. P. Finikov. Translated from the 1960 Russian edition by Vladislav V. Goldberg and with a foreword by S. S. Chern. Zbl 1016.53002
Cartan, Élie
2001
An introduction to Riemann-Finsler geometry. Zbl 0954.53001
Bao, D.; Chern, S.-S.; Shen, Z.
2000
Wolf prize in mathematics. Vol. 1. Zbl 0972.01032
2000
Lectures on differential geometry. Zbl 0940.53001
Chern, S. S.; Chen, W. H.; Lam, K. S.
1999
Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures. Zbl 0943.74016
Chen, X.; Tan, C. P.; Haberfield, C. M.
1999
Wave propagation under curvature effects in a heterogeneous medium. Zbl 0878.35009
Chen, X.; Namah, G.
1997
Rigidity issues on Finsler surfaces. Zbl 0933.53033
Bou, D.; Chern, S. S.; Shen, Z.
1997
Finsler geometry is just Riemannian geometry without the quadratic restriction. Zbl 1044.53512
Chern, Shiing-Shen
1996
A note on the Gauss-Bonnet theorem for Finsler spaces. Zbl 0849.53046
Bao, David; Chern, S. S.
1996
On the Riemann mapping theorem. Zbl 0872.32016
Chern, Shiing-Shen; Ji, Shanyu
1996
Riemannian geometry as a special case of Finsler geometry. Zbl 0868.53051
Chern, Shiing-shen
1996
Finsler geometry. Joint summer research conference, July 16-20, 1995, Seattle, WA, USA. Zbl 0844.00019
1996
On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces. Zbl 0864.53053
Bao, David; Chern, S. S.; Shen, Z.
1996
Blank development and the prediction of earing in cup drawing. Zbl 0843.73035
Chen, X.; Sowerby, R.
1996
Finsler geometry over the reals. Zbl 0854.53023
Bao, D.; Chern, S. S.; Shen, Z.
1996
The mathematics of China. Zbl 0872.01040
Chern, S. S.
1996
A mathematician and his mathematical work. Selected papers of S. S. Chern. Edited and with a foreword by S. Y. Cheng, P. Li and G. Tian. Zbl 0924.01033
Chern, S. S.
1996
Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). Revised printing of the second edition 1979. Zbl 1101.32301
Chern, Shiing-Shen
1995
Projective geometry and Riemann’s mapping problem. Zbl 0843.32013
Chern, Shiing-Shen; Ji, Shanyu
1995
Analysis of arbitrary Mindlin plates or bridge decks by spline finite strip method. Zbl 0877.73078
Ng, S. F.; Chen, X.
1995
Effect of frictional force and nose shape on axisymmetric deformations of a thick thermoviscoplastic target. Zbl 0848.73017
Batra, R. C.; Chen, X.
1994
On a notable connection in Finsler geometry. Zbl 0787.53018
Bao, David; Chern, S. S.
1993
Effect of frictional force on the steady state axisymmetric deformations of a viscoplastic target. Zbl 0825.73636
Chen, X.; Batra, R. C.
1993
On Finsler geometry. Zbl 0755.53044
Chern, Shiing-Shen
1992
Exterior differential systems. Zbl 0726.58002
Bryant, Robert L.; Chern, S. S.; Gardner, Robert B.; Goldschmidt, Hubert L.; Griffiths, P. A.
1991
Transgression in associated bundles. Zbl 0768.53014
Chern, Shiing-Shen
1991
Surface theory with Darboux and Bianchi. Zbl 0734.53008
Chern, Shiing-Shen
1991
What is geometry? Zbl 0717.51002
Chern, Shiing-Shen
1990
Historical remarks on Gauss-Bonnet. Zbl 0701.53039
Chern, Shing-Shen
1990
Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern. 2nd ed. Zbl 0669.53001
Hopf, Heinz
1989
Dupin submanifolds in Lie sphere geometry. Zbl 0678.53003
Cecil, Thomas E.; Chern, Shiing-Shen
1989
Curves and surfaces in Euclidean space. Zbl 0683.53002
Chern, S. S.
1989
Global differential geometry. 2nd ed. Zbl 0683.53001
1989
Vector bundles with a connection. Zbl 0683.53026
Chern, S. S.
1989
Selected papers. Volume II-IV. Zbl 0682.01017
Chern, Shiing-Shen
1989
Harmonic maps of the two-sphere into a complex Grassmann manifold. II. Zbl 0627.58017
Chern, Shiing-Shen; Wolfson, Jon G.
1987
Tautness and Lie sphere geometry. Zbl 0635.53029
Cecil, Thomas E.; Chern, Shiing-Shen
1987
Pseudospherical surfaces and evolution equations. Zbl 0605.35080
Chern, S. S.; Tenenblat, K.
1986
On a conformal invariant of three-dimensional manifolds. Zbl 0589.53011
Chern, Shiing-shen
1986
On Riemannian metrics adapted to three-dimensional contact manifolds. Zbl 0561.53039
Chern, S. S.; Hamilton, R. S.
1985
Deformation of surfaces preserving principal curvatures. Zbl 0566.53002
Chern, Shiing-shen
1985
Harmonic maps of $$S^ 2$$ into a complex Grassmann manifold. Zbl 0601.58023
Chern, Shiing Shen; Wolfson, Jon
1985
Collected works. Vol. 4: Affine differential geometry. Differential geometry of circle and sphere groups. (Gesammelte Werke. Hrsg. von W. Burau, S. S. Chern, K. Leichtweiß, H. R. Müller, L. A. Santalo, U. Simon, K. Strubecker. Band 4: Affine Differentialgeometrie. Differentialgeometrie der Kreis- und Kugelgruppen. Kommentiert von Werner Burau und Udo Simon.) Zbl 0656.53002
Blaschke, Wilhelm
1985
Collected works. Vol. 3: Convex geometry. (Gesammelte Werke. Hrsg. von W. Burau, S. S. Chern, K. Leichtweiß, H. R. Müller, L. A. Santalo, U. Simon, K. Strubecker. Band 3: Konvexgeometrie. Kommentiert von Kurt Leichtweiß.) Zbl 0655.52001
Blaschke, Wilhelm
1985
Minimal surfaces by moving frames. Zbl 0521.53050
Chern, Shiing-shen; Wolfson, Jon Gordon
1983
On surfaces of constant mean curvature in a three-dimensional space of constant curvature. Zbl 0521.53006
Chern, Shiing-shen
1983
Real hypersurfaces in complex manifolds. Zbl 0519.32014
Chern, S. S.; Moser, Jürgen K.
1983
Web geometry. Zbl 0483.53013
Chern, Shiing-Shen
1982
Exterior differential systems. Zbl 0516.58003
Bryant, Robert L.; Chern, Shiing-shen; Griffiths, Phillip A.
1982
Projective geometry, contact transformations, and CR-structures. Zbl 0456.53023
Chern, Shiing-shen
1982
Geometrical interpretation of the sinh-Gordon equation. Zbl 0497.53056
Chern, Shiing-Shen
1981
Corrections and addenda to our paper: Abel’s theorem and webs. Zbl 0474.14003
Chern, S. S.; Griffiths, P.
1981
Foliations on a surface of constant curvature and the modified Korteweg- de Vries equations. Zbl 0483.53019
Chern, Shiing-Shen; Tenenblat, Keti
1981
Remarks on the Riemannian metric of a minimal submanifold. Zbl 0477.53056
Chern, S.-S.; Osserman, R.
1981
A simple proof of Frobenius theorem. Zbl 0481.58007
Chern, Shiing-shen; Wolfson, Jon G.
1981
An analogue of Bäcklund’s theorem in affine geometry. Zbl 0407.53002
Chern, Shing-Shen; Terng, Chuu-Lian
1980
Geometry and physics. Zbl 0455.53052
Chern, Shiing-shen
1980
Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed. Zbl 0444.32004
Chern, Shiing-shen
1979
Lie groups and KdV equations. Zbl 0408.35074
Chern, Shiing-shen; Peng, Chia-kuei
1979
From triangles to manifolds. Zbl 0425.53002
Chern, Shiing-Shen
1979
Affine minimal hypersurfaces. Zbl 0439.53008
Chern, Shiing-Shen
1979
Abel’s theorem and webs. Zbl 0386.14002
Chern, S. S.; Griffiths, Phillip
1978
An inequality for the rank of a web and webs of maximum rank. Zbl 0402.57001
Chern, Shiing-Shen; Griffiths, Phillip A.
1978
Selected papers. Vol. 1. Zbl 0403.01012
Chern, Shiing-shen
1978
The Chauvenet papers. A collection of prize-winning expository papers in mathematics. Vols. I and II. Zbl 0384.01013
1978
Circle bundles. Zbl 0356.55005
Chern, Shiing-shen
1977
Linearization of webs of codimension one and maximum rank. Zbl 0406.14003
Chern, Shiing-shen; Griffiths, Phillip A.
1977
Duality properties of characteristic forms. Zbl 0343.53015
Chern, Shiing-shen; White, James
1976
Real hypersurfaces in complex manifolds. Zbl 0302.32015
Chern, S. S.; Moser, Jürgen K.
1975
On the volume decreasing property of a class of real harmonic mappings. Zbl 0303.53049
Chern, Shiing-shen; Goldberg, Samuel I.
1975
On the projective structure of a real hypersurface in $$C_{n+1}$$. Zbl 0305.53019
Chern, Shiing-Shen
1975
Characteristic forms and geometric invariants. Zbl 0283.53036
Chern, Shiing-shen; Simons, James
1974
Meromorphic vector fields and characteristic numbers. Zbl 0265.32013
Chern, Shiing-Shen
1973
The mathematical works of Wilhelm Blaschke. Zbl 0264.01021
Chern, Shiing-shen
1973
Geometry of characteristic classes. Zbl 0292.57016
Chern, S. S.
1973
Geometry of characteristic classes. Zbl 0269.57013
Chern, Shiing-shen
1972
Holomorphic curves in the plane. Zbl 0249.32016
Chern, Shiing-Shen
1972
Some cohomology classes in principal fiber bundles and their application to Riemannian geometry. Zbl 0209.25401
Chern, S. S.; Simons, J.
1971
Differential geometry; its past and its future. Zbl 0232.53001
Chern, Shiing-shen
1971
Brief survey of minimal submanifolds. Zbl 0218.53070
Chern, S.-s.
1971
Minimal submanifolds of a sphere with second fundamental form of constant length. Zbl 0216.44001
Chern, S. S.; do Carmo, Manfredo Perdigão; Kobayashi, S.
1970
On the minimal immersions of the two-sphere in a space of constant curvature. Zbl 0217.47601
Chern, S.-s.
1970
On minimal spheres in the four-sphere. Zbl 0212.26402
Chern, S.-S.
1970
Some formulas related to complex transgression. Zbl 0203.54202
Bott, Raoul; Chern, S. S.
1970
Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections. Zbl 0208.35101
Bott, Raoul; Chern, S. S.
1970
Global analysis. Proceedings of the symposium in pure mathematics of the American Mathematical Society held at the University of California, Berkeley, California July 1-26, 1968. Part 1. Zbl 0204.07601
Chern, S.-S.; Smale, S.
1970
Global analysis. Proceedings of the symposium in pure mathematics of the American Mathematical Society held at the University of California, Berkeley, California July 1-26, 1968. Part 2. Zbl 0204.07602
Chern, S.-S.; Smale, S.
1970
...and 78 more Documents
all top 5
### Cited by 3,350 Authors
28 Jiao, Xiaoxiang 25 Deng, Shaoqiang 23 Xu, Hongwei 22 Mo, Xiaohuan 22 Xu, Ming 21 Morozov, Alexei Yurievich 21 Tenenblat, Keti 20 Huang, Xiaojun 19 Bidabad, Behroz 19 Chen, Bang-Yen 19 Loboda, Aleksandr Vasil’evich 18 Beloshapka, Valeriĭ K. 18 Shen, Yibing 17 Lamel, Bernhard 17 Li, Jiayu 16 Ezhov, Vladimir Vladimirovich 16 Merker, Joël 16 Mironov, Andrei D. 16 Otsuki, Tominosuke 16 Schmalz, Gerd 16 Zaitsev, Dmitri 15 Bracken, Paul Francis 15 Ebenfelt, Peter 15 Gilkey, Peter B. 15 Kossovskiy, Il’ya Grigor’evich 15 Kristály, Alexandru 15 Kruglikov, Boris S. 15 Li, Haizhong 14 Kolář, Martin 14 Sabau, Sorin Vasile 14 Zhong, Chunping 13 Fei, Jie 13 Ohta, Shin-ichi 13 Shen, Zhongmin 12 Bismut, Jean-Michel 12 Chern, Shiing-Shen 12 Griffiths, Phillip Augustus 12 Salimi Moghaddam, Hamid Reza 12 Shanker, Gauree 12 Wang, Jun 12 Xu, Xiaowei 11 Alías, Luis J. 11 Cheng, Xinyue 11 Han, Xiaoli 11 Huang, Libing 11 Isaev, Alexander 11 Javaloyes, Miguel Angel 11 Lin, Chang-Shou 11 Perrone, Domenico 11 Wu, Bingye 11 Xia, Qiaoling 10 Aldea, Nicoleta 10 Baouendi, Mohammed Salah 10 Forstnerič, Franc 10 Ji, Shanyu 10 Latifi, Dariush 10 Musso, Emilio 10 Qiu, Chunhui 10 Tayebi, Akbar 10 Vincze, Csaba 10 Yau, Shing-Tung 9 Angella, Daniele 9 Braga Brito, Fabiano Gustavo 9 Bucataru, Ioan 9 Burns, Daniel M. jun. 9 Caponio, Erasmo 9 He, Qun 9 Hsiang, Wu-Yi 9 Matveev, Vladimir S. 9 Meylan, Francine 9 Muzsnay, Zoltán 9 Peyghan, Esmaeil 9 Romero, Alfonso 9 Rothschild, Linda Preiss 9 Simon, Udo 9 Vlachos, Theodoros 9 Xia, Changyu 9 Yano, Kentaro 9 Yin, Songting 8 Alesker, Semyon 8 Antonelli, Peter Louis 8 Bedford, Eric 8 Bryant, Robert L. 8 Cheng, Jih-Hsin 8 Duan, Yishi 8 Han, Chong-Kyu 8 Hartman, Philip 8 Kamran, Niky 8 Kim, Sung-Yeon 8 Kopacz, Piotr 8 Lychagin, Valentin V. 8 Mir, Nordine 8 Peng, Chiakuei 8 Prástaro, Agostino 8 Reyes, Enrique G. 8 Ru, Min 8 Webster, Sidney M. 8 Yajima, Takahiro 8 Yan, Zaili 8 Zhao, Wei ...and 3,250 more Authors
all top 5
### Cited in 433 Serials
165 Differential Geometry and its Applications 130 Journal of Geometry and Physics 127 Transactions of the American Mathematical Society 114 Mathematische Annalen 105 Proceedings of the American Mathematical Society 103 Mathematische Zeitschrift 97 Advances in Mathematics 95 The Journal of Geometric Analysis 73 Tôhoku Mathematical Journal. Second Series 63 Journal of Mathematical Physics 63 Inventiones Mathematicae 58 Communications in Mathematical Physics 55 Annali di Matematica Pura ed Applicata. Serie Quarta 53 Annals of Global Analysis and Geometry 50 Journal of Mathematical Analysis and Applications 46 Science China. Mathematics 45 Duke Mathematical Journal 44 Geometriae Dedicata 44 Manuscripta Mathematica 44 Results in Mathematics 43 Kodai Mathematical Journal 40 International Journal of Geometric Methods in Modern Physics 40 Bulletin of the American Mathematical Society 35 International Journal of Mathematics 33 Journal of Mathematical Sciences (New York) 33 Acta Mathematica Sinica. English Series 32 Calculus of Variations and Partial Differential Equations 31 Journal of High Energy Physics 31 Kodai Mathematical Seminar Reports 30 Mathematical Notes 30 Annales de l’Institut Fourier 29 Comptes Rendus. Mathématique. Académie des Sciences, Paris 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 27 Archiv der Mathematik 27 Journal of Differential Equations 27 Bulletin of the American Mathematical Society. New Series 25 Journal of Functional Analysis 23 Nagoya Mathematical Journal 22 Journal of Geometry 20 Israel Journal of Mathematics 20 Journal of Soviet Mathematics 20 Monatshefte für Mathematik 20 Nonlinear Analysis. Real World Applications 19 International Journal of Theoretical Physics 19 Reports on Mathematical Physics 18 Acta Mathematica 18 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 18 Acta Applicandae Mathematicae 17 Letters in Mathematical Physics 17 Mathematical Proceedings of the Cambridge Philosophical Society 17 Chinese Annals of Mathematics. Series B 16 Frontiers of Mathematics in China 15 Theoretical and Mathematical Physics 15 Journal für die Reine und Angewandte Mathematik 15 Rendiconti del Circolo Matemàtico di Palermo. Serie II 15 Science in China. Series A 14 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 14 Compositio Mathematica 14 Topology and its Applications 13 Rocky Mountain Journal of Mathematics 13 Bulletin de la Société Mathématique de France 13 Journal of the American Mathematical Society 13 Journal de Mathématiques Pures et Appliquées. Neuvième Série 13 Mediterranean Journal of Mathematics 12 General Relativity and Gravitation 12 Nuclear Physics. B 12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 12 Siberian Mathematical Journal 12 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 12 Acta Mathematica Sinica. New Series 12 Proceedings of the Steklov Institute of Mathematics 11 Classical and Quantum Gravity 11 Physics Letters. B 11 Czechoslovak Mathematical Journal 11 Osaka Journal of Mathematics 11 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 11 Geometry & Topology 11 Journal of the European Mathematical Society (JEMS) 11 European Journal of Mathematics 10 Geometric and Functional Analysis. GAFA 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Applied Mathematics. Series B (English Edition) 10 Russian Journal of Mathematical Physics 10 Complex Analysis and its Synergies 9 Bulletin of the Australian Mathematical Society 9 Balkan Journal of Geometry and its Applications (BJGA) 9 Advances in Geometry 8 Modern Physics Letters A 8 Periodica Mathematica Hungarica 8 Functional Analysis and its Applications 8 Illinois Journal of Mathematics 8 Journal of the Korean Mathematical Society 8 Pacific Journal of Mathematics 8 Annals of Physics 8 Vietnam Journal of Mathematics 8 Journal of Dynamical and Control Systems 8 Communications in Contemporary Mathematics 8 DGDS. Differential Geometry – Dynamical Systems 8 Bulletin of the Brazilian Mathematical Society. New Series 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications ...and 333 more Serials
all top 5
### Cited in 59 Fields
2,321 Differential geometry (53-XX) 680 Global analysis, analysis on manifolds (58-XX) 647 Several complex variables and analytic spaces (32-XX) 359 Partial differential equations (35-XX) 359 Manifolds and cell complexes (57-XX) 225 Quantum theory (81-XX) 174 Dynamical systems and ergodic theory (37-XX) 163 Algebraic geometry (14-XX) 160 Relativity and gravitational theory (83-XX) 114 Algebraic topology (55-XX) 99 Calculus of variations and optimal control; optimization (49-XX) 93 Ordinary differential equations (34-XX) 92 Topological groups, Lie groups (22-XX) 85 Functions of a complex variable (30-XX) 73 Mechanics of particles and systems (70-XX) 54 Convex and discrete geometry (52-XX) 49 Nonassociative rings and algebras (17-XX) 37 Functional analysis (46-XX) 37 Geometry (51-XX) 34 Linear and multilinear algebra; matrix theory (15-XX) 32 Group theory and generalizations (20-XX) 30 Mechanics of deformable solids (74-XX) 30 Systems theory; control (93-XX) 29 Operator theory (47-XX) 27 Potential theory (31-XX) 26 History and biography (01-XX) 26 Probability theory and stochastic processes (60-XX) 26 Numerical analysis (65-XX) 22 Number theory (11-XX) 20 Computer science (68-XX) 19 $$K$$-theory (19-XX) 19 Fluid mechanics (76-XX) 18 Biology and other natural sciences (92-XX) 16 Real functions (26-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Combinatorics (05-XX) 13 Category theory; homological algebra (18-XX) 13 Statistical mechanics, structure of matter (82-XX) 12 Measure and integration (28-XX) 11 Associative rings and algebras (16-XX) 10 Commutative algebra (13-XX) 10 Operations research, mathematical programming (90-XX) 9 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 8 Statistics (62-XX) 8 Optics, electromagnetic theory (78-XX) 8 Information and communication theory, circuits (94-XX) 7 General topology (54-XX) 6 Geophysics (86-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 5 Integral transforms, operational calculus (44-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Mathematical logic and foundations (03-XX) 3 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 1 Approximations and expansions (41-XX) 1 Astronomy and astrophysics (85-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2023-03-29T16:27:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4515615701675415, "perplexity": 11141.654809086476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949009.11/warc/CC-MAIN-20230329151629-20230329181629-00523.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Afarhat.charbel-h | ## Farhat, Charbel H.
Compute Distance To:
Author ID: farhat.charbel-h Published as: Farhat, Charbel; Farhat, C.; Farhat, Charbel H. more...less Homepage: https://profiles.stanford.edu/charbel-farhat External Links: ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef · theses.fr
Documents Indexed: 188 Publications since 1987 5 Contributions as Editor Co-Authors: 124 Co-Authors with 187 Joint Publications 2,331 Co-Co-Authors
all top 5
### Co-Authors
5 single-authored 32 Tezaur, Radek 20 Lesoinne, Michel 14 Avery, Philip 12 Roux, François-Xavier 11 Amsallem, David 11 Hetmaniuk, Ulrich L. 11 Koobus, Bruno 10 Djellouli, Rabia 8 Macedo, Antonini P. 7 Cortial, Julien 7 Harari, Isaac 7 Mandel, Jan 6 Chen, Po-Shu 6 Géradin, Michel 6 Rixen, Daniel J. 5 Carlberg, Kevin T. 5 Franca, Leopoldo Luis Cabo Penna 5 Geuzaine, Philippe 5 Le Tallec, Patrick 5 Li, Jing 5 Pierson, Kendall H. 4 Crivelli, Luis A. 4 Dervieux, Alain 4 Main, Alex 4 Rallu, Arthur 3 Brown, Gregory W. 3 Grimberg, Sebastian 3 Kalashnikova, Irina 3 Lardat, Raphael 3 Maute, Kurt 3 Nikbay, Melike 3 Piperno, Serge 3 Schall, Eric 3 Sobh, Nahil Atef 3 Toivanen, Jari 3 Wilson, Edward L. 2 Argrow, Brian M. 2 Balajewicz, Maciej J. 2 Bavestrello, Henri 2 Boncoraglio, Gabriele 2 Borker, Raunak 2 Brogniez, Sebastien 2 Cai, Xiao-Chuan 2 Chapman, Todd 2 Chiou, J. C. 2 Choi, Youngsoo 2 de Borst, René 2 de la Bourdonnaye, Armel 2 Degand, C. 2 Felippa, Carlos A. 2 Fish, Jacob 2 Gerbeau, Jean-Frédéric 2 Ghosh, Debraj 2 Grandmont, Céline 2 Hemez, François M. 2 Huang, Daniel Zhengyu 2 Keunings, Roland 2 Lakshminarayan, Vinod K. 2 Lanteri, Stéphane 2 Magoulès, Frédéric 2 Maman, Nathan 2 Massimi, Paolo 2 Perić, Djordje 2 Rajasekharan, Ajaykumar 2 Sarkis, Marcus V. 2 Vanderstraeten, Denis 2 Wang, Dalei 2 Zahr, Matthew J. 2 Zeng, Xianyi 1 Amara, Mohamed 1 Anderson, Spenser 1 As’ad, Faisal 1 Barnett, Joshua 1 Belytschko, Ted Bohdan 1 Bergmann, Michel 1 Bhardwaj, Manoj 1 Bou-Mosleh, Charbel 1 Carpentier, Romuald 1 Chandesris, Marion 1 Darve, Eric 1 Dastillung, Climène 1 De Santis, Dante 1 Della Piéta, Patrick 1 Dolbow, John E. 1 Dostál, Zdeněk 1 Downer, Janice D. 1 Dubois-Pèlerin, Yves 1 Dureisseix, David 1 Fezoui, Loula 1 Gmati, Nabil 1 Grétarsson, Jón Tómas 1 Guery, Jean-François 1 Guillard, Hervé 1 Haasdonk, Bernard 1 Hachem, Elie 1 Horák, David 1 Iollo, Angelo 1 Lacour, Catherine 1 Larrouturou, Bernard 1 Lea, Patrick ...and 24 more Co-Authors
all top 5
### Serials
63 International Journal for Numerical Methods in Engineering 44 Computer Methods in Applied Mechanics and Engineering 21 Journal of Computational Physics 7 International Journal for Numerical Methods in Fluids 5 Revue Européenne des Éléments Finis 3 AIAA Journal 3 SIAM Journal on Scientific Computing 3 Journal of Computational Acoustics 2 Computers and Structures 2 SIAM Journal on Numerical Analysis 2 Applied Numerical Mathematics 2 Communications in Applied Numerical Methods 2 International Journal of High Speed Computing 1 Computers and Fluids 1 IMA Journal of Applied Mathematics 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Wave Motion 1 Numerische Mathematik 1 SIAM Journal on Scientific and Statistical Computing 1 Journal of Scientific Computing 1 Engineering with Computers 1 Computational Mechanics Advances 1 Numerical Linear Algebra with Applications 1 International Journal of Computational Fluid Dynamics 1 Contemporary Mathematics 1 Revue Européenne de Mécanique Numérique 1 European Journal of Computational Mechanics
all top 5
### Fields
103 Mechanics of deformable solids (74-XX) 95 Fluid mechanics (76-XX) 94 Numerical analysis (65-XX) 18 Partial differential equations (35-XX) 7 Computer science (68-XX) 5 Systems theory; control (93-XX) 4 Mechanics of particles and systems (70-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Optics, electromagnetic theory (78-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX)
### Citations contained in zbMATH Open
173 Publications have been cited 5,505 times in 2,689 Documents Cited by Year
A method of finite element tearing and interconnecting and its parallel solution algorithm. Zbl 0758.65075
Farhat, Charbel; Roux, Francois-Xavier
1991
FETI-DP: A dual-prime unified FETI method. I: A faster alternative to the two-level FETI method. Zbl 1008.74076
Farhat, Charbel; Lesoinne, Michel; LeTallec, Patrick; Pierson, Kendall; Rixen, Daniel
2001
The discontinuous enrichment method. Zbl 1002.76065
Farhat, Charbel; Harari, Isaac; Franca, Leopoldo P.
2001
Partitioned analysis of coupled mechanical systems. Zbl 0985.76075
Felippa, Carlos A.; Park, K. C.; Farhat, Charbel
2001
The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. Zbl 1299.76180
Carlberg, Kevin; Farhat, Charbel; Cortial, Julien; Amsallem, David
2013
Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity. Zbl 0951.74015
Farhat, C.; Lesoinne, M.; LeTallec, P.
1998
Efficient non linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. Zbl 1235.74351
Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel
2011
The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. Zbl 1157.76372
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001
Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations. Zbl 0896.76044
Lesoinne, Michel; Farhat, Charbel
1996
Bubble functions prompt unusual stabilized finite element methods. Zbl 1067.76567
Franca, Leopoldo P.; Farhat, Charbel
1995
A scalable dual-primal domain decomposition method. Zbl 1051.65119
Farhat, Charbel; Lesoinne, Michael; Pierson, Kendall
2000
A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Zbl 1027.76028
Farhat, Charbel; Harari, Isaac; Hetmaniuk, Ulrich
2003
Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Zbl 0991.74069
Farhat, C.; Lesoinne, M.
2000
Partitioned procedures for the transient solution of coupled aeroelastic problems. I: Model problem, theory and two-dimensional application. Zbl 1067.74521
Piperno, Serge; Farhat, Charbel; Larrouturou, Bernard
1995
Torsional springs for two-dimensional dynamic unstructured fluid meshes. Zbl 0961.76070
Farhat, C.; Degand, C.; Koobus, B.; Lesoinne, M.
1998
Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Zbl 1178.76259
Farhat, Charbel; Van der Zee, Kristoffer G.; Geuzaine, Philippe
2006
Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution. Zbl 0865.76038
Farhat, Charbel; Lesoinne, Michel; Maman, Nathan
1995
Implicit parallel processing in structural mechanics. Zbl 0805.73062
Farhat, Charbel; Roux, François-Xavier
1994
Residual-free bubbles for the Helmholtz equation. Zbl 0897.73062
Franca, Leopoldo P.; Farhat, Charbel; Macedo, Antonini P.; Lesoinne, Michel
1997
Partitioned procedures for the transient solution of coupled aeroelastic problems. II: Energy transfer analysis and three-dimensional applications. Zbl 1015.74009
Piperno, Serge; Farhat, Charbel
2001
A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes –application to vortex shedding. Zbl 1079.76567
Koobus, Bruno; Farhat, Charbel
2004
Reduced-order fluid/structure modeling of a complete aircraft configuration. Zbl 1124.76042
Lieu, T.; Farhat, C.; Lesoinne, M.
2006
Nonlinear model order reduction based on local reduced-order bases. Zbl 1352.65212
Amsallem, David; Zahr, Matthew J.; Farhat, Charbel
2012
On the significance of the geometric conservation law for flow computations on moving meshes. Zbl 0993.76049
Guillard, Hervé; Farhat, Charbel
2000
Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid-structure applications. Zbl 1032.74701
Farhat, Charbel; Chandesris, Marion
2003
An online method for interpolating linear parametric reduced-order models. Zbl 1269.65059
Amsallem, David; Farhat, Charbel
2011
A method for interpolating on manifolds structural dynamics reduced-order models. Zbl 1176.74077
Amsallem, David; Cortial, Julien; Carlberg, Kevin; Farhat, Charbel
2009
A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems. Zbl 0940.74067
Rixen, Daniel J.; Farhat, Charbel
1999
Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes. Zbl 0943.76055
Koobus, Bruno; Farhat, Charbel
1999
An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element systems. Zbl 0746.65086
Farhat, Charbel; Roux, Francois-Xavier
1992
The two-level FETI method for static and dynamic plate problems I: An optimal iterative solver for biharmonic systems. Zbl 0964.74062
Farhat, Charbel; Mandel, Jan
1998
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency. Zbl 1352.74348
Farhat, Charbel; Avery, Philip; Chapman, Todd; Cortial, Julien
2014
The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems. Zbl 0981.74064
Farhat, Charbel; Pierson, Kendall; Lesoinne, Michel
2000
A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems. Zbl 0965.65133
Farhat, Charbel; Macedo, Antonini; Lesoinne, Michel
2000
Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Zbl 1009.76518
Farhat, Charbel; Geuzaine, Philippe; Brown, Gregory
2003
Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Zbl 0979.76046
Farhat, Charbel; Macedo, Antonini; Lesoinne, Michel; Roux, Francois-Xavier; Magoulès, Frédéric; de la Bourdonnaye, Armel
2000
A scalable Lagrange multiplier based domain decomposition method for time-dependent problems. Zbl 0844.73077
Farhat, Charbel; Chen, Po-Shu; Mandel, Jan
1995
A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions. Zbl 1269.76073
Farhat, Charbel; Rallu, Arthur; Shankaran, Sriram
2008
Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. Zbl 1110.76319
2006
Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations. Zbl 1051.76038
Geuzaine, Philippe; Grandmont, Céline; Farhat, Charbel
2003
The discontinuous enrichment method for multiscale analysis. Zbl 1054.76048
Farhat, Charbel; Harari, Isaac; Hetmaniuk, Ulrich
2003
Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models. Zbl 1352.74349
Farhat, Charbel; Chapman, Todd; Avery, Philip
2015
A numerically scalable domain decomposition method for the solution of frictionless contact problems. Zbl 0988.74064
Dureisseix, D.; Farhat, C.
2001
Stabilization of projection-based reduced-order models. Zbl 1253.90184
Amsallem, David; Farhat, Charbel
2012
Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Zbl 1068.76063
Farhat, Charbel; Geuzaine, Philippe
2004
The two-level FETI method II: Extension to shell problems, parallel implementation and performance results. Zbl 1040.74513
Farhat, Charbel; Chen, Po-Shu; Mandel, Jan; Roux, Francois Xavier
1998
On the general solution by a direct method of a large-scale singular system of linear equations: Application to the analysis of floating structures. Zbl 0908.73092
1998
Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses. Zbl 1113.74023
Farhat, Charbel; Cortial, Julien; Dastillung, Climène; Bavestrello, Henri
2006
Progressive construction of a parametric reduced-order model for PDE-constrained optimization. Zbl 1352.49029
Zahr, Matthew J.; Farhat, Charbel
2015
A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems. Zbl 1235.74352
Carlberg, Kevin; Farhat, Charbel
2011
A scalable substructuring method by Lagrange multipliers for plate bending problems. Zbl 0956.74059
Mandel, Jan; Tezaur, Radek; Farhat, Charbel
1999
Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly nonlinear compressible fluid-structure interaction problems. Zbl 1202.74167
Farhat, C.; Rallu, A.; Wang, K.; Belytschko, T.
2010
Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver. Zbl 0977.74065
Rixen, Daniel J.; Farhat, Charbel; Tezaur, Radek; Mandel, Jan
1999
Application of the FETI method to ASCI problems – scalability results on 1000 processors and discussion of highly heterogeneous problems. Zbl 0970.74069
Bhardwaj, Manoj; Day, David; Farhat, Charbel; Lesoinne, Michel; Pierson, Kendall; Rixen, Daniel
2000
A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems. Zbl 1194.74476
Tezaur, Radek; Zhang, Lin; Farhat, Charbel
2008
Extending substructure based iterative solvers to multiple load and repeated analyses. Zbl 0851.73059
Farhat, Charbel; Crivelli, Luis; Roux, François Xavier
1994
FETI-DPH: a dual-primal domain decomposition method for acoustic scattering. Zbl 1189.76338
Farhat, Charbel; Avery, Philip; Tezaur, Radek; Li, Jing
2005
The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime. Zbl 1110.74860
Zhang, Lin; Tezaur, Radek; Farhat, Charbel
2006
Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. Zbl 0996.76058
Tezaur, Radek; Macedo, Antonini; Farhat, Charbel; Djellouli, Rabia
2002
Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries. Zbl 1360.76131
Djellouli, Rabia; Farhat, Charbel; Macedo, Antonini; Tezaur, Radek
2000
A transient FETI methodology for large-scale parallel implicit computations in structural mechanics. Zbl 0824.73067
Farhat, Charbel; Crivelli, Luis; Roux, Francois-Xavier
1994
Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Zbl 0825.73997
Farhat, Charbel; Lesoinne, Michel
1993
Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems. Zbl 1075.76572
Farhat, Charbel; Tezaur, Radek; Weidemann-Goiran, Paul
2004
A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers. Zbl 0907.73059
Farhat, Charbel; Chen, Po-Shu; Risler, Franck; Roux, Francois-Xavier
1998
A dynamic variational multiscale method for large eddy simulations on unstructured meshes. Zbl 1116.76046
Farhat, Charbel; Rajasekharan, Ajaykumar; Koobus, Bruno
2006
Updating finite element dynamic models using an element-by-element sensitivity methodology. Zbl 0783.73068
Farhat, Charbel; Hemez, Francois M.
1993
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers. Zbl 1171.76417
Farhat, Charbel; Tezaur, Radek; Toivanen, Jari
2009
A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain. Zbl 1183.76813
Petersen, Steffen; Farhat, Charbel; Tezaur, Radek
2009
On a component mode synthesis method and its application to incompatible substructures. Zbl 0900.73338
1994
Mesh partitioning for implicit computations via iterative domain decomposition: Impact and optimization of the subdomain aspect ratio. Zbl 0825.73780
Farhat, Charbel; Maman, Nathan; Brown, Gregory W.
1995
Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems. Zbl 1246.74023
Hetmaniuk, U.; Tezaur, R.; Farhat, C.
2012
Unusual stabilized finite element methods and residual free bubbles. Zbl 0904.76045
Franca, Leopoldo P.; Farhat, Charbel; Lesoinne, Michel; Russo, Alessandro
1998
FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps. Zbl 1284.76264
Farhat, Charbel; Gerbeau, Jean-Frédéric; Rallu, Arthur
2012
Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid – structure interaction problems. Zbl 1426.76436
Wang, K.; Rallu, A.; Gerbeau, J.-F.; Farhat, C.
2011
Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons. Zbl 1242.76143
Wang, Dalei; Tezaur, Radek; Toivanen, Jari; Farhat, Charbel
2012
An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems. Zbl 0764.73081
Farhat, Charbel; Park, K. C.; Dubois-Pelerin, Yves
1991
A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid – solid media. Zbl 1195.74292
Massimi, Paolo; Tezaur, Radek; Farhat, Charbel
2008
A FETI-preconditioned conjugate gradient method for large-scale stochastic finite element problems. Zbl 1176.74182
Ghosh, Debraj; Avery, Philip; Farhat, Charbel
2009
A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes. Zbl 1163.74344
Farhat, Charbel; Wiedemann-Goiran, Paul; Tezaur, Radek
2004
A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Zbl 0936.76036
Cai, Xiao-Chuan; Farhat, Charbel; Sarkis, Marcus
1998
On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method. Zbl 1009.35088
Farhat, Charbel; Tezaur, Radek; Djellouli, Rabia
2002
Learning constitutive relations from indirect observations using deep neural networks. Zbl 1437.65192
Huang, Daniel Z.; Xu, Kailai; Farhat, Charbel; Darve, Eric
2020
A numerically scalable dual-primal substructuring method for the solution of contact problems. I: The frictionless case. Zbl 1067.74572
Avery, Philip; Rebel, Gert; Lesoinne, Michel; Farhat, Charbel
2004
A non-overlapping domain decomposition method for the exterior Helmholtz problem. Zbl 0909.65103
de La Bourdonnaye, Armel; Farhat, Charbel; Macedo, Antonini; Magoulès, Frédéric; Roux, François-Xavier
1998
Sensitivity analysis and design optimization of three-dimensional nonlinear aeroelastic systems by the adjoint method. Zbl 1078.74633
Maute, K.; Nikbay, M.; Farhat, C.
2003
A higher-order discontinuous enrichment method for the solution of high Péclet advection-diffusion problems on unstructured meshes. Zbl 1183.76805
Farhat, C.; Kalashnikova, I.; Tezaur, R.
2010
Strain and stress computations in stochastic finite element methods. Zbl 1159.74425
Ghosh, Debraj; Farhat, Charbel
2008
A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid-structure interaction problems. Zbl 1426.76443
Zeng, Xianyi; Farhat, Charbel
2012
An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems. Zbl 1352.74132
Hetmaniuk, Ulrich; Tezaur, Radek; Farhat, Charbel
2013
Fast frequency sweep computations using a multi-point Padé-based reconstruction method and an efficient iterative solver. Zbl 1194.74107
Avery, Philip; Farhat, Charbel; Reese, Garth
2007
Convergence analysis of a discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of Helmholtz problems. Zbl 1205.65298
Amara, Mohamed; Djellouli, Rabia; Farhat, Charbel
2009
Improved accuracy for the Helmholtz equation in unbounded domains. Zbl 1060.76650
Turkel, Eli; Farhat, Charbel; Hetmaniuk, Ulrich
2004
A time-parallel implicit method for accelerating the solution of nonlinear structural dynamics problems. Zbl 1155.74428
Cortial, Julien; Farhat, Charbel
2009
Incorporation of linear multipoint constraints in substructure based iterative solvers. I: A numerically scalable algorithm. Zbl 0944.74071
Farhat, Charbel; Lacour, Catherine; Rixen, Daniel
1998
Implicit time integration of a class of constrained hybrid formulations. I. Spectral stability theory. Zbl 1067.74592
Farhat, Charbel; Crivelli, Luis; Géradin, Michel
1995
The discontinuous enrichment method for medium-frequency Helmholtz problems with a spatially variable wavenumber. Zbl 1295.76030
Tezaur, Radek; Kalashnikova, Irina; Farhat, Charbel
2014
A discontinuous enrichment method for variable-coefficient advection-diffusion at high Péclet number. Zbl 1242.76125
Kalashnikova, Irina; Tezaur, Radek; Farhat, Charbel
2011
The FETI family of domain decomposition methods for inequality-constrained quadratic programming: application to contact problems with conforming and nonconforming interfaces. Zbl 1227.74062
Avery, Philip; Farhat, Charbel
2009
An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid-structure interaction problems. Zbl 1349.76117
Farhat, Charbel; Lakshminarayan, Vinod K.
2014
Two-dimensional viscous flow computations on the Connection Machine: Unstructured meshes, upwind schemes and massively parallel computations. Zbl 0767.76049
Farhat, Charbel; Fezoui, Loula; Lanteri, Stéphane
1993
Computational bottlenecks for PROMs: precomputation and hyperreduction. Zbl 1483.65154
Farhat, Charbel; Grimberg, Sebastian; Manzoni, Andrea; Quarteroni, Alfio
2021
The DGDD method for reduced-order modeling of conservation laws. Zbl 07505919
Riffaud, Sébastien; Bergmann, Michel; Farhat, Charbel; Grimberg, Sebastian; Iollo, Angelo
2021
Learning constitutive relations from indirect observations using deep neural networks. Zbl 1437.65192
Huang, Daniel Z.; Xu, Kailai; Farhat, Charbel; Darve, Eric
2020
On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows. Zbl 07507241
Grimberg, Sebastian; Farhat, Charbel; Youkilis, Noah
2020
Gradient-based constrained optimization using a database of linear reduced-order models. Zbl 07508406
Choi, Youngsoo; Boncoraglio, Gabriele; Anderson, Spenser; Amsallem, David; Farhat, Charbel
2020
A family of position- and orientation-independent embedded boundary methods for viscous flow and fluid-structure interaction problems. Zbl 1395.76044
Huang, Daniel Z.; De Santis, Dante; Farhat, Charbel
2018
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017
An enhanced FIVER method for multi-material flow problems with second-order convergence rate. Zbl 1406.76061
Main, Alex; Zeng, Xianyi; Avery, Philip; Farhat, Charbel
2017
A discontinuous Galerkin method with Lagrange multipliers for spatially-dependent advection-diffusion problems. Zbl 1439.76052
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017
Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes. Zbl 1373.68446
Amsallem, David; Tezaur, Radek; Farhat, Charbel
2016
Projection-based model reduction for contact problems. Zbl 1352.74196
Balajewicz, Maciej; Amsallem, David; Farhat, Charbel
2016
Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models. Zbl 1352.74349
Farhat, Charbel; Chapman, Todd; Avery, Philip
2015
Progressive construction of a parametric reduced-order model for PDE-constrained optimization. Zbl 1352.49029
Zahr, Matthew J.; Farhat, Charbel
2015
A practical factorization of a Schur complement for PDE-constrained distributed optimal control. Zbl 1327.65225
Choi, Youngsoo; Farhat, Charbel; Murray, Walter; Saunders, Michael
2015
A computational framework for the simulation of high-speed multi-material fluid-structure interaction problems with dynamic fracture. Zbl 1352.76079
Wang, Kevin Guanyuan; Lea, Patrick; Farhat, Charbel
2015
Special issue: Advances in embedded interface methods. Zbl 1351.65002
2015
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency. Zbl 1352.74348
Farhat, Charbel; Avery, Philip; Chapman, Todd; Cortial, Julien
2014
The discontinuous enrichment method for medium-frequency Helmholtz problems with a spatially variable wavenumber. Zbl 1295.76030
Tezaur, Radek; Kalashnikova, Irina; Farhat, Charbel
2014
An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid-structure interaction problems. Zbl 1349.76117
Farhat, Charbel; Lakshminarayan, Vinod K.
2014
Reduction of nonlinear embedded boundary models for problems with evolving interfaces. Zbl 1352.65322
Balajewicz, Maciej; Farhat, Charbel
2014
A second-order time-accurate implicit finite volume method with exact two-phase Riemann problems for compressible multi-phase fluid and fluid-structure problems. Zbl 1349.76362
Main, Alex; Farhat, Charbel
2014
A hybrid discontinuous in space and time Galerkin method for wave propagation problems. Zbl 1352.65376
Wang, Dalei; Tezaur, Radek; Farhat, Charbel
2014
On the stability of reduced-order linearized computational fluid dynamics models based on POD and Galerkin projection: descriptor vs non-descriptor forms. Zbl 1359.76215
Amsallem, David; Farhat, Charbel
2014
The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. Zbl 1299.76180
Carlberg, Kevin; Farhat, Charbel; Cortial, Julien; Amsallem, David
2013
An adaptive scheme for a class of interpolatory model reduction methods for frequency response problems. Zbl 1352.74132
Hetmaniuk, Ulrich; Tezaur, Radek; Farhat, Charbel
2013
A high-order discontinuous Galerkin method with Lagrange multipliers for advection-diffusion problems. Zbl 1286.65150
Brogniez, S.; Farhat, C.; Hachem, E.
2013
Nonlinear model order reduction based on local reduced-order bases. Zbl 1352.65212
Amsallem, David; Zahr, Matthew J.; Farhat, Charbel
2012
Stabilization of projection-based reduced-order models. Zbl 1253.90184
Amsallem, David; Farhat, Charbel
2012
Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems. Zbl 1246.74023
Hetmaniuk, U.; Tezaur, R.; Farhat, C.
2012
FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps. Zbl 1284.76264
Farhat, Charbel; Gerbeau, Jean-Frédéric; Rallu, Arthur
2012
Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons. Zbl 1242.76143
Wang, Dalei; Tezaur, Radek; Toivanen, Jari; Farhat, Charbel
2012
A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid-structure interaction problems. Zbl 1426.76443
Zeng, Xianyi; Farhat, Charbel
2012
Computational algorithms for tracking dynamic fluid-structure interfaces in embedded boundary methods. Zbl 1412.74035
Wang, K.; Grétarsson, J.; Main, A.; Farhat, C.
2012
A dual-primal FETI method for solving a class of fluid-structure interaction problems in the frequency domain. Zbl 1242.74136
Li, Jing; Farhat, Charbel; Avery, Philip; Tezaur, Radek
2012
A hybrid discontinuous Galerkin method for computing the ground state solution of Bose-Einstein condensates. Zbl 1250.81040
Farhat, Charbel; Toivanen, Jari
2012
Provably stable and time-accurate extensions of Runge-Kutta schemes for CFD computations on moving grids. Zbl 1253.76023
Brogniez, Sebastien; Rajasekharan, Ajaykumar; Farhat, Charbel
2012
Efficient non linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. Zbl 1235.74351
Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel
2011
An online method for interpolating linear parametric reduced-order models. Zbl 1269.65059
Amsallem, David; Farhat, Charbel
2011
A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems. Zbl 1235.74352
Carlberg, Kevin; Farhat, Charbel
2011
Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid – structure interaction problems. Zbl 1426.76436
Wang, K.; Rallu, A.; Gerbeau, J.-F.; Farhat, C.
2011
A discontinuous enrichment method for variable-coefficient advection-diffusion at high Péclet number. Zbl 1242.76125
Kalashnikova, Irina; Tezaur, Radek; Farhat, Charbel
2011
Robust and provably second-order explicit-explicit and implicit-explicit staggered time-integrators for highly nonlinear compressible fluid-structure interaction problems. Zbl 1202.74167
Farhat, C.; Rallu, A.; Wang, K.; Belytschko, T.
2010
A higher-order discontinuous enrichment method for the solution of high Péclet advection-diffusion problems on unstructured meshes. Zbl 1183.76805
Farhat, C.; Kalashnikova, I.; Tezaur, R.
2010
A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium-frequency regime. Zbl 1202.74201
Massimi, Paolo; Tezaur, Radek; Farhat, Charbel
2010
Total energy conservation in ALE schemes for compressible flows. Zbl 1329.76201
Dervieux, Alain; Farhat, Charbel; Koobus, Bruno; Vázquez, Mariano
2010
A method for interpolating on manifolds structural dynamics reduced-order models. Zbl 1176.74077
Amsallem, David; Cortial, Julien; Carlberg, Kevin; Farhat, Charbel
2009
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers. Zbl 1171.76417
Farhat, Charbel; Tezaur, Radek; Toivanen, Jari
2009
A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain. Zbl 1183.76813
Petersen, Steffen; Farhat, Charbel; Tezaur, Radek
2009
A FETI-preconditioned conjugate gradient method for large-scale stochastic finite element problems. Zbl 1176.74182
Ghosh, Debraj; Avery, Philip; Farhat, Charbel
2009
Convergence analysis of a discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of Helmholtz problems. Zbl 1205.65298
Amara, Mohamed; Djellouli, Rabia; Farhat, Charbel
2009
A time-parallel implicit method for accelerating the solution of nonlinear structural dynamics problems. Zbl 1155.74428
Cortial, Julien; Farhat, Charbel
2009
The FETI family of domain decomposition methods for inequality-constrained quadratic programming: application to contact problems with conforming and nonconforming interfaces. Zbl 1227.74062
Avery, Philip; Farhat, Charbel
2009
A Padé-based factorization-free algorithm for identifying the eigenvalues missed by a generalized symmetric eigensolver. Zbl 1171.74462
Avery, P.; Farhat, C.; Hetmaniuk, U.
2009
A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions. Zbl 1269.76073
Farhat, Charbel; Rallu, Arthur; Shankaran, Sriram
2008
A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems. Zbl 1194.74476
Tezaur, Radek; Zhang, Lin; Farhat, Charbel
2008
A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid – solid media. Zbl 1195.74292
Massimi, Paolo; Tezaur, Radek; Farhat, Charbel
2008
Strain and stress computations in stochastic finite element methods. Zbl 1159.74425
Ghosh, Debraj; Farhat, Charbel
2008
Scalable FETI algorithms for frictionless contact problems. Zbl 1137.74052
Dostál, Zdeněk; Vondrák, Vít; Horák, David; Farhat, Charbel; Avery, Philip
2008
Fast frequency sweep computations using a multi-point Padé-based reconstruction method and an efficient iterative solver. Zbl 1194.74107
Avery, Philip; Farhat, Charbel; Reese, Garth
2007
Incorporation of linear multipoint constraints in domain-decomposition-based iterative solvers. II: Blending FETI-DP and mortar methods and assembling floating substructures. Zbl 1173.74399
Bavestrello, H.; Avery, P.; Farhat, C.
2007
Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Zbl 1178.76259
Farhat, Charbel; Van der Zee, Kristoffer G.; Geuzaine, Philippe
2006
Reduced-order fluid/structure modeling of a complete aircraft configuration. Zbl 1124.76042
Lieu, T.; Farhat, C.; Lesoinne, M.
2006
Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. Zbl 1110.76319
2006
Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses. Zbl 1113.74023
Farhat, Charbel; Cortial, Julien; Dastillung, Climène; Bavestrello, Henri
2006
The discontinuous enrichment method for elastic wave propagation in the medium-frequency regime. Zbl 1110.74860
Zhang, Lin; Tezaur, Radek; Farhat, Charbel
2006
A dynamic variational multiscale method for large eddy simulations on unstructured meshes. Zbl 1116.76046
Farhat, Charbel; Rajasekharan, Ajaykumar; Koobus, Bruno
2006
A study of higher-order discontinuous Galerkin and quadratic least-squares stabilized finite element computations for acoustics. Zbl 1198.76069
Harari, Isaac; Tezaur, Radek; Farhat, Charbel
2006
FETI-DPH: a dual-primal domain decomposition method for acoustic scattering. Zbl 1189.76338
Farhat, Charbel; Avery, Philip; Tezaur, Radek; Li, Jing
2005
An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics. Zbl 1086.74039
Farhat, Charbel; Li, Jing
2005
A FETI-DP method for the parallel iterative solution of indefinite and complex-valued solid and shell vibration problems. Zbl 1140.74550
Farhat, Charbel; Li, Jing; Avery, Philip
2005
CFD on moving grids: from theory to realistic flutter, maneuvering, and multidisciplinary optimization. Zbl 1184.76808
Farhat, Charbel
2005
A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes –application to vortex shedding. Zbl 1079.76567
Koobus, Bruno; Farhat, Charbel
2004
Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Zbl 1068.76063
Farhat, Charbel; Geuzaine, Philippe
2004
Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems. Zbl 1075.76572
Farhat, Charbel; Tezaur, Radek; Weidemann-Goiran, Paul
2004
A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes. Zbl 1163.74344
Farhat, Charbel; Wiedemann-Goiran, Paul; Tezaur, Radek
2004
A numerically scalable dual-primal substructuring method for the solution of contact problems. I: The frictionless case. Zbl 1067.74572
Avery, Philip; Rebel, Gert; Lesoinne, Michel; Farhat, Charbel
2004
Improved accuracy for the Helmholtz equation in unbounded domains. Zbl 1060.76650
Turkel, Eli; Farhat, Charbel; Hetmaniuk, Ulrich
2004
A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime. Zbl 1027.76028
Farhat, Charbel; Harari, Isaac; Hetmaniuk, Ulrich
2003
Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid-structure applications. Zbl 1032.74701
Farhat, Charbel; Chandesris, Marion
2003
Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Zbl 1009.76518
Farhat, Charbel; Geuzaine, Philippe; Brown, Gregory
2003
Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations. Zbl 1051.76038
Geuzaine, Philippe; Grandmont, Céline; Farhat, Charbel
2003
The discontinuous enrichment method for multiscale analysis. Zbl 1054.76048
Farhat, Charbel; Harari, Isaac; Hetmaniuk, Ulrich
2003
Sensitivity analysis and design optimization of three-dimensional nonlinear aeroelastic systems by the adjoint method. Zbl 1078.74633
Maute, K.; Nikbay, M.; Farhat, C.
2003
A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. II: Neumann boundary conditions. Zbl 1032.76595
Hetmaniuk, U.; Farhat, C.
2003
On the solution of inverse obstacle acoustic scattering problems with a limited aperture. Zbl 1048.76053
Djellouli, Rabia; Tezaur, Radek; Farhat, Charbel
2003
Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. Zbl 0996.76058
Tezaur, Radek; Macedo, Antonini; Farhat, Charbel; Djellouli, Rabia
2002
On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method. Zbl 1009.35088
Farhat, Charbel; Tezaur, Radek; Djellouli, Rabia
2002
A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. I: Dirichlet boundary conditions. Zbl 1008.76039
Farhat, Charbel; Hetmaniuk, Ulrich
2002
A blended fictitious/real domain decomposition method for partially axisymmetric exterior Helmholtz problems with Dirichlet boundary conditions. Zbl 1013.65137
Hetmaniuk, Ulrich; Farhat, Charbel
2002
FETI-DP: A dual-prime unified FETI method. I: A faster alternative to the two-level FETI method. Zbl 1008.74076
Farhat, Charbel; Lesoinne, Michel; LeTallec, Patrick; Pierson, Kendall; Rixen, Daniel
2001
The discontinuous enrichment method. Zbl 1002.76065
Farhat, Charbel; Harari, Isaac; Franca, Leopoldo P.
2001
Partitioned analysis of coupled mechanical systems. Zbl 0985.76075
Felippa, Carlos A.; Park, K. C.; Farhat, Charbel
2001
The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. Zbl 1157.76372
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001
Partitioned procedures for the transient solution of coupled aeroelastic problems. II: Energy transfer analysis and three-dimensional applications. Zbl 1015.74009
Piperno, Serge; Farhat, Charbel
2001
A numerically scalable domain decomposition method for the solution of frictionless contact problems. Zbl 0988.74064
Dureisseix, D.; Farhat, C.
2001
A linearized method for the frequency analysis of three-dimensional fluid-structure interaction problems in all flow regimes. Zbl 1013.74020
Lesoinne, Michel; Sarkis, Marcus; Hetmaniuk, Ulrich; Farhat, Charbel
2001
Iterative solution of large-scale acoustic scattering problems with multiple right hand-sides by a domain decomposition method with Lagrange multipliers. Zbl 1002.76072
Tezaur, Radek; Macedo, Antonini; Farhat, Charbel
2001
A fast method for solving acoustic scattering problems in frequency bands. Zbl 1153.76394
Djellouli, Rabia; Farhat, Charbel; Tezaur, Radek
2001
Multidisciplinary simulation of the maneuvering of an aircraft. Zbl 1002.68531
Farhat, C.; Pierson, K.; Degand, C.
2001
A scalable dual-primal domain decomposition method. Zbl 1051.65119
Farhat, Charbel; Lesoinne, Michael; Pierson, Kendall
2000
...and 73 more Documents
all top 5
### Cited by 3,938 Authors
110 Farhat, Charbel H. 28 Dostál, Zdeněk 27 Ladevèze, Pierre 25 Klawonn, Axel 25 Tezaur, Radek 23 Hughes, Thomas J. R. 23 Rozza, Gianluigi 21 Harari, Isaac 21 Rheinbach, Oliver 21 Wall, Wolfgang A. 20 Carlberg, Kevin T. 19 Bazilevs, Yuri 19 Masud, Arif 19 Oñate Ibáñez de Navarra, Eugenio 19 Trevelyan, Jon 18 Codina, Ramon 18 Desmet, Wim 18 Franca, Leopoldo Luis Cabo Penna 18 Magoulès, Frédéric 18 Rixen, Daniel J. 17 Dureisseix, David 17 Gosselet, Pierre 16 Gravemeier, Volker 16 Houzeaux, Guillaume 16 Kozubek, Tomas 16 Néron, David 16 Papadrakakis, Manolis 16 Scovazzi, Guglielmo 15 Mandel, Jan 15 Quarteroni, Alfio M. 14 Bijl, Hester 14 Gander, Martin Jakob 14 Laghrouche, Omar 14 Lesoinne, Michel 14 Maday, Yvon 14 Nobile, Fabio 13 Allix, Olivier 13 Benner, Peter 13 Brzobohatý, Tomáš 13 Djellouli, Rabia 13 Manzoni, Andrea 13 Perugia, Ilaria 13 Stabile, Giovanni 13 Vazquez, Mariano 13 Wu, Shulin 12 Amsallem, David 12 Bochev, Pavel B. 12 Felippa, Carlos A. 12 Hetmaniuk, Ulrich L. 12 Horák, David 12 Lanser, Martin 12 Mohamed, M. Shadi 12 Riou, Hervé 12 Roux, François-Xavier 12 Soize, Christian 12 van Zuijlen, Alexander H. 11 Antoine, Xavier 11 Badia, Santiago 11 Degroote, Joris 11 Fernández, Miguel Ángel 11 Gerbeau, Jean-Frédéric 11 Kim, Hyea Hyun 11 Navon, Ionel Michael 11 Pain, Christopher C. 11 Pavarino, Luca Franco 11 Rey, Christian A. 11 Willcox, Karen E. 10 Avery, Philip 10 Fang, Fangxin 10 Koobus, Bruno 10 Lee, Chang-Ock 10 Lew, Adrian J. 10 Liu, Gui-Rong 10 Peherstorfer, Benjamin 10 Soulaimani, Azzeddine 10 Van Brummelen, Harald 10 Widlund, Olof B. 9 Barucq, Hélène 9 Chung, Tsz Shun Eric 9 Combescure, Alain 9 de Borst, René 9 Dolean, Victorita 9 Düster, Alexander 9 Gravouil, Anthony 9 Hachem, Elie 9 Idelsohn, Sergio Rodolfo 9 Jiang, Yaolin 9 Matthies, Hermann Georg 9 Nakshatrala, K. B. 9 Ohayon, Roger 9 Ricchiuto, Mario 9 Tezduyar, Tayfun E. 9 Turkel, Eli L. 9 Valentin, Frédéric 9 Vandepitte, Dirk 9 Vierendeels, Jan 9 Wang, Zhu 9 Zampini, Stefano 8 Akkerman, Ido 8 Belytschko, Ted Bohdan ...and 3,838 more Authors
all top 5
### Cited in 186 Serials
647 Computer Methods in Applied Mechanics and Engineering 336 Journal of Computational Physics 264 International Journal for Numerical Methods in Engineering 130 Computational Mechanics 117 Computers and Fluids 84 SIAM Journal on Scientific Computing 57 Journal of Computational and Applied Mathematics 54 Computers & Mathematics with Applications 43 Journal of Scientific Computing 39 International Journal for Numerical Methods in Fluids 34 Advances in Computational Mathematics 32 Applied Mathematical Modelling 30 Applied Mathematics and Computation 30 Applied Numerical Mathematics 30 Engineering Analysis with Boundary Elements 29 Archives of Computational Methods in Engineering 23 International Journal of Computational Fluid Dynamics 22 Numerische Mathematik 21 SIAM Journal on Numerical Analysis 21 Communications in Numerical Methods in Engineering 21 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 17 Mathematics and Computers in Simulation 16 Journal of Computational Acoustics 15 International Journal of Computational Methods 14 Mathematics of Computation 14 Engineering Computations 12 Journal of Fluid Mechanics 12 Numerical Methods for Partial Differential Equations 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Communications in Computational Physics 9 Wave Motion 9 Numerical Algorithms 9 Numerical Linear Algebra with Applications 9 International Journal of Numerical Methods for Heat & Fluid Flow 9 ETNA. Electronic Transactions on Numerical Analysis 9 Computational Geosciences 9 SIAM/ASA Journal on Uncertainty Quantification 8 SIAM Journal on Matrix Analysis and Applications 8 Computing and Visualization in Science 8 Mathematical and Computer Modelling of Dynamical Systems 8 European Journal of Mechanics. B. Fluids 7 Mathematical Problems in Engineering 7 Structural and Multidisciplinary Optimization 6 Acta Mechanica 6 Journal of Mathematical Analysis and Applications 6 International Journal of Computer Mathematics 6 Advances in Engineering Software 6 Physics of Fluids 6 European Journal of Mechanics. A. Solids 6 International Journal for Numerical Methods in Biomedical Engineering 5 Applicable Analysis 5 Computing 5 Archive of Applied Mechanics 5 Computational Optimization and Applications 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 Computational Methods in Applied Mathematics 5 Multiscale Modeling & Simulation 5 International Journal for Computational Methods in Engineering Science and Mechanics 4 Inverse Problems 4 Journal of the Franklin Institute 4 Calcolo 4 COMPEL 4 Applications of Mathematics 4 SIAM Review 4 Multibody System Dynamics 4 Nonlinear Dynamics 4 Journal of Numerical Mathematics 4 GAMM-Mitteilungen 4 Communications on Applied Mathematics and Computation 3 Mathematical Methods in the Applied Sciences 3 BIT 3 Physica D 3 Mathematical and Computer Modelling 3 Linear Algebra and its Applications 3 SIAM Journal on Mathematical Analysis 3 Computational and Applied Mathematics 3 Journal of Vibration and Control 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Communications in Nonlinear Science and Numerical Simulation 3 SIAM Journal on Applied Dynamical Systems 3 Advances in Applied Mathematics and Mechanics 3 Communications in Applied and Industrial Mathematics 3 Research in the Mathematical Sciences 2 International Journal of Modern Physics B 2 Computer Physics Communications 2 Communications on Pure and Applied Mathematics 2 International Journal of Engineering Science 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Mechanics Research Communications 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Systems & Control Letters 2 Computer Aided Geometric Design 2 Finite Elements in Analysis and Design 2 Applied Mathematics Letters 2 Mathematics and Mechanics of Solids 2 Vietnam Journal of Mathematics 2 Journal of Mathematical Fluid Mechanics 2 Optimization and Engineering 2 Thai Journal of Mathematics ...and 86 more Serials
all top 5
### Cited in 39 Fields
1,586 Numerical analysis (65-XX) 1,163 Fluid mechanics (76-XX) 1,070 Mechanics of deformable solids (74-XX) 490 Partial differential equations (35-XX) 97 Biology and other natural sciences (92-XX) 76 Optics, electromagnetic theory (78-XX) 76 Systems theory; control (93-XX) 66 Computer science (68-XX) 52 Calculus of variations and optimal control; optimization (49-XX) 49 Classical thermodynamics, heat transfer (80-XX) 47 Operations research, mathematical programming (90-XX) 46 Mechanics of particles and systems (70-XX) 41 Geophysics (86-XX) 32 Dynamical systems and ergodic theory (37-XX) 26 Statistics (62-XX) 24 Ordinary differential equations (34-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 19 Probability theory and stochastic processes (60-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Approximations and expansions (41-XX) 11 Information and communication theory, circuits (94-XX) 7 Integral equations (45-XX) 6 Differential geometry (53-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Potential theory (31-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Operator theory (47-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Category theory; homological algebra (18-XX) 1 Global analysis, analysis on manifolds (58-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-09-29T14:25:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4621565043926239, "perplexity": 13560.413689878595}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335355.2/warc/CC-MAIN-20220929131813-20220929161813-00708.warc.gz"} |
https://docs.nersc.gov/filesystems/unix-file-permissions/ | # Unix File Permissions¶
## Brief Overview¶
Every file (and directory) has an owner, an associated Unix group, and a set of permission flags that specify separate read, write, and execute permissions for the "user" (owner), "group", and "other". Group permissions apply to all users who belong to the group associated with the file. "Other" is also sometimes known as "world" permissions, and applies to all users who can login to the system. The command ls -l displays the permissions and associated group for any file. Here is an example of the output of this command:
drwx------ 2 elvis elvis 2048 Jun 12 2012 private
-rw------- 2 elvis elvis 1327 Apr 9 2012 try.f90
-rwx------ 2 elvis elvis 12040 Apr 9 2012 a.out
drwxr-x--- 2 elvis bigsci 2048 Oct 17 2011 share
drwxr-xr-x 3 elvis bigsci 2048 Nov 13 2011 public
From left to right, the fields above represent:
1. set of ten permission flags
2. link count (irrelevant to this topic)
3. owner
4. associated group
5. size
6. date of last modification
7. name of file
The permission flags from left to right are:
Position Meaning
1 "d" if a directory, "-" if a normal file
2, 3, 4 read, write, execute permission for user (owner) of file
5, 6, 7 read, write, execute permission for group
8, 9, 10 read, write, execute permission for other (world)
and have the following meanings:
Value Meaning
- Flag is not set.
w File is writable. For directories, files may be created or removed.
x File is executable. For directories, files may be listed.
s Set group ID (sgid). For directories, files created therein will be associated with the same group as the directory, rather than default group of the user. Subdirectories created therein will not only have the same group, but will also inherit the sgid setting.
These definitions can be used to interpret the example output of ls -l presented above:
drwx------ 2 elvis elvis 2048 Jun 12 2012 private
This is a directory named "private", owned by user elvis and associated with Unix group elvis. The directory has read, write, and execute permissions for the owner, and no permissions for any other user.
-rw------- 2 elvis elvis 1327 Apr 9 2012 try.f90
This is a normal file named "try.f90", owned by user elvis and associated with group elvis. It is readable and writable by the owner, but is not accessible to any other user.
-rwx------ 2 elvis elvis 12040 Apr 9 2012 a.out
This is a normal file named "a.out", owned by user elvis and associated with group elvis. It is executable, as well as readable and writable, for the owner only.
drwxr-x--- 2 elvis bigsci 2048 Oct 17 2011 share
This is a directory named "share", owned by user elvis and associated with group bigsci. The owner can read and write the directory; all members of the file group bigsci can list the contents of the directory. Presumably, this directory would contain files that also have "group read" permissions.
drwxr-xr-x 3 elvis bigsci 2048 Nov 13 2011 public
This is a directory named "public", owned by user elvis and associated with group bigsci. The owner can read and write the directory; all other users can only read the contents of the directory. A directory such as this would most likely contain files that have "world read" permissions.
## Useful File Permission Commands¶
When a file is created, the permission flags are set according to the file mode creation mask, which can be set using the "umask" command. The file mode creation mask (sometimes referred to as "the umask") is a three-digit octal value whose nine bits correspond to fields 2-10 of the permission flags. The resulting permissions are calculated via the bitwise AND of the unary complement of the argument (using bitwise NOT) and the default permissions specified by the shell (typically 666 for files and 777 for directories). Common useful values are:
umask value File Permissions Directory Permissions
002 -rw-rw-r-- drwxrwxr-x
007 -rw-rw---- drwxrwx---
022 -rw-r--r-- drwxr-xr-x
027 -rw-r----- drwxr-x---
077 -rw------- drwx------
Note that at NERSC, a default umask of 007 is set in .bash_profile. This is read after .bashrc, so setting umask in your .bashrc.ext won't work, you will need to set it in your .bash_profile.ext.
### chmod¶
The chmod ("change mode") command is used to change the permission flags on existing files. It can be applied recursively using the "-R" option. It can be invoked with either octal values representing the permission flags, or with symbolic representations of the flags. The octal values have the following meaning:
Octal Digit Binary Representation (rwx) Permission
0 000 none
1 001 execute only
2 010 write only
3 011 write and execute
7 111 read, write, and execute (full permissions)
Here is an example of chmod using octal values:
nersc$umask 0077 nersc$ touch foo
nersc$ls -l foo -rw------- 1 elvis elvis 0 Nov 19 14:49 foo nersc$ chmod 755 foo
nersc$ls -l foo -rwxr-xr-x 1 elvis elvis 0 Nov 19 14:49 foo In the above example, the umask for user elvis results in a file that is read-write for the user, with no other permissions. The chmod command specifies read-write-execute permissions for the user, and read-execute permissions for group and other. Here is the format of the chmod command when using symbolic values: chmod [-R] [classes][operator][modes] file ... The classes determine to which combination of user/group/other the operation will apply, the operator specifies whether permissions are being added or removed, and the modes specify the permissions to be added or removed. Classes are formed by combining one or more of the following letters: Letter Class Description u user Owner of the file g group Users who are members of the file's group o other Users who are not the owner of the file or members of the file's group a all All of the above (equivalent to "ugo") The following operators are supported: Operator Description + Add the specified modes to the specified classes. - Remove the specified modes from the specified classes. = The specified modes are made the exact modes for the specified classes. The modes specify which permissions are to be added to or removed from the specified classes. There are three primary values which correspond to the basic permissions, and two less frequently-used values that are useful in specific circumstances: Mode Name Description r read Read a file or list a directory's contents. w write Write to a file or directory. x execute Execute a file or traverse a directory. X "special" execute This is a slightly more restrictive version of "x". It applies execute permissions to directories in all cases, and to files only if at least one execute permission bit is already set. It is typically used with the "+" operator and the "-R" option, to give group and/or other access to a large directory tree, without setting execute permissions on normal (non-executable) files (e.g., text files). For example, chmod -R go+rx bigdir would set read and execute permissions on every file (including text files) and directory in the bigdir directory, recursively, for group and other. The command chmod -R go+rX bigdir would set read and execute permissions on every directory, and would set group and other read and execute permissions on files that were already executable by the owner. s setgid or sgid This setting is typically applied to directories. If set, any file created in that directory will be associated with the directory's group, rather than with the default file group of the owner. This is useful in setting up directories where many users share access. This setting is sometimes referred to as the "sticky bit", although that phrase has a historical meaning unrelated to this context. Sets of class/operator/mode may separated by commas. Using the above definitions, the previous (octal notation) example can be done symbolically: nersc$ umask
0077
nersc$touch foo nersc$ ls -l foo
-rw------- 1 elvis elvis 0 Nov 19 14:49 foo
nersc$chmod u+x,go+rx foo nersc$ ls -l foo
-rwxr-xr-x 1 elvis elvis 0 Nov 19 14:49 foo
## Unix File Groups¶
Unix file groups provide a means to control access to shared data on disk and tape.
### Overview of Unix Groups¶
Every user on a Unix system is a member of one or more Unix groups, including their primary or default group. Every file (or directory) on the system has an owner and an associated group. When a user creates a file, the file's associated group will be the user's default group. The user (owner) has the ability to change the associated group to any of the groups to which the user belongs. Unix groups can be defined that allow users to share data with other users who belong to the same group.
### Unix Groups at NERSC¶
Group names are limited to eight characters. A user's default group is the same as their username. NERSC users usually belong to several other groups, including groups associated with specific research projects. For example, consider a NERSC user named "elvis", who is working with the "Big Science" research project. This project has an allocation on NERSC's MPP systems, controlled by the repository (repo) "bigsci". Associated with this the repo is the Unix group "bigsci". The user (elvis) would then be a member of two file groups, elvis and bigsci. Because a NERSC user can be a member of more than one research project, such a user would be a member of more than one repo-associated Unix groups.
NERSC PIs, PI Proxies, and Project Managers can manage group membership within Iris. Continuing with the example above, if user elvis wants to collaborate with another user "jimi", but does not want other members of bigsci to be able to see the data, the PI for Big Science could create a new group (for example, "ejdata", for elvis and jimi's data). The PI would then add elvis and jimi to the ejdata group. Those two users could then use "group permissions" on directories and files to share data with one another. Currently, PIs who wish to create a new Unix group should contact NERSC Consulting.
### Useful Unix Group Commands¶
Command Description | 2020-01-22T04:26:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1715032458305359, "perplexity": 6406.7404161921695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250606696.26/warc/CC-MAIN-20200122042145-20200122071145-00005.warc.gz"} |
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_212_Calculus_III/Chapter_13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.A%3A_Lagrange_Multipliers |
# 13.10: Lagrange Multipliers
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Solving optimization problems for functions of two or more variables can be similar to solving such problems in single-variable calculus. However, techniques for dealing with multiple variables allow us to solve more varied optimization problems for which we need to deal with additional conditions or constraints. In this section, we examine one of the more common and useful methods for solving optimization problems with constraints.
### Lagrange Multipliers
In the previous section, an applied situation was explored involving maximizing a profit function, subject to certain constraints. In that example, the constraints involved a maximum number of golf balls that could be produced and sold in $$1$$ month $$(x),$$ and a maximum number of advertising hours that could be purchased per month $$(y)$$. Suppose these were combined into a single budgetary constraint, such as $$20x+4y≤216$$, that took into account both the cost of producing the golf balls and the number of advertising hours purchased per month. The goal is still to maximize profit, but now there is a different type of constraint on the values of $$x$$ and $$y$$. This constraint and the corresponding profit function
$f(x,y)=48x+96y−x^2−2xy−9y^2$
is an example of an optimization problem, and the function $$f(x,y)$$ is called the objective function. A graph of various level curves of the function $$f(x,y)$$ follows.
Figure $$\PageIndex{1}$$: Graph showing level curves of the function $$f(x,y)=48x+96y−x^2−2xy−9y^2$$ corresponding to $$c=150,250,350,$$ and $$400.$$
In Figure $$\PageIndex{1}$$, the value $$c$$ represents different profit levels (i.e., values of the function $$f$$). As the value of $$c$$ increases, the curve shifts to the right. Since our goal is to maximize profit, we want to choose a curve as far to the right as possible. If there were no restrictions on the number of golf balls the company could produce or the number of units of advertising available, then we could produce as many golf balls as we want, and advertise as much as we want, and there would be not be a maximum profit for the company. Unfortunately, we have a budgetary constraint that is modeled by the inequality $$20x+4y≤216.$$ To see how this constraint interacts with the profit function, Figure $$PageIndex{2}$$ shows the graph of the line $$20x+4y=216$$ superimposed on the previous graph.
Figure $$\PageIndex{2}$$: Graph of level curves of the function $$f(x,y)=48x+96y−x^2−2xy−9y^2$$ corresponding to $$c=150,250,350,$$ and $$395$$. The red graph is the constraint function.
As mentioned previously, the maximum profit occurs when the level curve is as far to the right as possible. However, the level of production corresponding to this maximum profit must also satisfy the budgetary constraint, so the point at which this profit occurs must also lie on (or to the left of) the red line in Figure $$\PageIndex{2}$$. Inspection of this graph reveals that this point exists where the line is tangent to the level curve of $$f$$. Trial and error reveals that this profit level seems to be around $$395$$, when $$x$$ and $$y$$ are both just less than $$5$$. We return to the solution of this problem later in this section. From a theoretical standpoint, at the point where the profit curve is tangent to the constraint line, the gradient of both of the functions evaluated at that point must point in the same (or opposite) direction. Recall that the gradient of a function of more than one variable is a vector. If two vectors point in the same (or opposite) directions, then one must be a constant multiple of the other. This idea is the basis of the method of Lagrange multipliers.
Method of Lagrange Multipliers: One Constraint
Theorem $$\PageIndex{1}$$: Let $$f$$ and $$g$$ be functions of two variables with continuous partial derivatives at every point of some open set containing the smooth curve $$g(x,y)=k$$, where $$k$$ is a constant. Suppose that $$f$$, when restricted to points on the curve $$g(x,y)=k$$, has a local extremum at the point $$(x_0,y_0)$$ and that $$\vecs ∇g(x_0,y_0)≠0$$. Then there is a number $$λ$$ called a Lagrange multiplier, for which
$\vecs ∇f(x_0,y_0)=λ\vecs ∇g(x_0,y_0).$
Proof
Assume that a constrained extremum occurs at the point $$(x_0,y_0).$$ Furthermore, we assume that the equation $$g(x,y)=k$$ can be smoothly parameterized as
$$x=x(s) \; \text{and}\; y=y(s)$$
where $$s$$ is an arc length parameter with reference point $$(x_0,y_0)$$ at $$s=0$$. Therefore, the quantity $$z=f(x(s),y(s))$$ has a relative maximum or relative minimum at $$s=0$$, and this implies that $$\dfrac{dz}{ds}=0$$ at that point. From the chain rule,
\begin{align*} \dfrac{dz}{ds} &=\dfrac{∂f}{∂x}⋅\dfrac{∂x}{∂s}+\dfrac{∂f}{∂y}⋅\dfrac{∂y}{∂s} \\[5pt] &=\left(\dfrac{∂f}{∂x}\hat{\mathbf i}+\dfrac{∂f}{∂y}\hat{\mathbf j}\right)⋅\left(\dfrac{∂x}{∂s}\hat{\mathbf i}+\dfrac{∂y}{∂s}\hat{\mathbf j}\right)\\[5pt] &=0, \end{align*}
where the derivatives are all evaluated at $$s=0$$. However, the first factor in the dot product is the gradient of $$f$$, and the second factor is the unit tangent vector $$\vec{\mathbf T}(0)$$ to the constraint curve. Since the point $$(x_0,y_0)$$ corresponds to $$s=0$$, it follows from this equation that
$\vecs ∇f(x_0,y_0)⋅\vecs{\mathbf T}(0)=0, \nonumber$
which implies that the gradient is either the zero vector $$\vecs 0$$ or it is normal to the constraint curve at a constrained relative extremum. However, the constraint curve $$g(x,y)=k$$ is a level curve for the function $$g(x,y)$$ so that if $$\vecs ∇g(x_0,y_0)≠0$$ then $$\vecs ∇g(x_0,y_0)$$ is normal to this curve at $$(x_0,y_0)$$ It follows, then, that there is some scalar $$λ$$ such that
$\vecs ∇f(x_0,y_0)=λ\vecs ∇g(x_0,y_0) \nonumber$
$$\square$$
To apply Theorem $$\PageIndex{1}$$ to an optimization problem similar to that for the golf ball manufacturer, we need a problem-solving strategy.
Problem-Solving Strategy: Steps for Using Lagrange Multipliers
1. Determine the objective function $$f(x,y)$$ and the constraint function $$g(x,y).$$ Does the optimization problem involve maximizing or minimizing the objective function?
2. Set up a system of equations using the following template: \begin{align} \vecs ∇f(x,y) &=λ\vecs ∇g(x,y) \\[5pt] g(x,y)&=k \end{align}.
3. Solve for $$x$$ and $$y$$ to determine the Lagrange points, i.e., points that satisfy the Lagrange multiplier equation.
4. If the objective function is continuous on the constraint and the constraint is a closed curve (like a circle or an ellipse), then the largest of the values of $$f$$ at the solutions found in step $$3$$ maximizes $$f$$, subject to the constraint; the smallest of those values minimizes $$f$$, subject to the constraint.
But in other cases, we need to evaluate the objective functions $$f$$ at points from the constraint on either side of each Lagrange point to determine whether we have obtained a relative maximum or a relative minimum.
Note that it is possible that our objective function will not have a relative maximum or a relative minimum at a given Lagrange point. This can occur in a couple situations, but most often when the Lagrange point is also a critical point of the objective function giving us a saddle point. Most of the time we will still get a relative extremum at a saddle point subject to a constraint, but sometimes we will not. See Figure $$\PageIndex{3}$$ for an example of this case.
Figure $$\PageIndex{3}$$: Graph of $$f(x,y)=x^2-y^3$$ along with the constraint $$(x-1)^2 + y^2 = 1$$. Note that there is no relative extremum at $$(0,0)$$, although this point will satisfy the Lagrange Multiplier equation with $$\lambda=0$$.
Example $$\PageIndex{1}$$: Using Lagrange Multipliers
Use the method of Lagrange multipliers to find the minimum value of $$f(x,y)=x^2+4y^2−2x+8y$$ subject to the constraint $$x+2y=7.$$
Solution
Let’s follow the problem-solving strategy:
1. The objective function is $$f(x,y)=x^2+4y^2−2x+8y.$$ The constraint function is equal to the left-hand side of the constraint equation when only a constant is on the right-hand side. So here $$g(x,y)=x+2y$$. The problem asks us to solve for the minimum value of $$f$$, subject to the constraint (Figure $$\PageIndex{4}$$).
Figure $$\PageIndex{4}$$: Graph of level curves of the function $$f(x,y)=x^2+4y^2−2x+8y$$ corresponding to $$c=10$$ and $$26$$. The red graph is the constraint function.
2. We then must calculate the gradients of both $$f$$ and $$g$$:
$\vecs \nabla f \left( x, y \right) = \left( 2x - 2 \right) \hat{\mathbf{i}} + \left( 8y + 7 \right) \hat{\mathbf{j}} \\ \vecs \nabla g \left( x, y \right) = \hat{\mathbf{i}} + 2 \hat{\mathbf{j}}.$
The equation $$\vecs \nabla f \left( x, y \right) = \lambda \vecs \nabla g \left( x, y \right)$$ becomes
$\left( 2 x - 2 \right) \hat{\mathbf{i}} + \left( 8 y + 9 \right) \hat{\mathbf{j}} = \lambda \left( \hat{\mathbf{i}} + 2 \hat{\mathbf{j}} \right),$
which can be rewritten as
$\left( 2 x - 2 \right) \hat{\mathbf{i}} + \left( 8 y + 8 \right) \hat{\mathbf{j}} = \lambda \hat{\mathbf{i}} + 2 \lambda \hat{\mathbf{j}}.$
Next, we set the coefficients of $$\hat{\mathbf{i}}$$ and $$\hat{\mathbf{j}}$$ equal to each other:
\begin{align} 2 x - 2 &= \lambda \\ 8 y + 8 &= 2 \lambda. \end{align}
The equation $$g \left( x, y \right) = k$$ becomes $$x + 2 y = 7$$. Therefore, the system of equations that needs to be solved is
\begin{align} 2 x - 2 &= \lambda \\ 8 y + 8 &= 2 \lambda \\ x + 2 y &= 7. \end{align}
3. This is a linear system of three equations in three variables. We start by solving the second equation for $$λ$$ and substituting it into the first equation. This gives $$λ=4y+4$$, so substituting this into the first equation gives $2x−2=4y+4.\nonumber$ Solving this equation for $$x$$ gives $$x=2y+3$$. We then substitute this into the third equation: \begin{align*} (2y+3)+2y&=7 \\[5pt]4y&=4 \\[5pt]y&=1. \end{align*} Since $$x=2y+3,$$ this gives $$x=5.$$
4. Next, we evaluate $$f(x,y)=x^2+4y^2−2x+8y$$ at the point $$(5,1)$$, $f(5,1)=5^2+4(1)^2−2(5)+8(1)=27.$To ensure this corresponds to a minimum value on the constraint function, let’s try some other points on the constraint from either side of the point $$(5,1)$$, such as the intercepts of $$g(x,y)=0$$, Which are $$(7,0)$$ and $$(0,3.5)$$.
We get $$f(7,0)=35 \gt 27$$ and $$f(0,3.5)=77 \gt 27$$.
So it appears that $$f$$ has a relative minimum of $$27$$ at $$(5,1)$$, subject to the given constraint.
Exercise $$\PageIndex{1}$$
Use the method of Lagrange multipliers to find the maximum value of
$f(x,y)=9x^2+36xy−4y^2−18x−8y \nonumber$
subject to the constraint $$3x+4y=32.$$
Hint
Use the problem-solving strategy for the method of Lagrange multipliers.
Subject to the given constraint, $$f$$ has a maximum value of $$976$$ at the point $$(8,2)$$.
Let’s now return to the problem posed at the beginning of the section.
Example $$\PageIndex{2}$$: Golf Balls and Lagrange Multipliers
The golf ball manufacturer, Pro-T, has developed a profit model that depends on the number $$x$$ of golf balls sold per month (measured in thousands), and the number of hours per month of advertising y, according to the function
$z=f(x,y)=48x+96y−x^2−2xy−9y^2, \nonumber$
where $$z$$ is measured in thousands of dollars. The budgetary constraint function relating the cost of the production of thousands golf balls and advertising units is given by $$20x+4y=216.$$ Find the values of $$x$$ and $$y$$ that maximize profit, and find the maximum profit.
Solution:
Again, we follow the problem-solving strategy:
1. The objective function is $$f(x,y)=48x+96y−x^2−2xy−9y^2.$$ To determine the constraint function, we divide both sides by $$4$$, which gives $$5x+y=54.$$ The constraint function is equal to the left-hand side, so $$g(x,y)=5x+y.$$ The problem asks us to solve for the maximum value of $$f$$, subject to this constraint.
2. So, we calculate the gradients of both $$f$$ and $$g$$: \begin{align*} \vecs ∇f(x,y)&=(48−2x−2y)\hat{\mathbf i}+(96−2x−18y)\hat{\mathbf j}\\[5pt]\vecs ∇g(x,y)&=5\hat{\mathbf i}+\hat{\mathbf j}. \end{align*} The equation $$\vecs ∇f(x,y)=λ\vecs ∇g(x,y)$$ becomes $(48−2x−2y)\hat{i}+(96−2x−18y)\hat{\mathbf j}=λ(5\hat{\mathbf i}+\hat{\mathbf j}),\nonumber$ which can be rewritten as $(48−2x−2y)\hat{\mathbf i}+(96−2x−18y)\hat{\mathbf j}=λ5\hat{\mathbf i}+λ\hat{\mathbf j}.\nonumber$ We then set the coefficients of $$\hat{\mathbf i}$$ and $$\hat{\mathbf j}$$ equal to each other: \begin{align*} 48−2x−2y&=5λ \\[5pt] 96−2x−18y&=λ. \end{align*} The equation $$g(x,y)=k$$ becomes $$5x+y=54$$. Therefore, the system of equations that needs to be solved is \begin{align*} 48−2x−2y&=5λ \\[5pt] 96−2x−18y&=λ \\[5pt]5x+y&=54. \end{align*}
3. We use the left-hand side of the second equation to replace $$λ$$ in the first equation: \begin{align*} 48−2x−2y&=5(96−2x−18y) \\[5pt]48−2x−2y&=480−10x−90y \\[5pt] 8x&=432−88y \\[5pt] x&=54−11y. \end{align*} Then we substitute this into the third equation: \begin{align*} 5(54−11y)+y&=54\\[5pt] 270−55y+y&=54\\[5pt]216&=54y \\[5pt]y&=4. \end{align*} Since $$x=54−11y,$$ this gives $$x=10.$$
4. We then substitute $$(10,4)$$ into $$f(x,y)=48x+96y−x^2−2xy−9y^2,$$ which gives \begin{align*} f(10,4)&=48(10)+96(4)−(10)^2−2(10)(4)−9(4)^2 \\[5pt] & =480+384−100−80−144=540.\end{align*} Therefore the maximum profit that can be attained, subject to budgetary constraints, is $$540,000$$ with a production level of $$10,000$$ golf balls and $$4$$ hours of advertising bought per month. Let’s check to make sure this truly is a maximum. The endpoints of the line that defines the constraint are $$(10.8,0)$$ and $$(0,54)$$ Let’s evaluate $$f$$ at both of these points: \begin{align*} f(10.8,0)&=48(10.8)+96(0)−10.8^2−2(10.8)(0)−9(0^2) \\[5pt] &=401.76 \\[5pt] f(0,54)&=48(0)+96(54)−0^2−2(0)(54)−9(54^2) \\[5pt] &=−21,060. \end{align*} The second value represents a loss, since no golf balls are produced. Neither of these values exceed $$540$$, so it seems that our extremum is a maximum value of $$f$$, subject to the given constraint.
Exercise $$\PageIndex{2}$$: Optimizing the Cobb-Douglas function
A company has determined that its production level is given by the Cobb-Douglas function $$f(x,y)=2.5x^{0.45}y^{0.55}$$ where $$x$$ represents the total number of labor hours in $$1$$ year and $$y$$ represents the total capital input for the company. Suppose $$1$$ unit of labor costs $$40$$ and $$1$$ unit of capital costs $$50$$. Use the method of Lagrange multipliers to find the maximum value of $$f(x,y)=2.5x^{0.45}y^{0.55}$$ subject to a budgetary constraint of $$500,000$$ per year.
Hint
Use the problem-solving strategy for the method of Lagrange multipliers.
Subject to the given constraint, a maximum production level of $$13890$$ occurs with $$5625$$ labor hours and $$5500$$ of total capital input.
In the case of an objective function with three variables and a single constraint function, it is possible to use the method of Lagrange multipliers to solve an optimization problem as well. An example of an objective function with three variables could be the Cobb-Douglas function in Exercise $$\PageIndex{2}$$: $$f(x,y,z)=x^{0.2}y^{0.4}z^{0.4},$$ where $$x$$ represents the cost of labor, $$y$$ represents capital input, and $$z$$ represents the cost of advertising. The method is the same as for the method with a function of two variables; the equations to be solved are
\begin{align*} \vecs ∇f(x,y,z)&=λ\vecs ∇g(x,y,z) \\[5pt] g(x,y,z)&=k. \end{align*}
Example $$\PageIndex{3}$$: Lagrange Multipliers with a Three-Variable objective function
Maximize the function $$f(x,y,z)=x^2+y^2+z^2$$ subject to the constraint $$x+y+z=1.$$
Solution:
1. The objective function is $$f(x,y,z)=x^2+y^2+z^2.$$ To determine the constraint function, we set it equal to the variable expression on the left-hand side of the constraint equation: $$x+y+z=1$$ which gives the constraint function as $$g(x,y,z)=x+y+z.$$
2. Next, we calculate $$\vecs ∇f(x,y,z)$$ and $$\vecs ∇g(x,y,z):$$ \begin{align*} \vecs ∇f(x,y,z)&=⟨2x,2y,2z⟩ \\[5pt] \vecs ∇g(x,y,z)&=⟨1,1,1⟩. \end{align*} This leads to the equations \begin{align*} ⟨2x,2y,2z⟩&=λ⟨1,1,1⟩ \\[5pt] x+y+z&=1 \end{align*} which can be rewritten in the following form: \begin{align*} 2x&=λ\\[5pt]2y&=λ \\[5pt]2z&=λ \\[5pt]x+y+z&=1. \end{align*}
3. Since each of the first three equations has $$λ$$ on the right-hand side, we know that $$2x=2y=2z$$ and all three variables are equal to each other. Substituting $$y=x$$ and $$z=x$$ into the last equation yields $$3x=1,$$ so $$x=\dfrac{1}{3}$$ and $$y=\dfrac{1}{3}$$ and $$z=\dfrac{1}{3}$$ which corresponds to a critical point on the constraint curve.
4. Then, we evaluate $$f$$ at the point $$(\dfrac{1}{3},\dfrac{1}{3},\dfrac{1}{3})$$: $f(\dfrac{1}{3},\dfrac{1}{3},\dfrac{1}{3})=(\dfrac{1}{3})^2+(\dfrac{1}{3})^2+(\dfrac{1}{3})^2=\dfrac{3}{9}=\dfrac{1}{3}$ Therefore, a possible extremum of the function is $$\dfrac{1}{3}$$. To verify it is a minimum, choose other points that satisfy the constraint from either side of the point we obtained above and calculate $$f$$ at those points. For example, \begin{align*} f(1,0,0)&=1^2+0^2+0^2=1 \\[5pt] f(0,−2,3)&=0^2++(−2)^2+3^2=13. \end{align*} Both of these values are greater than $$\dfrac{1}{3}$$, leading us to believe the extremum is a minimum, subject to the given constraint.
Exercise $$\PageIndex{3}$$:
Use the method of Lagrange multipliers to find the minimum value of the function
$f(x,y,z)=x+y+z \nonumber$
subject to the constraint $$x^2+y^2+z^2=1.$$
Hint
Use the problem-solving strategy for the method of Lagrange multipliers with an objective function of three variables.
Evaluating $$f$$ at both points we obtained, gives us, \begin{align*} f\left(\dfrac{\sqrt{3}}{3},\dfrac{\sqrt{3}}{3},\dfrac{\sqrt{3}}{3}\right)&=\dfrac{\sqrt{3}}{3}+\dfrac{\sqrt{3}}{3}+\dfrac{\sqrt{3}}{3}=\sqrt{3} \\ f\left(−\dfrac{\sqrt{3}}{3},−\dfrac{\sqrt{3}}{3},−\dfrac{\sqrt{3}}{3}\right)&=−\dfrac{\sqrt{3}}{3}−\dfrac{\sqrt{3}}{3}−\dfrac{\sqrt{3}}{3}=−\sqrt{3}\end{align*} Since the constraint is continuous, we compare these values and conclude that $$f$$ has a relative minimum of $$−\sqrt{3}$$ at the point $$\left(−\dfrac{\sqrt{3}}{3},−\dfrac{\sqrt{3}}{3},−\dfrac{\sqrt{3}}{3}\right)$$, subject to the given constraint.
### Problems with Two Constraints
The method of Lagrange multipliers can be applied to problems with more than one constraint. In this case the objective function, $$w$$ is a function of three variables:
$w=f(x,y,z)$
and it is subject to two constraints:
$g(x,y,z)=0 \; \text{and} \; h(x,y,z)=0.$
There are two Lagrange multipliers, $$λ_1$$ and $$λ_2$$, and the system of equations becomes
\begin{align*} \vecs ∇f(x_0,y_0,z_0)&=λ_1\vecs ∇g(x_0,y_0,z_0)+λ_2\vecs ∇h(x_0,y_0,z_0) \\[5pt] g(x_0,y_0,z_0)&=0\\[5pt] h(x_0,y_0,z_0)&=0 \end{align*}
Example $$\PageIndex{4}$$: Lagrange Multipliers with Two Constraints
Find the maximum and minimum values of the function
$f(x,y,z)=x^2+y^2+z^2 \nonumber$
subject to the constraints $$z^2=x^2+y^2$$ and $$x+y−z+1=0.$$
Solution:
Let’s follow the problem-solving strategy:
1. The objective function is $$f(x,y,z)=x^2+y^2+z^2.$$ To determine the constraint functions, we first subtract $$z^2$$ from both sides of the first constraint, which gives $$x^2+y^2−z^2=0$$, so $$g(x,y,z)=x^2+y^2−z^2$$. The second constraint function is $$h(x,y,z)=x+y−z+1.$$
2. We then calculate the gradients of $$f,g,$$ and $$h$$: \begin{align*} \vecs ∇f(x,y,z)&=2x\hat{\mathbf i}+2y\hat{\mathbf j}+2z\hat{\mathbf k} \\[5pt] \vecs ∇g(x,y,z)&=2x\hat{\mathbf i}+2y\hat{\mathbf j}−2z\hat{\mathbf k} \\[5pt] \vecs ∇h(x,y,z)&=\hat{\mathbf i}+\hat{\mathbf j}−\hat{\mathbf k}. \end{align*} The equation $$\vecs ∇f(x,y,z)=λ_1\vecs ∇g(x,y,z)+λ_2\vecs ∇h(x,y,z)$$ becomes $2x\hat{\mathbf i}+2y\hat{\mathbf j}+2z\hat{\mathbf k}=λ_1(2x\hat{\mathbf i}+2y\hat{\mathbf j}−2z\hat{\mathbf k})+λ_2(\hat{\mathbf i}+\hat{\mathbf j}−\hat{\mathbf k}),$ which can be rewritten as $2x\hat{\mathbf i}+2y\hat{\mathbf j}+2z\hat{\mathbf k}=(2λ_1x+λ_2)\hat{\mathbf i}+(2λ_1y+λ_2)\hat{\mathbf j}−(2λ_1z+λ_2)\hat{\mathbf k}.$ Next, we set the coefficients of $$\hat{\mathbf i}$$ and $$\hat{\mathbf j}$$ equal to each other: \begin{align*}2x&=2λ_1x+λ_2 \\[5pt]2y&=2λ_1y+λ_2 \\[5pt]2z&=−2λ_1z−λ_2. \end{align*} The two equations that arise from the constraints are $$z^2=x^2+y^2$$ and $$x+y−z+1=0$$. Combining these equations with the previous three equations gives \begin{align*} 2x&=2λ_1x+λ_2 \\[5pt]2y&=2λ_1y+λ_2 \\[5pt]2z&=−2λ_1z−λ_2 \\[5pt]z^2&=x^2+y^2 \\[5pt]x+y−z+1&=0. \end{align*}
3. The first three equations contain the variable $$λ_2$$. Solving the third equation for $$λ_2$$ and replacing into the first and second equations reduces the number of equations to four: \begin{align*}2x&=2λ_1x−2λ_1z−2z \\[5pt] 2y&=2λ_1y−2λ_1z−2z\\[5pt] z^2&=x^2+y^2\\[5pt] x+y−z+1&=0. \end{align*} Next, we solve the first and second equation for $$λ_1$$. The first equation gives $$λ_1=\dfrac{x+z}{x−z}$$, the second equation gives $$λ_1=\dfrac{y+z}{y−z}$$. We set the right-hand side of each equation equal to each other and cross-multiply: \begin{align*} \dfrac{x+z}{x−z}&=\dfrac{y+z}{y−z} \\[5pt](x+z)(y−z)&=(x−z)(y+z) \\[5pt]xy−xz+yz−z^2&=xy+xz−yz−z^2 \\[5pt]2yz−2xz&=0 \\[5pt]2z(y−x)&=0. \end{align*} Therefore, either $$z=0$$ or $$y=x$$. If $$z=0$$, then the first constraint becomes $$0=x^2+y^2$$. The only real solution to this equation is $$x=0$$ and $$y=0$$, which gives the ordered triple $$(0,0,0)$$. This point does not satisfy the second constraint, so it is not a solution. Next, we consider $$y=x$$, which reduces the number of equations to three: \begin{align*}y &= x \\[5pt] z^2 &= x^2 +y^2 \\[5pt] x + y -z+1&=0. \end{align*} We substitute the first equation into the second and third equations: \begin{align*} z^2 &= x^2 +x^2 \\[5pt] &= x+x-z+1 =0. \end{align*} Then, we solve the second equation for $$z$$, which gives $$z=2x+1$$. We then substitute this into the first equation, \begin{align*} z^2 &= 2x^2 \\[5pt] (2x^2 +1)^2 &= 2x^2 \\[5pt] 4x^2 + 4x +1 &= 2x^2 \\[5pt] 2x^2 +4x +1 &=0, \end{align*} and use the quadratic formula to solve for $$x$$: $x = \dfrac{-4 \pm \sqrt{4^2 -4(2)(1)} }{2(2)} = \dfrac{-4\pm \sqrt{8}}{4} = \dfrac{-4 \pm 2\sqrt{2}}{4} = -1 \pm \dfrac{\sqrt{2}}{2}.$ Recall $$y=x$$, so this solves for $$y$$ as well. Then, $$z=2x+1$$, so $z = 2x +1 =2 \left( -1 \pm \dfrac{\sqrt{2}}{2} \right) +1 = -2 + 1 \pm \sqrt{2} = -1 \pm \sqrt{2} .$ Therefore, there are two ordered triplet solutions: $\left( -1 + \dfrac{\sqrt{2}}{2} , -1 + \dfrac{\sqrt{2}}{2} , -1 + \sqrt{2} \right) \; \text{and} \; \left( -1 -\dfrac{\sqrt{2}}{2} , -1 -\dfrac{\sqrt{2}}{2} , -1 -\sqrt{2} \right).$
4. We substitute $$\left(−1+\dfrac{\sqrt{2}}{2},−1+\dfrac{\sqrt{2}}{2}, −1+\sqrt{2}\right)$$ into $$f(x,y,z)=x^2+y^2+z^2$$, which gives \begin{align*} f\left( -1 + \dfrac{\sqrt{2}}{2}, -1 + \dfrac{\sqrt{2}}{2} , -1 + \sqrt{2} \right) &= \left( -1+\dfrac{\sqrt{2}}{2} \right)^2 + \left( -1 + \dfrac{\sqrt{2}}{2} \right)^2 + (-1+\sqrt{2})^2 \\[5pt] &= \left( 1-\sqrt{2}+\dfrac{1}{2} \right) + \left( 1-\sqrt{2}+\dfrac{1}{2} \right) + (1 -2\sqrt{2} +2) \\[5pt] &= 6-4\sqrt{2}. \end{align*} Then, we substitute $$\left(−1−\dfrac{\sqrt{2}}{2}, -1+\dfrac{\sqrt{2}}{2}, -1+\sqrt{2}\right)$$ into $$f(x,y,z)=x^2+y^2+z^2$$, which gives \begin{align*} f\left(−1−\dfrac{\sqrt{2}}{2}, -1+\dfrac{\sqrt{2}}{2}, -1+\sqrt{2} \right) &= \left( -1-\dfrac{\sqrt{2}}{2} \right)^2 + \left( -1 - \dfrac{\sqrt{2}}{2} \right)^2 + (-1-\sqrt{2})^2 \\[5pt] &= \left( 1+\sqrt{2}+\dfrac{1}{2} \right) + \left( 1+\sqrt{2}+\dfrac{1}{2} \right) + (1 +2\sqrt{2} +2) \\[5pt] &= 6+4\sqrt{2}. \end{align*} $$6+4\sqrt{2}$$ is the maximum value and $$6−4\sqrt{2}$$ is the minimum value of $$f(x,y,z)$$, subject to the given constraints.
Exercise $$\PageIndex{4}$$
Use the method of Lagrange multipliers to find the minimum value of the function
$f(x,y,z)=x^2+y^2+z^2$
subject to the constraints $$2x+y+2z=9$$ and $$5x+5y+7z=29.$$
Hint
Use the problem-solving strategy for the method of Lagrange multipliers with two constraints.
$$f(2,1,2)=9$$ is a relative minimum of $$f$$, subject to the given constraints
## Key Concepts
• An objective function combined with one or more constraints is an example of an optimization problem.
• To solve optimization problems, we apply the method of Lagrange multipliers using a four-step problem-solving strategy.
### Key Equations
• Method of Lagrange multipliers, one constraint
$$\vecs ∇f(x,y)=λ\vecs ∇g(x,y)$$
$$g(x,y)=k$$
• Method of Lagrange multipliers, two constraints
$$\vecs ∇f(x_0,y_0,z_0)=λ_1\vecs ∇g(x_0,y_0,z_0)+λ_2\vecs ∇h(x_0,y_0,z_0)$$
$$g(x_0,y_0,z_0)=0$$
$$h(x_0,y_0,z_0)=0$$
### Glossary
constraint
an inequality or equation involving one or more variables that is used in an optimization problem; the constraint enforces a limit on the possible solutions for the problem
Lagrange multiplier
the constant (or constants) used in the method of Lagrange multipliers; in the case of one constant, it is represented by the variable $$λ$$
method of Lagrange multipliers
a method of solving an optimization problem subject to one or more constraints
objective function
the function that is to be maximized or minimized in an optimization problem
optimization problem
calculation of a maximum or minimum value of a function of several variables, often using Lagrange multipliers
### Contributors
• Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org. | 2019-02-23T13:51:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9901452660560608, "perplexity": 267.3107222027181}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249501174.94/warc/CC-MAIN-20190223122420-20190223144420-00135.warc.gz"} |
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=840254 | # Publication Citation: Gain-Asisted Large and Rapidly-Responding Kerr Effect Using a Room-Temperature Active Raman Gain Medium
NIST Authors in Bold
Author(s): Lu Deng; M Payne; Gain-Asisted Large and Rapidly-Responding Kerr Effect Using a Room-Temperature Active Raman Gain Medium Date Unknown A four-level $N$-scheme with a two-mode active-Raman-gain-core is investigated for large and rapidly-responding Kerr effect enhancement at room-temperature. The new scheme is fundamentally different from electromagnetically-induced-transparency (EIT)-based ultra-slow-wave Kerr effect enhancement scheme. It eliminates the requirement of group velocity matching and multi-specie medium. It also eliminates significant probe field attenuation or distortion associated with weakly-driven EIT-based schemes. We show that a probe field can acquire a large, frequency tunable, gain-assisted nonlinear phase shift and yet travel with gain-assisted {\em superluminal} propagation velocity. This raises the possibility of rapidly-responding, frequency tunable nonlinear phase switching and phase gates for information science. Physical Review Letters nonlinear optics;superluminal nonlinear phase gate | 2014-09-01T11:12:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6417779922485352, "perplexity": 13366.153633118729}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535917663.12/warc/CC-MAIN-20140901014517-00321-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://malaysia.trade.gov.pl/en/news/188508,questionnaires-on-free-trade-agreement-with-the-philippines.html.pdf | %PDF-1.4 % 3 0 obj <> /Contents 4 0 R>> endobj 4 0 obj <> stream xRMO1s;vi'x0 Y@ ]>d̼b-L"2>Ywؗ=J &)J)ZT86I":jimj)bg[qЮO B;x(ևΫpZ>V8**t 8+dB+` &hdp.S !ִ҄-i6bT514P0hL[Lʒ*k|@{GŮׂA[&t/Ϩ6q\e1Spv )ûk|5gp:G48wsM[ݎќRn endstream endobj 5 0 obj <> /Annots [ 9 0 R 10 0 R 11 0 R ] /Contents 6 0 R>> endobj 6 0 obj <> stream xrurWbٜtmY,ʉ-1JI> @ׯy=3RVD5W-*cyك$YcYK nӼ{ʜ}e 8Fթ,xZ"KreEU&x]d\BDAP]9-1/ >5~1Ob.S_T#^Eo?F"L,SE(a&%ya U(+(&# + D@c [kt8AOmE8yq'?jC .(F߅CcԂpu I <(ĬLojh!VƸƄ2 Bz6h ۳L UƽuH 9[9'w=Ɂ5}ĜPyP35U2K !"*^ hZmh읶OН͝;#3TW3&<=ުa/L_ctϞv~ӡ͜BeZ {f}CB ) fqqXYU^, QSWЬ:N#k(Fol!ıN*)UWwQ?9u, o)iohE!4J/sVSKw,Owot%@#{n:dB EGȒb' JĻ~eR ߓ=566[ZW\ /A8C\&ł߇PR/&!{B O}KTt(Qc VIs 4"?0kZɷ5怦G> /Contents 8 0 R>> endobj 8 0 obj <> stream xP=O@ e_FVTUDb@L-RPпIH$ gāLN؏@pā Hc4 W(i@QZ]'r.{kgӷc%߈hN!9%=>_8JAO 十=Rj(Rޠ~ %N=>ɀYnڟ4z1')~We 슍 -p~.PB/XMELXA5'zb S endstream endobj 9 0 obj <> >> endobj 10 0 obj <> >> endobj 11 0 obj <> >> endobj 1 0 obj <> endobj 12 0 obj <> endobj 13 0 obj <> endobj 14 0 obj <> endobj 15 0 obj <> stream /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo <> def /CMapName /Adobe-Identity-UCS def /CMapType 2 def 1 begincodespacerange <0000> endcodespacerange 1 beginbfrange <0000> <0000> endbfrange endcmap CMapName currentdict /CMap defineresource pop end end endstream endobj 16 0 obj <> endobj 17 0 obj < >> /FontFile2 19 0 R >> endobj 18 0 obj <> stream xωRo,YS ?75fy;߭imCk}pܖ퍴ogݞ pGhǚx':t:ݙv]bܕvhvub߃ =izދ^mz߇>}kޏ~k,-Jjr> stream x| \T9;03"⊐ l C3k悥b"ehhffhiXim>2[43^ {ν >[^>?e=o{3"jf!2RC .4I>pݙ]jSP~ pOss [: !\ Ip[Ps0@}<Xe˃ >Y #p_,0g9Bcp M%<)wAhb lb* f~2!L2R8tTɧ(GOT:n&qXr7 I:.b-: :\ mI_+"_d;݆NM[#q'² OK Oѝd5uPIwYx-VJ՝B@EtmCpD~#&;b?_nm>g<[{K}jԨRq M-63={ {.*b izபgYr،4ɻ辱yP M gtyPA: v a;w]q5iHq %,e0nlbҸ^vWϖWo _1wʕ笜'OwR0=wŊT'}|5L [ ss-=Npkح쌘 זWDҍ݈!<2Dzz>̨KXAGoěW ̥t=|Yd;}Ʒt c 07<645Z0D; :קmW!OaHYIC ?Qws;_v pm}|~>}̟ٔRϏtW_Aϝo2~H -d%ș M_Q Q_ E_Csp՛pց720:9#d˦o/SUTW$~~L]#V^+B N_aI0~ J&aj$gi{a&6?l 5 5C῭_ !6@R"V ߁|FxKO?KJGpV:.Vx }Ao)"(Y,AᵸG}]h[w˿O,ЧpUܔQG}g; bUYwY Bαڡb/ ~^O13~WWV==|Q5/%,e~ :'|)i]Rv>U!Ec (ެh^g_{%) 9Z Ǚ p T{3/j":Iݿn+O \fUmmU^5֭O?^V}ҕ6 lߥij @C><P@9|G2b} CPCb2ݰlOgzqzw Y*UK XE2 ӤuHx9 k v:j ^fF^b6TJzdC~;6g/"rviܹ%+,\3Aes ~⬝Jw?6:*,w0[i*'+J k/ x>Pd|2<; 6s=?߿O[ ӂU<ë~V?Yc 9&J1b5} GI_pm8\j{gJ1dg@q66lrI]m"0#ʁ:rVZ\ !E7&zkةw-|RÈ cӷ~7rtR@7IG)~4;c\>b UV^6B Ń.сj^D"tڅɡn8d}^_ؾ8AmO~< 5ڕ?ig6_ ?Ǯ}sEˡ/0)ph!w8Zj;N~ %F|z%]]ɇ D 'R&҃ X97Lrêjt":62\ яAHӡV_bxKR^K*XK8h ju^5N1_}~@Y6BKMś߯ս qx (?hX/c hp$UVt~ e _'/죬_Tqk<ŭ_gvHպ^Rz$o vخ& 330BڎmqM]/kԚT/'?;nSvz^T)wtwZ&z?]j;; HW 6<^$[/OvE3앧ϝ;mj>si&'١1 xNUYA:}ߍ"}@O] 60t& Ԡjۆ=O\F]H/mwjq%CΝ? gVdJ?9!&jЫNS3m[(v=+7L(<fj[tޒ6ݿ߬lSv>C?<:Nw~};ve1^nebXK!Kj. 3cUS X~vh=Dcɥc.EwQi85,C±ް ୯kmZh@t$=;Cgͷ#.KƵp|mp"N>@|y =_j$p-lÖhʕBNAUj8 OT<ɹK:^y\S)> zwse%-q-6 j Þct93zryЇS/ub9Sx&6L@/Qσ "ZpOF&l Ns^KB. x$}p) Eз A rZ ܴ zwXuug=sG36߿uBxδ,gz 1}f. ֭ {t?u K 3b Ѿ{Ξc^wf!sR^>q }M\Чk>:άȰ $vΝcW~K6 1b[^g =ӫWM. P+r 27Z]5xٳQJZJZa?n1p4vWihEO^T:}ܸ6n]ǎۛ3== {b͞ w{<˸ Jja/8t/.|/| Leee3/ ܛ$TټyIϽ(l֮[}dpӀ: ??b:HhfpZA}{'9O^2u?m ]i y3oBm3_ۄ@)qåItjB@O 7꓆NTd9fUTNrk *K/fPŌ!ݸ浧 Y#] v7vܬZ m?Mt9;oMyN_'>||uw}*zHNx4C <߂ Dysc} ž]'T|1ݚ]Rϳ}<|C>yilv$M7{=5vl>zeɝ{?x~-ґ xn93w67S\x4:IzA玖+jݧ$=l |µF/Vm2e*=btf p\K E>FsGJvIn(WZv+~%tbWq3 eUr1;]@pMң[G4T 9;p]QEuOj1 fr$!(fK ͋ ~3.([*q8'A J;|-9k4 =al o q B!E$T .$+.vxBx1iWKMM=ۡ;&VunWp >1*½ŀ+Z; #mRJP.x=/ O0m 6( XcXB+X;&ݴ@JqK[?^cHmZ f69w6 rZjcz wickc u&D{Ad6n4,ƭPBmxjco3n̨! Gaԁ(0t7a 06d˂LȀ !>F^ T?-+3 pJ گkp*^E0o IJ" cF P)tN|3p75£e<=vJV2&N-lŃBC@$j.dr̖\SH c\$p#9nLAƴ31Aؚe=4V&cZ1ʬf,%,y Τ.i7FWsan,/2^m?P6o"ϰ(,䶞 sfirjD25W.Ry=X-cjsE XKfڴעi56.X *ˎg% Bw++p ~2ςlBNW ɁQIetroUqtڄ1l5X˂U_Uyȷes6HV©6c W%fB>窑CKT-6 vr]*oGp(*|ͪMk S-nhuNp{G6^ihrh,1 9=?Zesx([۫aeg& خW\k7V"im\k+u6pe^ƚj u/1f * ~/l|'b;A(nlR-*wf .Q URfS]αkF52rI\d_U99jG ourH)k8#}t4s=-Xw˿I5cu늓c|~0iuĵppµ2r쇝 C5n%ԜnnvDGj~33L.{xE55b]1#7)y+ݪht8qԺjjOj*XՇ7Wj:jg92uEhJGdyLYTɍU?YnU#6m?iT,s>I($KCcLkq0@ +pǾ Wzgc(&tNKq0h+ݍDph,j Yw0& xb]ʏ}E%ckS8Gd pcUu8N #6NT-©31ʌfHl:'\*g$Y6.z. U(q }!'[qJ > q šTɒ4/JfKUfFΩ\xx)\4 H눝[HEr;$q9 "g|cĥx%ۋI 9Er6w[*C 8c 5JJS{5&]ud \ZLEr5Ղi ߩHw͜OԼ'sNk*cx.9T$ujcM$Oo0g H3QuvjJyp\j w,-9˜6aP 3ASf\ɍ2RO+>(_:]yfσ}®CyJwɤd Sz(ieDAYqU/,6[l&c1*S!0{ld=d1(h {GÂ9C:V٠,s"&Ka.ߪ,&k1;h1K)XCQRlXe J6--Sv-I:bF O6K ME6ɓ_N(r%՜c܃Kb1[ƒl'cJl&&!ܜ]PbdLɷKl Laƈq%Vg+&Ě# 5[ up@&㌦A݀ܐSb)&h4+Vsb-ɚdʶ_)m.23=d9 ̥&E\ (2 Vuyb3Y&j d" RhU[r (Dj Ѝ9, 6=Q5WMJ 12E\\5WE!XC Ip '8pR ʔ|0:?9,X!_ a3Y8hU:7ag۱ wfiۙ <K 2Q- 03=dQ Ő^[Pul ;g)y+P45 :gt"&ST jx+Z,ۘ J +bCdC.(yXdYj h*aBꕘ4%5)&mLd^KUS2JT KMJOS"%21mD&SF%F+)T9)EKH\\bT|zt\e8%&)q qi@4-jX>%*n#ǥ c&D*ɑ)iqQ)JrzJrR hDĸĘOЃ@(*)y\J܈ش@J9-%2Z2*XbIrAB@J3rjld|2<.-5-E uF$&%嘤ȴDe T WeU#ȄL 4F)Jj>* q)4 KsqSa ,1zQ\2~"%52&.U Dĥ2Ĥ$̟I1<yGl()L Bt 6XlkɭF^F̣V-# q9>m 2:jusnl;VK// ݰXj helͬLɷL-ЬyPeZi(4kMJvlŖ|@bɷA1Q %0kɟmm(N gqP巘ŰK嗚 B2.I~QR͗mhlJ.'n4d%7DeqvgA)}; >H+ٜձg4Ӡ:JW7z%YWՄC'JWR~g$7 ~G$߬WRnW]z%m.~Ejd]RP$7?7-\dVp$-Lo[&Lr-[Z&9-2#ad;2wuGS? ɎH#ݑ );펔? m(|G |GGO74604!G3&Όz!0aP )+*;Lܗ*]JO 3z aְk_0 rL/3܊\ " .RS{\#?Pr~~89Gwa췩 -~JΜԑӡJ0/9UA|:l/9A'tro#Fc Qq{% R%Sr 9Q:B0.%Oޢ%oR%S%)y}o eJ+dwi^{XRT;aX &DvQbI yJsȶA6#Z#m "5>Y:͔TSD[IO#Y +:J>))ORTe$k*5HY-')YURZEIEKVV[I+ue{)YV>AZ,%/ 'a ŋBŔ, !EzH }ɣ dL,0Ad7Kɜ Jf{G(ELJ5̘>]Aa#'M "S))Vd')I %:b#: )LI%d2%KRI>%yI.PbHI6%Y:2ѓL~JdXYWGd;iLɠ$ 8'i~${Iw_2zdi4%$/)/O(XE8/idסEb[T}$J-EՑ{I(2{)gt/:4ԇ R25ܒ d %JH~^R_/CE"> endobj 21 0 obj <> endobj 22 0 obj <> stream /CIDInit /ProcSet findresource begin 12 dict begin begincmap /CIDSystemInfo <> def /CMapName /Adobe-Identity-UCS def /CMapType 2 def 1 begincodespacerange <0000> endcodespacerange 1 beginbfrange <0000> <0000> endbfrange endcmap CMapName currentdict /CMap defineresource pop end end endstream endobj 23 0 obj <> endobj 24 0 obj < >> /FontFile2 26 0 R >> endobj 25 0 obj <> stream xVQfd%{dT*l-Ȉ_sڥ}@;t:NtSn3msBhJWnt[Nw^{&lGM7l{z^4^7]B-J V[K}[}G?fVnw endstream endobj 26 0 obj <> stream x} |EpUW$trp Dr$3I23E5*""* B@/Ve1*"* D2UuO2z~K^z]Bh!"$xe 9gqhc @sC r+,,wTX' #$>/T] VT.SDxF(bah.SEܣuCDx 4﮲ c#ߴg9tωEςgfg -Ϗ"4mn\nAX Ncq͗! hI c@z' r=H#:Q/ FGI )& QJCq,A.]vb~pƓAHB:К?jdQX-j= A( #:uC݁HQz^7n@}Q,P4 D( Bh0nDCQnBhJF)h$JEi( eL4 eh F9(|4P*DECD4 MFSTTrQ-TO#rep!xS-*E Vq-|x4 TnVע^J[4uQڏKChh[EVEh \ '9!q8d|<GN8M8qGqbWvi4,MП-R flQ*{to;sR?H&КHWZhC Gc"c zѕ~.8u}׃7!=SO L}hTO5wj l& pX .c'9/ 1II a$hv&FG *>;q?oƈ .~ .{x@1n9i]u܇t^q:ȳSx.2 yýp}88hOaC7 #o»4Uo>9߲rjDZO'd~; >X7lnض|y?*_'twmF0%1=qX*}#G2 %44rfÁ訞.Bs 8䌌{<Ȩ/Sws|8#St͙rYǎ=pDtt?Ny.\n[[I x 7!:G Q8 A ] L aǀlSW,\ǩ=J {wMMҏ|Fod{tǚÎ-?1-qZ3wJO68j =fkM 殰Z;qwh>V vA̓{ 3B ~=8v ?bY:q/sCO$ o *= pK7 o8vS3=<aK I?F~i ߱tӋK_~p I RWd" @o_$z?^<#Kq%Y(EpH-Nt-x =D 5gLoi=l%ղj )xm-'+Ɠ #ܮ'x E*Hϯ$1uVoK" +XXNѯ詯 Rj+ jڇd h˜/1}G8ou4QX7r"\sʀ7~ӓ'?}p7.PR2aTg)#CXԅT=E^쎂GF?b}σ;~X鱩/ '*'Mġ}AO8pA ݅sK,Kz.!bV#G.v%t ]2uC~aFP3d6E4b0La9l!FÉXJox]/.&6r=>t ^R9# |rOr RD= xg.]2_[f, d]7MMJ0.'k$c_f& 頻_hXP4hR\F^HtC^-}|ЛNj!ͦO^VO= o̐=21A-.zR tbtT^r5(V壅3SƎZ26 5bV^ɟQX0(6>ly5·J&Γ% YG?rfv[weO͠ 9?pK-y?v}~ϘO6gva MS+̛vGϛ{OOsYҽg~,#4AQϿZxSy_x;vTWW ,6@6\X%YjiS mY,z PTdx #9n?=D"?7g,}*-3lSז~TW{&Bl ? oQ~{H!BgqPqWYhr#~w襯Ҳ @=fr ԚAr?6 N:i*O8[n=٧_hL/=hvÙ;9*ٱ<&|(4C*>NOùQ]ٜ0Y/&HF #(uݰF2._?tE뭟:}['8"tgdp Y* YJ۶Q쵂%MiE<7B1bƛ-a(l #j2zV5>J= \eZX;7S:TCHX>Yi4g3!3ᜐc;LQu9i]í[0 ZnDs쯀 t}.5 i HfަxkGA!<Ԡ?0o4kzx .6o^O4lh-M (m8 m7g;P}&'Tq*cDsdoF 9?Y4nщ FU ]K'!RK'wwhaeԩU鳂 ?.\yZ3d-"zT~": n!lyzt=k|ۑ)sgO[q2w iE 6̹.,^ׇܘSjwknp"N)9[?; Gym64>KG+n>1 N]sZ!^Ncp k+O= Yаǃp7^6Iex2 e[\;! 8G!8/q_рw_^G-mxd%'}IЇ >BG)zO0 /eq#=qR#ڰsP 4YM7X&J/|q* Iu_7 ǿ&B*OX*9 =QJ,ᣴ[=?Y;& П^8!d _L\Q}c qC 8=ڕc,,24c{pZ9+c!@ߦ+wY<^Ljs c|*8\"|h rCĹ2JY~rX3{A֜ÕX_ .ϢuYƎ.EyqqXߥ뷌f ЬX @W+ZiVV5ﴬI{/ׯ^~SOmJ'ɥk) 2L|㓯e>9rG]+Wޕ}1O.j}^8~?On Hu@tWXdIзN|bϩ3IʭVR+̚I8 8&7 ҰS="۽TC ƑB6:a|oMn+$ϟF 5r 'Vϫ!o#Q|]MYJⷦ !,ݽz}o6դU] q84[ K{^F,TH|^Hdw혶:4t~2 Ek 3٫*ǞI82NTAO/ГJ$08f-ѭ]YڇWe2@.xZ6608$&km٦ =v [^/>9 /|N]'>8[=GtXry.~a_ 6V6eu6Wqb6oۉLKd0e= ϠBMg=ІkOǹB:pBɫ|E Hz2|y˴MM= ij&W>MUZϝ t9}SQ;oxsT,Y;la/1iu5m iX='@^dO?<;1o3poġplK:c7A-nV g6* ~x> aI.b < "XlD nѪ5jLo*m?]TuMJ@[w] xKzĒ 63Tȋ~+u VnaodSžIRxsgLuw*, ዟ:$$hn J:5n}|gJx> tǗq66 =իUFDcr408 ߸S,ay=eؔ{>ӄm,6)ݴ o^pLgDŽ>WaY :f]8*.d IC7lA7"} t5j G.&B3:|q }w}>}yaMlg}!.< jáZn;>y}̆1amp]4х9ec!Y!6H7D,4zAIgz@ Cػ ô5]vی Yh7/[fY=eޕ՟W ܷĸ=yX8qvu]_~W+v 4Cph3}#5 ˈu랸?O܉tVr-|/ o20\_i<O_DPo?MKF8eGaEuhaLdd4Z B-*< ]tj8 '{p)Cli9j#EQhT6ߨӡ l|LzW ~7 _ 3} .~ >6 hip9Fd0>A{ IP_(D:C8^kcM#,gu^x'Z;u%kvP'{7h4&QkC7z| z݀6A.Z[UkKGkGQd@I\kA̩T9FkC7 z(ّFNdAsx(ZF.8ȌȊb7 >Z) ?n93jHgP D(Z F(Ak+FQFgD 0p ̷u# 8TTe}x0HvX%VTU)R f9l:M-4ΰN*kLL3O3W+eF[٥fbS եU2d-6ଥ\@&\*W Fm\-&Um.%n3m.3t*6>^e%橭V .[. l>DžNnSz5~Wd(kMrD:^60|qt_%p4 3G ̵ f+JۑԿ Ψs٫er g3p^/FƘf ]f֎f,'BL 0| \.frh97) +4y E42 ɮzZZ: V~jn#2oyB+t賃 /L|ʱ5ǝT̚\MzfwZ*5T|ٹm|Cm 5 h^8TMN7J*pU^ Z]eo2֊(n9#O| &̣ <ʱW?Ъ"wX2dUguz Pɳ[ӌJ+Unc}VnOֲOqkgAYEjK__jTn M |5{]D3>?7yVi}(шwiQ0^%Il^ iK .XYXtjgff \ l֢+.s.Tmk:UPlosl+[YDq-4uL'Et^y4iTԣrtjyWP#_-Vkq0jiEcfxvkk v^FQM3|[J~wi<']Om+Zb5>ᯍUV+hF j6%Fp,̫䦬GfkKUň[[˛45 s:y(4玏v|~gu;>ώ ~ UQN鰧82؇>vJ>O3>zdVvTaw&i*)N C^~G|r3bӨ5}^Pw O%*WPdvMf9]_EN?^gq)fhU86=dhYaUvh8NLAcPQ)etWz*+[ ܕ >}*L岗Y@O6˪ff[HF>A)gpNfn.3s4& f)vr 沪jd]iv3VFQp.g*V3Z⪌h;U Ҍ9@v˪8XWMf(vڀO4=VqUN3Y^*L&+I >%P36R{U )JcU\jִl@[i_8inUl=a.78Vln[zFK |UW2#d2,6F0y /?+)12 3V@gX|\f8 e䰬bdv|fڝ&Qw@baU İV Nf-Mg!be,2UvrQ*nf[ 0knRm3i 7*sT gUE573Qbb 0M7V6\9U REsU9cjT[eK1+YJ!8+-=MJ)Xe\VᨼB ) %%w2&+7-VI oH/( JVN~vV:efef*#a^n^UH T UVzCnH )# 'Y3()J~0+(;Š G0tO0de*I+RsR cb@"\%M.*,(40Xܼt9#(7-0+/WNWyQRSrbL&SiV&dRc,=fS 9 4M-H [ %+I)9炸 OaqYJ!YÐ2{ep(}2j2lMl@X,xW2|[ n554XjδA} D_uּ8VM<}wWka b,̴xhk2V1ŢCA4V4W-J.tZܐLc5:-i˰S[JJsrPw]X,3U2ΉVnwZ5ѹIRTp&[;+Yo.~2~:HV Ars :HҒ|[j%[+ d5S\+)V[VU+)?V}j%mQ.zI*d\R~S7%l+dגIJ&חL%kJ&ՒI%%\R3:2WUGr俥:Ց[#ٷ:R~UuZ ):b"P 3 >-k_иɼh[3؟M?;3:_ 3---f9* yr~[]{W~Sۅ'k pTO( QZ_cm> k7 LpW>ukμvίa80v{~m<o˟X }A/E"hׅek2 m}NJ :.į""\"~EɍḦ́Rp9Vjr,KOȥLc=H|O"(|ۍY:KI9-Kē2|,\/<(9Iɿ(9A|Fɧ' &IGrlu7阉||4F ! >' ~*}N>k'}JڑH+H'@ c? M* I;^z/ lOޅwwBNɁ'Kv ŷߊޞLNߊ!oR;uJw!Q&I{ɫ/FH&=;K{Z3VՓ];]m@ { l#/'d%dkR'%l<&m'/0> /Mask [0 0 ] /Length 34339>> stream xRְC @=EƲta 8r֮ɶа555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555Ž CN5=]]]ݼ-=w~A'Ү \j !@}5ݶl_Yv@;pkk!4L,ok2ЀMA@ 6mkMX24Nak:ЈMA@+ 6kX"^hM5;^hyM:53^hMZ5Ɯ+^hyMz5#^h&M@6Z4o5XФ9M56lr F4jk:z U\k͚#^h&@æ6Z6m5X'д)MJ5Mlr J4nkZz u\k͛"^hkfz \Ukk0.^X1&: 6kVbh5X=ÂM5lr .^X|5z E&"55\ˠV%lr .^Xx5z e&b5\ˡV'lr .^Xz5z j&556ER_50z &5*\֪;\ Z]&5: 6Hq5Hz Mek lr .^Xkp}Fkk lr .^Xkp\. @PHo 6Hz sM%k+wk .^X\lpy FEkkgÿylpl\"^?k .^X\5H^ Vj?zMktk&5U:̵^lpi a 60z s\>'vk .^X\;5DMG V+:zMkҙk]&b5Uε^lp)r\"\+ˠ֣k^lpjsk .^X\+ V/zzM5u͵^lzz s^XJk+P˵J 6X7оjzM5sk L.k^lbz q\ km Z^hZ,B&@˂5+͵ 6X'ЮpE{M*5fs-k H*k^lBz Q\KkmJZ^hR.R&m@5+̵ק=L5rC(^hN&^nl" &E@kv\k>ȵ\6a VC%kB]]]G&^hJ&* @K27CrC% C4AfWO*5vdVrj85kS5^lz ] J+y컋 HA@#RnhjMA@r[ן^yMA@rʵw 6h^hA.ׂC7DN4 k_<5es-Zwmkt{>s=kW z 3 gϵz{d&5௺j R˵75Ձfzm5?W=_5loz6r?t5C^5 9=Chrmε5j Qk=M)aϫwv^{ ]ץ_:kAWi{ dЅkEڢvhۄr6vF[4tk߶ Z.Cۿ 6-l'} H]rg\u [GnSꨳMA^E2V-?@g-lr V(L=^UIJ6ez VLFΦeg6=ك2v%HTٙMA ~mD\;s5>1*E6-ч+EvkOsX& Z\ LLvM"3\,jNwslkc;K5kl%t>r'=\bg6uz \ WكMA^5s%*l@%*lklCs%R 6k5kf dl15[ tlr m@}lkklk^\0plX^!5:w& A8FT״6&6z ä6 Q5i5Hk]& 5], MA^4YmtoMlr @mښ&&MA^(&i)2IkMriz d^L456a56ٻc4٣gP62&\cܡ&|s z I sINu05>#m⽤ n F N0z ||k0^70&ϵ< RPz bP͐k:C <\@̀%׆ v\tX5t͔kϔk,P r-{r-}hc5T͘kϘkɃ5EDm\ ~\K ^8z l\{y~] 95I-k/w_%Xž"k/{#y}(r kA92ȗrcwυDhz *l\{;ip'տ&ko]<5j%r>]Gj_ɵMaHվH@\%X> Y42X H( +_% z 72Vrl\ 2k=ڛk_ɵ\%*z lW 7C2楃LF r &r Yȣ}tej!u<G)|\5KV밥r1σr &:-A}R+v ksʭk0 vl\L'N8kD&NX@QxXs:Mh}NZ˵P]m#dFr5^b/ؒVYG's!8 уk0-0O%s}B|9keE>=lr 9|X?kC?p _KLE l\ ZlE-k2xlr & Dv H~-k^K^5^;2H-ksr &:G֚ 33*G^jﱱD]Lk{ 6^xMkO'-} 6^h[p+i*ӯ,ېd?RSk &Uj]7z3l00DǦ{ VRuNrm;vi5zw1-v2Hw}>[ ?D@Ϟk{@hX?[v~Ε=63=Jx>f5*\]_V_篴Jkb#ɵLHd5W-2:^}Z.:;z7{M@~}Z.N_8 Tڧ3\5#5RtZ:2V*J[ k kul%z=[Jk FkUd{\=J[V5c5)Z.½<[^V5#5)Z*آWߑBlw}٫} RV?q\{ I~]V*|ZnlMc5om^zuϵJǂ=2mXr=r*{ YTb١\M9lP׀,k6 N&u[SbC7D-kH'&ؠ^d .8r I]͵ lAW6~ lFVR -k(^t+*>KJb+z l\{C 68׀f"赽It ^ D1 .^,P\ho3To4 ^I\~v|L|jJK(sGI}.^Us6GmBp{.DԤ}.^ׇ6{bdϵLE1ko&-8 v dz lsupE1\I߹5xE1s8mwcwUNk<@ܴ/4 %%XA#lODw25m:&7fs- lb7DcC[lܱ*lu;k 7.-2;εdnZJ Fk ;]dmI@ s@@^ȸIhR{OT՟ MjuZ.^S}rcz ~ 28ݹ @6gs-lgbw"RˤHjr-lL L #5L[Qε\gR-r傭ެ ,lcsmЗk{ 653ln~踛&%k0^H{~Kf̫R/ \ I-ג/ tGlh@^t:\ˮvI \K.1 Py>cZvVψZv͐Uz v_l0ZzׇCdѵh7~6mt@^8h--k%ks[<@I& L 6h^8\l\l<p\/ز&qz 6WsM ɵymH 6X^߰\#؆e5 ͵mh 6X^\:؆%5ɵimL 6X^\25Y͵ml 6X^\*5Mk&!z >6M 6X^T6>ئ5ks.t& z &Sڸ2,@c\lk:׆Թ& ϵ6} 68709rmX͑k LLo\lk+6W 68+0r-lsk3r6g 68#0ys-lk;̵98g4E-kOW{6wdlp z BȵXr6Tl BL< LnOjm^̹r l\{tu^rl\{<δ_Ȣ! &9_D3O4Λk}6]]]% -k8w-k/gmt kS8-Gn#l0/0%r;rUs:l<02l] N= IhKir-2l0'0rv l-oB<5̵Kk(66^g\doFo 6^e\ۛUKw_Ul050v7aMsKtf(4By,h!Z3zi Z& z e>n^ک\;\H=>?x \k vuN-k%%ډ\;dJ= α6k0/f~=ӒV^X*ڱ\;lL>6)8,L3'?zľ^;ҝk ϩ/.\.>'*ATU~0vk]\58{z&kzTn<.keځRuZ6R&|u MU^X_Zkkɨ\3k/5vnw;=z\+Z.&쫥C_v=E_/^>赵ɵR*kr J_8&{_'^[\+Z&½&U2flk֛k^KU^JFt> s7jk \skPTɈB{/^[JZ8b&U2".uk+V˵^&V^JF]6^\dEzMU2Zmjsk \%5(dD"Oe<뵷 qor<<|ucrkЪ\E5(dD"ƇW{}vVv.yzfn7 ^{{m7Gzv 巻F7zp葧ɵjERkr נm6)w{w@^ { o@v@HnF8\Z j&!z *bv9o!P*#@מ#=Tg.UU PN,k^V,EAQ]l]_W {5knBkH ۮ:(wFjp\5(\TQe!b6Y=2:NbA=<~XS=g-hz\&9z *Wb㪿 ϿL)MkZp^BG|,qz(kO#k^DW_5X^5|O~/Ql&pﶘ8^{KM-ezcd\ Zv\%5(\Zi E4h?7>½ܱ:gDE{7ʽ&Qz *zmڧMmɳ zmĬTix^Kކ +Pcer-k}U5kPT^Okd8Q SZ::>l\ZO|zMU.^ DMdž= T^{3xLeZU5KkPTZOk ?{m k336^Czՠ~s-k]ᯁkPTXOkLϰQ7C?uD׆,;.sds-k쵻HAQZ]Q'fvCUu\M1+uqX \vϐu:IZ kr נr}rogTM3+^ lѩ#2^ *xis 1;Ygu\5(\mE鵷qk|X,kC'Oo D.vAm?^kEKL9sU~-rTvP y<Rֱ &&DG\65(\2hWi:N #u Lvwwlǽ&נz *W{?;#zmN /<2+\{,lNBAQB]OqMD ﵷ)6v|wx{}DS3翃4CAQB]tgZym_;{m"ڈ )uIq0U ^kE uioݗ6]S? o,k^n SzP7]iMmwO{֛B ݬ^kEkaoR/;Z+{-vi ]/k,so }_}uP e[w6dOkr ڢנhإ0&%>cyw{UB;*W:{R/ϻGunv{IڻQvNmJ;oV[v5~y}kr נr),Zd IsÉOu-:z?v}(nzx:-|;-ǞkJ\J?o}\5(\ {-Po~E > ,^닡Mi^꿓{8IAfmNn]#<7ږȍo7f/|o&נz *W^ UR隿yga _+/w|=CֱRϹ j[m^KZtr#]5h^ʅB/RUK}]MJ;khTeqooo{E;'W֕=iPVu J*dM2ע>ov\5(\z-0uZvhڇ'Z3y뎻2ocv*Jw0kzN2ukE aeYjtm+V8ZB{fX^@~ç츭کu^KZxÇr#?\5(\O.ӯKkO@u kѧv=jk &|=.&נ-z *ShM٣rOnծا5Czd_=5~G zq"赽kE}y:Ex݆Ok6A.[}%Y zmO9G t?*0-E btOɫ'Zsb' eڿ[s4Gנ1z Ĥ{v>y^m0g/ >ϯ]ڦ~o+ؠ-z Ĥ9ھRWt8 V[뫼f^ϩUF8z IJMkP &%2ZLͱcp%kVyosZ}皽CEz Ĝ^B65R{C{-ÐyV{b[@CͮL{L~8E bŽV,{r'phվh}vm\6lU{-o؟Ul Ea[ZϜ'kJs9:ު# g}z7}&5( ]vŭF kч\Wsˈ^{N2Ebyxc=GPnƒ5kP .ݚ ;Q˨,K݆Vki ">v4z D&=c/Ǟb ؠ1z äoo~+kǥ32 1^#7&vY"lz#TA[ {N}A}ZxsS7K^{ ?VIx!KZ k x6h^)Wyl ﵁7D?]_r 9iZ[zwMlQZoMAKMs5u_wz-葛ɳxvMko JF(/+ؠ!z 9ɵڜUS]gwYT^8Лk/M]-k"շv5(Z4k#')vOzsTqƂ3664DAф·jRJF=asH, }o$q7C? 6h^c9?o Y3PYe{wIsm^{~uw;U_ נh+z\z\$e,rxS~Ҳwz [k Zנh zacm::sEfm;V_#i^/@ "&ؠz &a|=0&1X;_=ǝÉ{퇻],֢&ؠ z k2;f6ڃ[cW&9DEsMAMq-؆=O JVa&Yz *12}]XɳbMQb 2{}(HK굡&Qz *12}[+ 5Ne^{H,ϖXh^k נ/ӵn+W'2u.ۨ^M)V@^k נ/ӵ+QO3?ϻqVvG'F^k נ/ӵPmWv'qVd^k נ\+еʯ>A8T&U{m| 6X^JFLpMH~E鷎{sڇI]ޗ4tMk נ\+SݫM4u-2 Crq^&,CAQ%#&Lx|mL~|>pu{^*,BAш.>)R-r:wV k/y]5watU"|U^.,AAQ% LW祾~F {"7E{f|h壥YMk נS\75 Z_:Z~Wnsly3j?iT{m\lp~z WA\mEsk]CϱnB0AU>ٽ!k Թ&U\=V]CWR 쵎n %J;һ=9y>^s\7Ds>SL^{| zq1k TrjsuϻZ|Y+5gנ _nZ^+>,w}xt EGG{;syrMy5(:e:f^ V6p2 WV+n5gנ,꒹t_CZ}{zW_M|&2]]mR6_{Nk]kݸ6 ' ~m\lpFz *.ͳL << )GkA=dk g2o 68 E+TS)3L DVXSZ+z- 5rU%w̵ׇBlp&z *Wzm Mb:k9 ;Pr]ڢ_^ʅyGRѵA~f0Duװ^KKLwٽRֱj&_kPT0Ok5Ղ۶{{d{-^^RF I]&^9.nG95(\{{6X^>Q5gsLYhG1L7FN .^uy¥&} \<5ݻ~V %=2ַ}5(:ume.^{w=O(M a &z-k6h^3^_&{wT^Yi6iyb'0hmclצ?5(:uy Uwdp0}['x* RT4@AQ26<4VlO}q7D%9עSeGG}~G^ ZȣcV(l0/E2ko!goxE'؎*S?&&"{+kUQ* 6^Ul^ǾtJ=jI_諘,YOVS;Y-c#O6< IUf&mܛR(v _'*dV_k럃itB mۣo J O|Egg5L(#K S T>tf78QO>wԃjs @zy7cȝsuwggy[Ϥ 5ػBvOH<9}o# ~vOM_ӄ I&;#-:z "|A78xCdev5 膲wk_l0p) \Ԃ .F2آKH[hYбVT|.~l 6^ "[vO| ¹0%pIrv}Zg'#͵LI\TE&"k{k .K*OE_ϵ^l0pa2Vۓjx9 zMTK ~ 6^8{+ؠBU'vk\{.ؠ^^%r-A~)p[&ރvu8WvE?A;n3 m>\0߃05 7zs\ |k>t킽sp{5sz }{ ڼ 8 P5-vCy1ek u 5-2fz FkH[ 6O8z S{N0^C&؞+2h5d7 g +\:@m#4@Lav3k^:~KΫ0@IjYImkv:xۿ+s+&(Knpp :z f#yz ^ 'iz k6X^Ju l @5B,F#)z kD 6X^ L"q Hl@k68;@sk 683@k 68+@sk C68 F0sk LC 68 B0sk c6^k#nz L0y5Fl0+x 5 >z I6^ 5" z |ˢw-=,z }ÀˢҿLJ0mAekmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkmkm[_s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ Xc-3I^Z:gV7tnz kIZ݀095s&iukXKLΙ XgMuoBA[ k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;zzgBZL]_Z k@k3w~ hw&.د΄5ޙл;v X]_C ל:gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs&tn^Z :gB5Ιйz hs& k endstream endobj 28 0 obj <> stream x __?cC ^:?7p}D@ endstream endobj 29 0 obj <> /Mask [0 0 ] /Length 70278>> stream xFwG&R:;}1Uۀ([3q;6,. | @55t_ | @75t_ | @75׀^ /.C _joߜW2{TR׀VNor16]_:y',}5@Ik@%7kW4tP}_ yP]{ ,5ǁ{ _x2]Cm:/ 8&yB!5LOXc89ў t 5䰵fJZ@.Oe ƺPAok46_k^d}*z-}@VеibNkkoo[+]dv=8_okozq2ㄮ5Ցך3Հ!'tvæ .aR1 ](l#tnvx/d^E[]6Cc#x^@<; Ftr< V?L9:K_4aRt \ RUa㳽*^ ;l@ ^{{;8l >>;||z"^I9>]Υ/V;8]{;_k !>"RMtD1]Wl2>wksܞ! K_ k: q } *koo78(_|rC5 Lѭ ^z@8ʉ*KATאZ).*g}tZ _%@&XtZ" PM(t b ]6kuXԢ\V-kzZk@=fO۩u?H#dKpHku.AX?-Ztc]0/OJEA!8e@}hzb8O d5Bls @(Z|m}wB#tKK\3յ7ZĞ.~6hﺋ; еֈ}p/:BA_Y\[email protected] 8 +6Pמ{<NDUC*ٱ-o59θz~(k8ǡ%^)Vvr[ ۨ,fJ(kce+Gz|W +u]kZ2f !ޑ tTE1_of3*/C<8kGY#ekOgc3?O ϴtM( @B? {RDeZuD^~C͡-D)_Gq3Z8ؔ[Z춛mHU,9OZ)k;y-Ȼ)Int)7Z>]#]Dk(B:k+P4v̝qd[o|RJk[CBhAEk%Bt5B.rM<3W4Qu)7(خwLY~Ql78a'-~ZJb5B2 ?ھ y p8&0Z k%;lXdyP6Xo@ &G;cD0GUt +(kC_q-Zz}zqw _< ?{fÆ,SشsD_KS,Wh_hĮ.͟]+/@;WrtF_ SU \/3]{m Iv-5| }zG Q=7E!Rc㗑_: Ɏ[OCk0^H6 k l|(Y=MSV f=~ci4lO lgV &E{aAe /l76I)k CKkfJU=8@".l!l2v-Ưq7KhiL:INU,kKwE/Tr/+˵蒌{ V -TeQ^( f^vMj"=_,]Z[ Y1tEj 5! 47Zֵ(GD9xzݱ_LΙ? ,P@> selPaY"WS;zr_+0X=\\ >5f!߃q^N/ƏtѲEG k4@;%|m#?9G9*-!v%= tM SGc9s] kkK[X(w 6@B5W2t[ݙXtڨKqۺ(ځ}f&\}rl>mi9G rh_ zn{jMx(8^zuMɡTǼ2&_{Cv~Q5P<D{!<ں>) ]ӆx+_&_ rm\PE|m.ٰ0]KX+}:N&0h0(n[@D=dCCudO;)ck|23uXF}?P3"l G2P% 4Y5l"8Ȗ'B42]<= "f婆UR[]!h-=G]I|5TPyp=GOͳdrߌ't J)k 1aHFEū_YD!XaA_C U P"(kƂZQa30yؑtM仑:)*rmap(t z)k)Dҵv7_xt5fM7SYJK kK!_{ۍkA\tqa; = VƳ "KnE!_{E.m6y5H I:t^_xSB?@,PO{A3ygM泘TB%Mp0*]nJ 6Z֑K̬@Mr>4k^ tp.p]SIc-U4ǠM:J6LVL&ʹ]#[xHb[~% 7qWA*-]-#lYzеZ rzlfI}DkZ@<( &4>[#E@dnrT?U,% n5jצ ێ dVF̊>'i;%>'JJM:Af{-Y&hZ]Y3>o#*!4y(OR36Mf{-f<t6h#˜vZ oQ^@]R|J_iG\_b]+ lqYLkAk\ת&He(0^-ũ]Gą-pN|{"ئk~uVki!' bם5e5^H*wa-]K#<6mDPR ͲOHk\?*I507__B z|*T/CD% I [Ƃ еziy5IJXM ** XYځaCXg*a.YL)KfXmTT> Ϭ@?wʓ z}N4Q7'Zv3D*4ʮ ._㣣\ɞ - y)-Bڀ&~> :Q"倏cY!V\3h]ߌc&t!tHdj_[/5& 7(@,Px/ H7a.gXLdYе Aa)_ľf-Nu'/ϷxT X{oFw Wr9R1ଫw#p@vn5X .kɢw1d+kV}S3[5pk/b-ck @+,g*mGϐ5k\< x%9xaWy [ljiVVЖʮ*+ĬNuSi]zIݠF ~ 46=Ѫ,Y/.I9H|rp*kkffZͼDq Vf|*R1svAE5egh 1_+kAJ// Rl5GSU)H' Ah _ͩ7ץ| !HB)gcе&tܷ>=t"ba, Sd[Ur% VD5ލNvƴ4KP'uJK\=IG*d;ܵ6Z**L5 Rn41Zu kӮtuڳxЁʉޟiī-E| I5f 5~P9*xzڧkA1v-P_/1'AE2Έ-u"\BYvi2 ٣ohXߠӏuFND^@gZY|MY3;-ckv<;߶ģêD{; >Qf)Oq_ u+3WTf'w7izEpH_Nk \aV+,Z5z x}BBz_faJon=Y m}kVAڬ KuNYu=2 }]vD?![}}@/&'5Ukָ#-&B׀ Vbe6t7~im F[jUk:/KľV}ZAl4+=2 9[M;5֢TfFo]DkiӐ䨤6]b7t ,B^ͰyN:,19٫uwnkD'_pG}WӇ3|W Wfe4xeCư @I0I;N/Os 6C3 b[ER̼&"ō9NG7.1d'E(GJ_SBv #ֱk51ҙ6kU7x vA75xn2 'GGc8}3}# vF1?vO0TP Tz3ךյO|i3 @@܂cf4ftUȮkv x _kYCgM]D .~yZ#1wnp<|7>kw>4kV3Q33sd@Utk|v&Jn˩UaS sM }9@_e'O.|5WŧggBHAr Es7ۂ O.=Yiq}( BcE6,|,AsT]KVNH,I#aHo'zanVDY/_k 9 (VzooF2,'Dgax=ҳe=.jv-~8v ECCctNDwTͰXDLk# stZ%v oa1Kl mm욅3Q*-H"kVڊkRA㬱2! ;q#t _S젿Fz zH})5 \iV3m^K8+5 Xp}%(ķ)~2VpDD)k决bZ25Ox ȃ!d(,k0+uϖe^@ }*\!{4yQF<*Jr'G'PAL&>O~FD. Ҕ5~x'_[ 衪y I/}X9@:FJ>.d< (B1&}H آykK| _IZK "P8 HuFrp +'Y?uN0e#<ek<0{s_1 BMC#lmXm)H o@ Ϟ*y2JUI,[b%ټ U5+/rX-)ےxKwVqkoO|zjK ~.cC@X=v!.H^G+f6#w~}14P|:/8?|{ܱ;v%p{:}s'NS*վ{)TY%3cvUf5u^᳆\ryLrh%>׳OR}.78@4B*FKdCtR;75x^{pz@ ,ʔE7WZv/M %Z>㬰Gk%yty@hyAGɮ* Jߢjߟ@/d4 6U>O;oi pkPkF(?Q[T zt5 : MW8;;mX)j2m~3at}f,{= b8o1CGG5_cE"AJ ;rJ+?*KfnBh f CRk! Otm F|0ǪգhO#w:t?>kר=5MG};qCrWGKN64 ?\,gQk]4WbG9%^l-)k V?EǙ7;]jނp:ꫥ[)]!lYrh5Z̢\m:52(jh Z cؘnN.S;Ƌ@{_meֵ95bIkRPhPBQkO.>ųM6 pk,~WM ƺ/VTרmc@(5>}b%^ &at/}m3 CƎ V*S(;~]19(\NX"cp\ }ni@غ SnWYQk#K3 *uM, G]gY8t1Tnux5:>m@*[keңRh|GbV'_IdMxSV«4Qv3LB"k,X>Ia)ji(_cї!t=~XԉR_)k|ٻfe?!uZ-+f56*Z[';{Z|CLQ1M,/}mqabz5U4kuojLp-h5UrmTTMi_c!)VТhD a>}vV]cRP3}U/9| V9o틘XBń.]A(@Ŕ50~Yql6~_cN}ۿY!e*p TLQ_cքv /y|~sn4D'f&|,_>'EQꥤޤ>;t-=G [- T ~IޙOeA}|Z ړUHo1>5[F;|eY Zu#X]P+|-歹 [Q& azaM zU-seH Ė@ (| ]d9=Rܕo~@H\ް&v{ 0JZŬڮ]|p;7߁.tE *ETz @,<8loɊγ}7'Ql>2B^k'*/]3;uRrUTו/9} ¦24O&Хڞ粩J(f 'TI_ZW*l L?(K @&ȑ1Q Dꦈ1]˚ȵ,+E̼sZ3ZK0];uՐsGsP_hg%|mdw۫V4ffbfg dt) b*MӘh@5SJPüuK{} ¦ )AḽZ3D5\ N6cv_I#MF5[浓a 6& iJ ?m2 Ҵ4&= [1m('TY9W"Ghh_E(-@>412 ds=) .mF("keRY\DIs#kHsZ% rDY_+Uш82DԽ:|7Y.-8JUyxS5'Tq] qBf97֔d 2Ê7#1'5.}}rR+y|-z6vT=75XN h5Fa A_+k@'TZs6Q_>5(rW6Js4x|\Nh59_V =e-S+N9_s<75Xf ,1y,| I<%t5KJ6mO2: =L,AS%^sjz ɷFQ5fϲuu5VCi?/:XZI\ߴ<[ ̉(zPBB4 =JL:S EEg=!YCL W2#Ad3( kJtͺE'vlwlȤ Lj T[pCJ&Z.ND_Fc:#ݑ5ɂmC~O^t}[HND _F e)8 %wuT }ޕ:+H%Ef[ QCt%laiy<' 6Yʶz= .A[/>}0lg ]{{cȝh"k-*wkuMA]Q@xƦCӵ>c[е% ЈY@7}\c̕<~1!>s>Jh\4/QK[Y%r >"f5@\֗?d8l5X·Z -Ƕ9c[Y:njеg4ܕ<~1k3h} yQ( }1krv:4yZG9[>?YARBu X6UD&tZh;sP 5^R@Gq:8O[EvO)p(~3ecORLMJb__eK5v濑L 2<[CWV݂74:@g1} j:_l Zպ&2jKV|b=-iQ T]& 1iG0˩ uN#Q ]3HfB>_ x8-b OSC HCJ_^>|*_p&Y.ak3:FDjւ} H]: bbf Ɠbg ."l|M_놈Paf+|ާZ@'|ZxAQ}v* NV蛌56^%wsߨD:Ll9b! hdV2%>-<8Eo|BXd/!u+]FR'WPJ*_kG>q>Y! CW%fw¡h4_J߈dJ {mhSh [@-|)]z b+֏Ic3g~ є3CZ4ZaFRPK_kL4:AcDM'Ew {H [|B=/OgUUYg flx:ks5[4s{lOQ)_ijn n/ e4YRZfX6-?xѪ/196 6+YCRO ȶMdG H@/ |I]TМ:tyH:'aSf kUr{rlv ?=Z2Z=#7G&DFױD\rWۓq \ׂi"w|(O,y.|ڟ Hn_{@][a|ML a-١Zp[h.*xo4^_k{R,c!N}YU)#f> dTbP0 hwjvZfF(җ(iM88G[;zR~Eo46sdH[q k @[u>:Ak jlY3ʬ1H'so4F/neh6|79z|]D m\W+kn-d]+fĔ &nY%wy乪l)o-5+/1Bg}pMCf̂rgMNGY30Q[<KAK8ԳOc :˥Bt0\99}ЀyZvTȒ YCwTu@e=:7E Q'ѵOeD@+y;/.@y6/G~TIQfI?+ha"u%H1a>=ߖd;hC@DZWf1{t 6Ũ=_OL8 l{ztP QC_դ-:Er2Sz\1--ZǦhAC%t *~uZɯ рޜu|0GW9}y0-/PvsຖxOM e7*=4uJ;X,RJ B5wSzoYJ媡Ҩ<d5qa# gkT!xqwv@M3#VZKjd _{|e|&"-L_BHlf Aiř ?@ts#V*aj'0Jp /7.uOܒuM\r~ '7)YNA~auI*.e_ Ä-ӋjY@u-xD_6d ]2|]otsBXkE b*_ۖ}qF 6(RfT &;L=xjaܵYhe6(hK| /Xӂ=D={F k6ipb725k֙ol= M.'~ V/Sq+oZ"6 l125 ;bSٚ\_ z=Z8^цL,s=8o ۴JZF&?]DEsI;6M,ѯ9clqkߟ*ke}>%en9W]W~ u3k;mʜ O^d<oV [u [ʿw1V5><"|ƶ 9buo*@_ۼof|&{t%ZH [ ~F<} cPӑ~&p}>~ VVaCiF !R3FI: /nw~ VI2 _Jt8F&DY5ގﻅtɘ4 Q6y_]5!a%b5#R"1(xm]#>OuP% j7yͲ 5açli^>Mk ox7Tv ("j&~u a 秔5ez'l@_G5'UWu5&z5ǃ|9hL)kրg<)%[~Xob^ȼzCZP8c)g uMB#5Zax[nDrM}5&8G }@@bPI)kL2 隦CP| cJ-0ܮQ 5PȕtbL Vgב!,Yw%7 _@p=?^E]}a"Ռb o_-q>ir-5-~ Hq]+XޟK**k|o r cò]9kl}7ckĺ㻒my5]eS(y eaTf+OV!t X5֠ D4 UؕeE .]+lӭb(xz|-4oп66ȿ.AJ ɑn YMHP^']IY5~WF7NeOEtz9/%,qZ<2WnȲTT4˾2#U)Ef/IR/Nzl 5B*Qr t/Z2UڱK&_Hw @,ړiGHl@=!~λǮ$^!L VrߨfL=;%l}Mvkك=zr.S0 QR~z<:7vI[_d|뚪"&lhi<>c^,Y1|Lޏ{p.6Za ř^ j]%lSBЫ/9_c{*O*b=[_e)giwl !lo55R=,ԑ(_Ӷܧg@غª@k\ۮ[ɆotNJX Ce (zZoGRLp>iD -"ܵZ aqǽף"pZJ c&E sca"e{X-s &҇3M?.5kľce* VP[Wur( ]Փ^ئO5ggv5\Bdws UgD +hڑ{Z.Kp@K}5X/1yS AƄM] H-.T GU."Zئ5tsa|: aTcܘ̍X @1 % +5+dwtk7M6ךյxa3w| 0]˜] }nWcАB ZgO @_*"ډ6?_{:v0T>{ m_i5rZ?ZP -ӦTtg\}-E{t ;J 4T h}ռ c4k45×x]^ ɗ_v&LFtL7 5c?ݐ'}VXzm_B Z< V7Z52'zo6|3v pa54O#]kz<W!o}Z*nm t'?=|F8;Nz~˷lG>ӯ!\>u8BlOcޟ¶~6 M:01̺x!k ?9 >?5iHH1:h<5ó+#] 6s7iwi>e|KҮSQq-ֶ)]kV3}U3}f=0y9⨣+;G[ƕEdtm[(6_; }H:U_;8芤 Gm(EZQ>Vp?q +}Z R=&^|cڿiˑObqu0\'"3 L7]\ _cq8¶k] ?^)Wp=u4k |r'8Ea6_ ?[}6*p_} t҆u)X_ez\ӵfz8dreyxMm{յ_|k.6t g} fGБhA]4%;~O};cmX7 kZȯ>-+=|>x]kאÖ{Fyg|? migu.c NYF׆ Yǚ a=5K<hM}N>oٔ BZf m+=o'kl>]bZ+,aS:xxZf݊q(2O땘Һw_3?asE{8*Xk^ _MaqרY=wx\, /q]X8L>[otw4(#^kp7.D4GVulZO*Dߎ ?r_G*cݎ<7388t[Y 5uY% #~F|-Aʬ4aaKXV,hbLaנk0Z8!xr擰|\/ ;K[*5 2 IxkEg}Ѯ/\krԆ~5?X5/LoL隣g2I{Ǐ Z_B 7G A 4clI֢ !/aO˱=t@&3t:^nU][' MLPGZ_<ݐZ5-0i{Vv\tjF25Jii@ ӵ&5@ODs%ʚC8 wGQ0 t}b/"9Yo- iC H 9е>aF.ibh"|>j/ ~Ӯrsi.fdT͌g_'kCNDP'T(5P&캬bi]ג4|337vb=LŊ,5.l?6eJN3-?W,Hs V o,'"y]#s@ɹyBa%Nr 6c\kq'?}9^)g.* c0Ϟ̳y]#ojix@¯7е_lf呙KM=45tӞ'أcd .d:g:Aa! a?[57R5,EP0iXi. kXvX]9? ,%۶8ӵV_ 31 2fg+tm vgض6"Io>vck,dĜ.tm>ϑ [k zo5>1z-;c75wG>tZu0a5%lIm݊a2|dCr _~ L N8|lAŭӉ}G' { +C l݊34kg0ܮ?\vs앛[_&|KCl/F7A2h]L5-qKnD/ULO Opo2qޞ ^v-GFPN_S~t fEA2 {o{0ﲞxh{I_-/ZK09Xk,ڵpt{%/gݻl&Њ]y},O +IySY,膮 _,^ ɕF Nظ+Fv:!eݺqgrm1n~. Ta^3 }:Vsx]/}7j2]ȧ\Ӗ[ZW9K{78?e/ {aMwlGԠZe_cۛ*Y ;{6vJ q?36= tjd}: h"d G> у X56giTtm Nu=I: 6уfǟ}8u OUْ<2X5Kѡ,t k2M>1]gW)U0_:~ކa#%2#5iU_cքG]#pq5 lԊ-lJ t͏Q*hH\eN ̣}2l]ZlihZfNI9])גԍT9QvG{1H[ Ϝޞe+HTo]#g |-ECp CXյõr\ )M6Æ T?_kG/aM_]bA5q;AYյBESZdm>6,aib!=N' ^ gpzoX gQlr- :qa]N&|-A[_E[ |~6(uVbat W,a\t-9@rhC}B;IdQІV]^ZkKLkKs/GOճX:,K. T Z,?k DmHYUmՕFa4bj%! KKcbEo?}0.l6#B dO^:]) &_Ol>v;d}-.ݎ ߯#)Di@p|ƷU0Af^Y|m[E3qN7h6<^*^8ln_ƫ]ZlP3Y" y|mynwmuTJ '9V-lR!X%XZB /: &E?ialTע[gE[U >rD &h~~/}=@9f [-'<#k2 E+lEVuǟa "W ,P_O?*Hv% u"2sе-䄅9TbtVag&A .ot2݉'d(4T?%+ -y4wbu}6^o& dt1݊5YaՅ kJP2ܥjϢ'ݳ(AY7r{|X EW7&šI EEܥ:ցR8]( D̤xkv XD O,a+VeX/CQ]; KH_B>oLה 0 ?|MaHFKk V&y>/]G~ tmY&g /Qzk헋{u<xkV :ڜ̾|d r; O vQ,c >7uPjT#lV Kُ5K:&9Ul>ʰ7X b b2 kv eAll]:=oIӊ 쀾 EAؼ &w+4w kvց.F bffpr|W;@o^-U\ l^T l7dx( F~y} mTսk6/ ߀y@/;} TbcahEqaB4@ {}m\X95mӘ]Z+FΟX]yALuQ:JP} 5lfA1,= p: 6mӨ(f[ kntLx\5GQ" Vg еek/w:㪰)FE5ZPoP)|^:D| dSTM :P>\][ô|o"y|)]\ 0 I͆g5ҾKې|}A2r:-)>t-ZOVC' Vsf-q5P.ژ@:a]1 |-? 3m 4)lf [|A9L4]= s.aDurs5Cؼ =j7krTk^E_+7dㇾQ Ѯww1U&kΫ&rxw 7}yr tƟPsvI?Vu9אҵ{71%hR\k>9F~_M{ {@e|j|*捻|mV4JJ+ sВk\Dp{[TCL4+?7UN[/S"Հg;x@6ǵrc Fď,2#k 3 }H;Υ/Nkifq#Ia5}eĄU c+ȁم=Apa!5ܟ D W,acIBQy|7,A w@|.x CppR_CD[x(٫&D24M4wcK3@rf] g.l L7 ~9\<Z 5 TmjA?M]L0e0 -$@ t'.lt usIO"@Q_',IcxGNJSZMa5~ a[v?Đ5;8e_dma˩k vOrJ"!lkf( 5;?eE2/~Ut ٌKr& lkN"@i_ BеH 5sK_J02zh 邘gZ a[n(."@q_ǿ ,X|DWפv>rG[ ɤk)R( lѕ 5tnȜDgvX{Utmpn;*'oO(Xܙ܃䦄كFňX#I1/>-nݡ&EZ n [}/9*2o,bWn&O_ t49B8~fmh*jY߰z/ꦿc Z9¶-S~CY~'еH2 l6 豝gQL6W)^.:'a˸M!_e x+% YÓUㆰؔsc!Ǐ6N٣7GSAh#=]kágK1_6 r] 5zw 7 ]bDr5 ]9l&]]i !bC(B9_ҭ?еHBo}k_ "vcֵO šJ Z/OF5DC;t- z49PvBؾ7;ɅTuu'u[e[T0='\jI|2.3KI_-6y}M #b KG4 _h*6]ܬVέdع|s6r5{^Jtc0)7lت56@Hb#=;Zoυ-Fѻ^RW}.(kV Z ,2:?w?c} C|' Zܗ=;Zt BX d)kdt.t-::Fl2>>=NTRLVzTgGAf=a%Iq_u# u 6 gյ-1RCVZ]sgxQ5Wu @ __=t 'a=au |#Lm ,jOeώd؟Pء(xaKZ_Z >w[w {nՎm ܖ O+F<: ,8YkqБzA ltm֤潖;*_'q |ݠIy Ok.RuM. %qS t-q<ԵO;SXǐC% lѨkXY1T*Hhsls];:SF@{ YW1;}C:ش [ƅ /ovYݵ*>o(Z3/kJGDu0ٜ = [j]*(YN 6ƣt^'6at~J_!'XPD|I]FGyz]If(XxmcƅD%ab_kT6[ a0F\dM^sgZWؘW ]Oy3_/=M ] C*YlJ^0Mj H.2Qo6{(~zZ hM*]i<%RL;p-O&{i8ԃ*s6v2LTcL^3 "p6;PqLtK6jgp JK_R^]cHH3QUUp *ZұztDب{R :koU+c O\:fh3ipUb+~5 r_K_"}q< I o֊J; 4}Y;S. Rӝj aЙ&Zb5ko:@,4?D 7Ea2ItER|,<84Ѣ7Zu=lu{"^l)lD p&-]AhqCiwξė=q#5SE* "q:(sq7 _-GXnk Vw͗}7=V3Q,x~\|u-8e*AŴ[{u_HvcHM@+ |mɝ.ar7ڌ:~^¶I7==ciuƱ^SJwr{qAU2 hN¯dP fAl% t knG ˼PmrAkl1j:1XuDr%˱ =#SϛS||vt8kG HQLԐiy*gs@ RfY0\ת.Ao&."H n_އwLG@gk [ Ķ;7#SnD_ RH "+=^<--6 18|۬9D_A% j X2 cxoZ|p &zCjw1aon3ckzqNkDCXp&jH<>UQˀVJ5 6 -Ͱu탮sBa kDž >g;y?{iV &A%¹5ì@oXAWaAlc=QAlr}e-_X4 3Z[gk;k-@n\gE^n6DimU7W0P:Mt//V ֑Eʜn%>4/Xc~FE_7@f o_v9ٛqIJ{;_Y)eu5OFt:QAl(ka/d" lk9hw2gwkj(hkW_bgj;\WDk]UaD3jc O\7R-S;MZ;]NƬY5:/!Nk+HigfT]) V =cxd|Z{jhdfK.uVұKd7 ߎYwÒ}MVqgbgt;*YCj()F1˩ؾXw'y4SS'݆8v? X56/ *~rf?z-qgv8а: ygV%(syA1!W9!C\څb[ "7eXP [l 3_] ԡcX:[ͰJtGY*l~h|\xI7\}f1e]غF mHѝؾT{-qeíz="6 oZ@{3ma˦\+ np 6Bh55aIT5NDUUN^#AmQ?N؍nc751O}emz.HkfoHPL^K^6Tʮ;;Di.e+<>Xdtsnz.HOiNv (wwL,D [}[DCl =}l~w K_M1fig;.}Q濍4 ;Xs{X*qQz,e79N\Rbl볕6 íZi>RLN~=@Z,_mݔϪ~Pƨ{j fVMg𖾚"x蚿 HX&tl%ޛ66'3imv+Ny@A{OU2!ֶ2.N|Tx4WWISjW3txVt;5Ear88?lj(O F6-Mo Ì 7|s t Vz(Ƶ)#+Xتq=x^/sZ'9}l >m u t1 ^Kp헶#"J}^[*pdN@֪KؚSZ&-c yw t 0AFrk0Inc̈vnג!NI.[K_T춬FgV.12چ#TQkxaydM6( lM^zgE[cRЋu ʩƌkZТ?\S\'=Ôa鱙 Z}puغXyM4;fmҭo*[£Wb'ѝͶ[汈6 L"E+ }ƦNH%pmRأLP8 vqhteDb \laS7ol 窭 cU^w bCP[>HE\Ă_D~F nt6 ka5.d^y=S+GquK 6j".68> g:ޚ[r2go Vukb2*5Ml7pKɶ QغV%k(D^_\ŭU2W 4/kA[Q /!&41Q%Q6t }H\cqb-X jl]k浂V_\-_ Cp6Eq4ѝ(Dsu> N7]嵢63^:ھ7 ^cE9 GUS]4Q xMglBMb*EUעDy|K>Xx\e 2 ^<^~Cۂ Y"֔s@~WUFV &Yv# :h05 5E-ʝ]p+6/kIWI^3o7uy%kpmu5j\#iSn! ϵ # l=B?) &.x i:Vyu>+Jy h{o&mBhoowmQ7\5Tۣ_ %kh/, Iׁd~P9 n6y<_hϹzT HՏrE@?AlU5+)^k^iI~#W3>fI ^~!ۼy ]-ɍ/2V~D{vASKpC*Luw2M5EYB s+˒x .Gn% mװOrlk4L ct\֤C rے5Pt9g \5p 2m75γ k T֒hg2Y1^C2Vݳkv. \+;׆qpGWvD=ެ pԻOtbpZns}+_ݎbSIZ:lؚqk@|5ISѨmp[Dл:0=#/H\?7HKQ{Wq\)(i,M YJFγ&Ч*Z|ZFUoMtQO0eS fiWV Tym6ራqMd{ÑhXafjs5դ.nP5˾7l^ptֽu\Gg8jpM +8Lz&#G4v ]s~vn=<*ml k* "˸\: 5 }#WJ(n]]T HĶ5eZurB u\{~GǵL 1;P@c.b00A@^}ZtٵQFx 7)54YQss%\߁q( 64{>ajFGKdÚf )="S'oØkW0ovU'|;~6 ;E+5^i#9}4vJk(k5|mKZ { q ^Gp&;/=ŸC pr͵\Lg͝G[ *EpM] Ķ e:C [5'\p= V'oy+kC N,0u%0,rx =+q7mF l hp=~'f wll9xM9Q\YK_5B cm#J!#ϦP* u\5aT{̓ 4F^mR ̋MrSwXK]oP ,&]J5ynqmFCTlrN8Y<7;5xh t-} ~oUڸT,*dbWT^krkgj(*XK4!kM% L&wr=LR]۱ 0+ k>A"O5%q<9 pG7oQ2)4nM,eD DϞwкx nC0eˎk~AnˊkѡjAw [)M?]GƇ͕ǯk2=hO%pM S0Q ^Gmur'®vǵ%A6fuޢC>qnN=m N ->9 k,k、s[U(XE4"B&~h[)vny~ YAǵeATbCCG X76t xktA({v;IUfd-bZߠx ur4gu$:&v:3י z,?(ۿeu Dkq5MK }nYQ]ؒwo˸v=LK&"#3Tܧ] S0:P ?L'!1!אAV J SmXѼɱX. G:}8!#2Oz5P6C#pJz_B.,m-5{s\ wGS,u:96OhUGµHNeOr8O92)?4@pQ,Im+1h;yKu7ֺ"f OiՔ"yMaK.v?Ӿ=?Gwh vUi̠6bʌYk v%fmPZ,t{=_/ְx A/>0Eopv/Ll&+=pmicz??:"N<1-"_x_&Q:4HtnF߶x jkJ}?.\كnϏ1i;y^Lg,&f_"d cϢl]Q m&)1!p +ڶh@pmD i+^aAl ru; 4rv#l+jia@a1\uM ?yGSJ vo#&JEs]A="lF.?e!,.ҹB-ֵEڶpxc#TE 30bR o}~&lWR?4>Ι֣m]{x5.Y50v#15k;5Z6k/KXW [F,(C :RPmG[K({E ΆQd5 F3 Vݸ"fсY5=W0ղ"B|Ip-EzϣC<]r<^8DW B嵗?^ bk8:Υusm>-FtUP^"Nq6 }O+嬒k˻'jfŷgrCAlI7o ,-:W YyN! ˾x U[ܾh\ռ/b czD:É)3D 3[Xw "@;'> ^fHE\S>c&k0w-k6k\AN0L&A*i_)ՠ.5@1 [RLۤA00 xT= xs3O%U^5VM0و(,iL}q:Xto-и.y u +UԶ":Zx.=5^CVCQn4aגkt:BTK/ ,uB' m7:0)\s)䉸 ͦm.aŮK&]Fv /uȺހh &;߂=DuN~2r첻IwVJ+vi:9MZq #b[т°Rb_VmU6Y)k8 I] ԁȖ-R0}Gw; tWy kq1& ̯2^Gxe6ⴛ_e~H5vVXČj H8 _>'v i0YAQ3cr};}يi'&sOpG ai"ꗎ͘c6&%; yë -Zǵ&eS?9ҳ > ǻŒ qmdk80*.lIJgd9; z絎k3i 6(ZS(o M- 061t(qzgȀu\ir]<(uz[25%X68~> wGL%7Vqہ\ݓz\}«HwUy^øfrT\> 0L?e/~V vy맜,Mx5zm+Q\3r+Qe s{uvls5ZޡE6e C&)"bs-UE'u90PA9u%br xޖx_>ӕ) )Ftf:,G,Bo k\-# Ą uSc~w@al'ڔx }B7K5]D b s 0;(KeXoi©kr<]ZǵE-^~\LlKϸ*]Iw˛OTܷ8Ώ^C ?zT^لT\SB[b AlӁ'?c?_K!a1B|5շW~}~7uŊ dX8ciނa\cG |z&ݯWƵkD In+Fk /^3 ^5|O-D{SF6i-x~Z TcA~7 kjqԃ߯<>~s~Rlb^xcX!1 4x)תUGD~SS\35:c5uAE?ൎkaiZzf[ ,P\%K|fؘz@ZevỴ! y佇^ D7"k-S%5AzX5*lFr&{ )el= 2y [5>׳!~}8 ײ?(~FiBtH6 ֛ilraJ^:m|wuePp^?5 J}γ%'XYQ&&TF&0kPKXWF^MC %W UGnzRDM6;ؐ #OV^l4Ӏe6S0pi& 3,: R*ywݕ?^C"&=mcB^'yf^G#O>kpE@6Nd ǂRfui%.0+^" m4/(@ Tъ^aИv9\Y< uggy ѓA?)~wiO"(@3 ^3[[m|>9-\x-df;07L62ӕ*yWqDS{4V8lZ"m uK7 1A; Upgֿb Ĉ; >)s -E*OcVŮ'X7ETvW'& [hFʽf1<-4dVp뉠 у3 [lȢ8YTTiU^Ciܰntf1OA=,O!ٞ :Ux:#>x']9**6X#ZLRq]ktnp"x^qKS(8 o>c[JF݀=TA kW^yZs{1p&6K6]˫K-5T:p&}Yļ 0}^^fDs!muȽTfPQow)o 0 DiFwN/Tl& # }V8۲N7f ):珇]&Ff,{ YU! TP*R52] CbkpNuLiw;) w+ a/ zJls,l ,i ^+#W͟kv->z!^p{I}1jZf#lGu)m6y|Dm5ssMК= 1g Θ yTy-G<[tKEolP)qRML^;7[X^:^گ0I7DW{aPHlѸr;Qj'H[ y#m+p0igo¢@q> 1٠U+TzW/f/FnjS5 icmIbj14_cӷA(.? 6Ie%F>9sܮ )'Ԥ|b\᧚RQ /ظJcʽp?ԛ4Ӏ3D(#aE 쩉Jk̩*+եD[> sg-rl Y-#U d 4.n^l o}%yu㕖%اJCoܲhr \lܮr {BrYה*璀![?;ko)Îۅ4oeIqM" ֶqnZo^+Wڼ~9uEnfS<8,,5,5)Fл=N>4l١O>>iu-C Wu^[_+W/?+ӉnյWie %'2g0|/l=Pl5A8SMC? kFȽ7S6 EUGIؒ/NpMw&UDڮ: <7n[j^ F=&Tbk"_DxT{!+l˿wEbsq[rh StS'Tu6'pBݱ~' PXᡬxf :(m#(4Iˋ^BI Gc Wk3 0B8F*:,kDƁ {Xya[d&%wd= K[/J/1 bp~!H-LQ-n]Ou^ :|XH5(FڈA~3XpD8OF #2&3i*5aO{G( l?y^T]N x<*[bټK\& lGOE4[*Zkv}vJV;O]SpVbנ8G,}交 IY -f4JWw%UXϓ]{@ypR-a嵌nV5bFD&5|TS(ӏJ)l346|)mW+3rAlyO[FyBJ5Yx*}xD+mSo gkSdT%-5b"ky}IŴ{~qoT5&ഊ8m/Qpi!D0e4 ("3Al)17Sޓ@^.D&e M dY^-X՛ɋIאBts!^ \[6N5@ {knar+}5Gx-oX'Ҳ Pei\CzPݥ+NאBwY"x4{'y y{ DD EAI m jSh ĽO%Q ~ѪnؤP:Aųǂ[p ^Lt T]gËFCP.X B\_h3oQȟ4WاFbQ;5(/|P'ԁˡJl0 L9 W wZL\,N.lѝՑ89 0tF1fkOĸvGW ͯP V,eJ¬x}Hu a\Kw\2v(Rq1Ѷ(|x˼"IPk[@l [1^Lgc"<~~t.j< >3Z@[ . xzY-A4a^pY 6yo#_0𧙬O:LE IJY(9MϙqDq6I[8h*!ZmimBkBtզOܻ5+ZP k;dsfsYmhükzdt4RnkRWc~#P*o+ %v/%%SLF]^KtAwOG=Zw^~_ 4_Ն%%kRdTol4mUO|QmRo~ȾXFs6l߸ I/+HW;oG/}F 5u;a^+ 9G' SG3t뢢- SvkɎ p?S%E,@;4l㗉.?d3<~ן &784g@䎵iEЕ 6kɸ,@ 64gj%y"}*+8)ߺWwk&W^I,dk4e4(a% b3mނka Gbǫ-s_ ܖ EDxvĝCSamGW-[g^V7ܻO6kpD?@A ~ X\emd8rF-+9r=:~ Ժ&I1m0"ohk(H දZ IV˅Bo,;ei xuz~|^C͊>75,?!ϡ* yMfnR6uʹ } gtԲ?TLhL]jM!QlL-Tzӱ{!NU;Mtl3[ LHI5#dRIyЧؤ-^˭?!\-NfӬN#Y\BmkF Zu)bxkЉ%xmTdO _VЗХ)^S+ 2ߋP k'&L l||tpb EPP 5*dKHj U1eKH5KV.p:92 vkٸbvtxVG4NzIrúcymy -?{ O\P嶁JnbՆx- @\5f5-=WZά:ט߱\yT[0[揿 Yp?~'143MQ {,[c* X2cW]5\SK7xk@iEfAaخ )Kά\̕y; NjQI}'-4~J :d 0鎬6k,Vj9#"cqd_&x1o0PH= l^8 j}2P0C˿sMʶŁ8E/,Bί2 6^c5 !PpYeJ X0X6N1~ǰ7\~̋Pm4N F^]\Qe ^ j;26rO3% l1+G e d 0ǟƯxڡpr:0 qc=PI%[JjZvQW˘ZkLSQM.Wdi~nt3ۚ=V{('HH86sT0qӍr; A!mhv5pnHV),Q0 txKj,xzimA+*EMl5~gMh@I½kp0F zьV*ySQw^jױdh1Y9F^cm;ln^SWx .,OySRأJ Xp|USҨhw.UZrGB=Bv4 uL2,۹. c;UPn"-KDA(]H0"e#S 5J-', nˇ. nFtSriLI-WW55>p|NG Vpl#m}4fThLM61Wm Rɣ;{[P PI Ey^3w+q6utOHE|?Yk1~)J8( =JQtG0H(^bfI âZ5F\1e(Q) },hY0Ӻm SDa:a,\;گ7l0 [% 5kxPf]شs 6+]pޔY):<Ꮆ2+yx B&doU ꘨m^;pNpa/e@;]j_m \B~q93kdVO@eE3ju c/RIa]4[% ó% m?u,Lct;tz-بY)#j}.N^Õ6 qe 3~9 GF+hLLl̓Hjh]BlXn}/SüƌkT4POwE/ HPj h<'Mm4D.}122zAЭۣ UqRpN mT /PcyH JZ?3]W=.l!q^DM%( Vm 1ܣ ܗ6 T#T-Ucܺ O*!c5b,MLCM{C-bkr}bP)6ш:R붜 zk\ y817ߟi9Va\Je |sگV&kx FLĦtnʝm 6S w| ymo 3d{., JZT[jdpmIPF*Ҧz{μ6tձ9=H{T#^O qe ʵ4QIɛ ܯW&ԗyhbVX0{>ub]OAj _y Qs֭GLsvRǰH(I"<YEUؚ{<5!\kOkӫO&Bl[||>BjOΙ]5 M@5}̘uVLr79^5pm2kx?;¥˲'t1?_"=%*lѲy!nD~|_N Ϩ5^5l+ LQwZCxíj㙦xEy @6,vgJTh9? mʹ\ջ-1^ƌUVy DyÕy{s{1F}]9f Av-2RJ5B { eCՏ~KP[q{#1knZa[{Γ <4KqVG o.Ψ[bTGC ?yrگZI)^5D0:ꮾt|t53Ew' ږP- ]: 17wv^gJFARCJfiiAY-6⚡v3:KC~﹐іEo@mVpVAv%S qsi6)ViHEpZ(M4etP ܯWRCqM-{ )"WpTmޗ4 >P)klr:U,Na \%,Ό e4:-F yC{5y ˲l [/^X gk̼vJ5r wK [^tߧ<ޡdg yCZL@\4C8!J#0}%,gf [CG{F9Fgsl ;ZA@wF {d~] OQw&(ч{x@׃p'U[S/|M^C"Ij(z?%Vz-L^"+Vy/KNYr]#v>HN]?o *[̟w5Sf[5R6xڗ.,qwo5kBA {<'شd#1IK =tւ-!Y D1iW>p>t~UFRzM0T{C}˯}HO%B:8#C>QTacu| Q|]bqG-^F7|;-{C3_<# <N*K w#m2laݪ 6'wgؚ%xDLxy-T )0Lpv[7TP- X[+&vJ=CFe.O ?^+: |IR6^xjmC MP--pM5Ft o>+P&m {9^wkAFvk^.[JcxœѤPIk)hװO4>]@mJb8ݯ?agV&y+D ^.L,L U&4 z 4& =Q5Zf+(a{ wnmTR&[tQRrd ^*IbqACPl,y ڢE5w1ڹ9 bXZ(e.[G{ւ8cym+רQHr,{.Jo勩v^&QU,?A^YvFe yR?ЯA=t>ߥ# lIp(aP3zʸ MԹ }G[0yx 7Y h*lmq5e=D\ y"Ky3׳";/>gЖ!V/7 k}[<8Ajw*Qc gE1#qnqKX^F':wM _!zym/7 .W*CdTV;Xژ68/Dϳzu'Mdm.;Ju b[9rۖ|Ѵ+e*UjU.7*k}]u&kPZ}w鸦XeP{ h6[!KL"kWO2l% ۫ZID=@CX-*k P)I?I>Oon.4}w?FGqme"\C[Jw/u+R^ X*2\e EMyEgH5~b5 [p0bĵx+yI]Ō hf?,ˈTwN^{Ns YFSM \)':n wI<2ˊ0VZ|D[3iڕZޑD:1^EUK[tZ%P\>ڜ 63C,%DV#Y 5Ιj_8;GͲi' 4,FDߓ tT%Ye ih[0Bu9AphRQ6'?AQ8%RᲩAu^#f Wkw<@PN<! p]݄j5C Ymr_tDj2I)Ѽۏu[ Ķk Rl; v= ?>ClV*5pƨA&7J Īx n3p߳Gn(ZΈx R{cԟCQ DKW<2 86x 06&sG)>k?G8}wy 6yT 73)Ed|+S@st_gkb@Q-ZcSu;5f.b ᚼ_/t ζC nz']qvSS7;&5Z5cNkɮ{UdPpB#^x@jC[ JuN|F5龊khFۥ MlQlf"m(˼+2zD+˭Rm6E߹?2?u!h#L 5ͨxxt 讉m66[a /q8/ŵK:ݲ|9ܿu8L08/+wI2^L]>?~BO3!Z V)Q!+lb;-+7^V4C%*g9r&yAd3Pe;Nf g㾟wyR\{ DyRi\S kO]:H ZQq%s?3usZYq U^56ki=br̞|: 5 SkW8p, l9J\<ܾ Î 4kEˠ 7,U[c2ْ_:+NeQM /GtXxB=2dfزx9B]VV8l^^#/h!֖%LH|vwx,1*kyh"^P]?sw|z4 p9V(q ؈'h WƅVj/Gq|xx*Ra{2miJK~RT5't،U J%-= Dͬ, K )kcY y|vR)}hI cD#J#DvTB@ j/iFRbR*W +JGmb*-<6kKXDv-E1 NOkZR8] C tU ޗRp=~G~vNG\:"wrV֍?זjװSt?@KwV}eO-B4i9N1 +tE}FP D/Jx ^nmSJVAdpûJwEAP~ GQZ7 n%ILF 1C]ր.ˢK2> >jZց:QŮJx Kp=GՀ8~t6& w!WBd\KP1 WZ6QfB]YIdgL4?yqhkVwx? 9ڳlD.[;t6L\+ lbM4y'Gc/0Srk\D cٍyd>^!Σֳ2EnOwvE a|2O:[a6aQiaTTˢr-8siO]Oy fyBNi;9"ky #5hS?!PXKۄlZBӸ\}s; g}'*&]5RX F%QHy ] Z)ݼVBx-Nbq93 P:ʣڶŁ-V272vΈweWZCg D Ṳ&ڣ 1F,Pm2k<}=~Fu!mh{NDRo>6燼xnW s?+)UVQv=?bֲyT~m 3C=KܽO=衈Ze]OJ;_7Q{ 2J?QZ.gV\wq. w\ޠQέwh5[ LJ 가iXy y0C<=cFC.0 T&OydKB_Ul-zu^3|iif0m %g;D (!I_dB,rq4a6 'l[j0 <đ~nM67yB}>.ׄ1Nx v mЍX&jU^aFyThޟ ށMhJKrYj']~gfQ)#In<:krk,5ٜ y9T>-i\#{ a wh jq|ɝ,_~zV[I- ،q0u֚KV5U^[Y^ 6NA5P Q)kiFXi9{Q߳- /PS )>l*7@o% mbU(Me]Ƶ"9>C6"Kx-;ETDze^Pf]܆7l=Y4e4&Ÿ ))AW%:*2xt6xӚ SZlU细:Z[czAIi C)< xQ o嵻e|^ ]#4- JKGx?Xj?EeP|߬/}< ƿ<l}iA^[^ؕ0 gq!p;U GxZbQ'J2JĤZ٦ ǣ'=^[>#_l3&76;t3Um( kM\TUQ<-3I&bc:KWx&mIf{cUx 6 5x(~ 7kiu= C{ *q~2{6O|v -O{ ə_ sip@H]x-(VU6^C[vmS'_ _3ٽ* i]YZz^mr %N7ϽQkʟv9(^kzr! u#ၖ4ZX}ڋ'>ZsC 0d۔=ߢL݃kG+v9}a kZ>+RQw* ~^ս 'Mp䶍=V0 5"/h^UM >kQ)a td-i!(FCyj]ͧ# 2>\~ѿ3 W"%ƿ jv&j*(j@x͋kP&b sc.,_"g?µzxn nZ琢"D[BOxˣ3|ႅT}uyCЍq:[+F" ~R膙XffP# [iͿA|F0ͮEp!O rnCvx VzA3MI)GV犴3~5Áqʹ<LuQB!=ڞbNe { BbPlN:Z+ĆB C (p7q,!(>-i2xnNJZhpbx*}xt 5VB& E'#h[l. 1xp_[@>|tlNKZve{ >OB{Upt]1[i{tEᵥ,47YUM5\e hGl dNw ^VD(ئދ 6] tK 5k45s7?EBl8C?VWO4 4%c>~ɽ !V,4Cos?HB n^)6Skz?ൄ '6f{SŸM)f~ 0=t pQT]jZ9gpm!dxjlBQX̘kVUpMf.z&:IYW"E%I >Q7UˡtթIȃ MnJ\N67tE~6vҼF^)< l6~eddq,DG$\R*,0Kl+_ Ը~ 6dkTk^31kp2 A1M0ފUquj}Kx mUD 8ɶ1 MݼfVeyiNh|Ec 6"Vm {+~,]_8][mD#v^jn( jc a+ SS3y_+" Vx)/>^Tb}z#sUk80<4zikPX<& pQNthE~0kz=5h~zcTC-?l'r\#H>\yֈ%nse~.)?TA5r7 pLAϑ 'b)4w!U ^g;O~"v1yWɼ^Kz@x-otw*gfwUqR,1l, W\<'ƸSqÃL? ̛~ٳ ĸ-قО)EjIUl2y 蘭JlřAt]CJ.t kB)y8?5تhIzRVp 7^M _!UW j+ 2B] :_tT(5wQ ^&11ryO*^ _wAzq3MqZܴՊ뻹ӡZXU O 0]*:aj qx k93ߢj&J O 7xbKj .{}ݠ"C{(?g)T9yͪy M6Y9keZk {YDRkNqX5.f%~ƿU.' OZ] +8j6*e^#k3¹ظ5R7xE5dӠdHnH.%뼶e =+:(y]25 ۈQlRFצ:g*=jL~3qLA &8-q6/ [6'x ^ߍO7VӔ- ݒU,㭹J*]^x2=tPZ|F|iznЍ Wvb\j Bٔ5zm~*ΘJHܴ@U 6y^|dUgpn7~aۥ{﨡DZ)'f_m H!>wCkO<!gx\1&oH]|x_ aTq ] J{־\8 Ř#x5z5۸x l:i K[5;~T?Uro;2,6k^:wngojċpELUCMH,ԟÇ9.G z]R56KcO\mö ~kxrچpE uŶwQ ro 8G4ސJ"-^0':WFW[ C4z8FWј.6.n p[}e9Ύ!6u3':-e'uv4ͮc%&-^C_+ntH Cb? Hj9o81*>ykF* HV{bB>A3"-AKՀE\a jnMJF/ tYL}dGy>6RI7(^ |@c[#Sn'6]Hv8Mxg2&8Eu#6 QEZҜ*t-/d+:051bN gC"s[r9u'B\u+ƁZO!l&7+^#Z>FL(Cmɽ?B5TiQ\.Miƈݢ5u 7Ώoq-D\KI lԭkMeUw ADE*mNTἶY\#DjΈ9Ph6 _sDQDčX4fr t}56Z#oơ>wK}<;chla\ûxhNEaBճ§AzA?ϸ E<|3K[y)XkCWH<= ~Mb{ 4 ]4b?X &MѮhj,w[nɚw47zw+t|ΊpPrlTFM 7Omcg90]?PAq=FdDu\#ݩ~69~dut ʊaqxr<@ug@-(8 Jc&%kGe .- g^װ.~k Hɔ^; Ea |=6a{ M;gkyT q^#1 [ 7år}8ZL(z? ⵎkOAqQPc B , ^su=pPD ,gh̕VKIҼv1 0ZP, _DrF<䂂"ch _C6^, =w\Wfü@n%Z&*Q6(ًqL#4႕K1[Op9Hy( [ൎkЩD_cL\UVr~3{#7SaX| Ƣ:[0z ̘иx+}& Z%ѬҦk ׀W}ǣM*ɮx x.FtGY"O\m柑}O/BFd-q\q8Vx\.)GZåxVyRYj ꅭ ]BxEO?J [+ӎ%k- F _viQdu\BAl#; Z8y7\N^C- ZjP4#OᑕLR3;z %kҲ v7ȯ;)*f-6c҃:RfcDVuSfgǵHn &M BD@|x2HXyw2(,5Jv&L٘y\AGd| nV5s _E={2u\0גj4huXq)&w^^CkmڡN<n@r=,Xˣ'"A^#k+S 䜴|#9^k+}YUi l>"u\_I +Oytek @WG#UE%>݊KH5A5<' Y }:y5RA^CG\aϫ-'5)v^CC'&G"t V/9)k,?^Nex%5!bMd oNWdx~SམߝvCجQ}V0cOԝx;7N,.ʂM^la=1ZqXP.p&%k54 V/JeeH0 Yy#v[d ;+zgz1/l-ΏϻRlۓ jS#hт/ u! ض~g8[q k ziX{]cl-k5. 3S,ID쎍U TmEmJȩ2*(L}p 5k2̸NV ώaLI jtPc<4SҒjAOsxIhn Uṣg~nǵu/ ,Y(5\nrv"P4G}K+ńڵ^F0{{.FqP3Y;zSƣU[ $$}f* a cV <^5lEpLI3Ak\;db[nQy ;e SF%8 [ y{; 72Zk- CIXlP^GJR{D'.fԡpM:Ou[DM; mkH,hH#ʀί,\v ^5k_Ӻy8e vC6y9e lMz1%o+VxݽK098R#+l rMk[r M&6ݾyI V,w^L25ܖwڨqm]Hdl8\PsH5lz bSg1-ݼVxyd>) lJ M!%eTfB1OnZam83G Yeȩfp8=GW6&6g{Xy.(36e6^4cb; <·k8 *-t%cT_?r9a % % Rrg'W hE-q*\ЏmDʯ=dI;8Giǵyx jKE.j{Jy n.9*b!QlݼVy_=O9@x-69¨:yt١xC}։}K]G]T7jEm6 ڪxm C*#LdYSY =Jel E65H/ kyך މF-T Oၣ lgd ܽ 9'Y)y6ȴTx 7b6ql(gX1WkIek8Ps{o#pf 'n 3z-(Ws &5Kae;Z:lbYjkU43@C;j,HDy-ؚO5mFs%(BѬj&RP XMW }ݼVxDSZR K Rp'gc)l#\kphk'l{5Z5r]U lc95[4˧~/xS xءe>*ҒIE]\Ux-lwd ^4hf ) ^gMM W&ukLn(%q @ w8PNy9 ^#/(4tZb5k{D *y}9?| QwՌ W\rT,!=o?{wߛ6W/U qŨh+J5U.X˽h>' NMo{\l v(hAG>_4] [ Bv&# cʙ[˚9hh%M>:M} VTh[k*54!Bs,Rڨbk 6 m^||EbPJbo,WX,]a ,+UyFr .(&iR67{=+A>YI*F ?@_k9 qƎs@oM Dl܁Sx-?׀|H0Bvn#qW. u7گqJa7Iu7ë/֬#8/r)R.o#?n<*2kκFeˤ6B4[ʚ\]ߑEU(8c> (o9f9EIi-U8H bZ9Fr R=Rw Sf*ҶxBפTo (mR) l IXc j & M-?G(ZFr RWlɷ[vϨQ\uqOhUft6 KI5MMUYC{_(_˾E/g{SZ u+Xr ~"+F\sڐfq=mp68AIC{Tx3 }{ݼt*LP\%lPyO6 |7x툟hRhɭ6;@<)UprM3I2/5D iRnĮ]ɼ5նl D7" t_Fp6՝Dp6ŀ ~mR,Nwn&F |7J]2ƵI vRxy;듘? #5 g [vK?>ޗl(^C|od{ ;]},תVM "Q\o/AdB|>KWV@oHZ;ZXpL+̃tY|08WT8o:ƑM [eyQnz.#VjJ 歽 [P|j_˿t la3|U endstream endobj 30 0 obj <> stream xTvp~pUfPbFX@S0E 7 3(Y:w endstream endobj 31 0 obj <> /Length 201449>> stream x[o U/p#"bM(O)0D/OR۪n۱38sJȕ@ .}f6{ ;t>h ӱs\nWn~OQZu[U !IBq6Zu} #fl 'x.V] R;E7ěٸ5I.HpWqmX(VHޫN78w߽Ղ|\> ɫ珎._k }eq շ3 =ѫ<'k Lkw7Ėk {DZft1U]% k s{Tvbo,\.k %̽v b U]9at\[мճ-̋k}.Lί[4?k (rZ6_=掊k}-uuãO,:٧o<2Pj=S\?sOP7n=ˎk .L#4 k&ݟ?x~^bEax/CD5nŵmbbK|7ǺQuۄ Z? s a鵷''eua\/ԣ3LTKq,{?ulJbEZu3qWqL_[֯ 9 q8jЃs"joPX)gJqVکp5 5 *uӽV}Vu Dzs?6t˵F *wWZ _uttX}»xn%q]fzn?(ݙ?'F1qXu ]ƵZmm(ٔkGfNN'k~Y ~@>BS̳ou7Yu n_.,9y[\O:T]elsqvS3]K ; U;G[\3?5f:Gu:+x.}%pˮYu yFkե!מ'Ư_vugez%qV{zf&MUU V(v ,U2(L}ֿ]u9@_J/뿹cO> G:v _]]krd>ZscgS6uļgg̮xz%ztN85ts-+WNU]^2bW8' _tx%0tVuꊳ:_T]baekZ~[o? MlƵJTοoUW,Zb! . zՋ+wP.CnVp#\?)T\vu "dGƎ\ եމo7Zzv}>8|\3֠EFǙGݑ_.7(MayDsށ虖?47"~nɡl\;>+D7ܑ骫]ts8ӹ5ieJ-%Qڸ fsqmZ?(]\s^ @\,Oەrz0=[jSwjfȗŵkvff9O/0*{'Vkj ]k?>K2B粸6Pv| ?;鉪kӕ>]BzGq7v#[z;w)=vT]2eޔ}y (ԁ,E[Z5&Δ;F>pLcgvug]Ɇ|S;@v/ u1zvwqKehd'"8W+ Lgk}]er;[tɊw :Zt Ok3ŝ"hm0w}\tT[SOq psH~X\վ!Dz<Ύ|\ 쾕^q>jǏV |rp+RovR_M.囲m +L𣺵nn: HTK J4k4bǝ}ؖ?N~ۛ@yGXn4 j\vz6jgW_?k"_n۶p d~иk.];&W⑾n/Br[\۵ +}Uz w|8|y lG70}!BS;Yk 5,Zj ۸Ŷ| qyNQrmٸV( _j~5%S\t% 8;[0Ul v}oZC urؾ)mhrH\X7CZ\O]=asL=Y3_h%O3| k^ gESCuj'l aK.m2t ymbIST?}T[|k2][ĥϔ'@|%J V[?{jahKv gbb4\oY*3]-r;<¾l=]BHۢۮ>8ۧBD[;DRJ ?eU <ֵnv~-<,k f2ؿ#֞.kD8sDqaԆ-WB[GdȾHlVԃQ(LȞf5 7{Kk2Zw 7kKztYp ^J8x/ƙS?o)^#;.;w?Lj ?ܫưlK!U> |0dx)2[x(7thd:aâ9dXWB{~7G C;37K=ؒ˶ rbɯ'CLqGŵ*T]u/}kjb [2Ji9KzgXLhljkQִM;o K D_d{h=hy-mvzb / mn"ZGN6M=8?.+-ö^#c!dz7j?Gu杲aZ+ʳMh ҕ).)vIahM K 56q xeƱOĬuԏLFm<r#oL>@8).U.4vdg]=ҿ6 wㅐ{O0F\ a,Mյ/b63+_ZaQG|O?l +Lظ5S3 MOxdڭ%v[ Z6Ҫ[o *pV?Ĭs[\Y Bdltӭ/5ʟ*l> =~G ycNś|_~mR銪 li;*"4rq X֚ٚ+/xbo \yϦ}?@hk<x>w ?-&JZ#t liJ* zYm^~[\۵ i#,8pr+kұbkFL5\WWGֆb_cs%l+18\!l> ~)sݝk>\jQ(a|iL'>&?utת lqyqτ }Ļ5VL 9rۅ,lDwZ}_Pl߫aj֝E_D̕\8J{;} "Sk5RZN6ĘO(/k%jg+N(Lfaڑ?ODiú۵u+8w"|l "^'ϒzNrc]?]w >|\+_]}pM>.H*:[kBo< ĵ&6'mVY7yV57uZREұԚsu/܁ &}1Jvk6\H )nkB5o;wZ_[D-|d>;j/YhƸ+'k5a\ۮ5ԑrOp_qmSA5 FJ?^l+zG{ʯ~4)v!پ֝LO_ZhkȌZlb;;d4Ҟ(/ޜ/;\mG{? Ϧn})䵅GrMANO1- ks%K,va}q%SӳIf[վ7v-0vxَ a'j*՝2_-+} ~AOZL8fk Nk}'y5/2Z2qdzaM ;#y'oF\ٴuR+;e6gGy-z\ۺf.ߗ:iAcEn62(W &hH'Em1|ZƵ].sO~,0p2' nq7_[:^?iFK]q"-g_[ L,ahwz?*,ٚ; JI2[0 XBcB7kwWoƵW;! fcY!nn7 ;kNj^2q{?-J)s 竢K ].u껕hkB d SH?/6=D% bH.'r틅^i^X3/}6e~w++ي6ؒѫݡߕd߷zzXk y#mq,#'[m{QHK )6 awEs-\Fl , 0P{]l+k!쿝k'- ,Bx[\#,)7*}ﭰ_JJvw okn2|uWŶ¼* .'ZkCgq V ,~)=U ׆z0kg JHW:V٧6B2WŖ浮zDhPtׯt[YYܥƧFD xmq|O*{0g"ڹt.- qSA46['?]{jEw%vvw+0>wܥjKTxIkۛJԋlm[+RnOy!Dͮ)C6jOKr+PkAM2?? 遲Zoĵ@\@!}鲳= ĵLv7 _i(:_ |a]H\[eBKms'_eE2u畭GZLNt8 [ȍWp9!<9i!̕sJk=׆ \AEM?џvOU'֏?yX \.y~3ZmI6_ȴC3iz9-sޔyz[ZAtr̽=@RH2s4; :kF~j9wG;ZjK)0v\[|Jtavh D_s=|&3ʷ5l~u^}͇7\̵ŵ% ,[2~,]ZHaLq L#ޛƑdN)Bɐ2E&o"JōOF˯ ; "RHQ5JUNUȪ hՅ6}ѸxA2aSJbx p;wcz5!q|(X w?|~9Cq 78d~jW5HQH+AAQ ky&8Rh&N1Kv9Cr욳%~է [CM ;:l5 !|AZ] J_L©F@B |]pa&%@SX: [2-&Vy V#FD n!cBҨn <-s *X4>INjռc,'g?C/S\c;դO\V>7N p]x35vY:A\5"?FВy뼝 )^xNqoLi-o7Å:ʝ.Gk\sXeTC=>hlz5'ROտ4 7k (j?AdX_ r3Ni F'n5<5 ꡭ"= x;ע% :P";(tF LWVj<}N57 4bKLֺn>Zmf#!w xH\ ]#7tX \S@@͇>fgFa+xUOx[vc ST̅UA8gXyEAkx:_2=9vrMH E ܮ5i~(d;/ff#!R ѲԈ|@[=l y?cuBc8?he-櫖Kl t,UY- K l%hAg2HD\ (hK/SթJy4Yy d}~UV6hvtV{|u\ ܠ! 2L쮃bNN\ 5!4q挳Vh6#Z8Z زǕǓbk+klAw@7*HEXY,1/uVU1"I*PjGh}Ɏ4KL9ʃ}4)I[x0 u/*&r0?>\{^]GrϨOZR+5K[TQ <б D˜lȾ,/FNrywըa }k Gdg R\SlLtL}+Qɽ]|rr~P2 AL"g/jڗ b_'9/'\yPx"|zA}%JqSsViZ/k_4 l~ðCAm /s,b^m{QĶ)gU FB[bỌy8>^&;JL?srMߒ-@Sю+ o 0u8~-!n^srt-!!ro;b[k\#\0R vsɒ2 TZhEt:P"d\V[q)6%90D kqkI4N; H-qMo;O? .i8qkzV "mRPpd!n՚y l%x%~D{{ة:\N.j)]Nq L9 D isz \OLz*.e },~eEEVIdD,NqD}U)&rh/O p%X(߰Gr ,gkMsT5ufjaKT2\>+@#7 ZRn 5Q3@հϳrM]mU|9t? KZA\#<%Xw Wk0ΩV H9ӷo ~= !.A۱gyv8r0َ؆{\]&FÏgd_]Yzf-GJsbICG GP7И^+kȵٻiy@e˶m\#C3zw @ tSիΦZrpJ+" Xz'Y5Q[U k'Zet[\_d%!F4 (- 8N K\\l{o6&zXʸBWN} MÙzk_^'?Frh贃8W4XR+{%UfL9k /'"Th]|} [2L8ɵ F@҃|1h/+8!hA}Bk2V U<1\ XL3Y֘ZQ91[p:i]LQ|D:kpAQ&j/6 㸹n J%5#5B :vaؖLgKrf^TUbbRfs36>n(. )f'93v̙uB;:P bhwrYu߿}jV.p%rB z_ f>\#K;ic3 F;{[ eyۗ>9zM6YR_yS3qzkqf~Xўmq|8r1%A ">h/px{ vΫ [GҕoվdhkRm _o1zʜQ>n+ qF{9^R+o497@www&÷6 g 햆|hsmX֓ ֺ;VV{K !݊\2h@5Q% ʵ4Lr&Qϖ FX{670d4oi] gVKYѣG>6zk* 9JTzNyU| W DٮS3q1#X=Frquk·"]Ѷ~[6twfnh /%5AF?v7xVe 0 ]+_e~A@4MGM pM ͜Of 3jm1* H3@;\W 5 T Z ĩC-|l?ΓAr d530͵h%W-""Xzwڡ9_GǚhX5ѮvI 271 ˅>?erb6Dm mr5<1WiIDfuǸ9 ["z߹8x oQOŋ A71ڄ@/j "%~Cr tqtRs ]ՀUnKގw{I8KƓoAa@翿}xm} n7 85e.roL94{T/ηToNnA!A3PgO [kr( {比\lnckP@ #iLտK쿦~H Zoj TM/i6,IOjqi놵QmI&/w_~7^22Z6kf!yu\m5T<{fqp6+3tk._ c5)_isq@ w}tU 6U>k1b9<7}v svF[ > ܂5- "h˸ !|b'}kkѡL6xŦ ><Kz3E bCrra5 Cvàp@Uf@%A HZ>vyxyN+6-qqڂ6\oeOօjN7{4/ [nhfʏL(؈_U6 e <=.h]0}5܍3R e_]wVM (uRHa\NB!_J% JmǖtAEHPh]0;([Ķ%c:XJGoLU2y ,ݙCeik& %^7g~zs\(\GoSu"m%&zuO V+= 5%{ԡG8 A}f1c!P8͡꧱e }6j9grMQ4)MpR9rnMDsAJ_ͯA{=;k|;Z # @r}Ɯ"w&EYg'~\tvOdh b7T̯*c&}94,L0Ϳ̙IM4IVQ: rR·k0Qm37is HI&RC\LKAre2Kӑ{eܤmlD=P9}4};ҾYr-oN|R3 Dɣ { RboʷF } =M8ܮ ]c}zI^ U(M.Ar- _kr_]5f5j^;'~p(܃w'HkEqAMoyԌܚ{uVn"wks7"!Z7NNc@O?^=z 4[+X5s<3T+jJWjӏР1@(s #TܑXWY0 +V-'[,Z R+#":@%riz ~gNչᢎ]4jP Zmc V8VJūwPzXPk Rb R ɯP}<hF 3]F)ǵSuL')t"i(+k5kqXTx8ya0ͽ'<_BZkdךӀv-ED \ d}opyZ9|nqmW+j5Q|%VOUFc;D") ]S_<7:z0/|MJWcI=H a#\.x>}]Ψ%iG)FzW Kg/wbo h233leyE*C!HvpOuaOvkW8[oZ?!b. \éb܁qw\}5UEAqJT>ɧ !I^ %x~/ .W1" dUd~O2}hu,V+G ܵKm6 \W-{ O;/1A' 6Tہ:鵒 4n3^C!0ưPg.H.wO7 \+P6 a#" ×8V#q(z߰+<,]^=Q[ (1<V|Ő4qTJ@OwkJJTЦ>OH%/,q8ۏv/p6]uпL ;5U.=vڟM*(j5kV=XS)(ژ7pĀWޕz(,{8*g-q;NXq>^էgvN ekŵy;faI~b|vCJ MZ v8&.(Znb=W 5&PިIlM '7u=h{MۘqD+n>_''aE3S%_x3h>qmLEH Vk9WzM,!I5&wH@@"6^;9 ( Sz ה^Τj;*cKfHOFd~ps>덊\g}W4),!RA ' 7 n=פڕj[f L ;s!kp%!{\ۨ#呾dW{A41,jm'&OmT@GG:8k) ؚ{n7OEiWǻkA]x2d a؞ p{ߥϱ^5lJ#G)0v^fltT r0 <~'}vPD+Lj ^!T@ zjT{0Tz|H G7@r;H h6|v߫rzm/vTOzlL59~ ;]Pn \Zjmŕl 't}1Jk;@=Ysћ^S}H9i8Yr;drvY|f;\89b y85):>K&CF.mQ EGfblBܨ aKw!0b]JHظŀPN¨S <(@ukG;9ÖZ<"3"kW믹6r? c- aE[ӡh?8b>AHp+tiLԎV05 5 '6, r}> ZXOc!lǂ y%Uka]HZq݀܃|7D5,ژ{Hd ?#mJHF-4 ȡ ,nak8k[EYéEQ4Öc_[z8̭Qqk 4>9Zbzmcbt?3A HaFӅk19oOR6 dܯV^S s]n(х[)ݢ'5q@Fd UZEe3 wHKgS2z܉u![aWAڭOu{bgVSΪczʢ:k#FqW{bX(G{"ZOζm+h[ Cl%Vc[ {mZA2 f7:2Fe][0~]i -m.5QQ:.QAǐyyߵ"X[1>NlZ^#7 4SkȬt}ϝbo8 c_>BL7C[X3|H |ˉSarV^#/9XP _% lI{BɩA< Y.LH &Ծ2]|O^ IEBR#( kk!m@~t@ AGVn1DuϾrea -N܊KYs#5ƘJ-b ڨ n?0\d>Aexu;p M v55* E^S5O]LN Vmk>K10rM1ûD3XMh5 t .JqM|[T1G xi<O{fF_\D3 tY\װN-dH}c@k=f0NHm A˵EEd4fsAmHE~GOkZM u5A/jؗr?DE,hӏ{KO,hSi<^>'خDMP <[xVYʝ\SSxxDW)pW pE,2i kHHkXA psC_'~Q/~o\ F6pN=A8 ӑlCq7ã "#֠H"}^ҟt Nٍ hS \LGpe LN![0 N0b cȋDn^M❤ 7_^ Tϥ6#Hk ,06 ~\fzbՂ"z9hS x Z'x-*-c6o6Xq'CqM Q ND^l9y03 oABDDr-ר"",Zm4RhH'D{>pKy ^^*sqhA+ >߳ :lu m٫ n4 '~p5wr ܒ GكyQԀzn5-VD6 (@~ώ5NgyW ^Ed9Lcy,ĆkToNnume+m AᇗkO t} Q 02v*77IcԀPvwMO !VD pL/'bJ FsY0^SinC81r3 ˬ vR#cx["JDmxӮ5ncnBa|kc-:!">S\R76 uQ܀ ")A@Zac4[5_^S 4npkknwp IGATkBkuηzݑl2^'*p^݃cw1Z:0Z9)Ig fD fQ!lmuڰ7p k:k?zgpn C [_dA NK>gP~f0^ScH7zTΛee=/MPX/HbÇmY# DuI[HDڌ p 6V*˗+])x9G1}& ? 5l*?v[b)SDyAčfMJkbBUȠ9 PM ϺE~k(Rú +FDHlc/zDKZ_X}G|=,'y MUYL^rx #-KlE(AAYl5jBG _/&ZCZJI(?UUkb4[UKD\۶=Fzoa.ހZ9xey4E Hp ,+pv'}AĉAn>Nׁ] ZoU 9\ [dΗ|؎=β"wd.WA -guWb밢-,T64ú~Jc#C},s~LB{v EDJȉTpMfe]t5x ^ wCA5-A/2<8 m YBnd^߭&a\k3!p Pͦ4l+:Dss鏃6 Yejm9-. >1&_)] b Px-t,A47 F<|TCʩ -ntKg-jc_ C_ 0*[ Iɖ&bjw3GDd \U ?Iu06,j+6:#I<;c_6lB(k3?hGY%~SMs6 \S[-/'3>4^S#LKuk,?Sb3C+Js+aj*d {@Y wASU| rM9o^SLVn%p=,%' .t>s&*(asEk2&ԜoT(kJɂr*MiuC*95YXfn m60|mS]Q+،'\ۛ? Dx]א{&H " Şf:h{c|tf_Vw+{!jpvąa,{U I5J }lcFj5Rq>;l=)Έ-Az/uA {)*rMQ2([߿*kC'kiiu{h"! oЭ/נRF9elܗrA<~ X)cl\XYTes iܒ jǁ Z,Aa>&~k H=!9UյQ]-2#۷YUT7c}lW;ڑ.K1 ( L퉖\ Kxi恌 ʘq@tcdzdo)G>4z_.2 tehGrsS N]4F@z0C|zm؟ k>A@Ɋoͳ(|1yV%l>& <[mɓ/. 5FsQM o%旲vϯ)J,k7t i= ~h>zu>n^ڒ[b8_uLxٵ+gM xFUUc-(?fIy&Y6QWsrJW,|{.=.O'%w, 5+h{~bE ?3죞}j}S 1|0v mSCz,FR)ݾ{qA hMaoljֆ0}菒 7G=k7 M {6IyĸS69(0j5 z;(^'- jgENÏDžy%>#a' c50ʓ'N7F(O Qc͋\s2 ̜ SW&6U7 m ME4 b3Yׅ萗v)p# RlX @My_[y{o?!П[+ P#>>VrVvFw#vk?0=ؼ?JdW- &0J6a"K&"tȵ7A# !}m0RZw] M /(5lbD4Mf +P⒞:qh-G҄B*v畎 /b]hPMwf:6vߊk50-zgt4ׇ%@G(#%myABLJ Z]wAK"K&"l{kXGwmHLtp5Q&:ۮ5ׄoU yK;E=ixKnȍ ԐRwII7_6|shS>a ."TYF"(wtޮ:Lk=n ҷCf_D0>- { ղ >.@~A;D+הP!W #%3}s6_&]u pCш6nfJl RhdMa r QےV.ic7A%ɵ># n"+e=Cp{ &zoq 6wK gNʴkInvͽ\gr]Z)5(6 RqA \ R䚅^ꌷx DwW@va81? (7rӰGTɴp&'ZrД.-ES MqAiV@Sup RL;1+4khW8NP9h"D.Uf䝋Feey,.z?la^sܔJ[b إDǵÛ.ܭq5hpi {pzeggt]4Y#p6,gdړNUF m9&Jm߭＋*з 0 c |bȿY^DUi[ iJ>?4r3-r@9414}Rʌ!g" K.|nll8X: S ND(k^#E@kD!&=@ ՔwKtBWCk^i-iT^H;H ]ߎ[\6QK8*zj j , f [굂V[zђ=??%Tb:jJ4{JZjN[ ϛ9@<"YO"58 {?I;sK;[XNۈ!*Z:Rm #4rxYϮH eț^97+ ;rw ^܊h, drTa}֑>Jyǟ -V2u bQ}Z8i9dY@'[1P )NUkTxfn9kkr>䚢qp,^xCmm.F9DqboK*26m҄tr+A%(U%_d2lAę6.)es5k:|jύ:&8 B܁5=RI@h^NTR埳"8y&'ؔ/m .J8AN5ޢog FGDYێRMt:BoEBS"zd:MKKk)# 6%9kIA\#X˵VZ}lXn"ېҪ Y[x7SkƍǏ1M34 JTgo/]ء8ܴвsɂM1y,ɩ7WЮ 4\n~U,s tٖH) W[n/1wl,ovP7@ִwy@\YH˨ QHDhnpA&&9AEh[UCRmǺvh"7x)V KpmZx ӷX>6k.ժm bNYoF~:QɃc%MA'7iCt<}[ԧJ9 i 0eW @ zM;#*H35qeSlU4 DaۘBʃ]6z'H'nIR[5gX9 ?r-Gr b3Js5 RJ H< A9I;JM[pՍ &i [:\m8\"Kp[c}ʾ %,צEODx^ ˬ P+x z]]f(rv0]үq CVZ\lŚ mND l_)6ƭ|o4-aOk+Cq%0*kQ\Y N3.~[8Aa"~c 5 :i>X#cQ[ù7kA^ ܍ h44wosRKy&ԃ^ }WtMl:mO8 ggSL+~8Q]6?0ɛf6HňlYi,[vsrM|],qu\;Br Lprm_Q9( g\e8~ŭoftZGF%ՠhpZ rl ],D%\#_}seL̔h[kle l5':,ŋ33=nZq1Iŝ7' vT58lJ.Xl>k"@kwЖ; gP pK*2qsesKv4%̮G[[|tWW/Ԙ;%'Jp6<-TrEpw>r+:b#"d"ZfZn&ճǙŵwGe_ Uk;XƖ˻w,Yp;MYyb}Wi4i [- ̞=o LJ+(w,~ L3áشkѴw== .ƥ jOr; ;>7X}̐3=ZԅO 1^]rὨD-2[qac{c d<+7 ZY '/[JsavH?h;=ٗiLF Ϙ/'x^8PV{+{l"[7t@˵ kcJrT!'[ SmFo5[Dbbk //sW涆ffJ]pa yт zFdJ\ \+l l2K. "H1.6L :/72KVҒLE2[S,U714\[% ;;fg';ڑ_ 8OHşnZ̈ &wdbKof#_\=1pc""| E RWNR.gz E68',~u~1-rMUo#5 ~Əuh)8O 0p g0v*R)Ǝ/#Cf 3O'^L:w ^Z S8/l5U2eѱNj^9ڪ5lMd*~lrvk{>6{Fqo ui1|EC n5 idADXBv"Ly8='p~M;L59X9PQ! Hcw.4š>.F7T{. =*l} ,''gzMA{[{H+yvWv,߳oQ\#8cp%_gF\j }Lʼn<]+XB "FGSŞQcP{ 8ڹRָ^)g2B_ΕN߆@L@ 2m[Z1p 8:oDma;O/<>ZV*( [j뵃n-rh:SAyn y].0lK?9l JP--^k Eíi.|ڌ L97klr G=ES9l}bѮ4{ Za!_r-pM^-&Y15rIj+}]qd'X-C5v; {}H>/=>xFHkPdF79e>7z =GAw Յ Ho.Ih'\@Ga=|Qk> HiT7 6[h^kQ2uc&Ǧ,2a MIR555IS92K Z{z5vO+*0{\d.!ö -66_iwD7Q:JFa{Jd^| m;;L ?5nIo7M;3< kHbڈqX탁xo |N X}.pV]#'2T45AC#ZO7ܯha/ k0kљ([ƴKq.% FDHrijĆ+V_z NP1 5MJozI!盵^|dhZtupu,BFk ~ r|kVFp qV@*8c oܖ 6AP 62~QA A= yWi[\sֆHŚ m;mPe^EmQ )d~k_ItlHDhcߝr9 mhN&yBe(b%SS&tF Zrm!jr'xI rA H7}* 7 壇 'xW9S1S(n7kO~ӏns~óGQ)(b^}O8 7A~giSP >\Uq1r9B5Yu.CPH4 s;漬_75ue6Iמ2k_?j6m"Xrg uV QzMԕĨdG =uzna nKvt HݦJq?c}!8C&\rZۧq2#%{PXZbp6)WzyyyU-.qۏy*l3 P_AbUϞ+ zR(n/dݞFKRNKN/Q"X{|^ ~uD08>Z XEG9vƨ P30U!Y\U@v_ZkXL#gzi[| 6w: Ab& Z,!;iPwz\[7G9i\ it٦;ۿ+[nsIH?(Q97Aly>w.E_v/ڡ:h5OA 1T;Uf2_r %c06eFԸ=5s-MBvpyq,j~]qZcnAT^kP@cg圕"/J7l4.b @k@R1oM V?#Z ܂TUL}k- :WcmV 'CE_)msVa 61 uoZ5s\ۙ҅sBĝAnPEl)4Kev\[[g F 4{\Cw8v7 eyp 2sG, 6Gz # & |<[J*i4-^ݑhBڮ:s rRn쉦\czŗs5A@DVlS ]˸p(5Brm.:'ț˚u͋tjS]]9v˗7wZcgu.ܽm&_a p[e7=Tf 5i-^>FmjUu<u @ALt.Ae [i[;lv? ,ŢuuuM7 F- 97ހRa1bծZGV_YT6 A K/_>pu Kue VtkW˗/_xqO"Xw߃ w] lx˵85okϪ]|}-\ ɳgddp}}ғ*5 =i-Fr e;G/zIkԓ^;踚v<3 U^98kg+%ݳNcdfgg_b xkWq=Uwp]Xř9FIjmvxռ\vߪ>ܒ_*56GTg_l r%v%VM3mX]{/ I+|e߈D1#z/wڂ tax PIq<24+D9W O xڕXmW!uVnޅZD T_5V߆- XT pvA]=J!'=vB7%꞉p @끍Tj-u4\Jzξ>pMgL&aINյQJcJl\SF[uF u8C"t.j}\jJ ɭ!U"qfq }xw<ݣLڻʒgCdM3kBq=rfGk ڣnzcŻ6#b~B4l } up^,?=ѽÉ,|frE-rbX+Lܷ~J4ߣ\CViѣ}D'ټ}I^)6&u 6^_w⫎\S&4Atp?í˕ o/Np'aW%Ck iFfA7U7˵~R rZ~m[g6^l1qtS'jy_M5\5!Kmm&J=f-X/S}KS' | >2v,_u%yRYЊ{DlL+3i%g{b&,B+pu~{6l7,YdI\ d6ҨMm_0ڝ)IMЖd[5X'y*\U]Sn xՍ]<*SdfɈ8q"bL*ڤB2?p0X)f DDXeP~Π 'pK ]<5)v /|\v2qmqn;w#9Mf0. a-%-\Q߹tNi+?&r 3bYb.k2(?w3m"}t_ЂmK=& @ %]C zm_@?<?^iЎ }L [7܊BC˵7 I6l7ǻ24_rDt J)m>6Gg RӴf/2 !@p~grXh 2?hv*ٽ#d !zm5!z&˝2t?mV6p(UeCXMK DMX8IXZ[Zs6zL K7Fcl;?<\" IkR!@Hct?8bBk;782ʦHteZŬox"v"9-y+?_ ek&'~0 m>\.*x3%8z~PH^r l/jI.0ZMiQe[fyhƀk n*"FI myi÷xd LGWS7G/e˧2 % ~n״ԧg.תĂӚ!9.vYR 4#R : t嚤o?~6{o@+rM1 (L"{H)@~ 6i3 J5*G}g݀ q>bg G_1-(c{Wuզp'} B4d/t[ ab)n^dύ6tX^F9gE (J;~~jY@-ZHFF9i *v;sm@Bγpк8MO@' R=]Т֦ktg>]UV![P7[zM5[zbdbi>TW0>ɐd l %.wE 7ʽfLtFDYZ\ĐH}εJ{amߪFIVʒ0~B4Ns3 !gI7 Rg%qU))cGŇi|aiO?r8W֒?ht'wM-n2P"bS# HN0t.H*+ i i˴\/Fa}2{hpN3W훚vm3Fqc3!EH[ E)ȮAsrΠ [x<QM*-JM3 ۴/Zz3嚪2>]vHvl O_; z:#rMyo>epW(H" 4t ?6<iNT&D] (Z2t5y4Kk|xyȸ8ɊKpk6@jfլ]ӶPG"6wTZUh6h#p/9MrM j YTOǹh)&>Z)IW1cܵ bm8wK8sS k Q⮦ŪMZC Q#Sc[v>*pin7Џ?8ZL|: 嚤.xF|AniPvlgSұ:5vU].QKgc[7^L \ DJ QDEJ88ۏF*bLʵx>%DD^ OT>İF{h' bVR>\5IC r/rh䚲>3vqʦؕG 9bOx=4-P·f @f ʹːmԩSj33NZ̰^H'ݙ@L<ʵ(aO;Ý dM*x6e?Ư~%P6k[sx hZ>yبq>) rAA>0iIR~6 P}3*al:&v kO#0h}EM\i43̩V 'O6)O]k#!W& 7آ>I%,]YI\vњ)f呄 t_IMS{ʹ @߆8~h7O<7S,G #Q]xn1E͛YZ%k0;ToǪyR Y]s_2ɪʣu%?%M|k>Kyr5*t}w"l214tdžSf,JCMnoXA5IXyZšWmY]rΓ[IK }T|hdu=ر|R!<ahfvJ=.ϠDDSxQlDιg>7y 6oYGnNgbvp@GsŋO::[&&y+Iy wkGR kVq2-rM9f>837n!eeYyD5-P}h --406&7n PK\S'gه]nmy)ZhͲ*JEMmkUV/) ḷ%z\x""]+Y6Ve|tfz-ɫ[H0_Noģ {QY92XgUvestSSgc 6DBqkXKx@ Ǥh&irM6o.9bQ['H};ֺ|@;&+MމFô{j!mlFe.;Pƕi* beħv> VW@rMQȐ5o{qB]Y\V 6X+ʇV jW>xd59:6k߀҅[j_֯qH5E!=k{3"F/O&X@JrJF%U9#ԃJЬOt,cNK&<_#a(*ה쮙YJ諈[ K5WlD'[ó>l}F.| p Sw!B\"TtDvׄ{K 4:CVXwkxgrx8 wp ]{0J>S=ŇE]L5#rMycZEG?v&1,^h1)bH>K3k vDnq f|~KMn A0| hxb᭺ሥޱ=M:Fѵ*R*zhN ]{ #r!j rץ70ƩKĐ;EjΛvzYO;5UŠtPG=ym e'ʝg2^i_)%=; /Zŗ60?V%5GCxuDmĊ6\dN@m 64Y)=K+>pޠ"*,mhyzL |D5!LGN% 3 =ȅAjA >qJ #|ikzNM g|e7 =٠X2 v>j_g[fJj?RrMrp+:,pKIcS?O qUkkt+6}2as,z菄LOr ]̯ 0L:Bc nL 5%F4?߰kݷlW4oq(jI+}H]m:*_+a/֯6N;. of܆mŖazy 6.g=v|cJ kSڋ BsDNq~"FU6Rd!ݿpp5ED^ed4l?]=vк),Vˊ ~mo者᳜rY Fv1rw>a?Ia]o[RZd*Ln RϾҕo":5'n[lbky:Us*.EUCѦ]R/4WAjST/5O/R̝4nQ ;Zf;ǻe?uܼ_v_ :OC= { :EZȉ/ش UىMʵ:~?6ۣgG^_fI/"i^{ Ɏl_-xkVl6/V䋔G& r_53?[UEe-.~M.] ~WI L*&'~jOrM 6G@l~W?=_/ !h6">"!p'Ed A*KJư \v{#R'+Zf2"ޯG;\dwIQ/SoZ@]bo4lкlE!5ITk;Jրo^tڭnV6H.פsMv,'ߟZ_skߞ´ NqhۭԪ)j#[59%eol9E %C|Ok!ZY]IMnLtj)rF5ݷ-(*E>\~r'OtY5H&(m}=rؼ*1c"kflwOM''/ Q.)IDCK?D1' h eC56yAKCv*0Ykrk;R٢F[0(S~'?'*czL+=]It0( m: 6:0FUۆlMPLS0.8fN=/Zc.21j_pOmę 6obתx'V 0p{\i - T:'*H4MKl N&X%ת'ƊM= eJ]H#gSrNxI)ךjwI@~<7;ByZrPSwl5)}@=QX%ܓ}DdRNfPM.si4F5۽j t\WF 6P\V̧Xk WdC1v꒞m&qHHωv㕥\sk87y '* e IlV+ת ^<6hX~ |U'OMl^ @yOω90C5gX2ףɫ^EнȵJ՛@fkG?\(G#2C^@٤*\i p1ow2O@kM M5i0NkV &Q-L?jOZPrkZ'l3"z.Y1QEQsH-}}՝QlxK|r#w-bwBJyn_Fڐ 6#xfl%) 6ԝ& \D8_W}8kI指Uk14 ],6F 6 AUjY}9 JO[)7ɕDWTVW~d9|wRaeBm?fkNq;a> Iz6?O;k%(~«A4"VFd(gy T@HBgBfY%Ism^sLdr kiZ yʵʭQWdD<*6 ~W'Im(Kȵ3RՅ:wXcL![Ϲ4j\ .6kqlxq8(EB .){@8%r I(_20kI ͻXӅױO KVʵ 6Z+*{= ^FdZk5p]VJ6ONQSc범k.#cwD6ꥍ?/&b Sb E}ML- , AQӽ @ZO5ITT {!Zc^=K%0Tz|zQ=~#|,|lhK,ņ@ .0 G-yrM]@]{_E5wqfJb fXٮ^}d"&Dն.镰aȵ=dOtGކAw0p%|';Iꀏ.@5U+ؤ^pliR-1 k>OD>tIIZUf6lGZoy69fBL]D ٫jbkK&ϻLş5 lx 6H&v\\xI:mB U_iTNg)r[so^^"Il3 kY{1EȢ1IJY8412H\VNluN3{P^{(N@] "\s EjSx<~?lXOaJl+3X29*JD!*a0ȶ6lQa-xGl@:|s}mRISKҹ iE[{) 9#h)[t)ת4Z#qFT 0>os4l c!DpNІ(xC@^"bIQ(R7yh~B6k/uV3I 0\{"I :C j{˵\RUlJ bCueq@ik H1J)%EF Pn"Z*6j0FuF .WPIR%u\9%@%)J~Һ4N LtnM *k\ӇCK8Batݙ ZQB h} ?P+ Nuʕ: +, |*c"78_X&lϩMbV֔J ^mKEowCuy|Wj.IJ龁lkZ+(;WsL*M %.WŦ忡@䜔kހX H%ZA|iu= Z OQ QrZiݎP, #U -{-< Af0FO:X tCH:8Ԫ)ל"um~- >yC0O;Ӄmu# L#v kz<ޥRku :(PNVvIGbK9>>{9O*ҖSZlz:%7La𧢇{E,4,K ( pQOnːm'#*Gf W4I|; MRnF KbNyg b.%ґkEHMeGq1|'T8|'oQCwi2eڂ5Thq2: U> AlH_r.;s+ZZ==ϻta[칟]FG^!6[v,*#'aFR 0~5ʟ^(J,ʶZvnXF>&E;x&2@zfXrI䀾:w s h^dE> !BU07вx["&!ٱoR ?q[ZŤè._^1Z wXLJ Lr-5kV5G ]"BF*HP H@*{.qIJ"N< \X PbO/T*iA kݶ5bCH-':\{ L鯾 h<|r_yh M !e" )V\XtyQ3 'Ǫ[H"I^mkƧ|7;bR~I8FFϾimd lPrH@znvڳO(_yMU, 4[~H< S5AΈ6?s\!gb LX_X 7OI .M-ym;5=굔y&\ҏ͋FXRjxfQ#e+N >2Y˵J;PEʃrfc"%a'k^ Mr^I6h Ef?FCCR].(QhGq#@lzlvZu-x́NF IX*m͖5 hBCܠrN xoWy>@ʺH> S g M0/k,pkj_(e~LH&|9gc?mnclxs;߸8?!BlB4 7<lm\D:tHWh=<[u.})Y^ Va 4XE#0' 9McņQJ(٢ B- )-kX>!6_VlZ,s{@mjI9bQ-zY6Dm)'IjC8[=:҈ d uO.c?Sל[)y<0>.Զk,:\Rpdh,ZIlC|vԬY'hH~DaV;r} ]Vy~c6 ce}4蜲T}%w }*]\PϫurMaׇh gc4t4/bRGpW>N d PpU[*n4ކX 6;>ȵgfɊ-tdm.Tr m+rmHCn9'(x5}H1ڦuFUwa[Dj ֳBxJZ5s |kڊ)ohJۻC 7eM⍥z!H?;n\{J*hhܝECF[|vcfPX +^34YE{HӆРvF_#GxG8\GrLkd+A _Q>Nٴ^._;;<s U>oέU A?K1syNihuH.ߖ3) <7@k #4 s)Eph0ZvCDup3q:43u1ϑԠyvl%r jPWSC/WH O*숹Ŋ|s A^;msԷ=' )0k& PѱэokDO,TB} 6 =gUZZ'['I}]){ }Ҕsj(n[gm;6gjC QbD!=8DB n.it,_Uۆ[bɪG1J*pʟwAUZUvZ}F~IϨ(=OIˍ\.7nC@}ycgI# #+,>[䵤Ex C}̫irڷ>IArmM S\m(^+ek^KWg I\1b VvKTZVÃn_K(dNe,f".ܵ _ QW4fi,3*^#VY5(gc~i_҇#*̤0˚{1ߤ+t+}xHD4%^vhAUfwaHelZV:|;Eőv\~)[UmPuK[MV~[|ObA ¬kxJU g Tq7I@אkQBN]h[ /烾 >^^ sh'%"Bx8 sdo=^yNn!ql; 5:'za/_Ɛt\hm d-J/z YRmz"*]ņhX>cCDu3#gkn*yL,gqIU lYɵ)zNUچ{gbiϑ 4>3)L]8@աP6ЏsU'|ЪU0U hnfѵjMfdM⌬#,heJz!=~. jKKG{gx/ <8(ձ @&F{Ȫ: gvwlݬHnʻ6k+Q"תgއX"n!nPNiҵ^tdqlq|!. I#bt=9؍ n K{NLgk_/K\nyNZ5L :T=S #WUFRCIhka-=77yJ j1^kEHGurl=P#FE,koGzA(ZH8iKBsJF#H [Jx4{1;OHEUz,i*qPur_.[jʈÉt]kSViψ{V:p^JhE'ה5' #3/ :ǑH )yAȭ_vV@GZZVf)ؠ/2 )k؈lU ;kq䩟ufUo E'=D Nb3ZYPyX0*T2A 7@4jY-{ɷ@ y GMs6Buw(F% !kGwp:,60NuEN=B\D-5do"->P. l7rZnͰ /qEf{ \]rr݁1Ъzy8MPkKlHFO;~A##غռײ8 e di{sFc\IuEqkWi6Y r-u\V M! H2m١!/X רH܉-9ϧya*frĞ 6QQճ 5RsB=j.S1X0GY o# lB?_ .alPUGg(ez.IlEd0Wp sQH Bg4bVZ).* 0,ׂ6 HP ƗҦuL xF Gi^M|Da. x@OA|n f#)+HѬ Tw)+ C?b':tPm#]o۽^tMc*5I Ê0iStGrԳYT]3Bu5b!r+x'|S^t'xRwa =x{q\EEL%!F6S7])Z=(Q)}fb N3B Yɵ K(ҿnF@b@w+TpE} m~'ȵGylEFF ;a,= :׆rͳ^;x: rRTbPV7g6( ,JX"w!v]b@n#KCnΨhi 'sXl8Z ʵ7 {kæ,+'E%v u[ ]f:v&ja}ޥI]:|I W*G;LiGDon76.|_(9 {& T}7(?z2 @[{c7IXOUBH5w /qR^I/t },G5IĤVF ͧQo4xlݿ+l0/h5aDkKf? z# X R ~sm5[Uwݑ7:Q P B"f !E/ zy+Crs#h XiT~>(h=WYZp]z^-Cn|450zA~jQG1#l1R s(zN,B<Y4^E*Li_f"L Ԟ>n ]8l1Ȼ45qgdoy.'E%_(d( gf c<FYzo gL珯:zwivIOyt☛ѩ[֟ к,k3 7\FZg#zF-rqgd2l!b@\0;; sy-Z0Zu'9jX1 5h[ƹHF|54~#?6aϰ̗rMɣ_y%8/[ 5NUg D46 ⫭WŢQjaUh"5bYS3[2MI;BkZ+fL:8ol=u_Zv8J5A ѬGeBo/gQl{z暃*'վ]aת{dZ&\N:YFHq3Ql)96 t}=6},c|{* nuh}O?X˸kը52X8-'T#\SZ?#xkHvh<: o<2D*{:ݞ&F#>=TX_ƧD-="/ DU:Ic*GaHW-h@3l\ V~8I1^Iq*Z)Bb9B5 tc)F=Q),zeQLIHէ k}L GIWU9*!=)hN[Ax PY)G 9J/#rUWl5TB. {%k @Ss^?+Cl.>\vu":@ ,c8^r n00^:"bU9TXr["U~1%!kR0UȤ2&j#n|_Rlv)jrp _ <w-Tj}EU e 1= Ԍ߿d]*~!Cl"h) k /n (D/(DZci L&ذ\Ȼ0^[dM: W+L"델-fو }zLSlOW^ d'\ \/X6 pZh3re5&kĺuбD?\B#W! \{QIS6Fr- rd}%ZXA[.y\9D:敢-7_{8Ƹs my/?*E \ p\# )0ITI(_(FȃlwL l-" ( -ÎQ[A5lz_0R rME)0Sf=H 'תRrM 7 *ƜyR4m(p<iI l7mkr-,1kJ~2Ϟʠ y%fxr Z)'DSrES o8O{V_#1YA*%bl So٧V^m1In&ȵj3Ḱ@O)p,|1X#Yj V@]=@ N6)b [Fʨ| ˚ JڀPG1%nro ]T>1ȥ y KHW 88FpIcvwg+|hzM Wh ѪڿRm*˵0h u݁U*O8pE6-wZFsE%Q'Oyz{^40 ຜ-x Ofr-t-ߙ ILF d (KgHUN8k1>Z<3Yⲉa~ɥ,^rz2ͬkH(6̥XSl@" Y?#% ~ک=qVpɾr-v\H1yf o z{PIɣUXʵ W !/*ъ|0,J]3vV0HebV9 }# 赡|+S0w7A2KJ^+JjO ;56iW|u0+Tuuz>w G X^S8*5nja 4kGy!T2r Y2%DF-캴\38 R'ֲλPPyLVy \(9Q +Q+<-S@w k%Uߡw'@]3 V!PZͶѷ v;zdҼ%aINPr赐.BCe5̽ mn,~["5#Ef zbrùmx!lq"Okr0C·~UӇ䜨N^] m; H5&.-[j+^{~ ǂ_ڋjA5e3#*x !xP+Y yv!Us3_o)#s3B]C9 ܮ0"ͨ}tBIXQ߬s8wZeh@\hl F@TT*elɓkoگ jb[(N a M}&Ɔ<HgUqt/PKWŁ[Z۠:竂LeB OU2͖rMܘ0Gi7Ca|agL >V" xiB 7%Y~ȵ{ }G@k+|L8zAo%(V;l6lBA0k_X[WvqS2(,Jj'ZpL * ~O%*m {iJvHջ 1 Szh[ )B 1TG_0>kVL]Lwi\l0 Iq95W/qk(DoA/XӚ^ [Mvw%>4J=Y 3KU|%[mȁ UZ[Z\{5U&R CԄ侹'uaPj^BJ|a 1yۻ.VKCWCy__NLڼ#]~EJ]KSĉƒD|ɻ0^GuvABʵmD?-%L5^hXlK6zMB&U^vv%nT~E L r9'.<ːbЂMʵ]p, jtY_0s ؽtǦ>rݵmA^{~ zzM}ܧbk3QCo# #6QCYvXír 1LyrTۆ]-MN WvdQo~@cm>ySoU6F[% o xZ̖Ђ +!T |PBY@e3A yd:Q*A!F diK Vp=MҗI1k 6)jxA˵fsImv酴EQh}+D1Vrm8*^Sr#eM*Cwi@M0K4CRTUcktͷ^sFs>)/|m:h 1IJ5ՙַa,d0"gyɁ r?@> 1 l\tHM5[PXCo2AU5vCg!(]xS\Ql7<3E²2ғvmmYF)? *^Sr7A*-Hxkud4aCO OmB7a9V7'A7k5=k;FD+n3(\#./|^ںƥI-]XlA(1~mU|)he ~,|MrCcC~v7л_6<2YDf ,VK75o͜Oկw.D@ >_x)J)&\H5{3 vGNCC5:S9S|6چG̸ =9YXZ8ǿ1hAEPHIcv -.lR5fV<2Zՠ8~cjժ'?>'wMyR|Kca Diulu#,ؒn# VE Kh~(Ұf7 | 6'4C_U ?o{N\ӟ&K3Z=_̏OG! ϻGFfRՂMOn!]QM 땈Azo!5a| !6}waB΄TB"<{oZEܨ078MCU ƋەTP M8>KRO还[~>g#{V" _ K*B ˎE8.D.p[\tcV#E-[Mȓ\ q?u=?>)˟?X×IE}c>^u_ Opkdec (T蟄 XGy&Fc0qAdc S5<~lPÚ+J-3HQC1\ 5ߦMVjW=(yv8v+%^Zm%d,͝Muqɵ"e γ-%j4Jg%7ARt7pS|58L /S5E"EL{/XݯkGZ2zj+JayawA[D"ɑk5]4f<_mgw_ b(ؠ{ wt ج#V?B'O5[ch;%7a砯~欧Lse _6}YzkjwZTs_Z)ն{2mڌF8 uD/h~~J\ۃ"Բw) wHB˵Ĥ[{h.h(_-87dz#7 jgkrmΜBOWo5*R <"XGfgۓl2ncc#\#6%gTUF~?sIXkч]ז _Y;^ol;JE|# T&\6e@yr6QB%NHC_y'L4^b&^ \Kۼp1%2ލx_@^Nedux:JYڹ)g~ 4FӟLG&چ ռ^eP{ DĒWUkuٜ |/!E/mEh@W+66;%Fr8h'ku*Yb'=f\巛7{exĭH ll *J(;Zx'l 4"qz V+춼 ^Jv)x.r*r X.?,r톓JpG2%f<ޜc __2.V+(RI\d2Xbʮa&T "x}m|" PGjuϹ.r d/7]?+lqTvۯA%TJ< k9R|ʱ;MeDQX-"& Nxa 3B~FnslƝR SּT<\J\\k\S_ECK9:} JYWHQ/snRfr2{egxu{|6L\S}C(2 ]j2 j1ˇ,ն7-}q51:WzM13 ñ eg(/_ ŜJ<-<6J}ond \Kft[kW&!\ ^Sʜjqb{.|˽eE磴- 6鵊!ʹEԿYEdž6X)mRqêyg+e)dQҠhk|@q 9Ǣ5WйبT7i*M׆l[Qsa KȑǖHsCir~Rq,\SJrk1ޱd95S?Z_4w bP9Cɢԉ5h oGlVaK,o7 [F{.%B3,wVJjH?m\ߚɻ{pH bӯS RD4Er6dvO=-a܁F) a)gV@_#GIk FYno *(#>;͑j"k]\JbMJ]5:S}Yd)G<8gl ZDEs-9vg7gSYƧ{_mPC ;iE}lf)s9uS^suu>#s܁6\;{s2{awRȵcB<NY#U(<ۉ/I_naJB5M6ǣ;C l @RfjfwW9&v57 )[Ho#vӒKs3 פE !הc<x.RNq 27岃DRِRF+^ ^jn(3¸OOg[F-J4Ge,})f_qOGp{ʌ(cy?!הup*|I>;\595CF٨^^hy1[56{mi9=,@ l굊yB2^k!/3vムr,8'#Xz(ClIx NTF]uX'#l Ä/+5%-SKE O r)xkqdkZ. lpX%h&ClIrJAaZ >doG}"^۴A5)̬'@8> {<Ⱦ9xrKf]s|lϤ 봷(+ |ڨqz}ƣpȵ)6ɻkp 9פk&7 NZ hj锪xrK 5Vzcai?v2p|q"6\Cܯ#ry a)CZXXr3 d\ˎ b\g"% R@ڇ]ȴM, k@yEkdi![o4,]ΉƟuZ6<ėl#ɛF*:etHG: vp勵Y4 @71Fq1;}>܌^IaI,G6 % BOl}rN4\ kRHqܸ?V 3ΏI=Ϝ&)z[nkJRU<{%WIR -Ђ %vE!;R%w;e>ܭXRFD--İq@Ҁ<z@) 8 øT*P7c lAB: GVe1:I&.,^*(:s z Vm[ǍzetD XKxp,x՟.6op;j<=y %nץ҅Ȩ5/w CV+> *P8NOͲyL+;~s2-PrkVR63 Wo gvU|N Z}A3يg,T[[?{Ʋ& !SĩrM sooy/Ū<:u_t:C19Yd5o)교2@Z5U?,0 q ?os|VqEطLYߜbv/TCT_h9li} GY]zeدO2 xˑ߿rG ]}:Ke[t zoKsQ\Yv^AV@ j)齸6aE:n[Ygq1W{&9H^G2 8pOɪ߶o3&)^C7٘bFzmnП]z<8tΐٖj6y8t =WJ# ![7?>sx#Cōe:Z 9{e3V6H6gj#&\⋥ s y2+Ǜ ۰vPPXG= "]c4Y(U @4| M8ľb'4B﹘R5Z+8vBisRO v)͢OϮ'"<Jc,ʁ2 JǛؿVy\A4&z@"Mfa3 % )rz5SHe -?o 4\a_0p~ō1Z ..78MGDT&kqN!@xx/fBw3 jssMǖ+h?>KϤ("N <s3( W tUk/KP|RqJS|C pB ~lPr' Qz=AYXɠ\y) p !v4 g?_8'}cn1c4N33(7/qlݝ5" \ALyy~W>l gC0!V8-f*M = ri ~k{< 9kF @-yc %%/ъYW犞|Y5 QsW)!FkzbHi.rtza,(f)uDŽ{T=?LySs_9"zԑNVyL>"g-Q%"RS 2/)VJjlVu i<Ǧha^61^cy+{ *64sI]gvqWЯC(U B\Fkr-D}1>闾9jspsigҊ TEOKVur Zڑ 59z{u2"zbRRaYj lzqai8YZ 2 ȤT(d-ߕBjtc}&Jmnw%_B +@U]GI>&+4# k;hl^BX]#8ZQH3o@)-eulc~ONFIN|WIQ= K 66ںaʸC-˥#\VFJ )MrmlΝ J98zEp1%u vj H{r .҅_Owv:"R^~vܗGVh1v>PL hSKr %7 iƌ4ldqjgvzk.=Ha\, %[k6P6Y33|;!TsLD W;b'Kߑfa1-q W+.'-)A^5ˇgrat4ۗ7.淺j}=SSxP0Y0jH: ?^"v*rXԼoUf3%uwI2U: ErM [sn֚)e3M6=ey*2NUzNzI8C˸ t[k? FQE& Q*8,"A"=wPj?azU_>R_B&ኀʝ ƴOEzxu=mXƅ^4A9~% k#z N=S>\;,ʺg#5*˦6goq6cn܍Tk}!ٳlHc!ƊmHrZ8B9iIwlB\AkOɵI.9@E~I͒z (F~ZɊ)m5JTLn{!u=R*vzFBAibKI>M?.}< t:6;.+T7m1V^^J !2A4\Z|Qk8 ?6L g[љ(DQ:wB#G{זG%ffWJ%÷b=N{KE{VW؋\ zl57>"~ 1'<c]z!R ժW[g zȲڭ!05oozs?:fR_yMR3O26kMrw? lehN}&R/S&|Fɒ>EcdR7ʿQ8H(鵶cz& WvTHpmvͪ @jY2\e/ӅzB ~ܛ'P 8Ӝ^N!%(#cR5#?IO5p 7rB!o[)38Esw@]u6 ̊r{T-A[Bz,DI' Oi]ޭOP9L# fqgvb|k)%/%sLL &/WC4uX*4gcp5Q"XỘ'ow8pkr-ϝPSs4r;c?F : N 6a%u= ޙ&dY 9Z&t&}82C6;y7)_-ט X29&U@ ݠ^YZ5p '7Y]ï 0~HsM#\ =c.R7VIMCSsrh]YPY%IoPsR/wq,,Ѣ6a݇tC>FnQ-#Ia^ 7FgY9K!(,po[Vo 3 /R{QU1AA݂ ~l֗I=cYl%#Ӫ&.ٍVuޜ~vSvMlدRZ+Qs>D2 {);sgx@ ltA.sto Ar 2N g @2:+UCd%t?<IwQ} R%SjaǗZp&%z)]mu F} !,Ed_kR'=pTkVEftPKβ.B_iaJizhcNw if,H:1:?iO܊5/d<|{w5}J QG{DHmCP z:OsR}K:P,7 &46y6d4KBa?܇-.1P&=G |qm glNnįr ^n#[ssYNī xL^Jv J_k҉M~/4A!/.yIBߘ]EhW6+w4k\Zf[ V8zhBNR*>Dԉ p-BXb߬x&M{' gW;k.ԍ{ԈdH_CRُ]Hf@FΪq&x%ƌ 2 骘G>7K w<>kEOU괾DMV;>Ôu 6%&}'W=ƣt3gl'K St*i\Z &yâ+6~zyJ6v+L;ͩL)-ĸzݨW RVe1?L j -|ϡk[hX(C<6ά)x* ~Ve{-~̄G m1Ke =犎8k+A<%WŚ}%DBA({C O_cuCtpecr# c+*Pkgo Om ~lT!dkox 5( H&Oɉ V .~䧞 q 5x~)Ͳ9XOH UZH#5 l0Bz B]ڍoƳbl1>0~˅iXKL!M*{mS4REv^G>[@t Mgj huBQmJݭ 8Ƙlyo\UGVkJX5dGSq(<{p¤'mB&(Y^՞ę6|} }̀PϟT2PP6%_;IǤK*y xvw^+d"pZTܪo%Z;ߤd" ZmԿծn qS(vIlO*ir 5Jވ& T?&Sy5R. Kh~Kp& #vQQ5!/cL*H~kNW"q)Քdޏi}qs1N=3a˭@=*xUmyy-)=s&{ Emb, (6js-Ўv.7}+] mP>g)gy'* @[r*v ^y)_,mBH3zaoDũ|ǴqkBhz7C"jV <I̔4i{2/h]LYE"#Y[M+Za,<3Ew 2فO{O v?;/b-ϖQ-ûE5PU9r2 @OºYیCc { Pm2˵P;6Ї(Zp="gfGDΰu [i, (d1ȅWޭJՕ * #(*-WZq i_~mLWx |B} L 'gρ\ !6OGrXDH 3}- 3_V]&/«Je?]6W[3E^Vxk Ej} 3GJ:6[kB흆 BXD:Pu~[Ƿ2۸k@z_w-u3Tj:tتjgZU TxKJ͠hXRjVCHܣz?wBMu\7j4g!#sY\R5{pg4h7?T 0nIVhc݇jyZp~D'DvB'I'k>Tm}Չ1 ԇ >?< =[+& y_&syhr\z It}pO-L3畦64Bo>)U Z-75vDŽ*N ZJ kb 2N=c^4U?C~2E_VjGA;t מL XhLmquʀ5odPU C,D tBeSmp ^W< D +<´6(MzKX [ WYWz4ܿ+8|7ɹ4EGKU@@~#RCr LP~zuk ku?Zd);&Zms# jj|Ru1tgJ=b\E5.N)e;oc86u10ȵ~k0OؔWhVK3 46vS@ֿZbV3#gN]t:9H.*[xg4G,RG.q\j F3?H3Zg?!ZKRKQ4 mLN- C54U ~Ek0DMTg폮̓;{rKUVR4Gp0~L;˖*cZ,dKnA BY;SQ41Uӑnp-(~҆c { wa4̏l-9e@ %} yLTZ9ig5Ex,h_q3ϪsBb~ T&cg&^ƙTb pdt(| )u#0ʟ >D[8Fҿs.BG [hjV!-ȴ}SAݞ גV+ a ܲj|s,O vaS)tGC aeݙ- x{ً,W;\4fGPZ;xt}i @Na+[J"wnvoV ZO3a7CK^y+_>B @_seM %]L (9d\ҏ=.T!b#BdEʰyf@h6i9/w-Y]Y@l bDsT[v+kl=<Z("w%0Q1vEi |{ &HlإUJ )- ǿぉ-& %7r ܜ@y i{ZmpԽ VAڟt uCƞN] v,[l YETDʵiloD6&EȿDr F@@Ə+" G ڵA v["H t k'7N=&șv>bpfU:vYi>ߦYAz^ 04buP\R2kŪCM1˛{2_lCDE4p xVA)bЬ{QM'NĦ84Mjn9Z:]}. -F 7N] ;HiTB|%B> ?p_{&ٳ*WׅL!T{S3 ^_\pcQ&p8UO9E6˵b7˸)nMD sӛk,q,غnN@CtTBb& DgMl{V տi&6@. բ_Dl7| ώiprzp_ 1uqEix 6C7)G K?Qk)usr m~2i]W[pw/q#^q{ϲ FH(بߤ 7C7*]g/&וFZQIЉ"gXԋk p8X*Z&~F) iK E {@k1 "C/l|}kul@ œ;k.=e p6l< ȩe)e JЂ~V*M}IucO; 9f^VȠ>\B]j) jX"Û̦GjCtNiၿJC0/]]^随.zV+ 4[j{[MKqȐ ) 6μ1Fi5X|Cue q'ڊ7Rݱp !c<0˵;"u2]!k\Dڃ_9F7QڎnJp49ѻaTJ7v :pgF@NuLlF EzǯN \_Pl 96Ryo |G}ޏPcw} oqߴVs}Qlx=}}\wvȺ\X;y"X}: b.Ȭ6xe~SFHb.PBB~ ,n *2 ^96 D얤* ^7Iw QߴUwf?<7&% ɇ_rѫa8} gT ' <횂Zhik/7lZ蔓GEuRGJr_cVMHmgЊd5wF!%;vǀ2 'Grir⬔cXK NqmZVbkvzdVk̬=yT+~K.9>x[TXңQ˵PA|Yop>(\à5 G"7,u (|m} g;ؠ~ ϏV##FMu7@-Y< G\@c@ V*Y{:#/i&qr O澵 ;d4VKf8e+G իZ7ե6_ЈJ(){Ga2 *EtMTz0ۨZ<pLP)8//Ƒٖ9Pmg6 䅅h4L&3Ѩ \H}~ 氍)&,'6ݰlfVKs3Eb5X*QVyTE [ZDFX!O2_;B.**6;fO H <)qbRy|߾Izݻ[[g. &+ H|<*YBn}ޙJxR1# |dK< zT-@Yj 6 kΒi:N7T\#} i^MIs 냴[LAÙ8v95 u1F]SL.ʹ=zG')9jΞYM !Z iMtM_DXÝsܜFq~Pr9Ȯ dd]4 r Q@Eq/>7Ql0L4(B3[u @VD %Fza*TU> 7e/s?jo̠OC hYA- /,(6]+)&ִkьD}Pވj?UvsgɽCqqǂ۪㕞Ed"ҫ#n\" z[FN"] ucMn[^Zħi7'\UA4/y5o1@>i RѱY߸kг-4ܫYK:ipzFm,lU R) 6ЎdItWxa ~ ^Ϯi. DPRrI P:ބ^P}3Bl퇃aq GM+D"Y%r믺+;ZHnB\[SkѴ9lL;[_ג! =طV'QH<@787-pgZ \Z^+.c 9xY;pjYdHAۦݱg^lK jzm.zIoe%sF YD |оvhDT^XEdpKmNC*twe>[ FwĎ~@gk[8jlT>*Պi'l6a%"N(ƃ}J2& ǒ;aSr-f;̐ؕƶ+4d(6FIl&cy^ vEM)qF8.ຏrO&+Jx&MsRMJU * 67VOsi4 6(pƗ0k(Zp#0;\ʵ 5D۾"{jxhGBNEܶ6]4Xr'y̜80g|:]FUu Z\ [;a־jZu S2ZSG Ro~_֚ DO(C %^ mɄ yO8#bpP 9&Fnlb^ r XցNduM2kY{ 'V,_w&S @![Q bp(Jh/ [,qq{HB5>6\;d|W!~;]tgǽ"MYDfvK[3!'[!bqu9%oZ5uǼ6qaf5= wj-.1B# Iou*Zg5? TZC ]II ^* 6F| NC(xp6~0BV_T֤&,G6mЅk;Ng4[5YRu6 0urӶԣT!=&-\kQ| /<31<ڠ *}LNicHTk]nE PN#>J ̞7X7^W5OQH}"!z؛ۏș^TLڑGϛg L5%H\ ٴ1Q}R99?I r ;>T DNjʵb<]F vWM}8lXKwP+;o/DZOw%k1]SLe*qExDBS تhL{ 0-:AZ]FKMF92BNkmq M5wGjuS+c 9=);opS.> nGo7OrB&Db4aKx%Jr-;֨(X(JxDQr?kg~m|e# GR|W !9sVa sC82 ^w-dXe\m__&DqyVWKAcBICġbI( 69G OhY( <(@cOWwK86 *?EcGy5s"c D|0p>x}Mi 3߫[c/}0[ &9CO%P!'fM@_3k7}ZٮeH2.3 .kZVv(⣣y!%q4 yc!Vû;@ g'+#:RH(%\70| CB b/g(>k Ll(7&X rMIE@^ |e|TłFnkݖXZQ +y}^@eT 6DA꽂T+LWg'O:''x}C"y³ez863ѻ^f:B+%8KD? تR![ub娟7,Vs%v׳ }ccÂmro mtt4[_?7thB+47!v oIwK d r% 9f32A/_|ZrM+G GŃtE2݊UKBș^VҋH'6FtP<i#XK%6ǨAt{y -h--?aC%VJ= @(B 9]fʆ4yvF9cK ؠvh @D :&O96ޝR.G^X;bP?H[M}5^N,Iѿmi Ժ'Y-@F06\pNj;CdZi?#SLܨr ^AjsVQrNu BHgд\Pxی H3yJK_Y>w90y[Ʀޑ)rZP\P&מNx(1qr{SPg]Oyf tl^.,_SӖPo 5uww+F6OIw-VqDť ".dlx %D? +27C5iHĪLS +i%KK oVsED d?a'Ti/c*2I U&DۍUZ" q Ҋֳyg Y2 oО?o^ ,Ztyl:2ߊA5ϡ)Csm#tx@^v#2m+ A/uXD W;=ݔ\ҡ[snZ#wK6P/2 Ϡp= 6+W_7=5. {9 }!?iC!V+} n7E731o!yMvқYG^Y3Cx o*nq-(Z@8|3zH[C:G5CT4 ;{Ҹ B=rc|aU;T_|"؈_,G~F'le 3% 9 FX)y!w.ޤT l\il,j(?lhp t7 8^ŢT 3{] *H꼁MLTCs.'wW<=RvDI"/l /]S?B5lQ.0eRHx,d{kޘHl|I-fWuv8~WӨo5@a!Eo=蝨VVEqa i]+rO&Ӟ%Mpu9&CQh2k6/Ѥ\N ' Qngkg-Pi -;pI ggP:Ajh!TKf~<^R퐯/y; xνm@b%l[iQ[0H K ס Zg5iH!b ؈ 2wjR PڐФدLM1&Wšr׃>@h'g5zxPZni;*Iqr~z6d{?̂!{iŽBH.b O E>EbFP<ϖ7svFd{Ҳp-FyVoyP1iKF6&ƪwq1b73 bXJuċ[j. 37G*2V/,@XC#qX\8=v6C \'nEoyG^cEQ:a?#JMfׯ<+fBr T[]=4YdPCc{ 阱Ќ8xmww]!GvaxD~>[Twy2fS3Vb,N4=t{*5jR0z ">0j KAGky8O(:ao92D^Bhu|9Q%Mq@wd+QBǔHm(I{ }X#vvq8p+B rPQR11:Z yIFtުM-[/vdGOVRnlI% d+@9/dAM5K< Ώ'nw]CDL@,&ɵP &fumh: ISk4M;IF8ǼjgP[N H l#c (/|@am2DLun%D6=;>- ~F&__i}"מң|g@x KZ\ <>ɨdPwl[䳨? !Zvaϡa8k8M@og6u4n=鈜'\6AF69.ñ.i 0H)6&CD hb^}Xh_sQm??ͧ P>/nj)قrhtYc ŽQ\+1-bcwQQp8N&Ɂ Ir\-'TO9SE62>~(϶̡_Zlrov0UjņU [킭@4ǽ k\LHɵgNcLN.! 0lƁx 9"9AnL 4kã+(&ٴp?(^YlAy̬:O&x4Dá MQSΎ>~|<8= "6"{tח"v 6؉ƇQ6 ޥ J+fϏ(6:Q ^ !j7@~1T%rk&x ״*jPڂCZrʯ\6KՑe9Lvb|bc)*7_ cÍ]?~TX3B tˬ+ ]?[|zM Jd5,[6 <lB쎯9Vlx y ;[PTwt+nƻ/ (] SU/K /RWT!͘XE *%!j A+7 7=İ1r\Ll*n "}Zf}f@+J[K>4 Av !(ю p;pч}28|[kd+~*E7ʮcWSbw/5Օ˥RnYF>9sHlL"=sdeڣlY: bY41z~P> Z%6~٣qQM6)ظ1xAI歇 TE2T/=FEȩeɈHCM{[>ڷexL,Vfl s)*( %OxEl1a7t]! gQЧ .o7ЂI'g I4hvhk#_[N#ɴOvrir# WhDzIݟ */z ۅ}\OJ .>>;7%RPi6'ȯTzPGmz;~S "k&DkP;s_#!nٕ8"ZC- lx?ZeΒ|=0D˴LS^fdLӁy6š .d;y Esim3 }=H^5O+J屢F[?wnˤRJ/T :" 7@^;gKmtS5lZ3Oc&ƥ+ȴJpA/[MF״L3e捳 tln}r⇻Ļ ٱ庣 VnavliFT?[ǎYAhK5ڂKPk,%fGA-:FҨw k?Ɣ H- X1Noʮ6oͶn6~A)i* lz@Yz:uAK_(}ŧeS J97SnvV6Uy&ֻ6] QTOΖ<#? T!#I.&ǨInGãL<)Y}+!v]0if|퉈2VλdH ᮄ/ZpR]iKK\ߏ)T&vRiEn<?}dI([B ?jHWFATQg-ϊRMj AH~C2&6Qִ at,=¬R\Gz D_ƧRn: L/Q2M+qV-]v?Fqp҉H w Ȝ:+Gm#^r6G=tm%vh Nr~/d&zb-5?KW|_[L ##LSaqTёA F:v!'W@v8 ,=lܞ {M^Pf/}-xE\CIVʵ]=@b +5_wYh2J:-,^';FF~ 6/2ÕNR֖fk}T̠S2p_6NJ1dH4܋6;NN]ɩB@m6d8 |MprKɵ[Vq #^KE^HL_##kleZ[YTc_LGGbEi0zY?tH:"gk.Qy ;?ZhZ!m&~hXxj'lhm-LceN+; TT_.DY!N'P_&)4Uk'5s|"tΙ@7[jyse6M됎~:H!/1TʧJ?lV㥱l*}QWy\Xlnݓ+W>}f-ͤYUKմYq0 Cs5"]7Ou\eSgјWl*l%تFٍ;{QOAHMZV5oF%dԯWJ@ ε &%AtN@ZPiOr:ljOT5OVN5 6G1w{j2Vӻ tV_|>@6[H > 4>l^*ovvI ' h@rv-p^ B+}3S簧UsڷQ.{Aƈ5nBI)Ů Hr7 'kj4v8 =^K{d.. l, ^D8s<J>e|kRsˍhNs@^Vf_.p15 T߳۠. [6Hڣ:GO#P SLԂz0kkx{(,Y>擵Vss|C9> 6N5{{BsҸfb 'gγc~3K+ =ə 6 x4;9fRhP 6qh 5S'HxtY5&< / 6a-~Y@P1ʵTec.TK\JGPZ)ctAbD3t6gt,MvW6VMwKuNk!Y PO/XqΌB.MsX.'ʬ݂.L!Y( zwQȵ1="9bmU;J{Rpoa]nĶ:ym kpG刚Rl^Q,@6yvb0 @;F_~;T ؘ*ֽA;xC?8}hNSD'\( 7A%?>\3np~hLx(*IP|j]V>/<lCeG*r k챒> +ώdP(g+bk民ɥ_/ ߾WAH?8m2SSe^SPQ\Ndf=36 ۦ' MQ!.7]GYk B]Yl5S\(Oo Q/}X }<*?97;my;㫬 "/fމkCfSs۴R/q*ZܞA]M97M"-׀ ?rf0CC@DNs3[ui<婨r ̰}uΑ2R1;5e* ˬ-aMvJfSYQB̧pF{zukko =:э)9Kp)SEk/} Hu6}ߨ < ʲl&\Kzpm2 2KF@8Xӝ #vv>3mMj:k] F47Ef,>LlmSĆI;& e8Dȡ66 } lg[o~ڃg6IJH8~!6Uam9uAGK=Ad= |{G"K>7 &ثN@,J!Lv |^!:{BDɔ?eՠ̗[',)?@GD ZMn%= [a7C zW5;6zlޡ2N?a{:wo3;OJDSݤ31>,VB|YsG䂍=.PRH|va '\i-"r-U&z6X\9CQ5Ne_r w_)&ssy*_z8yCkƗ+ZHӱs8 p/̞ Wu 2(Oj{-<pՠdyYEYWy ~y ԅY DOZ!/52 Wz}5|C# {{x 6BÂk]2eL3E iM oV|wQ&?1QSj:xd +-؋Kjh m z~ 5Q 4(oIT/Igri gı/"2v7 ,QA1órIȵ_.ycT>(Z[h18SRֿ <I~WՀe\<~I: O 14ڞf h[ KZshd.6L \c]4͠@t#vmИI2JrVk}nET w[#lf4s̳ ut1&Y'RKq]XܒK %}ѳU9GE 6UD)/s1&q=xqz;IGuEZuMʲ5Q65&a =Vr es rFF}pP,{r:@.XܙQHƹ8&}&3v6D*;4_moS㧙m'rȵ2z*^kVQTkaVe:Ti6gߛp~ R:0Q8BH2נ}ˌ:%: 6>z- CIz iwqZA-.^NJCK먽ot [+@|5tťC?(ĂmWT:+>]Co8 C:}Vҗ/nޅ~XF%ؘ^ xý7*.|@"k \B Aڱ7.U_n&DUS*գM@QĂ [ >_Ӳe LaxemM7ΌB H_RMIDؘ^d 6"܃"By!W*RsT>DA(+I,־D8ƪ 6 n=V1Bf @e .\g%2B*X!Z.I lNcz- sߨ_HerT"^wCS ;rF e9B{w d'~-2 19K}Gwɽ k> p3ʼnrPal"MA]}ϪC wMB'XaQN{{L{ǻL~r hV' x10W 6ajP\N4WCg}XOO!78Vo&徻^@ #N+99 {xA/dy9ˠ3 &T)#%ob"V\[2Fe1c6ABEVJڥmrl1w=Z␢y- (CEL;nIl0e d_X|TnNĦ/⒤?N Zg WH 1m AEsoX.c%WT xkq=.mi(X&Z vEP,QntKsD[{x: l'(pXkO\xG|kdYc]V&9B] 'xO8_uRU7+D=DE 5)rdq 4BXs˂5{1Vʼdx7#5dԟϺ745 [~w߯L-1g7\:0<k- \n R~wںC k)G>ػ̈L][L +B-kJdL nyD0܂mgIl [}OkZVYl @0[g\fE=L&peAkS Do] t.#6|yʔ;l h 55lۙ# ó z&F@ѕ2{Zo}r Y@nRiJDϗH/ڐ=x 5Ig <]NZ{\yok>=u-#{ a;XQAbyh?6y;Qx5 wF0S6fxf [Itҳݲy[ClKRDabuΜlҥI6Իlvuy=; 5vv': I(3H, I< !5y_[ MrxCȵʒ2h?{&91PܳU=,2 4< W={;M *7721@U xC(ImI7j[6y_rY&o D :7讃|Lŭ%o/r~V}*a"N L4 L6&/-ã kVIl˨C)q7P )[c <] 6Y>1q{-k_[7yZE D#%C扟ŝ aĸud v7& }ܝt[̊SA lJ1D'AKI W<+ \+ :Ii")"FRszSWuk_GcDNJ+e'.YderW+1MqQNkz-tlvKizk|)k .p-&*KR #-|r:>dGcf"ѲXA];bO7mh~+ n1a\( + ָ 1߅~(JAtzYCi0x?US Eݍum]r#¥Vi\JXei--R J Â!sEq>t07 W//B>XtNlhv׆W#|}hXJV ףQwc]YG5Zh }: w~<*\x( l9Pe4b f b2Ǖ9{~N< %aau_4PU,E*QJOX9@I .NuCu^Srm>TRUQ "2hNZ~N!Z L3.yw5|̐%PT!H)i\(LCUo0ne5ހ +\.@p\tDo՝ Z5,FZ{ޏ7t =^H5тvcsKe9nݾՉ;CW@kI55cd[p- DoNsHQs29*LHP8, ڇ 6v܈^Ĺ{ |D *6*7 P= yOtN]S} wx؊6Lr0W.fnjC;gZQh r=k]x ־ gVF c"~uPgj]ה\#@+R\[H 4A51>mTnz-ґ簌^TT#\"Q TCvLL)(l;8I|Q nM8Q )mg; Ff̋f~휔 >وR1Nw'xZOi<)m&-p7 \rb-F8( :j1!otqGu-@jo]9݀C\ Bw pQXo8z 5q֬ k-ZUHB\Gp#&r5~.]IU:U.]bV! Z :Ve\3H"פfsħ< uS +$$/MsNlg?Qt\kH:٩k3btֵŤY:,)s_%R'? W7B]hW@+ ځN6P*A& IoBrNk2|H(6~{ k5@Mw#5Pk|;HVr/͚(qϸﱳ 25((Nf lT%f|Afw> s37n&qAanDw[#^#z%j8'wb9*([> +%54a!78{ 1 >6?YY>"6lrRp4e o0)7!Z"R u yLkk@͇- E kwBA p:kh+J I܇\:ϽfL4N.Ѝ5Y Ƞ"IwJѸP=C9=^{oN?ˡ@4dYZiQ#J9QOĘh\/+ 6T'ذ㒯',fpǔ-I"Q-i. =7iuDQ>OZW|C} H*PLJ^ yQsH}BYzdL^5e]s>O{V@^zDL&W-v7Yz(̑e:BOw'y!Sō0vpT]o?co-38Ҝ_~mKDP7a %לHM odxJ3 v x;x 6!KX >:2}\ ZOy_vC}Փ:6-/V {d{Do lgogJHDg{/rŞ9#LI(w 9FajRB(t5t[fhυe ͓+u5 #P =Nr9@%͏Q#*N깈Lwg*Gcҗҿ ydEႍ ^|rw9˸ jb E\I!iT"+s\@i "VZclrR! Kű O>L[~5[I iR qmX5 zW=ʮ|5 ?,aC+yC7 ̠OE67s 6>zd+S?ĝWI!Vmc~Q>@JH!?#3̣3xy8/:9I9a?8"H,n5 ~ѫ DQKz;M"3J=%ؾ.k.N",9N%RɤN f_Esu߭Ge NXi 2YCդ k&X LIzZʀOLlm EkooVMs}@w5>> 6v_x[\2 g%לrYhV0<-":Bd-Vb\ L ]4q C|+U5x8E.?2im wnix͘FÔ}hO!ʼnmv۵ӶӼ+k. ژĆx#I"֤#ƇAɉKAR5qGg%'n YuﴐSkꁏi6%ϗR"199:c(H7% o&.[PuoY fZe=*r-IIjLyiTI[kR>@!aGlmw XEp* l Q0]0na9.Uܷ8ǽ7Vk)G6J3,9 /io5Q(\對O|:+A E+faa_y)c1=9^ ƔNK(\Ol-w!ʘ.z 8ϒ F!ѫA5rU \y+Az J \qL^CpxvBǭ[/ʼ&uX0𭑌˰':tZLxl֑kX~V[ X JXD{˨GLXqk Vb l7nZ@iS?D +ZKF릿9 *86pB\*)I(-\K?FΖ#~;q6Mg=OI=*)#dc O<-G\W"(3ٍi){貝N2Ym5"?Un2FO6t[A9Ih]L| 1ڛ0R&X9܇ ) xpa Ӥ+Mz z?p& {l7" AG Ǝ*l* Da+>MxMh6" VCfLnrP\rmd):] 61&X4]IJ;[wu@4?E*QF!śb{}=9# |k蜠}We^kaz.J*Y֫He~e(68kIԎpv]&i= !9QF5T ?ib\kC 䚬3&ho ud5ԇ?ܪ)tԅ #Vf=&86Ph?Bazޚ Xz.CgqM) g<*,9 {CaKx曮3 6b?XލNuO #J(GZ<˭* Qx{h^v61!<>RlFeZ3 Qkr2;NY{}ꆏhKP#; d;9' ,Wj=kZ X4-MmAPWg.W cwOϟ? ,bDaM5mY8V2EIjb pX~ǣVڼSv&r%Z ^ω6+ɊBHM9plW&Gh QhiV5r'bKG\YkHOf Sqw3=igp <{Н.Gu'.jiU|Dp Qx"د=qde~, % d) W r-@E#.Xgdsl-'0?qg lt5THz ;D[gVcklp'0rlgُ2loKgbSPpʰ Q1/׃ 0n%?! ugD uTQj295#sRak&iTǜu[d3Жw I&K OHY lSo>m )CI"0*;ɓKb\,Q qkڃx>RDZV6PEk%|^ӹS +yA\!#t6[9̷,߿ ~} l oG1Z2J@&̦jijxUۡby*{HEsvDFdH^Z Kf/lJ^SA-O4(^^ Y*?\u=zU,-L@5g1 mrkjA˒n 8/y'QFތ#h'- ~fqtA Mr2mJZ=NLEޏ7>0?>3ۏz| 6HB=iiDU&qp:W9gn#E z3adtKc+0N+Bݎ 2fw rLbBTO &pgk 4ٿ]B Hyo>lck.y C^t;ngye00-v Ɲ7쾟@frx Z~"ZGa='Qq b'Tyɑ ](ע|kƕK}NM,k/6!(,P}sx0oḌl5bE%f+rW˛XD|8Py007NIkSzM>ZYcƍ鎈Qd \s EY@đ]AOJ6tWCvcϺk2$$G,B%VIIYg0x-'[cޖ_d ;Wrw;m=~u^i>K a{Dou\nrIӎ}< {LMщZsr-jC K#|?Ȣl |RxBv#DR BZBۓ lū}qzl_1D! 4Fȅ(-YLvCLَ2H!Mp%G}vVdm2w]d {n۷o_߫'홈qhx椬ūB6jTnYwLS#ӴP|TC|~:l3 6γ çȊFwFz쥠UG5Ib qI3I}0 XolqI .Rv'%!,H 6,eG?"G"خE,:J6p#CRuH6I?ItlcX %hWo)38ab&Ā #5%~WXz-Nw5Ƃ0ǐmN:5u2OᇎaLj?;qg)lhOdj!K1sKSؚ ,VEY e khL}I&7C vԢ?v }MM"\KNğhI?]q6 lBH~ǽN4RYܓw:" UD ݈~ &¬\zcB.D_Ӻ§x %*|r 5X;CMk 6b;D_I3 X^c@ ?ll7#2YƼ>=g[G vTkǽQH|EYCfQSEYH6;щ+H}%+=s1fD+QYo7q|ݻ ArkZ< 9xNEGD~!=~U}5'miN2u+W[FTO 6 {6QfMI^ {i8#M\'gۨ:ST^SqOd2?,,.d_עX!<".<23ѾA폘3oFLNOT'ƃҨ Sp.uK.pEd+HS]c&=|5bL&6ʡxQT wOhL 6 NF;ѐM;(2(fM k- 94^ d%<4RPܷ8b'b .s 2cC{g'DB 3Ua, б;wN6QcsSL|Qo =Z-! *;J«_Y©Jn cd?[(:aNC-cIn3H" VdY@Ă;NJ| 6aDڍlcJ8dմ#NW <őŶ89kRĻqM"E# }Nc8\8;ͧ?;\ZGFaXG d% JAܝnw_i-mk-e=TjSm3"0keU^~p; B *X?lXZzDzͻˠ) 8s 裒1_d Keq!a B\+ 6k#,bOO<<kq,Z(LEMfr~VE4TLrF>lh bMk.,EȵTjzHGbt3H;Cxr/iFzF:V# :TխpKɻ1 ƦIEX^z|TE54*K8(?_ukZ RǁM H'FpC ڎAuU 4%yl,C"BiڱjgA)Xs?[V#V Fq 62stl K\0K)B ,Hrgx| s,b +1@mx!(gU>Uk,@jY]&Ri47kqN1¡4.|2Y j7-XF T: QO#q'-*.ˇPg*^.MH2?~ 31:5K!D8₼ yy#yB6 k(tz-e*pybpK2O*C8I Vu^ׯG8rM ğ8M'u!BF P?s'&W ĤeXE ܐYR xp8#fK19 t6~l D#Opvr/k|獙lCfܟȴGQA~(wKB5q(ggYlI4_B_OreV7^q9xSٴvc|gF 'ҍs%t2j+O7kN !^;(>i{2 V)%Cڽ1 Ρx9n߭[W37:"<߅%ylr Ybƕ# #z Ⱦ } 朁 .OV d! neݳLģ{\RGwd銯e 7И&9bNa|b(3OI1bJ4%h.rd=H'Wd *4Wnq?_KR9TtR)s{2Rx 6FEr,,kaC-Ad?X ݮ&!fx=Ă"e#{dh*eQS2UgZ+ʅMbЫH-8݈b7 wSw{sBpר4Q dk 6b^ y >yX ,f(݀* @+˳eq,ʲe {cGe]:mF,nu8iZXu vI#eexf_ܴuWd:2U63;McGؠ{l*h۶}үtSe68&ʰƏZ ljوDj^l.D䚀^GyE*++ 6PB)kS+5:\%^{]1s61;Mv'tqN* 2qEFԂ ƐE;lwRʼ" d"ר>[ڒg:ˊ ʚ 60@s S?Y ,x]<c|gM6WlWRZ;tq{\p bP> F֯r<Ŀ ӫʾX@ACZY. >l<́+ ú;PXr?.mQH : =q rWoJ^ kcy%բAFJ Pfa5鸳"^dzi IYzѿU@ pE +3ܦj+;|Mfq)3gJVFLۆ>S\FmgܜtkĒ-P.xι.w:p.ZD@vwIst ekOQr_>wvRDgG9"ѫFw|>gv_u^X6Uj0}+^ VdM2Uj\Y8ke {HGcq*j\*(J. mqܽ~nF, x']-BdkTWni9*D,f 6Wx MiW}eZYgݖ.J~ekS Z 2jk)0Wx)I B\{uB.W}jKbXxKƓk%k)(C5Qle ;3(#3ö.R_ wk(Ď u5{ &[n=x𠳳>+n3 sHe^cfo(Z莾&ynJ deZ sCǫ kg*hP@&V&GRm^ݹsrplX>1DZ<@R@#Gfޒl>&:5b7\YyqzŚVܶ k P!ID ]9.7Nj.t܉ݾ:Rftb i3 ~ >\U<=ǚ=MV& Le(Mǔl pal+:Ou,"fzYj1^˳jQqc3Jg3&E[gmh hʾA% G+w < ߩEX{Uy?%Hy Ǔg T i+L@=3X9z̩r.NۆTz[1K zNF_N#-!z۬F=ykM j*>rXZȵʊI>?c9EZ0Z>ʙ ^mQ2R/OoOף.T.LHbx;Rf51yTH\'pf?Gf9bE7ɑkWp*3C/??>;'tg3V|DŰ&}Clz\LrJ?&D5I*/GBށ[w▃ .}/WLjq 2/K_?)ƙDܧ1 \2?%䉢 xE+JK oPkV=߱?_4nk P ץ+{Wu5)y9c~W5l9o++}:_Tjqg0ٔdظuh ᵐ ݰ yAf1gQ!p֔(OF*\TG&= ]2QƓ]6zlYB/5GJ;J W4 [3 "Zb q]8:߿Ujfm=oCR43wł5=B==Ag J/GZMUcVCdlZE;TllDq"~#D uOݬIP!Pr/ jÃAqowOh4 ŝ 3E4_M=0x w.LHP)rmlG\Qz=Xux@^ R'~#//wbmD։)Ehܑ4VK9x3(g)+܁D41n2~5up L }ȼZ8 rڼJ"Y[@( 1]dhKϮG\ SbNԴҼ+IEf-T57OʫU coȵ1ȱ' %B*Htrlk[VBQ]NeWllPT- 45QE[Y~ñU=\u:m;gxͩ&1d4r-eb疰curKV>@Zec2?;Ww 赲YV~|F!j_㯭 TޞLAʾ9D SUĈyoY[~g3 w AuS_MDʵJ_W-)df>nGH\U&ekQg*G;NKUC{) tD|(;dLjCW\'b|燴( H}S_*kX]*l,h4\GmO- on' ~eϦ#EZPR0w5ktqͧ^;FMc#+?^vjaKcx E/]芽 }zLLVpVQ̮K#ONm ZnFxg,"Z 訌؉a d%ߗ:Џ˱m=*f*l[EW 5^Ęk)ΏRkG^ OSj0Va>TM~^U,7\xTh" =2r];_LIf=hAK䱶?)40_҄n :,RjARwDa] ,fGFޗJ+; >5G.2 {!4[WЖ뵪bЮv^t@*Gb3/lzk( t Z=gj VAkZtŤ-㳞 aVk)HmdA%eDZ1zdqM6o(Ĵ:U 1^ (~yqKi?Ϯ X l0j6svA++Z3ɰtV+)SU SNǯs} H=OadEb](g0q2m8 }mJŎZr-*zYyaҸ73&6F ~lCv*'8kS 6zrF([W(͉_gta;N_K>=i76;c9HK4mZS oW=i5mu k[SE^gPXҚZ}kIlO2NacW?4G^%ɵdGAD.ظ萟 ZɎM2x1 %;[8%tG0+UOQvj ~!\ɮUE8Tz]2>LlqqZE@Ca[C+_EaL7=.-@fwA VE-j3۪MQh:hX l4*v#-+(BVg*ܨ+⭦ڞioGI72m6E7;->ZRUq̮a5; T>28wL}ɖ]Q1OkEѽ7mLw͞=Zqa% jRYZSZoVݦڛ+ x4[ w kg\s/zLUbʵws R{EQ8Jm1॥^ &D#ߚ}b uVnX]r^+iD|跷Q HJ(rM笿l9{yu&RGaطam l!5c" o zr *V,}X_\7'%v@dʺ'O&_k;^<^+6!XS+@̙](hfeoaZ -^k[2^ QArNىH AE>GaDf&ݟxO,&yiKHAvJd N,m8AI!g|)Y9'*x٤~6/P4v}b8RU8Rm8Ӈ(V jAD( @,O CWdfX#6c4&z;M.'kݪw Km 6;8dm@^b/鷶b uHdTpgY4tg:_=Cغa՚hEyMF} x]>sWm[CTE rřL7f=k0GmK &v܊#Ԥ&_G]cD9٥H=y+Y t"/rjUΠ=BqnNmKNFn+=ϡ*{^yla ˗ Il/ߵ ۗ; ʠ>lSQ6q& ? Ml@*ni:NlyuѧmS][B4שּׁ_;4^eUck5љd;*@Gkyv4A'# 1ȸc7i!קЛ\cn jBznwpYC:y{|H5օ-u|.lrz@ز|kϡ]*hpن#^<r]Ł;^OfFH. Ӊfΐqk8}d 8+A~}t TE p@Y -M dF07a趰Ӎ+ժ=އ }su{Qa+iȺô .r̅L'bVD>y ^klr#lֳ뵊m} 6JTvxbs _d[Td̻K_L jUnG>*Ql(Q牊䚅퀪7un_70S֔rh 4UVDlA q1پhxGĂzV KGuN&66xZ'߃FM]N:jUrLc~a3:bmLq<PsE C#/)7>=X"̗vn7YYJbanj 1QD۬hf=I^i;}EFkZC&^p0ɵ=quUs<}zb8#jU: OVع?{oƵ҈)ɴX=n@ы K_0EҤ#jl KI)pt^4m},6Ykػ6)]6v}k5AɃ堎NgPlj.vV u[@lM)O>-'Ro;5A#5Y0wOL+˴2*.~7L(V I,PN\l\#׆ d:mbeVK:5 06%8m~u nK<; )ۏ'=aLUܒ;Rdc 6nq #mtRDiť|7cm\xb:5q3Nc5gCU4aKٝi4k6 :8EZEaCu!:~RɠIT ȵ/0BMmo%sǨW:RԏH9?ufR>J. bDϱu =.n&iQ0s(4lcZ;1K' 6xc:99kRMl~K:a:Nû[ɋST'?b5ٟvŦȵ0:R kȔTdc2p 4llwkD/+d0z%{ksO%W%X&f+).^FіկǥK9? 6BTi>d..(#57\/U}hbSP'^-10mAaM .XK)ᐑƮkPP˵Ͷio ɛ2gGS5X>>'oƛ+m,b˵^!i 63ZmJIYtQj''GGʼ|5^hE]ّ* ~x[L.ZhN%oDD=rVUS͂RL]h_Z.έGM{-cq&' ƛVg+Z.Vb˽y4;frIv +Nkmإ= }r}[,Ȼ˦s3o hZ6| t5 [RN]f}Y%EmlkvdZǥ 9?/' MôMjAOG\| rI1˖EanU1DJס4v{(r-7 V=4G^s?f!7pkіW&s.F 뛗 6#h u\2teP3*.XǺ-a/H1/'6*.tERҜHuwrȺ=ty8VE.2;"פY&_]Ԯ[WOb8,Nu1 lA C> ;u &Y5{ulӍRCf*Ҫ&^{|>?FuO!]kp@haZFl^~Vu1Μkzf 9i 悘wOme:QzyʫщyNdiȵWlK+侠*sl us~ Kl= {&&MfT'^sa6/5YYuBnPz ₴sALXU\l9ryE_ LR(r=ꮤl)y2tWQ7x%.8SQG2YF}&Xr}MUEjҏegZ}d"4wۦNgL^MZr)v˜m'J^%r[=/ĝMĊms:Bu4˖u4j9?=Q l[lS kNUʋ2?ϵ.PZNRdfR'}nM>3;T3mOZٷiO 6wF/s."/h{BfZdx_> "@vB(FA+bpɪekh渏!uM7 x}[נ9]]si"ywrbFym- ,.oN.N fI}kXM̏>&ē'-/=Ӗ7&KvF &y>uxbNKʋ"M g!Cvy[lA{jWX'Y&hݸ rORQ-j2<iZ^3 J556 S:T9Άv6" fWVW<sJlFڡarW\;.Tqĥg'kAuCw|竟i\RnVנ45'.X䁔5Ugטurk?'?alSV.;#MA\ Fud+vW_E˵KĮMs14vyx2de**B[yb y|+y{( rV5Y͉Va)FuiVV2kz#ZɵEa s4-4S;Iy,\z2D/wVuv)7nK{y vKhk}k0s& 4քtTZJd|P((})*,M@{~OP^M?wBp:*ˎo-yQEUl bu@N Lu3J 2gRòk{[JĖ5El1z6-MkS7,Y߱6}_澽MQY-@wA)uIߏy8LccL q+@cT-kF|B//ZX/ӘU-lnڠ\@Jma #h M6Nq * [iKKXM6"roHYF5XZL~]Kfגb=8FsScy)t2~ړU~֟| (_Gu7쉞O>z>uZq}6 NϾ lJ[h~DƠ҂ﵵM0b: 6GY-zl_,mל"Qb+mMQ^Zqx5llSщɧjK>|ƍsblJPsNe4;ȷe} 3NQܻBț[b94"dnԂ -XFKS SV\onFrRƮ~8?شذebԯ&,P@MnnݭC,|k;r?,ōb\jiZr &s{X 㤷46ob|]\q ,Ujo4Y>A_4tA5 SU<)oBT߄74="Zgj*j"QNdCצ wӐ17iɵ-|S<lz)*\uzdTDe4)r e?& Ҥ[rˊMը%b Hr Y_ސdN뷫=!7SUl>%;Ea(5[搅Ĥ( ǴT_dbT>3Er}g"b k(UǍ[k^lc 6 ~1UM]egPopu1ޯL63)+o/& j /ze*jWʊm\q_k\iCْO>ܳ(sx\7H먱7ŔQz#Vl' ؏NezvlBZՌk-ږlA/2H"Sf-ݣd}l%qh11zRNM詜i%ੴz .|ɞo |>Gl :X+ŕCA)O&5ut[aMna*4jTko[&Ķ1[--kd& Z<[ď˃-?T>鿒h I ]×[Ƹ=ҹp%--TGA<@_QR fn'3u q^ȋ R_IK/yV5~4Η5B"d;ȵ%BD* >ZL&J=N[1&s=ʿV֖P8ĦFDt]#v#]bTg/s)y8TEJa ߭h=aR kж/{ Yof}Jh+s[5Tq; GɅɸ t#\J;zLז|StV*ż{:Yv- UO_(%Id?_#T(GI_|+V9U{_n ^ ^v c[Mx;cWo{}xOrmmQz=rO,T js7&J+55HTJ[?EweCu1-(N쪁| H{ώ ۦ*_(V35|ECIwmcuکQK7&fgYWI t' PB3,^ Ӄu3Ld MQ;/Hy67'us [qU3-pb/P;tVy;YSG/: ԧg3lv HJ:mT|f~Z'j{na;囇GI,\t' {JĤṁķb| 2f;Nm):ĉal{O')* 6K|ׇ\oZ'@4E;:̆%jʄb6 ,?KD>/0?lcg6 FB\_hНf;ޗOGZ&{kHz7.K8Hz; \f PM Y/=H]㵣2h "i( =v &|4x!n\Yh}]Ko*Q')Ԭ<҅%=R,iP0 rkc ԗGظۘͨ%.6>vсރ]cGhh䶆&L<ݩkWH{nr_дp!y䱎o)*Jv|L=a'6n:Θ tE"+z-㯂,t\\Dd NQ9>6",帾uӻzߦ .KӼZrSLs ۭ ݏ5kvgN*n8j 3/.tI^̎ vo6j :g|i"rkߪ4mw*Kwс c]bĠtz Wl\sʵJ*؎'(8\=r1w { %W{J^e kosǸRg UFFUCqu?F )եۢ;m٤2YۃJ&.:[@FC\m j[yiYV#H,H 8F*ޔ'+ Ȅ?*M܆U.?a&F̄{4g5rYսimer}|QȲUµJHЈ;j5pM80z(++?scCZ@)UWCSj.CI^i\ eV=z*'vh2(H㠤t{9vrWm&xNL4UHB<1f}wT)7VbA6+E=.'ؤ^<W/c7G;>-ț}s5S3fkQУuX* 1ǵ?W H3x;ќ"8w-]& ?GY o(6y50: B5qA iyʱȵHe%jۏcF #N/G(+3£_Ҵ| Օ&JĆ+w\UFCsCFqx~Yx7ydqj*~O6DsMуe"DezqpDIcȝSB/)6VEVm]8ϸ;٣l)? )wN4dnIUt #6C: <{1J+[M /VƧɝ?2s7nbc /:+n&h$$hZԘߜTQ3Fkum^BELsws.U8 eYFBx~;2cFȔ]X!D fBa.;)-yOs60G㞠kIxJM CހnzRM%єStWH96wߗ"˵:Q},1^9cNq?.؟=( 6vil?o5O~CUM O | =+Euo9e0DAeW.j,gD{Bhvg:Wz ;t8g\#E*z@ .6r/B>6bYS̍4 WQg-՟GvslrFi7JZyl3">3Csj0߸T "HdDAhۙO>cc69Tx(th]ސ r"'ʺ~, 7 g[.r9Fm&Pzx\\w [_M*R/Jz ٿE[ {P~ \W&'uMkcʵZ1\A=_VzG5B+vR[VD*Ԉg\=/E& 0{ 7{C #VuXl:\aצ7N\rLh-(uMk *JG@"<fTt/|I _T;c ?N FBc@ 76am1BJo94{[YTMr/)ƚK@nve1tX.uEYRw)P nz b[<7m|dJ4͟cK1H" n]un/\=N*l:<ÖןZg4G96~G|Afǡ!u\l_8 .Xj .5F\X\q4;uQQv3t%V_k :6)6Я!fJT ٜٖ镟nEBETiБ'" _({Bd=ȠP)Uޜ;v%咢خ 06k04~.6DMe( ~ po\TfA! Tq7[U|3lKW4_2GxԕKZde ^&'M E K M( vIkꖞŦq-lr b6N|:yw|[H(܆ͣ4#v _-g/_t抹Qn-v0] ,cV\l1|@44%vՉNW h'ZJ299ɝV 8Krz羘b i>1;)%Wf8Þę QNSf@Ts3PfDaK,/ӒފJkqE'ZLݥ2dܡ@AxC'2k!כ٤Lݦ?xݡ(t ~Vt3% "5K̾ "Qܑ֬+0(#N ')X)>Sp 2ItS&>Hdlڗ_YB eŚ n)WZ J2¯+f( e2 (Zp- hx#O\3pJ*uECRW8 c%~LH ss< TMbbrDyHkDCꛊʵpj|%g%MQ&XzN9[Ta籃[e-R<aIQ˫?Q[ϻ!JP@燱QvF[l{8q(džk(xSSY>k[ K#K2wa [j@1%i-τ5n)C3z^|nv;>)I ,J_%gVlJ4calTZŘ k/3AX;P8EjrbE T'h[I~阶-{S< m=/Ar4_964F(y_W? S7V+gedz٠QJFK-O̲'fwCn&KxCkmSjGMm\l|)i*=A^2GWcqJG-Tbhn*At ^7< Ml6ʪl]ƹ 14YsX;j]siߔyNf p 2_cKA{+] O1NJ)| ww@nwՇ=p>~ᦕA4\gZbk'x{BW=& &(8By~*mU{5~]!>Y0i 'R龙5ӓY*JW5O>D5r'UOoEOG=nǵ JY/_9Ḷ=[LoCޮ,0ߡO1L iđ<7TsoV%|>bvV'>XF 1yc k-Vdˈ]bI_b &)W)PDO qbD}at@ދo- c]B^ۤ2ĝL뺅oas]ƻ p 4dn|vh*W3*#t%ُ5RiС T O+?N/@6}6pr-b JC%jVŨmk>Cd|V|J:^q !vUj8/=աǫ|6[k:g ~6 d"ڗߒ/_'^ɑ+Pk RV_g;ev)eGMZzU֧sŠowIo'-4Z6 7l\ƐMVn6/W-2J:fK6:MenPnnQ&BL9.WHTԕ|tFJ}eIq{E)t1kii#Lxj 7E;-/L){&7N7 ^yB#QȄ lcMr'p 2]~ @N+IG7;_ G['tS|;6E)_ kz^;4 z zcՁW ;.v0~3.ڪ5 , {d=K"qKȩa׀13I} K4 t=udI;9w y|OCybtbro|xۻبʵ\Gt{0! bovSsAY;2+pV-*I Ү >g.J|7dnNx.uJi0z ] ")Ki52g ]lTPS HwgtLjY}'kH ISo.j zȻcz- 8XImk4u".p7QeDN t9 kzfY8]#uD' .Ƚ/Y>d6k4َg'xlm.FY,[hEܓOK&o5*4{BNw~Nm|6ecMU'w]7em8k t5[٥({?pBn6_bv|)*L Ueآ)^;=>em"V˝fqu["we = F)fJw^Aj\'rɀ 5} ]}v,6x-1i{fRWuOtS B oyqvOGVо!Z^KkZ/j _,X{uS{{6j@vl9UY3-r)f:꼹_^gn 6q.Q Է9ûі.v̢\^q\YC赏Z :J 51 2aS\9w<ץKcOm d:ggb,MԻPَknwWD- юfU] Y 7J]Ϲцnrgb\aڢ5N@wk//8BꀔSL _l)}ech5V,ld?iNxٕY0 q{ f8Ѷ uH>; 3LL Ld*e|e[U_GqL䇶küIi|s2,۵6k v|Wp<Z ?I>q hQjy 5P5M}zqe(_ X-{ŕR=vcv՞(]3˵:kr9{mjW ]4yL";Gh hp~)ڡ yh\)7#DP !aڑVÿ]qWmS@R-wwtB5rI{hIʒn8 T ϫVbpEu@w0 Lʾ/2;H c.#|]Rg^D?Z Cs\3Jo94}sv.Mٛ 8mI⋷Jm kJJ҃q##z{a4xb#n\=}ǧvVU cu[ڗğ&m6d ^TdlqHc^Rf&˃ 6 @@.oݺ➂g]_[ Pj^ ZRǃ{B=hv=Ǝm7hvnY..Eu|=I<;wLV9wI%ȹ}4N?Q9s/pE Mn |DӬAIx;H8~6hF ,'*ZmKj 7vlu~o@ ￕmn[b+&ؤ^3te~q %Y^;.Z*dMq΄^k0q] yiU^S[g/No{rnz Tȋ&(YN]Un]T-w%GApgeQ|m,@W@?kj&*{Gzv^yl&{NZ Gm Q(B}X[R1R-^3V@@ :D b#VhHlAtEil[+γaLzyHFԶȎsӬ ӿE<;;ʱU u-@Xpjy:nf7,wc+A^ȵTeJm㼚 bkר/^lC$$-Fy:g'd ʱk2 ¶)0~-2QĢrGȵ\-)uKn<KRD亩,aK ; @9} =TKhQi 3v 1+\{t5hXgjp1T@)jh >j|"dӇj+R+^/G$ezfP\X]hFǿiXD )ȕ:F:Tq?ܒy]]ѝV jZcjgCaPkȞYWObrŅ #w]w7F9@ W%cnIxOgpfvHJYFZKU_W~&35vUd[ Lnafm2_wLbڔ^5NdܠurM:dA狇k7o.!oI >'KdVOZ%/ OWƾzɇ$B&JԆe [j*F UFhќ"#6tK8|ر߃ _"40y|JА"J ry@JYT4j H$T+I >T/ gի|US-lȊVik#lI%3xߩ 0Wbi(D mQ-, ; ʂ܄zm=w'mJ7pU+ R]l/:=T/>&$8DRwO6ײZxk\B>[T3,R7r + O~4_D kt{RS{cz'k w5Ƅ_DǞO%|hմYD]RGM hjm5 J(ox\#J?wnRAu-ߚUČܝ3f_2G;V**?ԺF'6k1휁V;Sl ;T\% ps &c@&%|D &|AK@F ~ԧ3r-5Y v|bIOrpyrQ:} ٫|eTf^bj^X χLe0k6 ^.'X)?-)rFC~ Дۗu5[7 б})+'/#_.lrsǒ[.|Y24&%Rbϵq ]bЉH:遾"c(f ȵV餩wѯpWרvCsw :1), 6Չ?OnLNyJ5rm1L ! ͫal- @3yFE˾nkmdLY,K]RЛE ;VKu;!J|)%zqc~}жA wruVמ(- +.kW>.Vk_ ^Xx2w̜+[wqx]ȄzDg4gvET;y)Wڶ(Yo| EU@ tbŻjoRkJmL[q'dU:C& hVq2)dE (?n֨mk Ѡ:mֲ14ȵ ڃ <-RWkV \ c2-""S27:Ǣh;=ͷcY۶:WK+ e&TM B'Ggb_k$[NnΌV e"Ğ4%;$*e1[_AY\X҅S OSZLʅEEBRW!: X_/ǹ{KԣwHmOˠYbmQ$ZDd"Z>ܮ K BY!/h *g 5bӪ "[OtaPN~^C|R3eUH r]rO&v5-\o*Jm8-lm~~&mB"d .>MiqԝS^ RILOʵTc1څ FiUrRy> %aSq1kĶ ] -i?Q:}/gz 7Vw^1')vSXd3ʳd3 e k3#WH6@W岻S=QJrZ7vFU%.fm;U^5TYLuL%xBMW|~2=(6@C6ӰO29[u< WXcl &F:mvbfO&Ť\*SSU᥄~t/Kh\ ~+ n]c ch6C_-p-&Fn mv6Wh*Oԑx F_W\_i<:iߵbMC:q:8?[фRcj; RۗCs1ڙP >>>55u|/~Pj%| 2t]}JC+^Mba){n vNo| ,uU~C>Nhy/n7oH lȤv?ڞ ѩ> *̜6uu6JXf[A_bhor]p>_ Aeݓb!o[\ HZݼ١D"t3.q/?Ey>k*?&(.K{Jrݶ 7^F0!|_!OJx0]rS"sʺMFU-tU~B[l"1Ѡ/<A({9gF+AlT =6˓C6gnr2pu($_m. ! **2u& ?$6N5l]잟Mfƶ gZOm fx_߭v#?6[Ub̪6BtF mY%;WFaU 4 LvK%QLMڶ D#Dh r- 'EGnqM%dK& ~@@}X\9v [>@y.H>s~ :4W=?O@ "sHlv:\w~;; :WSø Ժje'M YNɼ=yۻ64=2 ]KҏvD3pɣ?sɶ]O:}^kƫD#Ab] NG֚3PR7N]̰_K$3{mh(J>csd@wClU(͞ p?8kwҏ0]!ز!۹8 [3jl0 x LiIu7|-%Ś s5m cl[ x,ఢ''%܃lw7l RA𤃛kt_؇önYw9#S Pws/&6aQ'Bd V\l^۶LAlm(,V&wM6aBf"e~ϒmŦE]l4g\\:&(F?ʺ#w<߹y y3-ֿIyڔC9%0Ja7Ei ڠݰ#ZZz82pQm7㾋.A9iy wqiU' w$\6w uǙ2ZmoΛ5ONCf,|&"p&kԪ wэk'yTm!qPe) QPc=zbѺg7ҷ̧6&Ktr+Ǒmz1 B@˹^y[e⯊^K&wv[/܍/}th RԚ7MmPKM]eE^?kD;K\l]ycsaoRcqK ԧ ܰ϶ ? \nWt%.6&jsQXp]}#v\ #r|UyWc˽4i}]lHÉ6sMv'.,8BeCI%paJ4|6 W^bLj2AH/VЎ] \ivض}7nu)]s'848ADpL]G@ᩱ꿤 ?oB_w%6IqqP6]KZz(# |D"7|}|ARűnteYߍx:z|YU6 DWε()'6C]M(§xv-"b|u<֟p 2 D\ Ґ&;?FlHn}xW4sd~ k.&.{Pd$o[: 4m6KobM,k:0!+٦.osk 2M|;r@k6>ȷ'eߌ(e7b< Q[)nNZ?t&^=WZW j EK}qTuۚH rWb[dgmƘi lSz Tl.^?~QЩxC$].h3w(vEi}L ЧAUUni,JI ZǶ oXkm^~_jak\l6Xϻ= p̬" MfH)@#yצ ~RzGȥNwyYn֓qxٺRZ6uot%(rmkz y>_vyLf5EY] d @-R,b[L) ($c[QS2 pmnEMz\{;sI;ǁ8j~qz r h;{\KtC7ebI5Ԩ hr x9Οgt[x*g#]l6US/ x}"KHr-Wy2ЁTl\H.!۽y.6i5FwdF \3Jx H .Nsygo2y$wF6D<v{7.> 7JFyeNs-0O ٞϢ!A4g5VO =NqQj ?N mOnȰR|E$e{9\ˌýި"VWeŗ&Vyc\lN2Yļ'k@[ʵk3 բG~ \lLL%U 찙ЂlM"S#BϋD 9o"/yAlC5E<& z^e+Qlm^FٚH 硧p rCXSȂ "Z@E<<2;>9pT]\ډr ZRqI3w-%|lڨ b]3f@4T.JWA b;%}TĽP4m 9f@D>O꓅( D ZRۻtO| bsUKfl@[qEk=%VYUL lMQ6_Sv" ;m~Ŗ]ofDrIayhMIi_fؖ+mk\#Ŗ|j h/5V#jh8 !ňiiք Pجفw]Ee2Sk>%5#XAMًl;)6_p)ZRB uJ6l6TcKb h;NXdk|>nbf-~*st6tS,zl& @rjƃJ 9:f h'=Kbu:NNqUqe. aklS}N6)״P។C^ ?(ݩflͳ'T\oь*nA)~νYd2)&f@~.ɂ }Z{ M)wF=;ThrRyJU\l#l2 ֬F.]"v%TRQ%jՒ - r{CO n@\=kL&Y ]VEؿۙE >,Mv*$瓼c C [A |Otjƶ=llѳgb+M8HSٌIӊn @('uŶ=Y >c 90E \9/ zjNYsa3r 4eܲm"嚾DGYk]C@Uۄ1Q3QʵM_( kǯƬ(zRd,x|[,ڶQ0&RUq(i9ܮlwʒ11ru$=f%(r-d 33s5M,ɞh 7)W쌙Є*6:7CX(Ka/5Ir|."Mגt,9 HؠZ $vW\ ;87QOAQd7lHC; 0 P Mn iLAsU1h]2f m |ILɂ Iϩ{Nvtn%^23kw J'VУJb;;mᙕJE6rf b_Ulqٴh0KwNTGHRő Ǘ9܋5zL\S¶9@ȵ cqč яt.K/G 3C.μ@(6+URCq#9gBŰ 6eEr c˵ V* * Bmaݜy§f;\'w;/۹*9Xn>܊e˵ 5 ] na[4jES\mГxVJ4SS Yf 7lELfJ'$ e1X5Y0ӣ2 5'3%f !>2o=g27 ǤS Gޕ_ MOX^svKI"'O~?A6 YrޯNTrڊT+ WlKUEqLm b_ Gq00:r^GR юV_S \[*E~S#z7 ~7.d} q [x_#;~RKwU| i u{#go˵T!\kYk֯-@)^^KjOuLJ$}hv1d8*䚅NOa֘5h"t+^q rmoQZ[͠6(3.[k7\s&|mOl[.Ri_5dzn5j B"66B?(IA&׆m]2 '<=Q$,EXKHgQsVȵ{0(zkV"gm(zm<%B/xAY"U: mI> /2l$b7zm 7nB˵9nvCxSaڌmS̚vCM=oݽ)64CERҚ>۶[(vŶe.B8F=JϾ7zo%\oʑ/ H#Z!/_(wE8ځoچPe\[]s m( UZh1 >ެNN@[ASs'O|s\! ve+LxО{l?{w ՙI_Θr v$m@$ȁ)d+α&gO=wg'y39c933gڥ(FLe)G*mԾ5gt/P?{>YyY b.P3b zW3]5. "am{5eks= ګ/fmkElXSfHXA$ ( pVtwaM׀{q9EE2}jX|1: pϩʽC/& ks .~H(vo{_aaM׀{Dkf)5A^}apK=s%3Z.zX5 V^8<
[ ^8Iݰ5a& k+*>t Im <kp naM׀{F1& KI2EcQ3],Ȱ֖O5 pϨ/^ߜb.{:i.:yQ kujaM׀{G AwB+c3](kt5^qrkk-M p ^\$5A^!#^q&[S"C q-'|&k=dU~agg[uEzS(RjL 0y >t6rr<͇{gHu?h k?zYX5 R(=o̝5A^%'mz6PZX5TMa rWGʯ\Bb.#:%\^J6%B^f\59Iq:˟XWMvsdL .W #5A^f>(h8w46o: ه=vgR9ç'XXSrK H,5A^f' Vwun_s;\hֶ)_.\ؒy\_2ȱay35/Xy JՌk}#%%W2 yG, YL{8-/iY=]f}qExVQbX5Ϛ͘6 KZXvrǝ+r322V]7ǹSLOW|@,5:O8(GwXU;8͉=iܡ9r˻i4bH>5Eovuą,Oʹt6u+(j^{vp.y Q#Nœڢ-mwU0>N:0Ҝhмqn/JĠN)gB;kP^h6y Q#jϑ3+ksWXl/uZ|nsg54 joO:xP4 S? p863 ! P9l0ES"9Or)Ny"w) ԔW-7r15w#;ݶ9gjA >dt}_I?Syjq&&yVym~^|o5f^ T'?rE->8k ڳK[k~ʾ55f=p䉂[B Zz\pۗ _q0 ]Lu"2ߛ#7 } ysCPy{wL&ݱuz6L;}WkuHw7~?1̜%DjQXO lc iEA1Wd gz\N}䐨N=7SZ5zc1uv]Yy_-Dm}A~_gyݽ?P.F.F^fNJQo8rXN!VjK yn9Go-=iW3<> wgk8!|46,.WFݢR@e3p}in^; 9Jww }/uO^c.y 9E'ˇհ+5mlh0'Ay {qiW(t*#Y/3%Wz9 '~Gqh8/y 4ͼg 7H 3sp Wc!! T qMZrmՖ N \lt 瞢ѹlD}4'3.XK?B@^4M/vF^fPk?40CV|m.REށukTM tO^Q(;6q"c/ ҅s 0?SQP [#a>N\J~̠PHY?veXێVU9F k˪%DPL:Z.o_Z9Px~d>9*r'r^³B9Omkh(ɐ0MSk|5^\ft\#3tZ_g=/_-vCei[T}q!T WE[j},!d$9%AFC C3\WИvu@XYιd3)Ly 4ռŵ5037ޯlr+q-: p&vY !< ;7 6Xxu}%G:JKۏMY+: zH@W*\%B\ /Jx*PRS#Dz! IPY[!aw*NZS_u.K^fơl ѱz#\WF]2%T,c3h=f_u8zWdgR*z2.) Yyz2yCO Q\S}/X'TX7L."®7r]Vw{ny 4W5'Y̌η+KEHѺP6% PnyΜ? ,tqd6g % ZSCp έ,H/Z:{8ru8u5v:ng?<uPFQQQs>C} (KM8QT,(;-ꨯ8Xtɴ酖0g+[]&.[VrEmnO^ev]hIpK)Yy(\5OJA~v)b6(O>N ڗ*}>u+*:}ij _1(P% ݭ ks_d^e / U֘kYJѹu r wsgxЧZ( bSݝb J2nNXYa<(R ܿr^.n6MaMQ^y U| :[|#YC% (gVzs.]dY;e d ~Nm>.yU6uAwNLjr>{2rS t=uy6xjZmn55]N]bV5 , X<22m+1WՙM㊒>%z^;?_ #.huԼf/QS7 ^(t,Q[z^cll y$2?RQm%UuڮE~mwiYh]] {W"3 g9ճIEͺAO˫jőcբXӵ>X |B.?V? V͢|ě{)XW_QRTrwY\<>QJ3y1MMM/I'y_R;46)" z^kP ֿJ+]կ}JNvmZzs5k _oXD2 YhЭV ;@ʉ̷? \w <1u杻VceyYm8Uc5pD{Bi빡 +UYzQV ^*ݴlz iMX o).dW<C0 ֨iH: R Y&o}yM*c&ʍױ$.ȸxxzKY,\Iҿ5ekUG'Ey!2~TdZxpɷ\{ -'v KzZΛcYo?m}Ydj~?yNEmr?.bɇ&:ϓNúh?)_96O^& o-I^fBصJg⢑'ϝ >|lkΐu&WdVߟ;R!'skU)*j ~U朕LMNQg^C)8 t8TeӍ m(wMԕ>W=*FY ,rQK,shks bZQk^˝)ˀѠNEN Y4(֖l^eEhxAQ{pNY9?2$[6i^P}ش_ڟ?~3%mE 2>'Kb kی ;(_͓f)\ϣ{oNkزSپ:_(ޡ4o'sg :Yszi b,Hkpa?Bb%mrgg }Y@țq\[pw*DVjDn5~}L5W8=b\ \"a^[ jMD5]L^3ڨ"㱚הrE ZYzseaxV-cL Pl} t/P?pY|$ToQ%ܵn+j <-ڪDG_v+KKICٞ~wYG8888Y0XyiE\os 'LN<5\=T$yM S/?fŠPn{4UdgXZg֨(+۔bsqfܮg<9iVƳj cV輶K3:W[dIL^SB1cwZp;Ԫvjljl߂Z{wk1Es/G ޝ֯;)u9%3_xXq ymR^"y [CkSOmw)I(*"߯^q$yJ^Y5?V% :i^i59>M+3*^^SsBrCQnU{ԵnTDh_ܽ<ZWt^LݶeJx,B⼶[ j=JT[H^뽑02nդ[_q{)x׳Y>}Nf)嵷5W܅kSsI >B81wP|˸x_7u9ϟVSQ,={ ^ڐ#Fz' -yL#mk S3.R [52lPubZi| y=>6+*%䍶FŃ*n^]މk&{64 {^ kw|0]fٟq֓qKp1?N_eZx]F#,+Qާ-㊞<\-}lw[-;C5v/7 }-]{sw _UWcȪe|Uz\6hu%*uըF^yv;d\hMo =lRVѺBI";klf ƕ]#s :; ' B_h38r(8*DՁK7OֻWm =ks\= yKSڄt%pJyMWp ?DM6֞W:SP>@Ȉ3F3mިqV&T֘DF}MU:,~Mȼ>vҚ״3AT{߾(ymkf65O[^[.O'j#i_d'ƹKm|Uo5)I ym %4Yh*y͈ˣ[ |5kH5[|k;Mƌx洎oEq5襞Rm8C#Vw{ lϾj'Ů}-scl1-U-;zҽf-6}V/CZ隲ǟn[6=0+֤а2'ټh?w!҂S{R3~we͊qQT$ęO7W6A^S-ixmdDCݵ/(ʦxc4KڧkԒB9 B=&k'2"TfFg^Y6 WxyM:TemSF8E2D;v=TVs~SVw Ag51ġ\wfUVL4o-~!pqhV IqnvpٷܞyUmǷmj{OYdjk{2۷iy=+lכ1%Y|dXnnnpeMA~RQUZ\)S?^ly;K. ;Jsko9|19#5tc椁0܉ū.OF^sշByi-L)ab vOׄȖ * {L"UJĹ@bY&ω֍exF% 'r AeSj'mἦYX :+8Cm' ϸe#i˾VuqQxGmYΤL?L՞eH6 MdNey: F^yzy{^1ڏvʿ7s.FִZł> oYa}YΧgC}5ѡj'){+״GNP nPtqːym<~ }.<+|w')mZl^$E{^{O;W~oW5dS|Jwӟ}xJ~̉r]{pײ_Dz4Wb/qRv5Φ ڹ[~sĖڦdyMwpYN\M?whl%r\rӻDf@mVUu 5 ަs.2r)=ݨG^&k2,JNk.嵮mbN3?[}둚oѬڧ=6L$㣺iqwb#C --ITϝ Cn+sW JTkIY,R,ǣ]qyWKA*_2f[O5ZVfh_U07s-vo aG3sSnj_GZp٬+PV5ZMGJmW]H?$܇.3p Hw vzOگ-{NW'#G0g q]? z:|5AkzHj^[.Z/YmXM-2X+s@VSuˬ=5YF}_-OMrwZG>@6ͼ&~wG%-}+??6V7ϻ_7}9sCQyMx:yҙyMޒJyC4~yjkԟۣ7ۧJukФyz Ool՞j!5!%4{^ӗM3>[۴$̰WPXߐOT}M '߱$%0N;WVMP% [˭%.DZ/黶"jؠgE[^GiAHYm̎wY"Z]Ҿjk)}Z;ď t5|0{2_9ҳ9T$Ps5F:Qn_E+e. -[q7:8\&j:R! ^*K]fdRS̓*j8 ~C Xyͷk;_^ % yKY_f-(U_K%K>*6_D'kqyw #GG~}'<ٜ.~$L{~\x߿0GR"{\='m@bs Y"ns9ꃝϪ?R-Z^WWiRx\u:~'B.K}}]jyF{y^cKzlЫWciͶM-}-ëe=XQipo ʉUvix;3;#QQRUJaeoe~'\4z >(ۯ f QϘmN .~OGZN}SkP&A>6;]9y}⢽up擦܂e+7eH9V0dKU%Vd6:ƋK/MH^;#m=֦?r^uE6dkU,WX?7Fj(tј èZl9-29*bۍ;tv U*ʦaCDNn?F/j5OLg ,4Y^Dq8٥>o^Ae=]_N3>[N~:x "UYZ7zUZm N@ZY4PYW'sm^[7fQEoף;vM{^n핸ԏcG0onԛ{J[0KbZ1Aʜ#"/ls:*G [DL é$L Ո縺}MKתA5>CklPCo%k~8]2x&h\|am ̨"Ӎp?ż˶-[Zfw҂Dyz, D&E4%MݤzOUF+R,|j$dL0Q V,SpS+5y64xnỷuw ym$=2ܘK>>o^۩W_qڎO[igGK-=xg =z=/ԫU=so 20@ŋ5+^1[Aq PS 0~iD@kjj^w[Tk5f8y흄%k7@~gZ jſDg"FWpHңI3p-c͙sHS(SonkUCuBl5-ێv! ,MՁ4r ~7"kM_j 9yK5TfqZ5RK|_ؾ%&k S> k}(7.=?d@Oh9l>Ck7N B,LkpR[@7WnDP7H ?s~lw#ksɗcu/Dky B=ūvszO wG韭iBO?lZ^9zϛOi oO3bZ/q@^4C8])$N%qao/0b\Vh щ͖Nug[fV˵e*#yXY3*u&>ݹp1 kpߛn^KU~w6էӒ9kO6 M\5}T9n5KW"ͅete }<^ͣ5@>^/L\vSѪ,i P+ uAC5Uqe]o JxOңoWWlyw zlKpdqڛc_?M"EVݺUk߳ % EnQ~\_|r $mCv)HF0V2 }Y*3B )ۃ;sE]:ի qfaj>ΉEG$Y!g uCO=QrDMu%.gkkʗ sԈ#[{Nf̗}J ۬' +ȕw\:m[U%mH[TZƧf)K6 e,ͲFmry#fZHfY0ɨKT>_ycC eqc$1嶵v"ɳJ[/pC5B.Z[@CyǙrFo)]1Df^0Ik᷅x+qG&B^&k#qENyM|S,}o5=}gw"BKًs]҆L~Y'i-ҜcTI[oZjEc+zi ]<]kRqm4ym~7~mIluG$;i_D6/ن|W>ֺGj'G^j \._cZv;9.YhgP}a]}߳5x<} oCuKݾeú5mu;N4{fF+qp{S3NhCYǵibY'qFê4 <G p 'G U~ƀaok, G R5eEm\y77O Èqs+{r$T˓r' ͐#3$JW3 dvFay-o_[X͞˛ qSq3# skU;ؓ4yfڿh!|N yE}_ތ$mFwxy~ ^3i]?Q{X .m"?:ZckjCiZ -k{U4:}|~n"}rKݿѳ6P5tZ 9 w҇(~jjM_EgƍJ+W5:z>n)N+mw37Y"xW~2_yJiG QxB5 ӏysN@qaivb .2,i0- k.tڗ6 M듬51yM|Eݺ$yMo5G% Nf8| к,lʰ&ŤeV=TK=TnYq/ Sk- 懿g-1q^߀#)80 H˟{YkGq"knk: 4x2ifȆʦBҳ ǃYZ~@SD ˕ G,-=i%[$u)jxG SVV>wNM!azd5{(rk! ~=fTkc0{bt_{\kVCfh[a6g2ߙ%Oo)I;{U)拤MD?S=uHM"N_D,n^Ӄ?ʇF7 /ZXh;Ю@,71%z[um-SsOD&74QWdŻtҒ:_P1tO5LS¼]&Yw3ak+wŗaZ rކkԸ=b%fvҖ sf2e[̞=]$%JE╦{x(OcMkH55]# UOVGwClV]T68 TTƠ2K@26V FX J!g.mTTD11Ԛɻʛㅠ>AMIbLtoW Y}9י2HY ϾΜ{6gZr_MYsJĿ^y:\D~mruѥF=y{kˁ'?*tt-iz.Ɵ+_ 6j1V%a~pIq&SvLym21DQQ 8T >jC2.!58ZA&rB}M(h55 א\&^káLG_EXO8S T9_2z" S3U/r<^T 6mr J " mPȡX n vڻ4 M'QnMpXQS=nHAE4( ȗ{_SoCޚ|eGgt OҜ\x4Jk TP d.Y@· $]vvZwh@b'6Lvqb}he2>t 9ڰ0j:0י llɍ<^h"ĝk B2FO@s'{W8d'Qy@\9 #Zq]'6# iҺzؤAXJ x; %*,VT4&sjiY)pA[4U@ҧT }eɒeb@r9bd-J'vw,=|uW&e h ,q&5U\1>@]NwcojQB89$d'#qgTχݻ]0l3GbAAc4 Eb |c]wKxVWn8Rm^ ?%$d ewl,UXJz7j9s?@)?zm,^@Ƀ oƅLژ5jmySz Kc*RAbj"OD %? U"EAɃ:L> ]o4ب* 5 =Bzsa)]% D8 :N@Z8ϫ喩oZ*If_]u{kkʒ-ІLE'MdA{9Ht䅀ysͽi>I鬭_$ZNEK.k'3xxlfyfd,AxW(F▢BX*G閂 ZNK< ; )n5~WCyCBLZZ'l; zm[tEkoHV_z^M&D1/Bצ}81>& >=le6z I.mP&KM~YNEg-wz!O2&6ʼ@A_*Iz74*Zkyl}6%u":tŻ֛U9C 9eꛀ.%/GqC1)MZos}܊w)dwEwS/_f-7/xąkg8Pc:=/9YN"92J= ^gDg̿_r!Go6 9=@8([?;ܪ(^#6*wolR mP-Ep* _t&uv^z-ۥIWkI6x:"~ E?lgk_zLF(LKX#}F cnU?J&xT'!#*8G$I6g_*@, "ǭގ%$kBST4.N ^P+ͪ'(HE{U3itk;^x I*2QrMrf#)f_{ѫǵibX6Th'i*18 N\_Pb2N< ϛP - -ӬZqtl~f 7dbE&+ 3+fq|yH[Ur1FNWHh?h+CczmMUW#de ^Ɲ/6n >ţ7a$<Zo[|>#nz}K &58^FxϿJB*j dHG1IJq$ ;D}BiSS2|aڪhjq(g:_VV*>zr٤( ]k>>h Teze^zm;L4է H[%g"WG0amH$-\Gtt#Ɵ88n>c졄ģ1 Y|@sfnbҗHph1/r\9 9ʇT:Q~O Y] D*| ,ND"3@ӝ&T(sʸy'8F&";ܽHy e!&n tLbqb>sp Ki^kk Pc;_ pz!v=0\ koJƽg_Chr D} -j?OP]Bhj"53LtLBY(wߤ JiJV9NQO|RS( *>$:&_ШvE5aPS!5k\kJwze d..e(6aekWfI8?EU֩S =3'3NS̜wwc*ȋ* ?Ѩq$/M$UxawqU̲{ˣSs怊G @&:C{b;HL3&We Ak4A?# zq>^^VXWfb+ok+2asr4'/nNkSl 56kC M q>^scC_{#H1EYW2HMĿaW%rNճR;Įi* R-/DP g8 T|HBM!ϱ-TJ / 4}G } dh«jFE6Dj&Quy EZ'эHЖ S3- } _5p>-Zo^ËO[ yFIt{2+6+ Oרw>z~^,zrSƖ G< j+wM m<6'LM 67O&57ɵ1kzM S fg 0C aëAL$.J;6MU]9o=3U=Tj':{ i* ROUYkbUf,28aE]H i3,zCOҨg êpaP7{5+bSp #A zy~د+F(gG^HD99Sq:( "^I;=LT_sDp6[)[$(J:U^!OHT7ڹ>gCaJVޫH_X4&7Ғi\}EYȇdtPɵzMج@ atyp~.j+qCT:5 s@K.\:ލpVs*kx[u3k x,Ս[~77YYS:G9fwi9g'{WI /utr-Mgk@ NZZۈ]k4 V<>ֶFרSXujx7zy 8 U&kҔzW i;f8OuvT*7KIR>\>eʍ $v.X[)1Ҽ4wԿm +pYESm1vá}9!'NVӖ[cfW[d.9 @yx5qkkon 7VR$}]Z J&F)|ErJz b.R5n3;~%T>l+Z8roՆ7%ɦk Dd_tKr{k|zMSjxG]wj=6foGJ FQwz${]VlGln.ESI=ơ ѩ kGjtQӽ m xtezmo0 (%f¬GukNAzǁA3AENN'' e擠-Iac*K@AUB=3R%KͱrrU-N?[exd]d^ҏG,JS[^l@}o/nLV)Ė^*;X֑3AzLVS~1kzˊsb> e G76<>աVsG ڄBZ8OWٕ?Z9W.FK 1ē .ʔ33/ h e*kr-WyO l_y=m =} \xjۣ(frv*$ئ:njDox>hx գm KQV+j'Ճev6iuS gft>wT鶠 ͱdgt4Oi &-lly $,'C@THd*IƢsbBMv*~$Z%6} hp5&̙x ӉgE(TI(Scypd ١SP7v,\\Sk? : Ӹ!g0vB@k֍r ;k\ kmx_#}Uw06'xQej$bkk ɷXaVet93G״|ޠ6g>Vu<}$ַAiszU@G WWe覎xu6b/*+TTg5=:_ . {e>{ < zf=c> 8d®o{RO3( K~}Ě@'.,N2r6 A[Y(waJfW1JgDQZ7qT8ۂݛ f2s8 pZYlWOP،gu}D q7AZ W~]@L|(Wυw ݳ.9ȷ| dvk4$\n~q鵉»Ot\}$8zVH"}5!<š ]ߩ+E ^Cvo2$D%UGWiFG >$uK)RK:5@i25Z+ \3!]\\*{Jc n #ԭуx5[(CE*1&xtUBoN0;Ջ'4{ -S9qD;RNt,lcoA(3Fzkm<]$̫ "kx~kHb]_FRcԻs与812 Q ӈ ^N"j%=PYT>L1LF8wcM ~T%n1 z} X^ 2?4_,)8U*ѧ# 3ETAbZɌ.ƃiˑBj,!x0b* k24(%+WO.^)4(CE\ - T$"ҌΝT; 8լ?pvnHnC_gGAWff!|f[{uչ]p'Y=HRӌ L_oS]fCʼnɔYQ4>P UhG{=(LK""2e^cA [*B^c0Ɲ̜4K@U8Vɡ0V-5\.2Ǜ B+(P:@ћOj+5bOg> 2z* ~x]$Kz*3j)-V>z8# ,hCW02 [+3!wK)PO: PkZ@<4 u ?,Z (,QvDi^Y ԋk} LbK,~@0yj= qIL1apm_Np?\(k Ƹ 9ʨ^}fDϣ C煽_3L1V\xb- R KeSΜ@nˣ]HwU la\%ByX\܂,aYbY S-i (:b%=NbOEeA\(FD,/I ɕpNJy5?|O_pOjƃ6k d ! }wI'/P18;7tI+KU H%}BBN0 Ma f GLcwAfL B q+2ǿѽXt'Ϋ2Eni(K ւ+F*[VTq@L迹 TqZ36V͆ط8l8jk~5cQp2Lr+AeeQ Hu,FѷA輫eHT&2K JǾЁAx<*YG2%K|E$!q9P]4B}(3&_0K<X͠d^XI@ ժ~I,ZVaH\4*̈́p<&2$UTGBw /d zO/[#SQڄw#Sks.Ky,kcGͨ vȸ$r5_*߉tYPbќ3f sFIYMObJu%Y)g >ÌDܐ%drнWE&!^G/ĥsudGV+wаr ۆ-ڄK\ lv*.kcص6,4fvOQU gʪ f$B3ոqW>)-ZT^F,=4?*_*C,6E1mU t~ll%mWSP6 '{?.+QX2$ ^°Q2 0 k Z9xO?= F F鵉 #W) s^ k;]ף6āWBe7UgLZų@e]=Kv=.qQڭ9x1P^T Ae k1k~K4DdIur :_UFuwO$s ʨP9F1ik H1TgB)KrJU >%Zʬ9 _Y s}(tcXq{hz 9jS+GIHu+x݊pKpX!XUmt w.F2F+ ) ÇNu5(ZL!nû>O!مi۸_LM8a0R~ S~CW9 -0V=ԮXq!5x\Izhae:1Tp5#+V4ՉbI 侗s1Uuml=kmWCk@KMҳNʍR9 W$Q|[ĸdA143!x:o sKKINuHgƣ3+rKWՕ(n&H( $%ݗLeƵюQUR0{nPW1XKEGmQZB-D(y$e)kc!;gdrm>2ֳw[ZC>l}/tP-N {CnNZ_ \Cd+9*Ga/M8c_ 'd/䧳rapV /6r9 nkN^ + kC˵rrz폭Qmd:B( >$9có3pFATL+)RLF'$6کOسP=wщq X4 !)͒^#ݞCKKw}G:bQ,zx]p 44 y*PLp x 3 B4? #F/FTՠ-@oܴǑ&z굩psK$OGMK16Jqpçr^_whtX!/vkt im&/h8lp@;}}COMwakv~{v6jkƟ֢u.D{;zSUk?qiO 4|"q /;Q%\?=H[(俎w u q iQP ÔΆD? h)iv뵨zp emmBp /;]߫p> :/)G͂ N u! m9Q RgɊՠ-^_2s H +I!G#.l+$z-;pF1GVzJKFdkϋ b7pa3i [ !}?ϣ[A8fř 2m"\Mpۍ%1 ߧk3¶veUt?#귣hYz7~DY|O~]$O?Ղ^{8XOZkmqb#'Vm6]i|A8.X0STi2n s9R.JLI:2-1=>V^P[ dF,β=k S BU Sx<6hGQ6<|6&(t8LN{qg^"=N^[m+IG,&HZȓWV@VQ qee9-I-U^͛Zc[!kOLc,k5sy@ U=nut I|t1$*E6qT rwҞNX= &gpSLjHO^ Zzm: EBT]RW"99h*^m\rזҞ"t @<%h1HU jQPw[,ҋJqL' RLd,Ix1iu q\ltk=Hׇ&]E Ņ)PA4:;+W$JAA Bgdϴْu/=Nzaovt֨o_ n bHv! p[*˺ +8(ຠzt7.~%IBq%g> 8lܭn ElR |$n#,o$aH^m*/s,=92kz>nZZ(ofЗ8(?WH UB4u#đ˳ x i7uELtD) 5< i 6kHUc_ cXfo.bFt clv@p_v!)fbxI.7c Bzy[0 ȿĉzM-^oc:97b ŨZjM9ܩ=kk!#ub ^^!^*J OpgIX7Lk?1Y+h xXl qtXQiOf ohv~asL곎?bRkYbwpPg^b5tlus-- Sn҅.Y^[|XZyM]jʸˈՂKXN F0y"! _H35u#@b *]Q_V ?R h}ڞ zߵ F/̳6r^Jz1&ݳ*9PFh>: |";O^CtZڗqr<k+Ů*C>fn_}y@Mv"v%̩ܙ n<"QEHkK>,A(= g?"5||CD"/Q֩pEY_*,e 59UD^ΠbԱ~ ^%M3P Mp3W HAqI @Nx 6t\~H-&1 I!.GZO͘1 QOfpb5 B1ZkMwZqz 0 ㆈ1 LM(> z :l4z 6IR ^8- ;bU<J+nZxt>¨tӞ̱v 3UX)zhdAILJzc]vh48"l&s(CGd-aˊ#< }LZ>iwXq^.Zd }n麁(kP3 ۬H k-hsbDjG?@#EҨX6V| IpW" 1 /P?hrwl Ui1 {fSuH-z VxY*m5I\y )ٿ*F[k1,kFeYM^D s*~d :$2@ac,Z)W8Mse6J5R0k$Xa8~'@5j!/ Vz3zf H PYႫn{ˉ&fC'5m&9t ڵ eۋI ]xNRk.(X# ɓ|]4waxyYHP7h6BQLz]u P#){q֒8Iu(x8d*I -+ 4K) ^m)|4W{6]pYr,!yODc!dT!'^Qeo S;Ҹ]o )b7 ](T URibCץ<ڦr8 .F gKTgBeFB2S EHdT^]&ո 8Xt,Lz^.^n.CbH(h7 B) LmeSI5S'By<߈0+~nĿB^z 8 =uR^lFh+arpaAw/ & :W6(5pXOk^[D/ -} {ۏL-d, cqIEt+ . > Ņl{'6CN>.&蝢k.KzjDSNpٍ$~z۠kޏZ \B9apPՔqbjy@gbH z02w=E Xͻ~ןB壇 rQ[$Gl?+:!NxO*ٴ(vj$T轳JB#k;Q<ԁ+¶Ðy8Xzt.G"|&! +Ad7-mh|[ {?{g|*i݂sZy+z h x/]+Fظ D -5 dkFIawdE|a |8p I?il /([ t,R 6xrV >A\+Y[|6Jx}W}@R^$0 ]=vՇQ).N=[{ SH/+PD Zy~G۔؞bx;yR2^| eʸەcSRgsd/S~ KC>+#Y@ZjJUsb:,+U5+쫳+TA#u ّ@ o)dQ7{ cX T t:!Cg@?! f|l4A %AΉ4VERZZCGt8lr5 +B1RL@l g#8t7= Pb06Q3^]}wzip]@vvtP[H3f8xL| isb YH8q.]^$]Z$.1$9ck"C"qNTP U]D6%Vg3jFzAZ\$/ǨqS 6̋dQgHG2nm=qjGCh pFV#ijc>U^Ŋ3Sz8m V^zu%%UNjǫJć"Sε%ZI>%]H>{^NW#yUL?}oPz_,R^Z'^2:Ov Oy1B8↛ _vX^+Ht *L}ab< CIQ\1B17r\06Ap<>\{7H5O c =U<1F\1w9e u|VI}H:5c6Ϙڄ r-LgpX9Yk7E5caI E & N!fu2wus-c? k 5ӝUZIE .HzxJ)iFOȽ:%/1a3;+vu> 23^¦Ddl KwJT 5QyR L1M깮UʀF,\0c/~x)A'iEK9E2jVl',yD>2*T q^s^ /@AkNa _L1LN[]}GrV ] @rtIy.ܒ°ZQ!+.i[c|A7 F[C Z#2o^c0ƙdbnxBJ袊O)Gu 3=!t)Ӓ!|Ս ^ DU]>m-ܺ0 n2POqfzm5c|Yx΅Z25=SڀBժh.ya| w%qр6X& d:m< B՞.wuC۷R CaH1C^c0ƙ̼#XmjS"w<|%#n_˷&vfFx yjۊ g&l haz1MMu^G^krOcS k ƸRN(6$V%*&6&ўMۑMl bK9>er! 'Ϻ |Ѣ&(Q-~yȕ%j ?^c ^>qo^tBIwlIlɟZ& Kssܞ%nO4'0ԟx4 TvRgBt9=+L15PTc#k $܁Uebȹ2Pڻ$iPAL'C> bk]́X5-O5="CO a<;z1ޤ%hNWHxqrDҟO mQDNw.(??ei2mju]^^S I("cOlV5z Pc{QtlL1Lgo /7p۔-&??@j܂ӆNsbS'@r0uڅU*.@RY21RKO˃n o^3p LM<pep]-Wl;w _1$jhbPdl dI9AߪNm9cFe|}wY{iKx4Yh$Լ/ƫy -kS]^xz. r}[~?<]#wvTN E-ژ^c0ƙS߾nB ? N뢥Um ]UWt 8IwKЙ@E]XSUNRY)gј M ƭ q36ZFbFӠڷܱKnonj2egyFx{M UL1c(O]$gPbSe9ؓ Zz= ^טsDѫgzXd:l EGӐԻvz z \gXдg q[+l 69Ζ |X1_v]Sk x?ו^ #V^l| :*0.[XZ1',D.WFJPl4r !YFwMWr:c)QlݡB3AںwoiMuudhu4NU8W1$-/knt^V!pvweLO&~=:OZF9s*LM+u~2y<@h~H;1z ׀js8 l1 ^*+5$Wkk|ezg:'bhepeVL_\8w r\)qYNqOĔ' BU[zm qX' 1* i5 (gk C[7yM^sůݡ}v>E/>0 _FL F1Q0$h=L豐UFSB+5{O u x+ +yg0 QچtOJ u5GAWc ^D)65hUNǗ/tTtUW^<6e 1!^s)\Y M^p5c"S{]'}$wbMИuiϹ5]YFe^@D۶urC_t!6\?(N\9QE'nc0&HՎA6 1I]ՙLFc(uɍvm}nwBbTiո֒02XoO0f92LtRgSBڒ IV=x oyzTk Ə F{tǻ" &{ȧvgͫ6 {V.ޝ0Z -_w p ez$5RlpVvioUmv xlL1?6-]l[P^ \~ŴWPg 'H^c0~lXt22ؾ 1!^լnݰPv&H^c0~t=2z0Blum{e8AzǛX? R l+q!m3XW o$Cm7}F0A0 G'H5e6bjnu Rm20 B궭 ˌT5n0mEƧYk 0?4!x!LS]ǽ&H^c0 cwl'H%0 xBU[6CgTۖ?휢{n50qG u;A&H[Hyߵ6504Az_0Զk50m5iXOMT[x0 Qmx4种wm 0>&H0 c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n+0 15]ѡdV6]q ;vI6Ơ7>EG K j߯ǻ!7q} ꝟ5i?{!4͘qhLGk8v!͘1#@<+% _ Éi57SC+k7Fhu4)[B 5PK}D TG&7oūkƍf} Mt L]Ǭ~5:6#ʆsHͺҏ!pp [mƆqڻKk?EAqpλ\ǁnͣk &GCTSqwMwz mvo0~~Ԍ>|WQ($7|_qӄy*C#~M^] j@ӡz{?Uz#0HSY# 6?t ptvU:}C^\L: gLݢ{cXnhjz<#c2iR k٨U{aG͈?I0?iޫؠ7|_qLOJ+<#ހ9U VqdQNl ̈(2>οļwac1 L HLHB> (ýOOՑr_od{ZVZ]]U==VP| i+Yzn53 /^30l6Oo~.vO'+c%g u|x:caPr :@V]g]3fu0ܥm_Yȏ^]Uz!^ l' JSI<ʿ ~zܬd::cadڬyH[~ )6R!Oe7ГsLy95 B tvxκFy >U緾&~~uosݧNHΒUz!^ lt/ w'X@6ϗ.rozSD CȂR}^vz㵳'ޭ1/?fƓq |)k)۾x:cA_p!\@[Qg]#}Jb?xh~O6R@ް5Z[?Rjjr5xxhOK_2iحzrX1]Wvmo-# i]ivc~NJ#ҲE|+xDLAxaM-^G-tVMB'ăIs;Eu=[\Tk֭ dS8 Bn+؆WW/z.F\umlKQǗJGO|d74Zv-n4]9uR]596U۲7rRj)XyMbjDnWPNZX)H/W6JP˾>M4-z@ ~XYUlHE .m'Q+}oqfUP]_! g3\GNV9iiiE?v5{իʒ&ؕvӤ _~~.QWˇIdzv3Doq;:O--.gSW߆WCnQ359:R3&BJM(k-W'쪯Q JއQ^|e4v1/9!W61+zX Lf<&$rbچgJVU7w:Q_iarYuVWnL3R=zxrr.&RYG 66S3ևK<0q>IrAKt{Ӧ̯6웦]ZX7Mk61@$+<ߴIB IbJK~^v5Q~oݽ:aϛEf4N/l3bFSgNNҞ{z/3KIBť1xKϯj]7~ _kafұ+s6}^щْ$6 E Ǐ'Wis K&/0L@=g^R/ݻ #3]GlaL!8 ߹(McEg߿/eMA>4UN:Y5+&j*7 _~O0h~Tc3f(efJ|{mMѓapIJŴδ'b jH(jƙe2;rO+Zja:ZLv鼩+wp*C+7Cg{B W6UqtMBdp=frBg CWaMS+_Y:rkWnv-^G%#j .v)6϶֬ނqQZ/i;'m!4t,g c݁F#k/kUxgGM0$\Ied|㰎eٜ:i>Iu~+Nê3Y#fc㵻9wҮIIȜSy4LU^3 {4]x DNT3w͚:Md>kcSٗ-fyŶL967h¤?g̫uĄ ʇc)T2 Q 60k$oʀf9?S F{$_&]TYάMy좼kajPx+PNcm)쬩A'[{hoFD25߆WK717-JY0)kVOԱXJu> ZrTS..M]W7(auF< l8Bh qn,@"mC X=N2Y΄qWec~sΔsKnE<[ 4^U[3Ѱ;N1q?y؇j mQS$<.{ȫh>ԃ"n5: Ӻ5#BCIJ6R,V19ٙW#x~( )Eԁ9Yc~NQ?^S{6)>ޏ6'Iy*K 1^NTuKt"GƏ4m_ URM khn2. ԳgT Y3' .)u+(d-0s)TeIFUK7s:@R2_;7fV(5E<~>vT]L>PUUÛ}YS[;^!l6b\=Rg4 QFT>ύ9VoDx쓷o%ULƻݪ.Z)^&/8U&h$)%txLIe'6ܴ v:n_x8W ūIoaתd}ѝP|)_{#2SqmW6'IxFe1;1U-w[t3;vcn"{R^ xaMqf邏7]^a_[ fS\Q Y];Kқƙ L:&X (83qV& r=J$^)++!ml Tۨ9v# ̤ &w$A )/=ݟD R .ݠf": %% &Ϧҿ5Ԕި.^I[H 7% 㻼vb$QƏxH&͏+q=kI<UƳDإxM6JFcnj%E8㬩 jq r a7rk.'E54rt*t O% m 0]YU :MeY/KXM0^{%yQoH|fW}8y͵l P)T yzz[0^w4%K~7϶߱ecڂxd! *1:M72Yƞ3}ki \Q g?t bJ{2ͧԖ|6ŞܪJR]AHv2stnܢ~aq ;N'}H 41lRfUW{ J/Ţ%6\A[YY()ˮLJMi>==i:{LUu oJiK<4\MNb~ұxUzⵙd#IUV͡ c1KpQ㬩H=Oe7"i-o=&j>]. p--y\&lʔ O9xL||}х4x9-I=9dζsty!/+ܢ.gWkӛ+n<۩#=}J?ZBu?H>{^k0{-S1G [ ˧Y(xzw/Ȫb*ө< kB^~OWk @gx*W%cJθTo4{.&)xM-}}Kf94m~2JUH+ W,rs{͛ =PBӵuY:db\:).3xQ aTljkkޛ[MX!oq] IJ"G ~Kn=&d ub:Π.Cv%t}s(|ͳ|+Ѫo' (; zuRrf3\.*֜r5yfKM-Ձ_.z7\T@hdrfo _s3?! /008='iFs{VAvm>3 ]NKP+fWƗQՐeЌ9 %/+BR YW)JXjjkk~ % /gQ< Rk)jok#! %/&dM3ԫLTUTI㬪t e7 <{~e>I}$uuSt6f}i=~*q8,KcdӔ~b_&+h?8sR! l~:- ֟BūtxLV L5u,Iɵ##D ]q%-RdBW~6@PFV;/a9| A"$Â"GxV sy%= x% u-bvc|U *kt.nv %5+ 9*?WFgY%,5CgƓ7RxCt}NMj"b\tF˘Ur&=K;L+scawX8p-薵ⵞB:[>}η1Qx 7JDgܔpI 'QuNUgĴy˻U|HJ.5nJy6V5+Q ~v[yuRtdzOD eȄ(o>2=R I@a8e[(P)S|S6xcr5Q}lmrfIW* :KoC/:|10>\ZL[B|s %u!W^+Rvi2;};_JC+5Kʝ:k+ +%d}Ъzk寋ldUfs&,k{[G6n,p ͇<^ @Dl΅Slrk&y_螑r^F$v%De YvVB7*$fP ʙ3zSzW^0Y R]_:R af ]!CINa56NF=YW͔73VihVx)WALrFQSjFFofu]RQQ GJ^EnLwxG5sAw Wn$L=ߜӪnY+^Ӳd|̽ۑ]m.f߯?Ý&pC;De?6S".f8^{ 5綫xI L{IhǤzqw2B.53Y*)_B]o5#Ȯ88철Nŏޝ/T>ُ ve'ʀ-(x vG&WT-ݸc 3ePe; +vA3(2U'bwX d+K RZ.N ϩJ ;bFWPR~װRS Fi}_S7n3CWehVx)W'mO|ArYx2پMtWZcnY@9ٟlUc΅a!^ T; WnƦd1y dHVtZ}l9 Yjϛv$fb$-7jr:ṳ~1~tF.56F{!TABԈw-tGzd +]!oHb4og{Ý+,bh2cl5!{ nT /" kAJ)3_uv߶gy;sL{l)vH^\Ĩ3yL9ԠO}lle F)xb}3t+F #tё[W ZX\]!_(E1{.LA2|/F^)v_KZ4qZ vč5ڷ@B 8kmCv#X}dkuj=qZv-kk0n/,K#4iqO^{ bfe_cM׳[ߚTNRK GI?0JQ^79<8Ǣϫ=[ zƴ_8cuBv/72ɟ:d#jQ/\:2 VO<|r)C z?vps"i'܂eV5S&oo.1},S dzYNO5A1oM7s-.|U[ktL~ˁ1QSl)rk뷷Ly]zd 3RsƷĨ"HSs%WeU;L6] sƷo(g;7~gA:7 Ð$= a^U BF)ȇbd6=zqXH 埑;-ԫ&x3!ГLy/fz2, gvvjؖYW { >1X;j tWUrw 蕣_-n߸7220DQS&{G{WMpI7BdtBy LJnRJ' zhѾ[ itC'w2;g{ ?ה F3vSO y v (#n O^nK%N˗ c!X'Jqat1HbS ͷ.enXþSOԟxyP|R3H)eoP2RSGV}â"mJ*oëA3QΜIsn Mّ|R$7|(J yTw^ rt4E#P@PS *<BQtj #z@9/zvxIJ7E7Z?RL߳O zYQ_A1igB5v-ɉ9=~{RӿnDs===s Q?877hFsoOb. #KiL͚d.FHg&|A:_dsCYć4iyyy' J7U/T::2)y.P9\i'zDvFp c~ғ.gARgs aJ=Dth$1Lӓ$rM_\& 5Am> gv>7{b'\2!oL 5BTC~,?B3\̬vucbɩs=rR2,/eA0v-I#JoD}tTZQPX Qb0Cu#dyDJ..Hlj!rM/lEá@=m$,P'}}.{Wsd:K^bGfSk gU}UM8g۪,JZm7ړ|Rg ]UoZ x|kth/◲⒔J+p$Qz]',d*r̥Z)^ IfƩ*umB'K%$\N*%jyY팂 1xEz!=ǯ/֔ئsƞ+\/"Th gV!wC}*pu5WC݄^r~Tw|qٜPx0@fYL G4bYB_0e/RQ:YcUvcNwvP ! )$s̭z^|㡭߆Nٺ͘ȶ^kܶ͛t^ QSEd{2.H4N(uE &3^,įJg?c~-&xןEɜ3@AҴvl'(y5iN ~y)&Jm>Q7Zehh#ɍ {pwfkcnѻ mL &ςFtȄk 7( t,PЍ+u1^EZcyo\}OK[W'Wv{' H-c1eٯO< }roy ;1}Wz }dg=lR7< ^g Hw߆&tb]o zY0<\"E~:M- kG.1}~vJCv' H-}M 퓎 S_Vï2],~ @zdh>Jמe rGVW7i{to? -0fT3э$&BR:HvuU柖8+ɍ&vWx6RGM8*8#ScPgV#?zΣkQt ~6?o@'#3WO6ry,5tPVWf<5~zˏCgF |j/oxBw 'i#u{ߞQBN]v3j$~zh:zi8ӷ nჃϲQ0Q߂Nt-.[Xmzb> stream xqRbBU]n $tUjKaFX1GTdr|n|4N4Itaqv!9dqYi8M. 5 )~n|lz,B &=co>R/ L^2ky~H[*@Pb.D")0 8Q*/@JZ[l.E?Vdv#?Qb 1!>}_ohy~|xZkwcuAX?QI_)',?{et{xy|qzhwix$; 7gvfu+Sc2G3Mn`uqBr endstream endobj 2 0 obj <> /ExtGState << /GS1 12 0 R >> /XObject << /I1 27 0 R /I2 29 0 R /I3 31 0 R >> >> endobj 33 0 obj << /Producer (mPDF 6.1) /CreationDate (20180616162308+02'00') /ModDate (20180616162308+02'00') >> endobj 34 0 obj << /Type /Catalog /Pages 1 0 R /OpenAction [3 0 R /XYZ null null 1] /PageLayout /OneColumn >> endobj xref 0 35 0000000000 65535 f 0000005331 00000 n 0000341670 00000 n 0000000015 00000 n 0000000223 00000 n 0000000657 00000 n 0000000898 00000 n 0000003803 00000 n 0000004011 00000 n 0000004359 00000 n 0000004641 00000 n 0000004974 00000 n 0000005432 00000 n 0000005494 00000 n 0000005647 00000 n 0000006625 00000 n 0000007021 00000 n 0000007090 00000 n 0000007397 00000 n 0000007792 00000 n 0000019586 00000 n 0000019744 00000 n 0000020289 00000 n 0000020685 00000 n 0000020754 00000 n 0000021072 00000 n 0000021448 00000 n 0000033624 00000 n 0000068244 00000 n 0000068377 00000 n 0000138936 00000 n 0000139101 00000 n 0000340820 00000 n 0000341847 00000 n 0000341971 00000 n trailer << /Size 35 /Root 34 0 R /Info 33 0 R /ID [ ] >> startxref 342081 %%EOF
Questionnaires on Free Trade Agreement with the Philippines
2016-04-06 04:55:12
EU and the Philippines launch negotiations for a free trade agreement
EU Trade Commissioner Cecilia Malmström and Philippine Secretary of Trade and Industry Gregory Domingo agreed to start negotiations for an EU-Philippines free trade agreement (FTA).
Both sides share the ambition to conclude an agreement that covers a broad range of issues, including elimination of customs duties and other barriers to trade, services and investment, access to public procurement markets, as well as additional disciplines in the area of competition and protection of intellectual property rights. The prospective agreement will also include a comprehensive chapter that will ensure that closer economic relations between the EU and the Philippines go hand in hand with environmental protection and social development.
DG Trade has prepared two questionnaires to give stakeholders and interested parties the opportunity to provide information on trade matters in the agreement between the EU and the Philippines (FTA): one general for Industry and one specific on fisheries issues. Your reply to these questionnaires will be important in establishing priorities and taking decisions throughout the negotiating process and we thank you in advance for your contribution.
The general questionnaire is divided into the following sections: | 2022-06-25T04:42:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6367031931877136, "perplexity": 10562.204822453517}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034170.1/warc/CC-MAIN-20220625034751-20220625064751-00615.warc.gz"} |
https://par.nsf.gov/biblio/10371080-content-massive-red-spiral-galaxies-observed-fast | H i content of massive red spiral galaxies observed by FAST
ABSTRACT
A sample of 279 massive red spirals was selected optically by Guo et al., among which 166 galaxies have been observed by the ALFALFA survey. In this work, we observe H i content of the rest 113 massive red spiral galaxies using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). 75 of the 113 galaxies have H i detection with a signal-to-noise ratio (S/N) greater than 4.7. Compared with the red spirals in the same sample that have been observed by the ALFALFA survey, galaxies observed by FAST have on average a higher S/N, and reach to a lower H i mass. To investigate why many red spirals contain a significant amount of H i mass, we check colour profiles of the massive red spirals using images observed by the DESI Legacy Imaging Surveys. We find that galaxies with H i detection have bluer outer discs than the galaxies without H i detection, for both ALFALFA and FAST samples. For galaxies with H i detection, there exists a clear correlation between galaxy H i mass and g-r colour at outer radius: galaxies with higher H i masses have bluer outer discs. The results indicate that optically selected massive red spirals are not fully quenched, and the H i gas observed in more »
Authors:
; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10371080
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
516
Issue:
2
Page Range or eLocation-ID:
p. 2337-2347
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. The Arecibo Pisces-Perseus Supercluster Survey(APPSS) aims to measure the infall and mass density along the PPS filament using red-shift independent distances obtained from the Baryonic Tully-Fisher Relation (BTFR). We will combine photometric data from the Sloan Digital Sky Survey with HI line spectroscopy obtained with the Arecibo telescope to derive BTFR distances and peculiar velocities over the PPS volume and its immediate foreground and background. To supplement the ALFALFA detections in the PPS volume, we have conducted new HI line observations with the Arecibo L-band Wide receiver system of blue, low surface brightness galaxies identified by their photometric properties in the Sloan Digital Sky Survey (SDSS). These targets are predicted to lie in the PPS volume but with HI masses of 8.0 < log HI mass < 9.0, putting them below the ALFALFA detection limit at that distance. We compare a preliminary sample of 634 galaxies detected as part from the APPSS survey with the main ALFALFA survey and other public catalogs of local galaxies, confirming that the new APPSS HI line detections are rotation-dominated, HI bearing galaxies with low stellar mass. Nearly all are star-forming, bluer, and of lower surface brightness, extinction and metallicity than optically selected samples. Preliminarymore »
2. ABSTRACT
In our hierarchical structure-formation paradigm, the observed morphological evolution of massive galaxies – from rotationally supported discs to dispersion-dominated spheroids – is largely explained via galaxy merging. However, since mergers are likely to destroy discs, and the most massive galaxies have the richest merger histories, it is surprising that any discs exist at all at the highest stellar masses. Recent theoretical work by our group has used a cosmological, hydrodynamical simulation to suggest that extremely massive (M* > 1011.4 M⊙) discs form primarily via minor mergers between spheroids and gas-rich satellites, which create new rotational stellar components and leave discs as remnants. Here, we use UV-optical and H i data of massive galaxies, from the Sloan Digital Sky Survey, Galaxy Evolution Explorer, Dark Energy Camera Legacy Survey (DECaLS), and Arecibo Legacy Fast ALFA surveys, to test these theoretical predictions. Observed massive discs account for ∼13 per cent of massive galaxies, in good agreement with theory (∼11 per cent). ∼64 per cent of the observed massive discs exhibit tidal features, which are likely to indicate recent minor mergers, in the deep DECaLS images (compared to ∼60 per cent in their simulated counterparts). The incidence of these features is at least four times higher than in low-mass discs, suggesting that,more »
3. ABSTRACT
We present a catalogue of 16 551 edge-on galaxies created using the public DR2 data of the Pan-STARRS survey. The catalogue covers the three quarters of the sky above Dec. = −30°. The galaxies were selected using a convolutional neural network, trained on a sample of edge-on galaxies identified earlier in the SDSS survey. This approach allows us to dramatically improve the quality of the candidate selection and perform a thorough visual inspection in a reasonable amount of time. The catalogue provides homogeneous information on astrometry, SExtractor photometry, and non-parametric morphological statistics of the galaxies. The photometry is reliably for objects in the 13.8–17.4 r-band magnitude range. According to the HyperLeda data base, redshifts are known for about 63 per cent of the galaxies in the catalogue. Our sample is well separated into the red sequence and blue cloud galaxy populations. The edge-on galaxies of the red sequence are systematically Δ(g − i) ≈ 0.1 mag redder than galaxies oriented at an arbitrary angle to the observer. We found a variation of the galaxy thickness with the galaxy colour. The red sequence galaxies are thicker than the galaxies of the blue cloud. In the blue cloud, on average, thinner galaxies turn out to bemore »
4. ABSTRACT We present a detection of the splashback feature around galaxy clusters selected using the Sunyaev–Zel’dovich (SZ) signal. Recent measurements of the splashback feature around optically selected galaxy clusters have found that the splashback radius, rsp, is smaller than predicted by N-body simulations. A possible explanation for this discrepancy is that rsp inferred from the observed radial distribution of galaxies is affected by selection effects related to the optical cluster-finding algorithms. We test this possibility by measuring the splashback feature in clusters selected via the SZ effect in data from the South Pole Telescope SZ survey and the Atacama Cosmology Telescope Polarimeter survey. The measurement is accomplished by correlating these cluster samples with galaxies detected in the Dark Energy Survey Year 3 data. The SZ observable used to select clusters in this analysis is expected to have a tighter correlation with halo mass and to be more immune to projection effects and aperture-induced biases, potentially ameliorating causes of systematic error for optically selected clusters. We find that the measured rsp for SZ-selected clusters is consistent with the expectations from simulations, although the small number of SZ-selected clusters makes a precise comparison difficult. In agreement with previous work, when using opticallymore »
5. ABSTRACT
We present a pilot study to assess the potential of Hyper Suprime-Cam Public Data Release 2 (HSC-PDR2) images for the analysis of extended faint structures within groups of galaxies. We examine the intragroup light (IGL) of the group 400138 (Mdyn = 1.3 ± 0.5 × 1013 M⊙, z ∼ 0.2) from the Galaxy And Mass Assembly (GAMA) survey using Hyper Suprime-Cam Subaru Strategic Program Public Data Release 2 (HSC-SSP PDR2) images in g, r, and i bands. We present the most extended IGL measurement to date, reaching down to $\mu _{g}^{\rm {lim}}=30.76$ mag arcsec−2 (3σ; 10 × 10 arcsec2) at a semimajor axis of 275 kpc. The IGL shows mean colour values of g − i = 0.92, g − r = 0.60, and r − i = 0.32 (±0.01). The IGL stellar populations are younger (2–2.5 Gyr) and less metal rich ([Fe/H] ∼ −0.4) than those of the host group galaxies. We find a range of IGL fractions as a function of total group luminosity of ${\sim} 2\!-\!36 {{\ \rm per\ cent}}$ depending on the definition of IGL, with larger fractions the bluer the observation wavelength. The early-type to late-type galaxy ratio suggests that 400138 is a more evolved group, dominated by early-type galaxies, and the IGL fraction agrees with that of other similarly evolved groups.more » | 2023-03-21T00:37:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5167098641395569, "perplexity": 3545.4475804914955}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00511.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.06.010 | • •
内生性随机前沿模型估计方法研究：无需工具变量的Copula方法
• 出版日期:2019-06-25 发布日期:2019-06-13
The Estimation for Endogeneous Stochastic Frontier Models: Copula Approach without Instrumental Variables
Jiang Qingshan et al
• Online:2019-06-25 Published:2019-06-13
Abstract: Endogeneity is a common econometric problem. Ignoring Endogeneity will result in biased and inconsistent estimators. Some researches study the estimation methods for endogeneous stochastic frontier models, and these methods all need to find the instrumental variables for endogeneous independent variables. However the proper instrumental variables are usually hard to get. This paper aims at the situation when it’s hard to find the proper instrumental variables. Copula method and maximum simulated likelihood method are used to get the estimation of endogeneous stochastic frontier models and construct the new point estimation for technical inefficiencies. The new point estimation absorbs the information of endogeneous variables and is more efficient than the point estimation of JLMS. The numerical simulations show that the method in this paper gets higher accuracies compared with the existing methods. | 2022-11-29T10:39:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17774412035942078, "perplexity": 1855.90918878857}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710691.77/warc/CC-MAIN-20221129100233-20221129130233-00003.warc.gz"} |
https://gitee.com/wen-wei-li/Yanqi-Algebra-3 | ## 李文威 / Yanqi-Algebra-3 .gitee-modal { width: 500px !important; }
Explore and code with more than 8 million developers，Free private repositories ！：）
Notice: Creating folder will generate an empty file .keep, because not support in Git
This are the XeLaTeX sources for the my lecture notes on commutative algebra, entitled somewhat pompously as Yanqi Lake Lectures on Algebra, Part III. These notes have been used at
These notes are slightly outdated, poorly organized, and the mathematical contents have not been thoroughly checked yet. Please use them at your own risk. The author does not intend to publish these notes.
# How to compile
## System requirements
The source codes are to be compiled using XeLaTeX. The reader is assumed to work under the UN*X + bash environment.
The recipes below can be tweaked to work under Windows, but this is not recommended. The simplest solution is to go open-source.
We only need the standard packages and fonts, such as
The aforementioned OpenType fonts should be installed system-wide to be accessible by XeLaTeX.
For some strange reason, I used and installed the fonts TeX Gyre Heros Cn and TeX Gyre Pagella. In case of error messages related to these fonts, please look for the OTF files (in the directories in your computer which store TeX-related fonts) whose names begin with texgyreheroscn and texgyrepagella, then install them manually in your system.
Make sure that all the relevant packages/programs are installed. For reference, the author made the compilation using Arch-based Linux distributions with TeX Live 2018; the packages biber and texlive-science are required.
## Clone the files
Assume that Git has been installed on your computer. As a preparation for the compilation process, we will clone the files into ~/Yanqi-Algebra-3 in our home directory. In command line, type
cd ~
git clone https://github.com/wenweili/Yanqi-Algebra-3
All the source files are encoded in UTF-8, which is the de facto standard for storing multilingual texts (although the document is largely written in English). If you encounter problems in opening the source files under Windows, try to re-configure your editor or convert the encoding manually.
## Compile the TeX source
Move to the directory
cd ~/Yanqi-Algebra-3
Then, either type
latexmk -pdf -pdflatex="xelatex -shell-escape -interaction=nonstopmode %O %S" YAlg3
under bash, or more simply
make
The resulting PDF file should appear as YAlg3.pdf in the same directory. Note that the main file is YAlg3.tex.
To clean up everything in our directory except the PDF file, type
make clean
# The source codes
These notes are based on the standard book document class from LaTeX. Some other macros are outsourced to mycommands.sty and myarrows.sty.
# The cover page
The cover page is in the file Cover-page.pdf, which will automatically be included in the resulting main PDF file after compilation. It is made from the open source software Scribus; the source file in .sla format is not included here.
# Feedback
In case of problems of compilation, please kindly report to the author. Make sure that all the system requirements above are met, and provide detailed error messages. Other suggestions are also welcome.
Except possibly the photos and the logo of UCAS, the entire codebase is under CC BY-NC 4.0.
### Repository Comments ( 0 )
Yanqi Lake Lectures on Algebra, Part III expand collapse
CC-BY-4.0
No release | 2022-05-26T15:43:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5933253765106201, "perplexity": 5236.403067015915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00614.warc.gz"} |
http://dlmf.nist.gov/14.27 | # §14.27 Zeros
$\mathop{P^{\mu}_{\nu}\/}\nolimits\!\left(x\pm i0\right)$ (either side of the cut) has exactly one zero in the interval $(-\infty,-1)$ if either of the following sets of conditions holds:
• (a)
$\mu<0$, $\mu\notin\Integer$, $\nu\in\Integer$, and $\mathop{\sin\/}\nolimits\!\left((\mu-\nu)\pi\right)$ and $\mathop{\sin\/}\nolimits\!\left(\mu\pi\right)$ have opposite signs.
• (b)
$\mu,\nu\in\Integer$, $\mu+\nu<0$, and $\nu$ is odd.
For all other values of the parameters $\mathop{P^{\mu}_{\nu}\/}\nolimits\!\left(x\pm i0\right)$ has no zeros in the interval $(-\infty,-1)$.
For complex zeros of $\mathop{P^{\mu}_{\nu}\/}\nolimits\!\left(z\right)$ see Hobson (1931, §§233, 234, and 238). | 2016-05-29T15:26:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 13, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9075555801391602, "perplexity": 487.315022542194}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281363.50/warc/CC-MAIN-20160524002121-00177-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://npyb.wikidot.com/edit:wikidot-tutorial | Wikidot Tutorial
This page is dedicated to helping people understand how to write in Wikidot and format pages using Wikidot language. Although Wikidot is not a WYSIWYG editor, page content is not edited through HTML. Rather, Wikidot combines elements from HTML and CSS to create a unique system that everyone can understand.
Tool Bar
The first thing that you might notice when going to the editor is the tool bar. This tool bar is very useful for it will automatically place the necessary code for a certain thing to happen. For example, for bold text, you could press the large B button. This will create a **bold text**, and the text between the ** will be bold, like this.
Inline Formatting
Although you could use the tool bar, it is still useful to know what the raw coding is to yield various formatting. Observe the following table. This table shows inline text techniques that can be used to fine tune certain phrases or words and provide emphasis.
Text Style The Code What You Get
Bold **This is Bold** This is Bold
Italic //This is Italic// This is Italic
Underline __This is Underline__ This is Underline
Strikethrough --This is Strikethrough-- This is Strikethrough
Teletype {{This is Teletype}} This is Teletype
Superscript This is ^^superscript^^ This is superscript
Subscript This is ,,subscript,, This is subscript
Invisible Comment [!-- Invisible Comment --]
Combination //**Italic and Bold**// Italic and Bold
Change Color ##green|Green text## or ##AD5A12|Custom Color## Green text or Custom Color
Change Size Size by [[size x-small]]word[[/size]], [[size 130%]]percentage[[/size]], [[size 15px]]pixels[[/size]] Size by word, percentage, pixels
Literal Text @@ //This// **text** __is__ ^^literal^^ @@ //This// **text** __is__ ^^literal^^
Typography
There are other formatting things you can do. The ones above change the text directly. These will help with simple typography and basic page formatting.
The em Dash
An em dash is an elongated hyphen meant to show a break in thought. An em dash looks like — where a hyphen - is much shorter. To get an em dash, simply type two hyphens sequentially, like this: --. One thing you should know about the em dash is that there must be a space between the dash and the words if you have two of them in the same paragraph. Observe the examples below.
These -- em dashes -- have spaces.
These--em dashes--do not.
Only one--em dash.
These — em dashes — have spaces.
Theseem dashesdo not.
Only one—em dash.
Odds are, you won't need to worry about this anomaly.
Headings
You can create headings like the one above. There are six levels of headings that range in size. To create a heading, simply put plus signs in front of the word equal to the heading level.
+ Heading 1
++ Heading 2
+++ Heading 3
++++ Heading 4
+++++ Heading 5
++++++ Heading 6
++You need the space for the heading
A heading must be + on a new line.
Heading 1
Heading 2
Heading 3
Heading 4
Heading 5
Heading 6
++You need the space for the heading
A heading must be + on a new line.
Table of Contents
A table of contents is simply a box with all the headings in it. These headings are transcribed to links that short cut to the section. An example is the one at the top of this page. To create the table of contents, simply put [[toc]] on its own line. You can also direct where you want the table of contents to float left ([[f<toc]]) or float right ([[f>toc]]).
You can prevent a heading from showing up on the table of contents by appending the pluses with an asterisk.
++* This heading won't appear on the table of contents
Paragraphs
A paragraph on Wikidot is usually not indented. Rather, paragraphs are recognizable by new lines and spaces much like in a business letter.
This is one paragraph. This paragraph will talk about apples. Apples grow from trees known as apple trees. The apple is really a case for the seeds by which contain new apple trees. These casings are edible so that animals or humans would eat them and then deposit the seeds elsewhere.
This is a new paragraph. Rather than indenting, it is shown by pressing enter twice.
This paragraph is using indention. Notice that the indention does not render.
This is one paragraph. This paragraph will talk about apples. Apples grow from trees known as apple trees. The apple is really a case for the seeds by which contain new apple trees. These casings are edible so that animals or humans would eat them and then deposit the seeds elsewhere.
This is a new paragraph. Rather than indenting, it is shown by pressing enter twice.
This paragraph is using indention. Notice that the indention does not render.
Another thing to note is that pressing enter multiple times will not result in that many spaces. Pressing enter ten times will not create a large space. To counter this, on each new line, place a single underscore after a space.
Here is a code.
_
_
_
Just put a space and an underscore to forge a new line.
Here is a code.
Just put a space and an underscore to forge a new line.
Horizontal Divider
A horizontal divider is just a line that goes after a paragraph to represent a dramatic break in the text. All you have to do is type four or more hyphens (----) to get it.
The horizontal divider simply divides your paragraph further.
Lists
In Wikidot lists can be easily created. You can have bulleted lists or numbered lists.
Bulleted lists use an asterisk to display bullets.
* Item 1
* Item 2
* Item 2.1
• Item 1
• Item 2
• Item 2.1
Numbered lists use the pound sign to display numbers.
# Item 1
# Item 2
# Item 2.1
1. Item 1
2. Item 2
1. Item 2.1
The position in the list can be determined by the number of spaces placed before the asterisk or pound sign.
* Item
* Item
* Item
* Item
• Item
• Item
• Item
• Item
Links
One of the most important text renderings is the production of links. Links are like portals that when clicked take you to another place in the Internet. Links are usually a different color to show that it is a link, and its URL destination is shown in the bottom left corner.
In HTML, a link is usually defined with <a href="URL">Text</a>. However, Wikidot will not accept that particular syntax. Rather, links are usually surrounded by one or three square brackets. Here is a table of the different types of links you can make and their appropriate syntax.
Internal Links
This are links that map within the site.
Type The Code What you Get
Internal Link [[[Board]]] Board
Category Page [[[explicare:home]]] home
Custom Text [[[explicare:home| The Home Page]]] The Home Page
Non-existent Link [[[nowhere]]] nowhere
Link to a Section [[[explicare:home#toc0]]] home
External Links
These are links that go outside of the site.
Text Style The Code What You Get
External Link http://tarm.wikidot.com http://tarm.wikidot.com
Custom Text [http://tarm.wikidot.com The Archive] The Archive
New Window [*http://tarm.wikidot.com The Archive] The Archive
Fake Link [# Can't Click] Can't Click
Emails
Text Style The Code What You Get
Raw Email [email protected] moc.liamtoh|201soshc#moc.liamtoh|201soshc
Custom Text [[email protected] Sung] moc.liamtoh|201soshc#gnuS
Images
Images are an essential part in writing articles providing a little visual pizzazz and making the article slightly more appealing. The code for creating an image is relatively straightforward and not too hard to understand. To create an image, type in [[image URL]] where the URL is the image's URL. So, this code [[image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png]], will render the image.
You can do things to the image with attributes. These attributes follow the URL like this:
[[image URL attribute1="value1" attribute2="value2" ...]]
and you can align the image with the < or >.
[[f>image URL attribute1="value1" attribute2="value2" ...]] - Float right
[[f<image URL attribute1="value1" attribute2="value2" ...]] - Float left
[[>image URL attribute1="value1" attribute2="value2" ...]] - Align right
[[<image URL attribute1="value1" attribute2="value2" ...]] - Align left
[[=image URL attribute1="value1" attribute2="value2" ...]] - Center
The attributes could be any of these things in the table.
Attribute Example Function
link "http://npyb.wikidot.com" This allows the picture to link somewhere.
width "160px", "30%" This will change the width of the image. When no height is given, the image automatically scales itself.
height "160px" This will change the height of the image. When no width is given, the image automatically scales itself.
alt "Image Unavailable" This displays an alternate text in case the image is unavailable.
style "border:1px solid #000;" This will allow you to add CSS styling to the image
class "custom-image" This allows you to pull out a CSS name to render the image.
Here are some examples of images.
[[image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png link="http://npyb.wikidot.com"]]
[[image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png width="40px"]]
[[=image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png link="http://npyb.wikidot.com" width="60%" height="75px"]]
[[image http://npyb.wikidot.com/local--files/explicare:home/non-existantfile.png alt="No Image"]]
[[>image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png style="border:2px solid #F00;"]]
There is another type of way to display images. With the use of [[gallery]], you can showcase all the pictures that are uploaded to a particular page.
Code Block
To show code, use [[code]]...[[/code]].
For example:
{{@@[[>image http://npyb.wikidot.com/local--files/explicare:home/nopicinews.png style="border:2px solid #F00;"]]@@}}
You can specify the code type. For example, if we were displaying HTML code, we can do [[code type="html"]]...[[/code]].
<p>…that you can use <a href="/tanh">tanh</a>(<sub>E</sub>9X to compute the sign of X?</p>
</div></td>
</tr>
</table>
<table style="background: #4A537D; border: 1px solid #4A537D; width: 100%;">
<tr>
<td class="infobox" style="font-size:140%; text-align:center;"><strong><a href="/top-rated">Top Rated Programs</a></strong></td>
</tr>
<tr>
<td style="background: #FFF; padding: 0 2% 10px;"><div class="list-pages-box">
Collapsible Block
A collapsible block is a link type thing that when clicked pulls down some content.
To do this, simply follow this code.
[[collapsible]]
text here
[[/collapsible]]
The collapsible has the links "show block" and "hide block". You can change those by putting a show="text" and hide="text". For example,
[[collapsible show="+ Click here" hide="- Hide this now"]]
Hello!
[[/collapsible]]
Finally, you can determine whether or not you want it to originally start with it showing or hiding. By adding a folded="yes/no" attribute, you can determine whether it will be hidden first or showing first. If you type yes, then it will be hidden. If you type no, then it will be showing.
Div and Span Blocks
Div and span blocks are the core of the formatting world. These elements allow you to add CSS style to blocks of text or paragraphs. Span is used with [[span style="css"]]...[[/span]]. Span styles a line of text. Div is used with [[div style="css"]]...[[/div]]. Div styles a paragraph of text.
The css is a simple CSS styling to allow you to align text, change color or font, add background, and other things. The table below shows some of the basic attributes used for these.
Attribute Allowed Values Function
border:size style color px or em; solid, dashed, or dotted; hexadecimal code This adds a border around the element
background-color:color hexadecimal code This changed the color of the background
background-image:url(image URL) The image source This makes the background an image
margin:top right bottom left px, %, or em; auto This creates a margin of space. Four values are used for the top margin, right margin, bottom margin, and left margin. Auto centers the div
padding:top right bottom left px, %, or em This pads the text from the outside borders a specified space
color:color hexadecimal code This changes the color of the text.
width:width px, em, or %; auto This sets the width of the block
height:height px or em This sets the height of the block
font-family:font any font name This changes the font of the text
text-align:alignment left, right, or center This allows the text to be realigned
float:float left or right This floats the element which allows text to wrap around the element
text-decoration:decoration underline, overline, or blink This embellishes the text
font-size:size px, pt, or % This changes the text-size in the whole element
The primary difference between span and div is that span is used for inline text, whereas div is used for an entire section. So with span, I can do this, but I cannot with div. The disadvantage that span has is that it cannot use a lot of the attributes listed above. Div can use all of them, and you can use div to create a floating text box anywhere.
Here is an example of a div block with some span styles within it.
Using the div element, I have created a side bar. In this side bar, I can put any content I want. Explaining why I chose the attributes I did, I chose float:right so that this block goes to the right. The margin is set to 0 0 1em 1em. This means that the margin is 0 on top, 0 on the right, 1em on the bottom, and 1em on the left. The padding is set to 0 1em 0 1em which means the text will be 1em from the right and left sides on the inside of this block. So, margin is outside spacing, padding is inside spacing. The background is the hex color #FEEAB6. If you do not know about hexadecimal colors, read here. I set the border to only display on the left by adding the -left after border. You can do this for the top, right and bottom as well. To do combinations, you need separate border commands, for example border-right:code;border-left:code. The width is set to 20em so that it doesn't go the entire width of the screen. By the way, em is a form of measurement.
This text on the other side of the side bar because of the float attribute. Float allows text to "wrap around" a div block or image. This proves useful in formatting a new side bar like this or creating little note blocks.
Notice the horizontal rule does not cut through the div block. This is quite handy since Wikidot automatically resizes the line width. Span style can allow you to change inline text. This allows you to embellish text like making it blink, or changing its size. You can even change letter and word spacing. Of course, you can combine multiple things, as long as it looks pleasing!
The other thing is that within a span element, along with the div element, you can still use the wiki inline styles used before. Bold and italics still work for example.
There are so many possibilities you can do.
Good job! You found this! With span, you can make text white and therefore make it "invisible". The invisible comment syntax, [!-- Something --] will not let you highlight it making it "not present".
⇧⇧⇧ What's with the space? ⇧⇧⇧
Here is the code for the above example. Go ahead and study and learn. By the way, you can escape the float by typing four squiggles (~~~~).
[[div style="float:right; margin:0 0 1em 1em; padding:0 1em 0 1em; background-color:#FEEAB6; border-left:1px solid #000; width:20em;"]]
Using the div element, I have created a side bar. In this side bar, I can put any content I want. Explaining why I chose the attributes I did, I chose {{float:right}} so that this block goes to the right. The margin is set to {{0 0 1em 1em}}. This means that the margin is 0 on top, 0 on the right, 1em on the bottom, and 1em on the left. The padding is set to {{0 1em 0 1em}} which means the text will be 1em from the right and left sides on the inside of this block. **So, margin is outside spacing, padding is inside spacing.** The background is the hex color #FEEAB6. If you do not know about hexadecimal colors, read [*http://tarm.wikidot.com/art:computer-images here]. I set the border to only display on the left by adding the {{-left}} after {{border}}. You can do this for the top, right and bottom as well. To do combinations, you need separate border commands, for example {{border-right://code//;border-left://code//}}. The width is set to 20em so that it doesn't go the entire width of the screen. By the way, [*http://en.wikipedia.org/wiki/Em_(typography) em] is a form of measurement.
[[/div]]
This text on the other side of the side bar because of the float attribute. Float allows text to "wrap around" a div block or image. This proves useful in formatting a new side bar like this or creating little note blocks.
----
Notice the horizontal rule does not cut through the div block. This is quite handy since Wikidot automatically resizes the line width. [[span style="font-family:Times New Roman; color:#0060FF;"]]Span style can allow you to change inline text.[[/span]] This allows you to embellish text like [[span style="text-decoration:blink;"]]making it blink[[/span]], or [[span style="font-size:140%;"]]changing its size[[/span]]. You can even change [[span style="letter-spacing:3pt; word-spacing:6pt;"]]letter and word spacing[[/span]]. Of course, you can [[span style="text-decoration:overline; letter-spacing:-2px; color:#FF5623; font-size: 140%; font-family:Gothic Wide;"]]combine multiple things, as long as it looks pleasing![[/span]]
The other thing is that within a span element, along with the div element, you can still use the wiki inline styles used before. [[span style="color:teal;"]]**Bold** and //italics// still work for example.[[/span]]
There are so many possibilities you can do.
[[span style="color:#FFF;"]]Good job! You found this! With span, you can make text white and therefore make it "invisible". The invisible comment syntax, @@[!-- Something --]@@ will not let you highlight it making it "not present".[[/span]]
= ⇧⇧⇧ What's with the space? ⇧⇧⇧
~~~~
Tables
Tables are very useful being able to chart information in a quick and orderly fashion. Wikidot allows tables to be created very easily for quick tables. There are two types of tables one being quick and easy and the other being a little harder. With tables, you can even perform very advanced formatting that div blocks alone couldn't handle.
Simple Table
A simple table is one of which looks like the tables found above. They are simple in nature and show the information very quickly. Also, the coding is very simple as well.
To create a table, use || (two vertical dividers) to distinguish cells along a row. To create a new column, make a new line. So, this table here:
A B C D E F 1 2 3 4 5
Has the code:
|| ||A||B||C||D||E||F||
||1|| || || || || || ||
||2|| || || || || || ||
||3|| || || || || || ||
||4|| || || || || || ||
||5|| || || || || || ||
With this table, you can create header cells that make the cell a different color and bolds the text. To do that, simply put a squiggle right after the || and then a space. It would look like ||~ Text||. So, we can upgrade the table.
A B C D E F
1
2
3
4
5
||~ ||~ A||~ B||~ C||~ D||~ E||~ F||
||~ 1|| || || || || || ||
||~ 2|| || || || || || ||
||~ 3|| || || || || || ||
||~ 4|| || || || || || ||
||~ 5|| || || || || || ||
You can elongate cells by getting rid of some spaces between the ||'s. The length of the cell is determined by the number of ||'s put in front of the cell divided by two. You do not need to put that many after the cell. You cannot merge cells vertically.
A B C D E F
1
2
3
4
5
||~ ||~ A||~ B||~ C||~ D||~ E||~ F||
||~ 1|||| || || || || ||
||~ 2|| |||| || || || ||
||~ 3|| || || || || || ||
||~ 4|| |||||| || || ||
||~ 5|||||||||||| ||
Custom Tables
You can create more elaborate tables in case you are in need of style or column like formatting. With a custom table, you can define cell colors, borders, cell styles, and place the table. The formatting is much like that of the div block if you feel like getting stylish.
The basic code uses [[table]], [[row]], and [[cell]]. The [[table]] states that a table has started. When you put [[row]], then a new row (meaning horizontal) has been created. When [[cell]] is put, then a cell is made. To end these, use the [[/cell]] and such.
So, a super basic custom table would use those tags.
R1C1 R1C2 R2C1 R2C2
[[table]]
[[row]]
[[cell]]
R1C1
[[/cell]]
[[cell]]
R1C2
[[/cell]]
[[/row]]
[[row]]
[[cell]]
R2C1
[[/cell]]
[[cell]]
R2C2
[[/cell]]
[[/row]]
[[/table]]
That table made above was extremely simple with no customization at all. In order to customize the table, you use the CSS attributes like the ones used for the div blocks. Simply add the code style="css" in the tags. So, to customize the table, you would do [[table style="css"]], and this is similar for the row and cell tags.
Now you can really get down and dirty with tables. The best way to get good at custom tables is by experimenting with the CSS attributes. We can alter that super simple table above and make it so that each cell is a different color, each row has a different font size, and the entire table has a different font.
R1C1 R1C2 R2C1 R2C2
You can get rid of the space by adding the attribute border-collapse:collapse in the [[table style="css"]].
R1C1 R1C2 R2C1 R2C2
You can really get creative using tables and create these text boxes.
Text Box Using tables, this text box is able to be created. It is very simple. This box is really a two rows by one column table. The title is in the first row, first column, and this text is in the second row, first column. There are tons of things you can do with tables, and experimentation is the best way how!
Math Equations
Another thing that is useful is the math equations syntax. This allows you to easily display a math formula that may have various symbols and signs. Also, the font used makes it seem "mathish". Here are two examples, one is the quadratic formula and the other is a Pythagorean trigonometry rule.
(1)
\begin{align} {-b\pm\sqrt{b^2-4ac}} \over {2a} \\ \\ \sin^2\theta+\cos^2\theta=1 \end{align}
To create a math equation, use the tags [$]...[$]. The math coding uses LaTeX to interpret what is being displayed. LaTeX is much different from the ordinary wiki syntax, for example, a superscript like in x2 is written as x^2.
Special symbols and commands are identified with a backslash (\) preceding the command. For example, to display the plus-minus symbol, I typed \pm. The Theta ($\theta$) is written out with \theta.
As a reference, here is a link that leads to an index of the various math commands:
http://www.giss.nasa.gov/tools/latex/ltx-2.html
You can put mathematical expressions inline as well. To render that theta symbol above in between the parentheses, I couldn't use the normal [$]...[$] to display it. That command must create a new line. Rather, to put an equation inline, like $E=mc^2$, you must put the LaTeX commands and formatting in between [[$...$]]. That is, two brackets and a dollar sign. So, to render Einstein's equation, I put the code [[$E=mc^2$]] in between the "like" and "you".
Finally, you can reference math equations that use [[math label#]]...[[/math]]. If you look at the example above, you will notice a little "(1)" on the right side. This is a label. With that label in mind, I can make a reference to equation 1. To do this, simply put [[eref label//#//]] where you want it where # is the label number. As an additional requirement, you must also have the label# after the []. Here is the code for the math equation used above. [[math label1]] \begin{align} {-b\pm\sqrt{b^2-4ac}} \over {2a} \\ \\ \sin^2\theta+\cos^2\theta=1 \end{align} []
Tabview
Tabview is a special type of formatting used to create tabs with content under each tab. The tabview then allows you to click on the tabs so you can access content under various topics. This form of formatting is used rarely and can cause problems with the table of contents rendering.
As you can see, the tabview looks pretty neat. You are able to quickly switch between different topics of information. This text will be replaced with new text when you click on a new tab. Go ahead and see.
Embedding Code
In Wikidot, you are able to embed code from other sources to produce something like a gadget. With the [[embed]]...[[/embed]], you can take a code for a gadget of some sort and embed it into the site. For example, you can embed a zoho poll. Just put the code in between the embed tags and watch what happens!
[[embed]]
<iframe frameborder='0' src='http://zohopolls.com/external/redbeard/is-polling-cool' width='260' height='210'></iframe>
[[/embed]]
Be careful, however. Some codes will not work, and you will get this message:
Sorry, no match for the embedded content.
You can embed stuff using a different tag called [[iframe]]. Iframe words a little differently in that it allows you to embed any URL. Simply fill out the iframe in this way:
[[iframe URL attributes]]
The attributes could be anything in this chart.
Attribute Allowed Values Function
frameborder 0, 1 This will either turn the border off (0) or on (1). It is on by default.
align left, right, center, middle This aligns the iframe to a specified justification.
width px, % This sets the width of the element.
height px This sets the height of the element
scrolling yes, no This will toggle whether or not you are allowed to scroll if the URL element is too large for the border.
style any CSS attribute This of course lets you use CSS styling.
This concludes the general Wiki syntax tutorial. If you ever have a question, please ask in the forums. Thanks for reading!
Reference: http://www.wikidot.com/doc:wiki-syntax
Written by:
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License | 2018-04-25T22:06:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6033875346183777, "perplexity": 3017.0589355627963}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947968.96/warc/CC-MAIN-20180425213156-20180425233156-00429.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Arousseau.christiane | # zbMATH — the first resource for mathematics
## Rousseau, Christiane
Compute Distance To:
Author ID: rousseau.christiane Published as: Rousseau, C.; Rousseau, Christian; Rousseau, Christiane; Rousseau, Christine; Russo, K. Homepage: http://dms.umontreal.ca/fr/repertoire-departement/professeurs/portrait/rousseac External Links: MGP · Math-Net.Ru · Wikidata · ORCID · GND
Documents Indexed: 96 Publications since 1978, including 5 Books Biographic References: 2 Publications
all top 5
#### Co-Authors
25 single-authored 7 Christopher, Colin J. 7 Dumortier, Freddy 7 Patera, Jiří 6 Roussarie, Robert 5 Mardešić, Pavao 5 Schlomiuk, Dana I. 4 Lambert, Caroline 3 Klimeš, Martin 3 Li, Chengzhi 3 Saint-Aubin, Yvan 3 Toni, Bourama 3 Zhu, Huaiping 2 Guimond, Louis-Sébastien 2 Guzmán, Ana 2 Hurtubise, Jacques C. 2 Ilyashenko, Yulij Sergeevich 2 Kaper, Hans G. 2 Krauskopf, Bernd 2 Lopez, Salvatore 2 Żołądek, Henryk 1 Arriagada-Silva, Waldo 1 Blows, Terence R. 1 Colli, Eduardo 1 Coutu, Caroline 1 del Olmo, Mariano A. 1 El Morsalani, Mohamed 1 Etoua, Remy Magloire 1 Gagnon, Jean-François 1 Hénot, Olivier 1 Joyal, Pierre 1 Khibnik, Alexander I. 1 Koh, In-Guy 1 Koh, In-Gyu 1 La Sala, G. 1 Lamontagne, Yann 1 Laurin, Sophie 1 Moser-Jauslin, Lucy 1 Nemenzo, Fidel Ronquillo 1 Polthier, Konrad 1 Rodriquez, M. A. 1 Sabidussi, Gert 1 Shan, Chunhua 1 Świrszcz, Grzegorz M. 1 Teyssier, Loïc 1 Thibaudeau, Pierre 1 Wang, Xian
all top 5
#### Serials
20 Journal of Differential Equations 7 Nonlinearity 6 Journal of Mathematical Physics 6 Qualitative Theory of Dynamical Systems 6 Moscow Mathematical Journal 4 Journal of Dynamical and Control Systems 3 Annales des Sciences Mathématiques du Québec 3 Canadian Mathematical Bulletin 2 Canadian Journal of Mathematics 2 Journal of Pure and Applied Algebra 2 Ergodic Theory and Dynamical Systems 2 Notices of the American Mathematical Society 2 International Journal of Structural Stability and Dynamics 2 Springer Undergraduate Texts in Mathematics and Technology 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annales Polonici Mathematici 1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 1 Transactions of the Moscow Mathematical Society 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Publicacions Matemàtiques 1 IMRN. International Mathematics Research Notices 1 Journal of Physics A: Mathematical and General 1 Journal of Dynamics and Differential Equations 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Conformal Geometry and Dynamics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Nonlinear Analysis. Theory, Methods & Applications 1 Other Titles in Applied Mathematics 1 Springer-Lehrbuch
all top 5
#### Fields
53 Ordinary differential equations (34-XX) 44 Dynamical systems and ergodic theory (37-XX) 11 Several complex variables and analytic spaces (32-XX) 9 General and overarching topics; collections (00-XX) 6 Nonassociative rings and algebras (17-XX) 6 Category theory; homological algebra (18-XX) 5 Mathematical logic and foundations (03-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Topological groups, Lie groups (22-XX) 5 Geophysics (86-XX) 4 Functions of a complex variable (30-XX) 4 Biology and other natural sciences (92-XX) 3 History and biography (01-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mathematics education (97-XX) 2 Combinatorics (05-XX) 2 Special functions (33-XX) 2 Differential geometry (53-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Mechanics of particles and systems (70-XX)
#### Citations contained in zbMATH Open
73 Publications have been cited 957 times in 595 Documents Cited by Year
Linearization of isochronous centers. Zbl 0830.34023
Mardešić, P.; Rousseau, C.; Toni, B.
1995
Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028
Dumortier, F.; Roussarie, R.; Rousseau, C.
1994
Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $$\mathbb{C}^2$$. Zbl 1022.37035
Christopher, C.; Mardešić, P.; Rousseau, C.
2003
Cubic Liénard equations with linear damping. Zbl 0716.58023
Dumortier, Freddy; Rousseau, Christiane
1990
Local bifurcations of critical periods in the reduced Kukles system. Zbl 0885.34033
Rousseau, C.; Toni, B.
1997
Bifurcation at infinity in polynomial vector fields. Zbl 0778.34024
Blows, T. R.; Rousseau, C.
1993
Darboux linearization and isochronous centers with a rational first integral. Zbl 0881.34041
Mardešić, P.; Moser-Jauslin, L.; Rousseau, C.
1997
Local bifurcation of critical periods in vector fields with homogeneous nonlinearities of the third degree. Zbl 0792.58030
Rousseau, C.; Toni, B.
1993
Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043
Dumortier, F.; Roussarie, R.; Rousseau, C.
1994
Saddle quantities and applications. Zbl 0684.34033
Joyal, Pierre; Rousseau, Christian
1989
Bifurcation analysis of a predator-prey system with generalised Holling type III functional response. Zbl 1160.34047
Lamontagne, Yann; Coutu, Caroline; Rousseau, Christiane
2008
Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III. Zbl 1217.34080
Etoua, Remy Magloire; Rousseau, Christiane
2010
A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4. Zbl 0684.34048
Li, Chengzhi; Rousseau, Christine
1989
Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system. Zbl 1100.34022
Christopher, Colin; Rousseau, Christiane
2004
Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046
Dumortier, F.; El Morsalani, M.; Rousseau, C.
1996
Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type. Zbl 1012.34028
Zhu, Huaiping; Rousseau, Christiane
2002
Global study of a family of cubic Liénard equations. Zbl 0920.58034
Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane
1998
Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $$\mathbb C^2$$. Zbl 0984.34023
Christopher, C.; Rousseau, C.
2001
The centres in the reduced Kukles system. Zbl 0830.34025
Rousseau, Christiane; Schlomiuk, Dana; Thibaudeau, Pierre
1995
Zeroes of complete elliptic integrals for 1:2 resonance. Zbl 0738.33014
Rousseau, Christiane; Żołądek, Henryk
1991
Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms. Zbl 1077.37035
Mardešić, P.; Roussarie, R.; Rousseau, C.
2004
Cubic vector fields symmetric with respect to a center. Zbl 0839.34035
Rousseau, C.; Schlomiuk, D.
1995
Codimension 2 symmetric homoclinic bifurcations and application to 1:2 resonance. Zbl 0714.58039
Li, Chengzhi; Rousseau, Christiane
1990
Codimension-three unfoldings of reflectionally symmetric planar vector fields. Zbl 0904.34025
Krauskopf, Bernd; Rousseau, Christiane
1997
PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert’s 16th problem. Zbl 1046.34055
Rousseau, Christiane; Zhu, Huaiping
2004
Analytical moduli for unfoldings of saddle-node vector fields. Zbl 1165.37016
Rousseau, Christiane; Teyssier, Loïc
2008
Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle. Zbl 1127.37039
Rousseau, Christiane; Christopher, Colin
2007
Complete system of analytic invariants for unfolded differential linear systems with an rank $$k$$ irregular singularity of Poincaré. Zbl 1302.34131
Hurtubise, Jacques; Lambert, Caroline; Rousseau, Christiane
2014
Clebsch-Gordan coefficients for $$E_ 6$$ and SO(10) unification models. Zbl 0556.22011
Koh, In-Guy; Patera, J.; Rousseau, C.
1984
Complex orthogonal and symplectic matrices depending on parameters. Zbl 0495.17007
Patera, J.; Rousseau, C.
1982
Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1263.34127
Lambert, Caroline; Rousseau, Christiane
2012
Genericity conditions for finite cyclicity of elementary graphics. Zbl 0930.34020
Guzmán, Ana; Rousseau, Christiane
1999
Almost planar homoclinic loops in $$\mathbb{R}^ 3$$. Zbl 0849.34036
Roussarie, Robert; Rousseau, Christiane
1996
The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle. Zbl 1204.37048
Rousseau, Christiane
2010
Modulus of orbital analytic classification for a family unfolding a saddle-node. Zbl 1089.37018
Rousseau, Christiane
2005
Normalizability, synchronicity, and relative exactness for vector fields in $$\mathbb C^2$$. Zbl 1068.37030
Christopher, C.; Mardešić, P.; Rousseau, C.
2004
Versal deformations of elements of classical Jordan algebras. Zbl 0523.17001
Patera, J.; Rousseau, C.
1983
Topos theory and complex analysis. Zbl 0433.32003
Rousseau, Christiane
1979
Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044
Dumortier, F.; Ilyashenko, Y.; Rousseau, C.
2002
Generalized Hopf bifurcations and applications to planar quadratic systems. Zbl 0666.34035
Rousseau, C.; Schlomiuk, D.
1988
Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation. Zbl 0626.34021
Rousseau, Christiane
1987
Improving stability in the time-stepping analysis of structural nonlinear dynamics. Zbl 1205.74182
Lopez, Salvatore; Russo, K.
2008
The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation. Zbl 1147.34064
Lambert, Caroline; Rousseau, Christiane
2008
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1134.37021
Christopher, Colin; Rousseau, Christiane
2007
A simple proof for the unicity of the limit cycle in the Bogdanov-Takens system. Zbl 0706.34026
Li, Chengzhi; Rousseau, Christiane; Wang, Xian
1990
Clebsch-Gordan coefficients for SU(5)$$\supset SU(3)\times SU(2)\times U(1)$$ theories. Zbl 0552.22008
Koh, In-Gyu; Patera, J.; Rousseau, C.
1983
Generic $$2$$-parameter perturbations of parabolic singular points of vector fields in $$\mathbb C$$. Zbl 1403.37057
Klimeš, Martin; Rousseau, Christiane
2018
Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension $$k$$ parabolic point. Zbl 1308.32018
Rousseau, C.
2015
Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1292.34085
Lambert, Caroline; Rousseau, Christiane
2013
Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020
Dumortier, Freddy; Rousseau, Christiane
2009
Normal forms for germs of analytic families of planar vector fields unfolding a generic saddle-node or resonant saddle. Zbl 1103.34024
Rousseau, Christiane
2006
Cyclicity of graphics with semi-hyperbolic points inside quadratic systems. Zbl 0989.37047
Rousseau, C.; Świrszcz, G.; Żołądek, H.
1998
Hilbert’s 16-th problem for quadratic vector fields and cyclicity of graphics. Zbl 0895.34025
Rousseau, Christiane
1997
Bifurcation methods in polynomial systems. Zbl 0791.58080
Rousseau, Christiane
1993
Clebsch-Gordan coefficients for SU(5) unification models. Zbl 0617.22020
del Olmo, Mariano A.; Patera, J.; Rodriquez, M. A.; Rousseau, C.
1987
Versal deformations of elements of real classical Lie algebras. Zbl 0507.17006
Patera, J.; Rousseau, C.; Schlomiuk, D.
1982
The bifurcation diagram of cubic polynomial vector fields on $$\mathbb{C}\mathbb{P}^1$$. Zbl 1372.37095
Rousseau, C.
2017
Moduli space for generic unfolded differential linear systems. Zbl 1361.34099
Hurtubise, Jacques; Rousseau, Christiane
2017
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1351.37192
Christopher, Colin; Rousseau, Christiane
2014
The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations. Zbl 1242.58021
2011
Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III. Zbl 1236.34059
Laurin, Sophie; Rousseau, Christiane
2011
The root extraction problem. Zbl 1118.37016
Rousseau, C.
2007
Bifurcation methods in quadratic systems. Zbl 0649.34036
Rousseau, Christiane
1987
Dimensions of orbits and strata in complex and real classical Lie algebras. Zbl 0488.22037
Patera, J.; Rousseau, C.; Schlomiuk, D.
1982
Topos theory and complex analysis. Zbl 0378.02028
Rousseau, Christiane
1978
Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems. Zbl 1334.34077
Roussarie, Robert; Rousseau, Christiane
2015
An approach to statical and quasi-statical nonlinear analysis of structures in small strains and finite rotations hypotheses. Zbl 1359.74424
Lopez, S.; Russo, K.; La Sala, G.
2013
The modulus of unfoldings of cusps in conformal geometry. Zbl 1234.58009
Rousseau, C.
2012
Finite cyclicity of nilpotent graphics of pp-type surrounding a center. Zbl 1165.34019
Roussarie, R.; Rousseau, C.
2008
Mathematics and technology. With the participation of Hélène Antaya and Isabelle Ascah-Coallier. Translated by Chris Hamilton. Zbl 1211.00020
Rousseau, Christiane; Saint-Aubin, Yvan
2008
Mathematics and technology. With the collaboration of Hélène Antaya and Isabelle Ascah-Coallier. Zbl 1172.00001
Rousseau, Christiane; Saint-Aubin, Yvan
2008
Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062
Dumortier, F.; Guzmán, A.; Rousseau, C.
2002
Nombres réels et complexes dans les topos spatiaux. Zbl 0411.18004
Rousseau, Christiane
1979
Generic $$2$$-parameter perturbations of parabolic singular points of vector fields in $$\mathbb C$$. Zbl 1403.37057
Klimeš, Martin; Rousseau, Christiane
2018
The bifurcation diagram of cubic polynomial vector fields on $$\mathbb{C}\mathbb{P}^1$$. Zbl 1372.37095
Rousseau, C.
2017
Moduli space for generic unfolded differential linear systems. Zbl 1361.34099
Hurtubise, Jacques; Rousseau, Christiane
2017
Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension $$k$$ parabolic point. Zbl 1308.32018
Rousseau, C.
2015
Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems. Zbl 1334.34077
Roussarie, Robert; Rousseau, Christiane
2015
Complete system of analytic invariants for unfolded differential linear systems with an rank $$k$$ irregular singularity of Poincaré. Zbl 1302.34131
Hurtubise, Jacques; Lambert, Caroline; Rousseau, Christiane
2014
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1351.37192
Christopher, Colin; Rousseau, Christiane
2014
Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1292.34085
Lambert, Caroline; Rousseau, Christiane
2013
An approach to statical and quasi-statical nonlinear analysis of structures in small strains and finite rotations hypotheses. Zbl 1359.74424
Lopez, S.; Russo, K.; La Sala, G.
2013
Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1263.34127
Lambert, Caroline; Rousseau, Christiane
2012
The modulus of unfoldings of cusps in conformal geometry. Zbl 1234.58009
Rousseau, C.
2012
The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations. Zbl 1242.58021
2011
Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III. Zbl 1236.34059
Laurin, Sophie; Rousseau, Christiane
2011
Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III. Zbl 1217.34080
Etoua, Remy Magloire; Rousseau, Christiane
2010
The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle. Zbl 1204.37048
Rousseau, Christiane
2010
Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020
Dumortier, Freddy; Rousseau, Christiane
2009
Bifurcation analysis of a predator-prey system with generalised Holling type III functional response. Zbl 1160.34047
Lamontagne, Yann; Coutu, Caroline; Rousseau, Christiane
2008
Analytical moduli for unfoldings of saddle-node vector fields. Zbl 1165.37016
Rousseau, Christiane; Teyssier, Loïc
2008
Improving stability in the time-stepping analysis of structural nonlinear dynamics. Zbl 1205.74182
Lopez, Salvatore; Russo, K.
2008
The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation. Zbl 1147.34064
Lambert, Caroline; Rousseau, Christiane
2008
Finite cyclicity of nilpotent graphics of pp-type surrounding a center. Zbl 1165.34019
Roussarie, R.; Rousseau, C.
2008
Mathematics and technology. With the participation of Hélène Antaya and Isabelle Ascah-Coallier. Translated by Chris Hamilton. Zbl 1211.00020
Rousseau, Christiane; Saint-Aubin, Yvan
2008
Mathematics and technology. With the collaboration of Hélène Antaya and Isabelle Ascah-Coallier. Zbl 1172.00001
Rousseau, Christiane; Saint-Aubin, Yvan
2008
Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle. Zbl 1127.37039
Rousseau, Christiane; Christopher, Colin
2007
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1134.37021
Christopher, Colin; Rousseau, Christiane
2007
The root extraction problem. Zbl 1118.37016
Rousseau, C.
2007
Normal forms for germs of analytic families of planar vector fields unfolding a generic saddle-node or resonant saddle. Zbl 1103.34024
Rousseau, Christiane
2006
Modulus of orbital analytic classification for a family unfolding a saddle-node. Zbl 1089.37018
Rousseau, Christiane
2005
Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system. Zbl 1100.34022
Christopher, Colin; Rousseau, Christiane
2004
Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms. Zbl 1077.37035
Mardešić, P.; Roussarie, R.; Rousseau, C.
2004
PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert’s 16th problem. Zbl 1046.34055
Rousseau, Christiane; Zhu, Huaiping
2004
Normalizability, synchronicity, and relative exactness for vector fields in $$\mathbb C^2$$. Zbl 1068.37030
Christopher, C.; Mardešić, P.; Rousseau, C.
2004
Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $$\mathbb{C}^2$$. Zbl 1022.37035
Christopher, C.; Mardešić, P.; Rousseau, C.
2003
Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type. Zbl 1012.34028
Zhu, Huaiping; Rousseau, Christiane
2002
Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044
Dumortier, F.; Ilyashenko, Y.; Rousseau, C.
2002
Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062
Dumortier, F.; Guzmán, A.; Rousseau, C.
2002
Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $$\mathbb C^2$$. Zbl 0984.34023
Christopher, C.; Rousseau, C.
2001
Genericity conditions for finite cyclicity of elementary graphics. Zbl 0930.34020
Guzmán, Ana; Rousseau, Christiane
1999
Global study of a family of cubic Liénard equations. Zbl 0920.58034
Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane
1998
Cyclicity of graphics with semi-hyperbolic points inside quadratic systems. Zbl 0989.37047
Rousseau, C.; Świrszcz, G.; Żołądek, H.
1998
Local bifurcations of critical periods in the reduced Kukles system. Zbl 0885.34033
Rousseau, C.; Toni, B.
1997
Darboux linearization and isochronous centers with a rational first integral. Zbl 0881.34041
Mardešić, P.; Moser-Jauslin, L.; Rousseau, C.
1997
Codimension-three unfoldings of reflectionally symmetric planar vector fields. Zbl 0904.34025
Krauskopf, Bernd; Rousseau, Christiane
1997
Hilbert’s 16-th problem for quadratic vector fields and cyclicity of graphics. Zbl 0895.34025
Rousseau, Christiane
1997
Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046
Dumortier, F.; El Morsalani, M.; Rousseau, C.
1996
Almost planar homoclinic loops in $$\mathbb{R}^ 3$$. Zbl 0849.34036
Roussarie, Robert; Rousseau, Christiane
1996
Linearization of isochronous centers. Zbl 0830.34023
Mardešić, P.; Rousseau, C.; Toni, B.
1995
The centres in the reduced Kukles system. Zbl 0830.34025
Rousseau, Christiane; Schlomiuk, Dana; Thibaudeau, Pierre
1995
Cubic vector fields symmetric with respect to a center. Zbl 0839.34035
Rousseau, C.; Schlomiuk, D.
1995
Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028
Dumortier, F.; Roussarie, R.; Rousseau, C.
1994
Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043
Dumortier, F.; Roussarie, R.; Rousseau, C.
1994
Bifurcation at infinity in polynomial vector fields. Zbl 0778.34024
Blows, T. R.; Rousseau, C.
1993
Local bifurcation of critical periods in vector fields with homogeneous nonlinearities of the third degree. Zbl 0792.58030
Rousseau, C.; Toni, B.
1993
Bifurcation methods in polynomial systems. Zbl 0791.58080
Rousseau, Christiane
1993
Zeroes of complete elliptic integrals for 1:2 resonance. Zbl 0738.33014
Rousseau, Christiane; Żołądek, Henryk
1991
Cubic Liénard equations with linear damping. Zbl 0716.58023
Dumortier, Freddy; Rousseau, Christiane
1990
Codimension 2 symmetric homoclinic bifurcations and application to 1:2 resonance. Zbl 0714.58039
Li, Chengzhi; Rousseau, Christiane
1990
A simple proof for the unicity of the limit cycle in the Bogdanov-Takens system. Zbl 0706.34026
Li, Chengzhi; Rousseau, Christiane; Wang, Xian
1990
Saddle quantities and applications. Zbl 0684.34033
Joyal, Pierre; Rousseau, Christian
1989
A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4. Zbl 0684.34048
Li, Chengzhi; Rousseau, Christine
1989
Generalized Hopf bifurcations and applications to planar quadratic systems. Zbl 0666.34035
Rousseau, C.; Schlomiuk, D.
1988
Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation. Zbl 0626.34021
Rousseau, Christiane
1987
Clebsch-Gordan coefficients for SU(5) unification models. Zbl 0617.22020
del Olmo, Mariano A.; Patera, J.; Rodriquez, M. A.; Rousseau, C.
1987
Bifurcation methods in quadratic systems. Zbl 0649.34036
Rousseau, Christiane
1987
Clebsch-Gordan coefficients for $$E_ 6$$ and SO(10) unification models. Zbl 0556.22011
Koh, In-Guy; Patera, J.; Rousseau, C.
1984
Versal deformations of elements of classical Jordan algebras. Zbl 0523.17001
Patera, J.; Rousseau, C.
1983
Clebsch-Gordan coefficients for SU(5)$$\supset SU(3)\times SU(2)\times U(1)$$ theories. Zbl 0552.22008
Koh, In-Gyu; Patera, J.; Rousseau, C.
1983
Complex orthogonal and symplectic matrices depending on parameters. Zbl 0495.17007
Patera, J.; Rousseau, C.
1982
Versal deformations of elements of real classical Lie algebras. Zbl 0507.17006
Patera, J.; Rousseau, C.; Schlomiuk, D.
1982
Dimensions of orbits and strata in complex and real classical Lie algebras. Zbl 0488.22037
Patera, J.; Rousseau, C.; Schlomiuk, D.
1982
Topos theory and complex analysis. Zbl 0433.32003
Rousseau, Christiane
1979
Nombres réels et complexes dans les topos spatiaux. Zbl 0411.18004
Rousseau, Christiane
1979
Topos theory and complex analysis. Zbl 0378.02028
Rousseau, Christiane
1978
all top 5
#### Cited by 567 Authors
40 Llibre, Jaume 34 Romanovski, Valery G. 32 Rousseau, Christiane 30 Giné, Jaume 28 Han, Maoan 26 Liu, Yirong 20 Algaba, Antonio 19 Huang, Wentao 19 Valls Anglés, Cláudia 19 Villadelprat, Jordi 18 Chen, Xingwu 16 Zhang, Weinian 14 Chen, Hebai 14 Dumortier, Freddy 13 Zhao, Liqin 12 Gasull, Armengol 12 Wu, Yusen 11 García, Cristóbal 10 Li, Chengzhi 10 Oliveira, Regilene D. S. 10 Tang, Yilei 10 Wu, Yuhai 9 García, Isaac A. 9 Huang, Jicai 9 Reyes, Manuel 8 Ferčec, Brigita 8 Gaiko, Valery A. 8 Liu, Changjian 8 Mañosas, Francesc 8 Patera, Jiří 8 Rodríguez-Luis, Alejandro J. 8 Torregrosa, Joan 8 Zhang, Xiang 8 Zhu, Huaiping 7 Chavarriga, Javier 7 Christopher, Colin J. 7 Freire Macías, Emilio 7 Sabatini, Marco 7 Yu, Pei 7 Zhang, Zhifen 6 Gamero, Estanislao 6 Gavrilov, Lubomir 6 Grau, Maite 6 Klimeš, Martin 6 Wang, Qinlong 6 Xiao, Dongmei 6 Zhang, Qi 6 Zhao, Yulin 5 Artés, Joan Carles 5 Asheghi, Rasoul 5 Chen, Haibo 5 Feng, Zhaosheng 5 Fernandes, Wilker 5 Iliev, Iliya Dimov 5 Peng, Linping 5 Ponce, Enrique 5 Ruan, Shigui 5 Schlomiuk, Dana I. 5 Wang, Zhaoxia 5 Yang, Jihua 5 Zangeneh, Hamid R. Z. 5 Zhang, Tonghua 4 Bonckaert, Patrick 4 Caubergh, Magdalena 4 Chung, Kwok-Wai 4 Colak, Ilker E. 4 De Maesschalck, Peter 4 Dukarić, Maša 4 Huzak, Renato 4 Jarque, Xavier 4 Jiang, Jiao 4 Li, Weigu 4 Lloyd, Noel Glynne 4 Merino, Manuel 4 Pearson, Jane Margaret 4 Rojas, David 4 Sergeichuk, Vladimir Vasil’evich 4 Shafer, Douglas S. 4 Zhang, Cui 4 Zhang, Xinan 4 Żołądek, Henryk 3 Anderson, Gregory W. 3 Arriagada-Silva, Waldo 3 Aziz, Waleed 3 Blažek, Tomáš 3 Buică, Adriana 3 Cima, Anna 3 Dmytryshyn, Andrii R. 3 Dong, Guangfeng 3 Du, Chaoxiong 3 Edneral, Victor F. 3 Futorny, Vyacheslav M. 3 Garijo, Antonio 3 Homburg, Ale Jan 3 Hu, Zhaoping 3 Kazemi, Rasool 3 Li, Feng 3 Lu, Lianghaolong 3 Makhlouf, Amar 3 Mardešić, Pavao ...and 467 more Authors
all top 5
#### Cited in 111 Serials
95 Journal of Differential Equations 61 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 39 Journal of Mathematical Analysis and Applications 27 Qualitative Theory of Dynamical Systems 23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Applied Mathematics and Computation 18 Chaos, Solitons and Fractals 15 Bulletin des Sciences Mathématiques 13 Computers & Mathematics with Applications 13 Nonlinear Dynamics 12 Journal of Mathematical Physics 12 Nonlinear Analysis. Real World Applications 10 Physica D 9 Advances in Difference Equations 8 Journal of Computational and Applied Mathematics 8 Journal of Dynamics and Differential Equations 8 Discrete and Continuous Dynamical Systems 8 Journal of Dynamical and Control Systems 8 Discrete and Continuous Dynamical Systems. Series B 7 Acta Mathematica Sinica. English Series 7 Nonlinear Analysis. Theory, Methods & Applications 6 Proceedings of the American Mathematical Society 5 Acta Mathematicae Applicatae Sinica. English Series 5 Science in China. Series A 5 Linear Algebra and its Applications 5 SIAM Journal on Applied Dynamical Systems 4 Advances in Mathematics 4 Journal of Symbolic Computation 4 Applied Mathematics Letters 4 Journal of Nonlinear Science 4 Communications on Pure and Applied Analysis 3 Annales de l’Institut Fourier 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Transactions of the American Mathematical Society 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Abstract and Applied Analysis 3 Discrete Dynamics in Nature and Society 3 Journal of Nonlinear Mathematical Physics 3 Dynamical Systems 3 Journal of Applied Analysis and Computation 2 Bulletin of the Australian Mathematical Society 2 Nonlinearity 2 Rocky Mountain Journal of Mathematics 2 Programming and Computer Software 2 Results in Mathematics 2 Ergodic Theory and Dynamical Systems 2 Applied Mathematics and Mechanics. (English Edition) 2 Mathematical and Computer Modelling 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Mathematical Sciences (New York) 2 Journal of Difference Equations and Applications 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Regular and Chaotic Dynamics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 International Journal of Biomathematics 2 International Journal of Structural Stability and Dynamics 1 International Journal of Modern Physics A 1 Communications in Mathematical Physics 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Fuzzy Sets and Systems 1 International Journal of Mathematics and Mathematical Sciences 1 International Journal for Numerical Methods in Engineering 1 Journal of Pure and Applied Algebra 1 Journal of Soviet Mathematics 1 The Journal of Symbolic Logic 1 Mathematics and Computers in Simulation 1 Quaestiones Mathematicae 1 Quarterly of Applied Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Siberian Mathematical Journal 1 Transactions of the Moscow Mathematical Society 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 Dynamics and Stability of Systems 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Acta Mathematica Sinica. New Series 1 Acta Mechanica Sinica. (English Edition) 1 Chinese Science Bulletin 1 Applied Mathematics. Series B (English Edition) 1 Electronic Journal of Differential Equations (EJDE) 1 Doklady Mathematics 1 Functional Differential Equations 1 Differential Equations and Dynamical Systems 1 Open Systems & Information Dynamics 1 Conformal Geometry and Dynamics 1 Journal of Biological Systems 1 Lobachevskii Journal of Mathematics 1 Differential Equations 1 Nonlinear Analysis. Modelling and Control 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Journal of Applied Mathematics 1 Entropy ...and 11 more Serials
all top 5
#### Cited in 42 Fields
504 Ordinary differential equations (34-XX) 217 Dynamical systems and ergodic theory (37-XX) 67 Biology and other natural sciences (92-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Partial differential equations (35-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Numerical analysis (65-XX) 9 Mechanics of particles and systems (70-XX) 8 Topological groups, Lie groups (22-XX) 8 Computer science (68-XX) 7 Nonassociative rings and algebras (17-XX) 6 Operator theory (47-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Quantum theory (81-XX) 5 Mathematical logic and foundations (03-XX) 5 Mechanics of deformable solids (74-XX) 4 Algebraic geometry (14-XX) 4 Category theory; homological algebra (18-XX) 3 Commutative algebra (13-XX) 3 Functions of a complex variable (30-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Geometry (51-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-06-15T10:25:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6100764870643616, "perplexity": 7502.272826986455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487620971.25/warc/CC-MAIN-20210615084235-20210615114235-00633.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=Q123MR1 | #### ${\mathit m}_{{{\mathit s}}}/{\mathit m}_{{{\mathit d}}}$ MASS RATIO
VALUE DOCUMENT ID TECN COMMENT
$\bf{ \text{17 - 22}}$ OUR EVALUATION
$20.0$ 1
1997
THEO
$18.9$ $\pm0.8$ 2
1996
THEO Compilation
$21$ 3
1992
THEO
$18$ 4
1990
THEO
$18\text{ to }23$ 5
1990 B
THEO
1 GAO 1997 uses electromagnetic mass splittings of light mesons.
2 LEUTWYLER 1996 uses a combined fit to ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ and ${{\mathit \psi}^{\,'}}$ $\rightarrow$ ${{\mathit J / \psi}}$ (${{\mathit \pi}}$ ,${{\mathit \eta}}$ ) decay rates, and the electromagnetic mass differences of the ${{\mathit \pi}}$ and ${{\mathit K}}$ .
3 DONOGHUE 1992 result is from a combined analysis of meson masses, ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ using second-order chiral perturbation theory including nonanalytic terms, and ( ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit \pi}}$ )/( ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit \eta}}$ ).
4 GERARD 1990 uses large $\mathit N$ and ${{\mathit \eta}}-{{\mathit \eta}^{\,'}}$ mixing.
5 LEUTWYLER 1990B determines quark mass ratios using second-order chiral perturbation theory for the meson and baryon masses, including nonanalytic corrections. Also uses Weinberg sum rules to determine $\mathit L_{7}$.
References:
GAO 1997
PR D56 4115 Electromagnetic Mass Splittings of ${{\mathit \pi}}$ , ${{\mathit a}_{{1}}}$ , ${{\mathit K}}$ , ${{\mathit K}_{{1}}{(1400)}}$ and ${{\mathit K}^{*}{(892)}}$
LEUTWYLER 1996
PL B378 313 The Ratios of the Light Quark Masses
DONOGHUE 1992
PRL 69 3444 Mass Ratios of the Light Quarks
GERARD 1990
MPL A5 391 The Light Quark Current Mass Ratios and ${{\mathit \eta}}$ $\leftrightarrow$ ${{\mathit \eta}^{\,'}}$ Mixing
LEUTWYLER 1990B
NP B337 108 How About ${\mathit m}_{{{\mathit u}}}$ = 0? | 2023-03-21T23:21:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.824648380279541, "perplexity": 3832.668715382754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00022.warc.gz"} |
http://www.scstatehouse.gov/sess120_2013-2014/sj14/20140318.htm | South Carolina General Assembly
120th Session, 2013-2014
Journal of the Senate
NO. 29
JOURNAL
OF THE
SENATE
OF THE
STATE OF SOUTH CAROLINA
REGULAR SESSION BEGINNING TUESDAY, JANUARY 14, 2014
_________
TUESDAY, MARCH 18, 2014
Tuesday, March 18, 2014
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
The Psalmist proclaims:
"Let them give thanks to the Lord for his unfailing love and his wonderful deeds. . .for he satisfies the thirsty and fills the hungry with good things." (Psalm 107:8-9)
Join me as we pray, please:
Loving God, we pray today that You grant to each of these Senators compassionate and caring hearts. So many of our South Carolina sisters and brothers have incredible needs, O Lord, as we all know. May these servants -- the members of this Body and their assistants -- all labor diligently to bring about brighter hopes and better lives for our people -- for all of our people. Likewise, may each of our other public servants also seek to honor You, dear Lord, doing so through their own efforts to satisfy basic thirsts and hungers. In Your loving name we pray, O Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Remarks by Senator GROOMS
Members of the Senate, I wanted to brief you on an issue that may have significant impact within your districts sometime later this summer unless some things change in Congress. It has to do with the Federal Highway Trust Fund. The Federal Highway Trust Fund is something that our State is greatly dependent upon.
Our federal gasoline tax goes to Washington. It goes into the Federal Highway Trust Fund and has about $34 billion annually flowing into it. But it has about$46 billion flowing out of it. From time to time, over the last decade, Congress has authorized a transfer of other funds into the highway trust fund to keep it afloat, to keep it from being upside down. The latest projections show that the highway trust fund will be upside down sometime around August of this year. Having the Highway Trust Fund at a zero fund balance would greatly disrupt activities within our Department of Transportation and their on-going activities with highway projects. The DOT Commission was made aware of this at a budget briefing I attended this morning. They seem to be less concerned about this than I am. It will take congressional action sometime between now and August to transfer funds into the Highway Trust Fund in order to keep the fund afloat.
Should the Highway Trust Fund reach a zero balance, it would affect all the states in the union but some would be particularly hit hard, like South Carolina. Sometimes we apply to the Federal Highway Trust Fund four times a month for reimbursement on federal projects. Moneys are obligated to pay our State on federally-obligated projects but if the bank account is zero, there will be a disruption in those payments. A disruption in those payments for more than six weeks would then affect the Department of Transportation's ability to pay its vendors in a timely basis.
The cash flow crunch that the Department of Transportation had about two years ago could be minor compared to what would happen if Congress does not authorize additional transfers into the Federal Highway Trust Fund. I asked the acting Department of Transportation Secretary about two weeks ago if there was a plan for this and she said it would be a good idea if we had a plan for this.
I believe some commissioners are asking the same questions today. What happens six months out, three months out, two months out, one month out if the fund runs out of money? This is more than Congress just re-authorizing the current Federal Highway Bill. They have done that. The problem is current funding levels for the Federal Highway Bill are not sufficient for its federal obligations across the states. It would affect states a little bit differently. The State of Florida, for example, generally applies to the Federal Highway Administration once a year for obligations. Federally obligated roads in the State of Florida are paid for with their state dollars. Then once a year, they apply for federal government reimbursement. We do that sometimes four times a month. They could go nearly a year before there is a disruption in their highway projects, whereas we could go only about six weeks.
I bring this to the members' attention to let you know the dire circumstances. I am concerned at this point that we may run into a cash-flow crisis and I have shared those concerns.
***
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Nikki Randhawa Haley:
Local Appointments
Initial Appointment, Abbeville County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014
Philip D. Ray, 527 Noble Dr., Abbeville, SC 29620 VICE George T. Fergeson
Reppointment, Abbeville County Magistrate, with the term to commence April 30, 2014, and to expire April 30, 2018
Philip D. Ray, 527 Noble Dr., Abbeville, SC 29620
Reappointment, Horry County Board of Voter Registration, with the term to commence March 15, 2014, and to expire March 15, 2016
J. Michael Frazier, 731 Bucksport Rd., Conway, SC 29527
Reappointment, Horry County Board of Voter Registration, with the term to commence March 15, 2014, and to expire March 15, 2016
Maurice Jones, 4525 Canal Street, Loris, SC 29569
Doctor of the Day
Senator THURMOND introduced Dr. James McCoy, of North Charleston, S.C., Doctor of the Day.
Leave of Absence
On motion of Senator CAMPBELL at 12:05 P.M., Senator CAMPSEN was granted a leave of absence for today.
S. 865 (Word version) Sen. Shane Martin
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 1124 (Word version) -- Senators Fair, Hutto and Jackson: A SENATE RESOLUTION TO RECOGNIZE THAT ABUSE AND NEGLECT OF CHILDREN IS A SIGNIFICANT PROBLEM AND TO DECLARE TUESDAY, APRIL 8, 2014, AS "CHILDREN'S ADVOCACY DAY" IN SOUTH CAROLINA.
l:\council\bills\bh\26105dg14.docx
Senator FAIR spoke on the Resolution.
S. 1125 (Word version) -- Senator Hayes: A SENATE RESOLUTION TO RECOGNIZE THE RIGHTS OF CITIZENS WITH DOWN SYNDROME, TO PROMOTE THEIR INCLUSION AND WELL-BEING, AND TO DECLARE MARCH 21, 2014, AS "DOWN SYNDROME DAY" IN SOUTH CAROLINA.
l:\council\bills\rm\1525ahb14.docx
S. 1126 (Word version) -- Senator Bennett: A CONCURRENT RESOLUTION TO CONGRATULATE RACHEL REYNOLDS ON HER GRADUATION FROM SUMMERVILLE HIGH SCHOOL, TO COMMEND HER FOR HER COURAGE, AND TO WISH HER THE RICHEST BLESSINGS OF GOD IN THE DAYS AHEAD.
l:\council\bills\rm\1529dg14.docx
The Concurrent Resolution was adopted, ordered sent to the House.
S. 1127 (Word version) -- Senator Hutto: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 17-5-140 SO AS TO PROVIDE THAT THE FUNDS FROM THE SURCHARGE IMPOSED PURSUANT TO SECTION 44-63-84 MUST BE DISBURSED TO THE COUNTIES EQUALLY TO PAY THE DULY ELECTED FULL-TIME CORONER OR OTHER RELATED PERSONNEL OR EQUIPMENT AND TO PROVIDE THAT EXCESS FUNDS MUST BE USED BY THE CORONERS TRAINING ADVISORY COMMITTEE TO PERFORM ITS DUTIES; TO AMEND SECTION 17-5-130, AS AMENDED, RELATING TO THE CORONERS TRAINING ADVISORY COMMITTEE, SO AS TO PROVIDE ADDITIONAL DUTIES; AND TO AMEND SECTION 44-63-84, RELATING TO THE ISSUANCE OF A DEATH CERTIFICATE, SO AS TO IMPOSE A FIVE DOLLAR SURCHARGE FOR THE ISSUANCE OF AN INITIAL DEATH CERTIFICATE AND THREE DOLLARS FOR EACH SUBSEQUENT DEATH CERTIFICATE.
l:\council\bills\bh\26111dg14.docx
Read the first time and referred to the Committee on Judiciary.
S. 1128 (Word version) -- Senator Leatherman: A BILL TO AMEND SECTION 61-4-1100, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITED PRACTICES OF BEER PRODUCERS AND WHOLESALERS, SO AS TO PROHIBIT A BEER PRODUCER FROM SELLING BEER TO A BEER WHOLESALER IN THIS STATE AT A PRICE DIFFERENT FROM THAT CHARGED OTHER BEER WHOLESALERS IN THIS STATE, TO PROHIBIT A BEER PRODUCER FROM REQUIRING A BEER WHOLESALER TO PARTICIPATE IN AN ADVERTISING CAMPAIGN, AND TO PROHIBIT A BEER PRODUCER FROM WITHDRAWING FUNDS FROM A BEER WHOLESALER'S BANK ACCOUNT WITHOUT THE WHOLESALER'S WRITTEN CONSENT.
l:\council\bills\dka\3164jh14.docx
Read the first time and referred to the Committee on Judiciary.
S. 1129 (Word version) -- Senator Young: A BILL TO AMEND CHAPTER 3, TITLE 7 OF THE SOUTH CAROLINA CODE OF LAWS, 1976, RELATING TO THE STATE ELECTION COMMISSION, BY ADDING SECTION 7-3-80 TO PROVIDE THE AUTHORITY FOR THE COMMISSION TO ESTABLISH REGULATIONS RELATED TO THE CONDUCT OF POST ELECTION AUDITS PRIOR TO CERTIFICATION OF ELECTIONS, AND TO REQUIRE AUDIT DATA BE MADE PUBLIC; AND TO AMEND CHAPTER 13, TITLE 7, RELATING TO CONDUCT OF ELECTIONS, BY ADDING SECTION 7-13-1155, TO REQUIRE COUNTY ELECTION COMMISSIONS OR COUNTY BOARDS OF REGISTRATION AND ELECTIONS TO PERFORM POST ELECTION AUDITS BEFORE THE CERTIFICATION OF AN ELECTION.
l:\s-jud\bills\young\jud0102.rem.docx
Read the first time and referred to the Committee on Judiciary.
S. 1130 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE BUILDING CODES COUNCIL, RELATING TO IRC SECTION R312.2 WINDOW FALL PROTECTION, DESIGNATED AS REGULATION DOCUMENT NUMBER 4435, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
l:\council\bills\dbs\31155ac14.docx
Read the first time and ordered placed on the Calendar without reference.
S. 1131 (Word version) -- Senator Shealy: A SENATE RESOLUTION TO RECOGNIZE AND HONOR PATSY RAUTON LIGHTLE OF LEXINGTON FOR THIRTY-FIVE YEARS OF OUTSTANDING SERVICE AS A STATE LAW ENFORCEMENT DIVISION (SLED) AGENT, CHILD AND VULNERABLE ADULT ADVOCATE, AND PROFESSIONAL EDUCATOR, AND TO CONGRATULATE HER FOR HER UNTIRING EFFORTS TO ENHANCE THE INVESTIGATION AND PROSECUTION OF ABUSE AND THE QUALITY AND SAFETY OF LIFE FOR OUR VOICELESS VICTIMS.
l:\s-res\ks\037pats.mrh.ks.docx
S. 1132 (Word version) -- Senator Sheheen: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 5 TO CHAPTER 25, TITLE 16 SO AS TO ENACT THE "TEEN DATING VIOLENCE PREVENTION ACT", TO DEFINE NECESSARY TERMS, CREATE THE OFFENSE OF TEEN DATING VIOLENCE, PROVIDE A PENALTY, ALLOW VICTIMS TO SEEK ORDERS OF PROTECTION OR RESTRAINING ORDERS UNDER CERTAIN CIRCUMSTANCES, AND PROHIBIT A PERSON WHO VIOLATES THE PROVISIONS OF THE SECTION FROM PARTICIPATING IN A PRETRIAL INTERVENTION PROGRAM; TO AMEND SECTION 59-32-10, RELATING TO DEFINITIONS FOR PURPOSES OF THE COMPREHENSIVE HEALTH EDUCATION ACT, SO AS TO DEFINE THE TERM "TEEN DATING VIOLENCE"; AND TO AMEND SECTIONS 59-32-20, 59-32-30, AND 59-32-50, ALL RELATING TO THE REQUIREMENTS OF THE COMPREHENSIVE HEALTH EDUCATION ACT, ALL SO AS TO REQUIRE THE INCLUSION OF TEEN DATING VIOLENCE EDUCATION IN THE COMPREHENSIVE HEALTH EDUCATION CURRICULUM AND MAKE CONFORMING CHANGES.
l:\council\bills\dka\3163ahb14.docx
Read the first time and referred to the Committee on Judiciary.
REPORTS OF STANDING COMMITTEES
Senator COURSON from the Committee on Education submitted a majority favorable with amendment and Senator HUTTO a minority unfavorable report on:
S. 93 (Word version) -- Senator Young: A BILL TO AMEND SECTION 59-112-20 OF THE 1976 CODE, RELATING TO RATES OF TUITION AND FEES TO BE PAID BY STUDENTS ENTERING OR ATTENDING STATE INSTITUTIONS, TO PROVIDE FOR IN-STATE TUITION RATES TO ELIGIBLE PERSONS FUNDING THEIR POST-SECONDARY EDUCATION OR TRAINING WITH THE U.S. DEPARTMENT OF VETERANS AFFAIRS GI BILL.
Ordered for consideration tomorrow.
Senator COURSON from the Committee on Education submitted a majority favorable with amendment and Senator HUTTO a minority unfavorable report on:
H. 3086 (Word version) -- Reps. Daning, J.E. Smith, Crosby, R.L. Brown, M.S. McLeod, Taylor, J.R. Smith, Wells, Hixon, Rivers and Gilliard: A BILL TO AMEND SECTION 59-112-50, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO IN-STATE TUITION RATES FOR MILITARY PERSONNEL AND THEIR DEPENDENTS UNDER CERTAIN CONDITIONS, SO AS TO REVISE THE CRITERIA UNDER WHICH VETERANS WHO ARE HONORABLY DISCHARGED AND THEIR DEPENDENTS MAY RECEIVE IN-STATE TUITION RATES.
Ordered for consideration tomorrow.
Senator COURSON from the Committee on Education submitted a favorable with amendment report on:
H. 3919 (Word version) -- Reps. Owens, Bowen, Patrick, Taylor, Anderson, Allison, Brannon, Loftis, Ballentine, Rivers, Huggins, Knight, Simrill, King, Willis, Whitmire, McCoy, Anthony, Crosby, Neal, Clyburn, Barfield, Bedingfield, R.L. Brown, Cobb-Hunter, George, Hayes, Hiott, Hixon, Hosey, Lucas, Pope, Putnam, G.R. Smith, Wells, Wood, Whipper, Mitchell, Robinson-Simpson and Dillard: A BILL TO AMEND SECTION 59-18-310, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE EXIT EXAM REQUIRED FOR HIGH SCHOOL GRADUATION, SO AS TO PROVIDE THAT ALL STUDENTS MUST TAKE THE EXIT EXAM TO GRADUATE BUT NEED NOT ATTAIN ANY MINIMUM SCORE ON THE EXIT EXAM TO GRADUATE, TO PROVIDE AN ELIGIBLE STUDENT WHO PREVIOUSLY FAILED TO RECEIVE A HIGH SCHOOL DIPLOMA OR WAS DENIED GRADUATION SOLELY FOR FAILING THE EXIT EXAM MAY REENROLL IN HIGH SCHOOL AND WILL NOT HAVE TO PASS THE EXIT EXAM TO RECEIVE A HIGH SCHOOL DIPLOMA, AND TO REQUIRE THE DEPARTMENT OF EDUCATION TO REMOVE ANY CONFLICTING REQUIREMENTS AND PROMULGATE CONFORMING CHANGES IN ITS APPLICABLE REGULATIONS; TO AMEND SECTION 59-48-35, RELATING TO REQUIREMENTS FOR A DIPLOMA FROM THE SPECIAL SCHOOL OF SCIENCE AND MATHEMATICS, AND SECTION 59-139-60, RELATING TO THE DUTY OF THE STATE BOARD OF EDUCATION TO REVIEW STUDENT PERFORMANCE ON ASSESSMENT TESTING AND TO MONITOR THE PERFORMANCE OF SCHOOLS AND SCHOOL DISTRICTS, ALL SO AS TO MAKE CONFORMING CHANGES; AND TO CREATE THE HIGH SCHOOL ASSESSMENT STUDY COMMITTEE TO CONSIDER WHETHER THE HIGH SCHOOL ASSESSMENT PROGRAM SHOULD REMAIN THE ACCOUNTABILITY ASSESSMENT USED BY THE STATE AND TO RECOMMEND AN ALTERNATIVE IF NECESSARY, TO PROVIDE FOR THE COMPOSITION AND STAFFING OF THE STUDY COMMITTEE, TO REQUIRE THE COMMITTEE REPORT CERTAIN INFORMATION TO THE GENERAL ASSEMBLY, AND TO PROVIDE FOR THE TERMINATION OF THE STUDY COMMITTEE.
Ordered for consideration tomorrow.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
RETURNED TO THE HOUSE
H. 3231 (Word version) -- Reps. Atwater, Huggins, Toole, Ballentine, Taylor, Bingham, Pitts and Wood: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 57-1-90 SO AS TO PROVIDE THAT THE DEPARTMENT OF TRANSPORTATION SHALL NOT DISCRIMINATE AGAINST MOTORCYCLES, MOTORCYCLE OPERATORS, OR MOTORCYCLE PASSENGERS.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator GROOMS asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Senator GROOMS proposed the following amendment (3231R001.LKG), which was adopted:
Amend the bill, as and if amended, page 2, by striking line 4 and inserting:
/ for full-size vehicles.
(C) As used in this section, 'reasonable accomodations' shall not be interpreted to include, require, or otherwise mandate the structural or technological modification of parking structures constructed or substantially completed before July 1, 2014." /
Renumber sections to conform.
Amend title to conform.
Senator GROOMS explained the amendment.
The question then was third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Cleary
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Johnson Kimpson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey McElveen
McGill Nicholson O'Dell
Peeler Scott Setzler
Shealy Thurmond Turner
Verdin Young
Total--35
NAYS
Total--0
There being no further amendments, the Bill was read the third time, passed and ordered sent/returned to the House of Representatives with amendments.
H. 3231--Recorded Vote
Senator CAMPBELL desired to be recorded as voting in favor of third reading of the Bill.
The following Bills and Joint Resolution were read the third time and ordered sent to the House of Representatives:
S. 1007 (Word version) -- Senators Campbell and O'Dell: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 29-3-625 SO AS TO PROVIDE A PROCESS FOR EXPEDITING MORTGAGE FORECLOSURES AND TO DEFINE NECESSARY TERMINOLOGY.
S. 1075 (Word version) -- Labor, Commerce and Industry Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION - OFFICE OF STATE FIRE MARSHAL, RELATING TO OFFICE OF STATE FIRE MARSHAL, DESIGNATED AS REGULATION DOCUMENT NUMBER 4378, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
S. 985 (Word version) -- Senator Cleary: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 6 TO CHAPTER 1, TITLE 6, TO ENACT THE "FAIRNESS IN LODGING ACT" SO AS TO ALLOW MUNICIPALITIES AND COUNTIES BY ORDINANCE TO IMPLEMENT ADDITIONAL ENFORCEMENT PROVISIONS FOR THE BUSINESS LICENSE TAX AND THE LOCAL ACCOMMODATIONS TAX AS THOSE PROVISIONS APPLY TO THE OWNERS OF RESIDENTIAL REAL PROPERTY WHO RENT THE PROPERTY TO TOURISTS, INCLUDING DATA SHARING WITH THE SOUTH CAROLINA DEPARTMENT OF REVENUE, SPECIFIC NOTICE TO PROPERTY OWNERS INCLUDED IN PROPERTY TAX BILLS, AN ADDITIONAL PENALTY THAT MAY BE IMPOSED FOR NONCOMPLIANCE AFTER THE RECEIPT OF SUCH A NOTICE, AND DIRECTIONS TO THE SOUTH CAROLINA DEPARTMENT OF REVENUE TO IDENTIFY "RENTAL BY OWNER" WEBSITES ADVERTISING TOURISTS RENTALS AND REQUEST THEM TO POST ON THE WEBSITES A STATEMENT REGARDING THE LEGAL OBLIGATIONS OF THE OWNERS OF PROPERTY IN THIS STATE LISTED ON THE WEBSITE, TO PAY ALL APPLICABLE LOCAL AND STATE TAXES AND FEES WITH RESPECT TO SUCH RENTALS; AND TO AMEND SECTIONS 6-1-120, 12-54-240, AS AMENDED, AND 12-4-310, RELATING RESPECTIVELY TO THE CONFIDENTIALITY OF LOCAL AND STATE TAX DATA AND EXCEPTIONS THERETO, AND THE DUTIES OF THE SOUTH CAROLINA DEPARTMENT OF REVENUE, SO AS TO CONFORM THEM TO THE PROVISIONS OF THIS ACT.
S. 1034 (Word version) -- Senator L. Martin: A JOINT RESOLUTION TO ADOPT REVISED CODE VOLUMES 5 AND 8 OF THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO THE EXTENT OF THEIR CONTENTS, AS THE ONLY GENERAL PERMANENT STATUTORY LAW OF THE STATE AS OF JANUARY 1, 2014.
The Senate proceeded to a consideration of the Resolution, the question being the second reading of the Joint Resolution.
Senator MASSEY explained the Joint Resolution.
The question then was second reading of the Joint Resolution.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 36; Nays 0
AYES
Alexander Bennett Bright
Bryant Campbell Cleary
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hembree
Johnson Kimpson Leatherman
Malloy Martin, Larry Martin, Shane
Massey McElveen McGill
Nicholson O'Dell Peeler
Scott Setzler Shealy
Sheheen Thurmond Turner
Verdin Williams Young
Total--36
NAYS
Total--0
The Resolution was read the second time and ordered placed on the Third Reading Calendar.
H. 3784 (Word version) -- Reps. J.E. Smith, Pitts, Vick and Harrell: A BILL TO AMEND SECTION 59-114-30, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE NATIONAL GUARD COLLEGE ASSISTANCE PROGRAM, SO AS TO CLARIFY THAT EACH ACADEMIC YEAR'S ANNUAL MAXIMUM GRANT MUST BE BASED ON THE AMOUNT OF AVAILABLE PROGRAM FUNDS; TO AMEND SECTION 59-114-40, AS AMENDED, RELATING TO THE NATIONAL GUARD COLLEGE ASSISTANCE PROGRAM QUALIFICATION REQUIREMENTS, SO AS TO PROVIDE THAT NATIONAL GUARD MEMBERS BECOME ELIGIBLE FOR COLLEGE ASSISTANCE PROGRAM GRANTS UPON COMPLETION OF BASIC TRAINING AND ADVANCED INDIVIDUAL TRAINING; AND TO AMEND SECTION 59-114-65, RELATING TO GRANT AVAILABILITY, SO AS TO ALLOW APPROPRIATIONS TO THE NATIONAL GUARD COLLEGE ASSISTANCE PROGRAM TO BE CARRIED FORWARD TO A SUBSEQUENT FISCAL YEAR AND EXPENDED FOR THE SAME PURPOSE, AND TO EXEMPT APPROPRIATIONS TO THE NATIONAL GUARD COLLEGE ASSISTANCE PROGRAM FROM MIDYEAR BUDGET REDUCTIONS.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator SETZLER explained the Bill.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 33; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Cleary Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hembree Johnson Kimpson
Malloy Martin, Larry Martin, Shane
McGill Nicholson O'Dell
Peeler Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Total--33
NAYS
Total--0
The Bill was read the second time and ordered placed on the Third Reading Calendar.
H. 3784--Recorded Vote
Senators MASSEY and YOUNG desired to be recorded as voting in favor of second reading of the Bill as they were out of the chamber meeting with the Governor regarding the Savannah River Site.
H. 4347 (Word version) -- Reps. Bannister, Cobb-Hunter, McCoy, Allison, Whipper and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "SOUTH CAROLINA CHILDREN'S ADVOCACY MEDICAL RESPONSE SYSTEM ACT" BY ADDING ARTICLE 4 TO CHAPTER 11, TITLE 63 SO AS TO CREATE THE SOUTH CAROLINA CHILDREN'S ADVOCACY MEDICAL RESPONSE SYSTEM, A PROGRAM TO PROVIDE COORDINATION AND MEDICAL SERVICE RESOURCES STATEWIDE TO AGENCIES AND ENTITIES THAT RESPOND TO VICTIMS OF CHILD ABUSE AND NEGLECT, AND TO PROVIDE FOR THE DUTIES AND RESPONSIBILITIES OF THE PROGRAM; AND TO AMEND SECTION 63-11-310, RELATING TO RESPONSIBILITIES OF CHILDREN'S ADVOCACY CENTERS, SO AS TO REQUIRE THESE CENTERS TO COMPLY WITH REQUIREMENTS OF THE SOUTH CAROLINA CHILDREN'S MEDICAL RESPONSE SYSTEM AND OTHERWISE COORDINATE WITH THE PROGRAM.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD4347.001), which was adopted:
Amend the bill, as and if amended, page 1, by striking lines 28 through 38.
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 35; Nays 0
AYES
Alexander Bennett Bright
Bryant Campbell Cleary
Corbin Courson Cromer
Davis Grooms Hayes
Hembree Johnson Kimpson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Massey
Matthews McElveen McGill
Nicholson Peeler Scott
Setzler Shealy Sheheen
Thurmond Turner Verdin
Williams Young
Total--35
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 841 (Word version) -- Senator Cleary: A BILL TO AMEND ARTICLE 1, CHAPTER 13, TITLE 63, SOUTH CAROLINA CODE OF LAWS, 1976, RELATING TO THE REGULATION OF CHILDCARE FACILITIES, BY ADDING SECTION 63-13-185, SO AS TO PROHIBIT THE ADMINISTRATION OF MEDICATION TO A CHILD BY AN EMPLOYEE OR VOLUNTEER OF A CHILDCARE FACILITY WITHOUT PARENTAL PERMISSION, AND TO INCLUDE EXCEPTIONS IN CIRCUMSTANCES OF EMERGENCIES, AND TO PROVIDE PENALTIES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
The Committee on Judiciary proposed the following amendment (JUD0841.001), which was adopted:
Amend the bill, as and if amended, page 2, by striking line 15, in Section 63-13-185(E), as contained in SECTION 1, and inserting therein the following:
/ guilty of a misdemeanor and, upon conviction, may be imprisoned /
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Alexander Bennett Bright
Bryant Campbell Cleary
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Johnson Kimpson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey McElveen
McGill Nicholson O'Dell
Peeler Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--37
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 882 (Word version) -- Senator Sheheen: A BILL TO AMEND SECTION 41-27-210 OF THE 1976 CODE, RELATING TO THE DEFINITION OF EMPLOYMENT; TO PROVIDE THAT INDIVIDUALS THAT TRANSPORT VEHICLES FOR AUTOMOBILE DEALERS UNDER CERTAIN CIRCUMSTANCES ARE EXCLUDED FROM THE DEFINITION; AND TO PROVIDE FOR THOSE CIRCUMSTANCES.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Labor, Commerce and Industry.
The Committee on Labor, Commerce and Industry proposed the following amendment (882R005.TCA), which was adopted:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 41-27-260 of the 1976 Code is amended by adding an appropriately numbered new item to read:
"( ) an individual performing a service for an automobile dealer related to the transportation of individual vehicles to purchasers or sellers of vehicles, including, but not limited to an automobile auction, when the contract of service contemplates that the service is to be performed personally by the individual, the individual does not own the vehicle used in connection with the performance of the service, and the service is in the nature of a single transaction with no guarantee of a continuing relationship with the automobile dealer for whom the service is performed."
SECTION 2. This act takes effect upon approval by the Governor./
Renumber sections to conform.
Amend title to conform.
Senator BRYANT explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Cleary Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Johnson
Kimpson Leatherman Lourie
Martin, Larry Martin, Shane Massey
McElveen McGill Nicholson
Peeler Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--37
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
S. 1065 (Word version) -- Senator Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 5 TO CHAPTER 43, TITLE 38 SO AS TO PROVIDE FOR THE LIMITED LICENSING OF SELF-STORAGE FACILITIES TO SELL OR OFFER INSURANCE.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Banking and Insurance.
The Committee on Banking and Insurance proposed the following amendment (AGM\1065C002.AGM.AB14), which was adopted:
Amend the bill, as and if amended, by deleting all after the enacting words and inserting:
/ SECTION 1. Chapter 43, Title 38 of the 1976 Code is amended by adding:
"Article 5
Limited Licensing of Self-Service Storage Facilities to Sell or Offer Insurance
(2) 'Limited license' means the authority of a person authorized to sell certain insurance pursuant to the provisions of this article.
(3) 'Rental agreement' means a written agreement setting forth the terms and conditions governing the use of a storage space provided by a self-service storage facility for rental or lease.
(4) 'Owner' means the owner of a self-service storage facility or his agent.
(5) 'Occupant' means a person or his lessee, successor, or assignee entitled to the use of the storage space at a self-storage facility under a rental agreement to the exclusion of others.
(6) 'Self-service storage facility' means real property designed and used for the sole purpose of renting or leasing individual storage space to occupants given access to this storage space for the sole purpose of storing and removing personal property.
(7) 'Rental period' means the term of a rental agreement.
Section 38-43-620. The director or his designee may issue a limited license to an owner who has complied with the requirements of this article.
Section 38-43-630. (A) Before issuing a limited license, an application for a limited license must be filed with the director, signed by an officer of the applicant, on a form prescribed by the department. An applicant for a limited license must be approved and vouched for by an official or licensed representative of the insurer for which the applicant proposes to act pursuant to Section 38-43-40 and Section 38-43-50. An application must be accompanied by a forty dollar fee. A limited license must be renewed biennially before May first of odd numbered years on a renewal application form provided by the department, and this form must be accompanied by a forty dollar renewal fee. The department shall cancel a license that is not renewed as required by this section. The licensee may reinstate a license within six months after the renewal deadline by paying the forty dollar renewal fee and a forty dollar reinstatement fee. A limited license fee is not refundable.
(B) A limited license holder must not advertise, represent, or otherwise hold itself or its employee out as a licensed insurer, insurance agent, or insurance broker.
Section 38-43-640. (A) A licensee must be the owner of a self-service rental facility or his employee or agent.
(B) A licensee only may sell or offer to sell insurance in connection with, and incidental to, the rental of a self-storage space in the owner's facility. This insurance only may provide coverage for:
(1) casualty loss of the property contained in the self-storage space;
(2) liability insurance for personal injuries, excluding injuries compensable by workers' compensation, arising on the premises of the individual self-storage space; or
(3) both.
Section 38-43-650. (A) Prior to issuing a policy under the provisions of this chapter, a licensee shall provide a written document that:
(1) summarizes clearly and correctly the material terms of coverage offered to an occupant, including the identity of the insurer;
(2) discloses that the coverage offered by the self-service storage facility may provide a duplication of coverage already provided by a homeowners' insurance policy or other source of coverage in effect for the occupant;
(3) describes the process for filing a claim if the occupant elects to purchase coverage and in the event of a claim; and
(4) states that the charges for coverage are itemized and ancillary to the rental agreement.
(B) If the rental agreement requires the occupant to provide insurance of the type described in Section 38-43-640(B), this requirement may be satisfied if the occupant:
(1) purchases this coverage from a licensee; or
(2) provides evidence of this coverage from another source.
Section 38-43-660. (A) The employee or agent of an owner who is a licensee may act individually on behalf, and under the supervision of, the owner-licensee with respect to providing coverage for which the licensee is authorized to provide, but only if the owner instructs the employee or agent about the kinds of insurance sold pursuant to the owner's license.
(B) The provisions of this chapter do not prohibit:
(1) the payment or receipt of a commission for the sale of insurance that the licensee is authorized to sell; and
(2) the payment of a bonus, incentive payment, or compensation by a licensee to his employee or agent; provided, however, that these payments may not be made based on the completion of a sale of insurance coverage.
Section 38-43-670. Notwithstanding another provision of this chapter, a regulation promulgated by the department, or an order issued by the director, a licensee, his employee, and agent must not be required to:
(1) act as a fiduciary of money received from the sale of insurance authorized to be sold under the provisions of this chapter; or
(2) hold this money in a separate trust account if the insurer represented by the license holder provides written consent, signed by an officer of the insurer, that a premium is not required to be segregated from money received by the license holder because of the consumer transaction associated with the coverage.
Section 38-43-680. The director may, after notice and opportunity for a hearing, respond to a violation of a provision of this chapter under the provisions of Section 38-2-10 by:
(1) revoking or suspending a limited license; or
(2) imposing other penalties, including suspending the transaction of insurance at a specific rental location where a violation of this chapter occurred, as the director considers necessary or convenient to carry out the provisions of this chapter."
SECTION 2. This act takes effect upon approval by the Governor. /
Renumber sections to conform.
Amend title to conform.
Senator CROMER explained the committee amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 37; Nays 0
AYES
Alexander Bennett Bright
Bryant Campbell Cleary
Coleman Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hembree Johnson Kimpson
Lourie Malloy Martin, Larry
Martin, Shane Massey McElveen
McGill Nicholson O'Dell
Peeler Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--37
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
Senator SHANE MARTIN asked unanimous consent to allow Senator CLEARY to make an expression of personal interest.
There was no objection.
H. 3421--Expression of Personal Interest
Senator CLEARY rose for an Expression of Personal Interest.
S. 1097 (Word version) -- Senator Alexander: A CONCURRENT RESOLUTION TO AFFIRM THE DEDICATION OF THE GENERAL ASSEMBLY TO THE FUTURE SUCCESS OF SOUTH CAROLINA'S YOUNG PEOPLE AND TO THE PREVENTION OF CHILD ABUSE AND NEGLECT AND TO DECLARE THE MONTH OF APRIL AS "CHILD ABUSE PREVENTION MONTH" IN THE STATE OF SOUTH CAROLINA.
The Concurrent Resolution was adopted, ordered sent to the House.
H. 4748 (Word version) -- Reps. Owens, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H.A. Crawford, K.R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Munnerlyn, Murphy, Nanney, Neal, Newton, Norman, Norrell, R.L. Ott, Parks, Patrick, Pitts, Pope, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G.M. Smith, G.R. Smith, J.E. Smith, J.R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO RECOGNIZE AND EXPRESS DEEP APPRECIATION TO THE SOUTH CAROLINA TECHNICAL COLLEGE SYSTEM FOR ITS OUTSTANDING CONTRIBUTIONS IN EDUCATING AND TRAINING OUR STATE'S WORKFORCE AND TO DECLARE MARCH 25, 2014, AS SOUTH CAROLINA TECHNICAL COLLEGE SYSTEM DAY.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4766 (Word version) -- Reps. J.E. Smith, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H.A. Crawford, K.R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Munnerlyn, Murphy, Nanney, Neal, Newton, Norman, Norrell, R.L. Ott, Owens, Parks, Patrick, Pitts, Pope, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G.M. Smith, G.R. Smith, J.R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO DECLARE WEDNESDAY, MARCH 19, 2014, "NATIONAL GUARD DAY" IN SOUTH CAROLINA AND TO RECOGNIZE AND HONOR THE MANY SACRIFICES AND VALUABLE CONTRIBUTIONS THE SOUTH CAROLINA NATIONAL GUARD MAKES TO PROTECT THE FREEDOM, DEMOCRACY, AND SECURITY OF OUR STATE AND NATION.
The Concurrent Resolution was adopted, ordered returned to the House.
CARRIED OVER
S. 1033 (Word version) -- Senators Campbell, Leatherman, Setzler, O'Dell and Alexander: A BILL TO AMEND CHAPTER 2, TITLE 12 OF THE 1976 CODE, RELATING TO TAXATION, BY ADDING SECTION 12-2-110, TO PROVIDE AN OUT-OF-STATE BUSINESS THAT CONDUCTS OPERATIONS WITHIN THIS STATE FOR THE PURPOSES OF PERFORMING WORK OR SERVICES RELATED TO A DECLARED STATE DISASTER OR EMERGENCY DURING A DISASTER PERIOD MUST NOT BE CONSIDERED TO HAVE ESTABLISHED A LEVEL OF PRESENCE THAT WOULD REQUIRE THAT BUSINESS TO REGISTER, FILE, AND REMIT STATE OR LOCAL TAXES OR THAT WOULD REQUIRE THAT BUSINESS OR ITS OUT-OF-STATE EMPLOYEES TO BE SUBJECT TO ANY STATE LICENSING OR REGISTRATION REQUIREMENTS OR ANY COMBINATION OF THESE ACTIONS.
On motion of Senator MALLOY, the Bill was carried over.
S. 511 (Word version) -- Senator Campsen: A BILL TO AMEND SECTION 12-43-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE FOUR PERCENT SPECIAL ASSESSMENT RATIO, SO AS TO PROVIDE THAT AN ELIGIBILITY PROVISION REQUIRING A CERTAIN OWNERSHIP PERCENTAGE DOES NOT APPLY IF THE PROPERTY IS HELD BY A TRUST, FAMILY LIMITED PARTNERSHIP, OR LIMITED LIABILITY COMPANY UNDER CERTAIN SITUATIONS.
On motion of Senator MALLOY, the Bill was carried over.
S. 862 (Word version) -- Senators Shealy and Turner: A BILL TO AMEND SECTION 40-59-260 OF THE 1976 CODE, RELATING TO THE EXCEPTION FOR PROJECTS BY A PROPERTY OWNER FOR PERSONAL USE, TO PROVIDE THAT AN OWNER OF RESIDENTIAL PROPERTY WHO IMPROVES THE PROPERTY OR WHO BUILDS OR IMPROVES THE STRUCTURES OR APPURTENANCES ON THE PROPERTY AT A COST OF MORE THAN TWO THOUSAND FIVE HUNDRED DOLLARS SHALL NOT WITHIN TWO YEARS AFTER COMPLETION OR ISSUANCE OF A CERTIFICATE OFFER THE STRUCTURE FOR SALE OR RENT, AND CONSTRUCTION OR IMPROVEMENTS TO THE STRUCTURE, GROUP OF STRUCTURES, OR APPURTENANCES THAT COST THE OWNER-BUILDER LESS THAN TWO THOUSAND FIVE HUNDRED DOLLARS ARE NOT EVIDENCE OF "SALE" OR "RENT" FOR THE PURPOSES OF THIS SECTION.
On motion of Senator SHEALY, the Bill was carried over.
S. 343 (Word version) -- Senator Hayes: A BILL TO AMEND CHAPTER 7, TITLE 36, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ARTICLE 7 OF THE UNIFORM COMMERCIAL CODE, SO AS TO REVISE THE CHAPTER IN ITS ENTIRETY IN ORDER TO PROVIDE FOR THE USE OF ELECTRONIC DOCUMENTS OF TITLE AND TO MAKE CONFORMING CHANGES.
On motion of Senator BRIGHT, the Bill was carried over.
S. 1026 (Word version) -- Senator Alexander: A BILL TO AMEND SECTION 29-5-440, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO SUITS ON CONTRACTOR PAYMENT BONDS, SO AS TO PROVIDE THAT CERTAIN WRITTEN NOTICE REQUIRED OF A REMOTE CLAIMANT MUST BE SENT BY CERTIFIED OR REGISTERED MAIL, AND MUST GENERALLY CONFORM WITH STATUTORY LIMITS ON THE AGGREGATE AMOUNT OF LIENS FILED BY A SUB-SUBCONTRACTOR OR SUPPLIER; TO PROVIDE ANY PAYMENT BOND SURETY FOR THE BONDED CONTRACTOR SHALL HAVE THE SAME RIGHTS AND DEFENSES OF THE BONDED CONTRACTOR; TO MAKE THE LANGUAGE APPLICABLE TO ANY PAYMENT BOND WHETHER PRIVATE, COMMON LAW, PUBLIC, OR STATUTORY IN NATURE, WHEN THE BONDS ARE NOT OTHERWISE REQUIRED OR GOVERNED BY STATUTE; AND TO PROVIDE NECESSARY DEFINITIONS.
Senator CROMER explained the Bill.
On motion of Senator MALLOY, the Bill was carried over.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
At 1:12 P.M., on motion of Senator COURSON, the Senate agreed to adjourn.
LOCAL APPOINTMENTS
Confirmations
Having received a favorable report from the Senate, the following appointments were confirmed in open session:
Reappointment, Horry County Board of Voter Registration, with the term to commence March 15, 2014, and to expire March 15, 2016
J. Michael Frazier, 731 Bucksport Rd., Conway, SC 29527
Reappointment, Horry County Board of Voter Registration, with the term to commence March 15, 2014, and to expire March 15, 2016
Maurice Jones, 4525 Canal Street, Loris, SC 29569
Initial Appointment, Abbeville County Magistrate, with the term to commence April 30, 2010, and to expire April 30, 2014
Philip D. Ray, 527 Noble Dr., Abbeville, SC 29620 VICE George T. Fergeson
Reppointment, Abbeville County Magistrate, with the term to commence April 30, 2014, and to expire April 30, 2018
Philip D. Ray, 527 Noble Dr., Abbeville, SC 29620 | 2014-07-30T07:05:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32272157073020935, "perplexity": 13285.542557720708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510268734.38/warc/CC-MAIN-20140728011748-00180-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.scstatehouse.gov/sess123_2019-2020/sj19/20190424.htm | South Carolina General Assembly
123rd Session, 2019-2020
Journal of the Senate
NO. 62
JOURNAL
OF THE
SENATE
OF THE
STATE OF SOUTH CAROLINA
REGULAR SESSION BEGINNING TUESDAY, JANUARY 8, 2019
_________
WEDNESDAY, APRIL 24, 2019
Wednesday, April 24, 2019
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 12:00 Noon, the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
Isaiah 40:31
"...those who wait for the Lord shall renew their strength, they shall mount up with wings like eagles, they shall run and not be weary, they shall walk and not faint."
Let us pray. Gracious God, we begin this day with joyful hearts for the sheer delight of being alive and having the privilege of serving You. We are thankful for all that was accomplished last week through Your grace and the hard work and tenacity of our Senators. You have all power, O God, but You have chosen to work through these Senators to serve our State. Continue to inspire them with a positive attitude toward their work. Saturate their minds with Your wisdom and strengthen their wills with high resolve to trust that You will use them honorably and effectively to write another important page in our States history. Through our Lord and Savior we pray, Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Point of Quorum
At 2:03 P.M., Senator SETZLER made the point that a quorum was not present. It was ascertained that a quorum was not present.
Call of the Senate
Senator SETZLER moved that a Call of the Senate be made. The following Senators answered the Call:
Alexander Allen Bennett
Campbell Corbin Cromer
Davis Grooms Leatherman
Martin Massey Matthews, Margie
McLeod Nicholson Peeler
Rice Scott Setzler
Shealy Talley Turner
Verdin Williams Young
A quorum being present, the Senate resumed.
MESSAGE FROM THE GOVERNOR
The following appointments were transmitted by the Honorable Henry Dargan McMaster:
Local Appointment
Initial Appointment, Dillon County Magistrate, with the term to commence April 30, 2019, and to expire April 30, 2023
Andrew Bethea, 1062 Highway 917 W., Latta, SC 29565-4731 VICE James F. Rogers
Doctor of the Day
Senator NICHOLSON introduced Dr. Dan Robinson of Greenwood, S.C., Doctor of the Day.
Expression of Personal Interest
Senator CROMER rose for an Expression of Personal Interest.
S. 32 (Word version) Sen. Campbell
S. 719 (Word version) Sen. Fanning
S. 757 (Word version) Sen. Fanning
RECALLED
H. 3662 (Word version) -- Rep. McCoy: A BILL TO ADOPT REVISED CODE VOLUMES 3 AND 4 OF THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO THE EXTENT OF THEIR CONTENTS, AS THE ONLY GENERAL PERMANENT STATUTORY LAW OF THE STATE AS OF JANUARY 1, 2019.
Senator YOUNG asked unanimous consent to make a motion to recall the Bill from the Committee on Judiciary.
The Bill was recalled from the Committee on Judiciary and ordered placed on the Calendar for consideration tomorrow.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 782 (Word version) -- Senator Bennett: A SENATE RESOLUTION TO RECOGNIZE AND HONOR DOROTHY BROWN GLOVER FOR THE ENDURING AND ARTISTIC DESIGNS OF HER TRADITIONAL QUILTS AND TO CONGRATULATE HER UPON RECEIVING THE SOUTH CAROLINA ARTS COMMISSION'S 2019 FOLK HERITAGE AWARD.
l:\council\bills\gm\24199cm19.docx
S. 783 (Word version) -- Senator Nicholson: A SENATE RESOLUTION TO EXPRESS THE PROFOUND SORROW OF THE MEMBERS OF THE SOUTH CAROLINA SENATE UPON THE PASSING OF DEACON BRANSON JULIAN ROBINSON OF GREENWOOD AND TO EXTEND THE DEEPEST SYMPATHY TO HIS FAMILY AND MANY FRIENDS.
l:\council\bills\rm\1269sa19.docx
S. 784 (Word version) -- Senator Malloy: A SENATE RESOLUTION TO RECOGNIZE AN INCREDIBLE GROUP OF SOUTH CAROLINA CITIZENS FROM DARLINGTON COUNTY FOR THEIR ROLE IN THE FIGHT FOR DESEGREGATION AND FOR THEIR OUTSTANDING RESILIENCY IN THE FACE OF TRAUMA.
l:\s-res\gm\046darl.kmm.gm.docx
S. 785 (Word version) -- Senators Peeler, Leatherman, Setzler and Massey: A CONCURRENT RESOLUTION TO PROVIDE THAT, PURSUANT TO SECTION 9, ARTICLE III OF THE CONSTITUTION OF THIS STATE, 1895, WHEN THE RESPECTIVE HOUSES OF THE GENERAL ASSEMBLY ADJOURN ON THURSDAY, MAY 9, 2019, NOT LATER THAN 5:00 P.M., EACH HOUSE SHALL STAND ADJOURNED TO MEET IN STATEWIDE SESSION AT 12:00 NOON ON MONDAY, MAY 20, 2019, AND CONTINUE IN STATEWIDE SESSION, IF NECESSARY, UNTIL NOT LATER THAN 5:00 P.M. ON WEDNESDAY, MAY 22, 2019, FOR THE CONSIDERATION OF CERTAIN SPECIFIED MATTERS; TO PROVIDE THAT WHEN THE RESPECTIVE HOUSES OF THE GENERAL ASSEMBLY RECEDE ON WEDNESDAY, MAY 22, 2019, NOT LATER THAN 5:00 P.M., EACH HOUSE SHALL STAND IN RECESS SUBJECT TO THE CALL OF THE PRESIDENT OF THE SENATE FOR THE SENATE AND THE SPEAKER OF THE HOUSE OF REPRESENTATIVES FOR THE HOUSE OF REPRESENTATIVES AT TIMES THEY CONSIDER APPROPRIATE FOR THEIR RESPECTIVE BODIES TO MEET FOR THE CONSIDERATION OF CERTAIN SPECIFIED MATTERS; AND TO PROVIDE THAT WHEN THE RESPECTIVE HOUSES OF THE GENERAL ASSEMBLY ADJOURN NOT LATER THAN TUESDAY, JANUARY 14, 2020, THE GENERAL ASSEMBLY SHALL STAND ADJOURNED SINE DIE.
l:\s-res\hsp\003sine.kmm.hsp.docx
The Concurrent Resolution was introduced and referred to the Committee on Operations and Management.
S. 786 (Word version) -- Senator Davis: A SENATE RESOLUTION TO DECLARE THE WEEK OF MAY 6 THROUGH MAY 12, 2019, AS NATIONAL NURSES WEEK IN THE STATE OF SOUTH CAROLINA AND TO ENCOURAGE ALL SOUTH CAROLINIANS TO JOIN IN SHOWING APPRECIATION FOR THE NATION'S REGISTERED NURSES, IN HONORING THEM AS THEY CARE FOR THEIR PATIENTS, AND IN CELEBRATING THE ACCOMPLISHMENTS OF REGISTERED NURSES AND THEIR EFFORTS TO IMPROVE THE HEALTHCARE SYSTEM.
l:\council\bills\gm\24197wab19.docx
The Senate Resolution was introduced and referred to the Committee on Medical Affairs.
S. 787 (Word version) -- Senators Gambrell and Cash: A SENATE RESOLUTION TO HONOR THE TIMKEN COMPANY'S HONEA PATH PLANT AT THE CELEBRATION OF ITS FIFTIETH ANNIVERSARY, TO CONGRATULATE THE PLANT ON A HALF-CENTURY OF OUTSTANDING ENTREPRENEURIAL ENDEAVORS, AND TO EXTEND BEST WISHES FOR CONTINUED SUCCESS IN THE YEARS TO COME.
l:\council\bills\rm\1262sa19.docx
Read the first time and referred to the Committee on Labor, Commerce and Industry.
H. 4332 (Word version) -- Reps. G. M. Smith, Stavrinakis, Gilliard and Simrill: A BILL TO AMEND SECTIONS 11-41-20, 11-41-30, AND 11-41-70, CODE OF LAWS OF SOUTH CAROLINA, 1976, ALL RELATING TO THE STATE GENERAL OBLIGATION ECONOMIC DEVELOPMENT BOND ACT, SO AS TO PROVIDE FURTHER FINDINGS, TO PROVIDE FOR STRATEGIC INFRASTRUCTURE PROJECTS AS ECONOMIC DEVELOPMENT PROJECTS, AND TO ALLOW FOR FREIGHT TRANSPORTATION AS INFRASTRUCTURE.
Read the first time and referred to the Committee on Finance.
H. 4470 (Word version) -- Rep. Ridgeway: A CONCURRENT RESOLUTION TO WELCOME THE MARCH OF DIMES TO THE STATE HOUSE AND DECLARE WEDNESDAY, MAY 1, 2019, AS "SOUTH CAROLINA HEALTHY MOTHER'S DAY."
The Concurrent Resolution was introduced and referred to the Committee on Medical Affairs.
REPORTS OF STANDING COMMITTEES
Senator GROOMS from the Committee on Transportation submitted a favorable report on:
S. 635 (Word version) -- Senator Young: A BILL TO AMEND CHAPTER 3, TITLE 56 OF THE 1976 CODE, RELATING TO MOTOR VEHICLE REGISTRATION AND LICENSING, BY ADDING ARTICLE 147, TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ISSUE "DRIVERS FOR A CURE" SPECIAL LICENSE PLATES.
Ordered for consideration tomorrow.
Senator GROOMS from the Committee on Transportation submitted a favorable report on:
S. 656 (Word version) -- Senator Grooms: A BILL TO AMEND SECTION 56-5-5640 OF THE 1976 CODE, RELATING TO THE SALE OF UNCLAIMED VEHICLES AND THE DISPOSITION OF PROCEEDS, TO PROVIDE FOR THE TRANSFER OF A VEHICLE TO AN AUTOMOTIVE DISMANTLER OR RECYCLER OR SECONDARY METALS RECYCLER FOR DEMOLITION, WRECKING, OR DISMANTLING; TO AMEND SECTION 56-5-5670 OF THE 1976 CODE, RELATING TO THE DUTIES OF DEMOLISHERS AND THE DISPOSAL OF A VEHICLE TO A DEMOLISHER OR SECONDARY METALS RECYCLER, TO MAKE CONFORMING CHANGES; TO AMEND SECTION 56-5-5945 OF THE 1976 CODE, RELATING TO THE DUTIES OF DEMOLISHERS AND THE DISPOSAL OF A VEHICLE, TO MAKE CONFORMING CHANGES; TO AMEND SECTION 56-19-480(A) OF THE 1976 CODE, RELATING TO THE TRANSFER AND SURRENDER OF THE CERTIFICATES, LICENSE PLATES, REGISTRATION CARDS, AND MANUFACTURERS' SERIAL PLATES OF VEHICLES SOLD AS SALVAGE, ABANDONED, SCRAPPED, OR DESTROYED, TO MAKE CONFORMING CHANGES; TO AMEND SECTION 56-3-1380 OF THE 1976 CODE, RELATING TO THE RETURN OF A REGISTRATION CARD AND LICENSE PLATES FOR A WRECKED OR DISMANTLED VEHICLE, TO MAKE CONFORMING CHANGES; TO AMEND SECTION 16-17-680(D), (E), AND (J)(1)(e) OF THE 1976 CODE, RELATING TO A SECONDARY METALS RECYCLER PERMIT TO PURCHASE NONFERROUS METALS AND A PERMIT TO TRANSPORT AND SELL NONFERROUS METALS, TO MAKE CONFORMING CHANGES; AND TO DEFINE NECESSARY TERMS.
Ordered for consideration tomorrow.
Senator RANKIN from the Committee on Judiciary submitted a favorable with amendment report on:
H. 3035 (Word version) -- Reps. Funderburk, Thigpen, W. Newton, R. Williams and Wheeler: A BILL TO AMEND SECTION 7-13-110, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO POLL MANAGERS AND THEIR ASSISTANTS, SO AS TO PROVIDE THAT POLL WORKERS MUST BE RESIDENTS AND REGISTERED ELECTORS OF THE STATE OF SOUTH CAROLINA.
Ordered for consideration tomorrow.
Senator RANKIN from the Committee on Judiciary submitted a favorable with amendment report on:
H. 3145 (Word version) -- Reps. Ott, Clary, Cobb-Hunter, Collins, Jefferson, Kirby, Willis, Cogswell, D.C. Moss, G.R. Smith, Elliott, Sandifer, Lucas, Ballentine, Caskey, Simrill, West, Murphy, McKnight, Mace, Kimmons, Davis, Magnuson, Sottile, Hewitt, Hiott, B. Newton, Pope, Forrest, Bales, Rutherford, R. Williams, Gilliam, Norrell, Funderburk, G.M. Smith, Weeks, Ridgeway, Yow, W. Newton, Bamberg, Stavrinakis, McCoy, Erickson, Blackwell, Wheeler, Fry, Bannister, Calhoon, Huggins, Gilliard and Taylor: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 33-49-150 SO AS TO PROVIDE THAT THE OFFICE OF REGULATORY STAFF IS VESTED WITH THE AUTHORITY AND JURISDICTION TO CONDUCT AUDITS OF ELECTRIC COOPERATIVES IN THE SAME MANNER, TERMS, AND CONDITIONS IT IS AUTHORIZED TO CONDUCT AUDITS OF REGULATED PUBLIC UTILITIES AS PROVIDED BY LAW; TO AMEND SECTION 33-49-420, RELATING TO ANNUAL MEETINGS OF MEMBERS OF AN ELECTRIC COOPERATIVE, SO AS TO REVISE THE NOTICE REQUIREMENTS FOR CERTAIN MEETINGS; TO AMEND SECTION 33-49-430, RELATING TO A QUORUM AT MEETINGS OF ELECTRIC COOPERATIVES, SO AS TO ALLOW PERSONS CASTING EARLY VOTING BALLOTS FOR THE ELECTION OF TRUSTEES TO BE COUNTED FOR PURPOSES OF DETERMINING A QUORUM AT THE MEETING FOR THE ELECTION, AND TO PROHIBIT VOTING BY PROXY; TO AMEND SECTION 33-49-440, RELATING TO VOTING BY MEMBERS AND SECTION 33-49-620, RELATING TO VOTING DISTRICTS FROM WHICH SOME MEMBERS OF THE BOARD OF TRUSTEES MAY BE ELECTED, SO AS TO PERMIT EARLY VOTING FOR MEETINGS AT WHICH TRUSTEES ARE TO BE ELECTED AND THE PROCEDURES FOR EARLY VOTING; TO AMEND SECTION 33-49-610, RELATING TO THE BOARD OF TRUSTEES OF A COOPERATIVE, SO AS TO REVISE THE MANNER IN WHICH VACANCIES OCCURRING FOR ANY REASON OTHER THAN EXPIRATION OF A TERM ARE FILLED WHICH MUST BE FOR THE REMAINDER OF THE UNEXPIRED TERM ONLY; BY ADDING SECTION 33-49-615 SO AS TO REQUIRE ANNUAL PUBLIC DISCLOSURE OF COMPENSATION AND BENEFITS PAID TO OR PROVIDED FOR MEMBERS OF THE BOARD OF TRUSTEES; BY ADDING SECTION 33-49-625 SO AS TO REQUIRE SPECIFIED NOTICE OF MEETINGS TO THE COOPERATIVE MEMBERSHIP, TO REQUIRE VOTES OF TRUSTEES TO BE TAKEN IN OPEN SESSION WITH CERTAIN EXCEPTIONS, TO REQUIRE VOTES TAKEN IN EXECUTIVE SESSION TO BE RATIFIED IN OPEN SESSION, AND TO REQUIRE MINUTES OF ALL MEETINGS TO BE PROVIDED TO COOPERATIVE MEMBERS; AND BY ADDING SECTION 33-49-645 SO AS TO PROVIDE THAT IN THE CONDUCT OF ELECTIONS BY A COOPERATIVE, IT MUST PROHIBIT ADVOCACY OR CAMPAIGNING WITHIN A CERTAIN DISTANCE OF THE POLLING PLACE.
Ordered for consideration tomorrow.
Senator GROOMS from the Committee on Transportation submitted a favorable report on:
H. 3357 (Word version) -- Reps. Wooten, Collins, Brawley, Huggins, Taylor, Hixon and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 56-3-115 SO AS TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ADD A NOTATION TO A PRIVATE PASSENGER-CARRYING MOTOR VEHICLE REGISTRATION TO INDICATE THE VEHICLE OWNER MAY BE DEAF OR HARD OF HEARING.
Ordered for consideration tomorrow.
Senator RANKIN from the Committee on Judiciary submitted a favorable report on:
H. 3601 (Word version) -- Reps. Rose, McCoy and Caskey: A BILL TO AMEND SECTION 16-17-530, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PUBLIC DISORDERLY CONDUCT, SO AS TO ALLOW AND PROVIDE PROCEDURES FOR CONDITIONAL DISCHARGE FOR FIRST TIME OFFENDERS.
Ordered for consideration tomorrow.
Senator GROOMS from the Committee on Transportation submitted a favorable report on:
H. 3789 (Word version) -- Reps. Willis, Allison, Bennett, Elliott, Brown, Erickson, Bradley, Huggins, Forrest, Taylor and R. Williams: A BILL TO AMEND SECTIONS 56-1-35, 56-1-40, 56-1-140, 56-1-210, 56-1-2100, AND 56-1-3350, RELATING TO THE ISSUANCE, RENEWAL, AND EXPIRATION OF A DRIVER'S LICENSE, BEGINNER'S PERMIT, COMMERCIAL DRIVER LICENSE, AND SPECIAL IDENTIFICATION CARD, AND THE PLACEMENT OF A VETERAN DESIGNATION ON A DRIVER'S LICENSE OR SPECIAL IDENTIFICATION CARD, SO AS TO REVISE THE PERIOD IN WHICH A DRIVER'S LICENSE AND CERTAIN COMMERCIAL DRIVER LICENSES ARE VALID, TO REVISE THE FEE TO OBTAIN A DRIVER'S LICENSE, CERTAIN COMMERCIAL DRIVER LICENSES, AND SPECIAL IDENTIFICATION CARDS, TO REVISE THE DOCUMENTS THAT MUST BE PROVIDED TO THE DEPARTMENT OF MOTOR VEHICLES TO OBTAIN A VETERAN DESIGNATION ON A DRIVER'S LICENSE OR A SPECIAL IDENTIFICATION CARD, TO MAKE TECHNICAL CHANGES, AND TO PROVIDE THAT A PERSON IS PERMITTED TO ONLY HAVE ONE DRIVER'S LICENSE OR IDENTIFICATION CARD.
Ordered for consideration tomorrow.
Senator RANKIN from the Committee on Committee on Judiciary submitted a favorable with amendment report on:
H. 3973 (Word version) -- Reps. Crawford, Mace, Erickson, Thayer, Davis, Magnuson, Bennett, Allison, Bernstein, Cobb-Hunter, Henegan, McDaniel, Norrell, Funderburk, Brawley, Simmons, Henderson-Myers, Robinson, Collins, Calhoon, Dillard, Kimmons, Trantham, Caskey, Weeks and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 20 TO CHAPTER 3, TITLE 16 SO AS TO PROHIBIT GENITAL MUTILATION OF A FEMALE UNDER THE AGE OF EIGHTEEN YEARS AND TO CREATE THE OFFENSE OF FEMALE GENITAL MUTILATION OF A MINOR; AND TO AMEND SECTION 63-7-20, AS AMENDED, RELATING TO TERMS DEFINED IN THE CHILDREN'S CODE, SO AS TO ADD FEMALE GENITAL MUTILATION OF A MINOR TO THE DEFINITION OF "CHILD ABUSE OR NEGLECT" OR "HARM".
Ordered for consideration tomorrow.
INVITATIONS ACCEPTED
The PRESIDENT ordered the following invitations placed on the Calendar:
Wednesday, May 1, 2019 - 8:00am-10:00am
Members and Staff, Breakfast, 112 Blatt Building, by the SOUTH CAROLINA ASSOCIATIONS OF CONVENIENCE STORES
Wednesday, May 1, 2019 - 8:00am-10:00am
Members Only, Breakfast, Palmetto Club, by the SOUTH CAROLINA FAITH AND FREEDOM COALITION
Wednesday, May 1, 2019 - 11:30am-2:00pm
Members and Staff, Luncheon, SC State House Grounds, by the SOUTH CAROLINA TIRE MANUFACTURERS COUNCIL
Thursday, May 2, 2019 - 8:00am-10:00am
Members and Staff, Breakfast, 112 Blatt Building, by the SOUTH CAROLINA INSURANCE ASSOCIATION
Appointment Reported
Senator SHEALY from the Committee on Family and Veterans' Services submitted a report without recommendation on:
Statewide Appointment
Initial Appointment, South Carolina Department on Aging, with term coterminous with Governor
Director:
Stephen F. Morris, 320 Country Club Drive, Columbia, SC 29296-3202
HOUSE CONCURRENCE
S. 623 (Word version) -- Senator Shealy: A CONCURRENT RESOLUTION TO RECOGNIZE FEBRUARY 25 THROUGH MARCH 3, 2019, AS "EATING DISORDERS AWARENESS WEEK" IN THE STATE OF SOUTH CAROLINA, TO COINCIDE WITH NATIONAL EATING DISORDERS AWARENESS WEEK, AND TO RECOGNIZE FRIDAY, MARCH 1, 2019, AS "EATING DISORDERS AWARENESS DAY" IN SOUTH CAROLINA.
Returned with concurrence.
At 12:18 P.M., Senator MASSEY made a motion to invite the House of Representatives to attend the Senate Chamber for the purpose of ratifying Acts at a mutually convenient time.
The motion was adopted and a message was sent to the House accordingly.
THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE.
DEBATE INTERRUPTED
S. 678 (Word version) -- Senators Peeler, Climer, Davis and Fanning: A JOINT RESOLUTION TO PROVIDE THAT THE GOVERNOR SHALL UTILIZE THE DEPARTMENT OF ADMINISTRATION TO CONDUCT A COMPETITIVE BIDDING PROCESS FOR THE SALE OF SANTEE COOPER, TO PROVIDE THAT THE DEPARTMENT OF ADMINISTRATION SHALL EVALUATE BIDS, TO PROVIDE THAT THE GOVERNOR SHALL EXECUTE THE SALE OF SANTEE COOPER TO THE BIDDER WHOSE BID BEST PROTECTS THE INTERESTS OF SANTEE COOPER'S RATEPAYERS AND THE STATE'S TAXPAYERS, AND TO TRANSMIT THE PUBLIC SERVICE AUTHORITY EVALUATION AND RECOMMENDATION COMMITTEE'S WORK PRODUCT TO THE DEPARTMENT OF ADMINISTRATION.
The Senate proceeded to a consideration of the Joint Resolution.
The Committee on Finance proposed the following amendment (678R001.KMM.HSP):
Amend the joint resolution, as and if amended, by striking the joint resolution in its entirety and inserting:
/A JOINT RESOLUTION
TO PROVIDE THAT THE DEPARTMENT OF ADMINISTRATION SHALL CONDUCT A COMPETITIVE BIDDING PROCESS FOR THE SALE OF SANTEE COOPER, TO PROVIDE THAT THE DEPARTMENT OF ADMINISTRATION SHALL EVALUATE BIDS, TO PROVIDE THAT THE DEPARTMENT OF ADMINISTRATION SHALL MAKE A RECOMMENDATION CONCERNING THE SALE AND FORWARD THE RECOMMENDATION TO THE SENATE FINANCE COMMITTEE AND HOUSE OF REPRESENTATIVES WAYS AND MEANS COMMITTEE FOR REVIEW, TO PROVIDE THAT THE GENERAL ASSEMBLY SHALL BE CONVENED TO CONSIDER LEGISLATION CONCERNING THE SALE, TO PROVIDE THAT A SALE OF SANTEE COOPER MAY NOT BE FINALIZED UNTIL AFTER A JOINT RESOLUTION AUTHORIZING THE SALE IS ENACTED, TO PROVIDE THAT SANTEE COOPER MUST PROVIDE ANY AND ALL RESOURCES NECESSARY TO EFFECTUATE A SALE, AND TO PROVIDE THAT THE WORK PRODUCT OF THE PUBLIC SERVICE AUTHORITY EVALUATION AND RECOMMENDATION COMMITTEE MUST BE TURNED OVER TO THE DEPARTMENT OF ADMINISTRATION.
Be it enacted by the General Assembly of the State of South Carolina:
SECTION 1. (A) The Department of Administration shall conduct a competitive bidding process for the sale of some or all of the Public Service Authority ("Santee Cooper"). The department shall procure such professional services, including but not limited to financial institutions, legal counsel, and industry consultants, as are necessary to conduct the sale, the evaluation of bids received, and related activities.
(B) Staff from the State Fiscal Accountability Authority's Procurement Services Division shall assist the department in conducting the competitive bidding process and procuring necessary professional services.
SECTION 2. The department shall conduct a thorough evaluation of all bids received through the competitive bidding process. The evaluation must take into account at least the following:
(1) the financial capability of each bidder;
(2) the bidder's complete defeasement of all of Santee Cooper's bonds and other indebtedness;
(3) the bidder's agreement to provide meaningful short-term and long-term rate relief for all customer classes;
(4) the bidder's provision of reasonable financial and other protections for Santee Cooper employees and retirees in a manner that would not impact South Carolina's pension system liability or the liability associated with providing health insurance coverage to employees who have retired from employment at Santee Cooper;
(5) the bidder's proposed location for its headquarters post-acquisition;
(6) the bidder's agreement to comply with all applicable federal and state environmental protections regarding Lakes Marion and Moultrie, their rivers and tributaries, and other recreational assets of Santee Cooper, including a covenant to maintain the present status quo regarding these lakes and other resources and the quality of and access to them; and
(7) the bidder's agreement to partner with the State for future economic development projects.
At the conclusion of its evaluation of the bids, the department shall make a recommendation regarding the bid that the department considers to be in the best interest of the State, its taxpayers, and the ratepayers of Santee Cooper.
SECTION 3. The department shall present to the Chairman of the Senate Finance Committee and the Chairman of the House of Representatives Ways and Means Committee its full evaluation of each bid and its recommendation for a proposed purchaser for Santee Cooper, justifications for its recommendation, a proposed contract to execute the sale, and any supporting documents. The Finance Committee and the Ways and Means Committee shall each meet as soon as practicable to review and make a recommendation regarding the proposed sale. Upon receipt of the recommendation from their respective committees, the President of the Senate and the Speaker of the House of Representatives shall convene their respective bodies to consider any legislation concerning the sale.
The department must execute any documents necessary in order to effectuate the sale upon the enactment of a joint resolution approving the sale. The net proceeds of the sale shall be deposited in the State Retirement Systems Group Trust.
SECTION 4. Santee Cooper is directed to provide any and all resources necessary to conduct the competitive bidding process and evaluation of the bids received.
SECTION 5. The Public Service Authority Evaluation and Recommendation Committee, as created pursuant to Proviso 117.162 of Act 264 of 2018, shall provide to the department all of the committee's work product.
SECTION 6. This act takes effect upon approval by the Governor.
----XX---- /
Renumber sections to conform.
Amend title to conform.
Senator SETZLER spoke on the amendment.
Point of Quorum
At 12:47 P.M., Senator MASSEY made the point that a quorum was not present. It was ascertained that a quorum was present. The Senate resumed.
Call of the Senate
Senator MASSEY moved that a Call of the Senate be made. The following Senators answered the Call:
Alexander Allen Bennett
Campbell Campsen Cash
Climer Cromer Davis
Fanning Gambrell Goldfinch
Gregory Grooms Harpootlian
Hembree Jackson Johnson
Kimpson Leatherman Loftis
Malloy Martin Massey
Matthews, John McElveen Peeler
Reese Rice Scott
Setzler Shealy Sheheen
Talley Williams Young
A quorum being present, the Senate resumed.
Senator SETZLER resumed speaking on the amendment.
Senator HUTTO spoke on the amendment.
ACTING PRESIDENT PRESIDES
Senator ALEXANDER assumed the Chair.
Senator DAVIS spoke on the amendment.
Point of Quorum
At 3:22 P.M., Senator MARTIN made the point that a quorum was not present. It was ascertained that a quorum was present. The Senate resumed.
Senator DAVIS resumed speaking on the amendment.
PRESIDENT PRESIDES
At 3:26 P.M., the PRESIDENT assumed the Chair.
Point of Quorum
At 3:26 P.M., Senator LEATHERMAN made the point that a quorum was not present. It was ascertained that a quorum was not present.
Call of the Senate
Senator LEATHERMAN moved that a Call of the Senate be made. The following Senators answered the Call:
Alexander Allen Bennett
Campbell Campsen Cash
Climer Corbin Davis
Fanning Gambrell Goldfinch
Grooms Harpootlian Hembree
Hutto Jackson Johnson
Kimpson Leatherman Loftis
Malloy Martin Massey
Matthews, John Matthews, Margie McElveen
McLeod Nicholson Peeler
Rankin Rice Sabb
Scott Senn Setzler
Shealy Talley Turner
Williams Young
A quorum being present, the Senate resumed.
Senator DAVIS resumed speaking on the amendment.
On motion of Senator DAVIS, with unanimous consent and with Senator DAVIS retaining the floor on S. 678, the Senate agreed to stand adjourned.
LOCAL APPOINTMENT
Confirmation
Having received a favorable report from the Senate, the following appointment was confirmed in open session:
Initial Appointment, Dillon County Magistrate, with the term to commence April 30, 2019, and to expire April 30, 2023
Andrew Bethea, 1062 Highway 917 W., Latta, SC 29565-4731 VICE James F. Rogers | 2023-02-07T08:18:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38461118936538696, "perplexity": 11857.51442341634}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500392.45/warc/CC-MAIN-20230207071302-20230207101302-00139.warc.gz"} |
https://pos.sissa.it/364/361/ | Volume 364 - European Physical Society Conference on High Energy Physics (EPS-HEP2019) - Higgs Physics
Search for 2HDM neutral Higgs bosons through the process H $\rightarrow$ ZA $\rightarrow l^+l^-b\overline{b}$ with the CMS detector
A. Saggio* on behalf of the CMS collaboration
*corresponding author
Full text: Not available
Abstract
The inability of the standard model (SM) to explain some observed phenomena motivates theoretical models featuring an extension of the SM scalar sector that predict additional Higgs bosons. The Two-Higgs-doublet model (2HDM) is one of these. This note reports on a search for an extended scalar sector, where a new CP-even (odd) boson decays to a Z boson and a lighter CP-odd (even) boson, which further decays to $\mathrm{b}\overline{\mathrm{b}}$. The Z boson is reconstructed via its decays to leptons. The analysed data were recorded in proton-proton collisions at $\sqrt{s} = 13$ TeV, collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Data and predictions from the SM are in agreement within uncertainties. Upper limits at 95% confidence level are set on the signal production cross section times branching fraction, with masses of the resonances ranging up to 1000 GeV. The results are interpreted in the context of the Type-II 2HDM.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-09-23T01:08:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7057240605354309, "perplexity": 1413.8269727014995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400208095.31/warc/CC-MAIN-20200922224013-20200923014013-00438.warc.gz"} |
https://beerbanter.com/chloe-wilde-fergvn/~https:/www.P65Warnings.ca.gov/determinant-of-hat-matrix-4f76a0 | This program allows the user to enter the rows and columns elements of a 2 * 2 Matrix. But there are other methods (just so you know). The value of determinant of a matrix can be calculated by following procedure â For each element of first row or first column get cofactor of those elements and then multiply the element with the determinant of the corresponding cofactor, and finally add them with alternate signs. For example, here is the result for a 4 × 4 matrix: It means that any of the rows of the matrix is written as a linear combination of two other vectors, and the determinant can be calculated by "splitting" that row. The determinant of a matrix $A$ is a value computed from the elements of a square matrix.Determinants are very useful mathematically, such as for finding inverses and eigenvalues and eigenvectors of a matrix and diagonalization, among other things.Determinants are denoted as $\det(A)$ or $|A|$.A matrix that does not have a determinant of zero is called a nonsingular or nondegenerate matrix. a22. As a hint, I'll take the determinant of a very similar two by two matrix. Digits after the decimal point: 2. The determinant of this matrix, divided by the interior of the matrix two steps back, is the determinant of the original matrix. □. $\begingroup$ It is often taken as the definition of rank of a matrix. Here is how: For a 2Ã2 matrix (2 rows and 2 columns): |A| = ad â bc a31. 10:35. We derive a central limit theorem (CLT) for the logarithm of the determinant of $\hat{\mathbf {R}}_{n}$ for a big class of $\mathbf{R}_{n}$. If the determinant of a matrix is zero, it is called a singular determinant and if it is one, then it is known as unimodular. C programming, exercises, solution: Write a program in C to calculate determinant of a 3 x 3 matrix. \begin{matrix} \text{row}_4 \rightarrow \text{row}_1 \\ \text{row}_2 \rightarrow \text{row}_2 \\ \text{row}_3 \rightarrow \text{row}_3 \\ \text{row}_1 \rightarrow \text{row}_4 \end {matrix} \Rightarrow - &\begin{bmatrix} -21&0&0&0\\ -1&-2&0&0\\ 0&3&1&0\\ 1&2&2&1 \end{bmatrix}. Sarrus' rule is a shortcut for calculating the determinant of a 3×33 \times 33×3 matrix. 4. It describes the influence each response value has on each fitted value. |A| means the determinant of the matrix A, (Exactly the same symbol as absolute value.). There are various equivalent ways to define the determinant of a square matrix A, i.e. there is exactly one function satisfying the above 3 relations. The symbol for determinant is two vertical lines either side. The base case is simple: the determinant of a 1×11 \times 11×1 matrix with element aaa is simply aaa. The determinant of a square matrix is a value determined by the elements of the matrix. The determinant of a matrix is a special number that can be calculated from a square matrix. Perhaps the simplest way to express the determinant is by considering the elements in the top row and the respective minors; starting at the left, multiply the element by the minor, then subtract the product of the next element and its minor, and alternate adding and subtracting such products until all elements in the top row have been exhausted. The descending diagonal from left to right has a +++ sign , while the descending diagonal from right to left has a −-\text{}− sign. Multiply the main diagonal elements of the matrix - determinant is calculated. That area indicated in white, is the sum of the determinant of $\hat{i}$ and $\hat{j}$. Let σ\sigmaσ be a permutation of {1,2,3,…,n}\{1, 2, 3, \ldots, n\}{1,2,3,…,n}, and SSS the set of those permutations. For instance. det(A)=∑σ∈S(sgn(σ)∏i=1nai,σ(i))=1⋅a1,1a2,2+(−1)⋅a1,2a2,1=ad−bc.\text{det}(A) = \sum_{\sigma \in S}\left(\text{sgn}(\sigma)\prod_{i=1}^{n}a_{i,\sigma(i)}\right) = 1 \cdot a_{1,1}a_{2,2} + (-1) \cdot a_{1,2}a_{2,1} = ad-bc.det(A)=σ∈S∑(sgn(σ)i=1∏nai,σ(i))=1⋅a1,1a2,2+(−1)⋅a1,2a2,1=ad−bc. Calculate. In vector calculus, the Jacobian matrix (/ dÊ É Ë k oÊ b i É n /, / dÊ Éª-, j ɪ-/) of a vector-valued function in several variables is the matrix of all its first-order partial derivatives. The hat matrix provides a measure of leverage. Already have an account? det(abcd)=a det(d)−b det(c)=ad−bc. 1.3 Idempotency of the Hat Matrix H is an n nsquare matrix, and moreover, it is idempotent, which can be veri ed as follows, HH = X(XT X) 1XT X(XT X) 1XT = X(XT X) 1(XT X)(XT X) 1XT = X(XT X) 1XT = H: Similarly, I H can also be shown to be idempotent, (I H)(I H) = I 2H+ HH = (I H): Every square and idempotent matrix is a projection matrix. For a square matrix, i.e., a matrix with the same number of rows and columns, one can capture important information about the matrix in a just single number, called the determinant.The determinant is useful for solving linear equations, capturing how linear transformation change area or volume, and changing variables in integrals. Here are the key points: Notice that the top row elements namely a, b and c serve as scalar multipliers to a corresponding 2-by-2 matrix. while larger matrices have more complicated formulae. Matrix Determinants (2 of 3: The Determinant's Geometric Meaning) - Duration: 10:35. Rewrite the first two rows while occupying hypothetical fourth and fifth rows, respectively: determinant matrix changes under row operations and column operations. \end{aligned}[X]=row1→row1row2−2row1→row2row3−2row1→row3row4−3row1→row4⇒row1→row1row2→row2row3→row3row4+12row3→row4⇒row1→row1row2→row2row3→row3row4+17row2→row4⇒row4→row1row2→row2row3→row3row1→row4⇒−⎣⎢⎢⎡112−12274245−61223⎦⎥⎥⎤⎣⎢⎢⎡1−10−42−23−2201−121000⎦⎥⎥⎤⎣⎢⎢⎡1−10−42−233420101000⎦⎥⎥⎤⎣⎢⎢⎡1−10−212−23020101000⎦⎥⎥⎤⎣⎢⎢⎡−21−1010−23200120001⎦⎥⎥⎤., Therefore, det[X]=X=−(−21)(−2)(1)(1)=−42. 3. This is called the Vandermonde determinant or Vandermonde polynomial. a12. This method of calculation is called the "Laplace expansion" and I like it because the pattern is easy to remember. For row operations, this can be summarized as follows: R1 If two rows are swapped, the determinant of the matrix is negated. Hat Matrix and Leverage Hat Matrix Purpose. □\text{det}\begin{pmatrix}a&b\\c&d\end{pmatrix} = a ~\text{det}\begin{pmatrix}d\end{pmatrix} - b ~\text{det}\begin{pmatrix}c\end{pmatrix} = ad-bc.\ _\squaredet(acbd)=a det(d)−b det(c)=ad−bc. Note that this agrees with the conditions above, since, det(a)=a⋅det(1)=a\text{det}\begin{pmatrix}a\end{pmatrix} = a \cdot \text{det}\begin{pmatrix}1\end{pmatrix}=adet(a)=a⋅det(1)=a. Then the determinant of an n×nn \times nn×n matrix AAA is. ∣∣∣∣∣∣035157255∣∣∣∣∣∣. Hat matrix â a square matrix used in statistics to relate fitted values to observed values. R3 If a multiple of a row is added to another row, the determinant is unchanged. Without doing the calculation nor telling you the formula, the area would be 1. a13. Finding determinants of a matrix are helpful in solving the inverse of a matrix, a system of linear equations, and so on. "The determinant of A equals a times d minus b times c". The meaning of a projection can be under- Since the identity matrix is diagonal with all diagonal entries equal to one, we have: $\det I=1.$ We would like to use the determinant to decide whether a matrix is invertible. This is important to remember. a21. When this matrix is square , that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant . Determinant, in linear and multilinear algebra, a value, denoted det A, associated with a square matrix A of n rows and n columns. The determinant of a matrix does not change, if to some of its row (column) to add a linear combination of other rows (columns). \begin{matrix} \text{row}_1 \rightarrow \text{row}_1 \\ \text{row}_2 \rightarrow \text{row}_2 \\ \text{row}_3 \rightarrow \text{row}_3 \\ \text{row}_4 +17\text{row}_2 \rightarrow \text{row}_4 \end {matrix} \Rightarrow &\begin{bmatrix} 1&2&2&1\\ -1&-2&0&0\\ 0&3&1&0\\ -21&0&0&0 \end{bmatrix} \\\\\\ Sign up to read all wikis and quizzes in math, science, and engineering topics. Practice calculating the determinant of a matrix with these practice questions. \begin{matrix} \text{row}_1 \rightarrow \text{row}_1 \\ \text{row}_2 \rightarrow \text{row}_2 \\ \text{row}_3 \rightarrow \text{row}_3 \\ \text{row}_4 +12\text{row}_3 \rightarrow \text{row}_4 \end {matrix} \Rightarrow &\begin{bmatrix} 1&2&2&1\\ -1&-2&0&0\\ 0&3&1&0\\ -4&34&0&0 \end{bmatrix} \\\\\\ R2 If one row is multiplied by ï¬, then the determinant is multiplied by ï¬. The determinant of the 3x3 matrix is a 21 |A 21 | - a 22 |A 22 | + a 23 |A 23 |. [X]=[122112422752−14−63]row1→row1row2−2row1→row2row3−2row1→row3row4−3row1→row4⇒[1221−1−2000310−4−2−120]row1→row1row2→row2row3→row3row4+12row3→row4⇒[1221−1−2000310−43400]row1→row1row2→row2row3→row3row4+17row2→row4⇒[1221−1−2000310−21000]row4→row1row2→row2row3→row3row1→row4⇒−[−21000−1−20003101221].\begin{aligned} Write a c program for subtraction of two matrices. The pattern continues for 5Ã5 matrices and higher. The determinant is a very important function because it satisfies a number of additional properties that can be derived from the 3 conditions stated above. The determinant of 3x3 matrix is defined as. The determinant of a matrix is a number that is specially defined only for square matrices. In statistics, the projection matrix {\displaystyle }, sometimes also called the influence matrix or hat matrix {\displaystyle }, maps the vector of response values to the vector of fitted values. The determinant is linear in each row separately. Therefore we ask what happens to the determinant when row operations are applied to a matrix. If det(1a2b)=4\det\left(\begin{array}{cc}1& a\\2& b \end{array}\right)=4det(12ab)=4 and det(1b2a)=1,\det\left(\begin{array}{cc}1& b\\2& a \end{array}\right)=1,det(12ba)=1, what is a2+b2?a^2+b^2?a2+b2? We know that the determinant has the following three properties: 1. det I = 1 2. $\endgroup$ â Travis Willse Mar 24 '15 at 5:06 as det(1)=I\text{det}\begin{pmatrix}1\end{pmatrix} = Idet(1)=I. (This one has 2 Rows and 2 Columns) The determinant of that matrix is (calculations are explained later): 3×6 â 8×4 = 18 â 32 = â14. det (a b c d) = a d â b c, \text{det}\begin{pmatrix}a & b \\ c & d \end{pmatrix} = ad-bc, det (a c b d ) = a d â b c, while larger matrices have more complicated formulae. We can use these ten properties to ï¬nd a formula for the determinant of a 2 by 2 matrix: 0 Considering the constraints above, what is the value of the last equation? Orthostochastic matrix â doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some orthogonal matrix; Precision matrix â a symmetric n×n matrix, formed by inverting the covariance matrix. det(100023001)=2⋅det(100010001)+3⋅det(100001001)=2.\text{det}\begin{pmatrix}1&0&0\\0&2&3\\0&0&1\end{pmatrix} = 2 \cdot \text{det}\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}+3 \cdot \text{det}\begin{pmatrix}1&0&0\\0&0&1\\0&0&1\end{pmatrix}=2.det⎝⎛100020031⎠⎞=2⋅det⎝⎛100010001⎠⎞+3⋅det⎝⎛100000011⎠⎞=2. ∣123456789∣123456=1⋅5⋅9+4⋅8⋅3+7⋅2⋅6−3⋅5⋅7−6⋅8⋅1−9⋅2⋅4=0.\begin{matrix} \left| \begin {matrix}1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{matrix}\right| \\ \begin{matrix} 1 & 2 & 3 \\ 4& 5 & 6 \end{matrix}\end{matrix}= 1 \cdot 5 \cdot 9+4 \cdot 8\cdot 3+7\cdot 2 \cdot 6 -3\cdot 5 \cdot 7 -6 \cdot 8 \cdot 1 - 9 \cdot 2 \cdot 4 = 0.∣∣∣∣∣∣147258369∣∣∣∣∣∣142536=1⋅5⋅9+4⋅8⋅3+7⋅2⋅6−3⋅5⋅7−6⋅8⋅1−9⋅2⋅4=0. In the case of a 2×22 \times 22×2 matrix, the determinant is calculated by. They come as Theorem 8.5.7 and Corollary 8.5.8. A=(123456789) ⟹ A11=(5689).A = \begin{pmatrix}1&2&3\\4&5&6\\7&8&9\end{pmatrix} \implies A_{11} = \begin{pmatrix}5&6\\8&9\end{pmatrix}.A=⎝⎛147258369⎠⎞⟹A11=(5869). Matrices do not have definite value, but determinants have definite value. Everyone who receives the link will be able to view this calculation . Determinants and matrices, in linear algebra, are used to solve linear equations by applying Cramerâs rule to a set of non-homogeneous equations which are in linear form.Determinants are calculated for square matrices only. Difference between Matrix and a Determinant 1. Letâs now study about the determinant of a matrix. The matrix $\hat{\mathbf {R}}_{n}$ is a popular object in multivariate analysis and it has many connections to other problems. content_copy Link save Save extension Widget. The determinant by minors method calculates the determinant using recursion. Calculation precision. 5. The determinant of a matrix is a special number that can be calculated from a square matrix. [X]=&\begin{bmatrix} 1 & 2 & 2 & 1 \\ 1 & 2 & 4 & 2 \\ 2&7&5&2 \\ -1&4&-6&3 \end{bmatrix} \\\\\\ They are as follows: The multiplicative property is of particular importance, due in part to its applications to inverse matrices. Designating any element of the matrix by the symbol a r c (the subscript r identifies the row and c the column), the determinant is evaluated by finding the sum of n ! home Front End HTML CSS JavaScript HTML5 Schema.org php.js Twitter Bootstrap Responsive Web Design tutorial Zurb Foundation 3 tutorials Pure CSS HTML5 Canvas JavaScript Course Icon Angular React Vue Jest Mocha NPM Yarn Back End PHP Python Java ⦠Now we only have to calculate the cofactor of a single element. The determinant of that matrix is (calculations are explained later): The determinant helps us find the inverse of a matrix, tells us things about the matrix that are useful in systems of linear equations, calculus and more. Unfortunately, this is very difficult to work with for all but the simplest matrices, so an alternative definition is better to use. Write a c program to find out sum of diagonal element of a matrix. New user? a33. one with the same number of rows and columns. C Program to find Determinant of a Matrix â 2 * 2 Example. The sum of the determinant is especially used with Linear Transformation (read Linear Algebra 3). Write a c program for addition of two matrices. Determinants, despite their apparently contrived definition, have a number of applications throughout mathematics; for example, they appear in the shoelace formula for calculating areas, which is doubly useful as a collinearity condition as three collinear points define a triangle with area 0. have the same number of rows as columns). Definition. The determinant is the sum over all choices of these nnn elements. Write a c program for multiplication of two matrices. □(0\times 5\times 5)+(3\times 7\times 2)+(5\times 1\times 5)-(2\times 5\times 5)-(5\times 7\times 0)-(5\times 1\times 3)=2.\ _\square(0×5×5)+(3×7×2)+(5×1×5)−(2×5×5)−(5×7×0)−(5×1×3)=2. det(A)=∑i=1n(−1)i+1a1,idet(A1i)=a1,1detA11−a1,2detA12+⋯ .\text{det}(A) = \sum_{i=1}^n (-1)^{i+1}a_{1,i}\text{det}(A_{1i}) = a_{1,1}\text{det}A_{11}-a_{1,2}\text{det}A_{12}+\cdots.det(A)=i=1∑n(−1)i+1a1,idet(A1i)=a1,1detA11−a1,2detA12+⋯. There are two permutations of {1,2}\{1,2\}{1,2}: {1,2}\{1,2\}{1,2} itself and {2,1}\{2,1\}{2,1}. (Theorem 1.) w3resource. (Theorem 4.) The simplest cases to calculate the determinant are upper-triangular (and lower-triangular) matrices, by using the permutation method above: Diagonal determinant (elements which are under and above the main diagonal are zero): This definition is especially useful when the matrix contains many zeros, as then most of the products vanish. Determinant of 3x3 matrices. There are two major options: determinant by minors and determinant by permutations. \end{cases} } ⎩⎪⎪⎪⎨⎪⎪⎪⎧a2−b2c2+d2(ac)2−(bd)2(ad)2−(bc)2====574341?. Then the determinant is given by the following: The determinant of an n×nn \times nn×n matrix AAA is. Determinant of matrix has defined as: a00(a11*a22 â a21*a12) + a01(a10*a22 â a20*a12) + a02(a10*a21 â a20*a11) 1. (10−19110−6−19110013−8013000970000−5).\left(\begin{array}{cc}1&0&-1&9&11\\0&-6&-1&9&11\\0&0&\frac{1}{3}&-80&\frac{1}{3}\\0&0&0&9&7\\0&0&0&0&-5 \end{array}\right).⎝⎜⎜⎜⎜⎛100000−6000−1−1310099−80901111317−5⎠⎟⎟⎟⎟⎞. det(abcd)=ad−bc,\text{det}\begin{pmatrix}a & b \\ c & d \end{pmatrix} = ad-bc,det(acbd)=ad−bc. A Matrix "The determinant of A equals ... etc". ∣012355575∣.\left| \begin{matrix} 0 & 1 & 2 \\ 3 & 5 & 5 \\ 5 & 7 & 5 \end{matrix} \right|. Then it is just basic arithmetic. URL copied to clipboard. Log in here. a11. What is the determinant of (abcd)?\begin{pmatrix}a&b\\c&d\end{pmatrix}?(acbd)? This is useful because matrices can be transformed into this form by row operations, which do not affect the determinant: X=∣122112422752−14−63∣.X=\begin{vmatrix} 1 & 2 & 2 & 1 \\ 1 & 2 & 4 & 2 \\ 2 & 7 & 5 & 2 \\ -1 & 4 & -6 & 3 \end{vmatrix}.X=∣∣∣∣∣∣∣∣112−12274245−61223∣∣∣∣∣∣∣∣. Copy link. To understand determinant calculation better input any example, choose "very detailed solution" option and examine the solution. Log in. The determinant of matrix A is calculated as. {\begin{cases} a^2 - b^2 &=& 5 \\ c^2 + d^2 &=& 74 \\ (ac)^2 - (bd)^2 &=& 341 \\ (ad)^2 - (bc)^2 &=& ? □. Assuming the standard basis vectors, we can find out just how much space has been squished or stretched after a ⦠For instance, in the below example, the second row (0,2,3)(0,2,3)(0,2,3) can be written as 2⋅(0,1,0)+3⋅(0,0,1)2 \cdot (0,1,0) + 3 \cdot (0,0,1)2⋅(0,1,0)+3⋅(0,0,1), so. ∣123456789∣⇒∣123456789∣ 123456\left| \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right| \Rightarrow \left| \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right| \\ \quad \quad \quad \quad \quad \quad \ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix}∣∣∣∣∣∣147258369∣∣∣∣∣∣⇒∣∣∣∣∣∣147258369∣∣∣∣∣∣ 142536. X=det∣a0000f0000k0000p∣=a×f×k×p.X=\text{det}\begin{vmatrix} a & 0 & 0 & 0 \\ 0 & f & 0 & 0 \\ 0 & 0 & k & 0 \\ 0 & 0 & 0 & p \end{vmatrix}=a\times f\times k\times p.X=det∣∣∣∣∣∣∣∣a0000f0000k0000p∣∣∣∣∣∣∣∣=a×f×k×p. Condensation vs. Cofactor Expansion Condensation wasnât exactly easy, and complications can occur if zeros spontaneously appear in the interiors of successive matrices. Calculate det(264−315937).\det\left(\begin{array}{cc}2&6&4\\-3&1&5\\9&3&7 \end{array}\right).det⎝⎛2−39613457⎠⎞. This may look more intimidating than the previous formula, but in fact it is more intuitive. Forgot password? An alternate method, determinant by permutations, calculates the determinant using permutations of the matrix's elements. Notice the +â+â pattern (+a... âb... +c... âd...). {a2−b2=5c2+d2=74(ac)2−(bd)2=341(ad)2−(bc)2=? First of all the matrix must be square (i.e. Sign up, Existing user? It means that the matrix should have an equal number of rows and columns. share my calculation. In the case of a 2 × 2 2 \times 2 2 × 2 matrix, the determinant is calculated by. |A| = a(ei â fh) â b(di â fg) + c(dh â eg), = 6Ã(â2Ã7 â 5Ã8) â 1Ã(4Ã7 â 5Ã2) + 1Ã(4Ã8 â (â2Ã2)), Sum them up, but remember the minus in front of the, The pattern continues for larger matrices: multiply. It is easy to remember when you think of a cross: For a 3Ã3 matrix (3 rows and 3 columns): |A| = a(ei â fh) â b(di â fg) + c(dh â eg) https://brilliant.org/wiki/expansion-of-determinants/, Upper triangular determinant (elements which are below the main diagonal are, Lower triangular determinant (elements which are above the main diagonal are. If terms a 22 and a 23 are both 0, our formula becomes a 21 |A 21 | - 0*|A 22 | + 0*|A 23 | = a 21 |A 21 | - 0 + 0 = a 21 |A 21 |. Unfortunately, these calculations can get quite tedious; already for 3×33 \times 33×3 matrices, the formula is too long to memorize in practice. The determinant of a square Vandermonde matrix (where m = n) can be expressed as det (V) = â 1 ⤠i < j ⤠n (α j â α i). \begin{matrix} \text{row}_1 \rightarrow \text{row}_1 \\ \text{row}_2 - 2\text{row}_1 \rightarrow \text{row}_2 \\ \text{row}_3 - 2\text{row}_1 \rightarrow \text{row}_3 \\ \text{row}_4 - 3\text{row}_1 \rightarrow \text{row}_4 \end {matrix} \Rightarrow &\begin{bmatrix} 1&2&2&1\\ -1&-2&0&0\\ 0&3&1&0\\ -4&-2&-12&0 \end{bmatrix} \\\\\\ Unsurprisingly, this is the same result as above. To find any matrix such as determinant of 2×2 matrix, determinant of 3×3 matrix, or n x n matrix, the matrix should be a square matrix. In a Matrix the number of rows and columns may be unequal, but in a Determi-nant the number of rows and columns must be equal. The scalar a is being multiplied to the 2×2 matrix of left-over elements created when vertical and horizontal line segments are drawn passing through a. (This one has 2 Rows and 2 Columns). Reduce this matrix to row echelon form using elementary row operations so that all the elements below diagonal are zero. ∣012355575∣⇒∣012355575∣012355\left| \begin{matrix} 0 & 1 & 2 \\ 3 & 5 & 5 \\ 5 & 7 & 5 \end{matrix} \right| \Rightarrow \left| \begin{matrix} 0 & 1 & 2 \\ 3 & 5 & 5 \\ 5 & 7 & 5 \end{matrix} \right| \\\quad \quad \quad\quad \quad \quad \begin{matrix} 0 & 1 & 2 \\ 3 & 5 & 5 \end{matrix}∣∣∣∣∣∣035157255∣∣∣∣∣∣⇒∣∣∣∣∣∣035157255∣∣∣∣∣∣031525, (0×5×5)+(3×7×2)+(5×1×5)−(2×5×5)−(5×7×0)−(5×1×3)=2. 3. On the other hand, each of the row reduction operations modifies the determinant of a matrix in a simple way, so one can easily compute the determinant by tracing these modifications through. The first has positive sign (as it has 0 transpositions) and the second has negative sign (as it has 1 transposition), so the determinant is. The recursive step is as follows: denote by AijA_{ij}Aij the matrix formed by deleting the ithi^\text{th}ith row and jthj^\text{th}jth column. 2. More generally, the determinant can be used to detect linear independence of certain vectors (or lack thereof). The determinant is also useful in multivariable calculus (especially in the Jacobian), and in calculating the cross product of vectors. The determinant of a matrix does not change, if to some of its row (column) to add another row (column) multiplied by some number. The diagonal elements of the projection matrix are the leverages, which describe the influence each response value has on the ⦠a32. 3. □_\square□. I see a proof of the "determinant rank" being the same as the "row rank" in the book Elementary Linear Algebra by Kenneth Kuttler, which I see in google books. Usually best to use a Matrix Calculator for those! It is useful for investigating whether one or more observations are outlying with regard to their X values, and therefore might be excessively influencing the regression results. □. Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations.Determinants also have wide applications in engineering, science, economics and social science as well. Determinant of a Matrix. Last class we listed seven consequences of these properties. {\displaystyle \det(V)=\prod _{1\leq i Risi E Bisi Marcella Hazan, Miami Beach Condo For Sale Under 100k, Calories In 12 Fried Shrimp, Arctostaphylos Uva-ursi 'massachusetts', Newel Post Height On Decking, Honda Odyssey 2019 Price, Sales Executive Description, Oracle Q4 Results 2020, What Is A Government, Ranchu Growth Stages, K Fold Cross Validation R, Heavenly Sword And Dragon Sabre 2009, Pepperidge Farm Puff Pastry, | 2021-07-30T22:09:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9986791610717773, "perplexity": 636.6529149779258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154032.75/warc/CC-MAIN-20210730220317-20210731010317-00693.warc.gz"} |
https://indico.fnal.gov/event/8433/ | We continue to review all events currently planned for the next sixty days and organizers will be notified if their event must be canceled, postponed, or held remotely. Please, check back on Indico during this time for updates regarding your meeting specifics.
As DOE O 142.3A, Unclassified Foreign Visits and Assignments Program (FVA) applies not only to physical access to DOE sites, technologies, and equipment, but also information, all remote events hosted by Fermilab must comply with FVA requirements. This includes participant registration and agenda review. Please contact Melissa Ormond, FVA Manager, with any questions.
Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
Librarian's Meeting
US/Central
WH9SE
WH9SE
Notes from LArSoft Librarians Meeting, April 22, 2014
-----------------------------------------------------
Agenda:
o Status of releases
o Priority changes, issues and discussion
o Geant4 macros
o Managing random number engines and seeds
Status of releases (Erica)
Will release v1.01.00 at the same time
Only difference will be changes to underlying products in v1.01.00
The changes directed toward OSX Maverick build. Required using
gcc 4.8.2, which required changes to a number of other underlying proudcts,
including art and root.
No other known release requests from experiments, so will then continue
with weekly integration releases
Priority changes, issues and discussion (Erica)
o Region of interest code ok to go into integration release after v1.01.00
Old files deprecated (but few have wire data in them)
o Making existing code work for LBNE and uBooNE
-- Optimizations directed at this
-- Hit-finding / clustering workflows are different for uBooNE and LBNE
Would prefer a solution where these differences were in configuration
rather than coded into different modules and hardcoded workflows.
Will convene a small sub-group to look at the issue and make a proposal.
Want to get this done by the next Librarians Meeting
o Track interface changes
-- Proposed some time ago. Had an agreement forged in a subsequent sub-group
meeting. Erica to make a proposal, but has not yet
-- Target next librarians meeting for a proposal
o Integration system requirements
-- Drafting specification for LArSoft.
SCD working on a CI service. Dropped a number of suggested requirements
pertaining to managing the CI tasks and results as out of scope. Will
need to define these requirements (if there are any) as part of the
LArSoft requirements, which will then be used to define our program
of work for the system.
-- Hope to have something ready by next librarians meeting, and possibly by
the stakeholders meeting next week
o PMT geometry changes for uBooNE
Re-assign the ticket to Matt Toups pending creation of the optical response library
New way of handling Geant 4 macros (Lynn Garren)
o Currently in lib directory, which th en needs to be added to FW_SEARCH_PATH by hand
since this is how the files are found by the G4 module(s)
o Propose using the 'install_gdml' macro to put them into a directory that
is automatically put onto FW_SEARCH_PATH.
Works because there are no GDML files in there.
Also propose naming the directory G4
o All is approved.
Managing random number generators and seeds (Gianluca Petrillo)
o This work stems from tickets opened requesting centralized control of random
number seeds and generators
o Art provides a random number service
-- RandomGeneratorService
-- can request a random number engine of a particular type
-- will know the module from which it is called, so can have distinct engines of
the same type from multiple modules
-- can also supply an additional "label" that can be used to distinguish
distinct instances of engines within a given module
-- The service can write state to a text file, can initialize state from
the same file
An accompanying module, RandomNumberSaver, will save the state of all generators
to the event.
-- RandomGeneratorService can then read the state from the file and use that
to initialize the generators
o Seed service: provide a service to consolidate management of seeds
-- Can define many different policies for the seed service:
o Use a single "master" seed to algorithmically generate seeds to all
other generators. Lots of algorithms possible (see below)
o Use a single "master" seed everywhere
o Read and write to files or to/from the event
o etc...
o Questions and issues
-- Is zero a magic seed (eg, takes a value from machine clock)
-- What is the range of seeds? (0 to 999,999,999 suggested)
Genie:
-- Uses TRandom internally. Genie cannot depend on CLHEP since it is used
in contexts independent of that.
-- Need a TRandom wrapper around CLHEP random generators for Genie to be
-- A per-event seed depending upon information associated with the event
(such as run and event numbers)
-- Are all the use cases for seed management needed?
Action items and decisions
o Merge existing ROI code into next integration release
Ok to deprecate old data (so do not need a backward compatible schema
evolution solution)
o Convene small group to work on hit-finding workflow solution that would
make uBoone and LBNE configurable differences
o Assign ticket for PMT geometry to Matt Toups for optical response library
o Ok to relocate Geant4 macros to new G4 sub-directory, as proposed
o Project will develop a random number seed service that will allow
multiple seeding policies
-- Project will adapt existing code to use the service
-- Experiments will adapt the existing fcl files
o (from Lynn after the meeting) ifdh_art version to use is v1_4_1a for art v1_09_2,
and v1_4_1 for art v1_08_10
There are minutes attached to this event. Show them.
• 1:00 PM 1:20 PM
News and announcements 20m
Speaker: Erica Snider (Fermilab)
• 1:20 PM 1:40 PM
Change to Geant4 macro location 20m
Speaker: Lynn Garren (Fermilab)
• 1:40 PM 2:00 PM
Random number service 20m
Speaker: Gianluca Petrillo (University of Rochester) | 2020-09-24T07:53:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21502794325351715, "perplexity": 13219.731954794528}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400214347.17/warc/CC-MAIN-20200924065412-20200924095412-00106.warc.gz"} |
https://par.nsf.gov/biblio/10166285 | The i-process yields of rapidly accreting white dwarfs from multicycle He-shell flash stellar evolution models with mixing parametrizations from 3D hydrodynamics simulations
ABSTRACT We have modelled the multicycle evolution of rapidly accreting CO white dwarfs (RAWDs) with stable H burning intermittent with strong He-shell flashes on their surfaces for 0.7 ≤ MRAWD/M⊙ ≤ 0.75 and [Fe/H] ranging from 0 to −2.6. We have also computed the i-process nucleosynthesis yields for these models. The i process occurs when convection driven by the He-shell flash ingests protons from the accreted H-rich surface layer, which results in maximum neutron densities Nn, max ≈ 1013–1015 cm−3. The H-ingestion rate and the convective boundary mixing (CBM) parameter ftop adopted in the one-dimensional nucleosynthesis and stellar evolution models are constrained through three-dimensional (3D) hydrodynamic simulations. The mass ingestion rate and, for the first time, the scaling laws for the CBM parameter ftop have been determined from 3D hydrodynamic simulations. We confirm our previous result that the high-metallicity RAWDs have a low mass retention efficiency ($\eta \lesssim 10{{\ \rm per\ cent}}$). A new result is that RAWDs with [Fe/H] $\lesssim -2$ have $\eta \gtrsim 20{{\ \rm per\ cent}}$; therefore, their masses may reach the Chandrasekhar limit and they may eventually explode as SNeIa. This result and the good fits of the i-process yields from the metal-poor RAWDs to the observed chemical more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10166285
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
488
Issue:
3
Page Range or eLocation-ID:
4258 to 4270
ISSN:
0035-8711
1. ABSTRACT We present two mixing models for post-processing of 3D hydrodynamic simulations applied to convective–reactive i-process nucleosynthesis in a rapidly accreting white dwarf (RAWD) with [Fe/H] = −2.6, in which H is ingested into a convective He shell. A 1D advective two-stream model adopts physically motivated radial and horizontal mixing coefficients constrained by 3D hydrodynamic simulations. A simpler approach uses diffusion coefficients calculated from the same simulations. All 3D simulations include the energy feedback of the 12C(p, γ)13N reaction from the H entrainment. Global oscillations of shell H ingestion in two of the RAWD simulations cause bursts of entrainment of H and non-radial hydrodynamic feedback. With the same nuclear network as in the 3D simulations, the 1D advective two-stream model reproduces the rate and location of the H burning within the He shell closely matching the 3D simulation predictions, as well as qualitatively displaying the asymmetry of the XH profiles between the upstream and downstream. With a full i-process network the advective mixing model captures the difference in the n-capture nucleosynthesis in the upstream and downstream. For example, 89Kr and 90Kr with half-lives of $3.18\,\,\mathrm{\mathrm{min}}$ and $32.3\,\,\mathrm{\mathrm{s}}$ differ by a factor 2–10 in the two streams. In this particular applicationmore »
3. ABSTRACT Carbon enhanced metal poor (CEMP)-no stars, a subset of CEMP stars ($\rm [C/Fe]\ge 0.7$ and $\rm [Fe/H]\lesssim -1$) have been discovered in ultra-faint dwarf (UFD) galaxies, with $M_{\rm vir}\approx 10^8{\, \mathrm{ M}_\odot }$ and $M_{\ast }\approx 10^3-10^4{\, \mathrm{ M}_\odot }$ at z = 0, as well as in the halo of the Milky Way (MW). These CEMP-no stars are local fossils that may reflect the properties of the first (Pop III) and second (Pop II) generation of stars. However, cosmological simulations have struggled to reproduce the observed level of carbon enhancement of the known CEMP-no stars. Here, we present new cosmological hydrodynamic zoom-in simulations of isolated UFDs that achieve a gas mass resolution of $m_{\rm gas}\approx 60{\, \mathrm{ M}_\odot }$. We include enrichment from Pop III faint supernovae (SNe), with ESN = 0.6 × 1051 erg, to understand the origin of CEMP-no stars. We confirm that Pop III and Pop II stars are mainly responsible for the formation of CEMP and C-normal stars, respectively. New to this study, we find that a majority of CEMP-no stars in the observed UFDs and the MW halo can be explained by Pop III SNe with normal explosion energy (ESN = 1.2 × 1051 erg) and Pop II enrichment, but faint SNe might also be neededmore » | 2022-10-01T23:32:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.684954822063446, "perplexity": 3710.24261732524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336978.73/warc/CC-MAIN-20221001230322-20221002020322-00138.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-0.4?code=se:4_7&pointInTime=20210106 | ### I-0.4 - Mining Tax Act
4.7. The rules to which section 4.6 refers and that apply to an operator in respect of a particular fiscal year are the following:
(1) the operator’s elected functional currency is to be used for the purpose of computing the operator’s Québec mining results for the particular fiscal year;
(2) unless the context requires otherwise, each reference in this Act or the regulations to an amount (other than in respect of a penalty or fine) that is described as a particular number of Canadian dollars is, in respect of the operator and the particular fiscal year, to be read as a reference to that amount expressed in the operator’s elected functional currency using the relevant spot rate for the first day of the particular fiscal year; and
(3) any amount that is relevant in computing the operator’s Québec mining results for the particular fiscal year and that is expressed in a currency other than the operator’s elected functional currency is to be converted to an amount expressed in the operator’s elected functional currency using the relevant spot rate for the day on which the amount arose.
2011, c. 6, s. 18. | 2021-02-26T22:40:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8277055025100708, "perplexity": 1604.945282297185}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357984.22/warc/CC-MAIN-20210226205107-20210226235107-00085.warc.gz"} |
https://www.atap.gov.au/tools-techniques/travel-demand-modelling/4-data.aspx | # 4. Data collection
## 4.1 Background
It is important that government funds are invested in areas that provide the greatest return. Capital investment in transport infrastructure projects must be underpinned by good information on travel demand patterns (how, why, when and where people travel). Effective allocation of resources to manage and operate transport systems requires good information on the transport system performance. This information can only be obtained from comprehensive and regularly updated surveys of travel activity and demand.
The availability of reliable existing travel demand data, together with the costs involved in collecting new data, may dictate the specification and structure of the transport modelling system. Being able to establish a valid Reference (Base) Year demand is critical in undertaking the modelling of any major transport infrastructure proposal. Attempts should always be made to make best use of available demand data. The appropriateness of available data (for example, its currency, coverage, robustness and reliability) should be ascertained early in any model development and application undertaking.
## 4.2 Travel demand surveys
The collection of travel demand data usually requires large-scale travel surveys using either a mail out/mail back self-completion survey or a household personal interview survey.
The mail out/mail back self-completion survey questionnaire is mailed to a household and mailed back to the survey firm or agency after all questions are answered by all members of the surveyed household. Postage costs are usually borne by the survey firm or agency. The Victorian Activity and Travel Survey (VATS) is an example of a mail out/mail back survey.
The household personal interview survey involves face-to-face personal interviews and records all responses by all members of the surveyed household. Personal interview surveys have, to date, provided the major form of data collection for developing and updating transport models. Household personal interview surveys generally have high response rates (in the order of 70–80%) and can be undertaken over a much shorter time period than mail out/mail back surveys.
Other forms of travel demand survey may involve a combination of the mail out/mail back and face-to-face interview surveys, as well as computer aided telephone interview (CATI) surveys. Increasing use is being made of GPS devices to track individuals and assist in the collection of activity or travel diary information.
One critical issue to be addressed in designing a travel demand survey is the survey sample size. Generally, the more detailed the travel demand model, the larger the survey sample size required to obtain statistically reliable estimates of the model parameters. Funding limitations will, to some extent, limit the survey sample size and will dictate the level of detail in the travel demand model. One way of dealing with this issue is to conduct relatively small annual travel demand surveys that accumulate to increasing sample sizes over the ensuing years, making it possible to develop a travel demand model that becomes more detailed over time.
## 4.3 Person travel demand data
The travel demand data collected by the above-mentioned survey approaches represent a snapshot of travel patterns on a particular day and may include the following:
• Household information:
• dwelling type
• ownership status of dwelling
• household size
• number of registered motor vehicles by type
• number of bicycles
• Data about people in the household
• age
• sex
• relationship to head of household
• employment status
• resident or visitor
• licence holding
• occupation
• industry of employment
• personal income
• if currently studying – primary, secondary, tertiary
• undertaking other activities
• Travel data for all travel made on the travel day, on a ‘stop’ basis
• Travel origin
• Time of travel, including departure time and arrival time
• Purpose for the travel
• Location of destination
• Mode of transport used
• If the travel was made by vehicle
• vehicle used
• number of occupants
• any toll paid and by who
• parking location, any parking fee paid and by who
• If travel was made by public transport
• type of ticket
• type of zone ticket
• type of fare paid
• reason for not travelling on the travel day.
GPS based household travel surveys are becoming more prevalent in Europe and North America. Such surveys require independent travellers, from households, to carry GPS devices such as loggers, or phone based applications. These surveys, particularly in combination with prompted recall interviews, enable the collection of more accurate and precise personal travel behaviour data. Further information will be provided in the next update.
## 4.4 Other data sources
Other data sources may include:
• Up-to-date traffic counts by hour and by direction aim to cover, as is practically possible, the main highway sections included in the model. Consideration should be given to establishing a regime of screenline traffic counts to provide information for model validation.
• Traffic signal count data.
• Bluetooth data for developing origin-destination movements and observed travel times.
• Smart card system data is an alternative source of public transport patronage data and may eliminate possible bias in survey design and conduct. Further detail on the advantages and possible limitations of this data is provided at the end of the section.
• On-board surveys or surveys at stations can provide data and information on boardings and alightings, loadings, and origins and destinations. These surveys may be used to augment household interview surveys or to provide detailed public transport patronage and demand data for specific areas of interest.
• Automatic number plate recognition (ANPR), matching vehicles passing distinct locations, both to provide information on travel times and, where the locations are organised in screenlines, a geographically coarse sector based identification of demand patterns. There are examples of similar use of Bluetooth detectors, although consideration should be given to potential bias from the vehicles and travellers sampled. Research, particularly in the US, seeks to exploit vehicle weight detection and the magnetic impulse characteristics of individual vehicles to match vehicles passing different locations.
• Automated Vehicle Location (AVL) data.
There is emerging work to collate data tracking GPS devices (based on direct location data) and mobile phone devices (based on the location of phone masts the device is linked to at different times). A number of products are available providing information on travel times, tracking GPS related devices. These can be linked to in vehicle devices (such as for vehicle theft of route finding) and can provide vehicular journey time and speed. It should be recognised that the source data may be biased (e.g. comprising a large proportion of commercial vehicles) and suitable care taken in drawing on these data sources. There is also emerging evidence of these data sources being used to establish trip matrices, based on a range of assumptions to interpret that data for this purpose. One fundamental issue here relates to sampling and expansion. Most GPS based sources involve particularly small and biased samples that may render them unsuitable as a primary source of data for travel patterns. While mobile operators generally have access to a large sample of the population, there are significant variations in market share, and quite different behaviours (e.g. in older and younger individuals) that require careful consideration. Consideration is required in respect of privacy legislation. Careful consideration of the processing methods and assumptions, together with direct verification of the outcomes is needed in exploring the usefulness of these data.
### Use of Smart Card System Data
Potential advantages of using smart card system data are:
• The collection of large effective samples sizes, compared to household travel survey data
• Travel by individuals can be analysed over time
• Boardings and alightings can be accumulated to accurately estimate the passenger load on any segment of a public transport service
• As smart card data is usually timestamped at stops, it can also be used to estimate the speed and the reliability of public transport services even without an Automatic Vehicle Location (AVL) system (refer Austroads National Performance Indicators for Public Transport in Australia)
• Data is generally available within days of collection
• Low cost to acquire
• As the data is collected continuously, the data can be analysed and adjusted for daily variability and seasonality. Variability and seasonality are key issues to understand network reliability and crowding.
Potential limitations of using smart card system data are:
• The absence of information on travel purpose and on traveller characteristics. Inference is required to determine these details
• The difficulty in reliably identifying trips involving interchanging. Inference is required
• The difficulty in allocating origin and destination of travel to specific stops and transport zones. Again inference is required.
## 4.5 Survey Methodology and Data Requirements
Models and analytical procedures need data. The data needs to be relevant, current and accurate if useful results are to be gained from modelling and analysis.
Data collection is expensive, time consuming and not always straightforward, so care is needed in the planning, design and conduct of surveys. Without this attention, resources – time, people and money – can easily be wasted for little gain. High quality and relevant data are essential for analysis and serve to support policy formulation and decision-making. Poor quality or inappropriate data are to the detriment of informed decision-making.
One useful way to approach data collection is to view the survey process from the systems perspective. Figure 8 below provides one such process model. This figure represents a transport survey data collection as a process, starting with the specification of objectives of the survey and running through to the archiving of results. Note the existence within Figure 8 of various feedback loops indicating that survey design is not a purely sequential process; for example, analysts must be prepared to modify their survey instruments and sample frames in the light of the outcome of the pilot survey.
Figure 8: Survey process modelSource: Taylor, Bonsall and Young 2002, p.138
This process model identifies a number of steps and stages in the collection and analysis of data. These steps may be grouped into three broad stages:
1. Preliminary planning, in which the purpose and specific objectives of the survey are identified, specifications of the requirements for new data are determined (in light of existing data sources) and resources available or required for the survey are identified.
2. Survey planning and design, in which the appropriate survey instrument is selected and the sample design (including target population, sampling frame, sampling method and sample size) is undertaken, leading to a survey plan and the conduct of a pilot survey to test all aspects of the plan and to ensure that it works and provides the required data, and that they are compatible with the proposed analysis. This is an iterative stage, in which pilot survey outcomes may lead to revisions in the survey plan. Good and successful surveys necessarily pay significant attention to getting this stage right.
3. Survey conduct, in which the full survey is undertaken, data extracted and analysed, study reports prepared and databases archived for future reference.
This process is fully explained in Taylor, Bonsall and Young (2000, pp.137–145).
## 4.6 Survey techniques
Surveys are used to obtain data, which are then used to estimate model parameters for predicting the behaviour of transport users in order to make demand forecasts and to estimate the economic and financial values of projects. Most transport data surveys are sample surveys, in that only a small fraction of the overall population (for example, travellers, vehicles, network links or customers) is surveyed to provide data that are then extrapolated to provide a description of the total population. Data are collected at a few locations taken to represent transport activity, travel movement and traffic flow across the study area or a sample of individual travellers, customers or operators is surveyed because it is infeasible, impractical or uneconomic to survey the entire population. This means that survey data often need expansion from the sample to represent the full population. As discussed in the following sections, care in survey organisation and attention to detail are needed to ensure that survey data can properly represent their parent population.
There are two broad approaches to data collection:
1. Observational (passive) surveys – where surveyors (human or mechanical) record the occurrence (and often time of occurrence) of specified transport events or phenomena, such as the passage of vehicles past a point on the road, the arrival of trucks at a warehouse, or the number of passengers exiting from a railway platform in a specified time interval
2. Interview (active) surveys – where the surveyors make contact with the individual travellers, customers or decision makers to seek information directly from them
The information gathered in active surveys can be much richer than information available from passive surveys because:
• Observations are limited in scope to the direct area under study. For instance, the arrival of a vehicle at a cordon line indicates the point at which the vehicle entered or left the study area, but provides little information on the actual origin or the ultimate destination of the trip, nor the frequency with which the vehicle makes that trip or the purpose for which it is made. An active interview or questionnaire survey could obtain this additional information.
• Observational surveys are limited to study of actual behaviour at the study site. They provide information on ‘revealed demand’ - the actual behaviour that is occurring under the environmental conditions pertaining to the study area at the time of the survey. Revealed demand is the observed use of an area or facility. Environmental states, such as traffic congestion or lack of parking and seasonal conditions (including time of day), may restrict the ability of some individuals to access the specific site or facility or to choose to use an alternative (for example, another destination). This phenomenon is known as ‘latent demand’ and its extent cannot be gauged using observational surveys. An active survey method could seek to determine the existence and extent of latent demand, especially if the survey is designed and applied to include ‘non-users’ of facility or service as well as the users.[1]
The passive surveys aim to make no interference with the normal operation of the survey site and to not disturb the behaviour of the individuals under observation. The active surveys cannot avoid some interference and may even create disturbances that could affect the behaviour of the respondents. Great care is needed in the survey design for both observational and active surveys to ensure any interference is minimised and that significant bias is not introduced into the survey results because of how the data were collected.
Active (‘interview’) surveys may be conducted in three alternative ways: direct personal interviews, questionnaire surveys and remote interviews (generally conducted by telephone, but also possible over the internet).
### 4.6.1 Direct personal interviews
Personal interviews may be conducted in a variety of locations. Interviews in people’s homes have been widely used for collecting detailed data on the travel behaviour of households and individual. Most metropolitan areas and other large cities have databases of personal travel conducted using ‘household interviews’. Household interview surveys were conducted in Adelaide in 1999 and Perth in 2002-03, among other cities, while Sydney has a rolling cycle of home interview surveys running continuously.
Direct interviews can be used to collect detailed data about businesses, households and individuals and their travel behaviour, and about other traits such as attitudes and perceptions. In some cases, direct interviews may be conducted in a laboratory setting as well as ‘in the field’. Stated preference studies are often undertaken in a laboratory where specialised resources can be used (for example, to create a simulated environment for the respondent to be immersed in the situational context behind the survey). Hensher, Brotchie and Gunn (1989) described a methodology for surveying rail passengers using active survey techniques. Hensher and Golob (1998) described an interview survey of shoppers and freight forwarders conducted in Sydney in 1996.
One problem with the direct interview is that it can take a considerable period of time to complete, which may cause significant inconvenience to the (volunteer) interviewee. A second problem is that the interviewer must make direct contact with the survey respondent. This may involve considerable time spent travelling by the interviewer to visit the respondents and the need for multiple ‘call backs’ if the respondent is not ‘at home’.
### 4.6.2 Questionnaire surveys
One solution to overcome the time constraints associated with direct interviews is to use questionnaire surveys, often to be returned through the post (‘mail back’) at some future time. Examples of these surveys are roadside or i-vehicle surveys. These can be attempted by direct interview, but individual travellers may be delayed and inconvenienced in the process, or may reach their destination before the conclusion of the interview. It may be more reasonable and effective to distribute a written questionnaire to the travellers, asking them to complete and return the survey once the journey is finished.
The questionnaire can contain questions similar to those posed in an interview, but there are many limitations. For example, the questions must be clear and unambiguous as it stands, as there is no opportunity for an interviewer to offer an explanation. Fewer questions can be asked, as excessively long questionnaires reduce the number of completed responses. There is also the possibility for the respondent to offer false or misleading answers that an interviewer would recognise as such, but that are much harder to detect on a written form. However, the major problem with questionnaire surveys of this type is the likelihood of a low response rate. While response rates of the order of 10–20% may be acceptable in some areas (such as general market research on consumer goods), there is a considerable body of transport research that suggests that much higher rates of response – 80% or better - may be necessary to properly gauge true levels of travel activity in a population. It is necessary to recognise that the problem of low response rates may introduce sample bias. To overcome this problem, the survey process needs to incorporate a random procedure to select respondents and require the interviewer to visit a household multiple times to meet the selected respondent for interview. Richardson, Ampt and Meyburg (1995) provide a full discussion of this issue, as well as detailed advice on the conduct of interview and questionnaire surveys.
### 4.6.3 Telephone and internet surveys
The third alternative is the use of telephone (or internet-based) surveys. These are similar to the direct interview except the interview is conducted remotely over a telecommunications network, with telephone interviews usually using random dial-up access. The advantages of this survey technique are cost and convenience. The interviewer stays in the one place (a call centre) and can make contact with a large number of respondents in a short time. Data entry can also be automated, as responses are directly entered into a computer database during the interview.
The disadvantages of the technique include the relatively short length of the interview that is normally possible over the telephone and perhaps a growing ‘consumer resistance’ to the telephone interview, given the method is widely used in general social and market research surveys and in direct marketing. Richardson, Ampt and Meyburg (1995), among many other transport survey researchers, maintain that good quality data on travel behaviour (at least of quality commensurate with that obtainable from face-to-face interviews and questionnaires) cannot be collected using telephone interviews.
Internet-based surveys are more like observational surveys in that respondents to the surveys generally find the survey website of their own volition, rather than through active encouragement by surveyors. This technique is being used, for instance, in studies on driver route choice, where detailed information is required that is quite difficult to obtain through more conventional survey approaches (see Abdel-Aty 2003). However, bias in sampling is quite likely to be an issue in these surveys and the field is as yet relatively unexplored.
### 4.6.4 Costs
Direct interview surveys are generally the most expensive, followed by questionnaire surveys (especially with regard to the number of valid completed questionnaires returned) and then telephone surveys. Observational surveys can be relatively inexpensive, at least in terms of elemental costs such as hourly wage rates or where automatic data loggers can be employed (as for automatic vehicle counts). However, large-scale observational surveys (such as vehicle number plate surveys that require a large number of observed vehicles) can prove very expensive and are sometimes not particularly efficient in terms of the collection of usable, quality data.
### 4.6.5 Revealed versus stated preferences
A further distinction in interview surveys should be drawn between the collection of revealed preference data (what people are seen to do or record that they have done) and stated preference data (what people say they would do in different circumstances, such as when faced with changes in transport fares, services or costs).
Generally, the household travel surveys concentrate on revealed preference data. They record historical data on travel behaviour, which then form a snapshot of travel activity in an area at one particular point in time. These data provide little information on how people might change their behaviour in response to new transport policies or to changing travel environments or to the availability of new modes or services. Stated preference data may be used for these purposes and stated preference experimental methods provide powerful tools in this regard. At the same time, there are considerable problems in ensuring that stated preference information is valid and reliable. Louviere, Hensher and Swait (2000) provide a full coverage of this survey methodology and its use. It should be noted that stated preference methods are a rich source of information for the development of discrete choice models of travel behaviour.
For further reading on transport survey methods see Taylor, Bonsall and Young (2000), Louviere, Hensher and Swait (2000) and Richardson, Ampt and Meyburg (1995).
## 4.7 Sample size estimation
As indicated in Section 4.17, most transport data surveys are sample surveys. Sampling is usually necessary because it is too expensive to survey all members of the population (for example, to obtain travel diaries from all inhabitants of a metropolitan area) or it is physically impossible to do so (such as testing the roadworthiness of all vehicles) or because the survey testing process would be destructive (such as determining the strength of railway sleepers).
Almost all transport surveys involve observing some members of a target population to infer something about the characteristics of that population. In this sense they are statistical sampling surveys. As the effectiveness of the survey is dependent upon choosing an appropriate sample, sample design is a fundamental part of the overall survey process.
• Definition of target population
• Definition of sampling unit
• Selection of sampling frame
• Choice of sample method
• Consideration of likely sampling errors and biases
• Determination of sample size.
Two main methods exist for selecting samples from a target population: judgement sampling and random sampling. In random sampling, all members of the target population have a chance of being selected in the sample, whereas judgement sampling uses personal knowledge, expertise and opinion to identify sample members.
Judgement samples have a certain convenience. They may have a particular role, such as ‘case studies’ of particular phenomena or behaviours. The difficulty is that because judgement samples have no statistical meaning, they cannot represent the target population. Statistical techniques cannot be applied to these samples to produce useful results as they are almost certainly biased.
There is a particular role for judgment sampling in exploratory or pilot surveys where the intention is to examine the possible extremes of outcomes with minimal resources. However, to go beyond such an exploration, the investigator cannot attempt to select ‘typical’ members or exclude ‘atypical’ members of a population, or to seek sampling by convenience or desire (choosing sample members on the basis of ease or pleasure of observation). Rather, a random sampling scheme should be adopted, to ensure the sample taken is statistically representative.
Random samples may be taken by one of four basic methods (Cochran 1977): simple random sampling, systematic sampling, stratified random sampling and cluster sampling. Taylor, Bonsall and Young (2000 pp. 155–58) describe each of these sampling methods and their applications, as do Richardson, Ampt and Meyburg (1995).
Simple random sampling allows each possible sample to have an equal probability of being chosen, and each unit in the target population has an equal probability of being included in any one sample. Sampling may be either ‘with replacement’ (any member may be selected more than once in any sample draw) or ‘without replacement’ (after selection in one sample, that unit is removed from the sampling frame for the remainder of the draw for that sample). Selection of the sample is by way of computerised randomisation techniques such as random number generation. The methods of statistical inferences applied to sample data analysis are predicated on the basis that a sample is chosen by simple random sampling. Data collected using other sampling methods need to be analysed using known techniques that include corrections to approximate simple random samples.
There is always a possibility that a sample may not adequately reflect the nature of the parent population. Random fluctuations (‘errors’), which are inherent in the sampling process, are not serious because they can be quantified and allow for using statistical methods.[2] However, if due to poor experimental design or survey execution there is a systematic pattern to the errors, this will introduce bias into the data and, unless it can be detected, it will distort the analysis. A principal objective of statistical theory is to infer valid conclusions about a population from unbiased sample data, bearing in mind the inherent variability introduced by sampling. Bias and sampling errors are two, quite different, sources of error in experimental observations. As described in Richardson, Ampt and Meyburg (1995, pp. 96–101), bias (or systematic error) needs to be removed from sample data before statistical analysis can be attempted, for statistical theory treats all errors as sampling errors.
A distribution of all the possible means of samples drawn from a target population is known as a sampling distribution. It can be partially described by its mean and standard deviation. The standard deviation of the sampling distribution is known as the standard error. It takes account of the anticipated amount of random variation inherent in the sampling process and can therefore be used to determine the precious of a given estimate of a population parameter from the sample.
Surveys for specific investigations usually attempt to provide data for the estimation of particular population parameters or to test statistical hypotheses about a population. In either case, the size of the sample selected will be an important element and the reliability of the estimate will increase as sample size increases. However, the cost of gathering the data will also increase with increased sample size - an important consideration in sample design. A trade-off may have to occur and the additional returns from an increase in sample size will need to be evaluated against the additional costs incurred. If the target population may be taken as infinite, then the standard error (sx) of variable X is given by
$S X - = s n$
[EQ 4.1]
where s is the estimated standard deviation of the population and n is the sample size, assuming that the sampling distribution is normal. Even when the sampling distribution is not normal, this method may still apply because to the Central Limit Theorem which states that the mean of n random variables form the same distribution will, in the limit as n approaches infinity, have a normal distribution even if the parent distribution is not normal. The standard deviation of the mean is inversely proportional to √n. The implication of equation 4.1 is that as sample size increases, standard error decreases in proportion to the square root of n. Here is an important result. The extra precision of a larger sample should be traded off against the cost of collecting that amount of data. To double the precision of an estimate will require the collection of four times as much data.
Similar results are found for other statistical parameters. For instance, the standard error (sp) of a proportion p (e.g. a measure such as ‘the proportion of households owning one vehicle’) is given by:
$S P = p ( 1 - p ) n$
[EQ 4.2]
The practical application of these results requires some prior knowledge of the population, such as a prior estimate of the sample standard deviation (s) in the case of the mean value of variable X or an initial estimate of the proportion p. The results of previous surveys, or the pilot survey, may be used to provide this knowledge.
[1] For example, on-board surveys conducted on bus, train or tram are often used to collect data on public transport users, but could not indicate much about those travellers who are potential users of public transport, but are currently using some other mode. This one reason for the use of home interviews in general travel surveys.
[2] Noting that minimisation of experimental errors is of course important in improving the precision of parameter estimates based on survey data. | 2019-07-18T11:57:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3983033001422882, "perplexity": 1613.7995727644068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525627.38/warc/CC-MAIN-20190718104512-20190718130512-00066.warc.gz"} |
https://lammps.sandia.gov/doc/Python_install.html | # 12.4. Installing LAMMPS in Python
For Python to invoke LAMMPS, there are 2 files it needs to know about:
• python/lammps.py
• src/liblammps.so
Lammps.py is the Python wrapper on the LAMMPS library interface. Liblammps.so is the shared LAMMPS library that Python loads, as described above.
You can insure Python can find these files in one of two ways:
• set two environment variables
• run the python/install.py script
If you set the paths to these files as environment variables, you only have to do it once. For the csh or tcsh shells, add something like this to your ~/.cshrc file, one line for each of the two files:
setenv PYTHONPATH ${PYTHONPATH}:/home/sjplimp/lammps/python setenv LD_LIBRARY_PATH${LD_LIBRARY_PATH}:/home/sjplimp/lammps/src
If you use the python/install.py script, you need to invoke it every time you rebuild LAMMPS (as a shared library) or make changes to the python/lammps.py file.
You can invoke install.py from the python directory as
% python install.py [libdir] [pydir]
The optional libdir is where to copy the LAMMPS shared library to; the default is /usr/local/lib. The optional pydir is where to copy the lammps.py file to; the default is the site-packages directory of the version of Python that is running the install script.
Note that libdir must be a location that is in your default LD_LIBRARY_PATH, like /usr/local/lib or /usr/lib. And pydir must be a location that Python looks in by default for imported modules, like its site-packages dir. If you want to copy these files to non-standard locations, such as within your own user space, you will need to set your PYTHONPATH and LD_LIBRARY_PATH environment variables accordingly, as above.
If the install.py script does not allow you to copy files into system directories, prefix the python command with “sudo”. If you do this, make sure that the Python that root runs is the same as the Python you run. E.g. you may need to do something like
% sudo /usr/local/bin/python install.py [libdir] [pydir]
You can also invoke install.py from the make command in the src directory as
% make install-python
In this mode you cannot append optional arguments. Again, you may need to prefix this with “sudo”. In this mode you cannot control which Python is invoked by root.
Note that if you want Python to be able to load different versions of the LAMMPS shared library (see this section), you will need to manually copy files like liblammps_g++.so into the appropriate system directory. This is not needed if you set the LD_LIBRARY_PATH environment variable as described above. | 2018-12-16T17:57:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3869726359844208, "perplexity": 4284.5192433346565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827963.70/warc/CC-MAIN-20181216165437-20181216191437-00413.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/proc.2011.2011.1271 | Article Contents
Article Contents
# Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities
• The Euler-Cauchy differential equation is one of the first, and simplest, forms of a higher order non-constant coefficient ordinary di erential equation that is encountered in an undergraduate differential equations course. For a non-homogeneous Euler-Cauchy equation, the particular solution is typically determined by either using the method of variation of parameters or transforming the equation to a constant-coefficient equation and applying the method of undetermined coefficients. This paper demonstrates the surprising form of the particular solution for the most general n$^(th)$ order Euler-Cauchy equation when the non-homogeneity is a polynomial. In addition, a formula that can be used to compute the unknown coecients in the form of the particular solution is presented.
Mathematics Subject Classification: Primary: 34-01; Secondary: 34A05.
Citation:
Open Access Under a Creative Commons license | 2023-03-21T11:09:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.5027303099632263, "perplexity": 433.3026733088612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00100.warc.gz"} |
https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Zero-width_space.html | # Zero-width space
The zero-width space (ZWSP) is a non-printing character used in computerized typesetting to indicate word boundaries to text processing systems when using scripts that do not use explicit spacing, or after characters (such as the slash) that are not followed by a visible space but after which there may nevertheless be a line break. Normally, it is not a visible separation, but it may expand in passages that are fully justified.[1]
## Usage
In HTML pages, the zero-width space can be used as a potential line-break in long words as an alternative to the <wbr> element. However, the zero-width space is not supported in all web browsers such as old versions of Internet Explorer (versions 6 and earlier).[2]
To show the effect of the zero-width space, the following words have been separated with zero-width spaces:
LoremIpsumDolorSitAmetConsecteturAdipiscingElitSedDoEiusmodTemporIncididuntUtLaboreEtDoloreMagnaAliquaUtEnimAdMinimVeniamQuisNostrudExercitationUllamcoLaborisNisiUtAliquipExEaCommodoConsequatDuisAuteIrureDolorInReprehenderitInVoluptateVelitEsseCillumDoloreEuFugiatNullaPariaturExcepteurSintOccaecatCupidatatNonProidentSuntInCulpaQuiOfficiaDeseruntMollitAnimIdEstLaborum
And following words are not separated with these spaces:
LoremIpsumDolorSitAmetConsecteturAdipiscingElitSedDoEiusmodTemporIncididuntUtLaboreEtDoloreMagnaAliquaUtEnimAdMinimVeniamQuisNostrudExercitationUllamcoLaborisNisiUtAliquipExEaCommodoConsequatDuisAuteIrureDolorInReprehenderitInVoluptateVelitEsseCillumDoloreEuFugiatNullaPariaturExcepteurSintOccaecatCupidatatNonProidentSuntInCulpaQuiOfficiaDeseruntMollitAnimIdEstLaborum
On browsers supporting zero-width spaces, resizing the window will re-break the first text only at word boundaries, while the second text will not be broken at all.
## Encoding
The zero-width space character is encoded in Unicode as U+200B ZERO WIDTH SPACE (HTML ​).[3]
The TeX representation is \hskip0pt; the LaTeX representation is \hspace{0pt};[4] and the groff representation is \:.[5]
Its semantics and HTML implementation are similar to the soft hyphen.
## External links
1. The Unicode Standard 6.1, p. 366
2. "Archived copy". Archived from the original on December 14, 2010. Retrieved December 3, 2009.
3. "General Punctuation – Unicode" (PDF). Retrieved 2013-07-20.
4. "The LaTeX Companion. Chapter 3: Basic Formatting Tools" (PDF). Retrieved 2014-02-08.
5. "groff(7) - Linux manual page". Retrieved 2014-02-08.
This article is issued from Wikipedia - version of the 12/2/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files. | 2022-05-24T09:00:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8615831732749939, "perplexity": 5181.106523352141}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00787.warc.gz"} |
https://dup.silverchair.com/demography/article/58/6/2065/220063/The-Poverty-Balancing-Equation-Expressing-Poverty | ## Abstract
The accurate measurement of poverty is essential for the development of effective poverty policy. Unfortunately, approaches that use poverty rates to assess the causes and consequences of poverty do not fully capture the components of change in the poverty population because changes in the conventional poverty rate can occur owing to processes of natural increase, migration, or transitions in and out of poverty. This article presents an accounting framework for changes in poverty within and between places. The framework, termed the poverty balancing equation, generates a series of summary statistics that can be used in place of the conventional poverty rate in future research. The approach is demonstrated using the 2014 panel of the Survey of Income and Program Participation to generate state-level estimates of the poverty components of change for three states in the American South between January and December of 2013. Results show that even when poverty rates remain constant, there is significant dynamism within poor and nonpoor populations. By applying this approach, either completely or in part, researchers can provide more specific and actionable evidence for poverty alleviation policy.
## Introduction
The negative ramifications of poverty for people, both immediate and long term, have been well documented by demographers and other social scientists. Experiencing poverty leads to lower physical and mental well-being (Burton et al. 2013; Desmond and Western 2018; Dreyer 2019; MacTavish 2007; Rhubart and Engle 2017) and decreased social mobility (Chetty et al. 2014; Desmond and Western 2018), while also predisposing individuals to later bouts of poverty and cumulative negative impacts throughout the life course (Barrett et al. 2016; Larrimore et al. 2020; Musick and Mare 2006; Rank and Hirschl 2009). Although poverty occurs at the level of the individual, scholars frequently focus on poverty of place (e.g., the level of poverty in a region). The reason for this is twofold. First, person-level data with detailed geographic information can be difficult to obtain, making aggregate studies a pragmatic approach when geography is of interest. Second, both empirical research and theory often intentionally focus on place-based policies, effects, outcomes, and causes. Research has consistently found that exposure to concentrated poverty, even absent poverty at the individual level, can have a host of negative socioeconomic outcomes (Chetty et al. 2016; Chetty et al. 2014; Sampson 2008; Sampson et al. 2002). Further, many theories of the causes and consequences of poverty argue that social structure and place-based policies, not individual behaviors, are the ultimate drivers of poverty among populations (Brady 2019; Tickamyer and Wornell 2017).
Although the study of poverty of place is robust, with a vast body of literature, the accounting of the dynamics of poverty populations within and between places remains underdeveloped. Scholars have frequently argued about the correct way to determine if someone is poor, with some advocating absolute measures of poverty, others arguing for relative approaches, and some advocating for approaches that move beyond income and account for the capabilities that income provides (Brady 2003; Hutto et al. 2011; Iceland 2005, 2013; Sen 2014). Although the importance of this ongoing conversation regarding poverty determination cannot be overstated, all of the popular approaches generally produce a single threshold of poverty. Poverty of place research uses one of these dichotomous measures at the individual level to produce an aggregate poverty rate—the percentage of those classified as poor relative to the total population—that is generally used as the variable of interest in place-based studies of poverty. Depending on study goals, researchers assess the impact of changes in the poverty rate on outcomes, or changes in independent variables on the poverty rate. Unfortunately, this approach does not fully capture the population dynamics of poverty occurring across space.
The reason the conventional poverty rate is insufficient is because the poverty rate of a place can change through six different factors: births, deaths, in-migration, out-migration, transitions into poverty, and transitions out of poverty. Thus, using the conventional poverty rate as the dependent variable does not tell us how poverty is changing within a region. It only tells us that it is changing. This poses significant difficulties for both policy design and evaluation. If the goal of a policy is to transition people out of poverty, processes of migration and natural increase could very well mask the efficacy of said policy. Further, a region may have a stable poverty rate while still having a considerable portion of the population transitioning into poverty. This is because transitions into poverty can be masked by a disproportionate in-migration of the nonpoor. Thus, the conventional poverty rate can lead policymakers to incorrectly believe poverty is not on the rise, or is even on the decline, depending on the differential population processes occurring within the poor and nonpoor populations.
In an effort to address these difficulties, this article presents a framework—the poverty balancing equation—that allows researchers to assess these factors individually, and in doing so fully capture the way poverty is changing within and between places. This framework is a valuable and necessary step for advancing poverty research. It provides a common language from which more precise poverty scholarship can proceed, while clearly articulating new summary statistics that can be calculated with both public and restricted data in future model-based and descriptive poverty alleviation efforts. Following the presentation of the framework, I demonstrate the approach using the first wave of the 2014 Survey of Income and Program Participation (SIPP) to generate estimates of the components of change in the poverty population for three states with different poverty trajectories in the American South—a region known for its disproportionately high levels of poverty relative to the rest of the United States (Baker 2020)—between January and December of 2013.
## Prior Work on Poverty and Population Processes
Researchers have frequently assessed specific demographic processes among the poor. Although, to the author's knowledge, there is scant work focused on aggregate natural increase of the poor population, the independent factors of mortality and fertility have received significant attention and are often heightened among the population in poverty. Elevated levels of poverty have been consistently related to higher rates of all-cause, cancer-related, child, and infant mortality (Cohen et al. 2003; Fleisch Marcus et al. 2017; Moncayo et al. 2019; Pool et al. 2018; Pritchard and Keen 2016; Sims et al. 2007; Smith and Waitzman 1994; Taylor-Robinson et al. 2019; Toprani et al. 2016). Further, fertility among poor households has been found to be higher than fertility among the nonpoor, with the risk of an infant being born into poverty increasing with each additional child (Thiede et al. 2018), and fertility declining faster among nonpoor households than poor households over the past 50 years (Lichter 1997).
There is also a sizable body of work on migration and poverty, both on the poverty of immigrants (Bárcena-Martín and Pérez-Moreno 2012; Chapman and Bernstein 2003; Crowley et al. 2006; Joo 2013; Kazemipur and Halli 2000; Lichter et al. 2005; Peri 2011; Raphael and Smolensky 2009; Smith and Ley 2008; Thiede and Brooks 2018; Van Hook et al. 2004) and on the migration patterns of the poor (Allard and Danziger 2000; Christiaensen et al. 2019; Cushing 2005; Foulkes and Newbold 2008; Foulkes and Schafft 2010; Frey 1995; Frey et al. 1996; Levine and Zimmerman 1999). Unlike the consistent findings of research on higher fertility and mortality among those living in poverty, research on the migration of the poor has been more varied in findings and focus. Such research related to welfare policy has focused on whether generous welfare policies act as “magnets” for the poor (Allard and Danziger 2000; Cushing 2005; Frey et al. 1996; Levine and Zimmerman 1999). Evidence suggests that generous policies have either modest (Cushing 2005; Frey et al. 1996) or no effect on migration (Allard and Danziger 2000; Levine and Zimmerman 1999). Beyond welfare magnet research, work on North American poverty has found that poverty is generally elevated among immigrant households and the children of immigrants (Crowley et al. 2006; Kazemipur and Halli 2000; Lichter et al. 2005; Thiede and Brooks 2018; Van Hook et al. 2004).
Beyond the bedrock population processes of mortality, fertility, and migration, the poverty rate can also change because of transitions in and out of poverty among those in the population. Although the notion of poverty being a consistent status shared by those in an “underclass” of society persists, this has never really been true and has only become less so in the modern era (Sandoval et al. 2009). Individual periods of poverty are often brief, with most lasting one or two years (Rank and Hirschl 2002). Further, the proportion of the population that will experience at least one bout of poverty in their lives is quite high, with the majority of Americans experiencing at least one bout of poverty by age 85 (Rank and Hirschl 1999, 2001, 2015). As noted by Sandoval et al. (2009), this means that even if the aggregate poverty rate stays constant from year to year, there can be considerable movement in and out of poverty within the population. Although research on transitions in and out of poverty—particularly that by Rank and Hirschl (2015)—has successfully demonstrated the dynamic and widespread nature of poverty, it ultimately maintains a focus on poverty of people, as opposed to poverty of place.
The work that is most methodologically aligned with the framework presented here focuses on the role of population composition in determining the level of poverty within regions (Chapman and Bernstein 2003; Christiaensen et al. 2019; Foulkes and Schafft 2010; Joo 2013; Wright 1996). This work targets the effect of migration on changes in aggregate poverty rates and empirically demonstrates how the poverty rate of a place can change owing to processes besides changes in income. For example, relying on a decomposition technique similar to that advanced by Kitagawa (1955), which both Chapman and Bernstein (2003) and Wright (1996) referred to as a “shift-share” technique, Chapman and Bernstein (2003) decomposed how much of a change in poverty rates was due to changes among migrants versus nonmigrants in the United States; they found that the increase in migrants was not a significant factor in the lack of poverty decline from 1989 to 1999.
Christiaensen et al. (2019) presented an analysis using a similar approach to assess changes in poverty rates due to migration in Tanzania and found that moves from urban to rural areas decreased aggregate poverty more than moves from rural to urban areas. From a different angle, Joo (2013) used a Oaxaca–Blinder regression decomposition to determine how much of the change in U.S. child poverty from 1993 to 2010 was attributable to the increase in children living in immigrant households versus other population factors. Notably, this study found that it did not play a significant role in the changes in poverty rates over the study period. Finally, Foulkes and Schafft (2010) used census migration data to assess the migration patterns of the poor and determine how those patterns reinforced concentrated poverty. Their results showed that migration rates were higher among the poor than the nonpoor, and that the poor moved in a pattern that increased the concentration of poverty within regions.
The work of Foulkes and Schafft (2010), as well as the decomposition studies performed by Chapman and Bernstein (2003), Christiaensen et al. (2019), and Joo (2013), all address the core problem posed by the conventional poverty rate, while providing only partial solutions. The stated studies assessed only the effect of migration on the level of poverty within regions. This focus, while valuable, limits the ability of researchers to compare the various forces driving changes in the poverty level of a region (e.g., migration vs. natural increase vs. changes in resources). Reliance on the decomposition of aggregated data limits the expansion of research questions on this topic, as the conventional poverty rate remains the ultimate dependent variable. Further, the decomposition methods used in these papers, while valuable for comparing migrants to nonmigrants or the poor to the nonpoor, break down when we attempt to account for all of the components of change in the poverty population at once.
In sum, although the demographic processes of the poor have received significant attention in the academic literature, there is a notable lack of work assessing the specific ways the poverty population is changing within and between places. The dearth of literature assessing the population dynamics of poverty of place, as well as the methodological limitations posed by the work that does exist, highlight the need for a more comprehensive approach for assessing changes in poverty. The goal of many poverty alleviation policies is lifting people out of poverty. But if we do not separate changes in aggregate poverty due to transitions in and out of poverty from changes due to migration or natural increase, then any estimates of policy impacts will be biased. To remedy this weakness in the literature, the framework outlined in the next section builds on the demographic balancing equation to provide a more comprehensive framework for assessing poverty dynamics.
## Poverty as a Population Process
### Components of Population Change in the Poverty Population
Before discussing the specifics of the poverty balancing equation and its relevant counterparts, an introduction to the components of change relevant to the case of poverty is necessary. As with any population, the poverty population is able to change via only a handful of mechanisms: natural increase,1 net migration,2 and net poverty transitions. These three processes are composed of six factors: births, deaths, in-migration, out-migration, transitions into poverty, and transitions out of poverty.
When considering the size of the total population in a region, natural increase and net migration are the only processes we need to consider. However, when we shift tothe poverty population of a region, there is one more important process—poverty transitions. This process, which I will refer to in formulas as NPov and NAff,3 accounts for the entry and exit of individuals from the poor or nonpoor populations through the changing ratio of household income to the poverty threshold among the constant population (i.e., those present in the region at the start and end of the period). The poverty balancing equation framework is agnostic to the measure of poverty used. All that is assumed is that the poor and nonpoor are defined using a dichotomous criterion. Thus, relative measures or absolute measures using any version of income calculation can be applied.
Net poverty transition is presented in Eq. (3), where F represents those who enter into the poverty population because their income fell below the poverty threshold and C represents those who exit the poverty population because their income has climbed above the poverty threshold. Equation (4) presents the inverse of this for net poverty transition among the nonpoor population.4 These three mutually exclusive processes—natural increase, net migration, and net poverty transition—form the building blocks of the poverty balancing equation framework.
$NPov=(F−C),$
(3)
$NAff=(C−F).$
(4)
### The Poverty Balancing Equation
The framework I present builds on the standard population balancing equation presented in Eq. (5), where Pop2 represents the population at time 2, Pop1 represents the population at time 1, NI is natural increase in the time period, and NM is net migration in the area during the time period:
$Pop2=Pop1+NI+NM.$
(5)
Although this formula is used to understand changes in the total population, with minor modifications we can adapt it to the population in poverty. For a given region, the population in poverty in that region can be expressed as the extension of Eq. (5) presented in Eq. (6). In this equation, Pov2 represents the population in poverty at time 2, Pov1 represents the population in poverty at time 1, NIpov is the natural increase of the poverty population during the time period, NMpov is the net migration of those in poverty to the region, and NPov is the net poverty transition among those within the population at the start and end of the period:
$Pov2=Pov1+NIpov+NMpov+NPov.$
(6)
Although the formula in Eq. (6) fully captures the unique ways an individual can move into or out of the poverty population in a region, it does not fully account for the other changes within a population. Take, for example, the in-migration of those in poverty, captured by NMpov. This in-migration does not have clear meaning unless we also account for the net migration of the nonpoor population. We can express these dynamics of the nonpoor in a manner similar to the way the population dynamics of those in poverty are expressed in Eq. (6). This gives us Eq. (7), where Aff2 is the population of a region not in poverty at time 2, Aff1 is the nonpoor population of a region at time 1, NIaff is the natural increase of the nonpoor population, NMaff is the net migration of the nonpoor population, and NAff is the net poverty transition of the nonpoor population:
$Aff2=Aff1+NIaff+NMaff+NAff.$
(7)
To understand all the dynamics of the total population while accounting for the unique dynamics of NPov and NAff, we can combine these equations to yield Eq. (8), which shows that the total population of a region at time 2 is simply the sum of the poor population and the nonpoor population at time 2. After substituting Eqs. (6) and (7) into Eq. (8), we see that Eq. (9) shows that Pop2 is the sum of two linked balancing equations:
$Pop2=Pov2+Aff2,$
(8)
$Pop2=Pov1+NIpov+NMpov+NPov+Aff1+NIaff+NMaff+NAff.$
(9)
Importantly, Eq. (9) simply reduces to Eq. (5). This is because the sum of NPov and NAff will always equal zero owing to their calculation, and the other components sum to the components of change for the entire population. This collapsing nature highlights the full logic of the accounting exercise, while illustrating the fact that we can understand changes in the total population from the perspective of relative changes in the poor and nonpoor populations. Equations (10) and (11) show that the poor and nonpoor components of change sum to the total population components of change and can be arranged to produce the share of each component due to the poor versus the nonpoor. This is presented in terms of births, B, and share of births, B%pov, but can also be calculated for deaths, in-migrants, and out-migrants.5 It cannot be calculated with NPov or NAff because of their canceling nature. The formulation presented in Eq. (11) allows us to answer the question, “What percentage of births in the overall population is made up of poor births?”
$Bpop=Bpov+Baff,$
(10)
$B%pov=BpovBpop * 100.$
(11)
The linked nature of poverty transitions between the poor and nonpoor populations highlights the difficulties the conventional poverty rate poses for a full accounting of the ways poverty of place can change, and thus the necessity of the approach detailed here. Equation (12) shows that the conventional poverty rate, PR, is a result of the ratio of the poverty population Pov2 to the total population Pop2. As shown in Eq. (8), Pop2 is simply the sum of both Pov2 and Aff2. Thus, when we substitute Eq. (9) into Eq. (12), we end up with Eq. (13). This equation shows the difficulties of accounting for the population processes underlying changes in the conventional poverty rate. Changes in each component of change for the poverty population influence both the numerator and the denominator. Further, changes in the nonpoor population influence the denominator, changing the interpretation of a change in the poverty population captured by the numerator. This changing denominator via linked populations makes traditional demographic decomposition of changes in poverty rates impossible while accounting for all poverty population dynamics. Thus, it is impossible to answer questions such as, “What portion of the change in overall poverty rate is due to the migration of the poor?” while also accounting for the coterminous population processes occurring among the nonpoor segment of the population.
$PR=Pov2Pov1,$
(12)
$PR=Pov1+NIpov+NMpov+NPovPov1+NIpov+NMpov+Aff1+NIaff+NMaff.$
(13)
Although the conventional poverty rate is limited in its ability to fully represent how poverty is changing in a place, by relating the poverty rate at the end of the interval to the share of each population component contributed by the poor during the interval (e.g., B%pov), we can understand the activity of the poor relative to their presence in the population. This approach is presented for births in Eq. (14), where B%pov is divided by the poverty rate at the end of the interval PR. This value can be calculated for all non–net population factors. If this value equals 1, then the poor in a region are contributing to the population factor (e.g., births) at a level representative of their prevalence in the population. If it is greater than 1, they are overrepresented, and if it is less than 1, then they are underrepresented.
$B%pov:PR=B%povPR.$
(14)
The values generated by Eqs. (11) and (14) are valuable because they cannot only tell us about a single region, but are comparable across regions. As currently presented, this is not true for the raw components of change. In order to facilitate this necessary comparison across regions, the overall, poor, and nonpoor balancing equations can be expressed as rates of change. This means that the initial population is subtracted from both sides of the equation and each term is divided by either the person-years lived in the interval or the midyear population.6Equations (15) through (17) present each of the relevant balancing equations in this format, where the individual terms for one region are put in context of its specific total population or subpopulation. This has the benefit of making each term for one region more comparable with another.
$(Pov1−Pov2)PYpop+(Aff1−Aff2)PYpop=NIpovPYpop+NMpovPYpop+NIaffPYpop+NMaffPYpop+NPovPYpop+NAffPYpop,$
(15)
$(Pov1−Pov2)PYpov=NIpovPYpov+NMpovPYpov+NPovPYpov,$
(16)
$(Aff1−Aff2)PYaff=NIaffPYaff+NMaffPYaff+NAffPYaff.$
(17)
Building on Eq. (15), we can produce one final important statistic for the cross-regional comparison of poverty population dynamics. This statistic, termed RNPov and presented in Eq. (18), is a special case of NPov expressed in rate format for the total constant population, PYcpop, and scaled by a constant k.7 As opposed to using the person-years lived or the midyear population as the denominator, RNPov uses the constant population, or the portion of a region's population present at the beginning and end of the time interval. This means the value generated is a summary statistic of the poverty changes due to actual poverty transitions absent the impact of natural increase and net migration among either subpopulation. This value, which more accurately reflects the goals of many poverty policies, allows to us ask, “At what rate did poverty within the population grow, shrink, or stay the same during the time interval due to transitions in and out of poverty?” For example, if RNPov was scaled by a constant of 1,000 and equal to 21, the statistic would tell us that for every 1,000 people in the constant population, 21 more were in poverty at the end of the interval owing to transitions in poverty status.
$RNPov=NPovPYcpop * k.$
(18)
### Summary and Value of the Approach
The formulas and summary statistics presented here comprise the poverty balancing equation framework for documenting the way poverty of place changes over time. All told, I have provided a variety of values that will likely be of interest to researchers and policymakers. These values are summarized in Table 1. The choice of which of these values to estimate and use as an independent or dependent variable will depend on the specific research questions being asked and the policies being tested, and it is not necessary to estimate all values presented to implement this framework. The large number of metrics presented here highlights the inherent complexity, and subsequent shortcomings, of using the conventional poverty rate as a variable of interest. Poverty rates can change or stay the same because of processes of natural increase, migration, or poverty transitions. Thus, an added level of specificity is needed if we are to accurately document the impact of economic shocks or poverty alleviation efforts. By applying this framework, demographers will be able to move beyond the conventional poverty rate and into a more specific understanding of the components of change of the poverty population.
Although all of these summary statistics are valuable for properly characterizing changes in the poverty population in a place, some clear recommendations appear warranted. When using this approach, I recommend demographers use at least one statistic for each component of change. If there is an interest in using just a few indicators, then the indicators that contrast the relative changes in the poverty population with changes in the total population will be the most effective. Thus, there are five indicators I view as the core recommended statistics of this framework: B%pov:PR, D%pov:PR, I%pov:PR, O%pov:PR, and RNPov.
It should be made clear that full implementation of this approach is data-intensiveand currently not possible with many of the publicly available data sets demographers are accustomed to using, which could limit its immediate uptake. Thus, a brief discussion of why this framework is valuable and warrants usage, in light of current methodological difficulties, is warranted. First, the importance of the components of change identified here should not be overlooked simply because of the methodological difficulties imposed by current data sets. Policy evaluation and demographic research presently rely on poverty rates as the dependent variable (whether the Official Poverty Rate, the Supplemental Poverty Rate, or any other) and are likely to draw inaccurate conclusions owing to the complicated influence of the components of change outlined within this framework. As will be highlighted for the case of Florida in the following analysis, it is quite possible to have dramatic movements among the poverty population and still see a stable poverty rate. Thus, the articulation of the framework I have presented represents a call to action for poverty scholars to begin pushing for better data on poverty populations across space, while also encouraging creativity in how poverty scholars generate the statistics they use as their independent and dependent variables.
Second, although not without barriers, at the time of writing, the approach can be fully implemented via Federal Restricted Data Centers, as well as with creative usage of resources such as Survey of Income and Program Participation, which I will demonstrate in the next section. That said, even partially implementing this approach with data sets unable to facilitate a full application goes a long way toward improving our understanding of poverty dynamics. Each component of change is valuable for scholars, and the construction of the entire poverty balancing equation is not necessary. For example, calculating just RNPov requires only the poverty status of a constant, nonmigratory population at two time periods. While ignoring net migration and natural increase, just calculating this value will allow poverty researchers to assess what is often of interest—the rate of people transitioning out of poverty in a place owing to changes in resources. At the very least, this framework illustrates that any study using the conventional poverty rate should acknowledge that the use of such a measure is a significant limitation because we do not know which underlying process is responsible for any change observed, or not observed, at the aggregate level.
Third, although this approach has clear application for future nationwide model-based analyses of poverty dynamics, it also presents a framework for the applied demographer to characterize poverty dynamics occurring within a city, county, or state. By applying this framework to existing government data, which applied demographers often have access to, researchers can present a clear picture to policymakers of what is, or is not, driving changes in hardship within their geographic area. To demonstrate the value of the approach to our understanding of poverty population dynamics, I will apply the poverty balancing equation to three states in the American South for the period of January to December of 2013 using the first wave of the 2014 Survey of Income and Program Participation.
## Empirical Demonstration for Three Southern States
### Data and Methods
The data for this analysis come from the 2014 panel of the SIPP, which is a recurring panel study of income dynamics in the U.S. civilian, noninstitutionalized population. Unlike prior panels, the 2014 panel was designed to be representative at the state level—although it should be noted that the first wave was designed to be state-reliable for only the 20 most populous states, and hence the estimates I provide for North Carolina and Florida should be interpreted as more reliable than those for Arkansas (U.S. Census Bureau 2019). The first wave of the 2014 SIPP asked respondents to provide monthly information on income, residence, and household composition for the prior calendar year (i.e., 2013) (U.S. Census Bureau 2019). I focus on this first wave and estimate changes in the poverty populations of each state in the United States, as wellas Washington, DC, between January and December of 2013.8 The SIPP involves a unique characteristic of the population: a respondent must be alive and in the sampled household at the time of the survey to be included. Because the survey was conducted from February to May of 2014, and all 12 months of 2013 are documented, I am able to generate state-level estimates of in-migrants and out-migrants by comparing where all sampled individuals lived at months 1 and 12 of the reference year. However, I am not able to generate precise estimates of international out-migration because I do not have data on areas outside the United States. If an individual out-migrated internationally in 2013 and returned to the United States by the time of survey administration in 2014, they are included, but otherwise international out-migration is absent. Thus, international migrants are captured in the overall in-migrant estimates but are not fully captured in the out-migrant estimates. More seriously, as a result of this sampling approach there are no reported deaths. This unique characteristic makes it impossible to understand how much of the changes in the poor or nonpoor populations was due to differentials in mortality between the poor and nonpoor. Natural increase cannot be calculated. In its stead, I report the summary statistics for births alone. Given that individuals in poverty generally experience higher rates of mortality (Fleisch Marcus et al. 2017; Moncayo et al. 2019; Pool et al. 2018; Smith and Waitzman 1994), future research should work to implement more robust data on vital statistics.
The issues described above mean that I am unable to separate the error due to generating point estimates from a weighted sample from the number of deaths and international out-migrants in the total population. I account for this by calculating an overall error term for the population between the two reference months. I do so by solving for the death portion of the overall, poor, and nonpoor balancing equations using the point estimates of the other components.9 Importantly, this value should be viewed as a combination of the number of deaths, the number of international out-migrants, and the error between the components of change in time 1 and time 2 due to weighting. I present this value alongside population estimates for the poor and nonpoor subpopulations, labeled as “error” to avoid confusion.
I calculate the components of the poverty balancing equation framework presented in Table 1 at the state level for the reference months of January and December of 2013. To do so, I determine each individual's monthly poverty status by comparing the total income of their household with their relevant poverty threshold as determined by the Official Poverty Measure of the United States. This is an absolute measure that sets a threshold of resources needed to meet material needs across the entire country for a given household size (Iceland 2005)—although it should be noted that the threshold it sets is regularly critiqued for not adequately capturing the needs of families and setting a “low bar” for poverty (Brady 2003; Rodems and Shaefer 2020). I consider an individual to be poor if the ratio of their monthly household income to the poverty threshold was less than 1.0. As indicated above, the Official Poverty Measure of the United States has received significant criticism, and a full discussion of these valid critiques is beyond the scope of this paper (see Iceland (2005) and Jensen and Ely (2017)). Given its status and its dominance in the literature, I rely on this measure. However, it should be noted that the framework presented here can easily be calculated for any dichotomous poverty measure. All that is required is that the method of poverty classification groups individuals as poor and not poor. Thus, fully relative measures such as share of regional median income (Iceland 2013), measures that are calculated using post-tax and post-transfer income (Brady 2003), or quasirelative measures such as the Supplemental Poverty Measure (Warren et al. 2020) could easily be used for this approach.10
I generalize to the state level using the provided monthly person weights from the SIPP. Because of the estimation of state subpopulations, I rely on SIPP documentation to generate 95% confidence intervals around point estimates using the SIPP-provided formulas and universe-specific parameters (U.S. Census Bureau 2017). I calculate confidence intervals for all point estimates except ratios of percentages. Although I was able to estimate all values for each state using the SIPP, I present data on only three states in the American South—Arkansas, Florida, and North Carolina—in this article.11 I use this comparative approach to facilitate an in-depth illustration of the framework. To ensure an illustrative example, I chose these states because of their varying changes in aggregate poverty rates over the study period: Arkansas saw a decrease in the poverty rate, Florida had a generally constant poverty rate, and North Carolina experienced an increase in the poverty rate. To be clear, the goal of this exercise is not to discern the causal reasons for why we see differing poverty dynamics across these three states. Instead, the goal here is to demonstrate the utility of the poverty balancing equation framework for fully describing and accounting for the complex ways poverty changes within places over time.
## Results
Total population estimates, along with the underlying sample sizes and poverty rates, are presented in Table 2. All rates were calculated using the midyear population of the relevant group, from the total population estimated by the SIPP for each state in the sixth month of the reference year (i.e., June of 2013). As can be seen in Table 2,although the sample for the SIPP is notably smaller than that of other sources such as the American Community Survey, the poverty rate estimates for 2013 via the SIPP are very similar to the poverty rates from the 2011–2015 American Community Survey estimates (Manson et al. 2020). The point estimates of poverty rates reflect what was stated earlier, with Arkansas seeing a decrease, Florida seeing a constant level, and North Carolina experiencing a minor increase (Table 2 and Figure 1).
As may be expected, the values of NPov varied among the three states, with poverty transitions playing the largest role in Arkansas. In that state, for every 1,000 poor people, there were 206 fewer in poverty at the end of the study period owing to poverty transitions alone. This was matched with an NAff of 48.06, meaning that for every 1,000 nonpoor people in the population, 48 were not poor at the end of the study period. These figures correspond with a large negative value for net poverty transition (RNPov), where for every 1,000 people in the constant population, 40 fewer were in poverty at the end of the study period. Although we see significant poverty transitions in Arkansas, the other states saw less movement, with the net poverty transition values hovering around zero. This suggests that any change in aggregate poverty rates in Florida and North Carolina over the study period did not occur as a result of poverty transitions among the constant population.
Table 3 and Figure 2 show the birth components of change for the three states. In the left panel of Figure 2 we see the overall birth rate (Bpop), the birth rate of the poor in reference to the whole population (Bpop:pov), and the birth rate of the nonpoor in reference to the whole population (Bpop:aff). It bears repeating that Bpop:pov and Bpop:aff sum to Bpop. In all three states, Bpop:pov was only slightly lower than Bpop:aff. Given that the poor population represents a much smaller share of the population than the nonpoor in all three states, this indicates that the birth rate was much higher among the poor than the nonpoor. In fact, the percentage of total births attributed to the poor was 41.7% in Arkansas, 28.0% in Florida, and 37.9% in North Carolina (see Table 3). This is further contextualized in the right panel of Figure 2, where B%pop:PR is the ratio of the percentage of births that are poor relative to the population prevalence of the poor. In both Arkansas and North Carolina, the poor were overrepresented in births relative to their population prevalence by a factor of greater than 2, while in Florida this overrepresentation was slightly less, at 1.7. These results highlight the fact that if we held net migration and poverty transitions constant, the portion of the population in poverty would have grown in all three states owing to births alone.
It is when we look at migration that we see the most dynamism between the poor and nonpoor populations (Table 4 and Figure 3). Beginning on the right panel of Figure 3, we can see that both in-migration and out-migration varied considerably among the three states. In Arkansas, where we saw the largest change in absolute poverty rate, we see that the poor are overrepresented in in-migration (I%pov:PR), but not out-migration (O%pov:PR). This is in contrast to Florida, where the inverse is true. In that state, we see that the poor are underrepresented in in-migration, but overrepresented in out-migration, which results in the poor population contributing a negative value, or a net out-migration, to the overall net migration. Considering the overrepresented birth rate among the poor and modestly negative level of NPov in Florida in 2013, it is likely that this imbalance in migration is responsible for the generally steady level of aggregate poverty over the study period. We can also see significant dynamism in migration in North Carolina, where the poor are overrepresented in both in-migration and outmigration. Looking at Figure 3, we can see that the overrepresentation in in-migration is greater than that of out-migration, with I%pov:PR being 2.25. This overrepresentation is echoed in the left panel of Figure 3, where we see the rate contribution to net migration among the poor and nonpoor being almost equal in North Carolina despite the poor representing a much smaller share of the population. This greater overrepresentation of in-migration than out-migration among the poor can likely explain the modest increase in the poverty rate seen in North Carolina over the study period.
### Summary
These three examples, while illustrating the benefits of using the poverty balancing equation framework to understand the poverty components of change, also allow us to make some conclusions about how poverty changed, or did not change, within these states over the study period. First, in Arkansas, it is clear that the majority of the decrease in the aggregate poverty rate can be attributed to actual transitions out of poverty among the constant population. We can conclude this because of the large negative rate of RNPov, the overrepresentation of the poor in in-migration but not out-migration, and the overrepresentation of the poor in births. Second, although Florida had a generally stable poverty rate, this does not mean people did not become poor in Florida during the study period. The steady poverty rate in Florida appears to be an artifact of an overrepresentation of the poor in out-migration, and an underrepresentation of the poor in in-migration, which was enough to offset any increase in poverty stemming from an overrepresentation in births. Third, the small growth in the aggregate poverty rate in North Carolina during the study period can be primarily attributed to in-migration of the poor and overrepresentation of births among the poor. It does not appear that poverty transitions among the constant population played a noticeable role in this increase. These three examples highlight the unique and nuanced ways in which poverty of place changes over time, and how we need to look beneath the surface of changing aggregate poverty rates if we are to understand the actual dynamics of poverty.
To take this further, it is necessary to highlight the benefits of this approach for poverty policy. First, these results show that those who are poor are more likely to have children in all three states. This highlights the need to make aid available to growing families while also ensuring reproductive autonomy among women, wherein birth control methods, if desired, are accessible and affordable (Senderowicz 2020). Second, although some of the growth in poverty in North Carolina was clearly driven by in-migration, the poor were more likely than the nonpoor to both move in and out of the state. As moving is both expensive and disruptive to families, this suggests that North Carolina may benefit from a poverty policy that helps those experiencing bouts of hardship stay put where they already live. Third, these results demonstrate that in Arkansas, the year 2013 was marked by a considerable portion of the poor transitioning out of poverty. Although the cause of this is not clear, it shows that these changes were attributable to a very real increase in income relative to family size for Arkansas residents who were previously in poverty. Finally, the results for Florida show that even though the poverty rate does not markedly change, there are still poverty population dynamics occurring that can inform specific ways the state should attempt to reduce poverty. For example, the overrepresentation of the poor among out-migrants suggests that many experiencing spells of poverty are not able to escape poverty while remaining in the state—meaning that Florida may benefit from targeted policies that help families escape bouts of poverty while still remaining where they live.
### Limitations
This analysis has two limitations. First, states are quite large for the application of this framework. Although I have been able to demonstrate significant dynamism in the poverty population, the vast majority of migration in the United States is not between states, but instead within and between counties (Molloy et al. 2011). Future work should use restricted data to apply this approach to smaller geographic units to better understand the migration of the poor versus the nonpoor.
Second, because of data limitations, there are no deaths in this sample, and international out-migrants are only partly captured. Future work should apply this framework to data in which deaths and international moves are fully captured. Mortality and migration among the poor are frequently higher than among the nonpoor (Cohen et al. 2003; Fleisch Marcus et al. 2017; Foulkes and Newbold 2008; Foulkes and Schafft 2010; Moncayo et al. 2019; Pool et al. 2018; Pritchard and Keen 2016; Sims et al. 2007; Smith and Waitzman 1994; Taylor-Robinson et al. 2019; Toprani et al. 2016). Thus, we cannot have a true accounting of poverty population dynamics until population processes are fully captured. This limitation highlights the difficulties posed in using this approach with only survey data, and not also with vital statistic data. Survey results will always be more susceptible to bias than more complete forms of data available through restricted data centers. In line with this, it is crucial that any statistics I have presented here be interpreted in tandem with their corresponding measures of uncertainty.
## Conclusions
In this article I have presented a framework for a full accounting of the ways poverty changes within and between places. The poverty balancing equation framework improves upon prior approaches by increasing the specificity available to those interested in generating either descriptive or causal statistics of changes in poverty of place. In identifying the key poverty components of change of natural increase, net migration, and net poverty transitions among the poor and nonpoor, the main argument I have made is that the conventional poverty rate, however it is determined, is an insufficient variable for understanding poverty dynamics. Accordingly, this paper represents a call for future researchers to carefully decide whether the conventional poverty rate is the appropriate variable of analysis and to tailor research questions to the specific mechanism of poverty population change in question. If a study aims to assess the efficacy of a policy for raising people out of poverty, then RNPov is a more suitable outcome variable. Similarly, if researchers wish to understand how population churn due to migration is, or is not, influencing the persistence of poverty in a region, then metrics such as I%pov:PR or O%pov:PR, which tell us how much the poor are over- or underrepresented in the components of migration, will be more valuable.
This study presents a unique and novel approach to fully understanding how poverty does or does not change within and between places. The framework I present is in many ways aspirational. Current scholars cannot immediately apply the full framework to many popular public data sets because of inherent limitations with the data. To be clear, this does not mean this framework is not valuable or should be ignored; instead, it means that demographers need to utilize the resources that do exist—such as Federal Restricted Data Centers—or be creative with what portions of the framework can be estimated using available public data. It also should be made clear that I am not the first to recognize this discrepancy in the usage of conventional poverty rates, as the work of prior scholars shows otherwise (Chapman and Bernstein 2003; Christiaensen et al. 2019; Foulkes and Schafft 2010; Joo 2013; Wright 1996). However, what is presented here does push us beyond prior work by asking demographers to deeply consider what we mean when we discuss changing poverty within a place. The poverty balancing equation framework provides a common language by which future theory and study design can proceed. With the articulation provided here, we can begin to more completely chart changes in poverty beyond swings in conventional poverty rates. To do so, we should not only apply this framework to existing data, but should also ensure that future data collection efforts are designed with this framework in mind.
The poverty balancing equation framework does not provide a single summary statistic for researchers to employ. That is by design. Poverty of place is a complicated problem involving a series of specific underlying demographic processes. As I have illustrated in the summaries of Arkansas, Florida, and North Carolina, each place has its own unique puzzle of poverty in need of attention. A decrease in the poverty rate of one area does not correspond to the same decrease in another. If the goal of research is an assessment of how poverty is changing across space, then it is imperative that demographers and other social scientists use the most specific outcome variable possible. Further, if applied demographers are interested in understanding the state of poverty within a given region, decomposing poverty into the components presented here is essential for appropriately documenting the problem and directing change. The solutions to poverty of place require us to ask specific questions and assess specific mechanisms. By employing the poverty balancing equation framework outlined here, future scholars can begin this necessary work.
## Acknowledgments
I would like to thank Matthew M. Brooks, Brian Thiede, and Ann R. Tickamyer for their comments and suggestions on this manuscript.
## Notes
1
Natural increase is simply the difference between births and deaths in the population and is presented in Eq. (1), where B is births and D is deaths (Rowland 2003). Natural increase tells us how much the poverty population would have grown or shrunk if there were no migration or poverty transitions in the population:
$NI=(B−D).$
(1)
2
Net migration accounts for population change due to the difference between in-migration and out-migration of a region (Rowland 2003) and is presented in Eq. (2), where I represents in-migrants and O represents out-migrants. Net migration allows us to isolate the impact of migration on population change within a region:
$NM=(I−O).$
(2)
3
Although affluent and nonpoor are not synonymous, I use Aff to refer to the nonpoor in the notation of this framework to ensure that the notation can be quickly interpreted, and thus Aff functions as a valuable trigger in the same way that Pov quickly provokes the idea of poverty.
4
The term net poverty transition is adopted, as opposed to something like net income dynamic, because this process is measured by the ratio of income to the poverty threshold, not changes in personal income. As poverty thresholds adjust for family size, constant residents can enter the poor population by either losing income or increasing the size of their family. For example, if a household of four was above the poverty threshold, but then had a birth that raised their poverty threshold and they did not generate more income, the whole family would now be considered poor. This would be counted at the end of the study period as one poor birth and four increases to the poverty population due to poverty transitions.
5
Although Eq. (10) holds for the net components (e.g., natural increase), Eq. (11) becomes uninterpretable when calculated using net components because of the opposing nature of constituent terms (e.g., births and deaths).
6
Although not shown explicitly in these equations, these rates will conventionally be scaled by a constant, as is common for demographic rates (e.g., per 1,000).
7
I have chosen to refer to this in the formulation of NPov due to the focus of the framework on the poor, but one could easily represent the rate of net poverty transition as its inverse generated from NAff.
8
I focus on just the first wave because of the difficulties posed by survey attrition in each additional wave. In subsequent waves, households dissolved and individuals exited the panel. This introduces significant difficulties for this framework owing to the inability to discern whether an exit was due to death, migration, institutionalization, or nonresponse. I also focus on Type 1 individuals because Type 2 individuals—those who lived in the residence during the reference period but not at the time of the survey—do not have their own record in the data, making their inclusion infeasible.
9
The formula for calculating deaths involves solving for deaths in the standard equation via algebra. Equation (19) demonstrates this for the poverty population:
$Deathspov=Pov1+Birthspov+NMpov+NPov−Pov2.$
(19)
10
An important dimension of poverty of place that is beyond the scope of this paper is the way income needs vary across space (Pacas and Rothwell 2020). Unfortunately, the official poverty measure does not adjust for cost of living in any way beyond family size. While I focus on the official poverty measure of the United States in this analysis owing to the constraints of available data, it should be made clear that the most sophisticated version of this approach would be one that uses the parameters of the poverty balancing equation alongside a poverty measure that adjusts for changing costs of living across space (e.g., the Supplemental Poverty Measure).
11
Code for replication and generating results for all 50 states and Washington, DC, is available at the corresponding Open Science Framework project for this paper at https://doi.org/10.17605/OSF.IO/6XZ9D.
## References
Allard, S. W., & Danziger, S. (
2000
).
Welfare magnets: Myth or reality?
Journal of Politics
,
62
,
350
368
.
Baker, R. S. (
2020
).
Why is the American South poorer?
Social Forces
,
99
,
126
154
.
Bárcena-Martín, E., & Pérez-Moreno, S. (
2012
).
Regional differences in the effect of immigration on poverty rates in Spain
.
International Scholarly and Scientific Research and Innovation
,
6
,
841
851
.
Barrett, C. B., Garg, T., & McBride, L. (
2016
).
Well-being dynamics and poverty traps
.
Annual Review of Resource Economics
,
8
,
303
327
.
2003
).
Rethinking the sociological measurement of poverty
.
Social Forces
,
81
,
715
751
.
2019
).
Theories of the causes of poverty
.
Annual Review of Sociology
,
45
,
155
175
.
Burton, L. M., Lichter, D. T., Baker, R. S., & Eason, J. M. (
2013
).
Inequality, family processes, and health in the “new” rural America
.
American Behavioral Scientist
,
57
,
1128
1151
.
Chapman, J., & Bernstein, J. (
2003
).
Immigration and poverty: How are they linked?
Monthly Labor Review
,
126
(April),
10
15
.
Chetty, R., Hendren, N., & Katz, L. F. (
2016
).
The effects of exposure to better neighborhoods on children: New evidence from the Moving to Opportunity experiment
.
American Economic Review
,
106
,
855
902
.
Chetty, R., Hendren, N., Kline, P., & Saez, E. (
2014
).
Where is the land of opportunity? The geography of intergenerational mobility in the United States
.
Quarterly Journal of Economics
,
129
,
1553
1623
.
Christiaensen, L., De Weerdt, J., & Kanbur, R. (
2019
).
Decomposing the contribution of migration to poverty reduction: Methodology and application to Tanzania
.
Applied Economics Letters
,
26
,
978
982
.
Cohen, D. A., Farley, T. A., & Mason, K. (
2003
).
Why is poverty unhealthy? Social and physical mediators
.
Social Science & Medicine
,
57
,
1631
1641
.
Crowley, M., Lichter, D. T., & Qian, Z. (
2006
).
Beyond gateway cities: Economic restructuring and poverty among Mexican immigrant families and children
.
Family Relations
,
55
,
345
360
.
Cushing, B. (
2005
,
November
).
The role of welfare and space in the migration of the poor
. Paper presented at the 52nd annual North American meetings of the Regional Science Association International,
Las Vegas, NV
.
Desmond, M., & Western, B. (
2018
).
Poverty in America: New directions and debates
.
Annual Review of Sociology
,
44
,
305
318
.
Dreyer, B. P. (
2019
).
Safety net policies, child poverty, and development across the lifespan
.
Annual Review of Developmental Psychology
,
1
,
337
357
.
Fleisch Marcus, A., Illescas, A. H., Hohl, B. C., & Llanos, A. A. M. (
2017
).
Relationships between social isolation, neighborhood poverty, and cancer mortality in a population-based study of US adults
.
PLoS One
,
12
,
e0173370
. https://doi.org/10.1371/journal.pone.0173370
Foulkes, M., & Newbold, K. B. (
2008
).
Poverty catchments: Migration, residential mobility, and population turnover in impoverished rural Illinois communities
.
Rural Sociology
,
73
,
440
462
.
Foulkes, M., & Schafft, K. A. (
2010
).
The impact of migration on poverty concentrations in the United States, 1995–2000
.
Rural Sociology
,
75
,
90
110
.
Frey, W. H. (
1995
).
Immigration impacts on internal migration of the poor: 1990 census evidence for U.S. states
.
International Journal of Population Geography
,
1
,
51
67
.
Frey, W. H., Liaw, K.-L., Xie, Y., & Carlson, M. J. (
1996
).
Interstate migration of the US poverty population: Immigration “pushes” and welfare magnet “pulls
.”
Population and Environment
,
17
,
491
533
.
Hutto, N., Waldfogel, J., Kaushal, N., & Garfinkel, I. (
2011
).
Improving the measurement of poverty
.
Social Service Review
,
85
,
39
74
.
Iceland, J. (
2005
).
Measuring poverty: Theoretical and empirical considerations
.
Measurement: Interdisciplinary Research and Perspectives
,
3
,
199
235
.
Iceland, J.. (
2013
).
Poverty in America: A handbook
(3rd ed.).
Berkeley
:
University of California Press
.
Jensen, L., & Ely, D. (
2017
).
Measures of poverty and implications for portraits of rural hardship
. In Tickamyer, A. R., Sherman, J., & Warlick, J. (Eds.),
Rural poverty in the United States
(pp.
67
83
).
New York, NY
:
Columbia University Press
.
Joo, M. (
2013
).
How much does change in the proportion of children living in immigrant families contribute to change in the poverty rate among children?
Social Service Review
,
87
,
556
585
.
Kazemipur, A., & Halli, S. S. (
2000
).
The colour of poverty: A study of the poverty of ethnic and immigrant groups in Canada
.
International Migration
,
38
,
89
108
.
Kitagawa, E. M. (
1955
).
Components of a difference between two rates
.
Journal of the American Statistical Association
,
50
,
1168
1194
.
Larrimore, J., Mortenson, J., & Splinter, D. (
2020
).
Presence and persistence of poverty in U.S. tax data
(NBER Working Paper 26966).
Cambridge, MA
:
National Bureau of Economic Research
.
Levine, P. B., & Zimmerman, D. J. (
1999
).
An empirical analysis of the welfare magnet debate using the NLSY
.
Journal of Population Economics
,
12
,
391
409
.
Lichter, D. T. (
1997
).
Poverty and inequality among children
.
Annual Review of Sociology
,
23
,
121
145
.
Lichter, D. T., Qian, Z., & Crowley, M. L. (
2005
).
Child poverty among racial minorities and immigrants: Explaining trends and differentials
.
Social Science Quarterly
,
86
,
1037
1059
.
MacTavish, K. A. (
2007
).
The wrong side of the tracks: Social inequality and mobile home park residence
.
Community Development
,
38
,
74
91
.
Manson, S., Schroeder, J., Van Riper, D., Kugler, T., & Ruggles, S. (
2020
).
IPUMS national historical geographic information system: Version 15.0
[Data set].
Minneapolis, MN
:
IPUMS
. http://doi.org/10.18128/D050.V15.0
Molloy, R., Smith, C. L., & Wozniak, A. (
2011
).
Internal migration in the United States
.
Journal of Economic Perspectives
,
25
(
3
),
173
196
.
Moncayo, A. L., Granizo, G., Grijalva, M. J., & Rasella, D. (
2019
).
Strong effect of Ecuador's conditional cash transfer program on childhood mortality from poverty-related diseases: A nationwide analysis
.
BMC Public Health
,
19
,
1132
. https://doi.org/10.1186/s12889-019-7457-y
Musick, K., & Mare, R. D. (
2006
).
Recent trends in the inheritance of poverty and family structure
.
Social Science Research
,
35
,
471
499
.
Pacas, J. D., & Rothwell, D. W. (
2020
).
Why is poverty higher in rural America according to the supplemental poverty measure? An investigation of the geographic adjustment
.
Population Research and Policy Review
,
39
,
941
975
.
Peri, G. (
2011
).
The impact of immigration on native poverty through labor market competition
(NBER Working Paper 17570).
Cambridge, MA
:
National Bureau of Economic Research
.
Pool, L. R., Burgard, S. A., Needham, B. L., Elliott, M. R., Langa, K. M., & Mendes de Leon, C. F. (
2018
).
Association of a negative wealth shock with all-cause mortality in middle-aged and older adults in the United States
.
JAMA
,
319
,
1341
1350
.
Pritchard, C., & Keen, S. (
2016
).
Child mortality and poverty in three world regions (the West, Asia and sub-Saharan Africa) 1988–2010: Evidence of relative intra-regional neglect?
Scandinavian Journal of Public Health
,
44
,
734
741
.
Rank, M. R., & Hirschl, T. A. (
1999
).
The likelihood of poverty across the American adult life span
.
Social Work
,
44
,
201
216
.
Rank, M. R., & Hirschl, T. A. (
2001
).
Rags or riches? Estimating the probabilities of poverty and affluence across the adult American life span
.
Social Science Quarterly
,
82
,
651
669
.
Rank, M. R., & Hirschl, T. A. (
2002
).
Welfare use as a life course event: Toward a new understanding of the U.S. safety net
.
Social Work
,
47
,
237
248
.
Rank, M. R., & Hirschl, T. A. (
2009
).
Estimating the risk of food stamp use and impoverishment during childhood
.
Archives of Pediatrics & Adolescent Medicine
,
163
,
994
999
.
Rank, M. R., & Hirschl, T. A. (
2015
).
The likelihood of experiencing relative poverty over the life course
.
PLoS One
,
10
,
e0133513
. https://doi.org/10.1371/journal.pone.0133513
Raphael, S., & Smolensky, E. (
2009
).
Immigration and poverty in the United States
.
American Economic Review: Papers & Proceedings
,
99
,
41
44
.
Rhubart, D. C., & Engle, E. W. (
2017
).
The environment and health
. In Tickamyer, A. R., Sherman, J., & Warlick, J. (Eds.),
Rural poverty in the United States
(pp.
299
322
).
New York, NY
:
ColumbiaUniversity Press
.
Rodems, R., & Shaefer, H. L. (
2020
).
Many of the kids are not alright: Material hardship among children in the United States
.
Children and Youth Services Review
,
112
,
104767
. https://doi.org/10.1016/j.childyouth.2020.104767
Rowland, D. T. (Ed.). (
2003
).
Demographic methods and concepts
.
Oxford, UK
:
Oxford University Press
.
Sampson, R. J. (
2008
).
Moving to inequality: Neighborhood effects and experiments meet social structure
.
American Journal of Sociology
,
114
,
189
231
.
Sampson, R. J., Morenoff, J. D., & Gannon-Rowley, T. (
2002
).
Assessing “neighborhood effects”: Social processes and new directions in research
.
Annual Review of Sociology
,
28
,
443
478
.
Sandoval, D. A., Rank, M. R., & Hirschl, T. A. (
2009
).
The increasing risk of poverty across the American life course
.
Demography
,
46
,
717
737
.
Sen, A. (
2014
). Development as freedom (1999). In Roberts, J. T., Hite, A. B., & Chorev, N. (Eds.),
The globalization and development reader: Perspectives on development and global change
(2nd ed., pp.
525
547
).
West Sussex, UK
:
Wiley Blackwell
.
Senderowicz, L. (
2020
).
Contraceptive autonomy: Conceptions and measurement of a novel family planning indicator
.
Studies in Family Planning
,
51
,
161
176
.
Sims, M., Sims, T. L., & Bruce, M. A. (
2007
).
Urban poverty and infant mortality rate disparities
.
Journal of the National Medical Association
,
99
,
349
356
.
Smith, H., & Ley, D. (
2008
).
Even in Canada? The multiscalar construction and experience of concentrated immigrant poverty in gateway cities
.
Annals of the Association of American Geographers
,
98
,
686
713
.
Smith, K. R., & Waitzman, N. J. (
1994
).
Double jeopardy: Interaction effects of marital and poverty status on the risk of mortality
.
Demography
,
31
,
487
507
.
Taylor-Robinson, D., Lai, E. T., Wickham, S., Rose, T., Norman, P., Bambra, C., . . . Barr, B. (
2019
).
Assessing the impact of rising child poverty on the unprecedented rise in infant mortality in England, 2000–2017: Time trend analysis
.
BMJ Open
,
9
,
e029424
. http://dx.doi.org/10.1136/bmjopen-2019-029424
Thiede, B. C., & Brooks, M. M. (
2018
).
Child poverty across immigrant generations in the United States, 1993–2016: Evidence using the official and supplemental poverty measures
.
Demographic Research
,
39
,
1065
1080
. https://doi.org/10.4054/DemRes.2018.39.40
Thiede, B. C., Sanders, S. R., & Lichter, D. T. (
2018
).
Born poor? Racial diversity, inequality, and the American pipeline
.
Sociology of Race and Ethnicity
,
4
,
206
228
.
Tickamyer, A. R., & Wornell, E. J. (
2017
).
How to explain poverty?
In Tickamyer, A. R., Sherman, J., & Warlick, J. (Eds.),
Rural poverty in the United States
(pp.
84
114
).
New York, NY
:
Columbia University Press
.
Toprani, A., Li, W., & Hadler, J. L. (
2016
).
Trends in mortality disparities by area-based poverty in New York City, 1990–2010
.
Journal of Urban Health
,
93
,
538
550
.
U.S. Census Bureau
. (
2017
).
Source and accuracy statement for the Survey of Income and Program Participation (SIPP) 2014 panel for wave 1 public use files
(Technical report).
Washington, DC
:
U.S. Census Bureau
.
U.S. Census Bureau
. (
2019
).
Survey of Income and Program Participation: 2014 panel users’ guide
(Technical report).
Washington, DC
:
U.S. Census Bureau
.
Van Hook, J., Brown, S. I., & Kwenda, M. N. (
2004
).
A decomposition of trends in poverty among children of immigrants
.
Demography
,
41
,
649
670
.
Warren, L., Fox, L., & Edwards, A. (
2020
).
The supplemental poverty measure in the Survey of Income and Program Participation
(SEHSD Working Paper No. 2020-20).
Washington, DC
:
U.S. Census Bureau
.
Wright, R. E. (
1996
).
Standardized poverty measurement
.
Journal of Economic Studies
,
23
(
4
),
3
17
.
This is an open access article distributed under the terms of a Creative Commons license (CC BY-NC-ND 4.0). | 2023-03-28T14:31:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 19, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4693252444267273, "perplexity": 2380.7172635877087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948867.32/warc/CC-MAIN-20230328135732-20230328165732-00109.warc.gz"} |
https://undergrad.gov.harvard.edu/browse/people?f%5B0%5D=sm_og_vocabulary%3Ataxonomy_term%3A116965&f%5B1%5D=sm_og_vocabulary%3Ataxonomy_term%3A116963&f%5B2%5D=sm_og_vocabulary%3Ataxonomy_term%3A116960&f%5B3%5D=sm_og_vocabulary%3Ataxonomy_term%3A117179&f%5B4%5D=sm_og_vocabulary%3Ataxonomy_term%3A117195 | # Aaron Watanabe
PhD Student in Government
I have been around the department since I took my first Gov class as an undergraduate in Spring 2011. I've since been a Gov concentrator, written a Gov... | 2023-02-04T12:31:01 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8259708881378174, "perplexity": 6486.6125947559285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00530.warc.gz"} |
https://lammps.sandia.gov/doc/processors.html | processors command
Syntax
processors Px Py Pz keyword args ...
• Px,Py,Pz = # of processors in each dimension of 3d grid overlaying the simulation domain
• zero or more keyword/arg pairs may be appended
• keyword = grid or map or part or file
grid arg = gstyle params ...
gstyle = onelevel or twolevel or numa or custom
onelevel params = none
twolevel params = Nc Cx Cy Cz
Nc = number of cores per node
Cx,Cy,Cz = # of cores in each dimension of 3d sub-grid assigned to each node
numa params = none
custom params = infile
infile = file containing grid layout
map arg = cart or cart/reorder or xyz or xzy or yxz or yzx or zxy or zyx
cart = use MPI_Cart() methods to map processors to 3d grid with reorder = 0
cart/reorder = use MPI_Cart() methods to map processors to 3d grid with reorder = 1
xyz,xzy,yxz,yzx,zxy,zyx = map processors to 3d grid in IJK ordering
numa arg = none
part args = Psend Precv cstyle
Psend = partition # (1 to Np) which will send its processor layout
Precv = partition # (1 to Np) which will recv the processor layout
cstyle = multiple
multiple = Psend grid will be multiple of Precv grid in each dimension
file arg = outfile
outfile = name of file to write 3d grid of processors to
Examples
processors * * 5
processors 2 4 4
processors * * 8 map xyz
processors * * * grid numa
processors * * * grid twolevel 4 * * 1
processors 4 8 16 grid custom myfile
processors * * * part 1 2 multiple
Description
Specify how processors are mapped as a regular 3d grid to the global simulation box. The mapping involves 2 steps. First if there are P processors it means choosing a factorization P = Px by Py by Pz so that there are Px processors in the x dimension, and similarly for the y and z dimensions. Second, the P processors are mapped to the regular 3d grid. The arguments to this command control each of these 2 steps.
The Px, Py, Pz parameters affect the factorization. Any of the 3 parameters can be specified with an asterisk “*”, which means LAMMPS will choose the number of processors in that dimension of the grid. It will do this based on the size and shape of the global simulation box so as to minimize the surface-to-volume ratio of each processor’s sub-domain.
Choosing explicit values for Px or Py or Pz can be used to override the default manner in which LAMMPS will create the regular 3d grid of processors, if it is known to be sub-optimal for a particular problem. E.g. a problem where the extent of atoms will change dramatically in a particular dimension over the course of the simulation.
The product of Px, Py, Pz must equal P, the total # of processors LAMMPS is running on. For a 2d simulation, Pz must equal 1.
Note that if you run on a prime number of processors P, then a grid such as 1 x P x 1 will be required, which may incur extra communication costs due to the high surface area of each processor’s sub-domain.
Also note that if multiple partitions are being used then P is the number of processors in this partition; see the -partition command-line switch doc page for details. Also note that you can prefix the processors command with the partition command to easily specify different Px,Py,Pz values for different partitions.
You can use the partition command to specify different processor grids for different partitions, e.g.
partition yes 1 processors 4 4 4
partition yes 2 processors 2 3 2
Note
This command only affects the initial regular 3d grid created when the simulation box is first specified via a create_box or read_data or read_restart command. Or if the simulation box is re-created via the replicate command. The same regular grid is initially created, regardless of which comm_style command is in effect.
If load-balancing is never invoked via the balance or fix balance commands, then the initial regular grid will persist for all simulations. If balancing is performed, some of the methods invoked by those commands retain the logical topology of the initial 3d grid, and the mapping of processors to the grid specified by the processors command. However the grid spacings in different dimensions may change, so that processors own sub-domains of different sizes. If the comm_style tiled command is used, methods invoked by the balancing commands may discard the 3d grid of processors and tile the simulation domain with sub-domains of different sizes and shapes which no longer have a logical 3d connectivity. If that occurs, all the information specified by the processors command is ignored.
The grid keyword affects the factorization of P into Px,Py,Pz and it can also affect how the P processor IDs are mapped to the 3d grid of processors.
The onelevel style creates a 3d grid that is compatible with the Px,Py,Pz settings, and which minimizes the surface-to-volume ratio of each processor’s sub-domain, as described above. The mapping of processors to the grid is determined by the map keyword setting.
The twolevel style can be used on machines with multicore nodes to minimize off-node communication. It insures that contiguous sub-sections of the 3d grid are assigned to all the cores of a node. For example if Nc is 4, then 2x2x1 or 2x1x2 or 1x2x2 sub-sections of the 3d grid will correspond to the cores of each node. This affects both the factorization and mapping steps.
The Cx, Cy, Cz settings are similar to the Px, Py, Pz settings, only their product should equal Nc. Any of the 3 parameters can be specified with an asterisk “*”, which means LAMMPS will choose the number of cores in that dimension of the node’s sub-grid. As with Px,Py,Pz, it will do this based on the size and shape of the global simulation box so as to minimize the surface-to-volume ratio of each processor’s sub-domain.
Note
For the twolevel style to work correctly, it assumes the MPI ranks of processors LAMMPS is running on are ordered by core and then by node. E.g. if you are running on 2 quad-core nodes, for a total of 8 processors, then it assumes processors 0,1,2,3 are on node 1, and processors 4,5,6,7 are on node 2. This is the default rank ordering for most MPI implementations, but some MPIs provide options for this ordering, e.g. via environment variable settings.
The numa style operates similar to the twolevel keyword except that it auto-detects which cores are running on which nodes. Currently, it does this in only 2 levels, but it may be extended in the future to account for socket topology and other non-uniform memory access (NUMA) costs. It also uses a different algorithm than the twolevel keyword for doing the two-level factorization of the simulation box into a 3d processor grid to minimize off-node communication, and it does its own MPI-based mapping of nodes and cores to the regular 3d grid. Thus it may produce a different layout of the processors than the twolevel options.
The numa style will give an error if the number of MPI processes is not divisible by the number of cores used per node, or any of the Px or Py of Pz values is greater than 1.
Note
Unlike the twolevel style, the numa style does not require any particular ordering of MPI ranks i norder to work correctly. This is because it auto-detects which processes are running on which nodes.
The custom style uses the file infile to define both the 3d factorization and the mapping of processors to the grid.
The file should have the following format. Any number of initial blank or comment lines (starting with a “#” character) can be present. The first non-blank, non-comment line should have 3 values:
Px Py Py
These must be compatible with the total number of processors and the Px, Py, Pz settings of the processors command.
This line should be immediately followed by P = Px*Py*Pz lines of the form:
ID I J K
where ID is a processor ID (from 0 to P-1) and I,J,K are the processors location in the 3d grid. I must be a number from 1 to Px (inclusive) and similarly for J and K. The P lines can be listed in any order, but no processor ID should appear more than once.
The map keyword affects how the P processor IDs (from 0 to P-1) are mapped to the 3d grid of processors. It is only used by the onelevel and twolevel grid settings.
The cart style uses the family of MPI Cartesian functions to perform the mapping, namely MPI_Cart_create(), MPI_Cart_get(), MPI_Cart_shift(), and MPI_Cart_rank(). It invokes the MPI_Cart_create() function with its reorder flag = 0, so that MPI is not free to reorder the processors.
The cart/reorder style does the same thing as the cart style except it sets the reorder flag to 1, so that MPI can reorder processors if it desires.
The xyz, xzy, yxz, yzx, zxy, and zyx styles are all similar. If the style is IJK, then it maps the P processors to the grid so that the processor ID in the I direction varies fastest, the processor ID in the J direction varies next fastest, and the processor ID in the K direction varies slowest. For example, if you select style xyz and you have a 2x2x2 grid of 8 processors, the assignments of the 8 octants of the simulation domain will be:
proc 0 = lo x, lo y, lo z octant
proc 1 = hi x, lo y, lo z octant
proc 2 = lo x, hi y, lo z octant
proc 3 = hi x, hi y, lo z octant
proc 4 = lo x, lo y, hi z octant
proc 5 = hi x, lo y, hi z octant
proc 6 = lo x, hi y, hi z octant
proc 7 = hi x, hi y, hi z octant
Note that, in principle, an MPI implementation on a particular machine should be aware of both the machine’s network topology and the specific subset of processors and nodes that were assigned to your simulation. Thus its MPI_Cart calls can optimize the assignment of MPI processes to the 3d grid to minimize communication costs. In practice, however, few if any MPI implementations actually do this. So it is likely that the cart and cart/reorder styles simply give the same result as one of the IJK styles.
Also note, that for the twolevel grid style, the map setting is used to first map the nodes to the 3d grid, then again to the cores within each node. For the latter step, the cart and cart/reorder styles are not supported, so an xyz style is used in their place.
The part keyword affects the factorization of P into Px,Py,Pz.
It can be useful when running in multi-partition mode, e.g. with the run_style verlet/split command. It specifies a dependency between a sending partition Psend and a receiving partition Precv which is enforced when each is setting up their own mapping of their processors to the simulation box. Each of Psend and Precv must be integers from 1 to Np, where Np is the number of partitions you have defined via the -partition command-line switch.
A “dependency” means that the sending partition will create its regular 3d grid as Px by Py by Pz and after it has done this, it will send the Px,Py,Pz values to the receiving partition. The receiving partition will wait to receive these values before creating its own regular 3d grid and will use the sender’s Px,Py,Pz values as a constraint. The nature of the constraint is determined by the cstyle argument.
For a cstyle of multiple, each dimension of the sender’s processor grid is required to be an integer multiple of the corresponding dimension in the receiver’s processor grid. This is a requirement of the run_style verlet/split command.
For example, assume the sending partition creates a 4x6x10 grid = 240 processor grid. If the receiving partition is running on 80 processors, it could create a 4x2x10 grid, but it will not create a 2x4x10 grid, since in the y-dimension, 6 is not an integer multiple of 4.
Note
If you use the partition command to invoke different “processors” commands on different partitions, and you also use the part keyword, then you must insure that both the sending and receiving partitions invoke the “processors” command that connects the 2 partitions via the part keyword. LAMMPS cannot easily check for this, but your simulation will likely hang in its setup phase if this error has been made.
The file keyword writes the mapping of the factorization of P processors and their mapping to the 3d grid to the specified file outfile. This is useful to check that you assigned physical processors in the manner you desired, which can be tricky to figure out, especially when running on multiple partitions or on, a multicore machine or when the processor ranks were reordered by use of the -reorder command-line switch or due to use of MPI-specific launch options such as a config file.
If you have multiple partitions you should insure that each one writes to a different file, e.g. using a world-style variable for the filename. The file has a self-explanatory header, followed by one-line per processor in this format:
world-ID universe-ID original-ID: I J K: name
The IDs are the processor’s rank in this simulation (the world), the universe (of multiple simulations), and the original MPI communicator used to instantiate LAMMPS, respectively. The world and universe IDs will only be different if you are running on more than one partition; see the -partition command-line switch. The universe and original IDs will only be different if you used the -reorder command-line switch to reorder the processors differently than their rank in the original communicator LAMMPS was instantiated with.
I,J,K are the indices of the processor in the regular 3d grid, each from 1 to Nd, where Nd is the number of processors in that dimension of the grid.
The name is what is returned by a call to MPI_Get_processor_name() and should represent an identifier relevant to the physical processors in your machine. Note that depending on the MPI implementation, multiple cores can have the same name.
Restrictions
This command cannot be used after the simulation box is defined by a read_data or create_box command. It can be used before a restart file is read to change the 3d processor grid from what is specified in the restart file.
The grid numa keyword only currently works with the map cart option.
The part keyword (for the receiving partition) only works with the grid onelevel or grid twolevel options.
Default
The option defaults are Px Py Pz = * * *, grid = onelevel, and map = cart. | 2018-11-17T18:09:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4904913902282715, "perplexity": 2125.4031749902115}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743717.31/warc/CC-MAIN-20181117164722-20181117190722-00308.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Amarkushevich.dimitri-g | # zbMATH — the first resource for mathematics
## Markushevich, Dimitri Genrikhovich
Compute Distance To:
Author ID: markushevich.dimitri-g Published as: Markushevich, D.; Markushevich, D. G.; Markushevich, Dimitri; Markushevich, Dimitri G.; Markushevich, Dmitri; Markushevich, Dmitri G.; Markushevish, Dimitri External Links: MGP · Math-Net.Ru · Wikidata
Documents Indexed: 52 Publications since 1981, including 1 Book
all top 5
#### Co-Authors
18 single-authored 10 Tikhomirov, Alexander Sergeevich 5 Bruzzo, Ugo 4 Iliev, Atanas Iliev 3 Olshanetsky, Mikhail A. 3 Perelomov, Askold M. 2 Jardim, Marcos 2 Kogan, Yan I. 2 Kuznetsov, Aleksandr Gennad’evich 2 Morozov, Alexei Yurievich 2 Prokhorov, Yuriĭ Gennad’evich 2 Rosly, A. A. 1 Bandman, Tatiana M. 1 Bertin, José 1 Boissière, Samuel 1 Cattaneo, Andrea 1 Fino, Anna 1 Frè, Pietro Giuseppe 1 Grassi, Pietro Antonio 1 Kaplunov, Julius D. 1 Kaplunov, Yuliĭ Davidovich 1 Konyagin, Sergeĭ Vladimirovich 1 Leibman, Alexander 1 Leprévost, Franck 1 Manivel, Laurent 1 Matveev, Vladimir B. 1 Ramm, Alexander G. 1 Roulleau, Xavier 1 Sarti, Alessandra 1 Trautmann, Günther 1 Treibich, Armando
all top 5
#### Serials
3 Mathematische Annalen 3 Izvestiya: Mathematics 2 International Journal of Modern Physics A 2 Moscow University Mathematics Bulletin 2 Journal of Geometry and Physics 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Mathematics of the USSR, Sbornik 2 Journal of Mathematical Sciences (New York) 2 Journal of Mathematical Sciences. University of Tokyo 2 Documenta Mathematica 2 Communications in Contemporary Mathematics 2 Central European Journal of Mathematics 1 Communications in Mathematical Physics 1 Journal of Mathematical Analysis and Applications 1 Letters in Mathematical Physics 1 Wave Motion 1 American Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Geometriae Dedicata 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematics of the USSR. Izvestiya 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Siberian Mathematical Journal 1 International Journal of Mathematics 1 Differential Geometry and its Applications 1 IMRN. International Mathematics Research Notices 1 Journal of Physics A: Mathematical and General 1 Soviet Physics. Doklady 1 Journal of Algebraic Geometry 1 Matemática Contemporânea 1 The Asian Journal of Mathematics 1 Advances in Geometry 1 Moscow Mathematical Journal 1 European Journal of Mathematics
all top 5
#### Fields
41 Algebraic geometry (14-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Differential geometry (53-XX) 5 Mechanics of particles and systems (70-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Quantum theory (81-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX)
#### Citations contained in zbMATH
42 Publications have been cited 241 times in 182 Documents Cited by Year
The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold. Zbl 0987.14028
Markushevich, D.; Tikhomirov, A. S.
2001
Symplectic structures on moduli spaces of sheaves via the Atiyah class. Zbl 1181.14049
Kuznetsov, A.; Markushevich, D.
2009
The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree $$14$$. Zbl 0938.14021
Iliev, A.; Markushevich, D.
2000
Rational Lagrangian fibrations on punctual Hilbert schemes of $$K3$$ surfaces. Zbl 1102.14031
Markushevich, Dimitri
2006
Description of a class of superstring compactifications related to semi- simple Lie algebras. Zbl 0628.53065
Markushevich, D. G.; Olshanetskij, M. A.; Perelomov, A. M.
1987
Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7. Zbl 1074.14039
Iliev, Atanas; Markushevich, Dimitri
2004
Minimal discrepancy for a terminal cDV singularity is 1. Zbl 0871.14003
Markushevich, Dimitri
1996
Quartic 3-fold: Pfaffians, vector bundles, and half-canonical curves. Zbl 1077.14551
Iliev, A.; Markushevich, D.
2000
Exceptional quotient singularities. Zbl 0958.14003
Markushevich, D.; Prokhorov, Yu. G.
1999
Resolution of $$\mathbb{C}^3/H_{168}$$. Zbl 0899.14016
Markushevich, Dimitri
1997
Plane vibrations and radiation of an elastic layer lying on a liquid half-space. Zbl 0776.73050
Kaplunov, J. D.; Markushevich, D. G.
1993
Moduli of framed sheaves on projective surfaces. Zbl 1222.14022
Bruzzo, Ugo; Markushevish, Dimitri
2011
Two infinite series of moduli spaces of rank 2 sheaves on $${\mathbb {P}}^3$$. Zbl 06783947
Jardim, Marcos; Markushevich, Dimitri; Tikhomirov, Alexander S.
2017
New symplectic $$V$$-manifolds of dimension four via the relative compactified Prymian. Zbl 1138.14032
Markushevich, D.; Tikhomirov, A. S.
2007
Parametrization of sing $$\Theta$$ for a Fano 3-fold of genus 7 by moduli of vector. Zbl 1136.14031
Iliev, Atanas; Markushevich, Dimitri
2007
Lagrangian families of Jacobians of genus 2 curves. Zbl 0903.14008
Markushevich, D.
1996
New divisors in the boundary of the instanton moduli space. Zbl 1439.14047
Jardim, Marcos; Markushevich, Dimitri; Tikhomirov, Alexander S.
2018
Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces. Zbl 1292.14031
Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander
2013
Moduli of symplectic instanton vector bundles of higher rank on projective space $$\mathbb P^3$$. Zbl 1282.14020
Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander S.
2012
Abel-Jacobi maps for hypersurfaces and noncommutative Calabi-Yau’s. Zbl 1201.14031
Kuznetsov, Alexander; Manivel, Laurent; Markushevich, Dmitri
2010
Kowalevski top and genus-2 curves. Zbl 0984.11030
Markushevich, Dimitri
2001
Completely integrable projective symplectic 4-dimensional varieties. Zbl 0839.58027
Markushevich, Dimitri G.
1995
On the number of rational maps between varieties of general type. Zbl 0824.14009
Bandman, T.; Markushevich, D.
1994
The $$D_ n$$ generalized pure braid group. Zbl 0794.20047
Markushevich, Dmitri G.
1991
Symplectic instanton bundles on $$\mathbb P^3$$ and ’t Hooft instantons. Zbl 1408.14040
Bruzzo, Ugo; Markushevich, Dimitri G.; Tikhomirov, Alexander S.
2016
Bubble tree compactification of moduli spaces of vector bundles on surfaces. Zbl 1303.14049
Markushevich, Dimitri; Tikhomirov, Alexander S.; Trautmann, Günther
2012
Symplectic structure on a moduli space of sheaves on a cubic fourfold. Zbl 1075.14040
Markushevich, D. G.; Tikhomirov, A. S.
2003
The monodromy of the Brieskorn bundle. Zbl 0840.20032
Leibman, A.; Markushevich, D.
1994
Non-abelian singularity quotients of dimension 3 and varieties of Calabi-Yau. Zbl 0801.32016
Bertin, J.; Markushevich, D.
1994
Integrable symplectic structures on compact complex manifolds. Zbl 0637.58004
Markushevich, D. G.
1988
Canonical singularities of three-dimensional hypersurfaces. Zbl 0595.14026
Markushevich, D. G.
1986
A parametrization of the theta divisor of the quartic double solid. Zbl 1048.14028
Markushevich, D. G.; Tikhomirov, A. S.
2003
A tower of genus two curves related to the Kowalewski top. Zbl 0961.11021
Leprévost, Franck; Markushevich, Dimitri
1999
Numerical invariants of families of lines on some Fano varieties. Zbl 0513.14021
Markushevich, D. G.
1983
Numerical invariants of families of straight lines of Fano manifolds. Zbl 0492.14026
Markushevich, D. G.
1981
Crepant resolutions of $$\mathbb{C}^3 / \mathbb{Z}_4$$ and the generalized Kronheimer construction (in view of the gauge/gravity correspondence). Zbl 1434.83157
Bruzzo, Ugo; Fino, Anna; Fré, Pietro; Grassi, Pietro Antonio; Markushevich, Dimitri
2019
An integrable system of $$K3$$-Fano flags. Zbl 1144.14039
Markushevich, D.
2008
Some algebro-geometric integrable systems versus classical ones. Zbl 1059.14046
Markushevich, Dimitri
2002
Klein’s group defines an exceptional singularity of dimension 3. Zbl 0947.14002
Markushevich, D. G.; Prokhorov, Yu. G.
1999
A criterion for property $$C$$. Zbl 0808.47006
Markushevich, D.; Ramm, A. G.
1993
A few examples of elliptic threefolds with trivial canonical bundle. Zbl 0779.14011
Markushevich, Dimitri
1993
Study of an elastic layer in a liquid half-space (two-dimensional problem). Zbl 0726.76088
Kaplunov, Yu. D.; Markushevich, D. G.
1990
Crepant resolutions of $$\mathbb{C}^3 / \mathbb{Z}_4$$ and the generalized Kronheimer construction (in view of the gauge/gravity correspondence). Zbl 1434.83157
Bruzzo, Ugo; Fino, Anna; Fré, Pietro; Grassi, Pietro Antonio; Markushevich, Dimitri
2019
New divisors in the boundary of the instanton moduli space. Zbl 1439.14047
Jardim, Marcos; Markushevich, Dimitri; Tikhomirov, Alexander S.
2018
Two infinite series of moduli spaces of rank 2 sheaves on $${\mathbb {P}}^3$$. Zbl 06783947
Jardim, Marcos; Markushevich, Dimitri; Tikhomirov, Alexander S.
2017
Symplectic instanton bundles on $$\mathbb P^3$$ and ’t Hooft instantons. Zbl 1408.14040
Bruzzo, Ugo; Markushevich, Dimitri G.; Tikhomirov, Alexander S.
2016
Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces. Zbl 1292.14031
Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander
2013
Moduli of symplectic instanton vector bundles of higher rank on projective space $$\mathbb P^3$$. Zbl 1282.14020
Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander S.
2012
Bubble tree compactification of moduli spaces of vector bundles on surfaces. Zbl 1303.14049
Markushevich, Dimitri; Tikhomirov, Alexander S.; Trautmann, Günther
2012
Moduli of framed sheaves on projective surfaces. Zbl 1222.14022
Bruzzo, Ugo; Markushevish, Dimitri
2011
Abel-Jacobi maps for hypersurfaces and noncommutative Calabi-Yau’s. Zbl 1201.14031
Kuznetsov, Alexander; Manivel, Laurent; Markushevich, Dmitri
2010
Symplectic structures on moduli spaces of sheaves via the Atiyah class. Zbl 1181.14049
Kuznetsov, A.; Markushevich, D.
2009
An integrable system of $$K3$$-Fano flags. Zbl 1144.14039
Markushevich, D.
2008
New symplectic $$V$$-manifolds of dimension four via the relative compactified Prymian. Zbl 1138.14032
Markushevich, D.; Tikhomirov, A. S.
2007
Parametrization of sing $$\Theta$$ for a Fano 3-fold of genus 7 by moduli of vector. Zbl 1136.14031
Iliev, Atanas; Markushevich, Dimitri
2007
Rational Lagrangian fibrations on punctual Hilbert schemes of $$K3$$ surfaces. Zbl 1102.14031
Markushevich, Dimitri
2006
Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7. Zbl 1074.14039
Iliev, Atanas; Markushevich, Dimitri
2004
Symplectic structure on a moduli space of sheaves on a cubic fourfold. Zbl 1075.14040
Markushevich, D. G.; Tikhomirov, A. S.
2003
A parametrization of the theta divisor of the quartic double solid. Zbl 1048.14028
Markushevich, D. G.; Tikhomirov, A. S.
2003
Some algebro-geometric integrable systems versus classical ones. Zbl 1059.14046
Markushevich, Dimitri
2002
The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold. Zbl 0987.14028
Markushevich, D.; Tikhomirov, A. S.
2001
Kowalevski top and genus-2 curves. Zbl 0984.11030
Markushevich, Dimitri
2001
The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree $$14$$. Zbl 0938.14021
Iliev, A.; Markushevich, D.
2000
Quartic 3-fold: Pfaffians, vector bundles, and half-canonical curves. Zbl 1077.14551
Iliev, A.; Markushevich, D.
2000
Exceptional quotient singularities. Zbl 0958.14003
Markushevich, D.; Prokhorov, Yu. G.
1999
A tower of genus two curves related to the Kowalewski top. Zbl 0961.11021
Leprévost, Franck; Markushevich, Dimitri
1999
Klein’s group defines an exceptional singularity of dimension 3. Zbl 0947.14002
Markushevich, D. G.; Prokhorov, Yu. G.
1999
Resolution of $$\mathbb{C}^3/H_{168}$$. Zbl 0899.14016
Markushevich, Dimitri
1997
Minimal discrepancy for a terminal cDV singularity is 1. Zbl 0871.14003
Markushevich, Dimitri
1996
Lagrangian families of Jacobians of genus 2 curves. Zbl 0903.14008
Markushevich, D.
1996
Completely integrable projective symplectic 4-dimensional varieties. Zbl 0839.58027
Markushevich, Dimitri G.
1995
On the number of rational maps between varieties of general type. Zbl 0824.14009
Bandman, T.; Markushevich, D.
1994
The monodromy of the Brieskorn bundle. Zbl 0840.20032
Leibman, A.; Markushevich, D.
1994
Non-abelian singularity quotients of dimension 3 and varieties of Calabi-Yau. Zbl 0801.32016
Bertin, J.; Markushevich, D.
1994
Plane vibrations and radiation of an elastic layer lying on a liquid half-space. Zbl 0776.73050
Kaplunov, J. D.; Markushevich, D. G.
1993
A criterion for property $$C$$. Zbl 0808.47006
Markushevich, D.; Ramm, A. G.
1993
A few examples of elliptic threefolds with trivial canonical bundle. Zbl 0779.14011
Markushevich, Dimitri
1993
The $$D_ n$$ generalized pure braid group. Zbl 0794.20047
Markushevich, Dmitri G.
1991
Study of an elastic layer in a liquid half-space (two-dimensional problem). Zbl 0726.76088
Kaplunov, Yu. D.; Markushevich, D. G.
1990
Integrable symplectic structures on compact complex manifolds. Zbl 0637.58004
Markushevich, D. G.
1988
Description of a class of superstring compactifications related to semi- simple Lie algebras. Zbl 0628.53065
Markushevich, D. G.; Olshanetskij, M. A.; Perelomov, A. M.
1987
Canonical singularities of three-dimensional hypersurfaces. Zbl 0595.14026
Markushevich, D. G.
1986
Numerical invariants of families of lines on some Fano varieties. Zbl 0513.14021
Markushevich, D. G.
1983
Numerical invariants of families of straight lines of Fano manifolds. Zbl 0492.14026
Markushevich, D. G.
1981
all top 5
#### Cited by 207 Authors
10 Markushevich, Dimitri Genrikhovich 8 Faenzi, Daniele 8 Tikhomirov, Alexander Sergeevich 7 Voisin, Claire 6 Bruzzo, Ugo 6 Cheltsov, Ivan Anatol’evich 6 Sawon, Justin 6 Shramov, Konstantin Aleksandrovich 5 Iliev, Atanas Iliev 5 Jardim, Marcos 5 Kuznetsov, Aleksandr Gennad’evich 5 Macrì, Emanuele 5 Prokhorov, Yuriĭ Gennad’evich 5 Rogerson, Graham A. 4 Kaplunov, Julius D. 4 Manivel, Laurent 3 Brambilla, Maria Chiara 3 Hassett, Brendan 3 Marin, Ivan 3 Menet, Grégoire 3 Sala, Francesco 3 Stellari, Paolo 3 Tikhomirov, Sergey A. 2 Bayer, Arend 2 Braun, Lukas 2 Debarre, Olivier 2 Donten-Bury, Maria 2 Fino, Anna 2 Frè, Pietro Giuseppe 2 Hayakawa, Takayuki 2 Ishii, Shihoko 2 Ito, Yukari 2 Kawakita, Masayuki 2 Klemm, Albrecht 2 Kollár, János 2 Lavrov, Aleksei N. 2 Lehn, Manfred 2 Lutianov, Michael 2 Marchesi, Simone 2 Mboro, René 2 Nol’de, E. V. 2 Ouchi, Genki 2 Park, Jihun 2 Perrin, Nicolas 2 Ranestad, Kristian 2 Roan, Shih-shyr 2 Romm, Ya. E. 2 Saccà, Giulia 2 Tschinkel, Yuri 2 Tsyganov, Andreĭ Vladimirovich 2 Yau, Shing-Tung 2 Yoshioka, Kōta 1 Addington, Nicolas M. 1 Ahmadinezhad, Hamid 1 Amerik, Ekaterina Yu. 1 Andrade, Aline Vilela 1 Andreatta, Marco 1 Andrianov, Igor V. 1 Arzhantsev, Ivan Vladimirovich 1 Aspinwall, Paul S. 1 Auel, Asher Natan 1 Bandman, Tatiana M. 1 Bartocci, Claudio 1 Beauville, Arnaud 1 Bernardara, Marcello 1 Bertin, José 1 Bianchi, Massimo 1 Biswas, Indranil 1 Biswas, Jishnu 1 Bottacin, Francesco 1 Bufalini, Davide 1 Bülles, Tim-Henrik 1 Caporaso, Lucia 1 Casnati, Gianfranco 1 Chiantini, Luca 1 Choi, Kang-Sin 1 Chowdhury, Atoshi 1 Chung, Kiryong 1 Ciliberto, Ciro 1 Cohen, Daniel C. 1 Craster, Richard V. 1 Cutillas Ripoll, Pascual 1 Dais, Dimitrios I. 1 Dethloff, Gerd-Eberhard 1 Diaconescu, Duiliu-Emanuel 1 Dragović, Vladimir 1 Du, Rong 1 Enolskiĭ, Viktor Zelikovich 1 Erler, Jens 1 Fania, Maria Lucia 1 Fedorov, Yuri N. 1 Flamini, Flaminio 1 Fu, Baohua 1 Gao, Yun 1 Gargate, Michael 1 Gerhardus, Andreas 1 Golubeva, Valentina Alekseevna 1 Grab, Maksymilian 1 Grassi, Pietro Antonio 1 Grigor’ev, Yuriĭ Aleksandrovich ...and 107 more Authors
all top 5
#### Cited in 72 Serials
11 Journal of Geometry and Physics 8 International Journal of Mathematics 7 Journal of Pure and Applied Algebra 7 Journal für die Reine und Angewandte Mathematik 7 Mathematische Zeitschrift 6 Communications in Mathematical Physics 6 Advances in Mathematics 6 Annales de l’Institut Fourier 6 Mathematische Annalen 6 Central European Journal of Mathematics 5 Compositio Mathematica 5 Manuscripta Mathematica 5 Journal of Algebraic Geometry 4 Geometriae Dedicata 4 Journal of the American Mathematical Society 4 European Journal of Mathematics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Inventiones Mathematicae 3 Proceedings of the Japan Academy. Series A 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Revista Matemática Complutense 2 Mathematical Notes 2 Journal of Algebra 2 Michigan Mathematical Journal 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Siberian Mathematical Journal 2 Transactions of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Cybernetics and Systems Analysis 2 Experimental Mathematics 2 Journal of Mathematical Sciences (New York) 2 Communications in Contemporary Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Japanese Journal of Mathematics. 3rd Series 1 International Journal of Modern Physics A 1 Acta Mechanica 1 Communications in Algebra 1 International Journal of Engineering Science 1 Israel Journal of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of the Mechanics and Physics of Solids 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Duke Mathematical Journal 1 Publications Mathématiques 1 Mathematische Nachrichten 1 Mechanics Research Communications 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Rendiconti del Seminario Matematico della Università di Padova 1 Tokyo Journal of Mathematics 1 Mathematical and Computer Modelling 1 Indagationes Mathematicae. New Series 1 Selecta Mathematica. New Series 1 Sbornik: Mathematics 1 Izvestiya: Mathematics 1 Documenta Mathematica 1 Mathematics and Mechanics of Solids 1 Taiwanese Journal of Mathematics 1 Geometry & Topology 1 Journal of Group Theory 1 Regular and Chaotic Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Dynamical and Control Systems 1 Journal of High Energy Physics 1 Nonlinear Analysis. Real World Applications 1 Proceedings of Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of the Institute of Mathematics of Jussieu 1 Proceedings of the Steklov Institute of Mathematics 1 Analysis and Mathematical Physics
all top 5
#### Cited in 32 Fields
146 Algebraic geometry (14-XX) 24 Several complex variables and analytic spaces (32-XX) 19 Differential geometry (53-XX) 14 Quantum theory (81-XX) 12 Category theory; homological algebra (18-XX) 12 Group theory and generalizations (20-XX) 9 Mechanics of deformable solids (74-XX) 7 Dynamical systems and ergodic theory (37-XX) 5 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 4 Nonassociative rings and algebras (17-XX) 4 Relativity and gravitational theory (83-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Partial differential equations (35-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Numerical analysis (65-XX) 2 Fluid mechanics (76-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 $$K$$-theory (19-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-01-20T01:45:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4917146861553192, "perplexity": 7140.688562835124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00351.warc.gz"} |
https://dlmf.nist.gov/25.14 | # §25.14 Lerch’s Transcendent
## §25.14(i) Definition
25.14.1 ${\Phi\left(z,s,a\right)\equiv\sum_{n=0}^{\infty}\frac{z^{n}}{(a+n)^{s}}},$ $|z|<1$; $\Re s>1,|z|=1$. ⓘ Defines: $\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)$: Lerch’s transcendent Symbols: $\equiv$: equals by definition, $\Re$: real part, $n$: nonnegative integer, $a$: real or complex parameter, $s$: complex variable and $z$: complex variable Keywords: definition, infinite series, series representation Source: Erdélyi et al. (1953a, (1.11.1), p. 27) Referenced by: (25.14.2), (25.14.3), §25.14(ii), §25.14, 3rd Erratum Permalink: http://dlmf.nist.gov/25.14.E1 Encodings: TeX, pMML, png Clarification (effective with 1.0.21): The previous constraint $a\neq 0,-1,-2,\dots,$ was removed. A clarification regarding the correct constraints for Lerch’s transcendent $\Phi\left(z,s,a\right)$ has been added in the text immediately below. See also: Annotations for §25.14(i), §25.14 and Ch.25
If $s$ is not an integer then $\left|\operatorname{ph}a\right|<\pi$; if $s$ is a positive integer then $a\neq 0,-1,-2,\dots$; if $s$ is a non-positive integer then $a$ can be any complex number. For other values of $z$, $\Phi\left(z,s,a\right)$ is defined by analytic continuation. This is the notation used in Erdélyi et al. (1953a, p. 27). Lerch (1887) used $\mathfrak{K}(a,x,s)=\Phi\left(e^{2\pi ix},s,a\right)$.
The Hurwitz zeta function $\zeta\left(s,a\right)$25.11) and the polylogarithm $\mathrm{Li}_{s}\left(z\right)$25.12(ii)) are special cases:
25.14.2 $\zeta\left(s,a\right)=\Phi\left(1,s,a\right),$ $\Re s>1$, $a\neq 0,-1,-2,\dots$, ⓘ Symbols: $\zeta\left(\NVar{s},\NVar{a}\right)$: Hurwitz zeta function, $\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)$: Lerch’s transcendent, $\Re$: real part, $a$: real or complex parameter and $s$: complex variable Keywords: specialization Source: Derivable from (25.11.1), (25.14.1). Permalink: http://dlmf.nist.gov/25.14.E2 Encodings: TeX, pMML, png See also: Annotations for §25.14(i), §25.14 and Ch.25
25.14.3 $\mathrm{Li}_{s}\left(z\right)=z\Phi\left(z,s,1\right),$ $\Re s>1$, $|z|\leq 1$. ⓘ Symbols: $\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)$: Lerch’s transcendent, $\mathrm{Li}_{\NVar{s}}\left(\NVar{z}\right)$: polylogarithm, $\Re$: real part, $s$: complex variable and $z$: complex variable Keywords: specialization Source: Derivable from (25.12.10) and (25.14.1). Referenced by: (25.12.12) Permalink: http://dlmf.nist.gov/25.14.E3 Encodings: TeX, pMML, png See also: Annotations for §25.14(i), §25.14 and Ch.25
## §25.14(ii) Properties
With the conditions of (25.14.1) and $m=1,2,3,\dots$,
25.14.4 $\Phi\left(z,s,a\right)=z^{m}\Phi\left(z,s,a+m\right)+\sum_{n=0}^{m-1}\frac{z^{% n}}{(a+n)^{s}}.$ ⓘ Symbols: $\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)$: Lerch’s transcendent, $m$: nonnegative integer, $n$: nonnegative integer, $a$: real or complex parameter, $s$: complex variable and $z$: complex variable Keywords: recurrence Source: Erdélyi et al. (1953a, (1.11.2), p. 27) Permalink: http://dlmf.nist.gov/25.14.E4 Encodings: TeX, pMML, png See also: Annotations for §25.14(ii), §25.14 and Ch.25
25.14.5 $\Phi\left(z,s,a\right)=\frac{1}{\Gamma\left(s\right)}\int_{0}^{\infty}\frac{x^% {s-1}e^{-ax}}{1-ze^{-x}}\mathrm{d}x,$ $\Re s>0$, $\Re a>0$, $z\in\mathbb{C}\setminus[1,\infty)$.
25.14.6 $\Phi\left(z,s,a\right)=\frac{1}{2}a^{-s}+\int_{0}^{\infty}\frac{z^{x}}{(a+x)^{% s}}\mathrm{d}x-2\int_{0}^{\infty}\frac{\sin\left(x\ln z-s\operatorname{arctan}% \left(x/a\right)\right)}{(a^{2}+x^{2})^{s/2}(e^{2\pi x}-1)}\mathrm{d}x,$ $\Re s>0$ if $|z|<1$; $\Re s>1$ if $|z|=1,\Re a>0$.
For these and further properties see Erdélyi et al. (1953a, pp. 27–31). | 2020-07-14T13:01:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 88, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9733591675758362, "perplexity": 10200.871576346424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880665.3/warc/CC-MAIN-20200714114524-20200714144524-00576.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Abak.anthony | # zbMATH — the first resource for mathematics
## Bak, Anthony
Compute Distance To:
Author ID: bak.anthony Published as: Bak, A.; Bak, Anthony Homepage: https://www.math.uni-bielefeld.de/~bak/ External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate · GND
Documents Indexed: 55 Publications since 1969, including 7 Books
all top 5
#### Co-Authors
18 single-authored 7 Morimoto, Masaharu 4 Muranov, Yuriĭ Vladimirovich 4 Vavilov, Nikolaĭ Aleksandrovich 3 Rehmann, Ulf 3 van Oystaeyen, Freddy 3 Verschoren, Alain H. M. J. 2 Brown, Ronald 2 Minian, Elias Gabriel 2 Porter, Timothy 2 Stepanov, Alexeĭ Vladimirovich 2 Tang, Guoping 2 Weibel, Charles A. 1 Basu, Rabeya 1 Donadze, Guram 1 Garge, Anuradha S. 1 Guoping, Tang 1 Hazrat, Roozbeh 1 Inassaridze, Nikoloz 1 Kolster, Manfred 1 Ladra González, Manuel 1 Petrov, Viktor 1 Preusser, Raimund 1 Rao, Ravi A. 1 Rosenberg, Jonathan Micah 1 Scharlau, Winfried 1 Ushitaki, Fumihiro
all top 5
#### Serials
6 Journal of Pure and Applied Algebra 4 $$K$$-Theory 2 Topology 2 Forum Mathematicum 2 Sbornik: Mathematics 2 General Topology and its Applications 2 Journal of Homotopy and Related Structures 2 Journal of $$K$$-Theory 1 Communications in Algebra 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Russian Mathematical Surveys 1 Advances in Mathematics 1 American Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 Inventiones Mathematicae 1 Journal of Algebra 1 Proceedings of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Rendiconti del Seminario Matematico della Università di Padova 1 Bulletin de la Société Mathématique de Belgique. Série A 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Algebra Colloquium 1 Journal of Mathematical Sciences (New York) 1 St. Petersburg Mathematical Journal 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Bulletin of the American Mathematical Society 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Annals of Mathematics Studies 1 Lecture Notes in Mathematics 1 Forum of Mathematics, Sigma
all top 5
#### Fields
21 Category theory; homological algebra (18-XX) 20 Manifolds and cell complexes (57-XX) 18 $$K$$-theory (19-XX) 15 Group theory and generalizations (20-XX) 11 Associative rings and algebras (16-XX) 8 Number theory (11-XX) 5 General and overarching topics; collections (00-XX) 5 Commutative algebra (13-XX) 5 Algebraic geometry (14-XX) 4 Algebraic topology (55-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX)
#### Citations contained in zbMATH
44 Publications have been cited 580 times in 278 Documents Cited by Year
K-theory of forms. Zbl 0465.10013
Bak, Anthony
1981
Structure of hyperbolic unitary groups. I: Elementary subgroups. Zbl 0963.20024
Bak, Anthony; Vavilov, Nikolai
2000
Nonabelian $$K$$-theory: The nilpotent class of $$K_ 1$$ and general stability. Zbl 0741.19001
Bak, Anthony
1991
On modules with quadratic forms. Zbl 0192.37202
Bak, A.
1969
Normality for elementary subgroup functors. Zbl 0857.20028
Bak, Anthony; Vavilov, Nikolai
1995
Localization-completion strikes again: relative $$K_1$$ is nilpotent by Abelian. Zbl 1167.19002
Bak, A.; Hazrat, R.; Vavilov, N.
2009
Stability for quadratic $$K_1$$. Zbl 1048.19001
Bak, Anthony; Petrov, Viktor; Guoping, Tang
2003
Stability for Hermitian $$K_1$$. Zbl 0961.19002
Bak, Anthony; Tang, Guoping
2000
Local-global principle for transvection groups. Zbl 1187.19001
Bak, A.; Basu, Rabeya; Rao, Ravi A.
2010
Grothendieck and Witt groups of orders and finite groups. Zbl 0288.16016
Bak, Anthony; Scharlau, Winfried
1974
The congruence subgroup and metaplectic problems for $$SL_{n>1}$$ of division algebras. Zbl 0495.20022
Bak, Anthony; Rehmann, Ulf
1982
Dimension theory and nonstable K-theory for net groups. Zbl 1072.19001
Bak, Anthony; Stepanov, Alexei
2001
Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion Abelian groups. Zbl 1068.16032
Bak, Anthony; Tang, Guoping
2004
The computation of surgery groups of finite groups with abelian 2- hyperelementary subgroups. Zbl 0346.57012
Bak, Anthony
1976
Odd dimension surgery groups of odd torsion groups vanish. Zbl 0322.57021
Bak, Anthony
1975
Subgroups of the general linear group normalized by relative elementary groups. Zbl 0536.20030
Bak, Anthony
1982
Equivariant surgery with middle dimensional singular sets. I. Zbl 0860.57028
Bak, Anthony; Morimoto, Masaharu
1996
$$K$$-theoretic groups with positioning map and equivariant surgery. Zbl 0822.57025
Bak, Anthony; Morimoto, Masaharu
1994
Equivariant surgery and applications. Zbl 1039.57502
Bak, Anthony; Morimoto, Masaharu
1992
$$K_ 2$$-analogs of Hasse’s norm theorems. Zbl 0539.12007
Bak, Anthony; Rehmann, Ulf
1984
The involution on Whitehead torsion. Zbl 0367.18011
Bak, Anthony
1977
Homology of multiplicative Lie rings. Zbl 1138.18007
2007
The dimension of spheres with smooth one fixed point actions. Zbl 1101.57018
Bak, Anthony; Morimoto, Masaharu
2005
Splitting along submanifolds and $$\mathbb L$$-spectra. Zbl 1078.57030
Bak, A.; Muranov, Yu. V.
2004
The computation of odd dimensional projective surgery groups of finite groups. Zbl 0465.57016
Bak, Anthony; Kolster, Manfred
1981
The computation of even dimension surgery groups of odd torsion groups. Zbl 0447.57022
Bak, Anthony
1978
The computation of surgery groups of odd torsion groups. Zbl 0336.18012
Bak, Anthony
1974
Global actions, groupoid atlases and applications. Zbl 1129.55009
Bak, A.; Brown, R.; Minian, G.; Porter, T.
2006
Le problème des sous-groupes de congruence et le problème metaplectique pour les groupes classiques de rang $$>1$$. Zbl 0461.20031
Bak, Anthony
1981
Induction for finite groups revisited. Zbl 0844.19001
Bak, Anthony
1995
Arf’s theorem for trace Noetherian and other rings. Zbl 0394.16010
Bak, Anthony
1979
The E-normal structure of odd dimensional unitary groups. Zbl 06865866
Bak, Anthony; Preusser, Raimund
2018
Splitting a simple homotopy equivalence along a submanifold with filtration. Zbl 1166.57019
Bak, A.; Muranov, Yu V.
2008
Le problème des sous-groupes de congruence dans $$SL_{n\geq 2}$$ sur un corps gauche. Zbl 0423.20045
Bak, Anthony; Rehmann, Ulf
1979
Grothendieck groups of modules and forms over commutative orders. Zbl 0369.16022
Bak, Anthony
1977
Definitions and problems in surgery and related groups. Zbl 0359.57018
Bak, Anthony
1977
Equivariant intersection theory and surgery theory for manifolds with middle dimensional singular sets. Zbl 1156.57028
Bak, Anthony; Morimoto, Masaharu
2008
Normal invariants of manifold pairs and assembly maps. Zbl 1148.57042
Bak, A.; Muranov, Yu. V.
2006
Presenting powers of augmentation ideals and Pfister forms. Zbl 0985.11016
Bak, Anthony; Vavilov, Nikolai
2000
Subring subgroups of symplectic groups in characteristic 2. Zbl 1365.14064
Bak, A.; Stepanov, A.
2017
Topological methods in algebra. Zbl 0914.18010
Bak, A.
1998
Global actions: The algebraic counterpart of a topological space. Zbl 0928.18005
Bak, A.
1997
Surgery on a pair of transversal manifolds. Zbl 1257.57034
Bak, A.; Muranov, Y. V.
2012
Algebraic K-theory, number theory, geometry and analysis. Proceedings of the International Conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982. Zbl 0518.00003
Bak, A. (ed.)
1984
The E-normal structure of odd dimensional unitary groups. Zbl 06865866
Bak, Anthony; Preusser, Raimund
2018
Subring subgroups of symplectic groups in characteristic 2. Zbl 1365.14064
Bak, A.; Stepanov, A.
2017
Surgery on a pair of transversal manifolds. Zbl 1257.57034
Bak, A.; Muranov, Y. V.
2012
Local-global principle for transvection groups. Zbl 1187.19001
Bak, A.; Basu, Rabeya; Rao, Ravi A.
2010
Localization-completion strikes again: relative $$K_1$$ is nilpotent by Abelian. Zbl 1167.19002
Bak, A.; Hazrat, R.; Vavilov, N.
2009
Splitting a simple homotopy equivalence along a submanifold with filtration. Zbl 1166.57019
Bak, A.; Muranov, Yu V.
2008
Equivariant intersection theory and surgery theory for manifolds with middle dimensional singular sets. Zbl 1156.57028
Bak, Anthony; Morimoto, Masaharu
2008
Homology of multiplicative Lie rings. Zbl 1138.18007
2007
Global actions, groupoid atlases and applications. Zbl 1129.55009
Bak, A.; Brown, R.; Minian, G.; Porter, T.
2006
Normal invariants of manifold pairs and assembly maps. Zbl 1148.57042
Bak, A.; Muranov, Yu. V.
2006
The dimension of spheres with smooth one fixed point actions. Zbl 1101.57018
Bak, Anthony; Morimoto, Masaharu
2005
Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion Abelian groups. Zbl 1068.16032
Bak, Anthony; Tang, Guoping
2004
Splitting along submanifolds and $$\mathbb L$$-spectra. Zbl 1078.57030
Bak, A.; Muranov, Yu. V.
2004
Stability for quadratic $$K_1$$. Zbl 1048.19001
Bak, Anthony; Petrov, Viktor; Guoping, Tang
2003
Dimension theory and nonstable K-theory for net groups. Zbl 1072.19001
Bak, Anthony; Stepanov, Alexei
2001
Structure of hyperbolic unitary groups. I: Elementary subgroups. Zbl 0963.20024
Bak, Anthony; Vavilov, Nikolai
2000
Stability for Hermitian $$K_1$$. Zbl 0961.19002
Bak, Anthony; Tang, Guoping
2000
Presenting powers of augmentation ideals and Pfister forms. Zbl 0985.11016
Bak, Anthony; Vavilov, Nikolai
2000
Topological methods in algebra. Zbl 0914.18010
Bak, A.
1998
Global actions: The algebraic counterpart of a topological space. Zbl 0928.18005
Bak, A.
1997
Equivariant surgery with middle dimensional singular sets. I. Zbl 0860.57028
Bak, Anthony; Morimoto, Masaharu
1996
Normality for elementary subgroup functors. Zbl 0857.20028
Bak, Anthony; Vavilov, Nikolai
1995
Induction for finite groups revisited. Zbl 0844.19001
Bak, Anthony
1995
$$K$$-theoretic groups with positioning map and equivariant surgery. Zbl 0822.57025
Bak, Anthony; Morimoto, Masaharu
1994
Equivariant surgery and applications. Zbl 1039.57502
Bak, Anthony; Morimoto, Masaharu
1992
Nonabelian $$K$$-theory: The nilpotent class of $$K_ 1$$ and general stability. Zbl 0741.19001
Bak, Anthony
1991
$$K_ 2$$-analogs of Hasse’s norm theorems. Zbl 0539.12007
Bak, Anthony; Rehmann, Ulf
1984
Algebraic K-theory, number theory, geometry and analysis. Proceedings of the International Conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982. Zbl 0518.00003
Bak, A. (ed.)
1984
The congruence subgroup and metaplectic problems for $$SL_{n>1}$$ of division algebras. Zbl 0495.20022
Bak, Anthony; Rehmann, Ulf
1982
Subgroups of the general linear group normalized by relative elementary groups. Zbl 0536.20030
Bak, Anthony
1982
K-theory of forms. Zbl 0465.10013
Bak, Anthony
1981
The computation of odd dimensional projective surgery groups of finite groups. Zbl 0465.57016
Bak, Anthony; Kolster, Manfred
1981
Le problème des sous-groupes de congruence et le problème metaplectique pour les groupes classiques de rang $$>1$$. Zbl 0461.20031
Bak, Anthony
1981
Arf’s theorem for trace Noetherian and other rings. Zbl 0394.16010
Bak, Anthony
1979
Le problème des sous-groupes de congruence dans $$SL_{n\geq 2}$$ sur un corps gauche. Zbl 0423.20045
Bak, Anthony; Rehmann, Ulf
1979
The computation of even dimension surgery groups of odd torsion groups. Zbl 0447.57022
Bak, Anthony
1978
The involution on Whitehead torsion. Zbl 0367.18011
Bak, Anthony
1977
Grothendieck groups of modules and forms over commutative orders. Zbl 0369.16022
Bak, Anthony
1977
Definitions and problems in surgery and related groups. Zbl 0359.57018
Bak, Anthony
1977
The computation of surgery groups of finite groups with abelian 2- hyperelementary subgroups. Zbl 0346.57012
Bak, Anthony
1976
Odd dimension surgery groups of odd torsion groups vanish. Zbl 0322.57021
Bak, Anthony
1975
Grothendieck and Witt groups of orders and finite groups. Zbl 0288.16016
Bak, Anthony; Scharlau, Winfried
1974
The computation of surgery groups of odd torsion groups. Zbl 0336.18012
Bak, Anthony
1974
On modules with quadratic forms. Zbl 0192.37202
Bak, A.
1969
all top 5
#### Cited by 205 Authors
43 Vavilov, Nikolaĭ Aleksandrovich 17 Bak, Anthony 14 Morimoto, Masaharu 13 Stepanov, Alexeĭ Vladimirovich 12 Hazrat, Roozbeh 12 Zhang, Zuhong 11 Rao, Ravi A. 9 Muranov, Yuriĭ Vladimirovich 9 You, Hong 6 Kwasik, Sławomir 6 Luzgarev, A. Yu. 6 Sinchuk, Sergeĭ Sergeevich 5 Basu, Rabeya 5 Preusser, Raimund 5 Schultz, Reinhard E. 5 Tang, Guoping 4 Ambily, Ambattu Asokan 4 Cavicchioli, Alberto 4 Jiménez Benitez, Rolando 4 Petrov, Viktor 4 Spaggiari, Fulvia 4 Stavrova, Anastasia K. 4 Vaserstein, Leonid N. 4 Ye, Shengkui 4 Yu, Weibo 3 Chang, Shan 3 Chattopadhyay, Pratyusha 3 Hambleton, Ian 3 Jespers, Eric 3 Jose, Selby 3 Raghunathan, Madabusi Santanam 3 Randal-Williams, Oscar 3 Song, Yongjin 3 Wall, Charles Terence Clegg 3 Zhou, Qingxia 2 Anan’evskii, A. S. 2 Bayer-Fluckiger, Eva 2 Bunina, E. I. 2 Donadze, Guram 2 Dybkova, E. V. 2 Galatius, Søren 2 Gvozdevsky, Pavel 2 Hegenbarth, Friedrich 2 Heidari, Mahin 2 Hughes, Mark C. 2 Inassaridze, Nikoloz 2 Jahren, Bjørn 2 Karoubi, Max 2 Kazakevich, V. G. 2 Keshari, Manoj Kumar 2 Khan, Qayum 2 Khanna, Reema 2 Kolster, Manfred 2 Ladra González, Manuel 2 Lavrenov, Andrei V. 2 Lück, Wolfgang 2 Milgram, Richard James 2 Minian, Elias Gabriel 2 Oliver, Bob 2 Pardon, William L. 2 Pearl, Elliott 2 Prasad, Gopal 2 Ranicki, Andrew A. 2 Rapinchuk, Andrei S. 2 Rehmann, Ulf 2 Repovš, Dušan D. 2 Rismanchian, Mohammad Reza 2 Scharlau, Winfried 2 Sharma, Sampat 2 Smolensky, Andrei 2 Voronetsky, E. Yu. 2 Voronetsky, Egor 2 Yamazaki, Takao 2 Zhou, Xuemei 1 Apte, Himanee 1 Araskhan, Mehdi 1 Asok, Aravind 1 Baeza, Ricardo 1 Banagl, Markus 1 Basu, Rudranil 1 Batalkin, K. O. 1 Baues, Hans-Joachim 1 Belegradek, Igor 1 Bertuccioni, Inta 1 Borowiecka, Agnieszka 1 Cencelj, Matija 1 Charney, Ruth M. 1 Chen, Sheng 1 Chen, Yu 1 Chen, Yu 1 Clouston, Ranald A. 1 Coleman, Donald B. 1 Corbas, B. 1 Cunningham, Joel 1 Dasgupta, Bhanumati 1 de A. e Silva, A. 1 del Hoyo, Matías L. 1 Dhorajia, Alpesh M. 1 Dietel, Gerhard 1 Dooms, Ann ...and 105 more Authors
all top 5
#### Cited in 75 Serials
33 Journal of Mathematical Sciences (New York) 26 Journal of Algebra 25 Journal of Pure and Applied Algebra 16 $$K$$-Theory 15 St. Petersburg Mathematical Journal 13 Communications in Algebra 9 Inventiones Mathematicae 8 Journal of $$K$$-Theory 7 Mathematische Annalen 6 Mathematische Zeitschrift 6 Transactions of the American Mathematical Society 6 Topology and its Applications 5 Journal of Group Theory 4 Israel Journal of Mathematics 4 Advances in Mathematics 4 Journal of Soviet Mathematics 4 Algebraic & Geometric Topology 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Czechoslovak Mathematical Journal 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Algebra Colloquium 3 Journal of Algebra and its Applications 3 Bulletin of the American Mathematical Society 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Rendiconti del Seminario Matematico della Università di Padova 2 Acta Applicandae Mathematicae 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Vestnik St. Petersburg University. Mathematics 2 Geometry & Topology 2 Mediterranean Journal of Mathematics 2 Journal of Homotopy and Related Structures 2 Annals of $$K$$-Theory 1 Mathematical Notes 1 Ukrainian Mathematical Journal 1 Mathematics of Computation 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Geometriae Dedicata 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Computer and System Sciences 1 Journal of the Mathematical Society of Japan 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Tohoku Mathematical Journal. Second Series 1 Transactions of the Moscow Mathematical Society 1 Order 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Science in China. Series A 1 International Journal of Mathematics 1 International Journal of Algebra and Computation 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Applied Categorical Structures 1 Documenta Mathematica 1 Transformation Groups 1 Trudy Instituta Matematiki 1 Central European Journal of Mathematics 1 Proceedings of the Japan Academy 1 Bulletin de la Société Mathématique de France. Supplément. Mémoires 1 Science China. Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Forum of Mathematics, Sigma
all top 5
#### Cited in 27 Fields
143 Group theory and generalizations (20-XX) 81 $$K$$-theory (19-XX) 71 Manifolds and cell complexes (57-XX) 44 Associative rings and algebras (16-XX) 38 Number theory (11-XX) 33 Category theory; homological algebra (18-XX) 32 Commutative algebra (13-XX) 26 Algebraic topology (55-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 13 Algebraic geometry (14-XX) 6 Field theory and polynomials (12-XX) 5 Nonassociative rings and algebras (17-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Topological groups, Lie groups (22-XX) 4 General topology (54-XX) 2 History and biography (01-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-03-04T10:10:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3823985755443573, "perplexity": 7281.146470136259}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368687.25/warc/CC-MAIN-20210304082345-20210304112345-00407.warc.gz"} |
https://lammps.sandia.gov/doc/Examples.html | # 9. Example scripts
The LAMMPS distribution includes an examples sub-directory with many sample problems. Many are 2d models that run quickly and are straightforward to visualize, requiring at most a couple of minutes to run on a desktop machine. Each problem has an input script (in.*) and produces a log file (log.*) when it runs. Some use a data file (data.*) of initial coordinates as additional input. A few sample log file run on different machines and different numbers of processors are included in the directories to compare your answers to. E.g. a log file like log.date.crack.foo.P means the “crack” example was run on P processors of machine “foo” on that date (i.e. with that version of LAMMPS).
Many of the input files have commented-out lines for creating dump files and image files.
If you uncomment the dump command in the input script, a text dump file will be produced, which can be animated by various visualization programs.
If you uncomment the dump image command in the input script, and assuming you have built LAMMPS with a JPG library, JPG snapshot images will be produced when the simulation runs. They can be quickly post-processed into a movie using commands described on the dump image doc page.
Animations of many of the examples can be viewed on the Movies section of the LAMMPS web site.
There are two kinds of sub-directories in the examples dir. Lowercase dirs contain one or a few simple, quick-to-run problems. Uppercase dirs contain up to several complex scripts that illustrate a particular kind of simulation method or model. Some of these run for longer times, e.g. to measure a particular quantity.
Lists of both kinds of directories are given below.
## 9.1. Lowercase directories
accelerate run with various acceleration options (OpenMP, GPU, Phi) airebo polyethylene with AIREBO potential atm Axilrod-Teller-Muto potential example balance dynamic load balancing, 2d system body body particles, 2d system cmap CMAP 5-body contributions to CHARMM force field colloid big colloid particles in a small particle solvent, 2d system comb models using the COMB potential controller use of fix controller as a thermostat coreshell core/shell model using CORESHELL package crack crack propagation in a 2d solid deposit deposit atoms and molecules on a surface dipole point dipolar particles, 2d system dreiding methanol via Dreiding FF eim NaCl using the EIM potential ellipse ellipsoidal particles in spherical solvent, 2d system flow Couette and Poiseuille flow in a 2d channel friction frictional contact of spherical asperities between 2d surfaces gcmc Grand Canonical Monte Carlo (GCMC) via the fix gcmc command granregion use of fix wall/region/gran as boundary on granular particles hugoniostat Hugoniostat shock dynamics hyper global and local hyperdynamics of diffusion on Pt surface indent spherical indenter into a 2d solid kim use of potentials from the OpenKIM Repository latte examples for using fix latte for DFTB via the LATTE library meam MEAM test for SiC and shear (same as shear examples) melt rapid melt of 3d LJ system message demos for LAMMPS client/server coupling with the MESSAGE package micelle self-assembly of small lipid-like molecules into 2d bilayers min energy minimization of 2d LJ melt mscg parameterize a multi-scale coarse-graining (MSCG) model msst MSST shock dynamics nb3b use of non-bonded 3-body harmonic pair style neb nudged elastic band (NEB) calculation for barrier finding nemd non-equilibrium MD of 2d sheared system obstacle flow around two voids in a 2d channel peptide dynamics of a small solvated peptide chain (5-mer) peri Peridynamic model of cylinder impacted by indenter pour pouring of granular particles into a 3d box, then chute flow prd parallel replica dynamics of vacancy diffusion in bulk Si python using embedded Python in a LAMMPS input script qeq use of the QEQ package for charge equilibration rdf-adf computing radial and angle distribution functions for water reax RDX and TATB models using the ReaxFF rigid rigid bodies modeled as independent or coupled shear sideways shear applied to 2d solid, with and without a void snap NVE dynamics for BCC tantalum crystal using SNAP potential srd stochastic rotation dynamics (SRD) particles as solvent streitz use of Streitz/Mintmire potential with charge equilibration tad temperature-accelerated dynamics of vacancy diffusion in bulk Si threebody regression test input for a variety of manybody potentials vashishta use of the Vashishta potential voronoi Voronoi tesselation via compute voronoi/atom command
Here is how you can run and visualize one of the sample problems:
cd indent
cp ../../src/lmp_linux . # copy LAMMPS executable to this dir
lmp_linux -in in.indent # run the problem
Running the simulation produces the files dump.indent and log.lammps. You can visualize the dump file of snapshots with a variety of 3rd-party tools highlighted on the Visualization page of the LAMMPS web site.
If you uncomment the dump image line(s) in the input script a series of JPG images will be produced by the run (assuming you built LAMMPS with JPG support; see the Build_settings doc page for details). These can be viewed individually or turned into a movie or animated by tools like ImageMagick or QuickTime or various Windows-based tools. See the dump image doc page for more details. E.g. this Imagemagick command would create a GIF file suitable for viewing in a browser.
% convert -loop 1 *.jpg foo.gif
## 9.2. Uppercase directories
ASPHERE various aspherical particle models, using ellipsoids, rigid bodies, line/triangle particles, etc COUPLE examples of how to use LAMMPS as a library DIFFUSE compute diffusion coefficients via several methods ELASTIC compute elastic constants at zero temperature ELASTIC_T compute elastic constants at finite temperature HEAT compute thermal conductivity for LJ and water via fix ehex KAPPA compute thermal conductivity via several methods MC using LAMMPS in a Monte Carlo mode to relax the energy of a system SPIN examples for features of the SPIN package USER examples for USER packages and USER-contributed commands VISCOSITY compute viscosity via several methods
Nearly all of these directories have README files which give more details on how to understand and use their contents.
The USER directory has a large number of sub-directories which correspond by name to a USER package. They contain scripts that illustrate how to use the command(s) provided in that package. Many of the sub-directories have their own README files which give further instructions. See the Packages_details doc page for more info on specific USER packages. | 2019-08-24T05:27:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38282498717308044, "perplexity": 8129.28652503534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319724.97/warc/CC-MAIN-20190824041053-20190824063053-00460.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GEDR3/Gaia_archive/chap_datamodel/sec_dm_external_catalogues/ssec_dm_tycho2tdsc_merge.html | # 13.2.1 tycho2tdsc_merge
Tycho-2 merged with the TDSC catalog and TDSC supplement.
The Tycho Double Star Catalogue, (TDSC, Fabricius et al. 2002) contains 98482 components of double and multiple systems processed in the Tycho-2 context. It includes either original Tycho-2 data or results from a dedicated re-processing aimed at binaries. As pointed out by P. Marrese (personal communication), the TDSC star with identifier 29583 is redundant and it was therefore skipped. The TDSC supplement contains data from an additional 4777 components from either Hipparcos or Tycho-1.
The Tycho-2 main catalogue (Høg et al. 2000) contains 2 539 913 sources, including many binaries, but a minimum separation of 0.8 arcsec was imposed during the catalogue construction. The Tycho-2 supplement-1 contains data for 17588 Hipparcos and Tycho-1 stars, which do not appear in the main catalogue, but only the 4777 stars relevant for TDSC are included here. The Tycho-2 supplement-2 contains an additional 1146 Tycho-1 stars of poor quality.
We have merged Tycho-2 (main) with the TDSC main and supplement, keeping the Tycho-2 data model and extending it to include TDSC–specific fields. This is only possible to a certain degree as specified in detail below. In particular, Tycho-2 includes fields for mean position, proper motion etc. for a combination of Tycho-2 and several ground based catalogues. These fields are inherited for TDSC main stars, but were not derived for the TDSC supplement, where we only provide HIP proper motions. For Tycho-2 stars not in TDSC, blank TDSC fields were appended.
For Tycho-2 stars in TDSC, the following fields were replaced by the corresponding TDSC fields:
• tyc1, tyc2, tyc3;
• hip;
• ccdm.
In addition, if the TDSC contains a new solution:
• bt_mag, e_bt_mag, vt_mag, e_vt_mag, ra_deg, de_deg, ep_ra1990, ep_de1990, e_ra_deg, eDeDec;
• The mean position flag, pflag, is set to ‘P’ (“photocentre”) if resolved and there are Tycho-2 mean positions. Mean position etc. are then repeated for both new components;
• The proximity indicator, prox, is set to blank if the Tycho-2 star was resolved in TDSC;
• The type-of-solution flag, posflg, set to ‘N’;
• For resolved Tycho-2 stars, two records are given.
For the few TDSC stars with new solutions, but not in Tycho-2, and for the TDSC supplement stars (Hipparcos or Tycho-1), the Tycho-2 part of the merged record was populated in the following way:
• TYC1..3 from TDSC;
• pflag set to TDSC pmflg (‘H’ or ‘X’), ‘H’ indicating Hip proper motions;
• no mean position and related fields;
• proper motions only for Hipparcos stars;
• $B_{\rm T},V_{\rm T}$ photometry from TDSC;
• Tycho-1 flag, tyc, is set to posflg, i.e. ‘T’ or ‘H’ although Hipparcos stars may well be in Tycho-1;
• Hipparcos, hip, and CCDM, ccdm, identifiers from TDSC;
• astrometry from TDSC, but the (ra, dec)-correlation, corr, is set to blank.
New TDSC specific fields added after the Tycho-2 part of the record:
• sys_no, cmp, n_main, n_sup, magflg, wds, note, hd;
• rcmp, pa, sep, e_pa, e_pa_sep, e_sep.
Columns description:
id : Tycho-2 identifier (string)
The Tycho-2 identifier id string TYC … is constructed from the GSC region number (tyc1), the running number within the region (tyc2) and a component identifier (tyc3) which is normally 1. Some non-GSC running numbers were constructed for the first Tycho Catalogue and for Tycho-2. The component identifier (tyc3) for TDSC entries is copied from TDSC. The recommended star designation contains a hyphen between the TYC numbers, e.g. TYC 1-13-1.
hip : Hipparcos number (int)
Hipparcos number identifier.
tyc1 : TYC1 component from TYC or GSC (string)
The TYC identifier string component tyc1) is constructed from the Guide Star Catalogue region number.
tyc2 : TYC2 component from TYC or GSC (string)
The TYC identifier string component tyc2 is constructed from the running number within the tyc1 region.
tyc3 : TYC3 component from TYC or TDSC (string)
The TYC identifier string component tyc3 is normally 1. Some non-GSC running numbers were constructed for the first Tycho Catalogue and for Tycho-2. The component identifier for Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) entries is copied from TDSC.
id_tycho : Numeric Tycho-2 identifier (long)
These are the IDs as published in Tycho-2. In Tycho-2 objects were identified by 3 numbers (tyc1, tyc2 and tyc3) and we have combined these into a single unique number given by (tyc1*1000000)+(tyc2*10)+(tyc3).
tyc : Tycho-1 star (string)
This field is specific to Tycho-2 and not found in the Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002).
• ‘ ’ indicates no Tycho-1 star was found within 0.8 arcsec (quality 1-8) or 2.4 arcsec (quality 9);
• ‘T’ indicates this is a Tycho-1 star. The Tycho-1 identifier is given in the beginning of the record. For Tycho-1 stars, resolved in Tycho-2 as a close pair, both components are flagged as a Tycho-1 star and the Tycho-1 TYC3 is assigned to the brightest (VT) component; The HIP-only stars given in Tycho-1 are not flagged as Tycho-1 stars.
• ‘H’ TDSC star not in Tycho-2 but in Hipparcos. It may also be in Tycho-1.
ra : Observed Tycho-2 Right Ascension, ICRS (double, Angle[deg])
Observed Tycho-2 Right Ascension, ICRS. This field is a convenience copy of ra_deg.
dec : Observed Tycho-2 Declination, ICRS (double, Angle[deg])
Observed Tycho-2 Declination, ICRS. This field is a convenience copy of the field de_deg.
ra_deg : Observed Tycho-2 Right Ascension, ICRS (double, Angle[deg])
Observed Tycho-2 Right Ascension, ICRS.
de_deg : Observed Tycho-2 Declination, ICRS (double, Angle[deg])
Observed Tycho-2 Declination, ICRS.
ra_mdeg : Mean Right Ascension, ICRS, epoch=J2000 (double, Angle[deg])
The mean position is a weighted mean for the catalogues contributing to the proper motion determination. This mean has then been brought to epoch 2000.0 by the computed proper motion. Tycho-2 is one of the several catalogues used to determine the mean position and proper motion. The Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) was not used when forming these mean positions. The observed Tycho-2 position is given in the fields RAdeg and DEdeg.
de_mdeg : Mean Declination, ICRS, at epoch=J2000 (double, Angle[deg])
Mean Declination, ICRS, at epoch=J2000
The mean position is a weighted mean for the catalogues contributing to the proper motion determination. This mean has then been brought to epoch 2000.0 by the computed proper motion. See Note(2) above for details. Tycho-2 is one of the several catalogues used to determine the mean position and proper motion. The Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) was not used when forming these mean positions. The observed Tycho-2 position is given in the fields RAdeg and DEdeg.
pm_ra : Proper motion in RA*cos(dec) (float, Angular Velocity[mas/year])
Some Hipparcos stars (having a positive number in the HIP column) have no proper motions; these are virtually all in multiple systems.
pm_de : Proper motion in Dec (float, Angular Velocity[mas/year])
Some Hipparcos stars (having a positive number in the HIP column) have no proper motions; these are virtually all in multiple systems.
ep_ra1990 : Epoch–1990 of ra_deg (float, Time[year])
Epoch–1990 of ra_deg.
ep_de1990 : Epoch–1990 of de_deg (float, Time[year])
Epoch–1990 of de_deg.
ep_ra_m : Mean epoch of RA. (float, Time[year])
Mean epoch of RA. The mean epochs are given in Julian years.
ep_de_m : Mean epoch of Dec. (float, Time[year])
Mean epoch of Dec. The mean epochs are given in Julian years.
num : Number of positions used for forming mean data (short)
Number of positions used in constructing the mean positions and proper motions, one of these contributing positions coming from Tycho-2.
e_ra_deg : Uncertainty RA*cos(dec), of observed Tycho-2 RA. (double, Angle[mas])
Uncertainty, $\sigma_{\alpha\cos\delta}$, of the observed Tycho-2 RA. The errors are based on error models.
e_de_deg : Uncertainty of observed Tycho-2 Dec. (double, Angle[mas])
Uncertainty of the observed Tycho-2 declination. The errors are based on error models.
Correlation (ra_deg, de_deg). For Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) stars not in Tycho-2, the field is blank.
e_ra_mdeg : Uncertainty RA*cos(dec),at mean epoch. (double, Angle[mas])
Uncertainty, $\sigma_{\alpha}\cos\delta$, for the right ascension direction at mean epoch. The errors are based on error models.
e_de_mdeg : Uncertainty of Dec at mean epoch. (double, Angle[mas])
Uncertainty, $\sigma_{\delta}$, for the declination at mean epoch. The errors are based on error models.
e_pm_ra : Uncertainty proper motion in RA*cos(dec). (float, Angular Velocity[mas/year])
Uncertainty, $\sigma_{\mu_{\alpha}\cos\delta}$, for the proper motion in right ascension direction. The errors are based on error models.
e_pm_de : Uncertainty of proper motion in Dec. (float, Angular Velocity[mas/year])
Uncertainty, $\sigma_{\mu_{\delta}}$, for the proper motion in declination. The errors are based on error models.
q_ra_mdeg : Goodness of fit for mean RA (float)
This goodness of fit is the ratio of the scatter-based and the model-based error. It is only defined when num $>2$. Values exceeding 9.9 are truncated to 9.9.
q_de_mdeg : Goodness of fit for mean Dec (float)
This goodness of fit is the ratio of the scatter-based and the model-based error. It is only defined when num $>2$. Values exceeding 9.9 are truncated to 9.9.
q_pm_de : Goodness of fit for pm_de (float)
This goodness of fit is the ratio of the scatter-based and the model-based error. It is only defined when num $>2$. Values exceeding 9.9 are truncated to 9.9.
q_pm_ra : Goodness of fit for pm_ra (float)
This goodness of fit is the ratio of the scatter-based and the model-based error. It is only defined when num $>2$. Values exceeding 9.9 are truncated to 9.9.
pflag : Mean position flag (string)
The mean position flag takes one of:
• ‘ ’:
normal mean position and proper motion;
• ‘P’:
the mean position, proper motion, etc., refer to the photocentre of two Tycho-2 entries, where the $B_{T}$ magnitudes were used in weighting the positions. It is also used for Tycho-2 stars resolved in the Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) and the mean positions and proper motions are then repeated;
• ‘X’:
no mean position, no proper motion;
• ‘H’:
no mean position, but proper motions from Hipparcos. This option is only used for TDSC stars not in Tycho-2.
posflg : Type of Tycho-2 solution (string)
The type of Tycho-2 solution takes one of:
• ‘ ’:
normal treatment, close stars were subtracted when possible;
• ‘D’:
double star treatment. Two stars were found. The companion is normally included as a separate Tycho-2 entry, but may have been rejected;
• ‘P’:
photocentre treatment, close stars were not subtracted. This special treatment was applied to known or suspected doubles which were not successfully (or reliably) resolved in the Tycho-2 double star processing.
Specific values for entries from the Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002):
• ‘N’:
New double star treatment for TDSC;
• ‘T’:
Tycho-1 position from the Tycho-2 Supplement_1;
• H’:
Hipparcos position from the Tycho-2 Supplement_1.
The values [TH] are only used in the TDSC supplement. In the TDSC main catalogue only flags [‘ ’N] are used.
ccdm : CCDM component identifier for HIP stars (string)
The CCDM component identifiers for double or multiple Hipparcos stars contributing to this Tycho-2 entry. For photocentre solutions, all components within 0.8 arcsec contribute. For double star solutions any unresolved component within 0.8 arcsec contributes. For single star solutions, the predicted signal from close stars were normally subtracted in the analysis of the photon counts and such stars therefore do not contribute to the solution. The components are given in lexical order.
For Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) entries, the HIP and CCDM fields are from TDSC. There, the separation limit of 0.8 arcsec does not applied.
prox : Proximity indicator (short, Angle[100mas])
Distance in units of 100 mas to the nearest entry in the Tycho-2 main catalogue or supplement. The distance is computed for the epoch 1991.25. A value of 999 (i.e. 99.9 arcsec) is given if the distance exceeds 99.9 arcsec.
This is a Tycho-2 specific field. For Tycho-2 stars resolved in the Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002), the field is blank.
bt_mag : Tycho-2 BT magnitude (float, Magnitude[mag])
Blank when no magnitude is available. Either bt_mag or vt_mag is always given. Approximate Johnson photometry may be obtained as: $V=V_{\rm T}-0.090(B_{\rm T}-V_{\rm T})$ and $B-V=0.850(B_{\rm T}-V_{\rm T})$. Consult Section 1.3 of Volume 1 of ESA (1997) for details.
Details for the Tycho Double Star Catalogue (TDSC, Fabricius et al. 2002) photometry are specified in ’magflg’.
vt_mag : Tycho-2 VT magnitude (float, Magnitude[mag])
Blank when no magnitude is available. See the description above for bt_mag for further details.
e_bt_mag : Uncertainty of BT (float, Magnitude[mag])
Uncertainty of bt_mag. Blank when no magnitude is available. See the description above for bt_mag for details of the photometric system.
e_vt_mag : Uncertainty of VT (float, Magnitude[mag])
Uncertainty of vt_mag. Blank when no magnitude is available. See the description above for bt_mag for details of the photometric system.
sys_no : TDSC identifier for the system (int)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
TDSC identifier for systems appearing in TDSC or its supplement.
cmp : Component designation (string)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002) of one or two characters. The TDSC system identifier (sys_no) plus the component designation give an unambiguous identification of the TDSC component. When possible, the component designation is from the Washington Double Star Catalog (WDS, Mason et al. 2001). In cases where a component designation is added to a WDS system, or to a system not in WDS, this was normally done using letters A,B,… according to the $V_{\rm T}$ magnitude. Cases where the designations deviate from the WDS designations in a non-trivial way are explained in the TDSC notes.
n_main : Number of components in TDSC main catalogue (byte)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Number of components for this system listed in the TDSC main catalogue. The TDSC main catalogue contains components detected in the Tycho-2 (Høg et al. 2000) processing or in the TDSC processing, while the supplement contains components copied across from the Tycho-2 Supplement. A system in TDSC may have components in both the main catalogue and in the supplement. A system known in the Washington Double Star Catalogue (WDS, Mason et al. 2001) may have just one component listed in the TDSC.
n_sup : Number of components in the TDSC supplement (byte)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002). Number of components for this system listed in the TDSC supplement (which is included in this merged version). The TDSC main catalogue contains components detected in the Tycho-2 (Høg et al. 2000) processing or in the TDSC processing, while the supplement contains components copied across from the Tycho-2 Supplement. A system in TDSC may have components in both the main catalogue and in the supplement. A system known in the Washington Double Star Catalog (WDS, Mason et al. 2001) may have just one component listed in the TDSC.
magflg : TDSC photometry flag (char)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002) giving details for the TDSC photometry.
Except for Hp, the photometry is always on the same system as in Tycho-2 (Høg et al. 2000). We expect the Tycho photometry of Hipparcos stars from Fabricius and Makarov (2000) to be more accurate than the normal Tycho-2 photometry.
• ‘ ’:
normal photometry, either from Tycho-2 or the TDSC processing;
• ‘A’:
normal photometry given here, but alternative photometry is given in Fabricius and Makarov (2000);
• ‘F’:
Tycho photometry from Fabricius and Makarov (2000);
• ‘T’:
Tycho photometry from Tycho-1 (ESA 1997);
• ‘B’:
$B_{\rm T}$ from Tycho-1, Hp is given instead of $V_{\rm T}$;
• ‘V’:
$V_{\rm T}$ from Tycho-1, no $B_{\rm T}$;
• ‘H’:
Hp is given instead of $V_{\rm T}$, no $B_{\rm T}$.
In the main TDSC catalogue only flags [‘ ’A] are used; in the TDSC supplement only flags [FTBVH].
wds : WDS identifier for the system (string)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
The Washington Double Star Catalogue (WDS, Mason et al. 2001) contains a 10 character field with approximate ICRS coordinates for the primary component in the form hhmmm+ddmm. This field together with the component designation identifies the relevant entries of the WDS. Exceptions and ambiguities are explained in the notes to the TDSC catalogue.
note : TDSC notes (char)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Flag for a note, normally to the identification in the Washington Double Star Catalog (WDS, Mason et al. 2001). Some WDS identifications need clarification, e.g. because the WDS entry gives no designation or because the star has more than one WDS designation. In other cases the identification is somewhat uncertain or a new component was added to a known system.
• ‘ ’:
no note;
• ‘A’:
alternative WDS designation exists;
• ‘D’:
dubious/uncertain WDS identification;
• ‘N’:
a non-specific note;
• ‘O’:
good quality orbit exists, cf. Fabricius et al. (2002), Table 2;
• ‘R’:
this WDS component is probably resolved;
• ‘S’:
a close companion to a WDS component (probably);
• ‘T’:
a Tycho single star, added to a WDS system;
• ‘U’:
undesignated in WDS (non-trivial) or unclear designation.
Notes [ANTU] are explained in detail in the file of notes accompanying the original TDSC.
hd : HD identifier for TDSC entries (int)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Identifier from the Henry Draper catalogue as listed in the original TDSC catalogue.
rcmp : Reference component for position angle and separation (string)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Reference component (cmp) for position angle and separation as detailed in the fields pa and sep.
pa : Position angle (float, Angle[deg])
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Position angle (degrees) of the present component (cmp) with respect to the reference component (rcmp).
Position angle and separation are computed at the mean observational epoch for the two stars by applying proper motion to the right ascensions and declinations at the individual epochs of observation. The position angle is given relative to the ICRS pole.
sep : Separation (float, Angle[arcsec])
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Separation (arcseconds) of the present component (cmp) with respect to the reference component (rcmp). See the detailed description for pa for further details.
e_pa : Uncertainty of the position angle (float, Angle[deg])
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Uncertainty (degrees) of the position angle of the present component (cmp) with respect to the reference component (rcmp).
e_pa_sep : Uncertainty of the position angle * separation (short)
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Uncertainty (mas) of the position angle, of the present component (cmp) with respect to the reference component (rcmp), multiplied by the separation.
e_sep : Uncertainty of the separation (short, Angle[mas])
Tycho Double Star Catalogue specific field (TDSC, Fabricius et al. 2002).
Uncertainty (mas) of the separation of the present component (cmp) with respect to the reference component (rcmp). | 2021-06-14T12:29:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 20, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6280724406242371, "perplexity": 10953.868316581189}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487612154.24/warc/CC-MAIN-20210614105241-20210614135241-00558.warc.gz"} |
http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/rms.htm | Dataplot Vol 2 Vol 1
# ROOT MEAN SQUARE ERROR
Name:
ROOT MEAN SQUARE ERROR (LET)
Type:
Let Subcommand
Purpose:
Compute the root means square error of a variable.
Description:
The root mean square error has the formula:
$$\mbox{RMS} = \sqrt{\frac{\sum_{i=1}^{n}{X_{i}^{2}}} {n}}$$
Syntax 1:
LET <par> = ROOT MEAN SQUARE ERROR <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed root mean square error is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
LET <par> = DIFFERENCE OF ROOT MEAN SQUARE ERROR <y1> <y2>
<SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
<par> is a parameter where the computed difference of root mean square errors is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax computes the root mean square error of <y1> and <y2> and then computes the difference of the two root mean square error values.
Examples:
LET A = ROOT MEAN SQUARE ERROR Y1
LET A = ROOT MEAN SQUARE ERROR Y1 SUBSET TAG > 2
LET A = DIFFERENCE OF ROOT MEAN SQUARE ERROR Y1 Y2
Note:
Dataplot statistics can be used in a number of commands. This is documented in the STATISICS HELP.
Default:
None
Synonyms:
RMS
Related Commands:
MEAN = Compute the mean of a variable. RANGE = Compute the range of a variable. STANDARD DEVIATION = Compute the standard deviation of a variable. VARIANCE = Compute the variance of a variable.
Applications:
Statistics
Implementation Date:
2010/1
Program:
LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100
LET RMS = ROOT MEAN SQUARE ERROR Y1
A value of 0.9256 is returned.
NIST is an agency of the U.S. Commerce Department.
Date created: 09/08/2010
Last updated: 10/07/2016
Please email comments on this WWW page to [email protected]. | 2017-10-17T05:41:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.881192147731781, "perplexity": 2694.468902441975}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820927.48/warc/CC-MAIN-20171017052945-20171017072945-00653.warc.gz"} |
https://le.utah.gov/~2001/pamend/HB179003.htm | H.B. 179
VOLUNTARY CONTRIBUTIONS ACT
House Committee Amendments
Amendment 3 January 29, 2001 8:50 am
Representative Buffmire proposes the following amendments:
1. Page 2, Lines 57-58: Delete lines 57-58 and renumber remaining subsections accordingly
2. Page 2, Line 66: Delete line 66
3. Page 2, Line 67: Delete "by an employer;"
4. Page 5, Line 130: Delete the semicolon and insert a comma
5. Page 5, Line 131: Delete "(a)"
6. Page 5, Line 132: Delete "(i)" and insert "(a)"
7. Page 5, Line 133: Delete "(ii)" and insert "(b)"
8. Page 5, Line 134: Delete "(iii)" and insert "(c)"
9. Page 5, Line 135: Delete "(iv)" and insert "(d)" and after "entity" delete "; and" and insert a period
10. Page 5, Lines 136-138: Delete lines 136-138
11. Page 5, Line 144: After "until" delete the colon
12. Page 5, Line 145: Delete "(a)"
13. Page 5, Lines 146-150: Delete lines 146-150 | 2022-01-28T20:04:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.836875319480896, "perplexity": 11978.386216582103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320306335.77/warc/CC-MAIN-20220128182552-20220128212552-00167.warc.gz"} |
https://tibia.fandom.com/wiki/Talk:Formulae | 18,492 Pages
## Magic Level Formula
I'm having a hard time coming up with a formula for determining the mana needed for a specific level. It appears to be an exponential formula, but I haven't been able to pin it down yet.
Using nonlinear regression on the values in the magic level table, I figure that the formula must be something similar to:
1600 * e(lvl * a)
Where "lvl" is the desired magic level, and "a" is the vocation multiplier. This formula is not correct, but pretty closly matches the shape of the curve.
If anyone else wants to take a crack at it, please do... and post your findings here.
-- WhitelacesTalk † χρισtoς αnεσtη, αληθως αnεσtη -- 14:51, 24 May 2006 (CDT)
I figured it out. Thanks to everyone that helped, well, nobody actually, but I did receive some moral support from a few friends.
-- WhitelacesTalk † χρισtoς αnεσtη, αληθως αnεσtη -- 12:43, 16 October 2006 (PDT)
I'm looking for someone to verify the amount of mana needed to go from magic level 4 to magic level 5 on a druid or sorcerer.
Is it 2340 or 2344 or something else?
--Erig 06:18, 21 March 2009 (UTC)
## Tibia hours?
Would 24 hours = 1 day mean that it's 2.4 seconds to a minute and not 2.5?
Not sure, every time I try to extrapolate the math, I end up confusing myself between tibia minutes and RL minutes.
I can promise without a doubt that 1 RL hour is equal to 24 Tibia hours. Midnight in Tibia is always on the hour.
As far as how many Tibia minutes are in one second, I find that information to be less useful.
RL Tibia
:00 12:00 Midnight
:15 6:00 AM
:30 12:00 Noon
:45 6:00 PM
-- WhitelacesTalk † χρισtoς αnεσtη, αληθως αnεσtη -- 12:43, 16 October 2006 (PDT)
There are 24 Tibian days in a rl day. So, 1 Tibian minute should be 1/24 minute irl. 60 / 24 = 2.5 seconds. So, 1 Tibian minute is 2.5 rl seconds.
## Separate precise formulas?
Should there be some distinction made between formulas that are clearly prcise, like those for Hit Points or Cap, and those that are 'best fits' based on observations, like average spell damage and character speed? AtarNajuat 09:32, 12 November 2006 (PST)
Technically, all of the formulas on this page are based on observed values with known factors. The only difference is in the level of subjectivity, where it is not known what factors affect the ultimate outcome, and we are therefore not truly able to develop a completely accurate formula.
That being said, I'm not sure if we need to actually separate the formulas based on that (a logical organization of the formulas based on function is MUCH more valuable), but it would be very feasable to add a small notation that indicates known level of accuracy of the function.
-- WhitelacesTalk † χρισtoς αnεσtη, αληθως αnεσtη -- 07:50, 13 November 2006 (PST)
## forum
I'm sorry if I destroy the composite of this post/site by saying this here (I am totally new here), but if you want the correct formulas for spell damage to all instant damage spells (both minimum and maximum damage), look at Thread ID 1371675 on the Tibia.com forum. // Arshalo
(There is also the exact numbers for how much damage the various amulets removes and how Armor works in that thread.)
Feel free to contact me about whatever you are wondering. The easiest way to contact me if probably by posting on the Inferna boards, since I don't understand one thing about how this site is working... If I knew how to post stuff here, I could post it.... But sadly I don't know how to post stuff here. It's kind of cool information. =)
Very cool post. I'm sure you will tell me that all of the informatoin there is completely accurate, but I mostly believe you already.
I'll start integrating your calculations into the damage calculator on the wiki here, and I'll post a message if anything looks funny.
-- WhitelacesTalk † χρισtoς αnεσtη, αληθως αnεσtη -- 07:15, 7 December 2006 (PST)
## Mana/hitpoints formula
Well that formula can be simplificated to: paladins-level*10+105 mages-level*5+145 knights-level*15+65
You are correct, but the way they are written now makes it clear that they only apply if the character was taken to the mainland at level 8. The formula needs to be modified if you go to mainland at level 9 or higher.
-- -- 10:10, 22 January 2007 (PST)
so im editing it and putting sidenotes about that left rookgaard on level stuff, much easier. User:Joao Henrique
### Formulas
I wonder why damage formula on this page is ((a * 1/3) + (b * 1/2)) * c, and Damage Calculator uses formula discovered/made by Arshalo. It doesn't make sense to me.
Djomla
Talk Contributions
I made the damage calculator, and based the calculations on Arshalo's research... I'm not sure why Wisling changed the formula on this page. He never explained his actions. Maybe this one is more accurate? I don't know.
-- Non curo. Si metrum non habet, non est poema.
-- -- 14:32, 20 February 2007 (PST)
## More Formulas
I've seen on other web sites articles on the formulas for skill advancement and weapon damage. I've not seen articles on the weapon hitting and shield effectiveness formulas. I am not qualified to add to this page, but has thought been given to adding these formulas? Bombur Thumper
Any information you have would be helpful. If there are known formulas for any of these things, it would be great to add them.
-- Non plaudite. Modo pecuniam jacite
-- -- 10:42, 6 April 2007 (PDT)
Someone posted a formule on the melee page, ive put it here, but the values arent exactly the same from the calculator template (on the weapon page)--Delatus 02:13, 4 May 2007 (PDT)
## Damage Formulas as of Summer Update 2007
Has anyone figured the new role of level in melee damage, and by how much is its meaning decreased in dealing magic damage?
Marian Moczymorda 13:26, 6 July 2007 (CET)
I have seen many damages since the summer update of 2007:
Full Attack :9
Balanced :7
Full Defence :5
22:37, 7 July 2007 (PDT)
---
dunno if anybody wants to work on the new magic damage formula, but i'm sure he will need some values:
with lvl 71 & mlvl 70, i had a max vis of 178
with lvl 72 & mlvl 70, i got a max vis of 181
Tharjah † 8 July 2007
---
I'm currently tasking a large group of knights and paladins on Trimera, in the guild Divine Horde in collecting data for proper calculation of damage. We have currently taken over 24000 hits worth of data, but more need to be taken to polish up our formulas. Mage damage will be coming soon after this.
Currently the formula is polished to 1.5% of accuracy, roughly. I'll update this when the formulas are polished.
- Caprizon - 08-03-07
---
I am not sure if the formula is correct (magic of vis), I check in tibia forums that they say for 12 lvls it is add 1 point of vis and 1.8 per ml. with test I get that.
The min Formula will be
Damage vis = (1.8*ml)+(lvl/12)
And the max
Damage vis = (2.5*ml)+(lvl/12) ==
## Formula For Blocking Melee With Armor
Is there any formula to know how much melee damage armor blocks?
I know that with a total armor of 38 I can block almost all rotworms hits.
-April-03-2008.
## Spell damage formula
I've been testing my icicle damage with 4 characters of different levels and magic levels. 1 character from each vocation was used. I tested on witches that doesn't have weakness or strength against ice damage so if you test on other monsters you might get different results (behemoths for example gives me 10% more damage so if you test on those you need to add 10% to the formula). I've found that this formula seems to be extremely accurate for the max damage:
(level*0.2+magic level*3)+18
I round the level*0.2 down since Craban stated you get +1 damage every 5 levels. So if you are for example level 38 you get 7.6 and you round it down to 7 (35 is the closest 5 level down and 35*0.2=7).
What I'm having problems with is the minimum damage. The closest I've gotten is not completely accurate for all characters.
Even if my formula for max damage seems to be accurate it doesn't look like a good formula for other types of runes/spells. Probably there's another variable somewhere in there. Maybe ((level*0.2+magic level*3)*1)+18 so that the *1 and +18 could be changed to make other spell damages.
All this needs more testing and if someone else wants to try the formula and see that it works for them it would be good.
Nevaran 15:48, 17 April 2008 (UTC)
After some more testing I've found a formula that seems to work for the minimum damage of icicles. However it still needs testing. Just because it works for me and one of my guildmates doesn't mean it's correct. Anyhow, here it is:
((level*0.2+magic level*1.81)*1)+10
Nevaran 00:49, 18 April 2008 (UTC)
I've done some tests with the strikespells on 4 mages of different levels and magic levels. This seems to be accurate:
Max damage (level*0.2+magic level*2.21)+13
Min damage (level*0.2+magic level*1.40)+8
level*0.2 should be rounded down like I explained earlier.
The icicle (and I assume fireball) damage seems to be what I posted before (it has been accurate on all charaters I've tried so far):
Max damage (level*0.2+magic level*3.00)+18
Min damage (level*0.2+magic level*1.81)+10
The conclusion is that the formula for spells is:
(level*0.2+magic level*x)+y
Where x is a decimal number and y is an integer.
If anyone feels that this observed data is enough to make an addition to the article feel free to do so. Also if anyone feels like finding the numbers for the rest of the runes and instant spells go ahead. I might do SD and/or avalanche someday if nobody else does it first.
Nevaran 02:52, 19 April 2008 (UTC)
i have also come to think that level/5 is like base damage for all spells using that ive done this SD formula:
Min = Level/5 + MagLevel*4 + 30 Max = Level/5 + MagLevel*7 + 60
Sajgra 18:27, 17 June 2008 (UTC)
That SD formula is not correct. According to that I could hit max 632 but I have in fact hit max ~650.
I've only tested well (5 bp's) with one character and blocked for a guild mate that used 1 bp (not enough for a confirmed min/max). The formula I've gotten from that is not accurate but I guess getting close:
min = (level*0.2 + magic level*4.53) + 34
max = (level*0.2 + magic level*7.59) + 36
Need to try at least 5 bp's more on each character and on more characters (to get more diversity of level and magic levels) to make a really accurate formula.
Nevaran 21:49, 17 June 2008 (UTC)
yea i know its not 100% accurate but i tried to keep it simple because i doubt they would use a very complex formula.
Sajgra 19:39, 19 June 2008 (UTC)
I've done some more testing and this seems to be a working formula for SD:
Max = (level*0.2 + magic level*7.395) + 46
Min = (level*0.2 + magic level*4.53) + 34
It still needs some testing, so if anyone's interested to check if it works the same for all levels/magic levels It'd be awesome. However I think it's as close as I can get.
Nevaran 13:33, 24 June 2008 (UTC)
Did somebody find any problem with Nevaran's formulas?
Let's test the formulas!
<·> Hunter of Dragoes <·> My Talk <·> My Contributions <·> 21:05, 11 November 2008 (UTC)
I've not tried it but they look fairly close to me. At the very least, they're closer than we had (I think we're still using the formulas from before the mage 'downgrade'?) -- Sixorish 23:23, 11 November 2008 (UTC)
I tested the formula for sds out, it said I could do 275 pvp. My best hit so far has been 274 (without eq) level 82 ml 66 so its very close, also the strike spells are accurate for me too. Not too sure on the icicles as when I use them I dont have much time to watch my hits. Beejay 03:47, 12 November 2008 (UTC)
I've figured out that my ice wave could sometimes onehit stalkers (neutral to ice) since level 48, and my magic level was around 50 by then (I don't remember the correct value), but the formula says that only now (level 60 and magic level 54) I should get 120 as maximum hit (and that is total stalker's hp). Kamiel, 19 April 2009
I don't know what formula you've used, but with my formula I get 121 as max (54 as min) when having level 45 (48 rounded down to 45) and magic level 50. This formula might not be exactly accurate, but it would allow one-hitting stalkers.
Nevaran 21:23, 19 April 2009 (UTC)
moved from top of section
The user pages calculate damage for Thunderstorm and Great Fireball differently, it looks like the min and max damages for GFB are about 10 higher. However, the formula page has them calculated exactly the same. Does anyone have any testing experience with either spell?
Miltonr 01:14, 2 June 2009 (UTC)MiltonR
The math behind them are indeed different: The template's is based on Nevaran's testing (User:Nevaran/Spelltests). -- Sixorish 02:53, 2 June 2009 (UTC)
## Easy way to calculate formula for blocking melee with armor
The Sea Shells do 200 melee damage if you are naked and they do less damage if you wear armor. I will test more by adding or removing armor, if any one else get seashell hit post how much you got hit and the total of armor you where wearing. (wearing or not a shield don't matter for this)
Edited: May 27
• Wearing total armor 31 blocked 22 and 24 got hit 178 and 176 of 200 damage
• Wearing total armor 21 blocked 19 got hit 181 of 200 damage
• Wearing total armor 12 blocked 7 got hit 193 of 200 damage
• Wearing total armor 0 blocked 0 got hit 200 of 200 damage
Seems even if the shell always hit 200, armor not always block the same damage like if you using total armor of 31 you block 20 to 9 damage.
-May-21-2008.
I think I took 176 damage from it yesterday. Wearing Helmet of the Deep (Arm:2), DSM (Arm:15), MMS (Def:37), G legs (Arm:9), BOH (Arm:0), Platinum Amulet (Arm:2) = wearing 28 total armor. But I am only 90% sure that it was 176...
Sadonic 07:09, 20 May 2008 (UTC)
Will try to check it out, though I have gotten either a pearl or 'Nothing is inside' for the last 2 weeks..
Temahk 07:25, 20 May 2008 (UTC)
Okay, inside the Pits of Inferno are some strange slits, which do 60 damage when I'm naked.
• Wearing total armor of 8, I got hit 53-56
• Wearing total armor of 10, I got hit 51-55
• Wearing total armor of 11, I got hit 51-55
• Wearing total armor of 18, I got hit 43-50
• Wearing total armor of 21, I got hit 41-50
• Wearing total armor of 29, I got hit 33-46
Cant be bothered to do more, and it seems damage isn't 100% certain on those things. But I figured I'd post it, might help someone :)
Temahk 17:59, 8 June 2008 (UTC)
This are the armor block formula in the link.
Min Reduced = Round(total armor value * 0 .475)
Max Reduced = Round{[(total armor value * 0.475)-1] + Min Reduced}
<·> Hunter of Dragoes <·> My Talk <·> My Contributions <·> 18:22, 8 June 2008 (UTC)
Wow from what I have tested those 2 formulas work for the damages I took and the ones Temahk took. Would be nice to get some of those formulas in tibianews link in the wiki formula page "can we take them?".
-June-8-2008.
I tried a formula for exura which worked very well The formula was average healed= 8+lv*0.2+ml*1.5
This formula seemed to work for a variety of lvs including; A lv16 sorcrer, a lv26 knight, a 47 druid, a lv127 knight and a lv260 paladin please check your average exura healing and compare it to the formula =D.
Your healing formula seems accurate for my knight if not a little low (level 50 ml 6). However my druid (level 82 ml 66) looks to be closer to the formula that wiki already uses and the same for my sorcerer. Beejay 17:56, 27 November 2008 (UTC)
## about ml formulas after 8.1 update
min = (level / 5) + (magic level * c value)
max = (level / 5) + (magic level * d value)
The c values are roughly:
0.6 for Light Magic Missiles (LMM) (note: if your min damage is lower than 10 then min damage is 10).
1.5 for Light Healing [exura]
1.4 for Strike Spells [exori vis/flam/mort/frigo/tera] (note: when you finish the operation add + 10) to get the correct damage.
1 for Ice Wave [exevo frigo hur]
1.2 for Fire Wave [exevo flam hur]
1.2 for Heavy Magic Missiles [HMM] (note: if your min damage is lower than 20 then min damage is 20).
1.2 for Stalagmite [S] (note: if your min damage is lower than 20 then min damage is 20).
1.8 for Fireball [FB] (note: when you finish the operation add + 10) to get the correct damage and (if your min damage is lower than 20 then min damage is 20).
1.8 for Icicle [I](note: when you finish the operation add + 10) to get the correct damage and (if your min damage is lower than 20 then min damage is 20).
0 for Explosion [adevo mas hur] (note: the min damage of this spell is 0).
5 for Intense Healing [exura gran]
1.4 for Stone Shower [SS] (note: if your min damage is lower than 40 then min damage is 40).
1.4 for Thunderstorm [T] (note: if your min damage is lower than 40 then min damage is 40).
1.4 for Great Fireball [GFB] (note: if your min damage is lower than 40 then min damage is 40).
1.4 for Avalanche [A] (note: if your min damage is lower than 40 then min damage is 40).
4 for Sudden Death [SD] (note: when you finish the operation add + 60) to get the correct damage.
2.5 for Energy Beam [exevo vis lux]
2.5 for Great Energy Beam [exevo gran vis lux]
4 for Divine Caldera [exevo mas san]
3.5 for Terra Wave [exevo tera hur]
4.5 for Energy Wave [exevo vis hur]
10 for Ultimate Healing [exura vita]
10 for Heal friend [exura sio]
11 for Wound Cleansing [exana mort]
5 for Rage of the sky's [exevo gran mas vis]
7 for Hell's core [exevo gran mas flam]
5 for Wraght of Nature [exevo gran mas tera]
6 for Eternal Winter [exevo gran mas frigo]
18.5 for Divine Healing [exura san]
The d values are roughly:
1 for Light Magic Missiles (LMM) (note: when you finish the operation add + 10) to get the correct damage and (if your max damage is lower than 20 then max damage is 20).
2 for Light Healing [exura]
2.1 for Strike Spells [exori vis/flam/mort/frigo/tera] (note: when you finish the operation add + 20) to get the correct damage.
2 for Ice Wave [exevo frigo hur]
2 for Fire Wave [exevo flam hur] (note: when you finish the operation add + 10) to get the correct damage.
2 for Heavy Magic Missiles [HMM] (note: when you finish the operation add + 10) to get the correct damage and (if your max damage is lower than 40 then max damage is 40).
2 for Stalagmite [S] (note: when you finish the operation add + 10) to get the correct damage and (if your max damage is lower than 40 then max damage is 40).
3 for Fireball [FB] (note: when you finish the operation add + 15) to get the correct damage and (if your max damage is lower than 40 then max damage is 40).
3 for Icicle [I](note: when you finish the operation add + 15) to get the correct damage and (if your max damage is lower than 40 then max damage is 40).
4.8 for Explosion [adevo mas hur]
6 for Intense Healing [exura gran]
2.8 for Stone Shower [SS] (note: if your max damage is lower than 70 then max damage is 70).
2.8 for Thunderstorm [T] (note: if your max damage is lower than 70 then max damage is 70).
2.8 for Great Fireball [GFB] (note: if your max damage is lower than 70 then max damage is 70).
2.8 for Avalanche [A] (note: if your max damage is lower than 70 then max damage is 70).
7 for Sudden Death [SD] (note: when you finish the operation add + 60) to get the correct damage.
5 for Energy Beam [exevo vis lux]
9 for Great Energy Beam [exevo gran vis lux]
6 for Divine Caldera [exevo mas san]
7 for Terra Wave [exevo tera hur]
9 for Energy Wave [exevo vis hur]
12 for Ultimate Healing [exura vita]
14 for Heal friend [exura sio]
15 for Wound Cleansing [exana mort]
12 for Rage of the sky's [exevo gran mas vis]
14 for Hell's core [exevo gran mas flam]
10 for Wraght of Nature [exevo gran mas tera]
12 for Eternal Winter [exevo gran mas frigo]
25 for Divine Healing [exura san] —The preceding unsigned comment was added by Zane voldemort (talkcontribs). Remember to sign your comments!
## Melee, Exori and Exori Gran
Problem Report #21626:
The formulas for melee damage are incorrect. Having done my own calculations, the maximum damage on full attack for a melee weapon with attack W with skill S and level L is 0.085*W*S (L/5). The maximum damage of exori is 0.05*W*S (L/5) and of exori gran is 0.12*W*S (L/5). These are providing the target has 0 armor and has no or -% to melee damage taken. I've tested these thoroughly and am convinced they are correct (I was encouraged to test them after I discovered the previous ones were inaccurate).
## Current Melee Formulas
The current melee formulas on this page are extremely inaccurate, I have hit far more than they predict on nightmares (upwards of 490), they do not take into the account the changes which were made around summer 2007 to knights. (Also, the exori gran and exori formulas are pretty inaccurate too!). I've been working on more accurate formulas, and have found almost certainly accurate formulas for both exori, exori gran and normal melee on full attack. Approximate formulas appear to be Melee = 0.086*W*S+(L/5); Exori = 0.05*W*S+(L/5); Exori Gran = 0.12*W*S+(L/5), L=Level, W=weapon attack, S=weapon skill, they are not perfect, but they are all very accurate and I've based them on both my damage and other peoples on my server (note: the melee formula also works for paladins!). All formulas assume 0% resistance to melee either way (not weak or strong) and 0 armor values (So they're really only completely accurate on say naked PVP targets (in which case the damage would be halved) or low armor non weak monsters like nightmares)
Necro Dragonheart 18:48, 19 May 2009 (UTC)
## Automated transfer of Problem Report #21626
The following message was left by Anonymous via PR #21626 on 2009-04-29 21:54:46 UTC
The formulas for melee damage are incorrect. Having done my own calculations, the maximum damage on full attack for a melee weapon with attack W with skill S and level L is 0.085*W*S (L/5). The maximum damage of exori is 0.05*W*S (L/5) and of exori gran is 0.12*W*S (L/5). These are providing the target has 0 armor and has no or -% to melee damage taken. I've tested these thoroughly and am convinced they are correct (I was encouraged to test them after I discovered the previous ones were inaccurate).
I have a question, to calculate the damage you recive from monsters, you first calculate min/max armor and then do the other formula, right?? Camioneto 21:51, 13 July 2009 (UTC)
I don't understand the formula to calculate how much a shield and skills block, can some one calculate for me, how much attack a monster has to have for a player with armor 41 / skills 80 / shield 37+3 so that the monster max melee ends in 252
--Kwigon the sharpshooter 01:03, 14 July 2009 (UTC)
## Exp from Killing other Players on PvP-Enforced World
I didn't quite understand the formula, but if I understood it right you would gain this much experience, if you're a level 30 killing a level 140:
(((140 * 1,1) - 30)/140) * (43812800 * 0,05) = 1940281 experience
Is this right, or have I gotten it all wrong?
Then a level 30 would gain 1,940,281 experience by killing a level 140. He would be almost level 54, by the cost of 100,000gp and 591,472 experience loss.
It would be expensive, indeed, but only an example.
Best regards,
Nymph.
I edited the section on maximum melee damage since the formulae were out of date and inaccurate. I replaced it with an accurate one but kept the format. I also edited the section on knights spells/abilities, the formulae for whirlwind throw and grounshaker were accurate, but those for berserk and fierce berserk were wrong, so I edited these to the correct formulae (the old ones gave me a max fierce berserk of like 800 when its closer to 670!). Again, I kept the old layout but just modified the formulae. Necro Dragonheart 15:18, September 18, 2009 (UTC)
## light healing formula
i believe the formula for light healing needs +10
eg a character of level 10 with magic level 0, using this formula the minimum amount would be
10/2+1.5*0=2 whereas it appears that the minimum amount for light healing is at least 10. Monti macaroi 02:45, September 22, 2009 (UTC)
Actually, most of those formulas are way off. I started testing formulas last year and posted them on User:Nevaran/Spelltests and there you can see that the minimum for light healing is (using your example):
10*0.2+0*1.4+8 = 10
Maximum is (still using your example):
10*0.2+0*1.795+11 = 13
The reason why I haven't posted them on this page yet is because they are not complete. Although most of the runes and instants are there, the ultimate and powerful waves aren't. Also a few healing spells that aren't there.
Nevaran 09:56, September 22, 2009 (UTC)
## Non working magic damage formulas
I tested with a program that tests different values on variables inside formulas. I have some accurate magic damage data now and I've found that these formulas will not work, whatever x, y and z values are(z can be zero or negative number too):
(lvl*x)+(mlvl*y)+z
(lvl/x)+(mlvl*y)+z
--Daniel Letalis 11:36, October 21, 2009 (UTC)
Did you test the formulas on the formula page or the formulas on my spell tests? My tests aren't complete (still missing some spells/runes and some aren't tested well enough), but they are more accurate than the ones on the formula page.
Nevaran 14:45, October 21, 2009 (UTC)
Yes as x,y and z are dynamic in the tests they included those formulas and millions more similar formulas. I will keep testing with formulas with 1 to 3 dynamic values, hope I can find some exact formula soon.
Also I don't know much about maths but I guess it should be possible, anyone knows about a math method to possibly find a formula having several values for lvl,ml,min and max damage?
--Daniel Letalis 22:44, October 21, 2009 (UTC)
That's weird. My formulas works in game for all my characters and my friends' characters.
x shouldn't be dynamic. CIP has said that you get +1 damage/healing every 5 levels. So the level parameter should always be level/5 or level*0.2 (rounded down).
y is a decimal number (does your program test with fractions or just integers?).
z is an integer.
If you test on a monster with weakness/resistance you have to add that after doing the base calculation. For example if you test exori frigo on a dragon you have to multiply the formula with 1.1 (10% weakness) to get the correct damage. That formula would then look like this: ((level/2) + (mlvl*y) + z) * 1.1
Oh, and by the way. These formulas are only for the minimum and maximum damages. Not for every damage you can do in between.
Nevaran 09:13, October 22, 2009 (UTC)
Tx for the 1 damage every 5 lvl tip I completly forgot. +1 damage every 5 lvl is not lvl*0.2, it is floor(lvl*0.2). I calculate weakness/streng before testing formulas so I'm always working with "base" damage, I'm only testing high damages so I guess there can't be wrong calculations for creatures weakness/strengh.
I applied the formula tester with a lot of damages(around 10,000 hits on different lvls/mls) from avalanche and thunderstorm using the floor() part and I can confirm that these 2 formulas are correct on min and max values
Thunderstorm
Max damage: floor(lvl*0.2)+(mlvl*2.6)+16
Min damage: floor(lvl*0.2)+(mlvl*1)+6
Avalanche
Max damage: floor(lvl*0.2)+(mlvl*2.8)+17
Min damage: floor(lvl*0.2)+(mlvl*1.2)+7
I will test other type of dagames when I have time.
As you are the one who got those formulas maybe you wanna start removing old formulas and adding confirmed formulas to the formula page.
Note: I found funny that the damages are increased 3 by 3 and 4 by 4 in both avalanche and thunderstorms.
Do you have any formula for rods/wands? Maybe their values only changes according to lvl damage bonus --Daniel Letalis 00:18, October 23, 2009 (UTC)
Floor() is a programming function? It means the same as the "rounded down" that I posted. I.e. that no matter if the end result is .1 or .9 it rounds down to 0 and not up to 1.
The rods/wands have fixed values. They don't change with level or magic level. I think I posted the rod damages on the rods' talk page, but the wands have been tested to do the same min/max for the same level wands.
If I have time this weekend I might start re-writing that part. I've been putting it off for so long because I've been wanting to get more accurate formulas for more spells/runes. I guess I can leave the old formulas for the ones I don't have yet...
Nevaran 14:03, October 23, 2009 (UTC)
## Armor Damage reduction
I've been making tests with Spikes that deal 60 damage on Greenshore, I wanted to test if the formula here was accurate.
Bad thing is I can't calculate the damage I'm receiving from spikes with different legs and platinum amulet. Can anyone tell me how should I calculate the minimum and maximum damage for all items, wearing only one item at a time of this list: blue legs, dwarven legs, golden legs and platinum amulet.
I have new and correct formulas for armor and physical protection reduction(and got interesting facts), but as I tested with spikes, I couldn't test physical protection influence over shielding, I want to update the formulas here but I have this question, is physical protection applied after or before shielding? Any ideas on how to test this? --Daniel Letalis 04:03, June 4, 2010 (UTC)
## Magic Power?
I just saw that there's a formula for "Magic Power" and my question is: What's magic power used for?
Nevaran 16:14, July 26, 2010 (UTC)
## Melee Skill Levels formula
It says "Number of blood hits required to advance to the next skill level:", but is this accurate? Unless it was changed recently, the number of blood hits are only indirectly related to advancing melee skills. Vlobben 12:23, October 5, 2010 (UTC)
## Maximum damage reduction
$R_{min} = \left \lfloor \frac{t}{2} \right \rfloor$
$R_{max} = \left\lfloor \frac{t}{2} \right\rfloor \cdot 2 - 1$
For $t \leq 1$, Rmax is negative. It would suffice for t=1 to use the absolute value, but then when t=0, Rmax=1. According to my own tests (albeit not very exhaustive), when t=0 Rmax=0. So I propose we change it to:
$R_{max} = \begin{cases} 0, & \mbox{if }t = 0 \\ t - 1, & \mbox{if }t \mid 2\mbox{ and if }t \neq 0\\ |t - 2|, & \mbox{if }t \nmid 2 \\ \end{cases}$
Thoughts? (the | indicates division, returning a Boolean value) -- Sixorish 03:44, November 27, 2010 (UTC)
Took me some time to get it, this formula would be more simple but maybe more complex for most users to understand. I can't think of a simpler way to write it. --Daniel Letalis 04:54, November 27, 2010 (UTC)
What makes it complex? The division symbol did seem an intricate thing to me before I studied some number theory, but that could be easily changed to any of these:
$R_{max} = \begin{cases} 0, & \mbox{if }t = 0 \\ t - 1, & \mbox{if }t\mbox{ is even and if }t \neq 0\\ |t - 2|, & \mbox{if }t\mbox{ is odd} \\ \end{cases}$ $R_{max} = \begin{cases} 0, & \mbox{if }t = 0 \\ t - 1, & \mbox{if }t \bmod 2 = 0\mbox{ and if }t \neq 0\\ |t - 2|, & \mbox{if }t \bmod 2 \neq 0 \\ \end{cases}$
The latter I suppose only CS/math majors would understand.
The example could exemplify how these operations work and why the formula is like this. Or, we could indicate that there are two "strands" of armor - one for even values and one for odd - that would make comprehension a lot easier but it might give the impression that odd or even values would be "better" than the other.
PS: I actually dislike this formula because of the inability(?) to convert |x| to a polynomial. -- Sixorish 05:33, November 27, 2010 (UTC)
I like it more with "odd" and "even", it took me some minutes to understand it (maybe lack of math knowledge or practice) and that's why I say it could be complex for other users. Also I don't understand why the "and if t ≠ 0" only on one case and why "|t - 2|" instead of "t - 2" --Daniel Letalis 06:05, November 27, 2010 (UTC)
Well if t=0 it couldn't be the last case because 0 is even, and the first line defines the case of 0 so only the second line needs t != 0. The |t-2| is there solely for the case of t=1 (being negative; -1 damage reduction?). It could also be expressed as $\sqrt{t^2 - 4t + 4}$ but that would be more complex still. -- Sixorish 06:23, November 27, 2010 (UTC)
I don't see the need of "if t ≠ 0" because the 1st case already is chosen if "t = 0". I still think this formula could be harder to understand for many users but as long as everything is explained, I guess is ok.
This one looks more easy for me: $R_{max} = \begin{cases} 0, & \mbox{if }t < 2 \\ t - 1, & \mbox{if }t\mbox{ is even} \\ t - 2, & \mbox{if }t\mbox{ is odd} \\ \end{cases}$
--Daniel Letalis 06:37, November 27, 2010 (UTC)
I think you mean this?
$R_{max} = \begin{cases} t, & \mbox{if }t < 2 \\ t - 1, & \mbox{if }t\mbox{ is even} \\ t - 2, & \mbox{if }t\mbox{ is odd} \\ \end{cases}$
When Rmax = 1, max damage reduction is 1. -- Sixorish 06:42, November 27, 2010 (UTC)
Yes, also I think minimum reduction formula needs change when armor is 1, I don't know how I missed this, my tests were very complete :/
--Daniel Letalis 07:08, November 27, 2010 (UTC)
## Cleanup
I think it's about time to clean this page up. Some of it's old and some of it contradicts with other sections because it's old.
Any objections to removing these? (I'm not certain if they're all old, so please check if you may know)
• Melee Skill Levels
• Magic Power
• Fishing
• Spell/Rune Damage/Healing
• Melee
• Melee based spells
• Distance
• Distance based spells
• Armor and Defense
This is one of the most neglected pages on the wiki, and I would argue the most interesting for many players. -- Sixorish 20:33, September 10, 2011 (UTC)
## Money you make from making runes
This is my first writing and thought if to this page could be added my formula of how much money you make per hour with each rune with only food. This is the fromula: P*Q*60/(M/(2/3)/60) p=price Q=quantity M=mana cost/ea (2/3) only if not promoted Smargoos (talk) 12:34, July 6, 2012 (UTC)
I wouldn't mind this being on a subpage but I think the Formula page should contain non-derived formulas only. This formula is derived from other constants and it's not a special formula defined in the game's coding. -- Sixorish (talk) 17:29, July 6, 2012 (UTC)
So should this be added some where?
Smargoos (talk) 21:16, July 6, 2012 (UTC)
## Magic formulas
There is an issue with the constants for the magic formulas.
For example, heal friend has a min value of 10 and max value of 14 in this page, which leads to false results.
You page states that my ED level 121 ml 70 has a minimum heal of ~700, when other calculators (like tibia-stat) shows min of 510.
I know for a fact that I sometimes heal ~550, so your constant is off by very much. I did some calculating, and found that tibia-stat's constants for heal friend are- min value is 6.3, max is 14.3
This ofcourse is just a symptom. I assume other values are incorrect as well. Can you ask other sites with calculators for their values? Maybe average all of those values together?
Mahatesh (talk) 05:04, January 10, 2016 (UTC)Mahatesh
Community content is available under CC-BY-SA unless otherwise noted. | 2020-08-08T04:38:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6642520427703857, "perplexity": 3530.4031426663564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737238.53/warc/CC-MAIN-20200808021257-20200808051257-00482.warc.gz"} |
https://googology.wikia.org/wiki/Toomolduplex | 10,973 Pages
The toomolduplex is equal to \( 10\uparrow\uparrow\uparrow10\uparrow\uparrow\uparrow10\uparrow\uparrow\uparrow1000\) using arrow notation.[1] The term was coined by Wikia user Username5243.
• In Bird's array notation, it would be equal to \([10,[10,[10,1000,3],3],3]\). (Trivially, this is \(\{10,\{10,\{10,1000,3\},3\},3\}\) in BEAF.)
• In the FGH, this is roughly equal to \(f_4^3(1000)\).
Sources
Community content is available under CC-BY-SA unless otherwise noted. | 2021-07-24T04:54:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8458117842674255, "perplexity": 7217.600871168495}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150129.50/warc/CC-MAIN-20210724032221-20210724062221-00131.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/06._Uniform_Circular_Motion_and_Gravitation/6.6%3A_Satellites_and_Kepler%E2%80%99s_Laws%3A_An_Argument_for_Simplicity | $$\require{cancel}$$
# 6.6: Satellites and Kepler’s Laws: An Argument for Simplicity
Examples of gravitational orbits abound. Hundreds of artificial satellites orbit Earth together with thousands of pieces of debris. The Moon’s orbit about Earth has intrigued humans from time immemorial. The orbits of planets, asteroids, meteors, and comets about the Sun are no less interesting. If we look further, we see almost unimaginable numbers of stars, galaxies, and other celestial objects orbiting one another and interacting through gravity.
All these motions are governed by gravitational force, and it is possible to describe them to various degrees of precision. Precise descriptions of complex systems must be made with large computers. However, we can describe an important class of orbits without the use of computers, and we shall find it instructive to study them. These orbits have the following characteristics:
1. A small mass $$m$$orbits a much larger mass $$M$$. This allows us to view the motion as if $$M$$ were stationary—in fact, as if from an inertial frame of reference placed on $$M$$ —without significant error. Mass $$m$$ is the satellite of $$M$$, if the orbit is gravitationally bound.
2. The system is isolated from other masses. This allows us to neglect any small effects due to outside masses.
The conditions are satisfied, to good approximation, by Earth’s satellites (including the Moon), by objects orbiting the Sun, and by the satellites of other planets. Historically, planets were studied first, and there is a classical set of three laws, called Kepler’s laws of planetary motion, that describe the orbits of all bodies satisfying the two previous conditions (not just planets in our solar system). These descriptive laws are named for the German astronomer Johannes Kepler (1571–1630), who devised them after careful study (over some 20 years) of a large amount of meticulously recorded observations of planetary motion done by Tycho Brahe (1546–1601). Such careful collection and detailed recording of methods and data are hallmarks of good science. Data constitute the evidence from which new interpretations and meanings can be constructed.
# Kepler’s Laws of Planetary Motion
Kepler's First Law
The orbit of each planet about the Sun is an ellipse with the Sun at one focus.
Figure $$\PageIndex{1}$$: (a) An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci $$(f_1 and f_2)$$ is a constant. You can draw an ellipse as shown by putting a pin at each focus, and then placing a string around a pencil and the pins and tracing a line on paper. A circle is a special case of an ellipse in which the two foci coincide (thus any point on the circle is the same distance from the center). (b) For any closed gravitational orbit, $$m$$ follows an elliptical path with $$M$$ at one focus. Kepler’s first law states this fact for planets orbiting the Sun.
Kepler's Second Law
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times (see Figure).
Kepler's Third Law
The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun. In equation form, this is $\dfrac{T_1^2}{T_2^2} =\dfrac{r_1^3}{r_2^3}$
where $$T$$ is the period (time for one orbit) and $$r$$ is the average radius. This equation is valid only for comparing two small masses orbiting the same large one. Most importantly, this is a descriptive equation only, giving no information as to the cause of the equality.
Figure $$\PageIndex{2}$$: The shaded regions have equal areas. It takes equal times for $$m$$ to go from A to B, from C to D, and from E to F. The mass $$m$$ moves fastest when it is closest to $$M$$. Kepler’s second law was originally devised for planets orbiting the Sun, but it has broader validity.
Note again that while, for historical reasons, Kepler’s laws are stated for planets orbiting the Sun, they are actually valid for all bodies satisfying the two previously stated conditions.
Example $$\PageIndex{1}$$: Find the Time for One Orbit of an Earth Satellite
Given that the Moon orbits Earth each 27.3 d and that it is an average distance of $$3.84 \times 10^8 \space m$$ from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1500 km above Earth’s surface.
Strategy
The period, or time for one orbit, is related to the radius of the orbit by Kepler’s third law, given in mathematical form in $$\frac{T_1^2}{T_2^2} =\frac{r_1^3}{r_2^3}$$. Let us use the subscript 1 for the Moon and the subscript 2 for the satellite. We are asked to find $$T_2$$. The given information tells us that the orbital radius of the Moon is $$r_1 = 3.84 \times 10^8 \space m$$, and that the period of the Moon is $$T_1 = 27.3 \space d$$.
The height of the artificial satellite above Earth’s surface is given, and so we must add the radius of Earth (6380 km) to get $$r_2 = (1500 +6380) km = 7880 \space km$$. Now all quantities are known, and so $$T_2$$ can be found.
Solution
Kepler’s third law is $\dfrac{T_1^2}{T_2^2} =\dfrac{r_1^3}{r_2^3}.$
To solve for $$T_2$$, we cross-multiply and take the square root, yielding
$T_2^2 = T_1^2 \left(\dfrac{r_2}{r_1} \right)^3$
$T_2 = T_1 \left(\dfrac{r_2}{r_1} \right)^{\frac{3}{2}}.$
Substituting known values yields
$T_2 = 27.3 \space d \times \dfrac {24 \space h}{d} \times \left( \dfrac {7880 \space km}{3.84 \times 10^5 km} \right )^{ \frac{3}{2}}$
$= 1.93 \space h.$
Discussion This is a reasonable period for a satellite in a fairly low orbit. It is interesting that any satellite at this altitude will orbit in the same amount of time. This fact is related to the condition that the satellite’s mass is small compared with that of Earth.
People immediately search for deeper meaning when broadly applicable laws, like Kepler’s, are discovered. It was Newton who took the next giant step when he proposed the law of universal gravitation. While Kepler was able to discover what was happening, Newton discovered that gravitational force was the cause.
# Derivation of Kepler’s Third Law for Circular Orbits
We shall derive Kepler’s third law, starting with Newton’s laws of motion and his universal law of gravitation. The point is to demonstrate that the force of gravity is the cause for Kepler’s laws (although we will only derive the third one).
Let us consider a circular orbit of a small mass $$m$$ around a large mass $$M$$, satisfying the two conditions stated at the beginning of this section. Gravity supplies the centripetal force to mass $$m$$. Starting with Newton’s second law applied to circular motion,
$F_{net} = ma_c = m\dfrac{v^2}{r}.$
The net external force on mass $$m$$ is gravity, and so we substitute the force of gravity for $$F_{net}$$:
$G\dfrac{mM}{r^2} = m\dfrac{v^2}{r}.$
The mass $$m$$ cancels, yielding
$G\dfrac{M}{r} = v^2.$
The fact that $$m$$ cancels out is another aspect of the oft-noted fact that at a given location all masses fall with the same acceleration. Here we see that at a given orbital radius $$r$$, all masses orbit at the same speed. (This was implied by the result of the preceding worked example.) Now, to get at Kepler’s third law, we must get the period $$T$$ into the equation. By definition, period $$T$$ is the time for one complete orbit. Now the average speed $$v$$ is the circumference divided by the period—that is,
$v = \dfrac{2\pi r}{T}.$
Substituting this into the previous equation gives $G\dfrac{M}{r} = \dfrac{4\pi^2 r^2}{T^2}.$
Solving for $$T^2$$ yields $T^2 = \dfrac{4\pi^2}{GM}r^3.$
Using subscripts 1 and 2 to denote two different satellites, and taking the ratio of the last equation for satellite 1 to satellite 2 yields
$\dfrac{T_1^2}{T_2^2} = \dfrac{r_1^3}{r_2^3}.$
This is Kepler’s third law. Note that Kepler’s third law is valid only for comparing satellites of the same parent body, because only then does the mass of the parent body $$M$$ cancel.
Now consider what we get if we solve $$T^2 = \frac{4\pi^2}{GM}r^3$$ for the ratio $$r^3/T^2$$. We obtain a relationship that can be used to determine the mass $$M$$ of a parent body from the orbits of its satellites:
$\dfrac{r^3}{T^2} = \dfrac{G}{4\pi^2}M.$
If $$r$$ and $$T$$ are known for a satellite, then the mass $$M$$ of the parent can be calculated. This principle has been used extensively to find the masses of heavenly bodies that have satellites. Furthermore, the ratio $$r^3/T^2$$ should be a constant for all satellites of the same parent body (because $$r^3/T^2 = GM/4\pi$$. (See Table).
It is clear from Table that the ratio of $$r^3/T^2$$ is constant, at least to the third digit, for all listed satellites of the Sun, and for those of Jupiter. Small variations in that ratio have two causes—uncertainties in the $$r$$ and $$T$$ data, and perturbations of the orbits due to other bodies. Interestingly, those perturbations can be—and have been—used to predict the location of new planets and moons. This is another verification of Newton’s universal law of gravitation.
MAKING CONNECTIONS
Newton’s universal law of gravitation is modified by Einstein’s general theory of relativity, as we shall see in Particle Physics. Newton’s gravity is not seriously in error—it was and still is an extremely good approximation for most situations. Einstein’s modification is most noticeable in extremely large gravitational fields, such as near black holes. However, general relativity also explains such phenomena as small but long-known deviations of the orbit of the planet Mercury from classical predictions.
# The Case for Simplicity
The development of the universal law of gravitation by Newton played a pivotal role in the history of ideas. While it is beyond the scope of this text to cover that history in any detail, we note some important points. The definition of planet set in 2006 by the International Astronomical Union (IAU) states that in the solar system, a planet is a celestial body that:
1. is in orbit around the Sun,
2. has sufficient mass to assume hydrostatic equilibrium and
3. has cleared the neighborhood around its orbit.
A non-satellite body fulfilling only the first two of the above criteria is classified as “dwarf planet.”
In 2006, Pluto was demoted to a ‘dwarf planet’ after scientists revised their definition of what constitutes a “true” planet.
Parent Satellite Average orbital radius r(km) Period T(y) $$r^3/T^2 (km^3/y^2)$$
Earth Moon
$$3.84 \times 10^5$$
3.84×105
0.07481
$$1.01 \times 10^{19}$$
1.01×1019
Sun Mercury
$$5.79 \times 10^7$$ 5.79
0.2409
$$3,34 \times 10^{24}$$
3.34×1024
Venus
$$1.082 \times 10^8$$
1.082×108
0.6150
$$3.35 \times 10^{24}$$
3.35×1024
Earth
$$1.496 \times 10^8$$
1.496×108
1.000
$$3.35 \times 10^{24}$$
3.35×1024
Mars
$$2.279 \times 10^8$$
2.279×108
1.881
$$3.35 \times 10^{24}$$
3.35×1024
Jupiter
$$7.783 \times 10^8$$
7.783×108
11.86
$$3.35 \times 10^{24}$$
3.35×1024
Saturn
$$1.427 \times 10^9$$
1.427×109
29.46
$$3.35 \times 10^{24}$$
3.35×1024
Neptune
$$4.497 \times 10^9$$
4.497×109
164.8
$$3.35 \times 10^{24}$$
3.35×1024
Pluto
$$5.90 \times 10^9$$
5.90×109
248.3
$$3.33 \times 10^{24}$$
3.33×1024
Jupiter Io
$$4.22 \times 10^5$$
4.22×105
0.00485 (1.77 d)
$$3.19 \times 10^{21}$$
3.19×1021
Europa
$$6.71 \times 10^5$$
6.71×105
0.00972 (3.55 d)
$$3.20 \times 10^{21}$$
3.20×1021
Ganymede
$$1.07 \times 10^6$$
1.07×106
0.0196 (7.16 d)
$$3.19 \times 10^{21}$$
3.19×1021
Callisto
$$1.88 \times 10^6$$
1.88×106
0.0457 (16.19 d)
$$3.20 \times 10^{21}$$
3.20×1021
The universal law of gravitation is a good example of a physical principle that is very broadly applicable. That single equation for the gravitational force describes all situations in which gravity acts. It gives a cause for a vast number of effects, such as the orbits of the planets and moons in the solar system. It epitomizes the underlying unity and simplicity of physics.
Before the discoveries of Kepler, Copernicus, Galileo, Newton, and others, the solar system was thought to revolve around Earth as shown in Figure (a). This is called the Ptolemaic view, for the Greek philosopher who lived in the second century AD. This model is characterized by a list of facts for the motions of planets with no cause and effect explanation. There tended to be a different rule for each heavenly body and a general lack of simplicity.
Figure (b) represents the modern or Copernican model. In this model, a small set of rules and a single underlying force explain not only all motions in the solar system, but all other situations involving gravity. The breadth and simplicity of the laws of physics are compelling. As our knowledge of nature has grown, the basic simplicity of its laws has become ever more evident.
Figure $$\PageIndex{3}$$: (a) The Ptolemaic model of the universe has Earth at the center with the Moon, the planets, the Sun, and the stars revolving about it in complex superpositions of circular paths. This geocentric model, which can be made progressively more accurate by adding more circles, is purely descriptive, containing no hints as to what are the causes of these motions. (b) The Copernican model has the Sun at the center of the solar system. It is fully explained by a small number of laws of physics, including Newton’s universal law of gravitation.
# Summary
• Kepler’s laws are stated for a small mass $$m$$ orbiting a larger mass $$M$$ in near-isolation. Kepler’s laws of planetary motion are then as follows:
Kepler’s first law
The orbit of each planet about the Sun is an ellipse with the Sun at one focus.
Kepler’s second law
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.
Kepler’s third law
The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun:
$\dfrac{T_1^2}{T_2^2} =\dfrac{r_1^3}{r_2^3},$
where T is the period (time for one orbit) and $$r$$ is the average radius of the orbit.
• The period and radius of a satellite’s orbit about a larger body M are related by
$T^2=\frac{4π^2}{GM}r^3$ or $\dfrac{r^3}{T^2} = \dfrac{G}{4\pi^2}M.$
## Contributors
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-01-17T13:36:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7374876141548157, "perplexity": 413.6097214595994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658981.19/warc/CC-MAIN-20190117123059-20190117145059-00046.warc.gz"} |
https://pdglive.lbl.gov/Particle.action?init=0&node=M222&home=MXXX025 | ${\boldsymbol {\boldsymbol c}}$ ${\boldsymbol {\overline{\boldsymbol c}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search
# ${{\boldsymbol \psi}{(4230)}}$ $I^G(J^{PC})$ = $0^-(1^{- -})$
also known as ${{\mathit Y}{(4230)}}$; was ${{\mathit X}{(4230)}}$
The recent measurement of ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \pi}}{{\mathit \pi}}$ (ABLIKIM 2017B) led to a downward shift in the mass of the ${{\mathit \psi}{(4260)}}$, also known as Y(4260), such that a distinction between the ${{\mathit \psi}{(4260)}}$ and ${{\mathit \psi}{(4230)}}$ no longer appears justified. Therefore, starting from this edition, we include the data of ABLIKIM 2017B in this node and have listed the ${{\mathit \psi}{(4230)}}$ in the summary tables instead of the ${{\mathit \psi}{(4260)}}$.
${{\mathit \psi}{(4230)}}$ MASS $4220 \pm15$ MeV
${{\mathit \psi}{(4230)}}$ WIDTH $20\text{ to }100$ MeV | 2020-11-29T17:02:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8914645910263062, "perplexity": 1009.2724477184254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141201836.36/warc/CC-MAIN-20201129153900-20201129183900-00586.warc.gz"} |
http://dlmf.nist.gov/14.21 | # §14.21 Definitions and Basic Properties
## §14.21(i) Associated Legendre Equation
Standard solutions: the associated Legendre functions , , , and . and exist for all values of , , and , except possibly and , which are branch points (or poles) of the functions, in general. When is complex , , and are defined by (14.3.6)–(14.3.10) with replaced by : the principal branches are obtained by taking the principal values of all the multivalued functions appearing in these representations when , and by continuity elsewhere in the -plane with a cut along the interval ; compare §4.2(i). The principal branches of and are real when , and .
## §14.21(ii) Numerically Satisfactory Solutions
When and , a numerically satisfactory pair of solutions of (14.21.1) in the half-plane is given by and .
## §14.21(iii) Properties
Many of the properties stated in preceding sections extend immediately from the -interval to the cut -plane . This includes, for example, the Wronskian relations (14.2.7)–(14.2.11); hypergeometric representations (14.3.6)–(14.3.10) and (14.3.15)–(14.3.20); results for integer orders (14.6.3)–(14.6.5), (14.6.7), (14.6.8), (14.7.6), (14.7.7), and (14.7.11)–(14.7.16); behavior at singularities (14.8.7)–(14.8.16); connection formulas (14.9.11)–(14.9.16); recurrence relations (14.10.3)–(14.10.7). The generating function expansions (14.7.19) (with replaced by ) and (14.7.22) apply when ; (14.7.21) (with replaced by ) applies when . | 2013-05-21T11:48:01 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8762121796607971, "perplexity": 2861.6641596904215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699924051/warc/CC-MAIN-20130516102524-00051-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://lammps.sandia.gov/doc/dump.html | # dump movie command
## Syntax
dump ID group-ID style N file args
• ID = user-assigned name for the dump
• group-ID = ID of the group of atoms to be dumped
• style = atom or atom/gz or atom/mpiio or cfg or cfg/gz or cfg/mpiio or custom or custom/gz or custom/mpiio or dcd or h5md or image or or local or molfile or movie or netcdf or netcdf/mpiio or vtk or xtc or xyz or xyz/gz or xyz/mpiio
• N = dump every this many timesteps
• file = name of file to write dump info to
• args = list of arguments for a particular style
atom args = none
atom/gz args = none
atom/mpiio args = none
cfg args = same as custom args, see below
cfg/gz args = same as custom args, see below
cfg/mpiio args = same as custom args, see below
custom, custom/gz, custom/mpiio args = see below
custom/adios args = same as custom args, discussed on dump adios doc page
dcd args = none
h5md args = discussed on dump h5md doc page
image args = discussed on dump image doc page
local args = see below
molfile args = discussed on dump molfile doc page
movie args = discussed on dump image doc page
netcdf args = discussed on dump netcdf doc page
netcdf/mpiio args = discussed on dump netcdf doc page
vtk args = same as custom args, see below, also dump vtk doc page
xtc args = none
xyz args = none
xyz/gz args = none
xyz/mpiio args = none
• custom or custom/gz or custom/mpiio or netcdf or netcdf/mpiio args = list of atom attributes
possible attributes = id, mol, proc, procp1, type, element, mass,
x, y, z, xs, ys, zs, xu, yu, zu,
xsu, ysu, zsu, ix, iy, iz,
vx, vy, vz, fx, fy, fz,
q, mux, muy, muz, mu,
angmomx, angmomy, angmomz, tqx, tqy, tqz,
c_ID, c_ID[N], f_ID, f_ID[N], v_name
id = atom ID
mol = molecule ID
proc = ID of processor that owns atom
procp1 = ID+1 of processor that owns atom
type = atom type
element = name of atom element, as defined by dump_modify command
mass = atom mass
x,y,z = unscaled atom coordinates
xs,ys,zs = scaled atom coordinates
xu,yu,zu = unwrapped atom coordinates
xsu,ysu,zsu = scaled unwrapped atom coordinates
ix,iy,iz = box image that the atom is in
vx,vy,vz = atom velocities
fx,fy,fz = forces on atoms
q = atom charge
mux,muy,muz = orientation of dipole moment of atom
mu = magnitude of dipole moment of atom
omegax,omegay,omegaz = angular velocity of spherical particle
angmomx,angmomy,angmomz = angular momentum of aspherical particle
tqx,tqy,tqz = torque on finite-size particles
c_ID = per-atom vector calculated by a compute with ID
c_ID[I] = Ith column of per-atom array calculated by a compute with ID, I can include wildcard (see below)
f_ID = per-atom vector calculated by a fix with ID
f_ID[I] = Ith column of per-atom array calculated by a fix with ID, I can include wildcard (see below)
v_name = per-atom vector calculated by an atom-style variable with name
d_name = per-atom floating point vector with name, managed by fix property/atom
i_name = per-atom integer vector with name, managed by fix property/atom
• local args = list of local attributes
possible attributes = index, c_ID, c_ID[I], f_ID, f_ID[I]
index = enumeration of local values
c_ID = local vector calculated by a compute with ID
c_ID[I] = Ith column of local array calculated by a compute with ID, I can include wildcard (see below)
f_ID = local vector calculated by a fix with ID
f_ID[I] = Ith column of local array calculated by a fix with ID, I can include wildcard (see below)
## Examples
dump myDump all atom 100 dump.atom
dump myDump all atom/mpiio 100 dump.atom.mpiio
dump myDump all atom/gz 100 dump.atom.gz
dump 2 subgroup atom 50 dump.run.bin
dump 2 subgroup atom 50 dump.run.mpiio.bin
dump 4a all custom 100 dump.myforce.* id type x y vx fx
dump 4b flow custom 100 dump.%.myforce id type c_myF[3] v_ke
dump 4b flow custom 100 dump.%.myforce id type c_myF[*] v_ke
dump 2 inner cfg 10 dump.snap.*.cfg mass type xs ys zs vx vy vz
dump snap all cfg 100 dump.config.*.cfg mass type xs ys zs id type c_Stress[2]
dump 1 all xtc 1000 file.xtc
## Description
Dump a snapshot of atom quantities to one or more files every N timesteps in one of several styles. The image and movie styles are the exception: the image style renders a JPG, PNG, or PPM image file of the atom configuration every N timesteps while the movie style combines and compresses them into a movie file; both are discussed in detail on the dump image doc page. The timesteps on which dump output is written can also be controlled by a variable. See the dump_modify every command.
Only information for atoms in the specified group is dumped. The dump_modify thresh and region and refresh commands can also alter what atoms are included. Not all styles support these options; see details on the dump_modify doc page.
As described below, the filename determines the kind of output (text or binary or gzipped, one big file or one per timestep, one big file or multiple smaller files).
Note
Because periodic boundary conditions are enforced only on timesteps when neighbor lists are rebuilt, the coordinates of an atom written to a dump file may be slightly outside the simulation box. Re-neighbor timesteps will not typically coincide with the timesteps dump snapshots are written. See the dump_modify pbc command if you with to force coordinates to be strictly inside the simulation box.
Note
Unless the dump_modify sort option is invoked, the lines of atom information written to dump files (typically one line per atom) will be in an indeterminate order for each snapshot. This is even true when running on a single processor, if the atom_modify sort option is on, which it is by default. In this case atoms are re-ordered periodically during a simulation, due to spatial sorting. It is also true when running in parallel, because data for a single snapshot is collected from multiple processors, each of which owns a subset of the atoms.
For the atom, custom, cfg, and local styles, sorting is off by default. For the dcd, xtc, xyz, and molfile styles, sorting by atom ID is on by default. See the dump_modify doc page for details.
The atom/gz, cfg/gz, custom/gz, and xyz/gz styles are identical in command syntax to the corresponding styles without “gz”, however, they generate compressed files using the zlib library. Thus the filename suffix “.gz” is mandatory. This is an alternative approach to writing compressed files via a pipe, as done by the regular dump styles, which may be required on clusters where the interface to the high-speed network disallows using the fork() library call (which is needed for a pipe). For the remainder of this doc page, you should thus consider the atom and atom/gz styles (etc) to be inter-changeable, with the exception of the required filename suffix.
As explained below, the atom/mpiio, cfg/mpiio, custom/mpiio, and xyz/mpiio styles are identical in command syntax and in the format of the dump files they create, to the corresponding styles without “mpiio”, except the single dump file they produce is written in parallel via the MPI-IO library. For the remainder of this doc page, you should thus consider the atom and atom/mpiio styles (etc) to be inter-changeable. The one exception is how the filename is specified for the MPI-IO styles, as explained below.
The precision of values output to text-based dump files can be controlled by the dump_modify format command and its options.
The style keyword determines what atom quantities are written to the file and in what format. Settings made via the dump_modify command can also alter the format of individual values and the file itself.
The atom, local, and custom styles create files in a simple text format that is self-explanatory when viewing a dump file. Some of the LAMMPS post-processing tools described on the Tools doc page, including Pizza.py, work with this format, as does the rerun command.
For post-processing purposes the atom, local, and custom text files are self-describing in the following sense.
The dimensions of the simulation box are included in each snapshot. For an orthogonal simulation box this information is is formatted as:
ITEM: BOX BOUNDS xx yy zz
xlo xhi
ylo yhi
zlo zhi
where xlo,xhi are the maximum extents of the simulation box in the x-dimension, and similarly for y and z. The “xx yy zz” represent 6 characters that encode the style of boundary for each of the 6 simulation box boundaries (xlo,xhi and ylo,yhi and zlo,zhi). Each of the 6 characters is either p = periodic, f = fixed, s = shrink wrap, or m = shrink wrapped with a minimum value. See the boundary command for details.
For triclinic simulation boxes (non-orthogonal), an orthogonal bounding box which encloses the triclinic simulation box is output, along with the 3 tilt factors (xy, xz, yz) of the triclinic box, formatted as follows:
ITEM: BOX BOUNDS xy xz yz xx yy zz
xlo_bound xhi_bound xy
ylo_bound yhi_bound xz
zlo_bound zhi_bound yz
The presence of the text “xy xz yz” in the ITEM line indicates that the 3 tilt factors will be included on each of the 3 following lines. This bounding box is convenient for many visualization programs. The meaning of the 6 character flags for “xx yy zz” is the same as above.
Note that the first two numbers on each line are now xlo_bound instead of xlo, etc, since they represent a bounding box. See the Howto triclinic doc page for a geometric description of triclinic boxes, as defined by LAMMPS, simple formulas for how the 6 bounding box extents (xlo_bound,xhi_bound,etc) are calculated from the triclinic parameters, and how to transform those parameters to and from other commonly used triclinic representations.
The “ITEM: ATOMS” line in each snapshot lists column descriptors for the per-atom lines that follow. For example, the descriptors would be “id type xs ys zs” for the default atom style, and would be the atom attributes you specify in the dump command for the custom style.
For style atom, atom coordinates are written to the file, along with the atom ID and atom type. By default, atom coords are written in a scaled format (from 0 to 1). I.e. an x value of 0.25 means the atom is at a location 1/4 of the distance from xlo to xhi of the box boundaries. The format can be changed to unscaled coords via the dump_modify settings. Image flags can also be added for each atom via dump_modify.
Style custom allows you to specify a list of atom attributes to be written to the dump file for each atom. Possible attributes are listed above and will appear in the order specified. You cannot specify a quantity that is not defined for a particular simulation - such as q for atom style bond, since that atom style doesn’t assign charges. Dumps occur at the very end of a timestep, so atom attributes will include effects due to fixes that are applied during the timestep. An explanation of the possible dump custom attributes is given below.
For style local, local output generated by computes and fixes is used to generate lines of output that is written to the dump file. This local data is typically calculated by each processor based on the atoms it owns, but there may be zero or more entities per atom, e.g. a list of bond distances. An explanation of the possible dump local attributes is given below. Note that by using input from the compute property/local command with dump local, it is possible to generate information on bonds, angles, etc that can be cut and pasted directly into a data file read by the read_data command.
Style cfg has the same command syntax as style custom and writes extended CFG format files, as used by the AtomEye visualization package. Since the extended CFG format uses a single snapshot of the system per file, a wildcard “*” must be included in the filename, as discussed below. The list of atom attributes for style cfg must begin with either “mass type xs ys zs” or “mass type xsu ysu zsu” since these quantities are needed to write the CFG files in the appropriate format (though the “mass” and “type” fields do not appear explicitly in the file). Any remaining attributes will be stored as “auxiliary properties” in the CFG files. Note that you will typically want to use the dump_modify element command with CFG-formatted files, to associate element names with atom types, so that AtomEye can render atoms appropriately. When unwrapped coordinates xsu, ysu, and zsu are requested, the nominal AtomEye periodic cell dimensions are expanded by a large factor UNWRAPEXPAND = 10.0, which ensures atoms that are displayed correctly for up to UNWRAPEXPAND/2 periodic boundary crossings in any direction. Beyond this, AtomEye will rewrap the unwrapped coordinates. The expansion causes the atoms to be drawn farther away from the viewer, but it is easy to zoom the atoms closer, and the interatomic distances are unaffected.
The dcd style writes DCD files, a standard atomic trajectory format used by the CHARMM, NAMD, and XPlor molecular dynamics packages. DCD files are binary and thus may not be portable to different machines. The number of atoms per snapshot cannot change with the dcd style. The unwrap option of the dump_modify command allows DCD coordinates to be written “unwrapped” by the image flags for each atom. Unwrapped means that if the atom has passed through a periodic boundary one or more times, the value is printed for what the coordinate would be if it had not been wrapped back into the periodic box. Note that these coordinates may thus be far outside the box size stored with the snapshot.
The xtc style writes XTC files, a compressed trajectory format used by the GROMACS molecular dynamics package, and described here. The precision used in XTC files can be adjusted via the dump_modify command. The default value of 1000 means that coordinates are stored to 1/1000 nanometer accuracy. XTC files are portable binary files written in the NFS XDR data format, so that any machine which supports XDR should be able to read them. The number of atoms per snapshot cannot change with the xtc style. The unwrap option of the dump_modify command allows XTC coordinates to be written “unwrapped” by the image flags for each atom. Unwrapped means that if the atom has passed through a periodic boundary one or more times, the value is printed for what the coordinate would be if it had not been wrapped back into the periodic box. Note that these coordinates may thus be far outside the box size stored with the snapshot.
The xyz style writes XYZ files, which is a simple text-based coordinate format that many codes can read. Specifically it has a line with the number of atoms, then a comment line that is usually ignored followed by one line per atom with the atom type and the x-, y-, and z-coordinate of that atom. You can use the dump_modify element option to change the output from using the (numerical) atom type to an element name (or some other label). This will help many visualization programs to guess bonds and colors.
Note that atom, custom, dcd, xtc, and xyz style dump files can be read directly by VMD, a popular molecular viewing program.
Dumps are performed on timesteps that are a multiple of N (including timestep 0) and on the last timestep of a minimization if the minimization converges. Note that this means a dump will not be performed on the initial timestep after the dump command is invoked, if the current timestep is not a multiple of N. This behavior can be changed via the dump_modify first command, which can also be useful if the dump command is invoked after a minimization ended on an arbitrary timestep. N can be changed between runs by using the dump_modify every command (not allowed for dcd style). The dump_modify every command also allows a variable to be used to determine the sequence of timesteps on which dump files are written. In this mode a dump on the first timestep of a run will also not be written unless the dump_modify first command is used.
The specified filename determines how the dump file(s) is written. The default is to write one large text file, which is opened when the dump command is invoked and closed when an undump command is used or when LAMMPS exits. For the dcd and xtc styles, this is a single large binary file.
Dump filenames can contain two wildcard characters. If a “*” character appears in the filename, then one file per snapshot is written and the “*” character is replaced with the timestep value. For example, tmp.dump.* becomes tmp.dump.0, tmp.dump.10000, tmp.dump.20000, etc. This option is not available for the dcd and xtc styles. Note that the dump_modify pad command can be used to insure all timestep numbers are the same length (e.g. 00010), which can make it easier to read a series of dump files in order with some post-processing tools.
If a “%” character appears in the filename, then each of P processors writes a portion of the dump file, and the “%” character is replaced with the processor ID from 0 to P-1. For example, tmp.dump.% becomes tmp.dump.0, tmp.dump.1, … tmp.dump.P-1, etc. This creates smaller files and can be a fast mode of output on parallel machines that support parallel I/O for output. This option is not available for the dcd, xtc, and xyz styles.
By default, P = the number of processors meaning one file per processor, but P can be set to a smaller value via the nfile or fileper keywords of the dump_modify command. These options can be the most efficient way of writing out dump files when running on large numbers of processors.
Note that using the “*” and “%” characters together can produce a large number of small dump files!
For the atom/mpiio, cfg/mpiio, custom/mpiio, and xyz/mpiio styles, a single dump file is written in parallel via the MPI-IO library, which is part of the MPI standard for versions 2.0 and above. Using MPI-IO requires two steps. First, build LAMMPS with its MPIIO package installed, e.g.
make yes-mpiio # installs the MPIIO package
make mpi # build LAMMPS for your platform
Second, use a dump filename which contains “.mpiio”. Note that it does not have to end in “.mpiio”, just contain those characters. Unlike MPI-IO restart files, which must be both written and read using MPI-IO, the dump files produced by these MPI-IO styles are identical in format to the files produced by their non-MPI-IO style counterparts. This means you can write a dump file using MPI-IO and use the read_dump command or perform other post-processing, just as if the dump file was not written using MPI-IO.
Note that MPI-IO dump files are one large file which all processors write to. You thus cannot use the “%” wildcard character described above in the filename since that specifies generation of multiple files. You can use the “.bin” suffix described below in an MPI-IO dump file; again this file will be written in parallel and have the same binary format as if it were written without MPI-IO.
If the filename ends with “.bin”, the dump file (or files, if “*” or “%” is also used) is written in binary format. A binary dump file will be about the same size as a text version, but will typically write out much faster. Of course, when post-processing, you will need to convert it back to text format (see the binary2txt tool) or write your own code to read the binary file. The format of the binary file can be understood by looking at the tools/binary2txt.cpp file. This option is only available for the atom and custom styles.
If the filename ends with “.gz”, the dump file (or files, if “*” or “%” is also used) is written in gzipped format. A gzipped dump file will be about 3x smaller than the text version, but will also take longer to write. This option is not available for the dcd and xtc styles.
Note that in the discussion which follows, for styles which can reference values from a compute or fix, like the custom, cfg, or local styles, the bracketed index I can be specified using a wildcard asterisk with the index to effectively specify multiple values. This takes the form “*” or “*n” or “n*” or “m*n”. If N = the size of the vector (for mode = scalar) or the number of columns in the array (for mode = vector), then an asterisk with no numeric values means all indices from 1 to N. A leading asterisk means all indices from 1 to n (inclusive). A trailing asterisk means all indices from n to N (inclusive). A middle asterisk means all indices from m to n (inclusive).
Using a wildcard is the same as if the individual columns of the array had been listed one by one. E.g. these 2 dump commands are equivalent, since the compute stress/atom command creates a per-atom array with 6 columns:
compute myPress all stress/atom NULL
dump 2 all custom 100 tmp.dump id myPress[*]
dump 2 all custom 100 tmp.dump id myPress[1] myPress[2] myPress[3] &
myPress[4] myPress[5] myPress[6]
This section explains the local attributes that can be specified as part of the local style.
The index attribute can be used to generate an index number from 1 to N for each line written into the dump file, where N is the total number of local datums from all processors, or lines of output that will appear in the snapshot. Note that because data from different processors depend on what atoms they currently own, and atoms migrate between processor, there is no guarantee that the same index will be used for the same info (e.g. a particular bond) in successive snapshots.
The c_ID and c_ID[I] attributes allow local vectors or arrays calculated by a compute to be output. The ID in the attribute should be replaced by the actual ID of the compute that has been defined previously in the input script. See the compute command for details. There are computes for calculating local information such as indices, types, and energies for bonds and angles.
Note that computes which calculate global or per-atom quantities, as opposed to local quantities, cannot be output in a dump local command. Instead, global quantities can be output by the thermo_style custom command, and per-atom quantities can be output by the dump custom command.
If c_ID is used as a attribute, then the local vector calculated by the compute is printed. If c_ID[I] is used, then I must be in the range from 1-M, which will print the Ith column of the local array with M columns calculated by the compute. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.
The f_ID and f_ID[I] attributes allow local vectors or arrays calculated by a fix to be output. The ID in the attribute should be replaced by the actual ID of the fix that has been defined previously in the input script.
If f_ID is used as a attribute, then the local vector calculated by the fix is printed. If f_ID[I] is used, then I must be in the range from 1-M, which will print the Ith column of the local with M columns calculated by the fix. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.
Here is an example of how to dump bond info for a system, including the distance and energy of each bond:
compute 1 all property/local batom1 batom2 btype
compute 2 all bond/local dist eng
dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_2[1] c_2[2]
This section explains the atom attributes that can be specified as part of the custom and cfg styles.
The id, mol, proc, procp1, type, element, mass, vx, vy, vz, fx, fy, fz, q attributes are self-explanatory.
Id is the atom ID. Mol is the molecule ID, included in the data file for molecular systems. Proc is the ID of the processor (0 to Nprocs-1) that currently owns the atom. Procp1 is the proc ID+1, which can be convenient in place of a type attribute (1 to Ntypes) for coloring atoms in a visualization program. Type is the atom type (1 to Ntypes). Element is typically the chemical name of an element, which you must assign to each type via the dump_modify element command. More generally, it can be any string you wish to associated with an atom type. Mass is the atom mass. Vx, vy, vz, fx, fy, fz, and q are components of atom velocity and force and atomic charge.
There are several options for outputting atom coordinates. The x, y, z attributes write atom coordinates “unscaled”, in the appropriate distance units (Angstroms, sigma, etc). Use xs, ys, zs if you want the coordinates “scaled” to the box size, so that each value is 0.0 to 1.0. If the simulation box is triclinic (tilted), then all atom coords will still be between 0.0 and 1.0. I.e. actual unscaled (x,y,z) = xs*A + ys*B + zs*C, where (A,B,C) are the non-orthogonal vectors of the simulation box edges, as discussed on the Howto triclinic doc page.
Use xu, yu, zu if you want the coordinates “unwrapped” by the image flags for each atom. Unwrapped means that if the atom has passed through a periodic boundary one or more times, the value is printed for what the coordinate would be if it had not been wrapped back into the periodic box. Note that using xu, yu, zu means that the coordinate values may be far outside the box bounds printed with the snapshot. Using xsu, ysu, zsu is similar to using xu, yu, zu, except that the unwrapped coordinates are scaled by the box size. Atoms that have passed through a periodic boundary will have the corresponding coordinate increased or decreased by 1.0.
The image flags can be printed directly using the ix, iy, iz attributes. For periodic dimensions, they specify which image of the simulation box the atom is considered to be in. An image of 0 means it is inside the box as defined. A value of 2 means add 2 box lengths to get the true value. A value of -1 means subtract 1 box length to get the true value. LAMMPS updates these flags as atoms cross periodic boundaries during the simulation.
The mux, muy, muz attributes are specific to dipolar systems defined with an atom style of dipole. They give the orientation of the atom’s point dipole moment. The mu attribute gives the magnitude of the atom’s dipole moment.
The radius and diameter attributes are specific to spherical particles that have a finite size, such as those defined with an atom style of sphere.
The omegax, omegay, and omegaz attributes are specific to finite-size spherical particles that have an angular velocity. Only certain atom styles, such as sphere define this quantity.
The angmomx, angmomy, and angmomz attributes are specific to finite-size aspherical particles that have an angular momentum. Only the ellipsoid atom style defines this quantity.
The tqx, tqy, tqz attributes are for finite-size particles that can sustain a rotational torque due to interactions with other particles.
The c_ID and c_ID[I] attributes allow per-atom vectors or arrays calculated by a compute to be output. The ID in the attribute should be replaced by the actual ID of the compute that has been defined previously in the input script. See the compute command for details. There are computes for calculating the per-atom energy, stress, centro-symmetry parameter, and coordination number of individual atoms.
Note that computes which calculate global or local quantities, as opposed to per-atom quantities, cannot be output in a dump custom command. Instead, global quantities can be output by the thermo_style custom command, and local quantities can be output by the dump local command.
If c_ID is used as a attribute, then the per-atom vector calculated by the compute is printed. If c_ID[I] is used, then I must be in the range from 1-M, which will print the Ith column of the per-atom array with M columns calculated by the compute. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.
The f_ID and f_ID[I] attributes allow vector or array per-atom quantities calculated by a fix to be output. The ID in the attribute should be replaced by the actual ID of the fix that has been defined previously in the input script. The fix ave/atom command is one that calculates per-atom quantities. Since it can time-average per-atom quantities produced by any compute, fix, or atom-style variable, this allows those time-averaged results to be written to a dump file.
If f_ID is used as a attribute, then the per-atom vector calculated by the fix is printed. If f_ID[I] is used, then I must be in the range from 1-M, which will print the Ith column of the per-atom array with M columns calculated by the fix. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.
The v_name attribute allows per-atom vectors calculated by a variable to be output. The name in the attribute should be replaced by the actual name of the variable that has been defined previously in the input script. Only an atom-style variable can be referenced, since it is the only style that generates per-atom values. Variables of style atom can reference individual atom attributes, per-atom atom attributes, thermodynamic keywords, or invoke other computes, fixes, or variables when they are evaluated, so this is a very general means of creating quantities to output to a dump file.
The d_name and i_name attributes allow to output custom per atom floating point or integer properties that are managed by fix property/atom.
See the Modify doc page for information on how to add new compute and fix styles to LAMMPS to calculate per-atom quantities which could then be output into dump files.
## Restrictions
To write gzipped dump files, you must either compile LAMMPS with the -DLAMMPS_GZIP option or use the styles from the COMPRESS package. See the Build settings doc page for details.
The atom/gz, cfg/gz, custom/gz, and xyz/gz styles are part of the COMPRESS package. They are only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
The atom/mpiio, cfg/mpiio, custom/mpiio, and xyz/mpiio styles are part of the MPIIO package. They are only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
The xtc style is part of the MISC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
## Default
The defaults for the image and movie styles are listed on the dump image doc page. | 2019-04-19T02:31:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5119351744651794, "perplexity": 3464.080562378239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578526966.26/warc/CC-MAIN-20190419021416-20190419043416-00289.warc.gz"} |
https://pos.sissa.it/367/015/ | Volume 367 - XXIX International Symposium on Lepton Photon Interactions at High Energies (LeptonPhoton2019) - Collider BSM
Constraints on New Physics from B Mesons
M. Blanke
Full text: pdf
Pre-published on: 2019 November 07
Published on: 2019 December 17
Abstract
These proceedings review the status of New Physics contributions to flavour violating $B$ decays. The anomalies in charged and neutral current $B$ decays related to lepton flavour universality violation have received a substantial amount of attention over the past years, and we discuss the current status in light of the new data presented earlier this year. We also recall a tension in the neutral $B$ meson mixing observables $\Delta M_d$ and $\Delta M_s$ and in particular their ratio, when compared with their SM predictions obtained using tree-level determinations of the CKM matrix and the recent lattice QCD results for the relevant hadronic matrix elements. Last but not least, we advocate kaon physics as a unique probe of very high energy scales and briefly discuss the current status of $\varepsilon'/\varepsilon$ and $K\to\pi\nu\bar\nu$.
DOI: https://doi.org/10.22323/1.367.0015
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-01-19T07:23:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.422244131565094, "perplexity": 1127.13438230048}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594333.5/warc/CC-MAIN-20200119064802-20200119092802-00557.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Amerle.frank | ## Merle, Frank
Compute Distance To:
Author ID: merle.frank Published as: Merle, Frank; Merle, F.; Merle, Franck more...less Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · IdRef · theses.fr
Documents Indexed: 159 Publications since 1987 4 Contributions as Editor Co-Authors: 33 Co-Authors with 137 Joint Publications 1,175 Co-Co-Authors
all top 5
### Co-Authors
26 single-authored 35 Martel, Yvan 28 Raphael, Pierre 24 Kenig, Carlos Eduardo 23 Zaag, Hatem 20 Duyckaerts, Thomas 9 Szeftel, Jérémie 6 Rodnianski, Igor 5 Peletier, Lambertus Adrianus 4 Berestycki, Henri 4 Hilhorst, Danielle 4 Mimura, Masayasu 4 Pakdaman, Khashayar 3 Brézis, Haïm 3 Collot, Charles 3 Matano, Hiroshi 2 Balabane, Mikhael 2 Cazenave, Thierry 2 Côte, Raphaël 2 Douady, Adrien 2 Fibich, Gadi 2 Filippas, Stathis 2 Glangetas, Léo 2 Golse, François 2 Rivière, Tristan 2 Tsai, Tai-Peng 2 Tsutsumi, Yoshio 2 Vega, Luis 1 Antonini, Christophe 1 Fermanian-Kammerer, Clotilde 1 Mizumachi, Tetsu 1 Nakanishi, Kenji 1 Roudenko, Svetlana 1 Serrin, James
all top 5
### Serials
16 Communications in Mathematical Physics 9 IMRN. International Mathematics Research Notices 9 Comptes Rendus de l’Académie des Sciences. Série I 7 Communications on Pure and Applied Mathematics 7 Geometric and Functional Analysis. GAFA 7 Séminaire Équations aux Dérivées Partielles 6 Archive for Rational Mechanics and Analysis 6 Duke Mathematical Journal 6 Inventiones Mathematicae 5 American Journal of Mathematics 5 Journal of Functional Analysis 5 Annals of Mathematics. Second Series 4 Mathematische Annalen 4 Journal of the American Mathematical Society 4 Discrete and Continuous Dynamical Systems 4 Journal of the European Mathematical Society (JEMS) 4 Networks and Heterogeneous Media 3 Journal of Differential Equations 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Nonlinearity 2 Acta Mathematica 2 Indiana University Mathematics Journal 2 Transactions of the American Mathematical Society 2 Physica D 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Cambridge Journal of Mathematics 2 Séminaire Laurent Schwartz. EDP et Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Russian Mathematical Surveys 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Methods and Applications of Analysis 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 Revista Matemática Complutense 1 Communications on Pure and Applied Analysis 1 Journal of Hyperbolic Differential Equations 1 IMRP. International Mathematics Research Papers
all top 5
### Fields
161 Partial differential equations (35-XX) 22 Dynamical systems and ergodic theory (37-XX) 8 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Ordinary differential equations (34-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX)
### Citations contained in zbMATH Open
138 Publications have been cited 5,267 times in 2,008 Documents Cited by Year
Uniform estimates and blow-up behavior for solutions of $$-\Delta{} u =V(x) e^ u$$ in two dimensions. Zbl 0746.35006
Brézis, Haïm; Merle, Frank
1991
Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125
Kenig, Carlos E.; Merle, Frank
2006
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202
Kenig, Carlos E.; Merle, Frank
2008
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263
Merle, Frank; Raphaël, Pierre
2005
Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141
Merle, F.
1993
On universality of blow up profile for $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
2004
Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021
Merle, Frank
1990
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Compactness at blow-up time for $$L^2$$ solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126
Merle, F.; Vega, L.
1998
On a sharp lower bound on the blow-up rate for the $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1075.35077
Merle, Frank; Raphaël, Pierre
2006
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2011
L$${}^ 2$$ concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047
Merle, Frank; Tsutsumi, Yoshio
1990
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
2003
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2013
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
2005
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Stability of the blow-up profile for equations of the type $$u_ t=\Delta u+| u| ^{p-1}u$$. Zbl 0872.35049
Merle, Frank; Zaag, Hatem
1997
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
2001
A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058
Martel, Yvan; Merle, Frank
2000
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
2009
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Scattering for $$\dot {H}^{1/2}$$ bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
2010
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
2009
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2012
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
2008
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154
Merle, F.
1988
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Quantization effects for $$-\Delta u=u(1-| u|^ 2)$$ in $$\mathbb{R}^ 2$$. Zbl 0809.35019
Brézis, Haïm; Merle, Frank; Rivière, Tristan
1994
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2012
Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012
Merle, Frank
1992
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2013
A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086
Merle, Frank; Zaag, Hatem
2000
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
2003
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
2011
On uniqueness and continuation properties after blow-up time of self- similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass. Zbl 0767.35084
Merle, Frank
1992
Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158
1988
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
2005
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
2007
Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204
Merle, Frank; Zaag, Hatem
2012
Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044
Merle, Frank; Zaag, Hatem
1998
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137
Glangetas, L.; Merle, F.
1994
Nonexistence of minimal blow-up solutions of equations $$iu_ t = -\Delta u - k(x)| u|^{4/N} u$$ in $$\mathbb{R}^ N$$. Zbl 0846.35129
Merle, Franck
1996
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046
Merle, Frank; Zaag, Hatem
2008
Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138
Glangetas, L.; Merle, F.
1994
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2014
Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2017
On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134
Merle, Frank; Zaag, Hatem
2015
Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024
Merle, F.; Zaag, H.
1998
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
2011
$$L^2$$ stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
2003
Proof of a spectral property related to the singularity formation for the $$L^{2}$$ critical nonlinear Schrödinger equation. Zbl 1100.35097
Fibich, Gadi; Merle, Frank; Raphaël, Pierre
2006
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view. Zbl 0971.35038
Fermanian Kammerer, C.; Merle, F.; Zaag, H.
2000
Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025
Merle, F.; Peletier, L. A.
1991
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Blow-up results of virial type for Zakharov equations. Zbl 0858.35117
Merle, Frank
1996
Blow up of the critical norm for some radial $$L^2$$ super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
2008
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
2012
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2015
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
2001
The instability of Bourgain-Wang solutions for the $$L^2$$ critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2013
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
2005
Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078
Merle, F.
1989
Stable self-similar blow-up dynamics for slightly $$L^{2}$$ super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2010
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2011
Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case. Zbl 0719.35004
Merle, F.; Peletier, L. A.
1990
Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062
Merle, Frank; Zaag, Hatem
2016
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
2011
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case. Zbl 0771.35008
Merle, F.; Peletier, L. A.
1992
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064
Côte, Raphaël; Kenig, Carlos E.; Merle, Frank
2008
Self-focusing on bounded domains. Zbl 0980.35154
2001
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2014
Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014
Merle, Frank
1996
Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020
Merle, Frank; Zaag, Hatem
1997
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
2020
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043
Filippas, Stathis; Merle, Frank
1995
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2015
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
2005
Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094
Merle, F.
1992
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
2002
On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384
Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie
2022
Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292
Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank
2022
Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2021
Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253
Collot, Charles; Merle, Frank; Raphaël, Pierre
2020
On strongly anisotropic type I blowup. Zbl 1432.35124
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2020
Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2020
Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2019
Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111
Martel, Yvan; Merle, Frank
2018
Universality of blow up profile for small blow up solutions to the energy critical wave map equation. Zbl 1421.35038
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2018
Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181
Merle, Frank; Zaag, Hatem
2018
Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276
Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank
2017
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Stability of ODE blow-up for the energy critical semilinear heat equation. (Stabilité de l’explosion type EDO pour l’équation de la chaleur énergie critique.) Zbl 1364.35156
Collot, Charles; Merle, Frank; Raphaël, Pierre
2017
Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062
Merle, Frank; Zaag, Hatem
2016
Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166
Martel, Yvan; Merle, Frank
2016
Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315
Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre
2016
Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2016
On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134
Merle, Frank; Zaag, Hatem
2015
Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2015
Type II blow up for the energy supercritical NLS. Zbl 1347.35215
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2015
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2015
On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191
Martel, Yvan; Merle, Frank
2015
Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2014
Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2014
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2014
Near soliton dynamics and singularity formation for $$L^2$$ critical problems. Zbl 1304.35650
Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J.
2014
Asymptotics for critical nonlinear dispersive equations. Zbl 1373.35049
Merle, Frank
2014
Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2013
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2013
The instability of Bourgain-Wang solutions for the $$L^2$$ critical NLS. Zbl 1294.35145
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2013
Blow up and near soliton dynamics for the $$L^2$$ critical gKdV equation. Zbl 1319.35224
Martel, Yvan; Merle, Frank; Raphaël, Pierre
2013
Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2012
Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank
2012
Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204
Merle, Frank; Zaag, Hatem
2012
Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320
Merle, Frank; Zaag, Hatem
2012
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019
Merle, Frank
2012
Two blow-up regimes for $$L^2$$. Zbl 1280.35140
Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie
2012
Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank
2011
Construction of multi-soliton solutions for the $$L^2$$-supercritical gKdV and NLS equations. Zbl 1273.35234
Côte, Raphaël; Martel, Yvan; Merle, Frank
2011
Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136
Kenig, Carlos E.; Merle, Frank
2011
Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045
Martel, Yvan; Merle, Frank
2011
Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088
Matano, Hiroshi; Merle, Frank
2011
Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121
Martel, Yvan; Merle, Frank
2011
Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor
2011
Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119
Kenig, Carlos E.; Merle, Frank
2011
Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126
Merle, Frank; Zaag, Hatem
2011
Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248
Martel, Yvan; Merle, Frank
2011
Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142
Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana
2011
Scattering for $$\dot {H}^{1/2}$$ bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180
Kenig, Carlos E.; Merle, Frank
2010
Stable self-similar blow-up dynamics for slightly $$L^{2}$$ super-critical NLS equations. Zbl 1204.35153
Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie
2010
Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267
Martel, Yvan; Merle, Frank; Mizumachi, Tetsu
2010
Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165
Martel, Yvan; Merle, Frank
2010
Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150
Duyckaerts, Thomas; Merle, Frank
2009
Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084
Matano, Hiroshi; Merle, Frank
2009
Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291
Martel, Yvan; Merle, Frank
2009
Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation. Zbl 1179.35189
Duyckaerts, Thomas; Merle, Frank
2009
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202
Kenig, Carlos E.; Merle, Frank
2008
Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043
Duyckaerts, Thomas; Merle, Frank
2008
Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068
Martel, Yvan; Merle, Frank
2008
Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046
Merle, Frank; Zaag, Hatem
2008
Blow up of the critical norm for some radial $$L^2$$ super critical nonlinear Schrödinger equations. Zbl 1188.35182
Merle, Frank; Raphaël, Pierre
2008
Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064
Côte, Raphaël; Kenig, Carlos E.; Merle, Frank
2008
Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062
Martel, Yvan; Merle, Frank
2008
Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164
Martel, Yvan; Merle, Frank
2008
Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070
Merle, Frank; Zaag, Hatem
2007
Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125
Kenig, Carlos E.; Merle, Frank
2006
On a sharp lower bound on the blow-up rate for the $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1075.35077
Merle, Frank; Raphaël, Pierre
2006
Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093
Martel, Yvan; Merle, Frank
2006
Stability in $$H^1$$ of the sum of $$K$$ solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2006
Proof of a spectral property related to the singularity formation for the $$L^{2}$$ critical nonlinear Schrödinger equation. Zbl 1100.35097
Fibich, Gadi; Merle, Frank; Raphaël, Pierre
2006
Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051
Kenig, Carlos E.; Merle, Frank
2006
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263
Merle, Frank; Raphaël, Pierre
2005
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137
Merle, Frank; Raphaël, Pierre
2005
Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171
Martel, Yvan; Merle, Frank
2005
Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055
Merle, Frank; Zaag, Hatem
2005
On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478
Merle, Frank; Zaag, Hatem
2005
On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075
Merle, Frank; Raphael, Pierre
2005
On universality of blow up profile for $$L^2$$ critical nonlinear Schrödinger equation. Zbl 1067.35110
Merle, Frank; Raphaël, Pierre
2004
On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098
Matano, Hiroshi; Merle, Frank
2004
Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114
Martel, Yvan; Merle, Frank
2004
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135
Merle, Frank; Raphaël, Pierre
2003
Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043
Merle, Frank; Zaag, Hatem
2003
$$L^2$$ stability of solitons for KdV equation. Zbl 1022.35061
Merle, F.; Vega, L.
2003
Qualitative results on the generalized critical KdV equation. Zbl 1044.35074
Martel, Yvan; Merle, Frank
2003
Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098
Martel, Yvan; Merle, Frank; Tsai, Tai-Peng
2002
Blow up in finite time and dynamics of blow up solutions for the $$L^2$$-critical generalized KdV equation. Zbl 0996.35064
Martel, Yvan; Merle, Frank
2002
Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081
Martel, Yvan; Merle, Frank
2002
Nonexistence of blow-up solution with minimal $$L^2$$-mass for the critical gKdV equation. Zbl 1033.35102
Martel, Yvan; Merle, Frank
2002
O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039
Merle, Frank; Zaag, Hatem
2002
Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073
Martel, Yvan; Merle, Frank
2001
Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128
Merle, Frank
2001
Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071
Martel, Y.; Merle, F.
2001
Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090
Antonini, Christophe; Merle, Frank
2001
Self-focusing on bounded domains. Zbl 0980.35154
2001
Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044
Merle, Frank; Zaag, Hatem
2001
...and 38 more Documents
all top 5
### Cited by 1,493 Authors
73 Merle, Frank 45 Martel, Yvan 45 Zaag, Hatem 44 Wei, Juncheng 40 Raphael, Pierre 34 Kenig, Carlos Eduardo 32 Bartolucci, Daniele 31 Lin, Chang-Shou 28 Muñoz, Claudio 25 Musso, Monica 24 Krieger, Joachim 24 Zhang, Jian 22 Saanouni, Tarek 21 Duyckaerts, Thomas 20 Roudenko, Svetlana 20 Zhu, Shihui 19 Miao, Changxing 19 Nakanishi, Kenji 19 Zhao, Lifeng 18 Côte, Raphaël 18 Del Pino, Manuel A. 18 Ding, Yanheng 18 Schlag, Wilhelm 17 Donninger, Roland 17 Mizoguchi, Noriko 17 Souplet, Philippe 17 Tarantello, Gabriella 17 Zheng, Jiqiang 16 Holmer, Justin 16 Yang, Wen 16 Zhou, Chunqin 15 Dinh, Van Duong 15 Dodson, Benjamin G. 15 Guo, Boling 15 Lee, Youngae 15 Martinazzi, Luca 15 Visan, Monica 14 Farah, Luiz Gustavo 14 Lawrie, Andrew G. W. 14 Malchiodi, Andrea 14 Tataru, Daniel 13 Cuccagna, Scipio 13 Ghoul, Tej-Eddine 13 Jevnikar, Aleks Yang Wen 13 Murphy, Jason 13 Suzuki, Takashi 13 Xu, Guixiang 13 Zhang, Xiaoyi 12 Ibrahim, Slim 12 Killip, Rowan 12 Kowalczyk, Michał 12 Nguyen, Van Tien 12 Wang, Guofang 12 Yang, Kai 11 Bahouri, Hajer 11 Jost, Jürgen 11 Maeda, Masaya 11 Masmoudi, Nader 11 Miyamoto, Yasuhito 10 Cazenave, Thierry 10 Jendrej, Jacek 10 Liu, Yue 10 Zhang, Lei 9 Carles, Rémi 9 Collot, Charles 9 Fibich, Gadi 9 Guzmán, Carlos M. 9 Hamza, Mohamed Ali 9 Li, Dong 9 Pastor, Ademir 9 Pistoia, Angela 9 Szeftel, Jérémie 9 Tzvetkov, Nikolay 8 Colliander, James E. 8 Deng, Shengbing 8 Fang, Daoyuan 8 Gan, Zaihui 8 Gao, Yanfang 8 Grossi, Massimo 8 Guo, Zihua 8 Klein, Christian 8 Lei, Yutian 8 Lenzmann, Enno 8 Li, Xiaoguang 8 Pausader, Benoît 8 Perelman, Galina 8 Struwe, Michael 8 Tao, Terence 8 Visciglia, Nicola 8 Wang, Zhong 8 Zhang, Jian 8 Zhao, Zehua 7 Akahori, Takafumi 7 Banica, Valeria 7 Cheng, Xing 7 Cho, Yonggeun 7 Choe, Kwangseok 7 D’Aprile, Teresa 7 Forcella, Luigi 7 Galaktionov, Victor Aleksandrovich ...and 1,393 more Authors
all top 5
### Cited in 249 Serials
151 Journal of Differential Equations 99 Journal of Functional Analysis 84 Calculus of Variations and Partial Differential Equations 82 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 78 Journal of Mathematical Analysis and Applications 77 Communications in Mathematical Physics 65 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 62 Communications in Partial Differential Equations 54 Discrete and Continuous Dynamical Systems 51 Transactions of the American Mathematical Society 48 Journal of Mathematical Physics 41 Archive for Rational Mechanics and Analysis 36 Communications on Pure and Applied Analysis 33 Mathematische Annalen 29 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Physica D 26 Communications in Contemporary Mathematics 25 Duke Mathematical Journal 24 Proceedings of the American Mathematical Society 24 SIAM Journal on Mathematical Analysis 24 Séminaire Laurent Schwartz. EDP et Applications 23 Advances in Mathematics 21 Acta Mathematica Sinica. English Series 20 Nonlinearity 20 Inventiones Mathematicae 19 NoDEA. Nonlinear Differential Equations and Applications 19 Journal of Evolution Equations 19 Annals of PDE 18 Journal of Hyperbolic Differential Equations 18 Analysis & PDE 17 Communications on Pure and Applied Mathematics 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 15 Applicable Analysis 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 14 Journal of the European Mathematical Society (JEMS) 13 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 Journal d’Analyse Mathématique 12 Journal of the American Mathematical Society 12 Journal of Dynamics and Differential Equations 12 Science China. Mathematics 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Nonlinear Analysis. Real World Applications 10 Revista Matemática Iberoamericana 10 The Journal of Geometric Analysis 9 Applied Mathematics Letters 9 Nonlinear Analysis. Theory, Methods & Applications 8 Mathematical Methods in the Applied Sciences 8 Applied Mathematics and Computation 8 Mathematische Zeitschrift 8 Journal of Nonlinear Science 8 Discrete and Continuous Dynamical Systems. Series B 8 Advanced Nonlinear Studies 7 Memoirs of the American Mathematical Society 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 Geometric and Functional Analysis. GAFA 7 Bulletin des Sciences Mathématiques 7 Annales Henri Poincaré 7 Boundary Value Problems 6 Journal of Computational Physics 6 Bulletin of the American Mathematical Society. New Series 6 Annals of Mathematics. Second Series 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 6 Discrete and Continuous Dynamical Systems. Series S 6 Advances in Nonlinear Analysis 5 Reviews in Mathematical Physics 5 Indiana University Mathematics Journal 5 Manuscripta Mathematica 5 Monatshefte für Mathematik 5 Chinese Annals of Mathematics. Series B 5 Asymptotic Analysis 5 Communications in Nonlinear Science and Numerical Simulation 5 Milan Journal of Mathematics 4 Computers & Mathematics with Applications 4 Annales de l’Institut Fourier 4 Bulletin de la Société Mathématique de France 4 Journal of Computational and Applied Mathematics 4 SIAM Journal on Numerical Analysis 4 SIAM Journal on Scientific Computing 4 Journal of Inequalities and Applications 4 Communications in Mathematics and Statistics 4 Journal of Elliptic and Parabolic Equations 4 SN Partial Differential Equations and Applications 3 Rocky Mountain Journal of Mathematics 3 Mathematics of Computation 3 Acta Mathematica 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Illinois Journal of Mathematics 3 Journal of the Korean Mathematical Society 3 Journal für die Reine und Angewandte Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 Acta Applicandae Mathematicae 3 Applied Numerical Mathematics 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Mediterranean Journal of Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 149 more Serials
all top 5
### Cited in 46 Fields
1,911 Partial differential equations (35-XX) 145 Dynamical systems and ergodic theory (37-XX) 132 Quantum theory (81-XX) 128 Fluid mechanics (76-XX) 126 Global analysis, analysis on manifolds (58-XX) 86 Differential geometry (53-XX) 71 Numerical analysis (65-XX) 59 Operator theory (47-XX) 55 Statistical mechanics, structure of matter (82-XX) 49 Calculus of variations and optimal control; optimization (49-XX) 42 Functional analysis (46-XX) 38 Ordinary differential equations (34-XX) 38 Optics, electromagnetic theory (78-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 24 Biology and other natural sciences (92-XX) 21 Real functions (26-XX) 20 Mechanics of deformable solids (74-XX) 14 Functions of a complex variable (30-XX) 13 Probability theory and stochastic processes (60-XX) 12 Potential theory (31-XX) 12 Mechanics of particles and systems (70-XX) 12 Relativity and gravitational theory (83-XX) 10 Systems theory; control (93-XX) 9 Astronomy and astrophysics (85-XX) 8 Integral equations (45-XX) 5 Special functions (33-XX) 4 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Measure and integration (28-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2023-03-31T03:52:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5118027925491333, "perplexity": 11759.508614831153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00375.warc.gz"} |
http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture7_2.htm | ##### Personal tools
•
You are here: Home Arithmetic Coding
# Arithmetic Coding
##### Document Actions
Introduction :: Probability Models :: Applications
## Probability models
Performance of the AC depends on having a good model for the source probabilities. The better the model, the better it might be expected that the code performs. In principle, any probabilistic model can be used. We mention here some useful concepts in developing one.
Suppose, as before, we deal with the case of independent events. We have outcomes a , b , and , with probabilities and . Let l be the number of outcomes (number of coin tosses). could be anywhere in the range [0,1], and we may not have any predisposition toward one value. We model this ambivalence by saying that
That is, it is uniformly distributed. This is a prior probability . If we had some predisposition about , this could be incorporated into the prior model (using something like a distribution, for example). The whole point of Bayesian estimation (which is what we find we are talking about here) is to merge our prior inclinations in with the observations. This is a problem of inference, which we can state this way: given a sequence of F bits, of which are a s and are b s, infer . The inference is accomplished by the posterior ("after'') -- the probability of after a measurement is made. We write
Now why this? Well, we can write down the conditional probability in the numerator:
(describe why). As we have seen elsewhere, it seems that the conditioning is always easiest they way you don't need it. We also find
So we could infer as the most probable value (the maximizer) of the posterior. For example, we find , with maximum of . Or we could infer based on the mean, which is 3/5. We also want to be able to make predictions. Given a sequence of length F as evidence we find the prediction of drawing an a as
Note that in this case, we are using the entire posterior probability, so we incorporate all of our uncertainty about p a . We also have (by its definition), so our predictor is
This update rule is known as Laplace's rule, and is the rule that was used in the coder above. We could write this as
Another model, known as the Dirichlet model, is more "responsive'':
Typically, is small, like 0.01.
This is not the only possible rule, and doesn't necessarily take into account the relationship that might exist between dependent variables.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 17). Arithmetic Coding. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture7_2.htm. This work is licensed under a Creative Commons License | 2017-09-26T21:47:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.873839259147644, "perplexity": 638.04998234002}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818696696.79/warc/CC-MAIN-20170926212817-20170926232817-00153.warc.gz"} |
http://pdglive.lbl.gov/Particle.action?node=M177&init=0&home=MXXX030 | ${\boldsymbol {\boldsymbol b}}$ ${\boldsymbol {\overline{\boldsymbol b}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search
# ${{\boldsymbol \Upsilon}_{{2}}{(1D)}}$ $I^G(J^{PC})$ = $0^-(2^{- -})$
was ${{\mathit \Upsilon}{(1D)}}$
First observed by BONVICINI 2004 in the decay to ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit \Upsilon}{(1S)}}$ and confirmed by DEL-AMO-SANCHEZ 2010R in the decay to ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \Upsilon}{(1S)}}$ . Data consistent with $\mathit J{}^{P} = 2{}^{-}$. The states with $\mathit J = 1$ and 3 also possibly seen, but need confirmation. | 2019-12-05T18:20:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8691096305847168, "perplexity": 2988.2765277714666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540481281.1/warc/CC-MAIN-20191205164243-20191205192243-00134.warc.gz"} |
https://control.com/textbook/creative-commons-attribution-license/legal-code/ | • Legal Code
# Legal Code
By exercising the Licensed Rights (defined below), You accept and agree to be bound by the terms and conditions of this Creative Commons Attribution 4.0 International Public License ("Public License"). To the extent this Public License may be interpreted as a contract, You are granted the Licensed Rights in consideration of Your acceptance of these terms and conditions, and the Licensor grants You such rights in consideration of benefits the Licensor receives from making the Licensed Material available under these terms and conditions.
Section 1 – Definitions.
a. Adapted Material means material subject to Copyright and Similar Rights that is derived from or based upon the Licensed Material and in which the Licensed Material is translated, altered, arranged, transformed, or otherwise modified in a manner requiring permission under the Copyright and Similar Rights held by the Licensor. For purposes of this Public License, where the Licensed Material is a musical work, performance, or sound recording, Adapted Material is always produced where the Licensed Material is synched in timed relation with a moving image.
c. Copyright and Similar Rights means copyright and/or similar rights closely related to copyright including, without limitation, performance, broadcast, sound recording, and Sui Generis Database Rights, without regard to how the rights are labeled or categorized. For purposes of this Public License, the rights specified in Section 2(b)(1)-(2) are not Copyright and Similar Rights.
d. Effective Technological Measures means those measures that, in the absence of proper authority, may not be circumvented under laws fulfilling obligations under Article 11 of the WIPO Copyright Treaty adopted on December 20, 1996, and/or similar international agreements.
e. Exceptions and Limitations means fair use, fair dealing, and/or any other exception or limitation to Copyright and Similar Rights that applies to Your use of the Licensed Material.
f. Licensed Material means the artistic or literary work, database, or other material to which the Licensor applied this Public License.
g. Licensed Rights means the rights granted to You subject to the terms and conditions of this Public License, which are limited to all Copyright and Similar Rights that apply to Your use of the Licensed Material and that the Licensor has authority to license.
h. Licensor means the individual(s) or entity(ies) granting rights under this Public License.
i. Share means to provide material to the public by any means or process that requires permission under the Licensed Rights, such as reproduction, public display, public performance, distribution, dissemination, communication, or importation, and to make material available to the public including in ways that members of the public may access the material from a place and at a time individually chosen by them.
j. Sui Generis Database Rights means rights other than copyright resulting from Directive 96/9/EC of the European Parliament and of the Council of 11 March 1996 on the legal protection of databases, as amended and/or succeeded, as well as other essentially equivalent rights anywhere in the world.
k. You means the individual or entity exercising the Licensed Rights under this Public License. Your has a corresponding meaning.
Section 2 – Scope.
1. Subject to the terms and conditions of this Public License, the Licensor hereby grants You a worldwide, royalty-free, non-sublicensable, non-exclusive, irrevocable license to exercise the Licensed Rights in the Licensed Material to:
A. reproduce and Share the Licensed Material, in whole or in part; and
B. produce, reproduce, and Share Adapted Material.
2. Exceptions and Limitations. For the avoidance of doubt, where Exceptions and Limitations apply to Your use, this Public License does not apply, and You do not need to comply with its terms and conditions.
3. Term. The term of this Public License is specified in Section 6(a).
4. Media and formats; technical modifications allowed. The Licensor authorizes You to exercise the Licensed Rights in all media and formats whether now known or hereafter created, and to make technical modifications necessary to do so. The Licensor waives and/or agrees not to assert any right or authority to forbid You from making technical modifications necessary to exercise the Licensed Rights, including technical modifications necessary to circumvent Effective Technological Measures. For purposes of this Public License, simply making modifications authorized by this Section 2(a)(4) never produces Adapted Material.
5. Downstream recipients.
A. Offer from the Licensor – Licensed Material. Every recipient of the Licensed Material automatically receives an offer from the Licensor to exercise the Licensed Rights under the terms and conditions of this Public License.
B. No downstream restrictions. You may not offer or impose any additional or different terms or conditions on, or apply any Effective Technological Measures to, the Licensed Material if doing so restricts exercise of the Licensed Rights by any recipient of the Licensed Material.
6. No endorsement. Nothing in this Public License constitutes or may be construed as permission to assert or imply that You are, or that Your use of the Licensed Material is, connected with, or sponsored, endorsed, or granted official status by, the Licensor or others designated to receive attribution as provided in Section 3(a)(1)(A)(i).
b. Other rights.
1. Moral rights, such as the right of integrity, are not licensed under this Public License, nor are publicity, privacy, and/or other similar personality rights; however, to the extent possible, the Licensor waives and/or agrees not to assert any such rights held by the Licensor to the limited extent necessary to allow You to exercise the Licensed Rights, but not otherwise.
3. To the extent possible, the Licensor waives any right to collect royalties from You for the exercise of the Licensed Rights, whether directly or through a collecting society under any voluntary or waivable statutory or compulsory licensing scheme. In all other cases the Licensor expressly reserves any right to collect such royalties.
1. If You Share the Licensed Material (including in modified form), You must:
A. retain the following if it is supplied by the Licensor with the Licensed Material:
i. identification of the creator(s) of the Licensed Material and any others designated to receive attribution, in any reasonable manner requested by the Licensor (including by pseudonym if designated);
iii. a notice that refers to this Public License;
iv. a notice that refers to the disclaimer of warranties;
v. a URI or hyperlink to the Licensed Material to the extent reasonably practicable;
B. indicate if You modified the Licensed Material and retain an indication of any previous modifications; and
2. You may satisfy the conditions in Section 3(a)(1) in any reasonable manner based on the medium, means, and context in which You Share the Licensed Material. For example, it may be reasonable to satisfy the conditions by providing a URI or hyperlink to a resource that includes the required information.
3. If requested by the Licensor, You must remove any of the information required by Section 3(a)(1)(A) to the extent reasonably practicable.
Section 4 – Sui Generis Database Rights.
Where the Licensed Rights include Sui Generis Database Rights that apply to Your use of the Licensed Material:
a. for the avoidance of doubt, Section 2(a)(1) grants You the right to extract, reuse, reproduce, and Share all or a substantial portion of the contents of the database;
b. if You include all or a substantial portion of the database contents in a database in which You have Sui Generis Database Rights, then the database in which You have Sui Generis Database Rights (but not its individual contents) is Adapted Material; and
c. You must comply with the conditions in Section 3(a) if You Share all or a substantial portion of the contents of the database.
For the avoidance of doubt, this Section 4 supplements and does not replace Your obligations under this Public License where the Licensed Rights include other Copyright and Similar Rights.
Section 5 – Disclaimer of Warranties and Limitation of Liability.
a. Unless otherwise separately undertaken by the Licensor, to the extent possible, the Licensor offers the Licensed Material as-is and as-available, and makes no representations or warranties of any kind concerning the Licensed Material, whether express, implied, statutory, or other. This includes, without limitation, warranties of title, merchantability, fitness for a particular purpose, non-infringement, absence of latent or other defects, accuracy, or the presence or absence of errors, whether or not known or discoverable. Where disclaimers of warranties are not allowed in full or in part, this disclaimer may not apply to You.
b. To the extent possible, in no event will the Licensor be liable to You on any legal theory (including, without limitation, negligence) or otherwise for any direct, special, indirect, incidental, consequential, punitive, exemplary, or other losses, costs, expenses, or damages arising out of this Public License or use of the Licensed Material, even if the Licensor has been advised of the possibility of such losses, costs, expenses, or damages. Where a limitation of liability is not allowed in full or in part, this limitation may not apply to You.
c. The disclaimer of warranties and limitation of liability provided above shall be interpreted in a manner that, to the extent possible, most closely approximates an absolute disclaimer and waiver of all liability.
Section 6 – Term and Termination.
a. This Public License applies for the term of the Copyright and Similar Rights licensed here. However, if You fail to comply with this Public License, then Your rights under this Public License terminate automatically.
b. Where Your right to use the Licensed Material has terminated under Section 6(a), it reinstates:
1. automatically as of the date the violation is cured, provided it is cured within 30 days of Your discovery of the violation; or
2. upon express reinstatement by the Licensor.
For the avoidance of doubt, this Section 6(b) does not affect any right the Licensor may have to seek remedies for Your violations of this Public License.
c. For the avoidance of doubt, the Licensor may also offer the Licensed Material under separate terms or conditions or stop distributing the Licensed Material at any time; however, doing so will not terminate this Public License.
d. Sections 1, 5, 6, 7, and 8 survive termination of this Public License.
Section 7 – Other Terms and Conditions.
a. The Licensor shall not be bound by any additional or different terms or conditions communicated by You unless expressly agreed.
b. Any arrangements, understandings, or agreements regarding the Licensed Material not stated herein are separate from and independent of the terms and conditions of this Public License.
Section 8 – Interpretation.
a. For the avoidance of doubt, this Public License does not, and shall not be interpreted to, reduce, limit, restrict, or impose conditions on any use of the Licensed Material that could lawfully be made without permission under this Public License.
b. To the extent possible, if any provision of this Public License is deemed unenforceable, it shall be automatically reformed to the minimum extent necessary to make it enforceable. If the provision cannot be reformed, it shall be severed from this Public License without affecting the enforceability of the remaining terms and conditions.
c. No term or condition of this Public License will be waived and no failure to comply consented to unless expressly agreed to by the Licensor.
d. Nothing in this Public License constitutes or may be interpreted as a limitation upon, or waiver of, any privileges and immunities that apply to the Licensor or You, including from the legal processes of any jurisdiction or authority.
Creative Commons is not a party to its public licenses. Notwithstanding, Creative Commons may elect to apply one of its public licenses to material it publishes and in those instances will be considered the “Licensor.” Except for the limited purpose of indicating that material is shared under a Creative Commons public license or as otherwise permitted by the Creative Commons policies published at creativecommons.org/policies, Creative Commons does not authorize the use of the trademark “Creative Commons” or any other trademark or logo of Creative Commons without its prior written consent including, without limitation, in connection with any unauthorized modifications to any of its public licenses or any other arrangements, understandings, or agreements concerning use of licensed material. For the avoidance of doubt, this paragraph does not form part of the public licenses.
Creative Commons may be contacted at creativecommons.org.
1. Version numbers ending in odd digits are developmental (e.g. 0.7, 1.23, 4.5), with only the latest revision made accessible to the public. Version numbers ending in even digits (e.g. 0.6, 1.0, 2.14) are considered “public-release” and will be archived. Version numbers beginning with zero (e.g. 0.1, 0.2, etc.) represent early editions that were substantially incomplete.↩︎
2. This includes selling copies of it, either electronic or print. Of course, you must include the Creative Commons license as part of the text you sell, which means anyone will be able to tell it is an open text and can probably figure out how to download an electronic copy off the Internet for free. The only way you’re going to make significant money selling this text is to add your own value to it, either in the form of expansions or bundled product (e.g. simulation software, learning exercises, etc.), which of course is perfectly fair – you must profit from your own labors. All my work does for you is give you a starting point.↩︎
3. In mathematics, the term rigor refers to a meticulous attention to detail and insistence that each and every step within a chain of mathematical reasoning be thoroughly justified by deductive logic, not intuition or analogy.↩︎
4. The book’s subtitle happens to be, Being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus. Not only did Thompson recognize the anti-pragmatic tone with which calculus is too often taught, but he also infused no small amount of humor in his work.↩︎
5. Isaac Newton referred to derivatives as fluxions, and in Silvanus Thompson’s day they were known as differential coefficients.↩︎
6. British units of measurement for velocity indicate this same process of division: the number of feet traveled in a time period of seconds yields a velocity in feet per second. There is nothing unique about metric units in this regard.↩︎
7. Most likely a thermal mass flowmeter or a Coriolis flowmeter.↩︎
8. Although we will measure time, and differentials of time, as positive quantities, the mass flowmeter should be configured to show a negative flow rate ($$W$$) when propane flows from the tank to the building. This way, the integrand (the product “inside” the integration symbol; $$W \> dt$$) will be a negative quantity, and thus the integral over a positive time interval (from 0 to $$x$$) will likewise be a negative quantity.↩︎
9. According to calculus convention, the differential $$dt$$ represents the end of the integrand. It is safe to regard the long “S” symbol and the differential ($$dx$$, $$dt$$, etc.) as complementary grouping symbols declaring the beginning and end of the integrand. This tells us $$m_0$$ is not part of the integrand, but rather comes after it. Using parentheses to explicitly declare the boundaries of the integrand, we may re-write the expression as $$m_x = (\int_0^x W \> dt) + m_0$$↩︎
10. Recall from the previous section (“The Concept of Differentiation”) that velocity could be defined as the time-derivative of position: $$v = {dx \over dt}$$ All we have done here is algebraically solved for changes in $$x$$ by first multiplying both sides of the equation by $$dt$$ to arrive at $$dx = v \> dt$$. Next, we integrate both sides of the equation in order to “un-do” the differential ($$d$$) applied to $$x$$: $$\int dx = \int v \> dt$$. Since accumulations ($$\int$$) of any differential ($$dx$$) yields a discrete change for that variable, we may substitute $$\Delta x$$ for $$\int dx$$ and get our final answer of $$\Delta x = \int v \> dt$$.↩︎
11. To be perfectly accurate, we must also include initial values for position and velocity. In other words, $$x = \int v \> dt + x_0$$ and $$v = \int a \> dt + v_0$$↩︎
12. For instance, at $$x=1$$, the original function tells us that $$y$$ will be equal to $$- {6 \over 7}$$. If we plug this same value of 1 into $$x$$ of the derivative function, the result $${dy \over dx} = -{40 \over 49}$$ tells us the original function $$y = f(x)$$ has a slope of $$-{40 \over 49}$$ when $$x=1$$.↩︎
13. Unlike the recording shown from Cassier’s Magazine, which runs chronologically from right to left, modern chart recordings all run from left to right.↩︎
14. Not only does a 5-minute rate calculation period miss a lot of detail, but it also results in a time delay of (up to) 5 minutes detecting a pipeline rupture.↩︎
15. The technical term for a line passing through a pair of points on a curve is called a secant line.↩︎
16. Please note that the pipeline pressure is not actually 340.0 PSI at a time of 1:37:30. This is simply a coordinate convenient to mark because it how it lines up with the divisions on the trend display. We choose coordinate points on the tangent line easy to visually discern, then calculate the tangent line’s slope using those coordinates.↩︎
17. “Pseudocode” is a name given to any imaginary computer language used for the purpose of illustrating some procedure or concept without having to make reference to any particular (real) computer programming language. I could have just as well shown you the same algorithm using BASIC, C, or Java code, but pseudocode does just as well without the burden of introducing unfamiliar syntax to the reader.↩︎
18. Another source of trouble for differentiation of live signals is when the signal originates from a digital sensor. Digital devices, by their very nature, break analog signals into a series of discrete amplitude steps. As a digital process transmitter encounters a steadily increasing or decreasing process variable, its output rises or falls in discrete “jumps” rather than continuously as a fully analog transmitter would. Now, each of these jumps is quite small, but since each one occurs almost instantly it still translates into an extremely large rate-of-change when detected by a differentiator sampling over small time increments or sampling continuously (as in the case of an analog differentiator circuit). This means the problem of false rates-of-change exists even in perfectly noiseless systems, when the detection device (and/or the information channel to the monitoring system) is digital rather than analog.↩︎
19. Once gain, we are looking for points where the tangent line happens to intersect with major divisions on the graph’s scale. This makes it relatively easy to calculate the line’s slope, since the pressure and distance values for those coordinates are easy to read.↩︎
20. The Foxboro model 14 totalizer’s design was quite ingenious, since centrifugal force varies with the square of angular velocity. This had the effect of naturally performing the square-root characterization required of most pneumatic flow-measuring instruments due to the quadratic nature of most primary flow-sensing elements (e.g. orifice plate, venturi tubes, pitot tubes, etc.).↩︎
21. Vehicles equipped with a trip odometer allow the driver to reset this integration constant to zero at will, thus allowing the tracking of mileage for individual trips instead of over the life of the automobile.↩︎
22. As we lower the mass to ground level, height ($$x$$) goes from being a positive value to zero. This means each differential (infinitesimal change in value) for $$x$$ will be negative, thus causing the integrand $$F \> dx$$ to have a negative value and thus causing the integrated total (work) to be negative as well.↩︎
23. While a longbow is really nothing more than a long and flexible stick with a straight string drawn across it, a compound bow is a sophisticated machine with multiple passes of string and cam-shaped pulleys providing the nonlinear force-draw relationship.↩︎
24. One simple way to do this is to cover the entire integration area using nothing but rectangles and triangles, then measuring all the sketched shapes to totalize their areas.↩︎
25. An interesting point to make here is the United States did get something right when they designed their monetary system of dollars and cents. This is essentially a metric system of measurement, with 100 cents per dollar. The founders of the USA wisely decided to avoid the utterly confusing denominations of the British, with their pounds, pence, farthings, shillings, etc. The denominations of penny, dime, dollar, and eagle ($10 gold coin) comprised a simple power-of-ten system for money. Credit goes to France for first adopting a metric system of general weights and measures as their national standard.↩︎ 26. A basic mathematical identity is that multiplication of any quantity by 1 does not change the value of that original quantity. If we multiply some quantity by a fraction having a physical value of 1, no matter how strange-looking that fraction may appear, the value of the original quantity will be left intact. The goal here is to judiciously choose a fraction with a physical value of 1 but with its units of measurement so arranged that we cancel out the original quantity’s unit(s) and replace them with the units we desire.↩︎ 27. Density figures taken or derived from tables in the CRC Handbook of Chemistry and Physics, 64th Edition. Most liquid densities taken from table on page F-3 and solid densities taken from table on page F-1. Some liquid densities taken from tables on pages E-27 through E-31. All temperatures at or near 20 $$^{o}$$C.↩︎ 28. The only exception to this rule being units of measurement for angles, over which there has not yet been full agreement whether the unit of the radian (and its solid counterpart, the steradian) is a base unit or a derived unit.↩︎ 29. The older name for the SI system was “MKS,” representing meters, kilograms, and seconds.↩︎ 30. I’m noting my sarcasm here, just in case you are immune to my odd sense of humor.↩︎ 31. Relativistic physics deals with phenomena arising as objects travel near the speed of light. Quantum physics deals with phenomena at the atomic level. Neither is germane to the vast majority of industrial instrument applications.↩︎ 32. A common definition of energy is the “ability to do work” which is not always true. There are some forms of energy which may not be harnessed to do work, such as the thermal motion of molecules in an environment where all objects are at the same temperature. Energy that has the ability to do work is more specifically referred to as exergy. While energy is always conserved (i.e. never lost, never gained), exergy is a quantity that can never be gained but can be lost. The inevitable loss of exergy is closely related to the concept of entropy, where energy naturally diffuses into less useful (more homogeneous) forms over time. This important concept explains why no machine can never be perfectly ($$100.\overline{0}$$%) efficient, among other things.↩︎ 33. A vector is a mathematical quantity possessing both a magnitude and a direction. Force ($$F$$), displacement ($$x$$), and velocity ($$v$$) are all vector quantities. Some physical quantities such as temperature ($$T$$), work ($$W$$), and energy ($$E$$) possess magnitude but no direction. We call these directionless quantities “scalar.” It would make no sense at all to speak of a temperature being “79 degrees Celsius due North” whereas it would make sense to speak of a force being “79 Newtons due North”. Physicists commonly use a little arrow symbol over the variable letter to represent that variable as a vector, when both magnitude and direction matter. Thus $$\vec{F}$$ represents a force vector with both magnitude and direction specified, while plain $$F$$ merely represents the magnitude of that force without a specified direction. A “dot-product” is one way in which vectors may be multiplied, and the result of a dot-product is always a scalar quantity.↩︎ 34. Note that this calculation will assume all the work of towing this load is being performed by a single wheel on the truck. Most likely this will not be the case, as most towing vehicles have multiple driving wheels (at least two). However, we will perform calculations for a single wheel in order to simplify the problem.↩︎ 35. Consider the example of applying torque to a stubbornly seized bolt using a wrench: the force applied to the wrench multiplied by the radius length from the bolt’s center to the perpendicular line of force yields torque, but absolutely no work is done on the bolt until the bolt begins to move (turn).↩︎ 36. In practice, we usually see heavy objects fall faster than light objects due to the resistance of air. Energy losses due to air friction nullify our assumption of constant total energy during free-fall. Energy lost due to air friction never translates to velocity, and so the heavier object ends up hitting the ground faster (and sooner) because it had much more energy than the light object did to start.↩︎ 37. Hooke’s Law may be written as $$F = kx$$ without the negative sign, in which case the force ($$F$$) is the force applied on the spring from an external source. Here, the negative sign represents the spring’s reaction force to being displaced (the restoring force). A spring’s reaction force always opposes the direction of displacement: compress a spring, and it pushes back on you; stretch a spring, and it pulls back. A negative sign is the mathematically symbolic way of expressing the opposing direction of a vector.↩︎ 38. Technically, it is a pseudovector, because it does not exhibit all the same properties of a true vector, but this is a mathematical abstraction far beyond the scope of this book!↩︎ 39. A “flywheel” is a disk on a shaft, designed to maintain rotary motion in the absence of a motivating torque for the function of machines such as piston engines. The rotational kinetic energy stored by an engine’s flywheel is necessary to give the pistons energy to compress the gas prior to the power stroke, during the times the other pistons are not producing power.↩︎ 40. Technically, mechanical advantage should be defined by the ratio of input motion to output motion, rather than being defined in terms of force. The reason for this is if friction happens to exist in the machine, it will cause a degradation of force but not of motion. Since “mechanical advantage” is supposed to represent the ideal ratio of the machine, it is always safest to define it in terms of motion where friction will not affect the calculation. For a frictionless machine, however, defining mechanical advantage in terms of force is perfectly legitimate, and in fact makes more intuitive sense, since a larger mechanical advantage always corresponds with force multiplication from input to output.↩︎ 41. “Torque” is to rotational motion as “force” is to linear motion. Mathematically, torque ($$\tau$$) is defined as the cross-product of force acting on a radius ($$\vec{\tau} = \vec{r} \times \vec{F}$$).↩︎ 42. I am indebted to NASA for this and the rest of the black-and-white gear illustrations found in this section. All these illustrations were taken from NASA technical reports on gearing.↩︎ 43. Here, each gear is shown simply as a toothless wheel for the sake of simplicity. Truth be told, your humble author has difficulty drawing realistic gear teeth!↩︎ 44. An interesting feature of many flat-belt sheaves is a slight “crown” shape to the sheave, such that the diameter is slightly larger at the sheave’s center than it is at either side edge. The purpose of this crown is to help the belt center itself while in operation. As it turns out, a flat belt naturally tends to find the point at which it operates under maximum tension. If the belt happens to wander off-center, it will naturally find its way back to the center of the sheave as it rotates because that is where the tension reaches a maximum.↩︎ 45. In practice, not all of these 24 “speeds” are recommended, because some of the front/rear sprocket selections would place the chain at an extreme angle as it engaged with both sprockets. In the interest of extending chain life, it should run as “straight” on each sprocket as possible.↩︎ 46. Helium at room temperature is a close approximation of an ideal, monatomic gas, and is often used as an example for illustrating the relationship between temperature and molecular velocity.↩︎ 47. Kelvin is typically expressed without the customary “degree” label, unlike the three other temperature units: (degrees) Celsius, (degrees) Fahrenheit, and (degrees) Rankine.↩︎ 48. Animals process food by performing a very slow version of combustion, whereby the carbon and hydrogen atoms in the food join with oxygen atoms inhaled to produce water and carbon dioxide gas (plus energy). Although it may seem strange to rate the energy content of food by measuring how much heat it gives off when burnt, burning is just a faster method of energy extraction than the relatively slow processes of biological metabolism.↩︎ 49. Heat may be forced to flow from cold to hot by the use of a machine called a heat pump, but this direction of heat flow does not happen naturally, which is what the word “spontaneous” implies. In truth, the rule of heat flowing from high-temperature to cold-temperature applies to heat pumps as well, just in a way that is not obvious from first inspection. Mechanical heat pumps cause heat to be drawn from a cool object by placing an even cooler object (the evaporator) in direct contact with it. That heat is then transferred to a hot object by placing an even hotter object (the condenser) in direct contact with it. Heat is moved against the natural (spontaneous) direction of flow from the evaporator to the condenser by means of mechanical compression and expansion of a refrigerant fluid.↩︎ 50. In this context, we are using the word “radiation” in a very general sense, to mean thermal energy radiated away from the hot source via photons. This is quite different from nuclear radiation, which is what some may assume this term means upon first glance.↩︎ 51. Or in degrees Rankine, provided a suitably units-corrected value for the Stefan-Boltzmann constant were used.↩︎ 52. Jim Cahill of Emerson wrote in April 2010 (“Reducing Distillation Column Energy Usage” Emerson Process Expert weblog) about a report estimating distillation column energy usage to account for approximately 6% of the total energy used in the United States. This same report tallied the number of columns in US industry to be approximately 40000 total, accounting for about 19% of all energy used in manufacturing processes!↩︎ 53. An important detail to note is that specific heat does not remain constant over wide temperature changes. This complicates calculations of heat required to change the temperature of a sample: instead of simply multiplying the temperature change by mass and specific heat ($$Q = mc \Delta T$$ or $$Q = mc [T_2 - T_1]$$), we must integrate specific heat over the range of temperature ($$Q = m \int_{T_1}^{T_2} c \> dT$$), summing up infinitesimal products of specific heat and temperature change ($$c \> dT$$) over the range starting from temperature $$T_1$$ through temperature $$T_2$$ then multiplying by the mass to calculate total heat required. So, the specific heat values given for substances at 25 $$^{o}$$C only hold true for relatively small temperature changes deviating from 25 $$^{o}$$C. To accurately calculate heat transfer over a large temperature change, one must incorporate values of $$c$$ for that substance at different temperatures along the expected range.↩︎ 54. In reality, the amount of heat actually absorbed by the pot will be less than this, because there will be heat losses from the warm pot to the surrounding (cooler) air. However, for the sake of simplicity, we will assume all the burner’s heat output goes into the pot and the water it holds.↩︎ 55. We will assume for the sake of this example that the container holding the water is of negligible mass, such as a Styrofoam cup. This way, we do not have to include the container’s mass or its specific heat into the calculation.↩︎ 56. An alternative way to set up the problem would be to calculate $$\Delta T$$ for each term as $$T_{final} - T_{start}$$, making the iron’s heat loss a negative quantity and the water’s heat gain a positive quantity, in which case we would have to set up the equation as a zero-sum balance, with $$Q_{iron} + Q_{water} = 0$$. I find this approach less intuitive than simply saying the iron’s heat loss will be equal to the water’s heat gain, and setting up the equation as two positive values equal to each other.↩︎ 57. This is not far from the hypotheses of eighteenth-century science, where heat was thought to be an invisible fluid called caloric.↩︎ 58. A useful analogy for enthalpy is the maximum available balance of a bank account. Suppose you have a bank account with a minimum balance requirement of$32 to maintain that account. Your maximum available balance at any time would be the total amount of money in that account minus $32, or to phrase this differently your maximum available balance is the most money you may spend from this account while still keeping that account open. Enthalpy is much the same: the amount of thermal energy a sample may “spend” (i.e. lose) before its temperature reaches 32 degrees Fahrenheit.↩︎ 59. Appealing to the maximum available balance analogy, if we compared the maximum available balance in your bank account before and after a transaction, we could determine how much money was deposited or withdrawn from your account simply by subtracting those two values.↩︎ 60. Following the formula $$Q = mc \Delta T$$, we may calculate the heat as (1)(1)($$170-125$$) = 45 BTU. This is obviously the same result we obtained by subtracting enthalpy values for water at 170 $$^{o}$$F and 125 $$^{o}$$F.↩︎ 61. The word “latent” refers to something with potential that is not yet realized. Here, heat exchange takes place without there being any realized change in temperature. By contrast, heat resulting in a temperature change ($$Q = mc \Delta T$$) is called sensible heat.↩︎ 62. Latent heat of vaporization also varies with pressure, as different amounts of heat are required to vaporize a liquid depending on the pressure that liquid is subject to. Generally, increased pressure (increased boiling temperature) results in less latent heat of vaporization.↩︎ 63. The reason specific heat values are identical between metric and British units, while latent heat values are not, is because latent heat does not involve temperature change, and therefore there is one less unit conversion taking place between metric and British when translating latent heats. Specific heat in both metric and British units is defined in such a way that the three different units for heat, mass, and temperature all cancel each other out. With latent heat, we are only dealing with mass and heat, and so we have a proportional conversion of $$5 \over 9$$ or $$9 \over 5$$ left over, just the same as if we were converting between degrees Celsius and Fahrenheit alone.↩︎ 64. Styrofoam and plastic cups work as well, but paper exhibits the furthest separation between the boiling point of water and the burning point of the cup material, and it is usually thin enough to ensure good heat transfer from the outside (impinging flame) to the inside (water).↩︎ 65. This is a lot of fun to do while camping!↩︎ 66. This may be done in a vacuum jar, or by traveling to a region of high altitude where the ambient air pressure is less than at sea level.↩︎ 67. The mechanism of this influence may be understood by considering what it means to boil a liquid into a vapor. Molecules in a liquid reside close enough to each other that they cohere, whereas molecules in a vapor or gas are relatively far apart and act as independent objects. The process of boiling requires that cohesion between liquid molecules to be broken, so the molecules may drift apart. Increased pressure encourages cohesion in liquid form by helping to hold the molecules together, while decreased pressure encourages the separation of molecules into a vapor/gas.↩︎ 68. As mentioned previously, a useful analogy for enthalpy is the maximum available balance for a bank account with a$32 minimum balance requirement: that is, how much money may be spent from that account without closing it out.↩︎
69. At first it may seem as though the enthalpy of steam is so easy to calculate it almost renders steam tables useless. If the specific heats of water and steam were constant, and the latent heat of vaporization for water likewise constant, this would be the case. However, both these values ($$c$$ and $$L$$) are not constant, but rather change with pressure and with temperature. Thus, steam tables end up being quite valuable to engineers, allowing them to quickly reference heat content of steam across a broad range of pressures and temperatures without having to account for changing $$c$$ and $$L$$ values (performing integral calculus in the form of $$Q = m \int_{T_1}^{T_2} c \> dT$$ for specific heat) in their heat calculations.↩︎
70. This is not unlike calculating the voltage dropped across an electrical load by measuring the voltage at each of the load’s two terminals with respect to ground, then subtracting those two measured voltage values. In this analogy, electrical “ground” is the equivalent of water at freezing temperature: a common reference point for energy level.↩︎
71. Applying the maximum available balance analogy to this scenario, it would be as if your bank account began with a maximum available balance of $1287 and then finished with a maximum available balance of$138 after an expenditure: the amount of money you spent is the different between the initial and final maximum available balances ($1287 $$-$$$138 = 1149).↩︎ 72. When H$$_{2}$$O is at its triple point, vapor (steam), liquid (water), and solid (ice) of water will co-exist in the same space. One way to visualize the triple point is to consider it the pressure at which the boiling and freezing temperatures of a substance become the same.↩︎ 73. Anywhere between the triple-point temperature and the critical temperature, to be exact.↩︎ 74. The triple point for any substance is the pressure at which the boiling and freezing temperatures become one and the same.↩︎ 75. The non-freedom of both pressure and temperature for a pure substance at its triple point means we may exploit different substances’ triple points as calibration standards for both pressure and temperature. Using suitable laboratory equipment and samples of sufficient purity, anyone in the world may force a substance to its triple point and calibrate pressure and/or temperature instruments against that sample.↩︎ 76. To be more precise, a propane tank acts like a Class II filled-bulb thermometer, with liquid and vapor coexisting in equilibrium.↩︎ 77. Steam boilers exhibit this same explosive tendency. The expansion ratio of water to steam is on the order of a thousand to one (1000:1), making steam boiler ruptures very violent even at relatively low operating pressures.↩︎ 78. Class IIA systems do suffer from elevation error where the indicator may read a higher or lower temperature than it should due to hydrostatic pressure exerted by the column of liquid inside the tube connecting the indicator to the sensing bulb. Class IIB systems do not suffer from this problem, as the gas inside the tube exerts no pressure over an elevation.↩︎ 79. Circulation pumps and a multitude of accessory devices are omitted from this diagram for the sake of simplicity.↩︎ 80. This is another example of an important thermodynamic concept: the distinction between heat and temperature. While the temperature of the pressurizer heating elements exceeds that of the reactor core, the total heat output of course does not. Typical comparative values for pressurizer power versus reactor core power are 1800 kW versus 3800 MW, respectively: a ratio exceeding three orders of magnitude. The pressurizer heating elements don’t have to dissipate much power (compared to the reactor core) because the pressurizer is not being cooled by a forced convection of water like the reactor core is.↩︎ 81. In this application, the heaters are the final control element for the reactor pressure control system.↩︎ 82. Since the relationship between saturated steam pressure and temperature does not follow a simple mathematical formula, it is more practical to consult published tables of pressure/temperature data for steam. A great many engineering manuals contain steam tables, and in fact entire books exist devoted to nothing but steam tables.↩︎ 83. An experiment illustrative of this point is to maintain an ice-water mixture in an open container, then to insert a sealed balloon containing liquid water into this mixture. The water inside the balloon will eventually equalize in temperature with the surrounding ice-water mix, but it will not itself freeze. Once the balloon’s water reaches 0 degrees Celsius, it stops losing heat to the surrounding ice-water mix, and therefore cannot make the phase change to solid form.↩︎ 84. The concept of pressure is also applicable to solid materials: applying either a compressive or tensile force to a solid object of given cross-sectional area generates a pressure within that object, also referred to as stress.↩︎ 85. To give some perspective on this, 1 pascal of pressure is equal to (only) 0.000145 pounds per square inch!↩︎ 86. There is actually a speed of propagation to this increase in pressure, and it is the speed of sound within that particular fluid. This makes sense, since sound waves are nothing more than rapidly-changing regions of pressure within a material.↩︎ 87. Interestingly, the amount of pressure generated by the weight of a fluid depends only on the height of that fluid column, not its cross-sectional area. Suppose we had a column of water the same height (144 feet) but in a tube having an area twice as large: 2 square inches instead of 1 square inch. Twice the area means twice the volume of water held in the tube, and therefore twice the weight (124.8 lbs). However, since this greater weight is distributed over a proportionately greater area at the bottom of the tube, the pressure there remains the same as before: 124.8 pounds $$\div$$ 2 square inches = 62.4 pounds per square inch.↩︎ 88. Suppose a 1 square inch piston were set on the top of this tall fluid column, and a downward force of 20 lbs were applied to it. This would apply an additional 20 PSI pressure to the fluid molecules at all points within the column. The pressure at the bottom would be 82.4 PSI, and the pressure at the middle would be 51.2 PSI.↩︎ 89. Usually, this standard temperature is 4 degrees Celsius, the point of maximum density for water. However, sometimes the specific gravity of a liquid will be expressed in relation to the density of water at some other temperature. In some cases specific gravity is expressed for a liquid at one temperature compared to water at another temperature, usually in the form of a superscript such as 20/4 (liquid at 20 degrees Celsius compared to water at 4 degrees Celsius).↩︎ 90. For each of these calculations, specific gravity is defined as the ratio of the liquid’s density at 60 degrees Fahrenheit to the density of pure water, also at 60 degrees Fahrenheit.↩︎ 91. A colleague of mine told me once of working in an industrial facility with a very old steam boiler, where boiler steam pressure was actually indicated by tall mercury manometers reaching from floor to ceiling. Operations personnel had to climb a ladder to accurately read pressure indicated by these manometers!↩︎ 92. To give some perspective on just how little the liquid level changes in the well, consider a well-type manometer with a 1/4 inch (inside) diameter viewing tube and a 4-inch diameter circular well. The ratio of diameters for these two liquid columns is 16:1, which means their ratio of areas is 256:1. Thus, for every inch of liquid motion in the viewing tube, the liquid inside the well moves only $$1 \over 256$$ of an inch. Unless the viewing tube is quite tall, the amount of error incurred by interpreting the tube’s liquid height directly as pressure will be minimal – quite likely less than what the human eye is able to discern on a ruler scale anyway. If the utmost accuracy is desired in a well manometer, however, we may compensate for the trifling motion of liquid in the well by building a custom ruler for the vertical tube – one with a $$255 \over 256$$ reduced scale (so that $$255 \over 256$$ of an inch of liquid motion in the tube reads as exactly 1 inch of liquid column) in the case of the 1/4 inch tube and 4 inch well dimensions.↩︎ 93. With few exceptions!↩︎ 94. The origin of this unit for pressure is the atmospheric pressure at sea level: 1 atmosphere, or 14.7 PSIA. The word “bar” is short for barometric, in reference to Earth’s ambient atmospheric pressure.↩︎ 95. At sea level, where the absolute pressure is 14.7 PSIA. Atmospheric pressure will be different at different elevations above (or below) sea level.↩︎ 96. It should be noted that many different values exist for $$R$$, depending on the units of measurement. For liters of volume, atmospheres of pressure, moles of substance, and Kelvin for temperature, $$R = 0.0821$$. If one prefers to work with different units of measurement for volume, pressure, molecular quantity, and/or temperature, different values of $$R$$ are available.↩︎ 97. The conservation law necessitating equal current at all points in a series electric circuit is the Law of Charge Conservation, which states that electric charges cannot be created or destroyed.↩︎ 98. Although not grammatically correct, this is a common use of the word in discussions of fluid dynamics. By definition, something that is “incompressible” cannot be compressed, but that is not how we are using the term here. We commonly use the term “incompressible” to refer to either a moving liquid (in which case the actual compressibility of the liquid is inconsequential) or a gas/vapor that does not happen to undergo substantial compression or expansion as it flows through a pipe. In other words, an “incompressible” flow is a moving fluid whose $$\rho$$ does not substantially change, whether by actual impossibility or by circumstance.↩︎ 99. According to Ven Te Chow in Open Channel Hydraulics, who quotes from Hunter Rouse and Simon Ince’s work History of Hydraulics, Bernoulli’s equation was first formulated by the great mathematician Leonhard Euler and made popular by Julius Weisbach, not by Daniel Bernoulli himself.↩︎ 100. Surely you’ve heard the expression, “Apples and Oranges don’t add up.” Well, pounds per square inch and pounds per square foot don’t add up either! A general mathematical rule in physics is that any quantities added to or subtracted from each other must bear the exact same units. This rule does not hold for multiplication or division, which is why we see units canceling in those operations. With addition and subtraction, no unit cancellation occurs.↩︎ 101. It is entirely possible to perform all our calculations using inches and/or minutes as the primary units instead of feet and seconds. The only caveat is that all units throughout all terms of Bernoulli’s equation must be consistent. This means we would also have to express mass density in units of slugs per cubic inch, the acceleration of gravity in inches per second squared (or inches per minute squared), and velocity in units of inches per second (or inches per minute). The only real benefit of doing this is that pressure would remain in the more customary units of pounds per square inch. My personal preference is to do all calculations using units of feet and seconds, then convert pressures in units of PSF to units of PSI at the very end.↩︎ 102. A simple approximation for pressure loss due to elevation gain is approximately 1 PSI for every 2 vertical feet of water (1 PSI for every 27.68 inches to be more exact).↩︎ 103. Technically, an eductor uses a liquid such as water to generate the vacuum, while an ejector uses a gas or a vapor such as steam.↩︎ 104. A piezometer tube is nothing more than a manometer (minus the well or the other half of the U-tube).↩︎ 105. For a moving fluid, potential energy is the sum of fluid height and static pressure.↩︎ 106. The form of Bernoulli’s equation with each term expressed in units of distance (e.g. $$z$$ = [feet] ; $$v^2 \over 2g$$ = [feet] ; $$P \over \gamma$$ = [feet]) was chosen so that the piezometers’ liquid heights would directly correspond.↩︎ 107. This generally means to seek the lowest gross potential energy, but there are important exceptions where chemical reactions actually proceed in the opposite direction (with atoms seeking higher energy states and absorbing energy from the surrounding environment to achieve those higher states). A more general and consistent understanding of matter and energy interactions involves a more complex concept called entropy, and a related concept known as Gibbs Free Energy.↩︎ 108. This statement is not perfectly honest. When atoms join to form molecules, the subsequent release of energy is translated into an incredibly small loss of mass for the molecule, as described by Albert Einstein’s famous mass-energy equation $$E = mc^2$$. However, this mass discrepancy is so small (typically less than one part per billion of the original mass!), we may safely ignore it for the purposes of understanding chemical reactions in industrial processes. This is what the humorous quote at the start of this chapter meant when it said “ignore the nuclear physicists at this point”.↩︎ 109. In order for a wave of light to be influenced at all by an object, that object must be at least the size of the wave’s length. To use an analogy with water waves, it would be comparing the interaction of a water wave on a beach against a large rock (a disturbance in the wave pattern) versus the non-disturbance of that same wave as it encounters a small buoy.↩︎ 110. One line represents a single bond, which is one electron shared per bound atom. Two parallel lines represent a double bond, where each carbon atom shares two of its valence electrons with the neighboring atom. Three parallel lines represent a triple bond, where each atom shares three of its outer electrons with the neighboring atom.↩︎ 111. Incidentally, nitrogen atoms preferentially form exactly three bonds, and oxygen atoms exactly two bonds. The reason for this pattern is the particular patterns of electrons orbiting each of these atoms, and their respective energy levels. For more information on this, see section 3.4 beginning on page .↩︎ 112. The amount of energy required to rearrange particles in the nucleus for even just a single atom is tremendous, lying well outside the energy ranges of chemical reactions. Such energy levels are the exclusive domain of nuclear reactions and high-energy radiation (subatomic particles traveling at high velocity). The extremely large energy “investment” required to alter an atom’s nucleus is why atomic identities are so stable. This is precisely why alchemists of antiquity utterly failed to turn lead into gold: no materials, processes, or techniques they had at their disposal were capable of the targeted energy necessary to dislodge three protons from a nucleus of lead ($$_{82}$$Pb) to that it would turn into a nucleus of gold ($$_{79}$$Au). That, and the fact the alchemists had no clue about atomic structure to begin with, made their endeavor fruitless.↩︎ 113. It used to be believed that these elements were completely inert: incapable of forming molecular bonds with other atoms. However, this is not precisely true, as some compounds are now known to integrate noble elements.↩︎ 114. All isotopes of astatine (At) are radioactive with very short half-lives, making this element difficult to isolate and study.↩︎ 115. These orbitals just happen to be the 1s, 2p, 3d, and 4f orbitals, as viewed from left to right. In each case, the nucleus lies at the geometric center of each shape. In a real atom, all orbitals share the same center, which means any atom having more than two electrons (that’s all elements except for hydrogen and helium!) will have multiple orbitals around one nucleus. This four-set of orbital visualizations shows what some orbitals would look like if viewed in isolation.↩︎ 116. Please understand that like all analogies, this one merely illustrates a complex concept in terms that are easier to recognize. Analogies do not explain why things work, but merely liken an abstract phenomenon to something more accessible to common experience.↩︎ 117. Truth be told, higher-order shells exist even in simple atoms like hydrogen, but are simply not occupied by that atom’s electron(s) unless they are “excited” into a higher energy state by an external input of energy.↩︎ 118. The letters s, p, d, and f refer to the words sharp, principal, diffuse, and fundamental, used to describe the appearance of spectral lines in the early days of atomic spectroscopy research. Higher-order subshells are labeled alphabetically after f: g, h, and i.↩︎ 119. The two electrons of any orbital have opposite spin values.↩︎ 120. The atomic number is the quantity of protons found in an atom’s nucleus, and may only be a whole number. Since any electrically balanced atom will have the same number of electrons as protons, we may look at the atomic number of an element as being the number of electrons in each atom of that element.↩︎ 121. Building on the amphitheater analogy for one atom of the element aluminum, we could say that there are two electrons occupying the “s” seating row on the first level, plus two electrons occupying the “s” seating row on the second level, plus six electrons occupying the “p” seating row on the second level, plus two electrons occupying the “s” seating row on the third level, plus one electron occupying the “p” seating row on the third level.↩︎ 122. Recall the definition of a “period” in the Periodic Table being a horizontal row, with each vertical column being called a “group”.↩︎ 123. Building on the amphitheater analogy once again for one atom of the element aluminum, we could say that all seats within levels 1 and 2 are occupied (just like an atom of neon), plus two electrons occupying the “s” seating row on the third level, plus one electron occupying the “p” seating row on the third level.↩︎ 124. This is the reason silicon-based photovoltaic solar cells are so inefficient, converting only a fraction of the incident light into electricity. The energy levels required to create an electron-hole pair at the P-N junction correspond to a narrow portion of the natural light spectrum. This means most of the photons striking a solar cell do not transfer their energy into electrical power because their individual energy levels are insufficient to create an electron-hole pair in the cell’s P-N junction. For photovoltaic cells to improve in efficiency, some way must be found to harness a broader spectrum of photon frequencies (light colors) than silicon P-N junctions can do, at least on their own.↩︎ 125. Solids and liquids tend to emit a broad spectrum of wavelengths when heated, in stark contrast to the distinct “lines” of color emitted by isolated atoms.↩︎ 126. To create these spectra, I used a computer program called Spectrum Explorer, or SPEX.↩︎ 127. Including wavelengths of 397 nm, 389 nm, and 384 nm.↩︎ 128. The wavelength of this light happens to lie within the visible range, at approximately 606 nm. Note the shell levels involved with this particular electron transition: between 2p$$^{10}$$ and 5d$$^{5}$$. Krypton in its ground (un-excited) state has a valence electron configuration of 4p$$^{6}$$, which tells us the electron’s transition occurs between an inner shell of the Krypton atom and an excited shell (higher than the ground-state outer shell of the atom). The wavelength of this photon (606 nm) resulting from a shell 5 to shell 2 transition also suggests different energy levels for those shells of a Krypton atom compared to shells 5 and 2 of a hydrogen atom. Recall that the Balmer line corresponding to a transition from $$n=5$$ to $$n=2$$ of a hydrogen atom had a wavelength value of 434 nm, a higher energy than 606 nm and therefore a larger jump between those corresponding shells.↩︎ 129. In fact, it is often easier to obtain an absorption spectrum of a sample than to create an emission spectrum, due to the relative simplicity of the absorption spectrometer test fixture. We don’t have to energize a sample to incandescence to obtain an absorption spectrum – all we must do is pass white light through enough of it to absorb the characteristic colors.↩︎ 130. One student described this to me as a “shadow” image of the hydrogen gas. The missing colors in the absorption spectrum are the shadows of hydrogen gas molecules blocking certain frequencies of the incident light from reaching the viewer.↩︎ 131. Truth be told, a “mole” is 602,200,000,000,000,000,000,000 counts of literally any discrete entities. Moles do not represent mass, or volume, or length, or area, but rather a quantity of individual units. There is nothing wrong with measuring the amount of eggs in the world using the unit of the mole, or the number of grains of sand in moles, or the number of bits in a collection of digital data. Think of “mole” as nothing more than a really big dozen, or more precisely, a really big half-dozen!↩︎ 132. Another way to define one mole is that it is the number of individual nucleons (i.e. protons and/or neutrons) necessary to comprise one gram of mass. Since protons and neutrons comprise the vast majority of an atom’s mass, we may essentially ignore the mass of an atom’s electrons when tabulating its mass and pay attention only to the nucleus. This is why one mole of Hydrogen atoms, each atom having just one lone proton in its nucleus, will have a combined mass of one gram. By extension, one mole of Carbon-12 atoms, each atom with 6 protons and 6 neutrons, will have a combined mass of twelve grams.↩︎ 133. Take the combustion of hydrogen and oxygen to form water, for example. We know we will need two H$$_{2}$$ molecules for every one O$$_{2}$$ molecule to produce two H$$_{2}$$O molecules. However, four hydrogen molecules combined with two oxygen molecules will make four water molecules just as well! Similarly, six hydrogen molecules combined with three oxygen molecules also perfectly balance, making six water molecules. So long as we consider all three molecular quantities to be unknown, we will never be able to solve for just one correct answer, because there is no one correct set of absolute quantities, only one correct set of ratios or proportions.↩︎ 134. Note that you cannot have a molecule comprised of 4.8 carbon atoms, 8.4 hydrogen atoms, and 2.2 oxygen atoms, since atoms exist in whole numbers only! This compositional formula merely shows us the relative proportions of each element in the complex mixture of molecules that make up sewage sludge.↩︎ 135. These assumptions are critically important to equating volumetric ratios with molar ratios. First, the compared substances must both be gases: the volume of one mole of steam is huge compared to the volume of one mole of liquid water. Next, we cannot assume temperatures and pressures will be the same after a reaction as before. This is especially true for our example here, where ethane and oxygen are burning to produce water vapor and carbon dioxide: clearly, the products will be at a greater temperature than the reactants!↩︎ 136. Looking at the unity-fraction problem, we see that “grams” (g) will cancel from top and bottom of the unity fraction, and “ethane” will cancel from the given quantity and from the bottom of the unity fraction. This leaves “kilograms” (kg) from the given quantity and “oxygen” from the top of the unity fraction as the only units remaining after cancellation, giving us the proper units for our answer: kilograms of oxygen.↩︎ 137. This notation is quite common in scientific and engineering literature, as a way to avoid having to typeset fractions in a text document. Instead of writing $$\hbox{kJ} \over \hbox{mol}$$ which requires a fraction bar, we may write $$\hbox{kJ mol}^{-1}$$ which is mathematically equivalent. Another common example of this notation is to express frequency in the unit of $$\hbox{s}^{-1}$$ (per second) rather than the unit of Hertz (Hz). Perhaps the most compelling reason to use negative exponents in unit expressions, though, is sociological: scientific studies have shown the regular use of this unit notation makes you appear 37.5% smarter than you actually are. Questioning statistical results of scientific studies, on the other hand, reduces your apparent intelligence by over 63%! Now, aren’t you glad you took the time to read this footnote?↩︎ 138. Just how catalysts perform this trick is a subject of continuing research. Catalysts used in industrial process industries are usually selected based on the results of empirical tests rather than by theory, since a general theoretical understanding of catalysis is lacking at this present time. Indeed, the specific selection of catalysts for high-value chemical processes is often a patented feature of those processes, reflecting the investment of time, finances, and effort finding a suitable catalyst for optimizing each chemical reaction.↩︎ 139. If this were not true, one could construct an over-unity (“perpetual motion”) machine by initiating an endothermic reaction and then reversing that reaction (exothermic) using a catalyst in either or both portions of the cycle to reap a net energy release from the system. So trustworthy is the Law of Energy Conservation that we may safely invoke the impossibility of over-unity energy production as a disproof of any given hypothesis permitting it. In other words, if any hypothesis allows for an over-unity process (i.e. violates the Law of Energy Conservation), we may reject that hypothesis with confidence! This form of disproof goes by the name reductio ad absurdum (Latin: “reducing to an absurdity”).↩︎ 140. At first it may seem non-sensical for the carbon dioxide product of this reaction to have a negative energy, until you realize the zero values given to both the carbon and oxygen reactants are entirely arbitrary. Viewed in this light, the negative heat of formation for CO$$_{2}$$ is nothing more than a relative expression of chemical potential energy in reference to the elements from which CO$$_{2}$$ originated. Therefore, a negative $$\Delta H_f^{\circ}$$ value for any molecule simply tells us that molecule has less energy (i.e. is more stable) than its constituent elements.↩︎ 141. We may also readily tell whether any given reaction will be exothermic or endothermic, based on the mathematical sign of this $$\Delta H$$ value.↩︎ 142. Of course, it is not necessary to look up $$\Delta H_f^{\circ}$$ for oxygen gas, as that is an element in its natural state at STP and therefore its standard heat of formation is defined to be zero. The heat of formation for carbon dioxide gas may be found from the preceding example, while the heat of formation for water may be found in the “Heats of Reaction and Activation Energy” subsection of this book. The only substance in this list of which the heat of formation is not defined as zero or given in this book is propane. Note that many thermochemical reference books will give heats of formation in units of kilocalories per mole rather than kilojoules per mole. The conversion factor between these is 1 calorie = 4.184 joules.↩︎ 143. These names have their origin in the terms used to classify positive and negative electrodes immersed in a liquid solution. The positive electrode is called the “anode” while the negative electrode is called the “cathode.” An anion is an ion attracted to the anode. A cation is an ion attracted to the cathode. Since opposite electrical charges tend to attract, this means “anions” are negatively charged and “cations” are positively charged.↩︎ 144. Ionic compounds are formed when oppositely charged atomic ions bind together by mutual attraction. The distinguishing characteristic of an ionic compound is that it is a conductor of electricity in its pure, liquid state. That is, it readily separates into anions and cations all by itself. Even in its solid form, an ionic compound is already ionized, with its constituent atoms held together by an imbalance of electric charge. Being in a liquid state simply gives those atoms the physical mobility needed to dissociate.↩︎ 145. Covalent compounds are formed when electrically neutral atoms bind together by the mutual sharing of valence electrons. Such compounds are not good conductors of electricity in their pure, liquid states.↩︎ 146. Actually, the more common form of positive ion in water is hydronium: H$$_{3}$$O$$^{+}$$, but we often simply refer to the positive half of an ionized water molecule as hydrogen (H$$^{+}$$).↩︎ 147. Free hydrogen ions (H$$^{+}$$) are rare in a liquid solution, and are more often found attached to whole water molecules to form a positive ion called hydronium (H$$_{3}$$O$$^{+}$$). However, process control professionals usually refer to these positive ions simply as “hydrogen” even though the truth is a bit more complicated.↩︎ 148. The letter “p” refers to “potential,” in reference to the logarithmic nature of the measurement. Other logarithmic measurements of concentration exist for molecular species, including pO$$_{2}$$ and pCO$$_{2}$$ (concentration of oxygen and carbon dioxide molecules in a liquid solution, respectively).↩︎ 149. Often, students assume that the 7 pH value of water is an arbitrary assignment, using water as a universal standard just like we use water as the standard for the Celsius temperature scale, viscosity units, specific gravity, etc. However, this is not the case here. Pure water at room temperature just happens to have an hydrogen ion molarity equivalent to a (nearly) round-number value of 7 pH.↩︎ 150. If the electrolyte is considered strong, all or nearly all of its molecules will dissociate into ions. A weak electrolyte is one where only a mere portion of its molecules dissociate into ions.↩︎ 151. For “strong” acids, all or nearly all molecules dissociate into ions. For “weak” acids, just a portion of the molecules dissociate.↩︎ 152. For “strong” bases, all or nearly all molecules dissociate into ions. For “weak” bases, just a portion of the molecules dissociate.↩︎ 153. It should be noted that the solution never becomes electrically imbalanced with the addition of an acid or caustic. It is merely the balance of hydrogen to hydroxyl ions we are referring to here. The net electrical charge for the solution should still be zero after the addition of an acid or caustic, because while the balance of hydrogen to hydroxyl ions does change, that electrical charge imbalance is made up by the other ions resulting from the addition of the electrolyte (anions for acids, cations for caustics). The end result is still one negative ion for every positive ion (equal and opposite charge numbers) in the solution no matter what substance(s) we dissolve into it.↩︎ 154. Exceptions do exist for strong concentrations, where hydrogen ions may be present in solution yet unable to react because of being “crowded out” by other ions in the solution.↩︎ 155. A battery is an electrochemical device producing an electrical voltage as the result of a chemical reaction.↩︎ 156. I have yet to read a document of any kind written by an equipment manufacturer using electron flow notation, and this is after scrutinizing literally hundreds of documents looking for this exact detail! For the record, though, most technical documents do not bother to draw a direction for current at all, leaving it to the imagination of the reader instead. It is only when a direction must be drawn that one sees a strong preference in industry for conventional flow notation.↩︎ 157. If by chance I have missed anyone’s digital electronics textbook that does use electron flow, please accept my apologies. I can only speak of what I have seen myself.↩︎ 158. Although the unit of the “watt” is commonly used for electrical power, other units are valid as well. The British unit of horsepower is every bit as valid for expressing electrical power as “watts,” although this usage is less common. Likewise, the “watt” may be used to express measurements of non-electrical power as well, such as the mechanical power output of an engine. European automobile manufacturers, for example, rate the power output of their cars’ engines in kilowatts, as opposed to American automobile manufacturers who rate their engines in horsepower. This choice of units is strictly a cultural convention, since any valid unit for power may be applied to any form of energy rate.↩︎ 159. Except in the noteworthy case of superconductivity, a phenomenon occurring at extremely low temperatures.↩︎ 160. Except in the noteworthy case of superfluidity, another phenomenon occurring at extremely low temperatures.↩︎ 161. Interesting exceptions do exist to this rule, but only on very short time scales, such as in cases where we examine the a transient (pulse) signal nanosecond by nanosecond, and/or when very high-frequency AC signals exist over comparatively long conductor lengths.↩︎ 162. Those exceptional cases mentioned earlier in the footnote are possible only because electric charge may be temporarily stored and released by a property called capacitance. Even then, the law of charge conservation is not violated because the stored charges re-emerge as current at later times. This is analogous to pouring water into a bucket: just because water is poured into a bucket but no water leaves the bucket does not mean that water is magically disappearing. It is merely being stored, and can re-emerge at a later time.↩︎ 163. An ideal conductor has no resistance, and so there is no reason for a difference of potential to exist along a pathway where nothing stands in the way of charge motion. If ever a potential difference developed, charge carriers within the conductor would simply move to new locations and neutralize the potential.↩︎ 164. Again, interesting exceptions do exist to this rule on very short time scales, such as in cases where we examine the a transient (pulse) signal nanosecond by nanosecond, and/or when very high-frequency AC signals exist over comparatively long conductor lengths.↩︎ 165. The exceptional cases mentioned in the previous footnote exist only because the electrical property of inductance allows potential energy to be stored in a magnetic field, manifesting as a voltage different along the length of a conductor. Even then, the Law of Energy Conservation is not violated because the stored energy re-emerges at a later time.↩︎ 166. But not always! There do exist positive-ground systems, particularly in telephone circuits and in some early automobile electrical systems.↩︎ 167. Both in the British system of measurement and the SI metric system of measurement! The older metric system (called “CGS” for Centimeter-Gram-Second) had a special unit of measurement called the Gilbert for expressing magnetic field strength, with 1 Gilbert (Gb) equal to 0.7958 Amp-turns (At).↩︎ 168. The term “ferrous” simply refers to any substance containing the element iron. This includes steel, which is a combination of iron and carbon.↩︎ 169. The word “solenoid” may also be used to describe a wire coil with no armature, but the more common industrial use of the word refers to the complete arrangement of coil and movable armature.↩︎ 170. There is also a left-hand rule for fans of electron flow, but in this book I will default to conventional flow. For a more complete discussion on this matter, see section 4.2.1 beginning on page .↩︎ 171. The term “ferrous” refers to any substance containing the element iron. Steel is one such substance, being a combination of iron and carbon.↩︎ 172. Unlike the charge/hold/discharge capacitor circuit, this inductor demonstration circuit would not function quite as well in real life. Real inductors contain substantial amounts of electrical resistance ($$R$$) in addition to inductance ($$L$$), which means real inductors have an inherent capacity to dissipate their own store of energy. If a real inductor were placed in a circuit such as this, it would not maintain its store of energy indefinitely in the switch’s “neutral” position as a capacitor would. Realistically, the inductor’s energy would likely dissipate in a matter of milliseconds following the switch to the “neutral” position.↩︎ 173. It is also acceptable to refer to electrical voltages and/or currents that vary periodically over time even if their directions never alternate, as AC superimposed on DC.↩︎ 174. Charles Proteus Steinmetz, in his book Theoretical Elements of Electrical Engineering, refers to the voltage and current values of a reactive component being “wattless” in honor of the fact that they transfer zero net power to or from the circuit (page 41). The voltage and current values of resistive components, by contrast, constitute real power dissipated in the circuit.↩︎ 175. At first it may seem strange to apply Faraday’s Law here, because this formula is typically used to describe the amount of voltage produced by a coil of wire exposed to a changing magnetic field, not the amount of magnetic field produced by an applied voltage. However, the two are closely related because the inductor must produce a voltage drop in equilibrium with the applied voltage just like any other component, in accordance with Kirchhoff’s Voltage Law. In a simple circuit such as this where the voltage source directly connects to the inductor (barring any resistive losses in the connecting wires), the coil’s induced voltage drop must exactly equal the source’s applied voltage at all points in time, and so Faraday’s Law works just as well to describe the source’s applied voltage as it does to describe the coil’s induced voltage. This is the principle of self-induction.↩︎ 176. In this context, “constant” means an alternating voltage with a consistent peak value, not “constant” in the sense that a DC source is constant at all points in time.↩︎ 177. In this context, “constant” means an alternating voltage with a consistent peak value, not “constant” in the sense that a DC source is constant at all points in time.↩︎ 178. These power losses take the form of core losses due to magnetic hysteresis in the ferrous core material, and winding losses due to electrical resistance in the wire coils. Core losses may be minimized by reducing magnetic flux density ($$H$$), which requires a core with a larger cross-section to disperse the flux ($$\phi$$) over a wider area. Winding losses may be minimized by increasing wire gauge (i.e. thicker wire coils). In either case, these modifications make for a bulkier and more expensive transformer.↩︎ 179. Transformers, of course, utilize the principle of electromagnetic induction to generate a voltage at the secondary winding which may power a load. Ideally, 100 percent of the magnetic flux generated by the energized primary winding “links” or “couples” to the secondary winding. However, imperfections in the windings, core material, etc. conspire to prevent every bit of magnetic flux from coupling with the secondary winding, and so any magnetic flux from the primary winding that doesn’t transfer power to the secondary winding simply absorbs and releases energy like a plain inductor. This is called “leakage” inductance because the flux in question has found a path to “leak” around the secondary winding. Leakage inductance may be modeled in a transformer as a separate series-connected inductance connected to the primary winding. Like any inductance, it presents a reactance equal to $$X_L = 2 \pi f L$$, and in a transformer serves to impede primary current.↩︎ 180. Although it is possible to express transformer impedance in the more familiar unit of Ohms ($$\Omega$$), percentage is greatly preferred for the simple reason that it applies identically to the primary and secondary sides of the transformer. Expressing transformer impedance in ohms would require a different value depending on whether the primary side or secondary side were being considered.↩︎ 181. The rather colorful term “bolted” refers to a short-circuit fault consisting of a large copper bus-bar physically attached to the transformer’s secondary terminal using bolts. In other words, a “bolted” fault is as close to a perfect short-circuit as you can get.↩︎ 182. A full circle contains 360 degrees, which is equal to $$2 \pi$$ radians. One “radian” is defined as the angle encompassing an arc-segment of a circle’s circumference equal in length to its radius, hence the name “radian”. Since the circumference of a circle is $$2 \pi$$ times as long as its radius, there are $$2 \pi$$ radians’ worth of rotation in a circle. Thus, while the “degree” is an arbitrary unit of angle measurement, the “radian” is a more natural unit of measurement because it is defined by the circle’s own radius.↩︎ 183. The definition of an imaginary number is the square root of a negative quantity. $$\sqrt{-1}$$ is the simplest case, and is symbolized by mathematicians as $$i$$ and by electrical engineers as $$j$$.↩︎ 184. The term “unit vector” simply refers to a vector with a length of 1 (“unity”).↩︎ 185. Although $$A$$ truly should represent a waveform’s peak value, and $$\theta$$ should be expressed in units of radians to be mathematically correct, it is more common in electrical engineering to express $$A$$ in RMS (root-mean-square) units and $$\theta$$ in degrees. For example, a 120 volt RMS sine wave voltage at a phase angle of 30 degrees will be written by an engineer as $$120e^{j30}$$ even though the true phase angle of this voltage is $$\pi \over 6$$ radians and the actual peak value is 169.7 volts.↩︎ 186. The fact that this graph shows the vertical (imaginary) projections of both phasors rather than the horizontal (real) projections is irrelevant to phase shift. Either way, the voltage waveform of source B will still lead the voltage waveform of source A by 60$$^{o}$$.↩︎ 187. One way to think of this is to imagine an AC voltage-measuring instrument having red and black test leads just like a regular voltmeter. To measure $$V_{BA}$$ you would connect the red test lead to the first point (B) and the black test lead to the second point (A).↩︎ 188. The necessity of a shared frequency is easily understood if one considers a case of two sine waves at different frequencies: their respective phasors would spin at different speeds. Given two phasors spinning at different speeds, the angle separating those two phasors would be constantly changing. It is only when two phasors spin around at precisely the same speed that we can sensibly talk about there being a fixed angular displacement between them. Fortunately this is the usual case in AC circuit analysis, where all voltages and currents share the same frequency.↩︎ 189. An important detail is that our phasometer must always spin counter-clockwise in order to maintain proper phasor convention. We can ensure this will happen by including a pair of shading coils (small copper rings wrapped around one corner of each magnetic pole) in the stator structure. For a more detailed discussion of shading coils, refer to the section on AC induction motors ([shading_coil]) starting on page .↩︎ 190. This, of course, assumes the generator powering the system is also a two-pole machine like the phasometer. If the generator has more poles, the shaft speed will not match the phasometer’s rotor speed even though the phasometer will still faithfully represent the generator’s cosine wave rotation.↩︎ 191. Automobile mechanics may be familiar with a tool called a timing light, consisting of a strobe light connected to the engine in such a way that the light flashes every time the #1 cylinder spark plug fires. By viewing the marks etched into the engine’s crankshaft with this strobe light, the mechanic is able to check the ignition timing of the engine.↩︎ 192. Recall from calculus that the derivative of the function $$e^x$$ with respect to $$x$$ is simply $$e^x$$. That is, the value of an exponential function’s slope is equal to the value of the original exponential function! If the exponent contains any constants multiplied by the independent variable, those constants become multiplying coefficients after differentiation. Thus, the derivative of $$e^{kx}$$ with respect to $$x$$ is simply $$ke^{kx}$$. Likewise, the derivative of $$e^{j \omega t}$$ with respect to $$t$$ is $$j \omega e^{j \omega t}$$.↩︎ 193. Note also one of the interesting properties of the imaginary operator: $${1 \over j} = -j$$. The proof of this is quite simple: $${1 \over j} = {j \over j^2} = {j \over -1} = -j$$.↩︎ 194. Note that we begin this analysis with an exponential expression of the current waveform rather than the voltage waveform as we did at the beginning of the capacitor analysis. It is possible to begin with voltage as a function of time and use calculus to determine current through the inductor, but unfortunately that would necessitate integration rather than differentiation. Differentiation is a simpler process, which is why this approach was chosen. If $$e^{j \omega t} = L {dI \over dt}$$ then $$e^{j \omega t} \> dt = L \> dI$$. Integrating both sides of the equation yields $$\int e^{j \omega t} \> dt = L \int dI$$. Solving for $$I$$ yields $$e^{j \omega t} \over j \omega L$$ plus a constant of integration representing a DC component of current that may or may not be zero depending on where the impressed voltage sinusoid begins in time. Solving for $$Z = V / I$$ finally gives the result we’re looking for: $$j \omega L$$. Ugly, no?↩︎ 195. A “unit” phasor is one having a length of 1.↩︎ 196. The fact that these impedance phasor quantities have fixed angles in AC circuits where the voltage and current phasors are in constant motion is not a contradiction. Since impedance represents the relationship between voltage and current for a component ($$Z = V / I$$), this fixed angle represents a relative phase shift between voltage and current. In other words, the fixed angle of an impedance phasor tells us the voltage and current waveforms will always remain that much out of step with each other despite the fact that the voltage and current phasors themselves are continuously rotating at the system frequency ($$\omega$$).↩︎ 197. With one notable exception: Joule’s Law ($$P = IV$$, $$P = V^2 / Z$$, $$P = I^2 Z$$) for calculating power does not apply in AC circuits because power is not a phasor quantity like voltage and current.↩︎ 198. Assuming a two-pole generator, where each period of the sinusoidal waveform corresponds exactly to one revolution of the generator shaft.↩︎ 199. When dividing two phasors in polar form, the arithmetic is as follows: divide the numerator’s magnitude by the denominator’s magnitude, then subtract the denominator’s angle from the numerator’s angle. The result in this case is 5 milliamps (5 volts divided by 1000 ohms) at an angle of 0 degrees (0 minus 0).↩︎ 200. The same arithmetic applies to this quotient as well: the current’s magnitude is 5 volts divided by 1000 ohms, while the current’s phase angle is 60 degrees minus a negative 90 degrees (150 degrees).↩︎ 201. $$\sigma$$ is equal to the reciprocal of the signal’s time constant $$\tau$$. In other words, $$\sigma = 1 / \tau$$.↩︎ 202. One value of $$\omega$$ not shown in this three-panel graphic comparison is a negative frequency. This is actually not as profound as it may seem at first. All a negative value of $$\omega$$ will do is ensure that the phasor will rotate in the opposite direction (clockwise, instead of counter-clockwise as phasor rotation is conventionally defined). The real portion of the sinusoid will be identical, tracing the same cosine-wave plot over time. Only the imaginary portion of the sinusoid will be different, as $$j \sin - \theta = - j \sin \theta$$.↩︎ 203. The expression used here to represent voltage is simply $$e^{st}$$. I could have used a more complete expression such as $$Ae^{st}$$ (where $$A$$ is the initial amplitude of the signal), but as it so happens this amplitude is irrelevant because there will be an “$$A$$” term in both the numerator and denominator of the impedance quotient. Therefore, $$A$$ cancels out and is of no consequence.↩︎ 204. What we are really doing here is applying a problem-solving technique I like to call limiting cases. This is where we simplify the analysis of some system by considering scenarios where the mathematical quantities are easy to compute.↩︎ 205. Of course, the mathematical plotting software cannot show a pole of truly infinite height, and so the pole has been truncated. This is why it appears to have a “flat” top.↩︎ 206. My first pole-zero plot using the ePiX C++ mathematical visualization library took several hours to get it just right. Subsequent plots went a lot faster, of course, but they still require substantial amounts of time to adjust for a useful and aesthetically pleasing appearance.↩︎ 207. A powerful mathematical technique known as a Laplace Transform does this very thing: translate any differential equation describing a physical system into functions of $$s$$, which may then be analyzed in terms of transfer functions and pole-zero plots.↩︎ 208. As before, this counter-intuitive condition is possible only because the capacitor in this circuit has the ability to store energy. If the capacitor is charged by some previous input signal event and then allowed to discharge through the resistor, it becomes possible for this circuit to develop an output voltage even with short-circuited input terminals.↩︎ 209. The two solutions for $$\omega$$ (one at +1 radian per second and the other at $$-1$$ radian per second) merely indicate the circuit is able to oscillate “forward” as well as “backward”. In other words, it is able to oscillate sinusoidally where the positive peak occurs at time $$t = 0$$ (+1 rad/sec) as well as oscillate sinusoidally where the negative peak occurs at time $$t = 0$$ ($$-1$$ rad/sec). We will find that solutions for $$s$$ in general are symmetrical about the real axis, meaning if there is any solution for $$s$$ requiring an imaginary number value, there will be two of them: one with a positive imaginary value and the other with a negative imaginary value.↩︎ 210. The only way to obtain a purely imaginary root for this polynomial is for the “$$b$$” coefficient to be equal to zero. For our example circuit, it means either $$R$$ or $$C$$ would have to be zero, which is impossible if both of those components are present and functioning. Thus, our RLC filter circuit will have either real poles or complex poles.↩︎ 211. Or, one might argue there are two repeated poles, one at $$s = -1 + j0$$ and another at $$s = -1 - j0$$.↩︎ 212. The center of the pole farthest from the plot’s origin actually lies outside the plotted area, which is why that pole appears to be vertically sliced. This plot’s domain was limited to the same values ($$\pm 2$$) as previous plots for the sake of visual continuity, the compromise here being an incomplete mapping of one pole.↩︎ 213. Low-pass filter circuits are typically used to “smooth” the ripple from the output of a rectifier. The greater the frequency of this ripple voltage, the easier it is to filter from the DC (which has a frequency of zero). All other factors being equal, a low-pass filter attenuates higher-frequency components to a greater extent than lower-frequency components.↩︎ 214. Here, the term “balanced” refers to a condition where all phase voltages and currents are symmetrically equal. Unbalanced conditions can and do exist in real polyphase power systems, but the degree of imbalance is usually quite small except in cases of component faults.↩︎ 215. You may recall from basic physics that while force and displacement are both vector quantities (having direction as well as magnitude), work and energy are not. Since power is nothing more than the rate of work over time, and neither work nor time are vector quantities, power is not a vector quantity either. This is closely analogous to voltage, current, and power in polyphase electrical networks, where both voltage and current are phasor quantities (having phase angle “direction” as well as magnitude) but where power merely has magnitude. We call such “directionless” quantities scalar. Scalar arithmetic is simple, with quantities adding and subtracting directly rather than trigonometrically.↩︎ 216. We end up with the same final result if we substitute line quantities in a wye-connected system, too. Instead of $$V_{line} = V_{phase}$$ and $$I_{phase} = {I_{line} \over \sqrt{3}}$$ in the delta connection we have $$I_{line} = I_{phase}$$ and $$V_{phase} = {V_{line} \over \sqrt{3}}$$ in the wye connection. The end-result is still $$P_{total} = (\sqrt{3}) (I_{line})(V_{line})$$ based on line quantities.↩︎ 217. A colorful term for this odd voltage is bastard voltage.↩︎ 218. If you are having difficulty seeing the A-B-C or A-C-B rotations of the positive and negative sequences, you may be incorrectly visualizing them. Remember that the phasors (arrows) themselves are rotating about the center point, and you (the observer) are stationary. If you imagine yourself standing where the tip of each “A” phasor now points, then imagine all the phasor arrows rotating counter-clockwise, you will see each phasor tip pass by your vantage point in the correct order.↩︎ 219. It is good to remember that each of the symmetrical components is perfectly balanced (i.e. the “b” and “c” phasors each have exactly the same magnitude as the “a” phasor in each sequential set), and as such each of the phasors for each symmetrical set will have exactly the same magnitude. It is common to denote the calculated phasors simply as $$V_1$$, $$V_2$$, and $$V_0$$ rather than $$V_{a1}$$, $$V_{a2}$$, and $$V_{a0}$$, the “a” phasor implied as the representative of each symmetrical component.↩︎ 220. A “shorthand” notation commonly seen in symmetrical component analysis is the use of a unit phasor called $$a$$, equal to $$1 \angle 120^o$$. Multiplying any phasor quantity by $$a$$ shifts that phasor’s phase angle by +120 degrees while leaving its magnitude unaffected. Multiplying any phasor quantity by $$a^2$$ shifts that phasor’s phase angle by +240 degrees while leaving its magnitude unaffected. An example of this “$$a$$” notation is seen in the following formula for calculating the positive sequence voltage phasor: $$V_{a1} = {1 \over 3} (V_a + a V_b + a^2 V_c)$$↩︎ 221. The battery-and-switch test circuit shown here is not just hypothetical, but may actually be used to test the polarity of an unmarked transformer. Simply connect a DC voltmeter to the secondary winding while pressing and releasing the pushbutton switch: the voltmeter’s polarity indicated while the button is pressed will indicate the relative phasing of the two windings. Note that the voltmeter’s polarity will reverse when the pushbutton switch is released and the magnetic field collapses in the transformer coil, so be sure to pay attention to the voltmeter’s indication only during the instant the switch !↩︎ 222. An autotransformer is any transformer configuration where the primary and secondary windings are connected rather than galvanically isolated from each other as is typical.↩︎ 223. This use of the term is entirely different from the same term’s use in the electric power industry, where a “transmission line” is a set of conductors used to send large amounts of electrical energy over long distances.↩︎ 224. The signal generator was set to a frequency of approximately 240 kHz with a Thévenin resistance of 118 ohms to closely match the cable’s characteristic impedance of 120 ohms. The signal amplitude was just over 6 volts peak-to-peak.↩︎ 225. The termination shown here is imperfect, as evidenced by the irregular amplitude of the square wave. The cable used for this experiment was a length of twin-lead speaker cable, with a characteristic impedance of approximately 120 ohms. I used a 120 ohm ($$\pm$$ 5%) resistor to terminate the cable, which apparently was not close enough to eliminate all reflections.↩︎ 226. A “polar” molecule is one where the constituent atoms are bound together in such a way that there is a definite electrical polarity from one end of the molecule to the other. Water (H$$_{2}$$O) is an example of a polar molecule: the positively charged hydrogen atoms are bound to the negatively charged oxygen atom in a “V” shape, so the molecule as a whole has a positive side and a negative side which allows the molecule to be influenced by external electric fields. Carbon dioxide (CO$$_{2}$$) is an example of a non-polar molecule whose constituent atoms lie in a straight line with no apparent electrical poles. Interestingly, microwave ovens exploit the fact of water molecules’ polarization by subjecting food containing water to a strong oscillating electric field (microwave energy in the gigahertz frequency range) which causes the water molecules to rotate as they continuously orient themselves to the changing field polarity. This oscillatory rotation manifests itself as heat within the food.↩︎ 227. An older term used by radio pioneers to describe antennas is radiator, which I personally find very descriptive. The word “antenna” does an admirable job describing the physical appearance of the structure – like antennas on an insect – but the word “radiator” actually describes its function, which is a far more useful principle for our purposes.↩︎ 228. In practice, the ideal length of a dipole antenna turns out to be just a bit shorter than theoretical, due to lumped-capacitive effects at the wire ends. Thus, a resonant 30 MHz half-wave dipole antenna should actually be about 4.75 meters in length rather than exactly 5 meters in length.↩︎ 229. For more information on conducting “thought experiments,” refer to the subsection of this book titled “Using Thought Experiments” (34.3.4) beginning on page .↩︎ 230. Many interesting points may be drawn from these two illustrations. Regarding the strip chart recording instrument itself, it is worth noting the ornate design of the metal frame (quite typical of machinery design from that era), the attractive glass dome used to shield the chart and mechanism from the environment, and the intricate mechanism used to drive the strip chart and move the pen. Unlike a circular chart, the length of a strip chart is limited only by the diameter of the paper roll, and may be made long enough to record many days’ worth of pressure measurements. The label seen on the front of this instrument (“Edson’s Recording and Alarm Gauge”) tells us this instrument has the ability to alert a human operator of abnormal conditions, and a close inspection of the mechanism reveals a bell on the top which presumably rings under alarm conditions. Regarding the strip chart record, note the “compressed” scale, whereby successive divisions of the vertical scale become closer in spacing, reflecting some inherent nonlinearity of the pressure-sensing mechanism.↩︎ 231. These might be float-driven switches, where each switch is mechanically actuated by the buoyancy of a hollow metal float resting on the surface of the water. Another technology uses metal electrodes inserted into the water from above, sensing water level by electrical conductivity: when the water level reaches the probe’s tip, an electrical circuit is closed. For more information on liquid level switches, refer to section 9.6 beginning on page .↩︎ 232. D.A. Strobhar, writing in The Instrument Engineers’ Handbook on the subject of alarm management, keenly observes that alarms are the only form of instrument “whose sole purpose is to alter the operator’s behavior.” Other instrument devices work to control the process, but only alarms work to control the human operator.↩︎ 233. When a complex machine or process with many shutdown sensors automatically shuts down, it may be difficult to discern after the fact which shutdown device was responsible. For instance, imagine an engine-powered generator automatically shutting down because one of the generator’s “trip” sensors detected an under-voltage condition. Once the engine shuts down, though, multiple trip sensors will show abnormal conditions simply because the engine is not running anymore. The oil pressure sensor is one example of this: once the engine shuts down, there will no longer be any oil pressure, thus causing that alarm to activate. The under-voltage alarm falls into this category as well: once the engine shuts down, the generator will no longer be turning and therefore its output voltage must be zero. The problem for any human operator encountering the shut-down engine is that he or she cannot tell which of these alarms was the initiating cause of the shutdown versus which of these alarms simply activated after the fact once the engine shut off. An annunciator panel showing both an under-voltage and a low oil pressure light does not tell us which event happened first to shut down the generator. A “first-event” (sometimes called a “first-out”) annunciator, however, shows which trip sensor was the first to activate, thus revealing the initiating cause of the event.↩︎ 234. A fun and informative essay to read on this subject is Mortimer Adler’s How to Mark a Book, widely disseminated on the Internet. In it, Adler argues persuasively for the habit of annotating the books you read, and gives some practical tips for doing so. He says reading a book should be a sort of conversation with the author where the flow of information is not just from the author to you, but also from you to yourself as you question, consider, and even argue the author’s points.↩︎ 235. Sometimes P&ID stands for Piping and Instrument Diagram. Either way, it means the same thing.↩︎ 236. It should be noted that the “zooming in” of scope in a P&ID does not necessarily mean the scope of other areas of the process must be “zoomed out.” In fact, it is rather typical in a P&ID that the entire process system is shown in finer detail than in a PFD, but not all on one page. In other words, while a PFD may depict a process in its entirely on one piece of paper, a comprehensive P&ID will typically span multiple pieces of paper, each one detailing a section of the process system.↩︎ 237. Compressor “surge” is a violent and potentially self-destructing action experienced by a centrifugal compressor if the pressure drop across it becomes too high and the flow rate through it becomes too low. Surging may be prevented by opening up a “recycle” valve from the compressor’s discharge line to the suction line, ensuring adequate flow through the compressor while simultaneously unloading the high pressure differential across it.↩︎ 238. Functional diagrams are sometimes referred to as SAMA diagrams in honor of the organization responsible for their standardization, the Scientific Apparatus Makers Association. This organization has been succeeded by the Measurement, Control, and Automation Association (MCAA), thus obsoleting the “SAMA” acronym.↩︎ 239. Exceptions do exist to this rule. For example, in a cascade or feedforward loop where multiple transmitters feed into one or more controllers, each transmitter is identified by the type of process variable it senses, and each controller’s identifying tag follows suit.↩︎ 240. EBAA Iron Sales, Inc published a two-page report in 1994 (“Connections” FL-01 2-94) summarizing the history of flange “pound” ratings, from the ASME/ANSI B16 standards.↩︎ 241. For example, 1/8 inch NPT pipe fittings have a thread pitch of 27 threads per inch. 1/4 inch and 3/8 inch NPT fittings are 18 threads per inch, 1/2 inch and 3/4 inch NPT fittings are 14 threads per inch, and 1 inch through 2 inch NPT fittings are 11.5 threads per inch.↩︎ 242. Impulse lines are alternatively called gauge lines or sensing lines.↩︎ 243. This happens to be a Swagelok brass instrument tube fitting being installed on a 3/8 inch copper tube.↩︎ 244. So is Gyrolok, Hoke, and a host of others. It is not my intent to advertise for different manufacturers in this textbook, but merely to point out some of the more common brands an industrial instrument technician might encounter on the job.↩︎ 245. It should be noted that the fitting nuts became seized onto the tube due to the tube’s swelling. The tube fittings may not have leaked during the test, but their constituent components are now damaged and should never be placed into service again.↩︎ 246. No one wants to become known as the person who “messed up” someone else’s neat wiring job!↩︎ 247. An occupational hazard for technicians performing work on screw terminations is carpal tunnel syndrome, where repetitive wrist motion (such as the motions required to loosen and tighten screw terminals) damages portions of the wrist where tendons pass.↩︎ 248. An exception is when the screw is equipped with a square washer underneath the head, designed to compress the end of a stranded wire with no shear forces. Many industrial instruments have termination points like this, for the express purpose of convenient termination to either solid or stranded wire ends.↩︎ 249. This is similar to people referring to adhesive bandages as “Band-Aids” or tongue-and-groove joint pliers as “Channelocks,” because those particular brands have become popular enough to represent an entire class.↩︎ 250. The principle at work here is the strength of the field generated by the noise-broadcasting conductor: electric field strength (involved with capacitive coupling) is directly proportional to voltage, while magnetic field strength (involved with inductive coupling) is directly proportional to current.↩︎ 251. Incidentally, cable shielding likewise guards against strong electric fields within the cable from capacitively coupling with conductors outside the cable. This means we may elect to shield “noisy” power cables instead of (or in addition to) shielding low-level signal cables. Either way, good shielding will prevent capacitive coupling between conductors on either side of a shield.↩︎ 252. This is not to say magnetic fields cannot induce common-mode noise voltage: on the contrary, magnetic fields are capable of inducing voltage in any electrically-conductive loop. For this reason, both differential and ground-referenced signals are susceptible to interference by magnetic fields.↩︎ 253. An example of this is the UTP (Unshielded, Twisted Pair) cabling used for Ethernet digital networks, where four pairs of wires having different twist rates are enclosed within the same cable sheath.↩︎ 254. This use of the term is entirely different from the same term’s use in the electric power industry, where a “transmission line” is a set of conductors used to send large amounts of electrical energy over long distances.↩︎ 255. A student of mine once noted that he has been doing this out of habit whenever he has a conversation with anyone in a racquetball court. All the hard surfaces (floor, walls) in a racquetball court create severe echoes, forcing players to speak slower in order to avoid confusion from the echoes.↩︎ 256. The characteristic, or “surge,” impedance of a cable is a function of its conductor geometry (wire diameter and spacing) and dielectric value of the insulation between the conductors. Any time a signal reaches an abrupt change in impedance, some (or all) of its energy is reflected in the reverse direction. This is why reflections happen at the unterminated end of a cable: an “open” is an infinite impedance, which is a huge shift from the finite impedance “seen” by the signal as it travels along the cable. This also means any sudden change in cable geometry such as a crimp, nick, twist, or sharp bend is capable of reflecting part of the signal. Thus, high-speed digital data cables must be installed more carefully than low-frequency or DC analog signal cables.↩︎ 257. Smoke signals are an ancient form of light-based communication!↩︎ 258. These are thin plastic or sheet metal tubes with mirrored internal surfaces, extending from a collector dome (made of glass or plastic) outside the dwelling to a diffusion lens inside the dwelling.↩︎ 259. Technicians working with optical fiber typically carry pressurized cans of dust-blowing air or other gas to clean connectors and sockets prior to joining the two.↩︎ 260. Chief of which is the potential to get optical fibers embedded in the body, where such transparent “slivers” are nearly impossible to find and extract.↩︎ 261. A “photon” is a quantity of light energy represented as a particle, along the same scale as an electron. It isn’t entirely fair to characterize light as either consisting of waves or as consisting of particles, because light tends to manifest properties of both. Actually, this may be said of any sub-atomic particle (such as an electron) as well: under certain conditions these particles act like clumps of matter, and under different conditions they tend to act as waves of electromagnetic energy. This particle-wave duality lies at the heart of quantum physics, and continues to be something of a philosophical mystery simply because the behavior defies the macroscopic constructs we are accustomed to using when modeling the natural world.↩︎ 262. Fluorescence is the phenomenon of a substance emitting a long-wavelength (low-energy) photon when “excited” by a short-wavelength (high-energy) photon. Perhaps the most familiar example of fluorescence is when certain materials emit visible light when exposed to ultraviolet light which is invisible to the human eye. The example of fluorescence discussed here with dissolved oxygen sensing happens to use two different colors (wavelengths) of visible light, but the basic principle is the same.↩︎ 263. Impurities such as metals and water are held to values less than 1 part per billion (ppb) in modern optical fiber-grade glass.↩︎ 264. The “index of refraction” ($$n$$) for any substance is the ratio of the speed of light through a vacuum ($$c$$) compared to the speed of light through that substance ($$v$$): $$n = {c \over v}$$. For all substances this value will be greater than one (i.e. the speed of light will always be greatest through a vacuum, at 299792458 meters per second or 186282.4 miles per second). Thus, the refractive index for an optically transparent substance is analogous to the reciprocal of the velocity factor of an electrical transmission line, where the permittivity and permeability of the cable materials act to slow down the propagation of electric and magnetic fields through the cable.↩︎ 265. All of these sizes refer to glass fibers. Plastic-based optical fibers are also manufactured, with much larger core diameters to offset the much greater optical losses through plastic compared to through ultra-pure glass. A typical plastic optical fiber (POF) standard is specified at a core diameter of 980 microns and a cladding diameter of 1000 microns (1 millimeter)!↩︎ 266. A common core size for “multi-mode” optical fiber is 50 microns, or 50 micro-meters. If a wavelength of 1310 nanometers (1.31 microns) is used, the core’s diameter will be $$50 \over 1.31$$ or over 38 times the wavelength.↩︎ 267. The most straight-forward way to make an optical fiber single-mode is to manufacture it with a skinnier core. However, this is also possible to achieve by increasing the wavelength of the light used! Remember that what makes a single-mode optical fiber only have one mode is the diameter of its core relative to the wavelength of the light. For any optical fiber there is a cutoff wavelength above which it will operate as single-mode and below which it will operate as multi-mode. However, there are practical limits to how long of a wavelength we can make the light before we run into other problems, and so single-mode optical fiber is made for standard light wavelengths by manufacturing the cable with an exceptionally small core diameter.↩︎ 268. Typically a few inches for multi-mode fiber.↩︎ 269. Not just light lost along the length of the fiber, but also at each connector on the fiber, since placing the test fiber within the optical path between the light source and optical power meter necessarily introduces another pair of connectors where light may be lost.↩︎ 270. Since distance along any path is simply the product of speed and time ($$x = vt$$), and the speed of light through an optical fiber is a well-defined quantity ($$v = {c \over n}$$ where $$n$$ is the core’s index of refraction), the distance between the OTDR and the flaw is trivial to calculate.↩︎ 271. Mistaken interpretations of switch status remains one of the most resilient misconceptions for students first learning this topic. It seems that a great many students prefer to think of a switch’s drawn status as its status at the present moment (e.g. when the process is running as expected). I believe the heart of this misconception is the meaning of the word “normal,” which to most peoples’ minds refers to “the way things typically are.”↩︎ 272. In this discussion I am deliberately omitting the detail of deadband for process switches, for the sake of simplicity.↩︎ 273. This curious label is used to describe switch contacts lacking their own built-in power source, as opposed to a switch contained in a device that also provides power to drive the switch circuit. Dry contacts may be mechanical in nature, or they may be electronic (e.g. transistor). By contrast, a “wet” contact is one already connected to an internal power source, ready to drive a load with no other external components needed.↩︎ 274. To be honest, one could use an NPN transistor to source current or a PNP to sink, but it would require the transistor be used in the common-collector configuration which does not allow for saturation. The engineers designing these proximity switches strive for complete saturation of the transistor, in order to achieve minimum “on” resistance, and that requires a common-emitter configuration.↩︎ 275. If the trip setting of a pressure switch is below atmospheric pressure, then it will be “actuated” at atmospheric pressure and in its “normal” status only when the pressure falls below that trip point (i.e. a vacuum).↩︎ 276. “Ferrous” simply means any iron-containing substance.↩︎ 277. The reason for this opposition is rooted in the roles of primary and secondary coils as power load and source, respectively. The voltage across each coil is a function of Faraday’s Law of Electromagnetic Induction: $$V = N{d \phi \over dt}$$. However, since the primary coil acts as a load (drawing power from the 120 VAC source) and the secondary coil acts as a source (sending power to the probes), the directions of current through the two coils will be opposite despite their common voltage polarities. The secondary coil’s opposite current direction causes an opposing magnetic force in that section of the core, reducing the magnetic flux there. In a normal power transformer, this reduction in magnetic flux caused by secondary current is also felt by the primary coil (since there is only one magnetic “path” in a power transformer’s core), which then causes the primary coil to draw more current and re-establish the core flux at its original magnitude. With the inductive relay, however, the opposing magnetic force created by the secondary coil simply forces more of the primary coil’s magnetic flux to bypass to the alternate route: through the armature.↩︎ 278. The B/W Controls model 5200 solid-state relay, for example, uses only 8 volts AC at the probe tips.↩︎ 279. If the trip setting of a temperature switch is below ambient temperature, then it will be “actuated” at ambient temperature and in its “normal” status only when the temperature falls below that trip point (i.e. colder than ambient).↩︎ 280. A plug valve is very much like a ball valve, the difference being the shape of the rotating element. Rather than a spherical ball, the plug valve uses a truncated cone as the rotary element, a slot cut through the cone serving as the passageway for fluid. The conical shape of a plug valve’s rotating element allows it to wedge tightly into the “closed” (shut) position for exceptional sealing.↩︎ 281. While it would be technically possible to use water instead of oil in a hydraulic power system, oil enjoys some distinct advantages. First, oil is a lubricating substance, and non-corrosive, unlike water. Second, oil enjoys a wider operating temperature range than water, which tends to both freeze and boil more readily.↩︎ 282. Note also how identical reservoir symbols may be placed at different locations of the diagram although they represent the exact same reservoir. This is analogous to “ground” symbols in electronic schematic diagrams, every ground symbol representing a common connection to the same zero-potential point.↩︎ 283. Close-coupled hydraulic systems with variable-displacement pumps and/or motors may achieve high efficiency, but they are the exception rather than the rule. One such system I have seen was used to couple a diesel engine to the drive axle of a large commercial truck, using a variable-displacement pump as a continuously-variable transmission to keep the diesel engine in its optimum speed range. The system was so efficient, it did not require a cooler for the hydraulic oil!↩︎ 284. Many kinds of hydraulic oils are flammable, so this is not a perfectly true statement. However, fire-resistant fluids such as Skydrol (introduced to the aviation industry for safety) are commercially available.↩︎ 285. Certain types of plastic pipe such as PVC should never be used in compressed air systems because it becomes brittle and liable to fracture over time. If you are considering the use of plastic for a high-pressure compressed air system, be sure the type of plastic is engineered for air pressure service!↩︎ 286. One could argue that enough fluid pressure could override the solenoid’s energized state as well, so why choose to have the fluid pressure act in the direction of helping the return spring? The answer to this (very good) question is that the solenoid’s energized force greatly exceeds that of the return spring. This is immediately obvious on first inspection, as the solenoid must be stronger than the return spring or else the solenoid valve would never actuate! Furthermore, the solenoid’s force must be significantly stronger than the spring, or else the valve would open rather slowly. Fast valve action demands a solenoid force that greatly exceeds spring force. Realizing this, now, we see that the spring is the weaker of the two forces, and thus it makes perfect sense why we should use the valve in such a way that the process pressure helps the spring: the solenoid’s force has the best chance of overcoming the force on the plug produced by process pressure, so those two forces should be placed in opposition, while the return spring’s force should work with (not against) the process pressure.↩︎ 287. In hydraulics, it is common to use the letter “T” to represent the tank or reservoir return connection rather than the letter “E” for exhaust, which is why the supply and vent lines on this valve are labeled “P” and “T”, respectively.↩︎ 288. The letters “IAS” refer to instrument air supply.↩︎ 289. This solenoid valve arrangement would be designated 1oo2 from the perspective of starting the turbine, since only one out of the two solenoids needs to trip in order to initiate the turbine start-up.↩︎ 290. If you examine this diagram closely, you will notice an error in it: it shows the top and bottom of the piston actuator connected together by air tubing, which if implemented in real life would prevent air pressure from imparting any force to the valve stem at all! Connecting the top and bottom of the actuator together would ensure the piston always sees zero differential pressure, and thus would never develop a resultant force. The output tube of PY-590 should only connect to the bottom of the piston actuator, not to the bottom and the top. A more minor error in this diagram snippet is the labeling of SOV-590A: it actually reads “SOV-59DA” if you look closely enough! My first inclination when sampling this real P&ID for inclusion in the book was to correct the errors, but I think an important lesson may be taught by leaving them in: documentation errors are a realistic challenge you will contend with on the job as an instrumentation professional!↩︎ 291. To view a flip-book animation of this sequence, turn to Appendix [animation_blinking_lights] beginning on page .↩︎ 292. To view a flip-book animation of this same sequence, turn to Appendix [animation_3phase_motor] beginning on page .↩︎ 293. A helpful analogy for this effect is to imagine a sailboat traveling directly downwind, its motive force provided by a sail oriented perpendicular to the direction of travel. It should be obvious that in this configuration the sailboat cannot travel faster than the wind. What is less obvious is the fact that the sailboat can’t even travel as fast as the wind, its top speed in this configuration being slightly less than the wind speed. If the sailboat somehow did manage to travel exactly at the wind’s speed, the sail would go slack because there would be no relative motion between the sail and the wind, and therefore the sail would cease to provide any motive force. Thus, the sailboat must “slip” or “lag” behind the wind speed just enough to fill the sails with enough force to overcome water friction and maintain speed.↩︎ 294. As a vivid illustration of this concept, I once worked at an aluminum foundry where an AC induction motor stator assembly was used to electromagnetically spin molten aluminum inside the mold as it cooled from molten to solid state. Even though aluminum is a non-magnetic material, it was still spun by the stator’s rotating magnetic field due to electromagnetic induction and Lenz’s Law.↩︎ 295. Two magnetic poles in the stator per phase, which is the lowest number possible because each phase naturally produces both a “north” and a “south” pole when energized. In the case of a three-phase induction or synchronous motor, this means a total of six magnetic stator poles.↩︎ 296. Doubling the number of magnetic poles increases the number of AC power cycles required for the rotating magnetic field to complete one full revolution. This effect is not unlike doubling the number of light bulbs in a chaser light array of fixed length, making it seem as though the light sequence is moving slower because there are more bulbs to blink along the same distance.↩︎ 297. As mentioned previously, the rotor can never fully achieve synchronous speed, because if it did there would be zero relative motion between the rotating magnetic field and the rotating rotor, and thus no induction of currents in the rotor bars to create the induced magnetic fields necessary to produce a reaction torque. Thus, the rotor must “slip” behind the speed of the rotating magnetic field in order to produce a torque, which is why the full-load speed of an induction motor is always just a bit slower than the synchronous speed of the rotating magnetic field (e.g. a 4-pole motor with a synchronous speed of 1800 RPM will rotate at approximately 1750 RPM).↩︎ 298. In this mode, the machine is called an induction alternator rather than an induction motor.↩︎ 299. Faraday’s Law of Electromagnetic Induction describes the voltage induced in a wire coil of $$N$$ turns as proportional to the rate of change of the magnetic flux: $$V = N {d \phi \over dt}$$. The greater the difference in speed between the rotor and the rotating magnetic field, the greater $${d \phi \over dt}$$, inducing greater voltages in the rotor and thus greater currents in the rotor.↩︎ 300. This principle is not difficult to visualize if you consider the phase sequence as a repeating pattern of letters, such as ABCABCABC. Obviously, the reverse of this sequence would be CBACBACBA, which is nothing more than the original sequence with letters A and C transposed. However, you will find that transposing any two letters of the original sequence transforms it into the opposite order: for example, transposing letters A and B turns the sequence ABCABCABC into BACBACBAC, which is the same order as the sequence CBACBACBA.↩︎ 301. I once encountered a washing machine induction motor with an “open” fault in the start winding. When energized, this motor remained still and hummed because it had no second phase to give its magnetic field a rotation. However, if you used your hand to give the motor a spin in either direction, the motor would accelerate to full speed in that direction!↩︎ 302. In this example, the direction of rotation is counter-clockwise. The shaded poles are oriented counter-clockwise of center, which means their delayed magnetic fields create an “appearance” of rotation in that direction: the magnetic field achieves its peak strength first at the pole centers, and then later (delayed) at the shaded poles, as though there were an actual magnet rotating in that direction.↩︎ 303. A convenient source of small shaded-pole motors is your nearest home improvement or hardware store, where they likely sell replacement electric motors for bathroom fans. Of course, you may also find such motors inside of a variety of discarded electric appliances as well. Being rather rugged devices, it is quite common to find the shaded-pole motor inside of an electrical appliance in perfect condition even though other parts of that appliance may have failed with age. In fact, the shaded-pole motor shown in the preceding photograph was salvaged from a “water-pic” electric toothbrush, the motor used to drive a small water pump (which in this case had mechanically failed) delivering water to the head of the toothbrush.↩︎ 304. This is not to say overload heaters cannot fail open, because they can and will under extraordinary circumstances. However, opening like a fuse is not the design function of an overload heater.↩︎ 305. For a more complete coverage of protective relays, refer to section 25.7 beginning on page .↩︎ 306. One way to help clarify the function of a protective relay is to envision circuit protection without one. Household and low-current industrial circuit breakers are constructed to have their own internal current-sensing elements (either thermal or magnetic) to force the circuit breaker open automatically when current exceeds a pre-set limit. With protective relays, the circuit breaker instead has a “trip coil” which will cause the breaker to trip when energized. The breaker then relies entirely on the (external) protective relay to tell it when to trip. By relegating the function of event detection to a sophisticated, external relay, the circuit breaker may act much “smarter” in protecting against a wider variety of faults and abnormal conditions than if it relied entirely on its own internal overcurrent-sensing mechanism.↩︎ 307. Potential transformers are also known as voltage transformers, abbreviated VT.↩︎ 308. This bucket was still under construction at the time the photograph was taken. As such, none of the motor leads have been connected, which is why there are no power conductors exiting the bottom of the bucket. Instead, all you see are three terminals ready to accept heavy-gauge motor leads.↩︎ 309. An unfortunately common tendency among novices is to sketch slash marks through relay contact symbols in order to show when they happen to be closed. This is a very bad habit, and should be discouraged at all times! Diagonal lines drawn through a contact symbol are supposed to denote the contact to be normally-closed, not closed: it shows that a switch contact will be in the closed (conducting) state when it is at rest. What we actually need is a different kind of symbol to show when a contact is closed during any arbitrary condition we may imagine. When someone uses this same symbology to denote a contact that happens to be closed during some condition, it needlessly confuses the concepts of closed versus normally-closed.↩︎ 310. If the diode were connected the other way, it would pass current whenever the proximity switch turned on, shorting past the relay coil and most likely damaging the proximity switch in doing so!↩︎ 311. A “contactor” is nothing more than a very large electromechanical relay, and itself is a form of interposing device. Its purpose is to make and break three-phase AC power to a heavy load (e.g. an electric motor) at the command of a much smaller electrical signal, in this case a 120 volt AC signal sent to the coil of the contactor.↩︎ 312. There are such things as soft PLCs, which consist of special-purpose software running on an ordinary personal computer (PC) with some common operating system. Soft PLCs enjoy the high speed and immense memory capacity of modern personal computers, but do not possess the same ruggedness either in hardware construction or in operating system design. Their applications should be limited to non-critical controls where neither main process production nor safety would be jeopardized by a control system failure.↩︎ 313. I/O “channels” are often referred to as “points” in industry lingo. Thus, a “32-point input card” refers to an input circuit with 32 separate channels through which to receive signals from on/off switches and sensors.↩︎ 314. By “control wire,” I mean the single conductor connecting the I/O card channel to the field device, as opposed to conductors directly common with either the positive or negative lead of the voltage source. If you focus your attention on this one wire, noting the direction of conventional-flow current through it, the task of determining whether a device is sourcing or sinking current becomes much simpler.↩︎ 315. Some modern PLCs such as the Koyo “CLICK” are also discrete-only. Analog I/O and processing is significantly more complex to engineer and more expensive to manufacture than discrete control, and so low-end PLCs are more likely to lack analog capability.↩︎ 316. A “de facto” standard is one arising naturally out of legacy rather than by an premeditated agreement between parties. Modbus and Profibus networks are considered “de facto” standards because those networks were designed, built, and marketed by pioneering firms prior to their acceptance as standards for others to conform to. In Latin, de facto means “from the fact,” which in this case refers to the fact of pre-existence: a standard agreed upon to conform to something already in popular use. By contrast, a standard intentionally agreed upon before its physical realization is a de jure standard (Latin for “from the law”). FOUNDATION Fieldbus is an example of a de jure standard, where a committee arrives at a consensus for a network design and specifications prior to that network being built and marketed by any firm.↩︎ 317. It should be noted that in some situations the programming software will fail to color the contacts properly, especially if their status changes too quickly for the software communication link to keep up, and/or if the bit(s) change state multiple times within one scan of the program. However, for simple programs and situations, this rule holds true and is a great help to beginning programmers as they learn the relationship between real-world conditions and conditions within the PLC’s “virtual” world.↩︎ 318. The electrical wiring shown in this diagram is incomplete, with the “Common” terminal shown unconnected for simplicity’s sake.↩︎ 319. For a PLC program contact, the shading represents virtual “conductivity.” For a PLC program coil, the shading represents a set (1) bit.↩︎ 320. It is worth noting the legitimacy of referencing virtual contacts to output bits (e.g. contact Y5), and not just to input bits. A “virtual contact” inside a PLC program is nothing more than an instruction to the PLC’s processor to read the status of a bit in memory. It matters not whether that bit is associated with a physical input channel, a physical output channel, or some abstract bit in the PLC’s memory. It would, however, be wrong to associate a virtual coil with an input bit, as coil instructions write bit values to memory, and input bits are supposed to be controlled solely by the energization states of their physical input channels.↩︎ 321. The most modern Allen-Bradley PLCs have all but done away with fixed-location I/O addressing, opting instead for tag name based I/O addressing. However, enough legacy Allen-Bradley PLC systems still exist in industry to warrant coverage of these addressing conventions.↩︎ 322. Also called the data table, this map shows the addressing of memory areas reserved for programs entered by the user. Other areas of memory exist within the SLC 500 processor, but these other areas are inaccessible to the technician writing PLC programs.↩︎ 323. This is not to say one cannot specify a particular bit in an otherwise whole word. In fact, this is one of the powerful advantages of Allen-Bradley’s addressing scheme: it gives you the ability to precisely specify portions of data, even if that data is not generally intended to be portioned into smaller pieces!↩︎ 324. Programmers familiar with languages such as C and C++ might refer to an Allen-Bradley “element” as a data structure, each type with a set configuration of words and/or bits.↩︎ 325. Referencing the Allen-Bradley engineering literature, we see that the accumulator word may alternatively be addressed by number rather than by mnemonic, T4:2.2 (word 2 being the accumulator word in the timer data structure), and that the “done” bit may be alternatively addressed as T4:2.0/13 (bit number 13 in word 0 of the timer’s data structure). The mnemonics provided by Allen-Bradley are certainly less confusing than referencing word and bit numbers for particular aspects of a timer’s function!↩︎ 326. Some systems such as the Texas Instruments 505 series used “X” labels to indicate discrete input channels and “Y” labels to indicate discrete output channels (e.g. input X9 and output Y14). This same labeling convention is still used by Koyo in its DirectLogic and “CLICK” PLC models. Siemens continues a similar tradition of I/O addressing by using the letter “I” to indicate discrete inputs and the letter “Q” to indicate discrete outputs (e.g. input channel I0.5 and output Q4.1).↩︎ 327. This particular program and editor is for the Koyo “CLICK” series of micro-PLCs.↩︎ 328. If this were a legacy Allen-Bradley PLC system using absolute addressing, we would be forced to address the three sensor inputs as I:1/0, I:1/1, and I:1/2 (slot 1, channels 0 through 2), and the indicator lamp output as O:2/0 (slot 2, channel 0). If this were a newer Logix5000 Allen-Bradley PLC, the default tag names would be Local:1:I.Data.0, Local:1:I.Data.1, and Local:1:I.Data.2 for the three inputs, and Local:2:O.Data.0 for the output. However, in either system we have the ability to assign symbolic addresses so we have a way to reference the I/O channels without having to rely on these cumbersome labels. The programs showing in this book exclusively use tag names rather than absolute addresses, since this is the more modern programming convention.↩︎ 329. The most likely reason why one out of two flame sensors might not detect the presence of a flame is some form of misalignment or fouling of the flame sensor. In fact, this is a good reason for using a 2-out-of-3 flame detection system rather than a simplex (1-out-of-1) detector scheme: to make the system more tolerant of occasional sensor problems without compromising burner safety.↩︎ 330. The particular input and output channels chosen for this example are completely arbitrary. There is no particular reason to choose input channels 6 and 7, or output channel 2, as I have shown in the wiring diagram. Any available I/O channels will suffice.↩︎ 331. While it is possible to wire the overload contact to one of the PLC’s discrete input channels and then program a virtual overload contact in series with the output coil to stop the motor in the event of a thermal overload, this strategy would rely on the PLC to perform a safety function which is probably better performed by hard-wired circuitry.↩︎ 332. A very common misconception among students first learning PLC Ladder Diagram programming is to always associate contacts with PLC inputs and coils with PLC outputs, thus it seems weird to have a contact bear the same label as an output. However, this is a false association. In reality, contacts and coils are read and write instructions, and thus it is possible to have the PLC read one of its own output bits as a part of some logic function. What would be truly strange is to label a coil with an input bit address or tag name, since the PLC is not electrically capable of setting the real-world energization status of any input channels.↩︎ 333. In an effort to alleviate this confusion, the Allen-Bradley corporation (Rockwell) uses the terms examine if closed (XIC) and examine if open (XIO) to describe “normally open” and “normally closed” virtual contacts, respectively, in their Ladder Diagram programming. The idea here is that a virtual contact drawn as a normally-open symbol will be “examined” (declared “true”) by the PLC’s processor if its corresponding input channel is energized (powered by a real-life contact in the closed state). Conversely, a virtual contact drawn as a normally-closed symbol (with a slash mark through the middle) will be “examined” by the PLC’s processor if its corresponding input channel is de-energized (if the real-life contact sending power to that terminal is in the open state). In my experience, I have found this nomenclature to be even more confusing to students than simply calling these virtual contacts “normally open” and “normally closed” like other PLC manufacturers do. The foundational concept for students to grasp here is that the virtual contact is not a direct representation of the real-life electrical switch contact – rather, it is a for the bit set by power coming from the real-life electrical switch contact.↩︎ 334. Referred to as “Latch” and “Unlatch” coils by Allen-Bradley.↩︎ 335. This represents the IEC 61131-3 standard, where each variable within an instruction may be “connected” to its own arbitrary tag name. Other programming conventions may differ somewhat. The Allen-Bradley Logix5000 series of controllers is one of those that differs, following a convention reminiscent of structure element addressing in the C programming language: each counter is given a tag name, and variables in each counter are addressed as elements within that structure. For example, a Logix5000 counter instruction might be named parts_count, with the accumulated count value (equivalent to the IEC’s “current value”) addressed as parts_count.ACC (each element within the counter specified as a suffix to the counter’s tag name).↩︎ 336. The “enable out” (ENO) signal on the timer instruction serves to indicate the instruction’s status: it activates when the enable input (EN) activates and de-activates when either the enable input de-activates or the instruction generates an error condition (as determined by the PLC manufacturer’s internal programming). The ENO output signal serves no useful purpose in this particular program, but it is available if there were any need for other rungs of the program to be “aware” of the run-time timer’s status.↩︎ 337. The enable (EN) input signals specified in the IEC 61131-3 programming standard make retentive off-delay timers possible (by de-activating the enable input while maintaining the “IN” input in an inactive state), but bear in mind that most PLC implementations of timers do not have separate EN and IN inputs. This means (for most PLC timer instructions) the only input available to activate the timer is the “IN” input, in which case it is impossible to create a retentive off-delay timer (since such a timer’s elapsed time value would be immediately re-set to zero each time the input re-activates).↩︎ 338. Perhaps two pumps performing the same pumping function, one serving as a backup to the other. Alternating motor control ensures the two motors’ run times are matched as closely as possible.↩︎ 339. The operation of the drum is not unlike that of an old player piano, where a strip of paper punched with holes caused hammers in the piano to automatically strike their respective strings as the strip was moved along at a set speed, thus playing a pre-programmed song.↩︎ 340. Perhaps the most practical way to give production personnel access to these bits without having them learn and use PLC programming software is to program an HMI panel to write to those memory areas of the PLC. This way, the operators may edit the sequence at any time simply by pressing “buttons” on the screen of the HMI panel, and the PLC need not have its program altered in any “hard” way by a technician or engineer.↩︎ 341. In this particular example, the mask value is FFFF hexadecimal, which means all 1’s in a 16-bit field. This mask value tells the sequencer instruction to regard all bits of each B3 word that is read. To contrast, if the mask were set to a value of 000F hexadecimal instead, the sequencer would only pay attention to the four least-significant bits of each B3 word that is read, while ignoring the 12 more-significant bits of each 16-bit word. The mask allows the SQO instruction to only write to selected bits of the destination word, rather than always writing all 16 bits of the indexed word to the destination word.↩︎ 342. An older term for an operator interface panel was the “Man-Machine Interface” or “MMI.” However, this fell out of favor due to its sexist tone.↩︎ 343. If the HMI is based on a personal computer platform (e.g. Rockwell RSView, Wonderware, FIX/Intellution software), it may even be equipped with a hard disk drive for enormous amounts of historical data storage.↩︎ 344. This particular trainer was partially constructed from recycled materials – the wooden platform, light switches, and power cord – to minimize cost.↩︎ 345. Not all industrial measurement and control signals are “live zero” like the 3-15 PSI and 4-20 mA standards. 0 to 10 volts DC is a common “dead zero” signal standard, although far more common in environmental (building heating and cooling) control systems than industrial control systems. I once encountered an old analog control system using $$-10$$ volts to +10 volts as its analog signal range, which meant 0 volts represented a 50% signal! A failed signal path in such a system could have been very misleading indeed, as a 50% signal value is not suspicious in the least.↩︎ 346. This is a temperature sensing element consisting of two different metal wires joined together, which generate a small voltage proportional to temperature. The correspondence between junction temperature and DC millivoltage is very well established by scientific testing, and so we may use this principle to sense process temperature.↩︎ 347. We could have just as easily chosen 100 percent for $$x$$ and 20 milliamps for $$y$$, for it would have yielded the same result of $$b = 4$$.↩︎ 348. A common misconception for people learning to apply the slope-intercept formula to linear instrument ranges is that they tend to assume $$b$$ will always be equal to the lower-range value (LRV) of the instrument’s output range. For example, given a transmitter with a 4-20 mA output range, the false assumption is that $$b = 4$$. This does happen to be true only if the instrument possesses a “dead-zero” input range, but it will not be true for instruments with a live-zero input range such in this case here where the temperature input range is 50 to 140 degrees.↩︎ 349. The “Source” and “Dest” parameters shown in this instruction box refer to special addresses in the PLC’s memory where the input (ADC count) and output (scaled flowrate) values will be found. You need not concern yourself with the meanings of I:4.2 and N7:15, because these addresses are unimportant to the task of deriving a scaling formula.↩︎ 350. Some of my students have referred to such a circuit as a smart load, since it functions as a load but nevertheless exerts control over the circuit current.↩︎ 351. Of course, a 1 ohm resistor would drop 4 mV at 4 mA loop current, and drop 20 mV at 20 mA loop current. These small voltage values necessitate a highly accurate DC voltmeter for field measurement!↩︎ 352. In the following illustrated examples, the transmitter is assumed to be a pressure transmitter with a calibrated range of 0 to 750 inches of water column, 4-20 mA. The controller’s PV (process variable) display is appropriately ranged to display 0 to 750 as well.↩︎ 353. Note the staggered layout of the tube fittings, intended to improve access to each one. Remember that the technician used a 9/16 inch wrench to loosen and tighten the tube fitting nuts, so it was important to have working room between fittings in which to maneuver a wrench.↩︎ 354. The numbers are difficult to see here, because the entire panel has been painted in a thick coat of grey paint. This particular panel was stripped of all pneumatic instruments and outfitted with electronic instruments, so the rows of bulkhead fittings no longer serve a purpose, but to remind us of legacy technology. I must wonder if some day in the future I will include a photograph of an empty terminal strip in another chapter of this book, as I explain how wired “legacy” instruments have all but been replaced by wireless (radio) instruments! Let the ghosts of the past speak to you, dear reader, testifying to the endless march of technological evolution.↩︎ 355. In ISA parlance, this would be a “WT” instrument, “W” signifying weight and “T” signifying transmitter.↩︎ 356. Compressed air is a valuable commodity because much energy is required to compress and distribute high-pressure air. Every pneumatic instrument’s nozzle is essentially a “leak” in the compressed air system, and the combined effect of many operating pneumatic instruments is that the air compressor(s) must continually run to meet demand.↩︎ 357. A more precise way to express gain as a ratio of changes is to use the “derivative” notation of calculus: $$d\hbox{Output} \over d\hbox{Input}$$↩︎ 358. An “order of magnitude” is nothing more than a ten-fold change. Do you want to sound like you’re really smart and impress those around you? Just start comparing ordinary differences in terms of orders of magnitude. “Hey dude, that last snowboarder’s jump was an order of magnitude higher than the one before!” “Whoa, that’s some big air . . .” Just don’t make the mistake of using decibels in the same way (“Whoa dude, that last jump was at least 10 dB higher than the one before!”) – you don’t want people to think you’re a nerd.↩︎ 359. In order for negative feedback to hold the input differential at zero volts, we must also assume the opamp has enough power supply voltage and output current capability to achieve this balance. No amplifier can output more voltage than its power supply gives it, nor can it output more current than its active components can conduct.↩︎ 360. In physics, the word moment refers to the product of force times lever length (the “moment arm”). This is alternatively known as torque. Thus, we could classify this pneumatic mechanism as a torque-balance system, since the two bellows’ forces are converted into torques (about the pivot point) which then cancel even though the forces themselves are unequal.↩︎ 361. An important feature of motion-balance mechanisms is that the bellows function as calibrated spring elements in addition to being force generators. Force-balance systems move so slightly that the spring characteristics of the bellows is irrelevant – not so with motion-balance mechanisms! In fact, some motion-balance mechanisms actually place coil springs inside of brass bellows to more precisely fix the elastic properties of the assembly.↩︎ 362. In my teaching experience, students try hard to find simplistic ways to distinguish force-balance from motion-balance systems. For example, many will try to associate fulcra with force-balance, assuming all motion-balance systems lack pivot points (which is not true!). Another example is to associate pivoting links with motion-balance mechanisms, which is likewise untrue. The problem with these efforts is that they are usually based on analysis of just a few different pneumatic mechanisms, making it easy to over-generalize. The truth of the matter is that a wide variety of pneumatic designs exist, defying easy categorization. My advice to you is the same as my advice to my students: you are going to have to think your way through the analysis of these mechanisms rather than memorize simple rules. Perform “thought experiments” whereby you imagine the effects of an increasing or decreasing input signal and then “see” for yourself whether the mechanism balances force with force or motion with motion, keeping in mind the simplifying assumption of an absolutely constant baffle/nozzle gap.↩︎ 363. This negating action is a hallmark of force-balance systems. When the system has reached a point of equilibrium, the components will have returned to (very nearly) their original positions. With motion-balance systems, this is not the case: one component moves, and then another component moves in response to keep the baffle/nozzle detector at a near-constant gap, but the components definitely do not return to their original positions or orientations.↩︎ 364. A good problem-solving technique to apply here is limiting cases, where we imagine the effects of extreme changes. In this case, we may imagine what would happen if the nozzle were moved all the way to the baffle’s axis, as a limiting case of moving closer to this axis. With the nozzle in this position, no amount of baffle rotation would cause the nozzle to move away, because there is no lateral motion at the axis. Only at some radius away from the axis will there be any tangential motion for the nozzle to detect and back away from, which is why the gain of the mechanism may be altered by changing the nozzle’s location with respect to the baffle’s axis.↩︎ 365. “Ferrous” simply means any substance containing the element iron.↩︎ 366. Recall the mathematical relationship between force, pressure, and area: $$F = PA$$. If we desire a greater pressure ($$P$$) to generate the same force ($$F$$) as before, we must decrease the area ($$A$$) upon which that pressure acts.↩︎ 367. It is quite easy to dislodge these small-section, large-diameter O-rings from their respective grooves during re-assembly of the unit. Be very careful when inserting the module back into the housing!↩︎ 368. Having said this, pneumatic instruments can be remarkably rugged devices. I once worked on a field-mounted pneumatic controller attached to the same support structure as a severely cavitating control valve. The vibrations of the control valve transferred to the controller through the support, causing the baffle to hammer repeatedly against the nozzle until the nozzle’s tip had been worn down to a flattened shape. Remarkably, the only indication of this problem was the fact the controller was having some difficulty maintaining setpoint. Other than that, it seemed to operate adequately! I doubt any electronic device would have fared as well, unless completely “potted” in epoxy.↩︎ 369. The technical term for the “speed limit” of any data communications channel is bandwidth, usually expressed as a frequency (in Hertz).↩︎ 370. HART communications occur at a rate of 1200 bits per second, and it is this slow by design: this slow data rate avoids signal reflection problems that would occur in unterminated cables at higher speeds. For more insight into how and why this works, refer to the “transmission lines” section 5.10 beginning on page . An example of a “slow” process variable suitable for HART digital monitoring or control is the temperature of a large building or machine, where the sheer mass of the object makes temperature changes slow by nature, and therefore does not require a fast digital data channel to report that temperature.↩︎ 371. The host system in this case is an Emerson DeltaV DCS, and the device manager software is Emerson AMS.↩︎ 372. This concept is not unlike HART, where audio-tone AC signals are superimposed on DC signal cables, so that digital data may be communicated along with DC signal and power.↩︎ 373. In the early days of personal computers, many microprocessor chips lacked floating-point processing capability. As a result, floating-point calculations had to be implemented in software, with programmed algorithms instructing the microprocessor how to do floating-point arithmetic. Later, floating-point processor chips were added alongside the regular microprocessor to implement these algorithms in hardware rather than emulated them through software, resulting in increased processing speed. After that, these floating-point circuits were simply added to the internal architecture of microprocessor chips as a standard feature. Even now, however, computer programmers understand that floating-point math requires more processor cycles than integer math, and should be avoided in applications where speed is essential and floating-point representation is not. In applications demanding a small microprocessor chip and optimum speed (e.g. embedded systems), fixed-point notation is best for representing numbers containing fractional quantities.↩︎ 374. Note how the place-weights shown for the exponent field do not seem to allow for negative values. There is no negative place-weight in the most significant position as one might expect, to allow negative exponents to be represented. Instead the IEEE standard implies a bias value of $$-127$$. For example, in a single-precision IEEE floating-point number, an exponent value of 11001101 represents a power of 78 (since 11001101 = 205, the exponent’s actual value is 205 $$-$$ 127 = 78).↩︎ 375. This motor may be “interlocked” to prevent start-up if certain conditions are not met, thereby automatically prohibiting the operator’s instruction to start.↩︎ 376. It is also possible to “simulate” fractional resolution using an integer number, by having the HMI insert a decimal point in the numerical display. For instance, one could use a 16-bit signed integer having a numerical range of $$-32768$$ to +32767 to represent motor temperature by programming the HMI to insert a decimal point between the hundreds’ and the tens’ place. This would give the motor temperature tag a (displayed) numerical range of $$-327.68$$ degrees to +327.67 degrees, and a (displayed) resolution of $$\pm$$0.01 degree. This is basically the concept of a fixed-point number, where a fixed decimal point demarcates whole digits (or bits) from fractional digits (or bits).↩︎ 377. Morse code is an example of a self-compressing code, already optimized in terms of minimum bit count. Fixed-field codes such as Baudot and the more modern ASCII tend to waste bandwidth, and may be “compressed” by removing redundant bits.↩︎ 378. For example, the Baudot code 11101 meant either “Q” or “1” depending on whether the last shift character was “letters” or “figures,” respectively. The code 01010 meant either “R” or “4”. The code 00001 meant either “T” or a “5”. This overloading of codes is equivalent to using the “shift” key on a computer keyboard to switch between numbers and symbols (e.g. “5” versus “%”, or “8” versus “*”). The use of a “shift” key on a keyboard allows single keys on the keyboard to represent multiple characters.↩︎ 379. Including the digital source code for this textbook!↩︎ 380. To illustrate, the first 128 Unicode characters (0000 through 007F hexadecimal) are identical to ASCII’s 128 characters (00 through 7F hexadecimal)↩︎ 381. The origin of this word has to do with the way many ADC circuits are designed, using binary counters. In the tracking design of ADC, for instance, an up-down binary counter “tracks” the varying analog input voltage signal. The binary output of this counter is fed to a DAC (digital-to-analog converter) sending an analog voltage to a comparator circuit, comparing the digital counter’s equivalent value to the value of the measured analog input. If one is greater than the other, the up-down counter is instructed to either count up or count down as necessary to equalize the two values. Thus, the up-down counter repeatedly steps up or down as needed to keep pace with the value of that analog voltage, its digital output literally “counting” steps along a fixed scale representing the full analog measurement range of the ADC circuit.↩︎ 382. Whether or not the actual ADC will round down depends on how it is designed. Some ADCs round down, others “bobble” equally between the two nearest digital values, and others yet “bobble” proportionately between the two nearest values. No matter how you round in your calculation of count value, you will never be more than 1 count off from the real ADC’s value.↩︎ 383. A less-commonly-used synonym for aliasing is folding.↩︎ 384. A mechanical demonstration of aliasing may be seen by using a stroboscope to “freeze” the motion of a rotating object. If the frequency of a flashing strobe light is set to exactly match the rotational speed of the object (e.g. 30 Hz flashing = 1800 RPM rotation), the object will appear to stand still because your eyes only see the object when it is at the exact same position every flash. This is equivalent to sampling a sinusoidal signal exactly once per cycle: the signal appears to be constant (DC) because the sine wave gets sampled at identical points along its amplitude each time. If the strobe light’s frequency is set slightly slower than the object’s rotational speed, the object will appear to slowly rotate in the forward direction because each successive flash reveals the object to be in a slightly further angle of rotation than it was before. This is equivalent to sampling a sinusoidal signal at a rate slightly slower than the signal’s frequency: the result appears to be a sinusoidal wave, but at a much slower frequency.↩︎ 385. Remember that an ADC has a finite number of “counts” to divide its received analog signal into. A 12-bit ADC, for example, has a count range of 0 to 4095. Used to digitize an analog signal spanning the full range of 0 to 5 VDC, this means each count will be “worth” 1.22 millivolts. This is the minimum amount of signal voltage that a 12-bit, 0-5 VDC converter is able to resolve: the smallest increment of signal it is able to uniquely respond to. 1.22 mV represents 0.037% of 3.3 volts, which means this ADC may “resolve” down to the very respectable fraction 0.037% of the solar panel’s 33 volt range. If we were to use the same ADC range to directly measure the shunt resistor’s voltage drop (0 to 0.54 VDC), however, it would only be able to resolve down to 0.226% of the 0 to 5.4 amp range, which is much poorer resolution.↩︎ 386. The relationship of temperature to $$V_{signal}$$ in this sensor circuit will not be precisely linear, especially if $$R_{fixed}$$ is not tremendously larger than $$R_{RTD}$$.↩︎ 387. To be fair, there is such a thing as a time-multiplexed analog system for industrial data communication (I’ve actually worked on one such system, used to measure voltages on electrolytic “pots” in the aluminum industry, communicating the voltages across hundreds of individual pots to a central control computer).↩︎ 388. There is, of course, the issue of reliability. Communicating thousands of process data points over a single cable may very well represent a dramatic cost savings in terms of wire, junction boxes, and electrical conduit. However, it also means you will lose all those thousands of data points if that one cable becomes severed! Even with digital technology, there may be reason to under-utilize the bandwidth of a signal cable.↩︎ 389. A common technique for high-speed parallel data communication over short distances (e.g. on a printed circuit board) is differential signaling, where each bit requires its own dedicated pair of conductors. A 16-bit parallel digital signal communicated this way would require 32 conductors between devices!↩︎ 390. I do not expect any reader of this book to have firsthand knowledge of what a “telegraph” is, but I suspect some will have never heard of one until this point. Basically, a telegraph was a primitive electrical communication system stretching between cities using a keyswitch at the transmitting end to transmit on-and-off pulses and a “sounder” to make those pulses audible on the receiving end. Trained human operators worked these systems, one at the transmitting end (encoding English-written messages into a series of pulses) and one at the receiving end (translating those pulses into English letters).↩︎ 391. A test message sent in 1924 between two teletype machines achieved a speed of 1920 characters per minute (32 characters per second), sending the sentence fragments “THE WESTERN ELECTRIC COMPANY”, “FRESHEST EGGS AT BOTTOM MARKET PRICES”, and “SHE IS HIS SISTER”.↩︎ 392. “Asynchronous” refers to the transmitting and receiving devices not having to be in perfect synchronization in order for data transfer to occur. Every industrial data communications standard I have ever seen is asynchronous rather than synchronous. In synchronous serial networks, a common “clock” signal maintains transmitting and receiving devices in a constant state of synchronization, so that data packets do not have to be preceded by “start” bits or followed by “stop” bits. Synchronous data communication networks are therefore more efficient (not having to include “extra” bits in the data stream) but also more complex. Most long-distance, heavy traffic digital networks (such as the “backbone” networks used for the Internet) are synchronous for this reason.↩︎ 393. Later versions of teletype systems employed audio tones instead of discrete electrical pulses so that many different channels of communication could be funneled along one telegraph line, each channel having its own unique audio tone frequency which could be filtered from other channels’ tones.↩︎ 394. This simply refers to the fact that the signal never settles at 0 volts.↩︎ 395. This is most definitely not the case with NRZ encoding. To see the difference for yourself, imagine a continuous string of either “0” or “1” bits transmitted in NRZ encoding: it would be nothing but a straight-line DC signal. In Manchester encoding, it is impossible to have a straight-line DC signal for an indefinite length of time. Manchester signals must oscillate at a minimum frequency equal to the clock speed, thereby guaranteeing all receiving devices the ability to detect that clock speed and thereby synchronize themselves with it.↩︎ 396. It is relatively easy to build an apparatus that makes HART tone signals audible: simply connect a small audio speaker to the low-impedance side of an audio transformer (8 ohms) and then connect the high-impedance side of that transformer (typically 1000 ohms) to the HART signal source through a coupling capacitor (a few microfarads is sufficient). When HART communications are taking place, you can hear the FSK tones reproduced by the speaker, which sound something like the noises made by a fax machine as it communicates over a telephone line.↩︎ 397. This is one of the advantages of Manchester encoding: it is a “self-clocking” signal.↩︎ 398. This is likely why “bit rate” and “baud rate” became intermingled in digital networking parlance: the earliest serial data networks requiring speed configuration were NRZ in nature, where “bps” and “baud” are one and the same.↩︎ 399. For Manchester encoding, “worst-case” is a sequence of identical bit states, such as 111111111111, where the signal must make an extra (down) transition in order to be “ready” for each meaningful (up) transition representing the next “1” state.↩︎ 400. An equivalent program for Microsoft Windows is Hyperterminal. A legacy application, available for both Microsoft Windows and UNIX operating systems, is the serial communications program called kermit.↩︎ 401. This is standard in EIA/TIA-232 communications.↩︎ 402. It should take only a moment or two of reflection to realize that such a parity check cannot detect an even number of corruptions, since flipping the states of any two or any four or any six (or even all eight!) bits will not alter the evenness/oddness of the bit count. So, parity is admittedly an imperfect error-detection scheme. However, it is certainly better than no error detection at all!↩︎ 403. The “XOFF” code tells the transmitting device to halt its serial data stream to give the receiving device a chance to “catch up.” In data terminal applications, the XOFF command may be issued by pressing the key combination $$<$$Ctrl$$><$$S$$>$$. This will “freeze” the stream of text data sent to the terminal by the host computer. The key combination $$<$$Ctrl$$><$$Q$$>$$ sends the “XON” code, enabling the host computer to resume data transmission to the terminal.↩︎ 404. I once encountered this very type of failure on the job, where a copper-to-fiber adapter on a personal computer’s Ethernet port jammed the entire network by constantly spewing a meaningless stream of data. Fortunately, indicator lights on all the channels of the communications equipment clearly showed where the offending device was on the network, allowing us to take it out of service for replacement.↩︎ 405. An additional layer sometimes added to the OSI model is layer 8, representing either the human user of the network system or the physical process interfacing with the network system. If the purpose of this model is to describe all the functioning portions of a communications link in the context of a system used for some practical purpose, layer 8 represents an essential part of that system and should not be ignored.↩︎ 406. If you are thinking the acronym should be “IOS” instead of “ISO,” you are thinking in terms of English. “ISO” is a non-English acronym!↩︎ 407. It should be noted here that some network standards incorporating the name “Modbus” actually do specify lower-level concerns. Modbus Plus is a layer 2 standard, for example.↩︎ 408. The designation of “RS-232” has been used for so many years that it still persists in modern writing and manufacturers’ documentation, despite the official status of the EIA/TIA label. The same is true for EIA/TIA-422 and EIA/TIA-485, which were formerly known as RS-422 and RS-485, respectively.↩︎ 409. “Daisy-chain” networks formed of more than two devices communicating via EIA/TIA-232 signals have been built, but they are rarely encountered, especially in industrial control applications.↩︎ 410. Often (incorrectly) called a “DB-9” connector.↩︎ 411. The way hardware-based flow control works in the EIA/TIA-232 standard involves two lines labeled RTS (“Request To Send”) and CTS (“Clear To Send”) connecting the two devices together on a point-to-point serial network in addition to the TD (“Transmitted Data”) and RD (“Received Data”) and signal ground lines. Like the TD and RD terminals which must be “crossed over” between devices such that the TD of one device connects to the RD of the other device and vice-versa, the RTS and CTS terminals of the two devices must be similarly crossed. The RTS is an output line while the CTS is an input, on both devices. When a device is able to receive data, it activates its RTS output line to request data. A device is not permitted to transmit data on its TD line until it is cleared to send data by an active state on its CTS input line.↩︎ 412. Also known by the unwieldy acronym DCTE (Data Circuit Terminating Equipment). Just think of “DTE” devices as being at the very end (“terminal”) of the line, whereas “DCE” devices are somewhere in the middle, helping to exchange serial data between DTE devices.↩︎ 413. In fact, the concept is not unique to digital systems at all. Try talking to someone using a telephone handset held upside-down, with the speaker near your mouth and the microphone hear your ear, and you will immediately understand the necessity of having “transmit” and “receive” channels swapped from one end of a network to the other!↩︎ 414. Once I experimented with the fastest data rate I could “push” an EIA/TIA-232 network to, using a “flat” (untwisted, unshielded pair) cable less than ten feet long, and it was 192 kbps with occasional data corruptions. Park, Mackay, and Wright, in their book Practical Data Communications for Instrumentation and Control document cable lengths as long as 20 meters at 115 kbps for EIA/TIA-232, and 50 meters (over 150 feet!) at 19.2 kbps: over three times better than the advertised EIA/TIA-232 standard.↩︎ 415. Former labels for EIA/TIA-422 and EIA/TIA-485 were RS-422 and RS-485, respectively. These older labels persist even today, to the extent that some people will not recognize what you are referring to if you say “EIA/TIA-422” or “EIA/TIA-485.”↩︎ 416. 1200 meters is the figure commonly cited in technical literature. However, Park, Mackay, and Wright, in their book Practical Data Communications for Instrumentation and Control document EIA/TIA-422 and EIA/TIA-485 networks operating with cable lengths up to 5 km (over 16000 feet!) at data rates of 1200 bps. Undoubtedly, such systems were installed with care, using high-quality cable and good wiring practices to minimize cable capacitance and noise.↩︎ 417. In fact, a great many EIA/TIA-485 networks in industry operate “unterminated” with no problems at all.↩︎ 418. For detailed explanation of how and why this is necessary, refer to section 5.10 beginning on page .↩︎ 419. Actually two terminating resistors in parallel, since one with be at each end of the cable! The actual DC biasing network will be more complicated as well if more than one device has its own set of internal bias resistors.↩︎ 420. These very same problems may arise in FOUNDATION Fieldbus networks, for the exact same reason: the cabling is passive (for increased reliability). This makes FOUNDATION Fieldbus instrument systems challenging to properly install for most applications (except in really simple cases where the cable route is straightforward), which in my mind is its single greatest weakness at the time of this writing (2009). I strongly suspect Ethernet’s history will repeat itself in FOUNDATION Fieldbus at some later date: a system of reliable “hub” devices will be introduced so that these problems may be averted, and installations made much simpler.↩︎ 421. There are practical limits as to how many hubs may be “daisy-chained” together in this manner, just as there are practical limits to how long a twisted-pair cable may be (up to 100 meters). If too many hubs are cascaded, the inevitable time delays caused by the process of repeating those electrical impulses will cause problems in the network. Also, I have neglected to specify the use of crossover cables to connect hubs to other hubs – this is a topic to be covered later in this book!↩︎ 422. With only half the available wire pairs used in a standard 10 Mbps or 100 Mbps Ethernet cable, this opens the possibility of routing two Ethernet channels over a single four-pair UTP cable and RJ-45 connector. Although this is non-standard wiring, it may be a useful way to “squeeze” more use out of existing cables in certain applications. In fact, “splitter” devices are sold to allow two RJ-45-tipped cables to be plugged into a single RJ-45 socket such that one four-pair cable will then support two Ethernet pathways.↩︎ 423. This means modern Ethernet is capable of full-duplex communication between two devices, whereas the original coaxial-based Ethernet was only capable of half-duplex communication.↩︎ 424. Even the cost difference is negligible. It should be noted, though, that switches may exhibit unintended behavior if a cable is unplugged from one of the ports and re-plugged into a different port. Since switches internally map ports to device addresses, swapping a device from one port to another will “confuse” the switch until it re-initializes the port identities. Re-initialization may be forced by cycling power to the switch, if the switch does not do so on its own.↩︎ 425. When packets travel between different kinds of networks, the “gateway” devices at those transition points may need to fragment large IP packets into smaller IP packets and then re-assemble those fragments at the other end. This fragmentation and reassembly is a function of Internet Protocol, but it happens at the packet level. The task of portioning a large data block into packet-sized pieces at the very start and then reassembling those packets into a facsimile of the original data at the very end, however, is beyond the scope of IP.↩︎ 426. In fact, this is precisely the state of affairs if you use a dial-up telephone connection to link your personal computer with the Internet. If you use dial-up, your PC may not use Ethernet at all to make the connection to your telephone provider’s network, but rather it might uses EIA/TIA-232 or USB to a modem (modulator/demodulator) device, which turns those bits into modulated waveforms transmittable over a voice-quality analog telephone line.↩︎ 427. The “ping” command is technically defined as an “Echo Request” command, which is part of the Internet Control Message Protocol (ICMP) suite.↩︎ 428. Prior to ICANN’s formation in 1999, the Internet Assigned Numbers Authority, or IANA was responsible for these functions. This effort was headed by a man named Jon Postel, who died in 1998.↩︎ 429. The term “loopback” refers to an old trick used by network technicians to diagnose suspect serial port connections on a computer. Using a short piece of copper wire (or even a paperclip) to “jumper” pins 2 and 3 on an EIA/TIA-232 serial port, any serial data transmitted (out of pin 3) would be immediately received (in pin 2), allowing the serial data to “loop back” to the computer where it could be read. This simple test, if passed, would prove the computer’s low-level communication software and hardware was working properly and that any networking problems must lie elsewhere.↩︎ 430. Also called “netmasks” or simply “masks.”↩︎ 431. These are real test cases I performed between two computers connected on a 10 Mbps Ethernet network. The error messages are those generated by the ping utility when communication was attempted between mis-matched computers.↩︎ 432. According to Douglas Giancoli’s Physics for Scientists and Engineers textbook, the mass of the Earth is $$5.98 \times 10^{24}$$ kg, or $$5.98 \times 10^{27}$$ grams. Dividing $$2^{128}$$ (the number of unique IPv6 addresses) by the Earth’s mass in grams yields the number of available IPv6 address per gram of Earth mass. Furthermore, if we assume a grain of sand has a mass of about 1 milligram, and that the Earth is modeled as a very large collection of sand grains (not quite the truth, but good enough for a dramatic illustration!), we arrive at 57 million IPv6 addresses per grain of sand on Earth.↩︎ 433. The fully-written loopback address is actually 0000:0000:0000:0000:0000:0000:0000:0001.↩︎ 434. While it is possible to use non-contiguous subnet mask values, the practice is frowned upon by most system administrators.↩︎ 435. Indeed, subnet masks for IPv4 can be specified in this manner as well, not just IPv6 subnet masks.↩︎ 436. The “ping” command is often used to test the response of a single IP node on a network, by issuing the command followed by the IP address of interest (e.g. ping 192.168.35.70). By contrast, a “broadcast” ping request attempts to contact a range of IP addresses within a subnet. For example, if we wished to ping all the IP addresses beginning with 192.168.35, we would issue the command with all 1’s in the last octet of the IP address field (e.g. ping 192.168.35.255).↩︎ 437. In UNIX-based operating systems the program used to access the command line is often called terminal or xterm. In Microsoft Windows systems it is simply called cmd.↩︎ 438. Both IPv4 and IPv6 reserve eight bits for this purpose.↩︎ 439. In this particular case, I typed netstat -an to specify all (a) ports with numerical (n) IP addresses and port numbers shown.↩︎ 440. A Device Description, or DD (DD) file, is analogous to a “driver” file used to instruct a personal computer how to communicate with a printer, scanner, or any other complex peripheral device. In this case, the file instructs the HART configuration computer on how it should access parameters inside the field instrument’s microcontroller. Without an appropriate DD file loaded on the configuration computer, many of the field instrument’s parameters may be inaccessible.↩︎ 441. A “DD” file, or Device Descriptor file, is akin to a driver file used in a personal computer to allow it to communicate data with some peripheral device such as a printer. DD files basically tell the HART communicator how it needs to access specific data points within the HART field instrument.↩︎ 442. Every byte (8 bits) of actual HART data is sent as an asynchronous serial frame with a start bit, parity bit, and stop bit, so that 11 bits’ worth of time are necessary to communicate 8 bits of real data. These “byte frames” are then packaged into larger message units called HART telegrams (similar to Ethernet data frames) which include bits for synchronizing receiving devices, specifying device addresses, specifying the length of the data payload, communicating device status, etc.↩︎ 443. The HART standard specifies “master” devices in a HART network transmit AC voltage signals, while “slave” devices transmit AC current signals.↩︎ 444. Truth be told, HART instruments configured to operate in burst mode are still able to respond to queries from a master device, just not as often. Between bursts, the HART slave device waits a short time to allow any master devices on the network to poll. When polled, the slave device will respond as it normally would, then resumes its bursts of unpolled data once again. This means that normal master/slave communication with a HART instrument set for burst mode will occur at a slower pace than if the instrument is set for normal mode.↩︎ 445. These Modbus data frames may be communicated directly in serial form, or “wrapped” in TCP segments and IP packets and Ethernet frames, or otherwise contained in any form of packet-based protocol as needed to transport the data from one device to another. Thus, Modbus does not “care” how the data is communicated, just what the data means for the end-device.↩︎ 446. Recall that each ASCII character requires 7 bits to encode. This impacts nearly every portion of the Modbus data frame. Slave address and function code portions, for example, require 14 bits each in ASCII but only 8 bits each in RTU. The data portion of a Modbus ASCII frame requires one ASCII character (7 bits) to represent each hexadecimal symbol that in turn represents just 4 bits of actual data. The data portion of a Modbus RTU frame, by contrast, codes the data bits directly (i.e. 8 bits of data appear as 8 bits within that portion of the frame). Additionally, RTU data frames use quiet periods (pauses) as delimiters, while ASCII data frames use three ASCII characters in total to mark the start and stop of each frame, at a “cost” of 21 additional bits. These additional delimiting bits do serve a practical purpose, though: they format each Modbus ASCII data frame as its own line on the screen of a terminal program.↩︎ 447. This C-language code is typed and saved as a plain-text file on the computer, and then a compiler program is run to convert this “source” code into an “executable” file that the computer may then run. The compiler I use on my Linux-based systems is gcc (the GNU C Compiler). If I save my Modbus program source code to a file named tony_modbus.c, then the command-line instruction I will need to issue to my computer instructing GCC to compile this source code will be gcc tony_modbus.c -lmodbus. The argument -lmodbus tells GCC to “link” my code to the code of the pre-installed libmodbus library in order to compile a working executable file. By default, GCC outputs the executable as a file named a.out. If I wish to rename the executable something more meaningful, I may either do so manually after compilation, or invoke the “outfile” option of gcc and specify the desired executable filename: (e.g. gcc -o tony.exe tony_modbus -lmodbus). Once compiled, the executable file many be run and the results of the Modbus query viewed on the computer’s display.↩︎ 448. Even for devices where the register size is less than two bytes (e.g. Modicon M84 and 484 model controllers have 10 bits within each register), data is still addressed as two bytes’ worth per register, with the leading bits simply set to zero to act as placeholders.↩︎ 449. Each FF terminator resistor is actually a series resistor/capacitor network. The capacitor blocks direct current, so that the 100 $$\Omega$$ resistor does not impose a DC load on the system. The substantial current that would be drawn by a 100 ohm resistor across 24 VDC source if not blocked by a series capacitor (24 V / 100 ohms = 240 mA) would not only waste power (nearly 6 watts per resistor!) but that much current would cause an unnecessary degradation of supply voltage at the field device terminals due to voltage drop along the length of the segment cable’s conductors.↩︎ 450. Be sure to check the specifications of the host system H1 interface card, because many are equipped with internal terminating resistors given the expectation that the host system will connect to one far end of the trunk!↩︎ 451. You should consult an NEC code book regarding specific limitations of ITC wiring. Some of the main points include limiting individual ITC cable lengths to a maximum of 50 feet, and mechanically securing the cable at intervals not to exceed 6 feet.↩︎ 452. Provided the metal enclosure’s door is left in the closed position at all times! Keying a radio transmitter near such a coupling device while the enclosure door is open invites trouble.↩︎ 453. Perusing documentation on an assortment of Emerson/Rosemount FF products, I found the following data: model 752 indicator = 17.5 mA, model 848L logic = 22 mA, model 848T temperature = 22 mA maximum, model 3244MV temperature = 17.5 mA typical, model DVC6000f valve positioner = 18 mA maximum, model 848L logic = 22 mA, model 848T temperature = 22 mA maximum, model 3244MV temperature = 17.5 mA typical, model 5500 guided-wave radar level = 21 mA, model 3095MV flow (differential pressure) = 17 mA approximate, model DVC6000f valve positioner = 18 mA maximum.↩︎ 454. I have successfully built several “demonstration” FF systems using cables of questionable quality, including lamp (“zip”) cord, with no termination resistors whatsoever! If the distances involved are short, just about any cable type or condition will suffice. When planning the installation of any real Fieldbus installation, however, you should never attempt to save money by purchasing lesser-grade cable. The problems you will likely encounter as a consequence of using sub-standard cable will more than offset the initial cost saved by its purchase.↩︎ 455. Total device current draw, spur length versus number, intrinsic safety voltage and current limitations, etc.↩︎ 456. At the time of this writing (2009), the ISA has yet to standardize new methods of FF documentation in the style of loop sheets and P&IDs. This is one of those circumstances where technology has outpaced convention.↩︎ 457. While many industrial control systems have been built using networks that are not strictly deterministic (e.g. Ethernet), generally good control behavior will result if the network latency time is arbitrarily short. Lack of “hard” determinism is more of a problem in safety shutdown systems where the system must respond within a certain amount of time in order to be effective in its safety function. An industrial example of a safety system requiring “hard” determinism is compressor surge control. An automotive example requiring “hard” determinism is anti-lock brake control.↩︎ 458. By “sequencing,” I mean the execution of all antecedent control functions prior to “downstream” functions requiring the processed data. If in a chain of function blocks we have some blocks lagging in their execution, other blocks relying on the output signals of those lagging blocks will be functioning on “old” data. This effectively adds dead time to the control system as a whole. The more antecedent blocks in the chain that lag in time behind the needs of their consequent blocks, the more dead time will be present in the entire system. To illustrate, if block A feeds data into block B which feeds data into block C, but the blocks are executed in reverse order (C, then B, then A) on the same period, a lag time of three whole execution periods will be manifest by the A-B-C algorithm.↩︎ 459. The engineers there are not without a sense of humor, choosing for their manufacturer code the same model number as the venerable model 1151 differential pressure transmitter, perhaps the most popular Rosemount industrial instrument in the company’s history!↩︎ 460. In addition to the main LAS, there may be “backup” LAS devices waiting ready to take over in the event the main LAS fails for any reason. These are Link Master devices configured to act as redundant Link Active Schedulers should the need arise. However, at any given time there will be only one LAS. In the event of an LAS device failure, the Link Master device with the lowest-number address will “step up” to become the new LAS.↩︎ 461. The Source/Sink VCR is the preferred method for communicating trend data, but trends may be communicated via any of the three VCR types. All other factors being equal, acyclic communication (either Source/Sink or Client/Server) of trend data occupies less network bandwidth than cyclic communication (Publisher/Subscriber).↩︎ 462. Some FF devices capable of performing advanced function block algorithms for certain process control schemes may have the raw computational power to be an LAS, but the manufacturer has decided not to make them Link Master capable simply to allow their computational power to be devoted to the function block processing rather than split between function block tasks and LAS tasks.↩︎ 463. “Reset windup” which is also known as “integral windup” is what happens when any loop controller possessing reset (integral) action senses a difference between PV and SP that it cannot eliminate. The reset action over time will drive the controller’s output to saturation. If the source of the problem is a control valve that cannot attain the desired position, the controller will “wind up” or “wind down” in a futile attempt to drive the valve to a position it cannot go. In an FF system where the final control element provides “back calculation” feedback to the PID algorithm, the controller will not attempt to drive the valve farther than it is able to respond.↩︎ 464. This is not an unreasonable loop execution time for a gas pressure control system. However, liquid pressure control is notoriously fast-acting, and will experience less than ideal response with a controller dead time of one second.↩︎ 465. For example, sub-statuses for a “Bad” status include out of service, device failure, sensor failure, and non-specific. Sub-statuses for an “Uncertain” status include last usable value (LUV), sensor conversion not accurate, engineering unit range violation, sub-normal, and non-specific.↩︎ 466. The great pioneer of mechanical computing technology, Charles Babbage, commented in his book Passages from the Life of a Philosopher in 1864 that not one but two members of the British parliament asked him whether his computer (which he called the Difference Engine) could output correct answers given incorrect data. His reaction was both frank and hilarious: “I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”↩︎ 467. One of the tasks of the Fieldbus Foundation is to maintain approved listings of FF devices in current manufacture. The concept is that whenever a manufacturer introduces a new FF device, it must be approved by the Fieldbus Foundation in order to receive the Fieldbus “badge” (a logo with a stylized letter “F”). Approved devices are cataloged by the Fieldbus Foundation, complete with their DD file sets. This process of approval is necessary for operational compatibility (called interoperability) between FF devices of different manufacture. Without some form of centralized standardization and approval, different manufacturers would invariably produce devices mutually incompatible with each other.↩︎ 468. On the Emerson DeltaV system, most options are available as drop-down menu selections following a right-mouse-button click on the appropriate icon.↩︎ 469. Animated graphics on the Emerson DeltaV control system prominently feature an anthropomorphized globe valve named Duncan. There’s nothing like a computer programmer with a sense of humor . . .↩︎ 470. Fieldbus transmitters often have multiple channels of measurement data to select from. For example, the multi-variable Rosemount 3095MV transmitter assigns channel 1 as differential pressure, channel 2 as static pressure, channel 3 as process temperature, channel 4 as sensor temperature, and channel 5 as calculated mass flow. Setting the Channel parameter properly in the AI block is therefore critical for linking it to the proper measurement variable.↩︎ 471. If I were king for a day, I would change the labels “direct” and “indirect” to “raw” and “scaled”, respectively. Alternatively, I would abandon the “direct” option altogether, because even when this option is chosen the OUT_Scale range still exists and may contain “scaled” values even though these are ignored in “direct” mode!↩︎ 472. It is important to note that you must correctly calculate the corresponding XD_Scale and OUT_Scale parameter values in order for this to work. The Fieldbus instrument does not calculate the parameters for you, because it does not “know” how many PSI correspond to how many feet of liquid level in the tank. These values must be calculated by some knowledgeable human technician or engineer and then entered into the instrument’s AI block, after which the instrument will execute the specified scaling as a purely mathematical function.↩︎ 473. When configuring the XD_Scale high and low range values, be sure to maintain consistency with the transducer block’s Primary_Value_Range parameter unit. Errors may result from mis-matched measurement units between the transducer block’s measurement channel and the analog input block’s XD_Scale parameter.↩︎ 474. An alternative method of shield grounding is to directly connect it to earth ground at one end, and then capacitively couple it to ground at other points along the segment length. The capacitor(s) provide an AC path to ground for “bleeding off” any induced AC noise without providing a DC path which would cause a ground loop.↩︎ 475. Bear in mind the tolerable level for noise will vary with signal voltage level as well. All other factors being equal, a strong signal is less affected by the presence of noise than a weak signal (i.e. the signal-to-noise ratio, or SNR, is crucial).↩︎ 476. It is impossible to “lock in” (trigger) non-periodic waveforms on an analog oscilloscope, and so most network communications will appear as an incomprehensible blur when viewed on this kind of test instrument. Digital oscilloscopes have the ability to “capture” and display momentary pulse streams, making it possible to “freeze” any portion of a network signal for visual analysis.↩︎ 477. For a more detailed discussion of antennas and their electrical characteristics, refer to section 5.11 beginning on page .↩︎ 478. Due to the “end effect” of lumped capacitance at the tip of the antenna, an actual quarter-wave antenna needs to be slightly shorter than an actual quarter of the wavelength. This holds true for dipoles and other antenna designs as well.↩︎ 479. It is interesting to note that although the “Bel” is a metric unit, it is seldom if ever used without the metric prefix “deci” ($$1 \over 10$$). One could express powers in microbels, megabels, or any other metric prefix desired, but it is never done in industry: only the decibel is used.↩︎ 480. The dominant mode of energy dissipation in an RF cable is dielectric heating, where the AC electric field between the cable conductors excites the molecules of the conductor insulation. This energy loss manifests as heat, which explains why there is less RF energy present at the load end of the cable than is input at the source end of the cable.↩︎ 481. In fact, logarithms are one of the simplest examples of a transform function, converting one type of mathematical problem into another type. Other examples of mathematical transform functions used in engineering include the Fourier transform (converting a time-domain function into a frequency-domain function) and the Laplace transform (converting a differential equation into an algebraic equation).↩︎ 482. This is precisely how a microwave oven works: water molecules are polar (that is to say, the electrical charges of the hydrogen and oxygen atoms are not symmetrical, and therefore each water molecule has one side that is more positive and an opposite side that is more negative), and therefore vibrate when subjected to electromagnetic fields. In a microwave oven, RF energy in the gigahertz frequency range is aimed at pieces of food, causing the water molecules within the food to heat up, thus indirectly heating the rest of the food. This is a practical example of an RF system where losses are not only expected, but are actually a design objective! The food represents a load to the RF energy, the goal being complete dissipation of all incident RF energy with no leakage outside the oven. In RF cable design, however, dissipative power losses are something to be avoided, the goal being complete delivery of RF power to the far end of the cable.↩︎ 483. One should not think that the outer edges of the shaded radiation patterns represents some “hard” boundary beyond which no radiation is emitted (or detected). In reality, the radiation patterns extend out to infinity (assuming otherwise empty space surrounding the antenna). Instead, the size of each shaded area simply represents how effective the antenna is in that direction compared to other directions. In the case of the vertical whip and dipole antennas, for instance, the radiation patterns show us that these antennas have zero effectiveness along the vertical ($$Y$$) axis centerline. To express this in anthropomorphic terms, these antenna designs are “deaf and mute” in those directions where the radiation pattern is sketched having zero radius from the antenna center.↩︎ 484. Or – applying the principle of reciprocity – antenna gain is really nothing more than a way to express how sensitive a receiving antenna is compared to a truly omnidirectional antenna.↩︎ 485. Actual signal power is typically expressed as a decibel ratio to a reference power of either 1 milliwatt (dBm) or 1 watt (dBW). Thus, 250 mW of RF power may be expressed as $$10 \log {250 \over 1}$$ = 23.98 dBm or as $$10 \log {0.25 \over 1}$$ = $$-6.02$$ dBW. Power expressed in unit of dBm will always be 30 dB greater ($$1 \times 10^3$$ greater) than power expressed in dBW.↩︎ 486. Noise power may be calculated using the formula $$P_n = kTB$$, where $$P_n$$ is the noise power in watts, $$k$$ is Boltzmann’s constant ($$1.38 \times 10^{-23}$$ J/K), $$T$$ is the absolute temperature in Kelvin, and $$B$$ is the bandwidth of the noise in Hertz. Noise power usually expressed in units of dBm rather than watts, because typical noise power values for ambient temperatures on Earth are so incredibly small.↩︎ 487. The inverse square law applies to any form of radiation that spreads from a point-source. In any such scenario, the intensity of the radiation received by an object from the point-source diminishes with the square of the distance from that source, simply because the rest of the radiated energy misses that target and goes elsewhere in space. This is why the path loss formula begins with a $$-20$$ multiplier rather than $$-10$$ as is customary for decibel calculations: given the fact that the inverse square law tells us path loss is proportional to the square of distance ($$D^2$$), there is a “hidden” second power in the formula. Following the logarithmic identity that exponents may be moved to the front of the logarithm function as multipliers, this means what would normally be a $$-10$$ multiplier turns into $$-20$$ and we are left with $$D$$ rather than $$D^2$$ in the fraction.↩︎ 488. “Margin” is the professionally accepted term to express extra allowance provided to compensate for unknowns. A more colorful phrase often used in the field to describe the same thing is fudge factor.↩︎ 489. I am indebted to Eric McCollum, Kei Hao, Shankar V. Achanta, Jeremy Blair, and David Kechalo for presenting this form of diagram in a technical paper presented at the 45th annual Western Protective Relay Conference in Spokane, Washington in October of 2018. I do not know if these authors are responsible for the invention of this form of graph, but it was certainly the first time I encountered one like it, and it so clearly showed all the fundamental quantities of an RF link budget that I had to include something similar in my book!↩︎ 490. The physics of Fresnel zones is highly non-intuitive, rooted in the wave-nature of electromagnetic radiation. It should be plain to see, though, that Fresnel zones cannot describe the actual electromagnetic field pattern between two antennas, because we know waves tend to spread out over space while Fresnel zones converge at each end. Likewise, Fresnel zones vary in size according to the distance between two antennas which we know radiation field patterns do not. It is more accurate to think of Fresnel zones as keep-clear areas necessary for reliable communication between two or more antennas rather than actual field patterns.↩︎ 491. Some obvious connecting paths between field devices have been omitted from this illustration if the path length exceeds a certain maximum distance. As you can see, the instruments in the far-left cluster must rely on data packet relaying by instruments closer to the gateway, since they themselves are too far away from the gateway to directly communicate.↩︎ 492. Another exciting technological development paralleling the implementation of WirelessHART in industry is that of energy-harvesting devices to generate DC electricity from nearby energy sources such as vibrating machines (mechanical motion), hot pipes (thermal differences), photovoltaic (solar) panels, and even small wind generators. Combined with rechargeable batteries to sustain instrument operation during times those energy sources are not producing, energy-harvesters promise great extension of battery life for wireless instruments of all types.↩︎ 493. The model 1420 gateway has been superseded by the Smart Wireless Gateway, also manufactured by Emerson.↩︎ 494. Device variables are addressed at the network gateway level by the device’s HART tag (long tag, not short tag) and internal device variable name. Thus, the primary variable (PV) of temperature transmitter TEMP2 is specified as TEMP2.PV using a period symbol (.) as the delimiting character between the device name and the internal variable name.↩︎ 495. This is an example of a first-generation Rosemount WirelessHART field instrument, back when the standard radio band was 900 MHz instead of 2.4 GHz. This explains why the antenna is longer than contemporary WirelessHART instruments.↩︎ 496. Each gateway device can of course have backup gateways with the same Network ID, just waiting to take over if the primary gateway fails. The point of the Network ID is that it identifies a single network with only one active gateway.↩︎ 497. However, it is actually quite rare to find an instrument where a change to the zero adjustment affects the instrument’s span.↩︎ 498. Various digital damping algorithms exist, but it may take as simple a form as successive averaging of buffered signal values coming out of a first-in-first-out (“FIFO”) shift register.↩︎ 499. Most popularly, using the HART digital-over-analog hybrid communication standard.↩︎ 500. Although those adjustments made on a digital transmitter tend to be easier to perform than repeated zero-and-span adjustments on analog transmitters due to the inevitable “interaction” between analog zero and span adjustments requiring repeated checking and re-adjustment during the calibration period.↩︎ 501. A 4% calibration error caused by sensor aging is enormous for any modern digital transmitter, and should be understood as an exaggeration presented only for the sake of illustrating how sensor error affects overall calibration in a smart transmitter. A more realistic amount of sensor error due to aging would be expressed in small fractions of a percent.↩︎ 502. HART is a hybrid analog/digital communication protocol used by a great many field instruments, allowing maintenance personnel to access and edit digital parameters inside the instrument using a computer-based interface. Hand-held HART communicators exist for this purpose, as does HART software designed to run on a personal computer. HART modems also exist to connect personal computers to HART-compatible field instruments.↩︎ 503. The NIST broadcasts audio transmissions of “Coordinated Universal Time” (UTC) on the shortwave radio frequencies 5 MHz, 10 MHz, 15 MHz, 20 MHz, and 25 MHz. Announcements of time, in English, occur at the top of every minute.↩︎ 504. In the case of pressure transmitters, re-trimming may be necessary if the device is ever re-mounted in a different orientation. Changing the physical orientation of a pressure transmitter alters the direction in which gravity tugs on the sensing element, causing it to respond as though a constant bias pressure were applied to it. This bias is often on the order of an inch of water column (or less), and usually consequential only for low-pressure applications such as furnace draft pressure.↩︎ 505. A noteworthy exception is the case of digital instruments, which output digital rather than analog signals. In this case, there is no need to compare the digital output signal against a standard, as digital numbers are not liable to calibration drift. However, the calibration of a digital instrument still requires comparison against a trusted standard in order to validate an analog quantity. For example, a digital pressure transmitter must still have its input calibration values validated by a pressure standard, even if the transmitter’s digital output signal cannot drift or be misinterpreted.↩︎ 506. Modern “smart” electronic pressure transmitters typically boast turndown ratios exceeding 100:1, with some having turndown ratios of 200:1 or more! Large turndown ratios are good because they allow users of instrumentation to maintain a smaller quantity of new transmitters in stock, since transmitters with large turndown ratios are more versatile (i.e. applicable to a wider variety of spans) than transmitters with small turndown ratios.↩︎ 507. According to Emerson product datasheet PS-00374, revision L, June 2009.↩︎ 508. According to the book Philosophy in Practice (second edition) published by Fluke, the initial expense of their Josephson Array in 1992 was85000, with another $25000 budgeted for start-up costs. The annual operating cost of the array is approximately$10000, mostly due to the cost of the liquid helium refrigerant necessary to keep the Josephson junction array at a superconducting temperature. This consumable cost does not include the salary of the personnel needed to maintain the system, either. Presumably, a metrology lab of this caliber would employ several engineers and scientists to maintain all standards in top condition and to perform continuing metrological research.↩︎
509. This brings to mind a good joke. Once there was a man who walked by an antique store every day on his way to work and noticed all the wall clocks on display at this store always perfectly matched in time. One day he happened to see the store owner and complimented him on the consistent accuracy of his display clocks, noting how he used the owner’s clocks as a standard to set his own wristwatch on his way to work. He then asked the owner how he kept all the clocks so perfectly set. The owner explained he set the clocks to the sound of the steam whistle at the local factory, which always blew precisely at noon. The store owner then asked the man what he did for a living. The man replied, “I operate the steam whistle at the factory.”↩︎
510. This, of course, assumes the potentiometer has a sufficiently fine adjustment capability that we may adjust the millivoltage signal to any desired precision. If we were forced to use a coarse potentiometer – incapable of being adjusted to the precise amount of millivoltage we desired – then the accuracy of our calibration would also be limited by our inability to precisely control the applied voltage.↩︎
511. The Celsius scale used to be called the Centigrade scale, which literally means “100 steps.” I personally prefer the name “Centigrade” to the name “Celsius” because the former actually describes something about the unit of measurement while the latter is a surname. In the same vein, I also prefer the older label “Cycles Per Second” (cps) to “Hertz” as the unit of measurement for frequency. You may have noticed by now that the instrumentation world does not yield to my opinions, much to my chagrin.↩︎
512. Three, if you count the triple point, but this requires more sophisticated testing apparatus to establish than either the freezing or boiling points.↩︎
513. Pressure does have some influence on the freezing point of most substances as well, but not nearly to the degree it has on the boiling point. For a comparison between the pressure-dependence of freezing versus boiling points, consult a phase diagram for the substance in question, and observe the slopes of the solid-liquid phase line and liquid-vapor phase line. A nearly-vertical solid-liquid phase line shows a weak pressure dependence, while the liquid-vapor phase lines are typically much closer to horizontal.↩︎
514. For each of these examples, the assumptions of a 100% pure sample and an airless testing environment are made. Impurities in the initial sample and/or resulting from chemical reactions with air at elevated temperatures, may introduce serious errors.↩︎
515. A “black body” is an idealized object having an emissivity value of exactly one (1). In other words, a black body is a perfect radiator of thermal energy. Interestingly, a blind hole drilled into any object at sufficient depth acts as a black body, and is sometimes referred to as a cavity radiator.↩︎
516. For example, a solution with a pH value of 4.7 has a concentration of $$10^{-4.7}$$ moles of active hydrogen ions per liter. For more information on “moles” and solution concentration, see section 3.7 beginning on page .↩︎
517. A clean and healthy pH probe should stabilize within about 30 seconds of being inserted in a buffer solution.↩︎
518. Carbon dioxide gas in ambient air will cause carbonic acid to form in an aqueous solution. This has an especially rapid effect on high-pH (alkaline) buffers.↩︎
519. It is assumed that the concentration of oxygen in ambient air is a stable enough quantity to serve as a calibration standard for most industrial applications. It is certainly an accessible standard!↩︎
520. If you are having difficulty understanding this concept, imagine a simple U-tube manometer where one of the tubes is opaque, and therefore one of the two liquid columns cannot be seen. In order to be able to measure pressure just by looking at one liquid column height, we would have to make a custom scale where every inch of height registered as two inches of water column pressure, because for each inch of height change in the liquid column we can see, the liquid column we can’t see also changes by an inch. A scale custom-made for a well-type manometer is just the same concept, only without such dramatic skewing of scales.↩︎
521. As of this writing, 2008.↩︎
522. For a simple demonstration of metal fatigue and metal “flow,” simply take a metal paper clip and repeatedly bend it back and forth until you feel the metal wire weaken. Gentle force applied to the paper clip will cause it to deform in such a way that it returns to its original shape when the force is removed. Greater force, however, will exceed the paper clip’s elastic limit, causing permanent deformation and also altering the spring characteristics of the clip.↩︎
523. In the following diagram, both the sensing diaphragm and the stationary metal surfaces are shown colored blue, to distinguish these electrical elements from the other structural components of the device.↩︎
524. A chop saw is admittedly not a tool of finesse, and it did a fair job of mangling this unfortunate differential capacitance cell. A bandsaw was tried at first, but made virtually no progress in cutting the hard stainless steel of the capsule assembly. The chop saw’s abrasive wheel created a lot of heat, discoloring the metal and turning the silicone fill fluid into a crystalline mass which had to be carefully chipped out by hand using an ice pick so as to not damage the thin metal sensing diaphragm. Keep these labors in mind, dear reader, as you enjoy this textbook!↩︎
525. Not only did applied torque of the four capsule bolts affect measurement accuracy in the older 1151 model design, but changes in temperature resulting in changing bolt tension also had a detrimental impact on accuracy. Most modern differential pressure transmitter designs strive to isolate the sensing diaphragm assembly from flange bolt stress for these reasons.↩︎
526. For example, a doubling of force results in a frequency increase of 1.414 (precisely equal to $$\sqrt{2}$$). A four-fold increase in pressure would be necessary to double the string’s resonant frequency. This particular form of nonlinearity, where diminishing returns are realized as the applied stimulus increases, yields excellent rangeability. In other words, the instrument is inherently more sensitive to changes in pressure at the low end of its sensing range, and “de-sensitizes” itself toward the high end of its sensing range.↩︎
527. This is an example of a micro-electro-mechanical system, or MEMS.↩︎
528. Based on the design of Foxboro’s popular model 13A pneumatic “DP cell” differential pressure transmitter.↩︎
529. Very loosely based on the design of Foxboro’s now-obsolete E13 electronic “DP cell” differential pressure transmitter.↩︎
530. One instrument technician I know referred to the Foxboro E13 differential pressure transmitter as “pig iron” after having to hoist it by hand to the top of a distillation column.↩︎
531. As far as I have been able to determine, the labels “D/P” and “DP cell” were originally trademarks of the Foxboro Company. Those particular transmitter models became so popular that the term “DP cell” came to be applied to nearly all makes and models of differential pressure transmitter, much like the trademark “Vise-Grip” is often used to describe any self-locking pliers, or “Band-Aid” is often used to describe any form of self-adhesive bandage.↩︎
532. One transmitter manufacturer I am aware of (ABB/Bailey) actually does use the “+” and “$$-$$” labels to denote high- and low-pressure ports rather than the more customary “H” and “L” labels found on other manufacturers’ DP products.↩︎
533. Perfect common-mode rejection is impossible for differential pressure instruments just as it is impossible for electronic voltage-measuring instruments, but in either case the effect is usually minimal. For differential pressure transmitters, the effect of common-mode pressure on the instrument’s output signal is sometimes referred to as the line pressure effect or static pressure effect, typically stated as a percentage of the instrument’s upper range limit per unit of common-mode pressure.↩︎
534. The electrical circuit shown on the right uses a pair of series-connected resistors to divide the source voltage into two parts, 5 volts and 95 volts. The pneumatic circuit shown on the left uses a pair of series-connected hand valves to divide the source pressure into two parts, 5 PSI and 95 PSI.↩︎
535. Also called impulse tubes, gauge tubes, or sensing tubes.↩︎
536. Truth be told, most process variables are inferred rather than directly measured. Even pressure, which is being used here to infer measurements such as liquid level and fluid flow, is itself inferred from some other variable inside the DP instrument (e.g. capacitance, strain gauge resistance, resonant frequency)!↩︎
537. We simply assume Earth’s gravitational acceleration ($$g$$) to be constant as well.↩︎
538. To return the transmitter to live service, simply reverse these steps: close the bleed valve, open the low-pressure block valve, close the equalizing valve, and finally open the high-pressure block valve.↩︎
539. The standard 3-valve manifold, for instance, does not provide a bleed valve – only block and equalizing valves.↩︎
540. This concept will be immediately familiar to anyone who has ever had to “bleed” air bubbles out of an automobile brake system. With air bubbles in the system, the brake pedal has a “spongy” feel when depressed, and much pedal motion is required to achieve adequate braking force. After bleeding all air out of the brake fluid tubes, the pedal motion feels much more “solid” than before, with minimal motion required to achieve adequate braking force. Imagine the brake pedal being the isolating diaphragm, and the brake pads being the pressure sensing element inside the instrument. If enough gas bubbles exist in the tubes, the brake pedal might stop against the floor when fully pressed, preventing full force from ever reaching the brake pads. Likewise, if the isolating diaphragm hits a hard motion limit due to gas bubbles in the fill fluid, the sensing element will not experience full process pressure.↩︎
541. So long as the isolating diaphragm is “slack” (i.e. has no appreciable tautness or resistance to movement), the pressure of the fill fluid inside the capillary tube will be equal to the pressure of whatever fluid is within the process vessel. If any pressure imbalance were to develop between the process and fill fluids, the isolating diaphragm would immediately shift position away from the higher-pressure fluid and toward the lower-pressure fluid until equal pressures were re-established. In real practice, isolating diaphragms do indeed have some stiffness opposing motion, and therefore do not perfectly transfer pressure from the process fluid to the fill fluid. However, this pressure difference is usually negligible.↩︎
542. Like all instrument diaphragms, this one is sensitive to damage from contact with sharp objects. If the diaphragm ever becomes nicked, dented, or creased, it will tend to exhibit hysteresis in its motion, causing calibration errors for the instrument. For this reason, isolating diaphragms are often protected from contact by a plastic plug when the instrument is shipped from the manufacturer. This plug must be removed from the instrument before placing it into service.↩︎
543. Anyone familiar with “bleeding” air bubbles out of automotive hydraulic brake systems will understand this concept. In order for the pedal-operated hydraulic brakes in an automobile to function as designed, the hydraulic system must be gas-free. Incompressible liquid transfers pressure without loss of motion, whereas compressible gas bubbles will “give” in to pressure and result in lost brake pad motion for any given brake pedal motion. Thus, an hydraulic brake system with air bubbles in it will have a “spongy” feel at the brake pedal, and may not give full braking force when needed.↩︎
544. Most pressure instrument manufacturers offer a range of fill fluids for different applications. Not only is temperature a consideration in the selection of the right fill fluid, but also potential contamination of or reaction with the process if the isolating diaphragm ever suffers a leak!↩︎
545. Truth be told, this is a requirement for all pressure transmitter fill fluids even when isolating diaphragms are in place to prevent mixing of process and fill fluids, because no diaphragm is 100% guaranteed to seal forever. This means every pressure transmitter must be chosen for the application in mind, since modern DP transmitters all use fill fluid in their internal sensors, whether or not the impulse lines are also filled with a non-reactive fluid.↩︎
546. In fact, after you become accustomed to the regular “popping” and “hissing” sounds of steam traps blowing down, you can interpret the blow-down frequency as a crude ambient temperature thermometer! Steam traps seldom blow down during warm weather, but their “popping” is much more regular (one every minute or less) when ambient temperatures drop well below the freezing point of water.↩︎
547. “Cryogenic” simply refers to a condition of extremely low temperature required to condense a gas into liquid. Such liquids will flash into vapor if raised to room temperature, and so it is quite easy to make impulse lines self-purging in such cases.↩︎
548. At least in the case of a liquid-filled impulse line generating its own hydrostatic pressure, that pressure is constant and may be compensated by “zero-shifting” the range of the pressure instrument. An impulse line that generates random surges of pressure cannot be compensated at all!↩︎
549. Although this fluid would not normally contact pure oxygen in the process, it could if the isolating diaphragm inside the transmitter were to ever leak.↩︎
550. Liquids are considered “miscible” if they may be mixed in any proportion to each other to form a solution. Immiscible liquids refuse to mix thoroughly, and therefore tend to separate.↩︎
551. A spring-loaded cable float only works with liquid level measurement, while a retracting float will measure liquids and solids with equal ease. The reason for this limitation is simple: a float that always contacts the material surface is likely to become buried if the material in question is a solid (powder or granules), which must be fed into the vessel from above.↩︎
552. We may prove this mathematically by algebraic substitution. Given that the total mass ($$m$$) of any liquid sample is equal to the product of that liquid’s mass density and its sample volume ($$m = \rho V$$), that volume ($$V$$) for any vessel of constant cross-sectional area ($$A$$) is given by the expression $$V = Ah$$, and that hydrostatic pressure is equal to $$P = \rho g h$$, we may combine these three equations to arrive at $$m = {AP \over g}$$. This final equation demonstrates how the total mass of liquid stored in a vessel ($$m$$) of constant cross-sectional area ($$A$$) is directly proportional to pressure ($$P$$), and independent of density ($$\rho$$).↩︎
553. Or alternatively, zero depression.↩︎
554. There is some disagreement among instrumentation professionals as to the definitions of these two terms. According to Béla G. Lipták’s Instrument Engineers’ Handbook, Process Measurement and Analysis (Fourth Edition, page 67), “suppressed zero range” refers to the transmitter being located below the 0% level (the LRV being a positive pressure value), while “suppression,” “suppressed range,” and “suppressed span” mean exactly the opposite (LRV is a negative value). The Yokogawa Corporation defines “suppression” as a condition where the LRV is a positive pressure (“Autolevel” Application Note), as does the Michael MacBeth in his CANDU Instrumentation & Control course (lesson 1, module 4, page 12), Foxboro’s technical notes on bubble tube installations (pages 4 through 7), and Rosemount’s product manual for their 1151 Alphaline pressure transmitter (page 3-7). Interestingly, the Rosemount document defines “zero range suppression” as synonymous with “suppression,” which disagrees with Lipták’s distinction. My advice: draw a picture if you want the other person to clearly understand what you mean!↩︎
555. As you are about to see, the calibration of an elevated transmitter depends on us knowing how much hydrostatic pressure (or vacuum, in this case) is generated within the tube connecting the transmitter to the process vessel. If liquid were to ever escape from this tube, the hydrostatic pressure would be unpredictable, and so would be the accuracy of our transmitter as a level-measuring instrument. A remote seal diaphragm guarantees no fill fluid will be lost if and when the process vessel goes empty.↩︎
556. The sea water’s positive pressure at the remote seal diaphragm adds to the negative pressure already generated by the downward length of the capillary tube’s fill fluid ($$-2.43$$ PSI), which explains why the transmitter only “sees” 2.46 PSI of pressure at the 100% full mark.↩︎
557. Sometimes this is done out of habit, other times because instrument technicians do not know the capabilities of new technology.↩︎
558. This is due to limited transmitter resolution. Imagine an application where the elevation head was 10 PSI (maximum) yet the vapor space pressure was 200 PSI. The majority of each transmitter’s working range would be “consumed” measuring gas pressure, with hydrostatic head being a mere 5% of the measurement range. This would make precise measurement of liquid level very difficult, akin to trying to measure the sound intensity of a whisper in a noisy room.↩︎
559. Assuming the liquid level is equal to or greater than $$x$$. Otherwise, the pressure difference between $$P_{bottom}$$ and $$P_{middle}$$ will depend on liquid density and liquid height. However, this condition is easy to check: the level computer simply checks to see if $$P_{middle}$$ and $$P_{top}$$ are unequal. If so, then the computer knows the liquid level exceeds $$x$$ and it is safe to calculate density. If not, and $$P_{middle}$$ registers the same as $$P_{top}$$, the computer knows those two transmitters are both registering gas pressure only, and it knows to stop calculating density.↩︎
560. The details of this math depend entirely on the shape of the tank. For vertical cylinders – the most common shape for vented storage tanks – volume and height are related by the simple formula $$V = \pi r^2 h$$ where $$r$$ is the radius of the tank’s circular base. Other tank shapes and orientations may require much more sophisticated formulae to calculate stored volume from height. See section 26.3 beginning on page , for more details on this subject.↩︎
561. Here I will calculate all hydrostatic pressures in units of inches water column. This is relatively easy because we have been given the specific gravities of each liquid, which make it easy to translate actual liquid column height into column heights of pure water.↩︎
562. Remember that a differential pressure instrument cannot “tell the difference” between a positive pressure applied to the low side, an equal vacuum applied to the high side, or an equivalent difference of two positive pressures with the low side’s pressure exceeding the high side’s pressure. Simulating the exact process pressures experienced in the field to a transmitter on a workbench would be exceedingly complicated, so we “cheat” by simplifying the calibration setup and applying the equivalent difference of pressure only to the “low” side.↩︎
563. This is not unlike the experience of feeling lighter when you are standing in a pool of water just deep enough to submerge most of your body with your feet touching the bottom. This reduction of apparent weight is due to the buoyant force of the water upward on your body, equal to the weight of water that your body displaces.↩︎
564. So-called for its ability to “knock out” (separate and collect) condensible vapors from the gas stream. This particular photograph was taken at a natural gas compression facility, where it is very important the gas to be compressed is dry (since liquids are essentially incompressible). Sending even relatively small amounts of liquid into a compressor may cause the compressor to catastrophically fail!↩︎
565. To anyone familiar with the front suspension of a 1960’s vintage Chevrolet truck, or the suspension of the original Volkswagen “Beetle” car, the concept of a torsion bar should be familiar. These vehicles used straight, spring-steel rods to provide suspension force instead of the more customary coil springs used in modern vehicles. However, even the familiar coil spring is an example of torsional forces at work: a coil spring is nothing more than a torsion bar bent in a coil shape. As a coil spring is stretched or compressed, torsional forces develop along the circumferential length of the spring coil, which is what makes the spring “try” to maintain a fixed height.↩︎
566. This illustration is simplified, omitting such details as access holes into the cage, block valves between the cage and process vessel, and any other pipes or instruments attached to the process vessel. Also, the position-sensing mechanism normally located at the far left of the assembly is absent from this drawing.↩︎
567. The general term for this form of measurement is time domain reflectometry.↩︎
568. My own experience with this trend is within the oil refining industry, where legacy displacer instruments (typically Fisher brand “Level-Trol” units) are being replaced with new guided-wave radar transmitters, both for vapor-liquid and liquid-liquid interface applications.↩︎
569. The speed of sound through any substance is a function of both the substance’s density and its bulk modulus (i.e. the compressibility of a substance). Mathematically, $$c = \sqrt{B \over \rho}$$ where $$c$$ is the sonic velocity, $$B$$ is the bulk modulus, and $$\rho$$ is the mass density. Water and air provide an excellent illustration of this principle: the speed of sound through water happens to be much faster than the speed of sound through air despite the vastly greater mass density of water, only because of the even greater disparity in bulk modulus between water and air.↩︎
570. In the industrial instrumentation world, the word “transducer” usually has a very specific meaning: a device used to process or convert standardized instrumentation signals, such as 4-20 mA converted into 3-15 PSI, etc. In the general scientific world, however, the word “transducer” describes any device converting one form of energy into another. It is this latter definition of the word that I am using when I describe an ultrasonic “transducer” – a device used to convert electrical energy into ultrasonic sound waves, and vice-versa.↩︎
571. “Radar” is an acronym: RAdio Detection And Ranging. First used as a method for detecting enemy ships and aircraft at long distances over the ocean in World War II, this technology is used for detecting the presence, distance, and/or speed of objects in a wide variety of applications.↩︎
572. In fact, it is a common retrofit practice to install a guided-wave radar level transmitter in the exact same cage that once housed a displacement-style level transmitter.↩︎
573. In actuality, both radio waves and light waves are electromagnetic in nature. The only difference between the two is frequency: while the radio waves used in radar systems are classified as “microwaves” with frequencies in the gigahertz (GHz) region, visible light waves range in the hundred of terahertz (THz)!↩︎
574. This formula assumes lossless conditions: that none of the wave’s energy is converted to heat while traveling through the dielectric. For many situations, this is true enough to assume.↩︎
575. Or if the chemical composition of the gas or vapor changes dramatically.↩︎
576. The pressure and temperature factors in this formula come from the Ideal Gas Law ($$PV = nRT$$), manipulating that equation to express molecular gas density in terms of pressure and temperature ($$\rho = {n \over V} = {P \over RT}$$). The fraction $${P T_{ref} \over P_{ref} T}$$ expresses a ratio of molecular densities: $$\rho \over \rho_{ref}$$.↩︎
577. Dielectric permittivity is one of the factors determining the speed of any electromagnetic wave through a substance, but not the only one. The material’s magnetic permeability is another factor, but it is far more common to encounter interfaces of gas-liquid or liquid-liquid where differences in permittivity rather than differences in permeability constitute the major reason for differences in radio wave velocity.↩︎
578. Rosemount’s “Replacing Displacers with Guided Wave Radar” technical note states that the difference in dielectric constant between the upper and lower liquids must be at least 10.↩︎
579. $$R = 0.5285$$ for the 1/40 interface; $$R = 0.02944$$ for the 40/80 interface; and $$R = 0.6382$$ for the 1/80 interface, all based on the formula $$R = {\left({\sqrt{\epsilon_{r}} - 1}\right)^2 \over \left(\sqrt{\epsilon_{r}} + 1 \right)^2}$$ using the pair of permittivity values at each interface.↩︎
580. It should be noted that the dielectric constant of the lowest medium (the liquid in a simple, non-interface, level measurement application) is irrelevant for calibration purposes. All we are concerned with is the propagation time of the signal to and from the level of interest, nothing below it.↩︎
581. For vented-tank level measurement applications where air is the only substance above the point of interest, the relative permittivity is so close to a value of 1 that there is little need for further consideration on this point. Where the permittivity of fluids becomes a problem for radar is in high-pressure (non-air) gas applications and liquid-liquid interface applications, especially where the upper substance composition is subject to change.↩︎
582. Probe mounting style will also influence the lower transition zone, in the case of flexible probes anchored to the bottom of the process vessel.↩︎
583. An approximate analogy for understanding the nature of this pulse may be performed using a length of rope. Laying a long piece of rope in a straight line on the ground, pick up one end and quickly move it in a tight circle using a “flip” motion of your wrist. You should be able to see the torsional pulse travel down the length of the rope until it either dies out from dissipation or it reaches the rope’s end. As with the torsional pulse in a magnetostrictive waveguide, this pulse in the rope is mechanical in nature: a movement of the rod’s (rope’s) molecules. As a mechanical wave, it may be properly understood as a form of sound.↩︎
584. This “dampener” is the mechanical equivalent of a termination resistor in an electrical transmission line: it makes the traveling wave “think” the waveguide is infinitely long, preventing any reflected pulses. For more information on electrical transmission lines and termination resistors, see section 5.10 beginning on page .↩︎
585. This particular transmitter happens to be one of the “M-Series” models manufactured by MTS.↩︎
586. One reference gives the speed of sound in a magnetostrictive level instrument as 2850 meters per second. Rounding this up to $$3 \times 10^3$$ m/s, we find that the speed of sound in the magnetostrictive waveguide is at least five orders of magnitude slower than the speed of light in a vacuum (approximately $$3 \times 10^8$$ m/s). This relative slowness of wave propagation is a good thing for our purposes here, as it gives more time for the electronic timing circuit to count, yielding a more precise measurement of distance traveled by the wave. This fact grants superior resolution of measurement to magnetostrictive level sensors over radar-based and laser-based level sensors. Open-air ultrasonic level instruments deal with propagation speeds even slower than this (principally because the bulk moduli of gases and vapors is far less than that of a solid metal rod) which at first might seem to give these level sensors the advantage in precision. However, open-air level sensors experience far greater propagation velocity variations caused by changes in pressure and temperature than magnetostrictive sensors. Unlike the speed of sound in gases or liquids, the speed of sound in a solid metal rod is very stable over a large range of process temperatures, and practically constant for a large range of process pressures. Another factor adding to the calibration stability of magnetostrictive instruments is that the composition of the medium never changes. With instruments measuring time-of-flight through process fluids, the chemical composition of those fluids often affects the wave velocity. In a magnetostrictive instrument, the waves are always traveling through the same material – the metal of the waveguide bar – and thus are not subject to variation with process changes.↩︎
587. Regardless of the vessel’s shape or internal structure, the measurement provided by a weight-sensing system is based on the true mass of the stored material. Unlike height-based level measurement technologies (float, ultrasonic, radar, etc.), no characterization will ever be necessary to convert a measurement of height into a measurement of mass.↩︎
588. If we happened to know, somehow, that the vessel’s weight was in fact equally shared by all supports, it would be sufficient to simply measure stress at one support to infer total vessel weight. In such an installation, assuming three supports, the total vessel weight would be the stress at any one support multiplied by three.↩︎
589. The particular “micro-brewery” process shown here is at the Pike’s Place Market in downtown Seattle, Washington. Three load cells measure the weight of a hopper filled with ingredients prior to brewing in the “mash tun” vessel.↩︎
590. One practical solution to this problem is to shut down the source of vibration (e.g. agitator motor, pump, etc.) for a long enough time to take a sample weight measurement, then run the machine again between measurements. So long as intermittent weight measurement is adequate for the needs of the process, the interference of machine vibration may be dealt with in this manner.↩︎
591. Beta particles are not orbital electrons, but rather than product of elementary particle decay in an atom’s nucleus. These electrons are spontaneously generated and subsequently ejected from the nucleus of the atom.↩︎
592. The half-life of a radioactive substance is the amount of time it takes for one-half of the original quantity to experience radioactive decay. To illustrate, a 10-gram quantity consisting of 100% Cobalt-60 atoms will only contain 5 grams of Cobalt-60 after 5.3 years, and then only 2.5 grams of Cobalt-60 after another 5.3 years (10.6 years from the start), and so on. The actual mass of the sample does not change significantly over this time period because the Cobalt atoms have decayed into atoms of Nickel, which still have the same atomic mass value. However, the intensity of the gamma radiation emitted by the sample decreases over time, proportional to the percentage of Cobalt remaining therein.↩︎
593. So much of the incident power is lost as the radar signal partially reflects off the gas-liquid interface, then the liquid-liquid interface, then again through the gas-liquid interface on its return trip to the instrument that every care must be taken to ensure optimum received signal strength. While twin-lead probes have been applied in liquid-liquid interface measurement service, the coaxial probe design is still the best for maintaining radar signal integrity.↩︎
594. Even this advantage is not always true. It is possible to build self-powered thermocouple temperature indicators, where an analog meter movement is driven by the electrical energy a thermocouple sensing junction outputs. Here, no external electrical power source is required! However, the accuracy of self-powered thermocouple systems is poor, as is the ability to measure small temperature ranges.↩︎
595. “Swamping” is the term given to the overshadowing of one effect by another. Here, the normal resistance of the thermistor greatly overshadows (“swamps”) any wire resistance in the circuit, such that wire resistance becomes negligible.↩︎
596. Remember that an ideal voltmeters has infinite input impedance, and modern semiconductor-amplified voltmeters have impedances of several mega-ohms or more.↩︎
597. Note that the middle wire resistance is of no effect because it does not carry the RTD’s current. The amount of current entering or exiting an operational amplifier is assumed to be zero for all practical purposes.↩︎
598. These errors will result only if the paralleled wires carry current. If the two wires you paralleled happen to join the transmitter’s sensing terminal to the RTD (the one carrying no current), no errors will result. However, many RTD transmitters do not document which of the terminals sense (carry no current) versus which of them excite (carry current to the RTD), and so there is a probability of getting it wrong if you simply guess. Given that there is no real benefit to having paralleled wires connecting the transmitter’s sensing terminal to the RTD, my advice is to either use all four wires and configure the transmitter for 4-wire mode, or don’t use the fourth wire at all.↩︎
599. By “first principles,” I mean the basic laws of electric circuits. In this case, the most important law to apply is Kirchhoff’s Voltage Law: the algebraic sum of voltages in any loop must be equal to zero.↩︎
600. The colors in this table apply only to the United States and Canada. A stunning diversity of colors has been “standardized” for each thermocouple type per nationality. The British and Czechs use their own color code, as do the Dutch and Germans. France has its own unique color code as well. Just for fun, an “international” color code also exists which doesn’t match any of the others. There are other deviations as well: the wire colors for type R and S thermocouples, for example, are standardized for extension-grade wire but not for thermocouple-grade wire.↩︎
601. By “oxidizing,” what is meant is any atmosphere containing sufficient oxygen molecules or molecules of a similar element such as chlorine or fluorine.↩︎
602. “Reducing” refers to atmospheres rich in elements that readily oxidize. Practically any fuel gas (hydrogen, methane, etc.) will create a reducing atmosphere in sufficient concentration.↩︎
603. It should be noted that no amount of engineering or design is able to completely prevent people from doing the wrong thing. I have seen this style of thermocouple plug forcibly mated the wrong way to a socket. The amount of insertion force necessary to make the plug fit backward into the socket was quite extraordinary, yet this apparently was not enough of a clue for this wayward individual to give them pause.↩︎
604. Grounded thermocouples often have thermal time constant values less than half that of comparable ungrounded thermocouples. Exposed-tip thermocouples are even faster than grounded-tip, typically by even larger ratios than grounded-tip thermocouples are to ungrounded thermocouples.↩︎
605. Early texts on thermocouple use describe multiple techniques for automatic compensation of the reference (“cold”) junction. One design placed a mercury bulb thermometer at the reference junction, with a loop of thin platinum wire dipped into the mercury. As junction temperature rose, the mercury column would rise and short past a greater length of the platinum wire loop, causing its resistance to decrease which in turn would electrically bias the measurement circuit to offset the effects of the reference junction’s voltage. Another design used a bi-metallic spring to offset the pointer of the meter movement, so that changes in temperature at the indicating instrument (where the reference junction was located) would result in the analog meter’s needle becoming offset from its normal “zero” point, thus compensating for the offset in voltage created by the reference junction.↩︎
606. For any two-phase mixture of any single substance (in this case, H$$_{2}$$O) the temperature of that mixture will be a strict function of pressure, the mixture possessing only one thermodynamic degree of freedom. Any addition or removal of heat from the ice/water mix results in a phase change (e.g. either more ice melts to become water, or more water freezes to become ice) rather than a temperature change. If even more precision is desired, a triple point cell may be used to fix the reference junction’s temperature, since any substance at its triple point will possess zero degrees of thermodynamic freedom (i.e. neither its pressure nor temperature can change).↩︎
607. Please note that “cold junction” is just a synonymous label for “reference junction.” In fact the “cold” reference junction may very well be at a warmer temperature than the so-called “hot” measurement junction! Nothing prevents anyone from using a thermocouple to measure temperatures below the freezing point of water.↩︎
608. A junction of copper and constantan just happens to be a type T thermocouple junction.↩︎
609. No coloring standard exists in the United States for platinum thermocouple-grade wire (e.g. types R, S, etc.).↩︎
610. The colors I list here are for thermocouples in the United States.↩︎
611. The effect will be exactly the same for an instrument with software compensation rather than hardware compensation. With software compensation, there is no literal $$V_{rjc}$$ voltage source, but the equivalent millivolt value is digitally added to the zero input measured at the thermocouple connection terminals, resulting in the same effect of measuring ambient temperature.↩︎
612. For those readers familiar with digital logic gate circuits, this resistor fulfills the same function as a pullup or pulldown resistor on the input of a digital gate: providing a stable logic state in the event of a floating input condition.↩︎
613. This is a good application of fail-safe design, where we choose the transmitter’s failure mode based on the safest outcome. For example, if our temperature transmitter were being used to sense the temperature of a furnace where excessive temperature was more dangerous than insufficient temperature, we would want to configure it for “high” burnout. This way if the thermocouple fails open, the transmitter will report a dangerous (but false) measurement of furnace temperature to the controller, which in turn will automatically act to decrease the furnace’s actual temperature (i.e. the safer condition.)↩︎
614. Although Seebeck discovered thermo-electricity in 1822, the technique of measuring temperature by sensing the voltage produced at a dissimilar-metal junction was delayed in practical development until 1886 when rugged and accurate electrical meters became available for industrial use.↩︎
615. Anyone who has ever used a magnifying glass (a concentrating lens) to concentrate sunlight knows how this works. If you were to use a magnifying glass to concentrate sunlight onto a thermocouple-type sensor, you could (at least in principle) infer the temperature of the sun in this manner.↩︎
616. Later versions of the Radiamatic (dubbed the Radiamatic II) were more than just a bare thermopile and optical concentrator, containing electronic circuitry to output a linearized 4-20 mA signal representing target temperature.↩︎
617. Comparing temperature ratios versus thermopile millivoltage ratios assumes linear thermocouple behavior, which we know is not exactly true. Even if the thermopile focal point temperatures precisely followed the ratios predicted by the Stefan-Boltzmann law, we would still expect some inconsistencies due to the non-linearities of thermocouple voltages. There will also be variations from predicted values due to shifts in radiated light frequencies, changes in emissivity factor, thermal losses within the sensing head, and other factors that refuse to remain constant over wide ranges of received radiation intensity. The lesson here is to not expect perfect agreement with theory!↩︎
618. An important caveat to this rule is so long as the target object completely fills the sensor’s field of view (FOV). The reason for this caveat will become clear at the conclusion of the explanation.↩︎
619. The field of view (a circle where the viewing “cone” intercepts the flat surface of the object) increases linearly in diameter with increases in distance between the sensor and the object. However, since the area of a circle is proportional to the square of its diameter ($$A = {\pi D^2 \over 4}$$ or $$A = \pi r^2$$), we may say that the viewing area increases with the square of the distance between the sensor and object.↩︎
620. In general, it is better to install a thermowell in a pipe rather than in a vessel because the greater fluid turbulence of flow in a pipe expedites heat transfer by convection as well as helps to clean solid fouling off of the thermowell’s surface.↩︎
621. The air gap acts as a thermal resistance while the mass of the element itself acts as a thermal capacitance. Thus, the inclusion of an air gap forms a thermal “RC time constant” delay network secondary to the thermal delay incurred by the thermowell. This adds another “order” of lag to the system, not just an increase in its thermal time constant. Generally speaking, multiple orders of lag are detrimental to process control because they increase phase shift in a feedback loop and may lead to oscillation.↩︎
622. Analytical (chemical composition) measurement is undeniably more complex and diverse than flow measurement, but analytical measurement covers a great deal of specific measurement types. As a single process variable, flow measurement is probably the most complex.↩︎
623. Sometimes referred to as a plug of fluid.↩︎
624. What really matters in Newton’s Second Law equation is the resultant force causing the acceleration. This is the vector sum of all forces acting on the mass. Likewise, what really matters in this scenario is the resultant pressure acting on the fluid plug, and this resultant pressure is the difference of pressure between one face of the plug and the other, since those two pressures impart two forces on the fluid mass in direct opposition to each other.↩︎
625. Think of a piezometer tube as nothing more than a manometer tube: the greater the fluid pressure at the bottom of the tube, the higher the liquid will rise inside the tube.↩︎
626. This is a very sound assumption for liquids, and a fair assumption for gases when pressure changes through the venturi tube are modest.↩︎
627. One of the simplifying assumptions we make in this derivation is that friction plays no significant role in the fluid’s behavior as it moves through the venturi tube. In truth, no industrial fluid flow is totally frictionless (especially through more primitive flow elements such as orifice plates), and so our “theoretical” equations must be adjusted a bit to match real life.↩︎
628. To see a graphical relationship between fluid acceleration and fluid pressures in a venturi tube, examine the illustration found in section [Fluid acceleration in a venturi] beginning on page .↩︎
629. This re-write is solidly grounded in the rules of algebra. We know that $$\sqrt{a} \sqrt{b} = \sqrt{ab}$$, which is what allows us to do the re-write.↩︎
630. For positive numbers only!↩︎
631. With so many modern instruments being capable of digitally implementing this square-root function, one must be careful to ensure it is only done once in the loop. I have personally witnessed flow-measurement installations where both the pressure transmitter and the indicating device were configured for square-root characterization. This essentially performed a fourth root characterization on the signal, which is just as bad as no characterization at all! Like anything else technical, the key to successful implementation is a correct understanding of how the system is supposed to work. Simply memorizing that “the instrument must be set up with square-root to measure flow” and blindly applying that mantra is a recipe for failure.↩︎
632. Despite the impressive craftsmanship and engineering that went into the design of pneumatic square root extractors, their obsolescence is mourned by no one. These devices were notoriously difficult to set up and calibrate accurately, especially as they aged.↩︎
633. L.K. Spink, in his book Principles and Practice of Flow Meter Engineering, notes that drain holes intended to pass solid objects may be useless in small pipe sizes, where the hole is so small it will probably become plugged with solid debris and cease to provide benefit. In such installations he recommends re-orienting the pipe vertically instead of horizontally. This allows solids to pass through the main bore of the orifice without “damming” on the upstream side of the orifice plate. I would add the suggestion to consider a different primary element entirely, such as a venturi tube. The small size of the line will limit the cost of such an element, and the performance is likely to be far better than an orifice plate anyway.↩︎
634. To read more about the concept of Reynolds number, refer to section [Reynolds number] beginning on page .↩︎
635. One significant source of error for customer-drilled tap holes is the interior finish of the holes. Even a small “burr” of metal left where the hole penetrates the inner surface of the pipe wall will cause substantial flow measurement errors!↩︎
636. What this means is that a “pipe tap” installation is actually measuring permanent pressure loss, which also happens to scale with the square of flow rate because the primary mechanism for energy loss in turbulent flow conditions is the translation of linear velocity to angular (swirling) velocity in the form of eddies. This kinetic energy is eventually dissipated in the form of heat as the eddies eventually succumb to viscosity.↩︎
637. One installation error seen in this photograph is a green plastic impulse tube with a bend extending above the upper flange tap. Any elevated portion of the impulse tube system will tend to collect gas bubbles over time, possibly causing measurement errors. A better installation would ensure the impulse tubes never extend above the flange tap they connect to on the liquid-bearing pipe.↩︎
638. If an orifice plate is a “donut,” the V-cone is a “donut hole.”↩︎
639. A “slurry” is a suspension of solid particles within a liquid. Mud is a common example of a slurry.↩︎
640. This phenomenon may be observed when watching the flow of water through a turn in a river, especially if the river is fast-moving. Water level at the far (outside) bank of the turn will be higher than the water level at the near (inside) bank of the turn, due to radial acceleration of the water and the pressure difference that acceleration generates. In fact, that difference in water height may even be used to estimate the river’s flow rate!↩︎
641. The fact that a pipe elbow generates small differential pressure is an accuracy concern because other sources of pressure become larger by comparison. Noise generated by fluid turbulence in the elbow, for example, becomes a significant portion of the pressure sensed by the transmitter when the differential pressure is so low (i.e. the signal-to-noise ratio becomes smaller). Errors caused by differences in elbow tap elevation and different impulse line fill fluids, for example, become more significant as well.↩︎
642. This is not always the case, as primary elements are often found on throttled process lines. In such cases where a control valve normally throttles the flow rate, any energy dissipated by the orifice plate is simply less energy that the valve would otherwise be required to dissipate. Therefore, the presence or absence of an orifice plate has no net impact on energy dissipation when used on a process flow throttled by a control valve.↩︎
643. This is not to be confused with micro-turbulence in the fluid, which cannot be eliminated at high Reynolds number values. In fact, “fully-developed turbulent flow” is desirable for head-based meter elements such as orifice plates because it means the flow profile will be relatively flat (even velocities across the pipe’s diameter) and frictional forces (viscosity) will be negligible. The thing we are trying to avoid is large-scale turbulent effects such as eddies, swirl, and asymmetrical flow profiles, which compromise the ability of most flowmeters to accurate measure flow rate.↩︎
644. L.K. Spink mentions in his book Principles and Practice of Flow Meter Engineering that certain tests have shown flow measurement errors induced from severe disturbances as far as 60 to 100 pipe diameters upstream of the primary flow element. The April 2000 update of API standard 14.3 (for custody-transfer measurement of natural gas using orifice plates) calls for upward of 145 pipe diameters of straight-length pipe upstream of the orifice plate!↩︎
645. Flow elements with low beta ratio values tolerate greater disturbance in the flow pattern because they accelerate the flowstream to a greater degree. This may be best visualized by a thought experiment where we imagine an orifice plate with a very large beta ratio (i.e. one where the bore size is nearly as large as the pipe diameter): such an orifice plate would hardly accelerate the fluid at all, which would mean a mis-shapen flow profile entering the bore would probably remain mis-shapen exiting it. The acceleration imparted to a flowstream by a low-beta element tends to overshadow any asymmetries in the flow profile. However, there are disadvantages to using low-beta elements, one of them being increased permanent pressure loss which may translate to increased operating costs due to energy loss.↩︎
646. Beauty is truly in the eye of the beholder. While a piping designer might see straight-run lengths of pipe in awkward locations – necessitating more pipe and/or more bends elsewhere in the system to accommodate – as wasteful and ugly, the instrument engineer sees it as a thing of beauty.↩︎
647. Richard W. Miller, in his outstanding book Flow Measurement Engineering Handbook, states that venturi tubes may come within 1 to 3 percent of ideal, while a square-edged orifice plate may perform as poorly as only 60 percent of theoretical!↩︎
648. Specified in Part 2 of the AGA Report #3, section 2.6.5, page 22. A major reason for this is von Kármán vortex shedding caused by the gas having to flow around the width of the thermowell. The “street” of vortices shed by the thermowell will cause serious pressure fluctuations at the orifice plate unless mitigated by a flow conditioner, or by locating the thermowell downstream so that the vortices do not reach the orifice.↩︎
649. This is especially true in the gas exploration industry, where natural gas coming out of the well is laden with mineral debris.↩︎
650. Liquids can and do compress, the measurement of their “compressibility” being what is called the bulk modulus. However, this compressibility is too slight to be of any consequence in most flow measurement applications. A notable exception is the metering of diesel fuel through a high-pressure injection pump, where liquid pressures range in the tens of thousands of PSI, and the compressibility of the liquid diesel fuel may affect the precise timing of individual injections into the engine cylinders.↩︎
651. “Swamping” is a term commonly used in electrical engineering, where a bad effect is overshadowed by some other effect much larger in magnitude, to the point where the undesirable effect is negligible in comparison.↩︎
652. This includes elaborate oil-bath systems where the laminar flow element is submerged in a temperature-controlled oil bath, the purpose of which is to hold temperature inside the laminar element constant despite sudden changes in the measured fluid’s temperature.↩︎
653. If we know that the plummet’s weight will remain constant, its drag area will remain constant, and that the force generated by the pressure drop will always be in equilibrium with the plummet’s weight for any steady flow rate, then the relationship $$F = P A$$ dictates a constant pressure. Thus, we may classify the rotameter as a constant-pressure, variable-area flowmeter. This stands in contrast to devices such as orifice plates, which are variable-pressure, constant-area.↩︎
654. Orifice plates are variable-pressure, constant-area flowmeters. Rotameters are constant-pressure, variable-area flowmeters. Weirs are variable-pressure, variable-area flowmeters. As one might expect, the mathematical functions describing each of these flowmeter types is unique!↩︎
655. It is also possible to operate a Parshall flume in fully submerged mode, where liquid level must be measured at both the upstream and throat sections of the flume. Correction factors must be applied to these equations if the flume is submerged.↩︎
656. These figures are reported in Béla Lipták’s excellent reference book Instrument Engineers’ Handbook – Process Measurement and Analysis Volume I (Fourth Edition). To be fair to closed-pipe elements such as orifice plates and venturi tubes, much improvement in the classic 3:1 rangeability limitation has been achieved through the use of microprocessor-based differential pressure sensors. Lipták reports rangeabilities for orifice plates as great as 10:1 through the use of such modern differential pressure instruments. However, even this pales in comparison to the rangeability of a typical weir or flume, which Lipták reports to be 75:1 for “most devices” in this category.↩︎
657. “Custody transfer” refers to measurement applications where a product is exchanging ownership. In other words, someone is selling, and someone else is buying, quantities of fluid as part of a business transaction. It is not difficult to understand why accuracy is important in such applications, as both parties have a vested interest in a fair exchange. Government institutions also have a stake in accurate metering, as taxes are typically levied on the sale of commodity fluids such as natural gas.↩︎
658. It is important to note that the vortex-shedding phenomenon ceases altogether if the Reynolds number is too low. Laminar flow produces no vortices, but rather stream-line flow around any object placed in its way.↩︎
659. Note that if flow rate is to be expressed in units of gallons per minute as is customary, the equation must contain a factor for minutes-to-seconds conversion: $$f = {kQ \over 60}$$↩︎
660. This $$k$$ factor is empirically determined for each flowmeter by the manufacturer using water as the test fluid (a factory “wet-calibration”), to ensure optimum accuracy.↩︎
661. In a practical sense, only liquid flows are measurable using this technique. Gases must be super-heated into a plasma state before they are able to conduct electricity, and so electromagnetic flowmeters cannot be used with most industrial gas flowstreams.↩︎
662. This is an application of the transitive property in mathematics: if two quantities are both equal to a common third quantity, they must also be equal to each other. This property applies to proportionalities as well as equalities: if two quantities are proportional to a common third quantity, they must also be proportional to each other.↩︎
663. The colloquial term in the United States for this sort of thing is fudge factor.↩︎
664. The obvious solution to this problem – relocating the pipes to give more clearance between flowmeters – would be quite expensive given the large pipe sizes involved. A “compromise” solution is to tilt the magnetic flowtubes as far as possible without the electrodes touching the adjacent flowtube. Horizontal electrode installation is ideal for horizontal pipes, but an angled installation will be better than a vertical installation.↩︎
665. As always, check the manufacturer’s literature for specific requirements, as variations do exist for different models and sizes of magtube.↩︎
666. Even electrically non-conducting solid matter is tolerated well by magnetic flowmeters, since the conducting liquid surrounding the solids still provides continuity from one electrode to the other.↩︎
667. Braided conductors do a better job of shunting radio-frequency currents, because at very high frequencies the skin effect makes the surface area of a conductor a greater factor in its conductivity than its cross-sectional area.↩︎
668. For example, in a condition of no liquid flow through the tube, the electrodes will intercept no voltage at all when the magnetic excitation is 60 Hz AC. When liquid moves slowly in the forward direction through the tube, a low-amplitude 60 Hz millivoltage signal will be detected at the electrodes. When liquid moves rapidly in the forward direction through the tube, the induced 60 Hz AC millivoltage will be greater in amplitude. Any liquid motion in the reverse direction induces a proportional 60 Hz AC voltage signal whose phase is 180$$^{o}$$ shifted from the excitation signal driving the magnetic coils of the flowtube.↩︎
669. We know this because the largest electrical noise sources in industry are electric motors, transformers, and other power devices operating on the exact same frequency (60 Hz in the United States, 50 Hz in Europe) as the flowtube coils.↩︎
670. In the industrial instrumentation world, the word “transducer” usually has a very specific meaning: a device used to process or convert standardized instrumentation signals, such as 4-20 mA converted into 3-15 PSI, etc. In the general scientific world, however, the word “transducer” describes any device converting one form of energy into another. It is this latter definition of the word that I am using when I describe an ultrasonic “transducer” – a device used to convert electrical energy into ultrasonic sound waves, and vice-versa.↩︎
671. This phenomenon is analogous to paddling a canoe across the width of a river, with the canoe bow angled upstream versus angled downstream. Angled upstream, the canoeist must overcome the velocity of the river and therefore takes longer to reach the other side. Angled downstream, the river’s velocity aids the canoeist’s efforts and therefore the trip takes less time.↩︎
672. If you would like to prove this to yourself, you may do so by substituting path length ($$L$$), fluid velocity ($$v$$), and sound velocity ($$c$$) for the times in the flow formula. Use $$t_{up} = {L \over {c-v}}$$ and $$t_{down} = {L \over {c+v}}$$ as your substitutions, then algebraically reduce the flow formula until you find that all the $$c$$ terms cancel. Your final result should be $$Q = {2kv \over L}$$.↩︎
673. An instrument called a gas chromatograph is able to provide live measurement of gas composition, with a computer calculating the average speed of sound for the gas given the known types and percentages of each molecular compound comprising the gas mixture. It just so happens that gas composition analysis by chromatograph is something typically done for custody transfer flow measurement of natural gas anyway, for the primary purpose of calculating the gas’s heating value as a fuel, and therefore no additional investment of instrumentation is necessary to calculate the gas’s speed of sound in this application.↩︎
674. See page 10 of Friedrich Hofmann’s Fundamentals of Ultrasonic Flow Measurement for industrial applications paper.↩︎
675. Most notably, the problem of achieving good acoustic coupling with the pipe wall so signal transmission to the fluid and signal reception back to the sensor may be optimized. Also, there is the potential for sound waves to “ring around the pipe” instead of travel through the fluid with clamp-on ultrasonic flowmeters because the sound waves must travel through the full thickness of the pipe walls in order to enter and exit the fluid stream.↩︎
676. Recall from algebra that we may perform any arithmetic operation we wish to any equation, so long as we apply that operation equally to both sides of the equation. Dividing one equation by another equation obeys this principle, because both sides of the second equation are equal. In other words, we could divide both sides of the first equation by $$P_A V_A$$ (although that would not give us the solution we are looking for), but dividing the left side by $$P_A V_A$$ and the right side by $$nR T_A$$ is really doing the same thing, since $$nR T_A$$ is identical in value to $$P_A V_A$$.↩︎
677. Division by $$t$$ does not alter the equation at all, since we are essentially multiplying the left-hand side by $$t \over t$$ which is multiplication by 1. This is why we did not have to apply $$t$$ to the right-hand side of the equation.↩︎
678. The wonderful thing about standards is that there are so many to choose from!↩︎
679. In some applications, such as the custody transfer of natural gas, we are interested in something even more abstract: heating value. However, in order to calculate the gross heating value of a fuel gas stream, we must begin with an accurate mass flow measurement – volumetric flow is not really helpful.↩︎
680. A “mole” is equal to a value of $$6.022 \times 10^{23}$$ entities. Therefore, one mole of carbon atoms is 602,200,000,000,000,000,000,000 carbon atoms. For a more detailed examination of this subject, refer to section 3.7 beginning on page .↩︎
681. I am purposely ignoring the fact that naturally occurring carbon has an average atomic mass of 12.011, and naturally occurring oxygen has an atomic mass of 15.9994.↩︎
682. The British unit of the “pound” is technically a measure of force or weight and not mass. The proper unit of mass measurement in the British system is the “slug.” However, for better or worse, the “slug” is rarely used, and so engineers have gotten into the habit of using “pound” as a mass measurement. In order to distinguish the use of “pound” to represent mass (an intrinsic property of matter) as opposed to the use of “pound” to represent weight (an incidental property of matter), the former is abbreviated lbm (literally, “pounds mass”). In Earth gravity, “lbm” and “lb” are synonymous. However, the standard Newtonian equation relating force, mass, and acceleration ($$F = ma$$) does not work when “lbm” is the unit used for mass and “lb” is used for force (it does when “slug” is used for mass and “lb” is used for force, though!). A weird unit of force invented to legitimize “pound” as an expression of mass is the poundal (“pdl”): one “poundal” of force is the reaction of one “pound” of mass (lbm) accelerated one foot per second squared. By this definition, a one-pound mass (1 lbm) in Earth gravity weighs 32 poundals!↩︎
683. One could argue that orifice plates and other pressure-based flowmeters respond primarily to mass flow rather than volumetric flow, since their operation is based on the pressure created by accelerating a mass. However, fluid density does affect the relationship between mass flow rate and differential pressure (note how the density term $$\rho$$ appears in the mass flow equation $$W = k\sqrt{\rho (P_1 - P_2)}$$, where it would not if differential pressure were a strict function of mass flow rate and nothing else), and so the raw output of these instruments must still be “compensated” by pressure and temperature measurements.↩︎
684. The impeller-turbine and twin-turbine mass flowmeter types are examples of mechanical true-mass flow technologies. Both work on the principle of fluid inertia. In the case of the impeller-turbine flowmeter, an impeller driven by a constant-speed electric motor imparts a “spin” to a moving fluid, which then impinges on a stationary turbine wheel to generate a measurable torque. The greater the mass flow rate, the greater the impulse force imparted to the turbine wheel. In the twin-turbine mass flowmeter, two rotating turbine wheels with different blade pitches are coupled together by a flexible coupling. As each turbine wheel attempts to spin at its own speed, the inertia of the fluid causes a differential torque to develop between the two wheels. The more mass flow rate, the greater the angular displacement (offset) between the two wheels.↩︎
685. In fact, this density-measuring function of Coriolis flowmeters is so precise that they often find use primarily as density meters, and only secondarily as flowmeters!↩︎
686. An interesting experiment to perform consists of holding a water hose in a U-shape and gently swinging the hose back and forth like a pendulum, then flowing water through that same hose while you continue to swing it. The hose will begin to undulate, its twisting motion becoming visually apparent.↩︎
687. This is an example of a vector cross-product where all three vectors are perpendicular to each other, and the directions follow the right-hand rule.↩︎
688. The Coriolis force generated by a flowing fire hose as firefighters work to point it in a different direction can be quite significant, owing to the high mass flow rate of the water as it flows through the hose and out the nozzle!↩︎
689. For those readers with an automotive bent, this is the same principle applied in opposed-cylinder engines (e.g. Porsche “boxer” air-cooled 6-cylinder engine, Volkswagen air-cooled 4-cylinder engine, BMW air-cooled motorcycle twin engine, Citroen 2CV 2-cylinder engine, Subaru 4- and 6-cylinder opposed engines, etc.). Opposite piston pairs are always 180$$^{o}$$ out of phase for the purpose of maintaining mechanical balance: both moving away from the crankshaft or both moving toward the crankshaft, at any given time.↩︎
690. An alternative to splitting the flow is to plumb the tubes in series so they must share the exact same flow rate, like series-connected resistors sharing the exact same amount of electrical current.↩︎
691. The force coil is powered by an electronic amplifier circuit, which receives feedback from the sensor coils. Like any amplifier circuit given positive (regenerative) feedback, it will begin to oscillate at a frequency determined by the feedback network. In this case, the feedback “network” consists of the force coil, tubes, and sensor coils. The tubes, having both resilience and mass, naturally possess their own resonant frequency. This mechanical resonance dominates the feedback characteristic of the amplifier loop, causing the amplifier circuit to oscillate at that same frequency.↩︎
692. This usually takes the form of a simple analog oscillator circuit, using the tubes and sensors as feedback elements. It is not unlike a crystal oscillator circuit where the mechanical resonance of a quartz crystal stabilizes the circuit’s frequency at one value. The feedback system naturally finds and maintains resonance, just as a crystal oscillator circuit naturally finds and maintains the resonant frequency of the quartz crystal when provided with ample regenerative (positive) feedback. As fluid density inside the tubes changes, the tubes’ mass changes accordingly, thus altering the resonant frequency of the system. The analog nature of this mechanical oscillator explains why some early versions of Coriolis flowmeters sometimes required a minor shake or tap to the flowtubes to start their oscillation!↩︎
693. If you consider each tube as a container with a fixed volume capacity, a change in fluid density (e.g. pounds per cubic foot) must result in a change in mass for each tube.↩︎
694. An important caveat is that the RTD sensing tube temperature in a Coriolis flowmeter really senses the tubes’ outside skin temperature, which may not be exactly the same as the temperature of the fluid inside the tube. If the ambient temperature near the flowmeter differs substantially from the fluid’s temperature, the tube skin temperature reading may not be accurate enough for the flowmeter to double as a fluid temperature transmitter.↩︎
695. Significant technological progress has been made on mixed-phase Coriolis flow measurement, to the point where this may no longer be a serious consideration in the future.↩︎
696. For example, the specific heat of water is 1.00 kcal / kg $$\cdot$$ $$^{o}$$C, meaning that the addition of 1000 calories of heat energy is required to raise the temperature of 1 kilogram of water by 1 degree Celsius, or that we must remove 1000 calories of heat energy to cool that same quantity of water by 1 degree Celsius. Ethyl alcohol, by contrast, has a specific heat value of only 0.58 kcal / kg $$\cdot$$ $$^{o}$$C, meaning it is almost twice as easy to warm up or cool down as water (little more than half the energy required to heat or cool water needs to be transferred to heat or cool the same mass quantity of ethyl alcohol by the same amount of temperature).↩︎
697. In a laminar flowstream, individual molecules do not cross paths, but rather travel in parallel lines. This means only those molecules traveling near the wall of a tube will be exposed to the temperature of the wall. The lack of “mixing” in a laminar flowstream means molecules traveling in the inner portions of the stream never contact the tube wall, and therefore never serve to transfer heat directly to or from the wall. At best, those inner-path molecules transfer heat by conduction with adjacent molecules which is a less efficient transfer mechanism than convection.↩︎
698. The proper mass flow rate value corresponding to these two measurements would be 45.0 lb/h.↩︎
699. While this may seem like a very informal definition of differential, it is actually rooted in a field of mathematics called nonstandard analysis, and closely compares with the conceptual notions envisioned by calculus’ founders.↩︎
700. To be precise, the equation describing the function of this analog differentiator circuit is: $$V_{out} = -RC {dV_{in} \over dt}$$. The negative sign is an artifact of the circuit design – being essentially an inverting amplifier with negative gain – and not an essential element of the math.↩︎
701. This is not always the case, as primary elements are often found on throttled process lines. In such cases where a control valve normally throttles the flow rate, any energy dissipated by the orifice plate is simply less energy that the valve would otherwise be required to dissipate. Therefore, the presence or absence of an orifice plate has no net impact on energy dissipation when used on a process flow throttled by a control valve, and therefore does not affect cost over time due to energy loss.↩︎
702. Truth be told, free hydrogen ions are extremely rare in an aqueous solution. You are far more likely to find them bound to normal water molecules to form positive hydronium ions (H$$_{3}$$O$$^{+}$$). For simplicity’s sake, though, professional literature often refers to these positive ions as “hydrogen” ions and even represent them symbolically as H$$^{+}$$.↩︎
703. Ionic compounds are formed when oppositely charged atomic ions bind together by mutual attraction. The distinguishing characteristic of an ionic compound is that it is a conductor of electricity in its pure, liquid state. That is, it readily separates into anions and cations all by itself. Even in its solid form, an ionic compound is already ionized, with its constituent atoms held together by an imbalance of electric charge. Being in a liquid state simply gives those atoms the physical mobility needed to dissociate.↩︎
704. Covalent compounds are formed when electrically neutral atoms bind together by the mutual sharing of valence electrons. Such compounds are not good conductors of electricity in their pure, liquid states.↩︎
705. It should be noted that the relationship between conductivity and electrolyte concentration in a solution is typically non-linear. Not only does the electrical conductivity of a solution not follow a set proportion to concentration, but even the slope of the relationship may change from positive to negative over a wide range of concentrations. This fact makes conductivity measurement in liquid solutions useful for concentration analysis only over limited ranges.↩︎
706. The use of alternating current forces the ions to switch directions of travel many times per second, thus reducing the chance they have of bonding to the metal electrodes.↩︎
707. There will be very little if any fouling on these electrodes anyway because they carry no current, and thus provide no reason for ions to migrate toward them.↩︎
708. Toroidal conductivity sensors may suffer calibration errors if the fouling is so bad that the hole becomes choked off with sludge, but this is an extreme condition. These sensors are far more tolerant to fouling than any form of contact-type (electrode) conductivity cell.↩︎
709. Note that this is opposite the behavior of a direct-contact conductivity cell, which produces less voltage as the liquid becomes more conductive.↩︎
710. Truth be told, the color of a hydrangea blossom is only indirectly determined by soil pH. Soil pH affects the plant’s uptake of aluminum, which is the direct cause of color change. Interestingly, the pH-color relationship of a hydrangea plant is exactly opposite that of common laboratory litmus paper: red litmus paper indicates an acidic solution while blue litmus paper indicates an alkaline solution; whereas red hydrangea blossoms indicate alkaline soil while blue (or violet) hydrangea blossoms indicate acidic soil.↩︎
711. Flavin, classified as an anthocyanin, is the pigment in red cabbage responsible for the pH-indicating behavior. This same pigment also changes color according to soil pH while the cabbage plant is growing, much like a hydrangea. Unlike hydrangeas, the coloring of a red cabbage is more akin to litmus paper, with red indicating acidic soil.↩︎
712. Of course, ions possess no agency and therefore cannot literally “attempt” anything. What is happening here is the normal process of diffusion whereby the random motions of individual molecules tends to evenly distribute those molecules throughout a space. If a membrane divides two solutions of differing ionic concentration, ions from the more concentrated region will, over time, migrate to the region of lower concentration until the two concentrations are equal to each other. Truth be told, ions are continually migrating in both directions through the porous membrane at all times, but the rate of migration from the high concentration to the low concentration solutions is greater than the other direction simply because there are more ions present to migrate that way. After the two solutions have become equal in ionic concentration, the random migration still proceeds in both directions, but now the rates in either direction are equal and therefore there is zero net migration.↩︎
713. This is apparent from a mathematical perspective by examination of the Nernst equation: if the concentrations are equal (i.e. $$C_1 = C_2$$), then the ratio of $$C_1 \over C_2$$ will be equal to 1. Since the logarithm of 1 is zero, this predicts zero voltage generated across the membrane. From a chemical perspective, this corresponds to the condition where random ion migration through the porous membrane is equal in both directions. In this condition, the Nernst potentials generated by the randomly-migrating ions are equal in magnitude and opposite in direction (polarity), and therefore the membrane generates zero overall voltage.↩︎
714. It is a proven fact that sodium ions in relatively high concentration (compared to hydrogen ions) will also cause a Nernst potential across the glass of a pH electrode, as will certain other ion species such as potassium, lithium, and silver. This effect is commonly referred to as sodium error, and it is usually only seen at high pH values where the hydrogen ion concentration is extremely low. Like any other analytical technology, pH measurement is subject to “interference” from species unrelated to the substance of interest.↩︎
715. Remember that voltage is always measured between two points!↩︎
716. Hydrogen ion concentration being practically the same as hydrogen ion activity for dilute solutions. In highly concentrated solutions, hydrogen ion concentration may exceed hydrogen ion activity because the ions may begin to interact with each other and with other ion species rather than act as independent entities. The ratio of activity to concentration is called the activity coefficient of the ion in that solution.↩︎
717. The mathematical sign of probe voltage is arbitrary. It depends entirely on whether we consider the reference (buffer) solution’s hydrogen ion activity to be $$C_1$$ or $$C_2$$ in the equation. Which ever way we choose to calculate this voltage, though, the polarity will be opposite for acidic pH values as compared to alkaline pH values↩︎
718. Glass is a very good insulator of electricity. With a thin layer of glass being an essential part of the sensor circuit, the typical impedance of that circuit will lie in the range of hundreds of mega-ohms!↩︎
719. Operational amplifier circuits with field-effect transistor inputs may easily achieve input impedances in the tera-ohm range ($$1 \times 10^{12} \> \Omega$$).↩︎
720. With all modern pH instruments being digital in design, this calibration process usually entails pressing a pushbutton on the faceplate of the instrument to “tell” it when the probe has stabilized in the buffer solution. Clean and healthy pH probes typically stabilize to the buffer solution’s pH value within 30 seconds of immersion.↩︎
721. A more obvious test would be to directly measure the pH probe assembly’s voltage while immersed in 7.0 pH buffer solution. However, most portable voltmeters lack sufficient input impedance to perform this measurement, and so it is easier to calibrate the pH instrument in 7.0 pH buffer and then check its zero-voltage pH value to see where the isopotential point is at.↩︎
722. This effect is particularly striking when paper-strip chromatography is used to analyze the composition of ink. It is really quite amazing to see how many different colors are contained in plain “black” ink!↩︎
723. Gas chromatographs are commonly used for industrial analysis on liquid sample streams, by using a heater at the inlet of the chromatograph to vaporize the liquid sample prior to analysis. In such applications the column and sample valve(s) must be maintained in a heated condition as well so that the sample does not condense back into liquid form during the analysis.↩︎
724. Stationary phase material used in many hydrocarbon GC’s looks much like oily sand.↩︎
725. This is not to say that one cannot use a selective sensor as a chromatograph detector. It’s just that selectivity between different process compounds is not a necessary requirement for a chromatograph detector.↩︎
726. It should be noted that the choice of carrier for any chromatography system, be it manual or automated, is not completely arbitrary. There are some limitations to which carrier fluids may be used, depending on the expected composition of the sample (e.g. you would not want to use a carrier that reacted chemically with any species in the sample so as to alter the sample’s composition!). However, the range of choices afforded to the person designing the chromatograph system lends a unique flexibility to this type of chemical analysis.↩︎
727. A “solute” being one of the sample species dissolved within the carrier gas↩︎
728. In fact, FID sensors are sometimes referred to as carbon counters, since their response is almost directly proportional to the number of carbon atoms passing through the flame.↩︎
729. See section [thermal mass flowmeter specific heat] beginning on page . The greater the specific heat value of a gas, the more heat energy it can carry away from a hot object through convection, all other factors being equal.↩︎
730. It is not uncommon to find chromatographs used in processes to measure the concentration of a single chemical species, even though the device is capable of measuring the concentrations of multiple species within that process stream. In those cases, chromatography is (or was at the time of installation) the most practical analytical technique to use for quantitative detection of that substance. Why else use an inherently multi-variable analyzer when you could have used a single-variable technology that was simpler? By analogy, it is possible to use a Coriolis flowmeter to measure nothing but fluid density, even though such a device is fully capable of measuring fluid density and mass flow rate and temperature.↩︎
731. Additionally, the data collected by this GC is used to improve the flow-measurement accuracy of their AGA3 honed-run orifice meters. By measuring the concentrations of different compounds in the natural gas, the GC tabulates an average density for the gas, which is then sent to the flow computer to achieve better flow-measuring accuracy than would be possible without this compensating measurement.↩︎
732. Laboratory chromatographs may take even longer to complete their analyses.↩︎
733. Whereas most liquids decrease in viscosity as temperature rises, gases increase in viscosity as they get hotter. In other words, a gas becomes “thicker” as it heats up, thus slowing down its progress through a chromatograph column. Since the flow regime through a chromatograph column is most definitely laminar and not turbulent, viscosity has a great effect on flow rate.↩︎
734. Since the degree of separation between species is roughly proportional to the species’ retention time, the slowest species (4, 5, and 6 in this case) do not need to go through two columns to be adequately separated. It is only the fastest species needing more retention time (through an additional column) to separate adequately from one another.↩︎
735. In physics, a “blackbody” is a perfect emitter of electromagnetic radiation (photons) as it is heated. The intensity of light emitted as a function of wavelength ($$\lambda$$) and temperature ($$T$$) is $$I = {{2 \pi h c^2 \lambda^{-5}} \over {e^{hc / \lambda k T} - 1}}$$.↩︎
736. Molecules typically have much more complex interactions with light than individual atoms. The optical signatures of atoms are principally defined by electron states, light absorbed when electrons are boosted into higher-energy states and light emitted when electrons fall into lower-energy states. Molecules, on the other hand, can absorb and release energy in the inter-atomic bonds as well as in the states of individual electrons. Since molecules have more degrees of freedom with respect to optical interactions, their optical signatures tend to be much broader. This is why molecular absorption spectra consist of broad bands of wavelengths (each band comprised of many discrete lines), while atomic absorption spectra consist of relatively few lines.↩︎
737. These photons have wavelengths longer than 700 nm, and so have energy values too low to boost electrons into higher levels. However, the attractive bonds between atoms in a molecule may be subject to the energy of these infrared photons, and so may dissipate the photons’ energy and thereby attenuate a beam of infrared light.↩︎
738. In an absorption spectrum diagram, a non-absorbing substance results in a straight line at the 100% mark. Compounds absorbing specific wavelengths of light will produce low “dips” in the graph at those wavelength values, showing how less light (of those wavelengths) is able to pass un-absorbed through the sample to be detected at the other end. By contrast emission spectra are usually plotted with the characteristic wavelengths shown as high “peaks” in a graph that normally resides at 0%.↩︎
739. Wavenumber, being the reciprocal of wavelengths in centimeters, may be thought of in terms of frequency: the greater the wavenumber, the higher the frequency of the light wave (the smaller its wavelength). In order to convert wavenumber into wavelength (in microns), reciprocate the wavenumber value and multiply by $$10^4$$. For example, a wavenumber of 2000 cm$$^{-1}$$ is equivalent to a wavelength of 5 microns. In order to convert wavenumber into wavelength (in nanometers), reciprocate the wavenumber value and multiply by $$10^7$$. For example, a wavenumber of 4000 cm$$^{-1}$$ is equivalent to a wavelength of 2500 nm.↩︎
740. One such analyzer I saw in industry had a path length of a quarter-mile (1320 feet), to better measure extremely low concentrations of a gas! The gas in question was ambient air inside of a large shelter housing a chemical process. The analyzer was mounted on one side of the shelter, aiming a beam of laser light all the way to the opposite wall of the shelter 660 feet away, where a reflector was mounted. The laser beam’s path length was therefore twice the length of the shelter, or 1320 feet.↩︎
741. You may use an old compact disk (CD) as a simple reflection and refraction grating. Holding the CD with the reflective (shiny) surface angled toward you, light reflected from a bright source such as a lamp (avoid using the sun, as you can easily damage your eyes viewing reflected sunlight!) will split into its constituent colors by reflection off the CD’s surface. Lines in the plastic of the CD perform the dispersion of wavelengths. You will likely have to experiment with the angle you hold the CD, pointing it more perpendicular to the lamp’s direction and more angled to your eyes, before you see the image of the lamp “smeared” as a colorful spectrum. To use the CD as a diffraction grating, you will have to carefully peel the reflective aluminum foil off the front side of the disk. Use a sharp tool to scribe the disk’s front surface from center to outer edge (tracing a radius line), then use sticky tape to carefully peel the scribed foil off the plastic disk. When you are finished removing all the foil, you may look through the transparent plastic and see spectra from light sources on the other side. Once again, experimentation is in order to find the optimum viewing angle, and be sure to avoid looking at the sun this way!↩︎
742. One might wonder why the sun does not produce a line-type emission spectrum of all its constituent elements, instead of the continuous spectrum it does. The answer to this question is that emission spectra are produced only when the “excited” atoms are in relative isolation from each other, such as is the case in a low-pressure gas. In solids, liquids, and high-pressure gases, the close proximity of the atoms to each other creates many different opportunities for electrons to “jump” to lower energy levels. With all those different alternatives, the electrons emit a whole range of different wavelength photons as they seek lower energy levels, not just the few wavelengths associated with the limited energy levels offered by an isolated atom. We see the same effect on Earth when we heat metals: the electrons in a solid or liquid metal sample have so many different optional energy levels to “fall” to, they end up emitting a broad spectrum of wavelengths instead of just a few. In this way, a molten metal is a good approximation of a blackbody photon source.↩︎
743. These details taken from pages 93-94 of Instrumentation and Control in the German Chemical Industry, a fascinating book detailing the state-of-the-art in process instrumentation in German chemical manufacturing facilities following the war.↩︎
744. There will still be a span shift resulting from degradation of the light source, but this is inevitable. At least with this design, the zero-shift problem is eliminated.↩︎
745. In analytical literature, you may read of some detectors having a catholic response. This is just a fancy way of saying the detector responds to a wide variety of things. The thermopiles shown in this NDIR instrument could be considered to have a catholic response to incident light. The word “catholic” in this context simply means “universal,” referring to the detector’s non-selectivity. Do not be dismayed if you encounter arcane terms such as “catholic” as you learn more about analytical instruments – the author is probably just trying to impress you with his or her vocabulary!↩︎
746. Recall that the absorption of light by an atom or a molecule causes the photon’s energy to dissipate. An absorbed photon’s energy is transferred to the molecule, often resulting in increased motion (kinetic energy), which as we know is the very definition of temperature. Increased temperature in a gas of confined volume and fixed molecular quantity must result in an increased pressure according to the Ideal Gas Law ($$PV = nRT$$).↩︎
747. The flow sensor is similar in design to thermal mass flow sensors discussed in the flow measurement chapter. See section 22.7.2 beginning on page for more information.↩︎
748. And hopefully after all this filtering we still have some (unfiltered) wavelengths unique to the gas of interest we seek to measure. Otherwise, there will be no wavelengths of light remaining to be absorbed by our gas of interest inside the sample cell, which means we will have no means of spectroscopically measuring its concentration!↩︎
749. Real GFC analyzers also have a chopper wheel preceding the filter wheel to create a pulsating light beam. This causes the detector signal to pulsate as well, allowing the analyzer to electronically filter out sensor “drift” just as in the dual-beam NDIR analyzer design. The chopper wheel has been eliminated from this diagram (and from the discussion) for simplicity. If it were not for the chopper wheel, the GFC analyzer would be prone to measurement errors caused by detector drift.↩︎
750. As previously mentioned, real GFC analyzers have a chopper wheel preceding the filter wheel to make the light beam pulse in addition to changing its spectral composition. This chopper wheel generates multiple light pulses per rotation of the filter wheel. Thus, the signal output by the detector is actually an amplitude-modulated waveform, with the “carrier” frequency being the chopper wheel’s pulsing and the slower “modulating” frequency being the filter wheel’s rotation cycle. Hopefully by now you see why I decided to omit the chopper wheel “for simplicity.”↩︎
751. The term “laser” is actually an acronym, standing for Light Amplification by Stimulated Emission of Radiation.↩︎
752. It is this coherence of laser light that enables the beam to remain highly focused, unlike light from other sources which tends to spread.↩︎
753. Such mirrors are partially silvered to let some light through while reflecting the rest of the light.↩︎
754. A term often applied to this phenomenon of a QCL’s frequency is chirp. A “chirp” refers to a burst of signal frequencies either increasing or decreasing along some range.↩︎
755. Blood, urine, semen, and various bodily proteins are known to fluoresce in the visible spectrum, making fluorescence a useful tool for crime-scene investigations. It’s also useful when purchasing a new house, to check for pet droppings in the carpet. Such analysis is not for the faint of heart.↩︎
756. There is another way that light from the UV lamp could conceivably “take a corner” and reach the detector, and that is if the gas sample happens to contain dust or condensation droplets that would scatter the light. However, since gas samples are always dried and filtered prior to entering the sample chamber, this possibility is eliminated.↩︎
757. If one were to install an optical filter in front of the photomultiplier tube designed to block fluorescent light emitted by hydrocarbon molecules, this filter would also block the light emitted by fluorescing SO$$_{2}$$ molecules thereby defeating the very purpose of the analyzer: measuring SO$$_{2}$$ concentration by optical fluorescence!↩︎
758. Combustion is primarily a reaction between carbon and/or hydrogen atoms in fuel, and oxygen atoms in air. However, about 78% of the air (by volume) is nitrogen, and only about 20.9% is oxygen, which means a lot of nitrogen gets pulled in with the oxygen during combustion. Some of these nitrogen atoms combine with oxygen atoms under the high temperature of combustion to form various oxides of nitrogen.↩︎
759. The measures used to mitigate nitric oxide emissions are the same measures used to mitigate the other oxides of nitrogen: reduce combustion temperature, and/or reduce the NO$$_{x}$$ compounds to elemental nitrogen by mixing the combustion exhaust gases with ammonia (NH$$_{3}$$) in the presence of a catalyst. So here we have a case where we really don’t care to distinguish NO from NO$$_{x}$$: we want to measure it all.↩︎
760. This particular interference compound is especially problematic if we are using the analyzer to control the NO$$_{x}$$ concentration in the exhaust of a combustion process, and the manipulated variable for the NO$$_{x}$$ control loop is pure ammonia injected into the exhaust. Un-reacted ammonia (commonly called ammonia slip in the industry) sampled by the analyzer will be falsely interpreted as NO$$_{x}$$, rendering the measurement meaningless, and therefore making control virtually impossible.↩︎
761. In-situ pH probes are manufactured for high-pressure applications, but they suffer short lifespans (due to the accelerated erosion of the measurement glass) and decreased sensitivity (due to the extra thickness of the measurement glass) and are substantially more expensive than pH probes designed for atmospheric pressure conditions.↩︎
762. Pressure control is important in gas analysis because changes in sample gas pressure will result in different gas densities, thereby directly affecting how many molecules of the gas of interest will be present and therefore detectable inside the analyzer.↩︎
763. Temperature control is important for similar reasons: the gas species of interest may become more reactive as temperature changes, thereby resulting in a stronger indication even when concentration remains constant.↩︎
764. It is important to thoroughly filter the gas input to an analyzer so that contaminants do not foul the sensing element(s). This is rather obvious in the case of optical analyzers, where the light to be analyzed must pass through a transparent window of some kind, and that window must be kept clean of dust, condensation, and any other substances that could interfere with the transmission of light.↩︎
765. Some types of plastic sample tubes are permeable to gases, and so represent potential contamination points when the concentrations of interest are in the range of parts per million (ppm) or parts per billion (ppb). In such critical applications, only metal sample tubes (stainless steel, typically) are appropriate.↩︎
766. The “other” gas in the mixture besides the gas or gases of interest.↩︎
767. Interestingly, there is a documented case of an NDIR “Luft” analyzer being used as a safety monitor for carbon monoxide, ranged 0 to 0.1% (0-1000 ppm), at one of I.G. Farbenindustrie’s chemical plants in Germany during the 1940’s. This was definitely not a portable analyzer, but rather stationary-mounted in a process unit where high concentrations of carbon monoxide gas existed in the pipes and reaction vessels. The relatively fast response and high selectivity of the NDIR technology made it an ideal match for the application, considering the other (more primitive) methods of carbon monoxide gas detection which could be “fooled” by hydrogen, methane, and other gases.↩︎
768. Some water treatment facilities use powerful ultraviolet lamps to disinfect water without the use of chemicals. Some potable (drinking) water treatment plants use ozone gas (O$$_{3}$$) as a disinfectant, which is generated on-site from atmospheric oxygen. A disadvantage to both chlorine-free approaches for drinking water is that neither one provides lasting disinfection throughout the distribution and storage system to the same degree that chlorine does.↩︎
769. The “spectrum analyzer” display often seen on high-quality audio reproduction equipment such as stereo equalizers and amplifiers is an example of the Fourier Transform applied to music. This exact same technology may be applied to the analysis of a machine’s vibration to indicate sources of vibration, since different components of a machine tend to generate vibratory waves of differing frequencies.↩︎
770. This rule makes intuitive sense as well: if a sine or cosine wave increases frequency while maintaining a constant peak-to-peak amplitude, the rate of its rise and fall must increase as well, since the higher frequency represents less time (shorter period) for the wave to travel the same amplitude. Since the derivative is the rate of change of the waveform, this means the derivative of a waveform must increase with that waveform’s frequency.↩︎
771. Recall that the derivative of the sinusoidal function $$\sin \omega t$$ is equal to $$\omega \cos \omega t$$, and that the second derivative of $$\sin \omega t$$ is equal to $$-\omega^2 \sin \omega t$$. With each differentiation, the constant of angular velocity ($$\omega$$) is applied as a multiplier to the entire function.↩︎
772. There is an additional term missing in this Fourier series, and that is the “DC” or “bias” term $$A_0$$. Many non-sinusoidal waveforms having peak values centered about zero on a graph or oscilloscope display actually have average values that are non-zero, and the $$A_0$$ term accounts for this. However, this is usually not relevant in discussions of machine vibration, which is why I have opted to present the simplified Fourier series here.↩︎
773. We have no way of knowing this from the Fourier spectrum plot, since that only shows us amplitude (height) and frequency (position on the x-axis).↩︎
774. Machines with reciprocating components, such as pistons, cam followers, poppet valves, and such are notorious for generating vibration signatures which are anything but sinusoidal even under normal operating circumstances!↩︎
775. From the perspective of measurement, it would be ideal to affix a velocimeter or accelerometer sensor directly to the rotating element of the machine, but this leads to the problem of electrically connecting the (now rotating!) sensor to stationary analysis equipment. Unless the velocity or acceleration sensor is wireless, the only practical mounting location is on the stationary frame of the machine.↩︎
776. Single-line electrical diagrams are similar to Process Flow Diagrams (PFDs) used in industrial instrumentation, concentrating on the process flows more than the monitoring and control equipment. It is important to note that single-line diagrams are not the same as electrical schematics: in a single-line diagram, each line represents a set of power conductors (typically three or four conductors if the power system is 3-phase, which most large-scale AC power systems are). For this reason, we must interpret a single-line diagram much more like a pipeline system than an electrical circuit, in that the electrical power flows in one direction at any given time through these single lines, never making a complete loop as is the case in real life and in an electrical schematic diagram.↩︎
777. In the electrical power industry, the color red universally represents an energized (closed breaker) condition while the color green represents a de-energized (open breaker) condition.↩︎
778. For example, a potential transformer (PT) constructed to step 13.8 kilovolts down to 120 volts for safe monitoring of that line voltage must have a turns ratio equivalent to 13800:120, or 115:1.↩︎
779. For example, a current transformer (CT) constructed to step 400 amps down to 5 amps for safe monitoring of that line current must have a turns ratio equivalent to 400:5, or 80:1. This means the single “turn” of the power conductor through the center of the CT is flanked by exactly 80 turns of wire wrapped around the toroidal iron core of the CT.↩︎
780. To review, the power factor of an AC circuit is the cosine of the phase angle between total (source) voltage and total (source) current. Power factor represents how much of the line current goes toward doing useful work. Reactive loads do not transform electrical energy into work, but rather alternately store and release electrical energy. Current at a purely reactive load, therefore, is not as useful as current at a purely resistive load. However, reactive current still “occupies” ampacity on a power line, and so the existence of a low power factor means the system is not delivering as much power as it could.↩︎
781. This legacy technology is called Power Line Carrier, or PLC which is unfortunately confusing because it has nothing to do with Programmable Logic Controllers (also abbreviated PLC). The concept is not unlike the HART analog-digital hybrid system used to communicate digital information to process transmitters over 4-20 mA analog signal lines, except in the case of power-line carrier systems the signal frequencies are much higher and the challenge of safely coupling these signals to high-voltage power line conductors is much greater.↩︎
782. To review, impedance is the sum total opposition to electric current in a circuit, consisting of resistance and/or reactance. Impedance is measured in ohms, and so a distance relay (21) is set to “pick up” a fault in a power line if the measured impedance of that line falls below a threshold value based on the length of that line.↩︎
783. The difference between an instantaneous overcurrent (50) function and a time-overcurrent (51) function is the amount of time delay between the detection of an overcurrent event and the relay’s command to trip the circuit breaker. Any detected level of line current in excess of the instantaneous overcurrent “pickup” threshold will immediately issue a trip command, while the level of line current in excess of the time-overcurrent “pickup” threshold will determine the amount of time delay before the issuance of a trip command.↩︎
784. Directional relays are useful for protecting electrical generators susceptible to acting as a motor and drawing power from the network rather than delivering power to the network. Generators driven by wind turbines are an example of this class: even a relatively small amount of power flowing in reverse direction (from the grid to the generator, “motoring” the generator) is undesirable, and so it is wise to isolate a “motoring” generator based on a much lower current than what would be considered unacceptable in the generating direction. A regular 50 or 51 overcurrent relay cannot discriminate between the two directions of power flow, but a 67 overcurrent relay can.↩︎
785. These mechanisms are similar in principle to the trigger, spring, and hammer of a firearm: the mechanical energy necessary to ignite the primer of a cartridge comes from a spring that has been “charged” either by manual operation of by the action of the gun during the last firing cycle. This spring energy is released by a sensitive sear mechanism driven by the finger-operated trigger, requiring very little energy to operate. In a similar manner, the operating springs of large circuit breakers are “charged” by an electric motor whenever a relaxed state is detected. That mechanical energy is then released by a relatively sensitive mechanism driven by an electric solenoid, allowing a small electrical signal to rapidly operate the large contact mechanism.↩︎
786. The sole purpose of transforming voltage and current levels in a power grid is to minimize power losses due to the electrical resistance of the conductors. Recall from basic DC electrical theory that the amount of power dissipated by a current-carrying resistance is $$P = I^2 R$$. This means doubling the current through a resistive conductor will increase that conductor’s power dissipation four-fold, all other factors being equal. Metal wire is expensive, especially when thousands of miles of it must be run to form a power grid. In the interest of reducing this expense, transformers are used to maintain long-distance power line voltages high and currents low, permitting the use of smaller-gauge conductors to carry that current.↩︎
787. Thomas Edison’s original DC-based power grid was limited in radius to the size of a city, because all components operated at one voltage level (about 110 VDC). Large copper busbars served as distribution lines from coal-fired generating stations to points throughout the city, the sheer mass of these copper bars necessitating their installation in underground trenches rather than as overhead lines. Voltage losses from the generating station to points at the furthest reaches of the DC grid were significant, meaning customers at the “end of the line” had to tolerate dimmer lamps than customers located nearer the generating station.↩︎
788. The source for this historical illustration is Cassier’s Magazine, which was an engineering periodical published in the late 1800’s and early 1900’s out of London, England. The Smithsonian Institute maintains online archives of Cassier’s spanning many years, and it is a treasure-trove for those interested in the history of mechanical, electrical, chemical, and civil engineering.↩︎
789. Other options may exist for some grids. For example, large-scale industrial customers may be requested to curtail their power consumption at certain times in order to offset a deficit in supply. An example of this might be an aluminum smelter (which uses hundreds of megawatts of electricity to reduce alumina powder to molten aluminum metal) operating as a sheddable load while the same grid employs a nuclear fission power plant as one of its sources. If the nuclear generator’s reactor happens to “scram” (shut down for any reason), that reactor’s power output will drop off the grid immediately, which may constitute hundreds of megawatts of lost generation. In such an event, the grid dispatch system may issue a “load shed” command to the aluminum smelter to drop a substantial portion of its consumption, as it may not be practical to immediately bring that much extra power on-line from some other source.↩︎
790. This phenomenon is just one more application of the Law of Energy Conservation, which states energy cannot be created or destroyed, but must be accounted for in all processes. Every joule of energy delivered to the load in this example circuit must be supplied by the generator, which in turn draws (at least) one joule of energy from the prime mover (e.g. engine, turbine). Since the power “grid” shown in this diagram has no means of storing energy for future use, the load’s demand must be instantaneously met by the generator, and in turn by the prime mover. Thus, sudden changes in load resistance result in instantaneous changes in power drawn from the prime mover, all in accordance with the Law of Energy Conservation.↩︎
791. The standard frequency for a power grid is typically 50 Hz or 60 Hz, depending on which part of the world you are in. North American power grids typically operate at 60 Hz, while 50 Hz is more common in Europe.↩︎
792. A common analogy for this is two children swinging on adjacent swings in a playground. Imagine the distance between the children being the amount of voltage difference between the two generators at any given point in time, with the amplitude of each child’s swing representing the peak voltage of each generator and the pace of each child’s oscillation being the frequency of each generator. When two children are swinging in perfect synchronization, the distance between them remains minimal at all times. When they swing 180$$^{o}$$ out of phase each other, the distance between them varies from minimal to maximal at a pace equal to the difference in their individual swinging rates.↩︎
793. This “coupling” is not perfectly rigid, but does allow for some degree of phase difference between the generator and the grid. A more accurate analogy would be to say the generators act as if their shafts were linked by a flexible coupling.↩︎
794. It should be noted that a grid-connected AC generator can in fact be over-sped with sufficient mechanical power input, but only if it “slips a pole” and falls out of synchronization as a result. Such an event can be catastrophically to the offending generator unless it is immediately disconnected from the grid to avoid damage from overcurrent.↩︎
795. In this example, three current transformers, or CTs, are shown stepping down the bus line current to levels safely measured by panel-mounted ammeters. Current transformers typically step down line current to a nominal value of 5 amps to drive meters, relays, and other monitoring instruments.↩︎
796. In the United States, the term “low voltage” with reference to power circuits usually refers to circuits of 600 volt or less potential.↩︎
797. For an equitable size comparison between the two different types of circuit breaker, consider the fact that the insulators on this gas-quenched circuit breaker are approximately the same physical height as the insulators on the previously-shown oil-tank circuit breaker.↩︎
798. While pure SF$$_{6}$$ gas is benign, it should be noted that one of the potential chemical byproducts of arcing in an SF$$_{6}$$-quenched circuit breaker is hydrofluoric acid (HF) which is extremely toxic. HF is formed when SF$$_{6}$$ gas arcs in the presence of water vapor (H$$_{2}$$O), the latter being nearly impossible to completely eliminate from the interior chambers of the circuit breaker. This means any maintenance work on an SF$$_{6}$$-quenched circuit breaker must take this chemical hazard into consideration.↩︎
799. This particular circuit breaker, like most live-tank circuit breakers, interrupts just one phase (i.e. one “pole”) of a three-phase bus. Portions of the second and third live-tank SF$$_{6}$$ breakers comprising the full three-phase breaker array for this bus may be seen near the left-hand edge of the photograph.↩︎
800. A “toroid” is shaped like a donut: a circular object with a hole through the center.↩︎
801. This raises an interesting possibility: if the power conductor were to be wrapped around the toroidal core of the CT so that it passes through the center twice instead of once, the current step-down ratio will be cut in half. For example, a 100:5 CT with the power conductor wrapped around so it passes through the center twice will exhibit an actual current ratio of only 50:5. If wrapped so that it passed through the CT’s center three times, the ratio would be reduced to 33.33:5. This useful “trick” may be used in applications where a lesser CT ratio cannot be found, and one must make do with whatever CT happens to be available. If you choose to do this, however, beware that the current-measuring capacity of the CT will be correspondingly reduced. Each extra turn of the power conductor adds to the magnetic flux experienced by the CT’s core for any given amount of line current, making it possible to magnetically saturate the core if the line current exceeds the reduced value (e.g. 50 amps for the home-made 50:5 CT where the line passes twice through the center of a 100:5 CT).↩︎
802. High-voltage devices situate their connection terminals at the ends of long insulators, to provide a large air gap between the conductors and the grounded metal chassis of the device. The point at which the long insulator (with a conductor inside of it) penetrates the housing of the device is called the bushing.↩︎
803. The battery-and-switch test circuit shown here is not just hypothetical, but may actually be used to test the polarity of an unmarked transformer. Simply connect a DC voltmeter to the secondary winding while pressing and releasing the pushbutton switch: the voltmeter’s polarity indicated while the button is pressed will indicate the relative phasing of the two windings. Note that the voltmeter’s polarity will reverse when the pushbutton switch is released and the magnetic field collapses in the transformer coil, so be sure to pay attention to the voltmeter’s indication only during the time of switch closure! This is an application where an analog voltmeter may actually be superior to a digital voltmeter, since the instantaneous movement of a mechanical needle (pointer) is easier to visually interpret than the sign of a digital number display.↩︎
804. The amount of magnetic force $$H$$ applied to the transformer’s core is a direct function of winding current. If the DC test source is capable of pushing significant amounts of current through the transformer, it may leave the core in a partially magnetized state which will then affect its performance when powered by AC. A relatively “weak” source such as a 9 volt “transistor” battery helps ensure this will not happen as a result of the polarity test.↩︎
805. The IEEE standard C57.12.00-2010 (“IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers”) states that single-phase transformers having power ratings of 200 kVA and below and high-voltage winding ratings of 8.66 kV and below must have additive polarity, and that all other types of power transformers must have subtractive polarity.↩︎
806. This particular transformer happens to be a tap-changing unit, designed to provide a number of ratio increments useful for adjusting voltages in a power distribution system. Its typical primary voltage is 115 kV and its typical secondary voltage is 12.5 kV. If the secondary voltage happens to sag due to a heavy-load conditions, the transformer’s tap setting may be manually adjusted to output a slightly greater secondary voltage (i.e. a lesser step-down ratio). This is how electric power distribution utilities manage to keep voltages to customers relatively stable despite ongoing changes in load conditions.↩︎
807. The hazards of an open-circuited CT can be spectacular. I have spoken with power electricians who have personally witnessed huge arcs develop across the opened terminals in a CT circuit! This safety tip is not one to be lightly regarded.↩︎
808. For example, in an application where the maximum fault current is expected to be 40,000 amps, we would choose a CT with a ratio of at least 2000:5 to drive the protective relay, because 40,000 amps is twenty times this CT’s primary current rating of 2000 amps. We could also select a CT with a larger ratio such as 3000:5. The point is to have the CT be able to faithfully transform any reasonable fault current into a proportionately lower value for the protective relay(s) to sense.↩︎
809. An illustrative example to consider is the venerable Westinghouse model CO-11 overcurrent relay, exhibiting a burden of 1.07 volt-amps at a CT secondary current of 5 amps with a 5-amp tap setting. By contrast, an SEL-551 digital overcurrent relay exhibits only 0.16 volt-amps of burden at the same CT current of 5 amps: nearly seven times less burden than the electromechanical relay. The reason for this stark disparity in burden values is the design of each relay: the electromechanical relay demands power from the CT to spin an aluminum disk against the restraining forces of a spring and a drag magnet, while the electronic relay receives operating power from a separate source (station power) and only requires that the CT drive the input of an analog-to-digital converter (ADC) circuit.↩︎
810. Iron and iron alloys (“ferrous”) reach a point of maximum magnetization where all the magnetic “domains” in a sample are oriented in the same direction, leaving no more left to orient. Once a sample of ferrous material has thus “saturated”, it is of no further benefit to the establishment of a magnetic field. Increases in magnetic force will still produce additional lines of magnetic flux, but not at the rate experienced when the material was not saturated. In other words, a magnetically saturated inductor or transformer core essentially behaves like an air-core inductor or transformer for all additional current values beyond full saturation.↩︎
811. In the electric power industry this is commonly referred to as a “rat/sat” test.↩︎
812. If you think carefully about this, you realize that the number of turns of wire in either CT must be identical, because there is only one “turn” of wire passing through the center of either CT. In order to achieve a 2000:5 ratio, you must have 400 turns of wire wrapped around the toroidal ferrous core per the 1 “turn” of wire passing through the center of that core.↩︎
813. Calculations based on the specific resistance of copper at 20 $$^{o}$$C place 10 AWG wire at 0.9989 ohms per 1000 feet. $$R = {\rho l \over A}$$↩︎
814. What this means is that the relay will permit the circuit breaker to remain in its closed state indefinitely so long as the current is at or below 100% of its rated value. If the current ever exceeds the 100% limit, the protective relay begins to measure the length of time for the overcurrent event, commanding the circuit breaker to trip open after a certain amount of time inversely proportional to the degree of overcurrent. A 300% overcurrent condition, for example, will cause the circuit breaker to trip in a shorter amount of time than a 200% overcurrent condition.↩︎
815. In many legacy electromechanical protective relays, the trip contact is designed to latch in the closed position even after the event prompting the breaker trip has passed. A special “seal-in” circuit with its own coil and contact provides this latching action, the purpose of which is to ensure the relay will continuously command the breaker to trip for as long as it takes for the breaker to reach the tripped condition. Only the 52a auxiliary contact inside the circuit breaker can interrupt a latched trip circuit, and that will only happen when the breaker achieves a tripped state.↩︎
816. It should be noted that some microprocessor-based protective relays may operate on DC or AC power, as well as at power supply voltages other than 125 volts, in addition to the standard of 125 VDC.↩︎
817. In protective relay circuit diagrams, it is conventional to show relay coils as “zig-zag” symbols rather than as actual coils of wire as is customary in electronic schematics. Those familiar with “ladder” style electrical wiring diagrams may recognize this as the symbol for a solenoid coil. Once again, we see here the context-dependence of symbols and diagram types: a component type may have multiple symbols depending on which type of diagram it’s represented in, while a common symbol may have different meanings in different diagrams.↩︎
818. Note that this General Electric relay provides pickup tap settings well in excess of 5 amps, which is the nominal full-load rating of most current transformers. CTs rated for protective relay applications are fully capable of exceeding their normal full-load capacity for short time periods, which is a necessary feature due to the extreme nature of fault current conditions. It is not uncommon for fault currents in a power system to exceed full-load current conditions by a factor of 20!↩︎
819. Geometrically, at least three points are required to define the shape of any curve, just as two points are the minimum for defining a line. However, since the curvature of a relay’s timing function is fixed by the construction of its components and therefore not liable to drift over time, it is common within the protective relay field to check the curve at just two points to ensure the adjustments are correct. The drag magnet is the principal adjustment for the timing of an electromechanical 51 relay.↩︎
820. If you examine the induction disk from a 51 relay, you will note a that the disk’s radius is not constant, and that there is actually a “step” along the circumference of the disk where its radius transitions from minimum to maximum. The amount of disk material exposed to the stator coil’s magnetic field to generate operating torque therefore changes with rotation angle, providing a nonlinear function altering the shape of the relay’s timing curve.↩︎
821. In practice, perfect cancellation of currents is nearly impossible due to mismatched CTs and other imperfections, and so a small amount of current typically passes through the differential relay’s operating coil even under normal circumstances. The pickup value of this relay must be set such that this small amount of current does not unnecessarily trip the relay.↩︎
822. Transformers exhibit inrush current for reasons different than capacitors (reactance) or motors (counter-EMF). Residual magnetism in a transformer core from the last time it was energized biases that core toward saturation in one direction. If the applied power happens to match that direction, and have sufficient magnitude, the transformer core will saturate on power-up which results in abnormally high current for multiple cycles until the core’s magnetic domains normalize.↩︎
823. Restraint coils are sometimes labeled as “RC” and other times labeled as “R”. It should be noted that the principle of a “restraining element” within a protective relay is not unique to differential (87) relays. Other relay types, notably distance (21) relays, also employ restraint coils or other mechanisms to prevent the relay from tripping under specific circumstances.↩︎
824. It should be mentioned that an external fault generating currents high enough to saturate one or more of the CTs used in the differential protection system may cause the differential current system to falsely trip, due to saturation causing the affected CT(s) to no longer faithfully represent line current to the relay.↩︎
825. Power-line carrier, or PLC as it is known in the electric power industry, consists of data communications conveyed over the power line conductors themselves. This usually takes the form of a high-frequency AC signal (in the hundreds of kilohertz range) which is then modulated with the data of interest, similar to radio communication except that the RF signals travel along power lines rather than through empty space as electromagnetic waves. Power-line carrier systems are generally less reliable than fiber optic networks, because the presence of faults on the protected line may compromise the pilot communication.↩︎
826. Schweitzer Engineering Laboratories manufactures a differential current relay specifically designed for line protection called the model 387L. It is billed as a “zero settings” relay because there are no parameters to configure. Simply set up a pair of 387L’s (one at each end of the line), each one connected to matched CTs monitoring current through all three line conductors, and then link the relays together via a pair of fiber optic cables, and it’s ready to work.↩︎
827. There is a potential problem arising from CT secondaries in Wye when those CTs are measuring currents on the Wye-connected side of a power transformer, and that is the problem of zero sequence currents. A “zero sequence” set of currents is equivalent to in-phase currents flowing through all three lines of a three-phase power system, lacking the normal 120 degree phase shift from each other. The mathematical foundations of this concept are beyond the immediate scope of this section (for more information, refer to section 5.8.4 on “Symmetrical Components” beginning on page ), but suffice to say zero-sequence currents are found in certain fault conditions as well as circuits containing “triplen” harmonics (i.e. harmonic frequencies that are some multiple of 3$$\times$$ the fundamental, e.g. 180 Hz, 240 Hz, 540 Hz for a 60 Hz power system). Zero-sequence currents flow through the neutral conductor in a 4-wire Wye-connected system, but circle through the phase elements of a Delta-connected system. This means a Wye-Delta connected transformer where a fourth conductor attaches to the center of the Wye winding set may experience line currents on the Wye side that are not seen in the line conductors of the Delta side, and may therefore cause a differential current relay to operate. This is another reason why connecting CTs differently than the power transformer windings they sense (i.e. Delta-connected CTs on a power transformer’s Wye side) is a good idea: any zero-sequence currents within the power transformer’s Wye-connected winding will circulate harmlessly through the Delta-connected CT secondaries and never enter the 87 relay. For digitally compensated 87 relay installations where all CTs are Wye-connected, the relay must also be configured to mathematically cancel out any zero-sequence currents on the Wye-connected side of the power transformer.↩︎
828. Note the reversal of polarity for the voltage drop across each line resistance in the DC example diagram. A shunt resistor intentionally placed in series with the generator current could fulfill that same directional-sensing role.↩︎
829. In the electric power industry, the probability that protective relays and associated equipment will reliably interrupt power in the event of a fault is called dependability.↩︎
830. In the electric power industry, the probability that protective relays and associated equipment will not interrupt power unnecessarily is called security. As one might guess, dependability and security are two competing interests in the design of any protection scheme, the challenge being how to strike a reasonable balance between the two.↩︎
831. This solution works best for measuring the flow rate of gases, not liquids, since the manometer obviously must use a liquid of its own to indicate pressure, and mixing or other interference between the process liquid and the manometer liquid could be problematic.↩︎
832. There is no theoretical limit to the number of points in a digital computer’s characterizer function given sufficient processing power and memory. There is, however, a limit to the patience of the human programmer who must encode all the necessary $$x,y$$ data points defining this function. Most of the piecewise characterizing functions I have seen available in digital instrumentation systems provide 10 to 20 ($$x,y$$) coordinate points to define the function. Fewer than 10 coordinate points risks excessive interpolation errors, and more than 20 would just be tedious to configure.↩︎
833. The configuration software is Emerson’s AMS, running on an engineering workstation in a DeltaV control system network. The radar level transmitter is a Rosemount model 3301 (guided-wave) unit.↩︎
834. To be honest, there are some valve body designs that work far better in on/off service (e.g. ball valves and plug valves) while other designs do a better job at throttling (e.g. double-ported globe valves). Many valve designs, however, may be pressed into either type of service merely by attaching the appropriate actuator.↩︎
835. The standard preparatory technique is called lapping. To “lap” a valve plug and seat assembly, an abrasive paste known as lapping compound is applied to the valve plug(s) and seat(s) at the areas of mutual contact when the valve is disassembled. The valve mechanism is reassembled, and the stem is then rotated in a cyclic motion such that the plug(s) grind into the seat(s), creating a matched fit. The precision of this fit may be checked by disassembling the valve, cleaning off all remaining lapping compound, applying a metal-staining compound such as Prussian blue, then reassembling. The stem is rotated once more such that the plug(s) will rub against the seat(s), wearing through the applied stain. Upon disassembly, the worn stain may be inspected to reveal the extend of metal-to-metal contact between the plug(s) and the seat(s). If the contact area is deemed insufficient, the lapping process may be repeated.↩︎
836. Of course, gate valves also offer obstructionless flow when wide-open, but their poor throttling characteristics give most rotary valve designs the overall advantage.↩︎
837. Some packing materials, most notably Teflon and graphite, tend to be self-lubricating.↩︎
838. Based on friction values shown on page 131 of Fisher’s Control Valve Handbook (Third Edition), Teflon packing friction is typically 5 to 10 times less than graphite packing for the same stem size!↩︎
839. Graphite packing is usable in services ranging from cryogenic temperatures to 1200 degrees Fahrenheit, as opposed to Teflon which is typically rated between $$-40$$ $$^{o}$$F and 450 $$^{o}$$F.↩︎
840. Asbestos fibers have the ability to permanently lodge in the air sacs of human lungs, leading to long-term health problems if those fibers are inhaled.↩︎
841. Bellows have a limited service life, which means the possibility of a rupture is likely. This is why a conventional packing assembly is always included in a bellows-equipped bonnet.↩︎
842. Data in this table taken from Fisher’s Control Valve Handbook.↩︎
843. The greater pressure rating of a piston actuator comes from the fact that the only “soft” component (the sealing ring) has far less surface area exposed to the high pressure than a rolling diaphragm. This results in significantly less stress on the elastic ring than there would be on an elastic diaphragm exposed to the same pressure. There really is no limit to the stroke length of a piston actuator as there is with the stroke length of a diaphragm actuator. It is possible to build a piston actuator miles long, but such a feat would be impossible for a diaphragm actuator, where the diaphragm must stretch (or roll) the entire stroke length.↩︎
844. Exceptions exist for valves designed to fail in place, where a valve may be engineered to “lock” in position through the action of an external device whether the valve itself is air-to-open or air-to-close.↩︎
845. Note that reverse indication is not the same thing as reverse action for a loop controller. Reverse indication simply means the output display shows 100% valve position at 4 mA output, and 0% valve position at 20 mA output. Reverse action means the output decreases when the input (process variable) increases.↩︎
846. 3 PSI could mean fully closed and 15 PSI fully open, or vice-versa, depending on what form of actuator is coupled to what form of valve body. A direct-acting actuator coupled to a direct-acting valve body will be open at low pressure and closed at high pressure (increasing pressure pushing the valve stem toward the body, closing off the valve trim), resulting in air-to-close action. Reversing either actuator or valve type (e.g. reverse actuator with direct valve or direct actuator with reverse valve) will result in air-to-open action.↩︎
847. The volume booster design shown here is loosely based on the Fisher model 2625 volume boosting relay.↩︎
848. One way to minimize dynamic forces on a globe valve plug is to use a double-ported plug design, or to use a balanced plug on a cage-guided globe valve. A disadvantage to both these valve plug designs, though, is greater difficulty achieving tight shut-off.↩︎
849. The technical term for this type of control system is cascade, where one controller’s output becomes the setpoint for a different controller. In the case of a valve positioner, the positioner receives a valve stem position setpoint from the main process controller. We could say that the main process controller in this case is the primary or master controller, while the valve positioner is the secondary or slave controller.↩︎
850. This is not to say valve positioners have no need for external volume boosters, just that the actuating air flow capacity of a typical positioner greatly exceeds the air flow capacity of a typical I/P transducer.↩︎
851. In an earlier chapter of this book, force- and motion-balance pneumatic mechanisms were likened to “tug-of-war” contestants versus ballroom dancers, respectively. Force-balance mechanisms pit force against force to achieve mechanical balance, like two teams competing in a tug-of-war where opposing forces are perfectly balanced and no motion takes place. Motion-balance mechanisms match one motion with another motion to achieve mechanical balance, like two ballroom dancers moving across a dance floor while maintaining a constant distance between each other. All valve positioner mechanisms require motion on the part of the valve stem, and so it is natural to assume all valve positioner mechanisms will be motion-balance because unlike a tug-of-war something is definitely moving. However, if we examine the simple force-balance positioner mechanism closely we will see that only the valve stem moves in this mechanism, while nothing else does. To apply the tug-of-war analogy to this application, it is as if one team of contestants pulls on a stiff rope while the other team pulls on an elastic rope, the two ropes tied together in a knot at the center. In order to achieve a perfect balance of forces so the knot won’t move to one side or the other, the team holding the elastic rope must stretch their rope further in order to balance an increased force from the team holding the stiff rope. The fact that one team is moving does not negate the fact that balance between the two teams is still a matter of force against force. To illustrate this point more vividly, we may ask the question: if the elastic rope is replaced by one that is even more elastic than before, will it advantage one team of contestants over the other? The answer to this question is no, as the two teams will still be equally matched if they were equally matched before. The only difference now is that the team holding the elastic rope will have to stretch the rope further than before to apply the same force as before. In a true motion-balance system, a greater motion imparted by one portion of the mechanism must be matched by a greater motion in the other portion of the mechanism.↩︎
852. Recall from basic physics that friction force always opposes the direction of motion. Thus, when the valve is opening, friction works against the actuator’s air pressure (assuming an air-to-open valve), requiring additional air pressure to maintain motion. When the valve is closing, though, packing friction works in the same direction as the actuator’s air pressure “helping” the valve stay more open than it should. This is why the positioner must maintain less actuator air pressure for any given position while moving closed than while the valve moves open. The difference in air pressure moving open versus moving closed at any given stem position is proportional to twice the dynamic packing friction. Stated mathematically, $$F_{packing} = {1 \over 2} (P_{opening} - P_{closing}) A$$.↩︎
853. Prior to the advent of motor-actuated valves, practically all shutoff valves in industrial facilities were manually operated. While this is an inconvenience for operations personnel, it did carry one advantage: the human operators tasked with closing these valves by hand could feel how each valve seated. The amount of effort and the onset of closing torque sensed while turning the valve handle shut gave operators tactile feedback on the condition of each valve seat. Motor-powered valve actuators eliminated the need for this routine manual labor, but also eliminated the routine collection of this valuable diagnostic information. Modern electric valve actuators now provide the best of both worlds: convenient and fast valve operation with accurate self-diagnostic assessment of valve seating.↩︎
854. I have searched in vain for standardized names to categorize different forms of control valve sequencing. The names “complementary,” “exclusive,” and “progressive” are my own invention. If I have missed someone else’s categorization of split-ranging in my research, I sincerely apologize.↩︎
855. In mathematics, a “complement” is a value whose sum with another quantity always results in a fixed total. Complementary angles, for instance, always add to 90$$^{o}$$ (a right angle).↩︎
856. Also known as a mixing valve or a diverting valve, depending on how it is applied to process service.↩︎
857. Although the HART standard does support “multidrop” mode where multiple devices exist on the same current loop, this mode is digital-only with no analog signal support. Not only do many host systems not support HART multidrop mode, but the relatively slow data communication rate of HART makes this choice unwise for most process control applications. If analog control of multiple HART valve positioner devices from the same 4-20 mA signal is desired, the address conflict problem may be resolved through the use of one or more isolator devices, allowing all devices to share the same analog current signal but isolating each other from HART signals.↩︎
858. To review, Fieldbus is an all-digital industrial control protocol, where instruments connect to a control system and to each other by means of a single network cable. Signals are routed not by specific wire connections, but rather by software entities called function blocks whereby the engineer or technician programs the instruments and control system what to do with those signals. The function blocks shown in this example would typically be accessed through the graphic display of a DCS in a real Fieldbus system, lines drawn between the blocks instructing the system where each of the instrument signals need to go.↩︎
859. Both controllers should be equipped with provisions for reset windup control (or have no integral action at all), such that the output signal values are predictable enough that they behave as a synchronized pair rather than as two separate controllers.↩︎
860. Valve noise may be severe in some cases, especially in certain gas flow applications. An important performance metric for control valves is noise production expressed in decibels (dB).↩︎
861. In case you were wondering, it is appropriate to express energy loss per unit volume in the same units of measurement as pressure. For a more detailed discussion of dimensional analysis, see section 2.11.13 beginning on page where Bernoulli’s equation is examined and you will see how the units of $${1 \over 2} \rho v^2$$ and $$P$$ are actually the same.↩︎
862. In a case of minimal throttling, almost none of the fluid’s kinetic energy is lost to turbulence, but rather passes right through the valve unrestricted.↩︎
863. The specification of certain British units of measurement for flow and pressure drop means that there is more to $$C_v$$ than just $$\sqrt{2 A^2 \over k \rho_{water}}$$. $$C_v$$ also incorporates a factor necessary to account for the arbitrary choice of units.↩︎
864. Such factors include fluid compressibility, viscosity, specific heat, vapor pressure to name a few. Not only will modern valve sizing software more accurately predict valve sizes for particular applications than these simple formulae, but this software may also provide estimations of noise levels produced by the valve.↩︎
865. This is a good example of a general problem-solving strategy in action: making some dramatic change to the scenario and then reasoning the consequences of that change to better understand general principles. For those readers who may be unfamiliar with American terminology, a fire hydrant is a large hand valve installed at intervals along public roadways, allowing connection of fire hoses to an underground water supply pipe in the event of an emergency fire. These valves are quite large, and would be comically oversized if installed inside a person’s house, for any purpose.↩︎
866. This is particularly true when one considers the piping changes usually necessary to accommodate a valve size change. Undersized valves installed in a pipe often require reducer fittings to “narrow” the full-bore size of the pipe down to the flange size of the control valve body. Upon replacement of the under-sized valve, these reducers must be removed to accommodate the larger valve body. The piping itself may need to be cut and re-welded to match the flange-to-flange dimensions of the new (larger) control valve. All of this requires time, labor, and material investment. If a large valve body with reduced-port trim were initially installed, however, most of this time, labor, and expense could be avoided when the time comes to replace the reduced-port trim with full-port trim.↩︎
867. Reduced-port cage-guided trim may also take the form of a cage, plug, and seat of reduced diameter, with flanges attached in such a way that this smaller trim still fits inside the larger valve body. The example illustrated here, with a full-diameter cage having narrower ports on it, is just one way of achieving reduced flow capacity in a cage-guided design but certainly not the only way.↩︎
868. The ISA Handbook of Control Valves cites this equation as being valid for conditions where the valve’s downstream pressure ($$P_2$$) is equal to or greater than one-half the upstream pressure ($$P_1$$), with both pressures expressed in absolute units. In other words, $$P_2 \geq 0.5P_1$$ or $$P_1 \leq 2P_2$$. An upstream:downstream pressure ratio in excess of 2:1 usually means flow through a valve will become choked.↩︎
869. Source for $$C_d$$ factors: of Béla Lipták’s Instrument Engineers’ Handbook, Process Control (Volume II), Third Edition, page 590.↩︎
870. For those readers with an electronics background, the concept of “characteristic curves” for a control valve is exactly the same as that of characteristic curves for transistors. Instead of plotting the amount of current a bipolar transistor will pass through its collector terminal ($$I_C$$) given varying amounts of collector-emitter voltage drop ($$V_{CE}$$), we are plotting the rate of water flow through the valve ($$Q$$) given varying amounts of supply pressure ($$\Delta P$$).↩︎
871. Once again, the exact same concept applied in transistor circuit analysis finds application here in control valve behavior! The load line for a transistor circuit describes the amount of voltage available to the transistor under different current conditions, just like the load line here describes the amount of pressure available to the valve under different flow conditions.↩︎
872. Load line plots are a graphical method of solving nonlinear, simultaneous equations. Since each curve represents a set of solutions to a particular equation, the intersection of two curves represents values uniquely satisfying both equations at the same time.↩︎
873. The precise determination of this curve is based on a model of the narrow pipe as a flow-restricting element, similar in behavior to an orifice, or to a control valve with a fixed stem position. Since pressure is dropped along the pipe’s length as a function of turbulence (velocity), the load “line” curves for the exact reason the valve’s own characteristic plots are curved: the relationship between fluid velocity and turbulent pressure loss is naturally non-linear.↩︎
874. Not only is the response of the valve altered by this degradation of upstream pressure, but we can also see from the load line that a certain maximum flow rate has been asserted by the narrow pipe which did not previously exist: 75 GPM. Even if we unbolted the control valve from the pipe and let water gush freely into the atmosphere, the flow rate would saturate at only 75 GPM because that is the amount of flow where all 20 PSI of hydrostatic “head” is lost to friction in the pipe. Contrast this against the close-coupled scenario, where the load line was vertical on the graph, implying no theoretical limit to flow at all! With an absolutely constant upstream pressure, the only limit on flow rate was the maximum $$C_v$$ of the valve (analogous to a perfect electrical voltage source with zero internal resistance, capable of sourcing any amount of current to a load).↩︎
875. The amount of fluid pressure output by any pump tends to vary with the fluid flow rate through the pump as well as the pump speed. This is especially true for centrifugal pumps, the most common pump design in process industries. Generally speaking, the discharge (output) pressure of a pump rises as flow rate decreases, and falls as flow rate increases. Variations in system fluid pressure caused by the pump constitutes one more variable for control valves to contend with.↩︎
876. Even then, achieving the ideal maximum flow rate may be impossible. Our previous 100% flow rate for the valve was 80.5 GPM, but this goal has been rendered impossible by the narrow pipe, which according to the load line limits flow to an absolute maximum of 75 GPM (even with an infinitely large control valve).↩︎
877. Note that the equal percentage formula given here can never achieve a $$C_v$$ value of zero, regardless of stem position. This is untrue for real control valves, which of course achieve $$C_v = 0$$ when the stem is in the fully closed position. Therefore, the equal percentage formula shown here cannot be precisely trusted at small stem position values.↩︎
878. Data for the three graphs were derived from actual $$C_v$$ factors published in Fisher’s ED, EAD, and EDR sliding-stem control valve product bulletin (51.1:ED). I did not copy the exact data, however; I “normalized” the data so all three valves would have the exact same full-open $$C_v$$ rating of 50.↩︎
879. Astute readers will also note how the stem diameter of the left-hand (linear) plug is significantly greater than the stem diameter of the right-hand (equal-percentage) plug. This has nothing to do with characterization, and is simply an irrelevant difference between the two plugs. The truth of the matter is, dear reader, that these are the only two valve plugs I had on hand suitable for illustrating the difference between linear and equal-percentage trim. One just happened to have a thicker stem than the other.↩︎
880. Such applications are typically found when the purpose of the control valve is to regulate process fluid pressure. Consider, for example, a control valve regulating upstream gas pressure in a vessel by venting gas from that vessel to atmosphere. In such an application, the valve’s upstream pressure ($$P_1$$) will be nearly constant due to the control loop’s action, and the valve’s downstream pressure ($$P_2$$) will be constant due to it being atmospheric pressure.↩︎
881. An example of such a process is temperature control through a heat exchanger where the controlled fluid flow regime happens to transition from laminar to turbulent as the control valve opens further: at low stem positions (nearly shut) where the flow is laminar and heat transfer is impeded, large changes in flow rate may be necessary to effect modest changes in temperature; at high stem positions (nearly open) where the flow is turbulent and heat transfer is efficient, only small changes in flow rate are necessary to create modest changes in temperature. In such an application a quick-opening installed characteristic may actually yield more consistent behavior than a linear installed characteristic.↩︎
882. Bellows seals are theoretically frictionless, but in practice bellows seals are almost always combined with standard packing to prevent catastrophic blow-out in the event of the bellows rupturing, and so the theoretical advantage of low friction is never realized.↩︎
883. Other measures of a control valve’s mechanical status, such as flow capacity, flow characterization, and seat shut-off, cannot be inferred from measurements of actuator force and stem position.↩︎
884. It should be noted that vapor pressure is a strong function of temperature. The warmer a liquid is, the more vapor pressure it will exhibit and thus the more prone it will be to flashing within a control valve.↩︎
885. The Control Valve Sourcebook – Power & Severe Service on page 6-3 and the ISA Handbook of Control Valves on page 211 both suggest that the mechanism for choking in liquid service may be related to the speed of sound just as it is for choked flow in gas services. Normally, liquids have higher sonic velocities than gases due to their far greater bulk moduli (incompressibility). This makes choking due to sonic velocity very unlikely in liquid flowstreams. However, when a liquid flashes into vapor, the speed of sound for that two-phase mixture of liquid and vapor will be much less than it is for the liquid itself, opening up the possibility of sonic velocity choking.↩︎
886. A colleague of mine humorously refers to these valve trim samples as “shock and awe,” because they so dramatically reveal the damaging nature of certain process fluid services.↩︎
887. Regulating fluid flow by using a throttling valve along with a constant-speed pump is analogous to regulating an automobile’s speed by applying varying force to the brake pedal while holding the accelerator pedal at its full-power position!↩︎
888. AC drives also vary the amount of voltage applied to the motor along with frequency, but this of secondary importance to the varying of frequency to control speed.↩︎
889. This includes using an AC induction motor as a servo for precise positioning control!↩︎
890. This equivalence was mathematically proven by Jean Baptiste Joseph Fourier (1768-1830), and is known as a Fourier series.↩︎
891. The difference between the synchronous speed and the rotor’s actual speed is called the motor’s slip speed.↩︎
892. Multi-speed motors do exist, with selectable pole configurations. An example of this is an electric motor with extra sets of stator windings, which may be connected to form a 4-pole configuration for high speed, and an 8-pole configuration for low speed. If the normal full-load “high” speed for this motor is 1740 RPM, the normal full-load “low” speed will be approximately half that, or 870 RPM. Given a fixed line frequency, this motor will only have these two speeds to choose from.↩︎
893. Note the reverse-connected diodes across the source and drain terminals of each power transistor. These diodes serve to protect the transistors against damage from reverse voltage drop, but they also permit the motor to “back feed” power to the DC bus (acting as a generator) when the motor’s speed exceeds that of the rotating magnetic field, which may happen when the drive commands the motor to slow down. This leads to interesting possibilities, such as regenerative braking, with the addition of some more components.↩︎
894. The VFD achieves variable output voltage using the same technique used to create variable output frequency: rapid pulse-width-modulation of the DC bus voltage through the output transistors. When lower output voltage is necessary, the duty cycle of the pulses are reduced throughout the cycle (i.e. transistors are turned on for shorter periods of time) to generate a lower average voltage of the synthesized sine wave.↩︎
895. For more precise control of AC motor speed (especially at low speeds where slip speed becomes a greater percentage of actual speed), speed sensors may indeed be necessary.↩︎
896. This equivalence was mathematically proven by Jean Baptiste Joseph Fourier (1768-1830), and is known as a Fourier series.↩︎
897. One such application is machine motion control, where one part of the machine always needs to slow down while another part is accelerating. Another application is coupling the drive motors of two conveyor belts together, where one conveyor always lifts the load uphill and the other conveyor always lowers the load downhill.↩︎
898. This is accomplished in very different ways for DC versus AC motors. To dynamically brake a DC motor, the field winding must be kept energized while a high-power load resistor is connected to the armature. As the motor turns, the armature will push current through the resistor, generating a braking torque as it does. One way to dynamically brake an AC motor is to inject a small DC current through the stator windings, causing large braking currents to be induced in the rotor. Another way is to regeneratively brake into a resistive load.↩︎
899. In Europe, the fundamental power line frequency is 50 Hz rather than 60 Hz. Also noteworthy is the fact that since the distortion caused by motor drives is typically symmetrical above and below the center-line of the AC waveform, the only significant harmonics will be odd and not even. In a 60 Hz system, the odd harmonics will include 180 Hz (3rd), 300 Hz (5th), 420 Hz (7th), and higher. For a 50 Hz system, the corresponding harmonic frequencies are 150 Hz, 250 Hz, 350 Hz, etc.↩︎
900. Harmonic voltages and currents whose frequencies are multiples of three of the fundamental (e.g. 3rd, 6th, 9th, 12th, 15th harmonics). The reason these particular harmonics are noteworthy in three-phase systems is due to their relative phase shifts. Whereas the fundamental phase shift angle between different phase elements of a three-phase electrical system is 120$$^{o}$$, the phase shift between triplen harmonics is zero. Thus, triplen harmonics are directly additive in three-phase systems.↩︎
901. As you may recall, any sufficiently long set of conductors will act as a transmission line for high-frequency pulse signals. An unterminated (or poorly-terminated) transmission line will reflect pulse signals reaching its ends. In the case of a motor drive circuit, these reflected pulses may constructively interfere to produce nodes of high voltage or high current, causing premature wiring failure. Output line reactors help minimize these effects by filtering out high-frequency pulse signals from reaching the long motor power conductors.↩︎
902. To be precise, this form of on/off control is known as differential gap because there are two setpoints with a gap in between. While on/off control is possible with a single setpoint (FCE on when below setpoint and off when above), it is usually not practical due to the frequent cycling of the final control element.↩︎
903. In electronics, the unit of decibels is commonly used to express gains. Thankfully, the world of process control was spared the introduction of decibels as a unit of measurement for controller gain. The last thing we need is a third way to express the degree of proportional action in a controller!↩︎
904. One could argue that the presence of loads actually justifies a control system, for if there were no loads, there would be nothing to compensate for, and therefore no need for an automatic control system at all! In the total absence of loads, a manually-set final control element would be enough to hold most process variables at setpoint.↩︎
905. An older term for this mode of control is floating, which I happen to think is particularly descriptive. With a “floating” controller, the final control element continually “floats” to whatever value it must in order to completely eliminate offset.↩︎
906. At least the old-fashioned mechanical odometers would. Modern cars use a pulse detector on the driveshaft which cannot tell the difference between forward and reverse, and therefore their odometers always increment. Shades of the movie Ferris Bueller’s Day Off.↩︎
907. The equation for a proportional + integral controller is often written without the bias term ($$b$$), because the presence of integral action makes it unnecessary. In fact, if we let the integral term completely replace the bias term, we may consider the integral term to be a self-resetting bias. This, in fact, is the meaning of the word “reset” in the context of PID controller action: the “reset” term of the controller acts to eliminate offset by continuously adjusting (resetting) the bias as necessary.↩︎
908. Since integration is fundamentally a process of multiplication followed by addition, the units of measurement are always the product (multiplication) of the function’s variables. In the case of reset (integral) control, we are multiplying controller error (the difference between PV and SP, usually expressed in percent) by time (usually expressed in minutes or seconds). Therefore the result will be an “error-time” product. In order for an integral controller to self-recover following windup, the error must switch signs and the error-time product accumulate to a sufficient value to cancel out the error-time product accumulated during the windup period.↩︎
909. An example of such an application is where the output of a loop controller may be “de-selected” or otherwise “over-ridden” by some other control function. This sort of control strategy is often used in energy-conserving controls, where multiple controllers monitoring different process variables selectively command a single FCE.↩︎
910. It should not be assumed that such spikes are always undesirable. In processes characterized by long lag times, such a response may be quite helpful in overcoming that lag for the purpose of rapidly achieving new setpoint values. Slave (secondary) controllers in cascaded systems – where the controller receives its setpoint signal from the output of another (primary, or master) controller – may similarly benefit from derivative action calculated on error instead of just PV. As usual, the specific needs of the application dictate the ideal controller configuration.↩︎
911. This is the meaning of the vertical-pointing arrowheads shown on the trend graph: momentary saturation of the output all the way up to 100%.↩︎
912. This is a good example of how integral controller action represents the history of the PV $$-$$ SP error. The continued offset of integral action from its starting point “remembers” the area accumulated under the rectangular “step” between PV and SP. This offset will go away only if a negative error appears having the same percent-minute product (area) as the positive error step.↩︎
913. This is the meaning of the vertical-pointing arrowheads shown on the trend graph: momentary saturation of the output all the way up to 100% (or down to 0%).↩︎
914. In this example, I have omitted the constant of integration ($$C$$) to keep things simple. The actual integral is as such: $$\int \sin x \> dx = - \cos x + C = \sin (x - 90^o) + C$$. This constant value is essential to explaining why the integral response does not immediately “step” like the derivative response does at the beginning of the PV sine wavelet.↩︎
915. An example of a case where it is better for gain ($$K_p$$) to influence all three control modes is when a technician re-ranges a transmitter to have a larger or smaller span than before, and must re-tune the controller to maintain the same loop gain as before. If the controller’s PID equation takes the parallel form, the technician must adjust the P, I, and D tuning parameters proportionately. If the controller’s PID equation uses $$K_p$$ as a factor in all three modes, the technician need only adjust $$K_p$$ to re-stabilize the loop.↩︎
916. This becomes especially apparent when using derivative action with low values of $$\tau_i$$ (aggressive integral action). The error-multiplying term $${\tau_d \over \tau_i} + 1$$ may become quite large if $$\tau_i$$ is small, even with modest $$\tau_d$$ values.↩︎
917. Being a motion-balance mechanism, these bellows must act as spring elements in order to produce consistent pressure/motion behavior. Some pneumatic controllers employ coil springs inside the brass bellows assembly to provide the necessary “stiffness” and repeatability.↩︎
918. Practical integral action also requires the elimination of the bias spring and adjustment, which formerly provided a constant downward force on the left-hand side of the beam to give the output signal the positive offset necessary to avoid saturation at 0 PSI. Not only is a bias adjustment completely unnecessary with the addition of integral action, but it would actually cause problems by making the integral action “think” an error existed between PV and SP when there was none.↩︎
919. These restrictor valves are designed to encourage laminar air flow, making the relationship between volumetric flow rate and differential pressure drop linear rather than quadratic as it is for large control valves. Thus, a doubling of pressure drop across the restrictor valve results in a doubling of flow rate into (or out of) the reset bellows, and a consequent doubling of integration rate. This is precisely what we desire and expect from a controller with integral action.↩︎
920. In case you are wondering, this controller happens to be reverse-acting instead of direct. This is of no consequence to the feature of external reset.↩︎
921. The reason for this is the low component count compared to a comparable digital control circuit. For any given technology, a simpler device will tend to be more reliable than a complex device if only due to there being fewer components to fail. This also suggests a third advantage of analog controllers over digital controllers, and that is the possibility of easily designing and constructing your own for some custom application such as a hobby project. A digital controller is not outside the reach of a serious hobbyist to design and build, but it is definitely more challenging due to the requirement of programming expertise in addition to electronic hardware expertise.↩︎
922. It is noteworthy that analog control systems are completely immune from “cyber-attacks” (malicious attempts to foil the integrity of a control system by remote access), due to the simple fact that their algorithms are fixed by physical laws and properties of electronic components rather than by code which may be edited. This new threat constitutes an inherent weakness of digital technology, and has spurred some thinkers in the field to reconsider analog controls for the most critical applications.↩︎
923. The real problem with digital controller speed is that the time delay between successive “scans” translates into dead time for the control loop. Dead time is the single greatest impediment to feedback control.↩︎
924. This circuit configuration is called “inverting” because the mathematical sign of the output is always opposite that of the input. This sign inversion is not an intentional circuit feature, but rather a consequence of the input signal facing the opamp’s inverting input. Non-inverting multiplier circuits also exist, but are more complicated when built to achieve multiplication factors less than one.↩︎
925. This inversion of function caused by the swapping of input and feedback components in an operational amplifier circuit points to a fundamental principle of negative feedback networks: namely, that placing a mathematical element within the feedback loop causes the amplifier to exhibit the inverse of that element’s intrinsic function. This is why voltage dividers placed within the feedback loop cause an opamp to have a multiplicative gain (division $$\rightarrow$$ multiplication). A circuit element exhibiting a logarithmic response, when placed within a negative feedback loop, will cause the amplifier to exhibit an exponential response (logarithm $$\rightarrow$$ exponent). Here, an element having a time-differentiating response, when placed inside the feedback loop, causes the amplifier to time-integrate (differentiation $$\rightarrow$$ integration). Since the opamp’s output voltage must assume any value possible to maintain (nearly) zero differential voltage at the input terminals, placing a mathematical function in the feedback loop forces the output to assume the inverse of that function in order to “cancel out” its effects and achieve balance at the input terminals.↩︎
926. If this is not apparent, imagine a scenario where the +1.7 volt input existed for precisely one second’s worth of time. However much the output voltage ramps in that amount of time must therefore be its rate of change in volts per second (assuming a linear ramp). Since we know the area accumulated under a constant value of 1.7 (high) over a time of 1 second (wide) must be 1.7 volt-seconds, and $$\tau_i$$ is equal to 3.807 seconds, the integrator circuit’s output voltage must ramp 0.447 volts during that interval of time. If the input voltage is positive and we know this is an inverting opamp circuit, the direction of the output voltage’s ramping must be negative, thus a ramping rate of $$-$$0.447 volts per second.↩︎
927. The two input terminals shown, Input$$_{(+)}$$ and Input$$_{(-)}$$ are used as PV and SP signal inputs, the correlation of each depending on whether one desires direct or reverse controller action.↩︎
928. This particular design has integral and derivative time value limits of 10 seconds, maximum. These relatively “quick” tuning values are the result of having to use non-polarized capacitors in the integrator and differentiator stages. The practical limits of cost and size restrict the maximum value of on-board capacitance to around 10 $$\mu$$F each.↩︎
929. An interesting example of engineering tradition is found in electronic PID controller designs. While it is not too terribly difficult to build an analog electronic controller implementing either the parallel or ideal PID equation (just a few more parts are needed), it is quite challenging to do the same in a pneumatic mechanism. When analog electronic controllers were first introduced to industry, they were often destined to replace old pneumatic controllers. In order to ease the transition from pneumatic to electronic control, manufacturers built their new electronic controllers to behave exactly the same as the old pneumatic controllers they would be replacing. The same legacy followed the advent of digital electronic controllers: many digital controllers were programmed to behave in the same manner as the old pneumatic controllers, for the sake of operational familiarity, not because it was easier to design a digital controller that way.↩︎
930. Although the SPEC 200 system – like most analog electronic control systems – is considered “mature” (Foxboro officially declared the SPEC 200 and SPEC 200 Micro systems as such in March 2007), working installations may still be found at the time of this writing (2010). A report published by the Electric Power Research Institute (see References at the end of this chapter) in 2001 documents a SPEC 200 analog control system installed in a nuclear power plant in the United States as recently as 1992, and another as recently as 2001 in a Korean nuclear power plant.↩︎
931. Foxboro provided the option of a self-contained, panel-mounted SPEC 200 controller unit with all electronics contained in a single module, but the split architecture of the display/nest areas was preferred for large installations where many dozens of loops (especially cascade, feedforward, ratio, and other multi-component control strategies) would be serviced by the same system.↩︎
932. I once encountered an engineer who joked that the number “200” in “SPEC 200” represented the number of years the system was designed to continuously operate. At another facility, I encountered instrument technicians who were a bit afraid of a SPEC 200 system running a section of their plant: the system had never suffered a failure of any kind since it was installed decades ago, and as a result no one in the shop had any experience troubleshooting it. As it turns out, the entire facility was eventually shut down and sold, with the SPEC 200 nest running faithfully until the day its power was turned off! The functioning SPEC 200 controllers shown in the photograph were in continuous use at British Columbia Institute of Technology at the time of the photograph, taken in December of 2014.↩︎
933. Thanks to the explosion of network growth accompanying personal computers in the workplace, Ethernet is ubiquitous. The relatively high speed and low cost of Ethernet communications equipment makes it an attractive network standard over which a great many high-level industrial protocols communicate.↩︎
934. An aspect common to many PLC implementations of PID control is the use of the “parallel” PID algorithm instead of the superior “ISA” or “non-interacting” algorithm. The choice of algorithm may have a profound effect on tuning, and on tuning procedures, especially when tuning parameters must be re-adjusted to accommodate changes in transmitter range.↩︎
935. Modern DDC systems of the type used for building automation (heating, cooling, security, etc.) almost always consist of networked control nodes, each node tasked with monitoring and control of a limited area. The same may be said for modern PLC technology, which not only exhibits advanced networking capability (fieldbus I/O networks, Ethernet, Modbus, wireless communications), but is often also capable of redundancy in both processing and I/O. As technology becomes more sophisticated, the distinction between a DDC (or a networked PLC system) and a DCS becomes more ambiguous.↩︎
936. An example of such a self-check is scheduled switching of the networks: if the system has been operating on network cable “A” for the past four hours, it might switch to cable “B” for the next four hours, then back again after another four hours to continually ensure both cables are functioning properly.↩︎
937. To be fair, the Yokogawa Electric Corporation of Japan introduced their CENTUM distributed control system the same year as Honeywell. Unfortunately, while I have personal experience maintaining and using the Honeywell TDC2000 system, I have zero personal experience with the Yokogawa CENTUM system, and neither have I been able to obtain technical documentation for the original incarnation of this DCS (Yokogawa’s latest DCS offering goes by the same name). Consequently, I can do little in this chapter but mention its existence, despite the fact that it deserves just as much recognition as the Honeywell TDC2000 system.↩︎
938. Just to give some perspective, the original TDC2000 system used whole-board processors rather than microprocessor chips, and magnetic core memory rather than static or dynamic RAM circuits! Communication between controller nodes and operator stations occurred over thick coaxial cables, implementing master/slave arbitration with a separate device (a “Hiway Traffic Director” or HTD) coordinating all communications between nodes. Like Bob Metcalfe’s original version of Ethernet, these coaxial cables were terminated at their end-points by termination resistors, with coaxial “tee” connectors providing branch points for multiple nodes to connect along the network.↩︎
939. I know of a major industrial manufacturing facility (which shall remain nameless) where a PLC vendor promised the same technical capability as a full DCS at approximately one-tenth the installed cost. Several years and several tens of thousands of man-hours later, the sad realization was this “bargain” did not live up to its promise, and the decision was made to remove the PLCs and go with a complete DCS from another manufacturer. Caveat emptor!↩︎
940. Although it is customary for the host system to be configured as the Link Active Scheduler (LAS) device to schedule and coordinate all fieldbus device communications, this is not absolutely necessary. Any suitable field instrument may also serve as the LAS, which means a host system is not even necessary except to provide DC power to the instruments, and serve as a point of interface for human operators, engineers, and technicians.↩︎
941. With the PID function block programmed in the flow transmitter, there will be twice as many scheduled communication events per macrocycle than if the function block is programmed into the valve positioner. This is evident by the number of signal lines connecting circled block(s) to circled block(s) in the above illustration.↩︎
942. The only reason I say “may” instead of “will” is because some modern digital controllers are designed to automatically switch to manual-mode operation in the event of a sensor or transmitter signal loss. Any controller not “smart” enough to shed its operating mode to manual in the event of PV signal loss will react dramatically when that PV signal dies, and this is not a good thing for an operating loop!↩︎
943. I once had the misfortune of working on an analog PID controller for a chlorine-based wastewater disinfection system that lacked output tracking. The chlorine sensor on this system would occasionally fail due to sample system plugging by algae in the wastewater. When this happened, the PV signal would fail low (indicating abnormally low levels of chlorine gas dissolved in the wastewater) even though the actual dissolved chlorine gas concentration was adequate. The controller, thinking the PV was well below SP, would ramp the chlorine gas control valve further and further open over time, as integral action attempted to reduce the error between PV and SP. The error never went away, of course, because the chlorine sensor was plugged with algae and simply could not detect the actual chlorine gas concentration in the wastewater. By the time I arrived to address the “low chlorine” alarm, the controller output was already wound up to 100%. After cleaning the sensor, and seeing the PV value jump up to some outrageously high level, the controller would take a long time to “wind down” its output because its integral action was very slow. I could not use manual mode to “unwind” the output signal, because this controller lacked the feature of output tracking. My “work-around” solution to this problem was to re-tune the integral term of the controller to some really fast time constant, watch the output “wind down” in fast-motion until it reached a reasonable value, then adjust the integral time constant back to its previous value for continued automatic operation.↩︎
944. Boiler steam drum water level control, for example, is a process where the setpoint really should be left at a 50% value at all times, even if there maybe legitimate reasons for occasionally switching the controller into manual mode.↩︎
945. It is very important to note that soft alarms are not a replacement for hard alarms. There is much wisdom in maintaining both hard and soft alarms for a process, so there will be redundant, non-interactive levels of alarming. Hard and soft alarms should complement each other in any critical process.↩︎
946. Some PID controllers limit manual-mode output values as well, so be sure to check the manufacturer’s documentation for output limiting on your particular PID controller!↩︎
947. I have used a typesetting convention to help make my pseudocode easier for human beings to read: all formal commands appear in bold-faced blue type, while all comments appear in italicized red type. All other text appears as normal-faced black type. One should remember that the computer running any program cares not for how the text is typeset: all it cares is that the commands are properly used (i.e. no “grammatical” or “syntactical” errors).↩︎
948. It should be noted that this is precisely what happens when you change the gain in a pneumatic or an analog electronic controller, since all analog PID controllers implement the “position” equation. Although the choice between “position” and “velocity” algorithms in a digital controller is arbitrary, it is much easier to build an analog mechanism or circuit implementing the position algorithm than it is to build an analog “velocity” controller.↩︎
949. We call this an adaptive gain control system.↩︎
950. Many instrument manufacturers sell simple, single-loop controllers for reasonable prices, comparable to the price of a college textbook. You need to get one that accepts 1-5 VDC input signals and generates 4-20 mA output signals, and has a “manual” mode of operation in addition to automatic – these features are very important! Avoid controllers that can only accept thermocouple inputs, and/or only have time-proportioning (PWM) outputs.↩︎
951. To illustrate, self-regulating processes require significant integral action from a controller in order to avoid large offsets between PV and SP, with minimal proportional action and no derivative action. Integrating processes, in contrast, may be successfully controlled primarily on proportional action, with minimal integral action to eliminate offset. Runaway processes absolutely require derivative action for dynamic stability, but derivative action alone is not enough: some integral action will be necessary to eliminate offset. Even if knowledge of a process’s dominant characteristic does not give enough information for us to quantify P, I, or D values, it will tell us which tuning constant will be most important for achieving stability.↩︎
952. Recall that wind-up is what happens when integral action “demands” more from a process than the process can deliver. If integral action is too aggressive for a process (i.e. fast integral controller action in a process with slow time lags), the output will ramp too quickly, causing the process variable to overshoot setpoint which then causes integral action to wind the other direction. As with proportional action, too much integral action will cause a self-regulating process to oscillate.↩︎
953. In a proportional-only controller, the output is a function of error (PV $$-$$ SP) and bias. When PV = SP, bias alone determines the output value (valve position). However, in a controller with integral action, the zero-offset output value is determined by how long and how far the PV has previously strayed from SP. In other words, there is no fixed bias value anymore. Thus, the output of a controller with integral action will not return to its previous value once the new SP is reached. In a purely integrating process, this means the PV will not reach stability at the new setpoint, but will continue to rise until all the “winding up” of integral action is un-done.↩︎
954. When a nucleus of uranium or plutonium undergoes fission (“splits”), it releases more neutrons capable of splitting additional uranium or plutonium nuclei. The ratio of new nuclei “split” versus old nuclei “split” is the multiplication factor. If this factor has a value of one (1), the chain reaction will sustain at a constant power level, with each new generation of atoms “split” equal to the number of atoms “split” in the previous generation. If this multiplication factor exceeds unity, the rate of fission will increase over time. If the factor is less than one, the rate of fission will decrease over time. Like an inverted pendulum, the chain reaction has a tendency to “fall” toward infinite activity or toward no activity, depending on the value of its multiplication factor.↩︎
955. The mechanism by which this occurs varies with the reactor design, and is too detailed to warrant a full explanation here. In pressurized light-water reactors – the dominant design in the United States of America – this action occurs due to the water’s ability to moderate (slow down) the velocity of neutrons. Slow neutrons have a greater probability of being “captured” by fissile nuclei than fast neutrons, and so the water’s moderating ability will have a direct effect on the reactor core’s multiplication factor. As a light-water reactor core increases temperature, the water becomes less dense and therefore less effective at moderating (slowing down) fast neutrons emitted by “splitting” nuclei. These fast(er) neutrons then “miss” the nuclei of atoms they would have otherwise split, effectively reducing the reactor’s multiplication factor without any need for regulatory control rod motion. The reactor’s power level therefore self-stabilizes as it warms, rather than “running away” to dangerously high levels, and may thus be classified as a self-regulating process.↩︎
956. Discounting, of course, the intentional discharge of nuclear weapons, whose sole design purpose is to self-destruct in a “runaway” chain reaction.↩︎
957. The general definition of gain is the ratio of output change over input change ($$\Delta \hbox{Out} \over \Delta \hbox{In}$$). Here, you may have noticed we calculate process gain by dividing the process variable change (7.5%) by the controller output change (10%). If this seems “inverted” to you because we placed the output change value in the denominator of the fraction instead of the numerator, you need to keep in mind the perspective of our gain measurement. We are not calculating the gain of the controller, but rather the gain of the process. Since the output of the controller is the “input” to the process, it is entirely appropriate to refer to the 10% manual step-change as the change of input when calculating process gain.↩︎
958. While this is true of analog-signal transmitters, it is not necessarily true of digital-signal transmitters such as Fieldbus or wireless (digital radio). The reason for this distinction is that in a digital-signal transmitter, the reported process variable value is scaled in engineering units rather than percent. Applied to this case, if the flow transmitter gets re-ranged from 0-200 LPM to 0-150 LPM, the controller sees no change in process gain because a change of 10 LPM is still reported as a change in 10 LPM regardless of the transmitter’s range.↩︎
959. For more information on different PID equations, refer to Section 29.10 beginning on page .↩︎
960. It is also possible to configure many instruments to deliberately damp their response to input conditions. This is called damping, and it is covered in more detail in section 18.4 beginning on page .↩︎
961. Assuming a constant discharge valve position. If someone alters the hand valve’s position, the relationship between incoming flow rate and final liquid level changes.↩︎
962. We will assume here the heating element reaches its final temperature immediately upon the application of power, with no lag time of its own.↩︎
963. Given the presence of water in the potato which turns to steam at 212 $$^{o}$$F, things are just a bit more complicated than this, but let’s ignore the effects of water in the potato for now!↩︎
964. The amount of time the potato’s temperature will continue to rise following the down-step in heating element power is equal to the time it takes for the oven’s air temperature to equal the potato’s temperature. The reason the potato’s temperature keeps rising after the heating element turns off is because the air inside the oven is (for a short time) still hotter than the potato, and therefore the potato continues to absorb thermal energy from the air for a time following power-off.↩︎
965. The so-called Barkhausen criterion for oscillation in a feedback system is that the total loop gain is at least unity (1) and the total loop phase shift is 360$$^{o}$$.↩︎
966. The conditions necessary for self-sustaining oscillations to occur is a total phase shift of 360$$^{o}$$ and a total loop gain of 1. Merely having positive feedback or having a total gain of 1 or more will not guarantee self-sustaining oscillations; both conditions must simultaneously exist. As a measure of how close any feedback system is to this critical confluence of conditions, we may quantify a system’s phase margin (how many degrees of phase shift the system is away from 360$$^{o}$$ while at a loop gain of 1) and/or a system’s gain margin (how many decibels of gain the system is away from 0 dB while at a phase shift of 360$$^{o}$$). The less phase or gain margin a feedback system has, the closer it is to a condition of instability.↩︎
967. At maximum phase shift, the gain of any first-order RC network is zero. Both phase shift and attenuation in an RC lag network are frequency-dependent: as frequency increases, phase shift grows larger (from 0$$^{o}$$ to a maximum of $$-90^{o}$$) and the output signal grows weaker. At its theoretical maximum phase shift of exactly $$-90^{o}$$, the output signal would be reduced to nothing!↩︎
968. In its pure, theoretical form at least. In practice, even a single-lag circuit may oscillate given enough gain due to the unavoidable presence of parasitic capacitances and inductances in the wiring and components causing multiple orders of lag (and even some dead time). By the same token, even a “pure” first-order process will oscillate given enough controller gain due to unavoidable lags and dead times in the field instrumentation (especially the control valve). The point I am trying to make here is that there is more to the question of stability (or instability) than loop gain.↩︎
969. Truth be told, the same principle holds for purely integrating processes as well. A purely integrating process always exhibits a phase shift of $$-90^{o}$$ at any frequency, because that is the nature of integration in calculus. A purely first-order lag process will exhibit a phase shift anywhere from 0$$^{o}$$ to $$-90^{o}$$ depending on frequency, but never more lagging than $$-90^{o}$$, which is not enough to turn negative feedback into positive feedback. In either case, so long as we don’t have process noise to deal with, we can increase the controller’s gain all the way to eleven. If that last sentence (a joke) does not make sense to you, be sure to watch the 1984 movie This is Spinal Tap as soon as possible. Seriously, I have used controller gains as high as 50 on low-noise, first-order processes such as furnace temperature control. With such high gain in the controller, response to setpoint and load changes is quite swift, and integral action is almost unnecessary because the offset is naturally so small.↩︎
970. A sophisticated way of saying this is that a dead-time function has no phase margin, only gain margin. All that is needed in a feedback system with dead time is sufficient gain to make the system oscillate.↩︎
971. Sometimes referred to as the Barkhausen criterion.↩︎
972. An interesting analogy is that of a narcoleptic human operator manually controlling a process with a lot of dead time. If we imagine this person helplessly falling asleep at periodic intervals, then waking up to re-check the process variable and make another valve adjustment before falling asleep again, we see that the dead time of the process disappears from the perspective of the operator. The operator never realizes the process even has dead time, because they don’t remain awake long enough to notice. So long as the poor operator’s narcolepsy occurs at just the right intervals (i.e. not too short so as to notice dead time, and not too long so as to miss important changes in setpoint or load), good control of the process is possible.↩︎
973. A 10% hysteresis value means that the signal must be changed by 10% following a reversal of direction before any movement is seen from the valve stem.↩︎
974. Some integral controllers are equipped with a useful feature called integral deadband or reset deadband. This is a special PID function inhibiting integration whenever the process variable comes close enough to setpoint, the “deadband” value specifying how close the PV must come to SP before integration stops. If this deadband value is set equal to or wider than the error caused by the valve’s stiction, the controller will stop its integral-driven cycling. The trade-off, of course, is that the controller will no longer work to eliminate all error, but rather will be content with an error equal to or less than the specified deadband.↩︎
975. An alternate solution is to install a positioner on the control valve, which acts as a secondary (cascaded) controller seeking to equalize stem position with the loop controller’s output signal at all times. However, this just “shifts” the problem from one controller to another. I have seen examples of control valves with severe packing friction which will self-oscillate their own positioners (i.e. the positioner will “hunt” back and forth for the correct valve stem position given a constant signal from the loop controller)! If valve stem friction can be minimized, it should be minimized.↩︎
976. Note that this is truly the gain of the controller, not the proportional band. If you were to enter a proportional band value one-half the proportional band value necessary to sustain oscillations, the controller would (obviously) oscillate completely out of control!↩︎
977. Either minutes per repeat or seconds per repeat. If the controller’s integral rate is expressed in units of repeats per minute (or second), the formula would be $$K_i = {1.2 \over P_u}$$.↩︎
978. Imagine informing the lead operations manager or a unit supervisor in a chemical processing facility you wish to over-tune the temperature controller in the main reaction furnace or the pressure controller in one of the larger distillation columns until it nearly oscillates out of control, and that doing so may necessitate hours of unstable operation before you find the perfect gain setting. Consider yourself fortunate if your declaration of intent does not result in security personnel escorting you out of the control room.↩︎
979. Unfortunately, Ziegler and Nichols chose to refer to dead time by the word lag in their paper. In modern technical parlance, “lag” refers to a first-order inverse-exponential function, which is fundamentally different from dead time.↩︎
980. Right away, we see a weakness in the Ziegler-Nichols open-loop method: it makes absolutely no distinction between self-regulating and integrating process types. We know this is problematic from the analysis of each process type in sections 30.1.1 and 30.1.2.↩︎
981. Ziegler and Nichols’ approach was to define a normalized reaction rate called the unit reaction rate, equal in value to $$R \over \Delta m$$. I opt to explicitly include $$\Delta m$$ in all the tuning parameter equations in order to avoid the possibility of confusing reaction rate with unit reaction rate.↩︎
982. This is very important: no degree of controller “tuning” will fix a poor control valve, noisy transmitter, or ill-designed process. If your open-loop tests reveal significant process problems, you must remedy them before attempting to tune the controller.↩︎
983. It is important to know which PID equation your controller implements in order to adjust just one action (P, I, or D) of the controller without affecting the others. Most PID controllers, for example, implement either the “Ideal” or “Series” equations, where the gain value ($$K_p$$) multiplies every action in the controller including integral and derivative. If you happen to be tuning such a controller for integral-dominant control, you cannot set the gain to zero (in order to minimize proportional action) because this will nullify integral action too! Instead, you must set $$K_p$$ to some value small enough that the proportional action is minimal while allowing integral action to function.↩︎
984. Recall that an open-loop response test consists of placing the loop controller in manual mode, introducing a step-change to the controller output (manipulated variable), and analyzing the time-domain response of the process variable as it reacts to that perturbation.↩︎
985. For reverse-acting controllers, I am ignoring the obvious 180$$^{o}$$ phase shift necessary for negative feedback control when I say “no phase shift” between PV and output waveforms. I am also ignoring dead time resulting from the scanning of the PID algorithm in the digital controller. For some controllers, this scan time may be significant enough to see on a trend!↩︎
986. The term “porpoise” comes from the movements of a porpoise swimming rapidly toward the water’s surface as it chases along the bow of a moving ship. In order to generate speed, the animal undulates its body up and down to powerfully drive forward with its horizontal tail, tracing a sinusoidal path on its way up to breaching the surface of the water.↩︎
987. You could try reducing the controller’s gain as a first step, but if the controller implements the Ideal or Series algorithm, reduction in gain will also reduce derivative action, which may mask an over-tuned derivative problem.↩︎
988. The astute observer will note the presence of some limiting (saturation) in the output waveform, as it attempts to go below zero percent. Normally, this is unacceptable while determining the ultimate gain of a process, but here it was impossible to make the process oscillate at consistent amplitude without saturating on the output signal. The gain of this process falls off quite a bit at the ultimate frequency, such that a high controller gain is necessary to sustain oscillations, causing the output waveform to have a large amplitude.↩︎
989. We would have to be very careful with the addition of damping, since the oscillations could create may not appear on the trend. Remember that the insertion of damping (low-pass filtering) in the PV signal is essentially an act of “lying” to the controller: telling the controller something that differs from the real, measured signal. If our PV trend shows us this damped signal and not the “raw” signal from the transmitter, it is possible for the process to oscillate and the PV trend to be deceptively stable!↩︎
990. Many instrument manufacturers sell simple, single-loop controllers for reasonable prices, comparable to the price of a college textbook. You need to get one that accepts 1-5 VDC input signals and generates 4-20 mA output signals, and has a “manual” mode of operation in addition to automatic – these features are very important! Avoid controllers that can only accept thermocouple inputs, and/or only have time-proportioning (PWM) outputs. Additionally, I strongly recommend you take the time to experimentally learn the actions of proportional, integral, and derivative as outlined in section 29.16 beginning on page before you embark on any PID tuning exercises.↩︎
991. Among these different controllers were a Distech ESP-410 building (HVAC) controller and a small PLC programmed with a custom PID control algorithm. In fact, a Desktop Process is ideal for courses where students create their own control algorithms in PLC or data acquisition hardware. The significance of controller scan rate becomes very easy to comprehend when controlling a process like this with such a short time constant. The contrast between a DDC controller with a 500 millisecond scan rate and a PLC with a 50 millisecond scan rate, for example, is marked.↩︎
992. In honor of the system’s ability to slowly “ramp” temperature up or down at a specified rate, then “soak” the metal at a constant temperature for set periods of time. Many single-loop process controllers have the ability to perform ramp-and-soak setpoint scheduling without the need of an external “supervisory” computer.↩︎
993. I once attended a meeting of industry representatives where one person talked at length about a highly automated lumber mill where logs were cut into lumber not only according to minimum waste, but also according to the real-time market value of different board types and stored inventory. The joke was, if the market value of wooden toothpicks suddenly spiked up, the control system would shred every log into toothpicks in an attempt to maximize profit!↩︎
994. Interestingly, servo motor control is one application where analog loop controllers have historically been favored over digital loop controllers, simply for their superior speed. An opamp-based P, PI, or PID controller is lightning-fast because it has no need to digitize any analog process variables (analog-to-digital conversion) nor does it require time for a clock to sequence step-by-step through a written program as a microprocessor does. Servomechanism processes are inherently fast-responding, and so the controller(s) used to control servos must be faster yet.↩︎
995. At one specific current level, the motor will develop just enough torque to hold the platform’s weight, at which point the acceleration will be zero. Any amount of current above this value will cause an upward acceleration, while any amount of current below this value will cause a downward acceleration.↩︎
996. The conversion from hydrocarbon and steam to hydrogen and carbon dioxide is typically a two-stage process: the first (reforming) stage produces hydrogen gas and carbon monoxide, while a second (water-gas-shift) stage adds more steam to convert the carbon monoxide into carbon dioxide with more hydrogen liberated. Both reactions are endothermic, with the reforming reaction being more endothermic than the water-gas-shift reaction.↩︎
997. Steam has a formula weight of 18 amu per molecule, with two hydrogen atoms (1 amu each) and one oxygen atom (16 amu). Methane has a formula weight of 16 amu per molecule, with one carbon atom (12 amu) and four hydrogen atoms (1 amu each). If we wish to have a molecular ratio of 2:1, steam-to-methane, this makes a formula weight ratio of 36:16, or 9:4.↩︎
998. It is quite common for industrial control systems to operate at ratios a little bit “skewed” from what is stoichiometrically ideal due to imperfect reaction efficiencies. Given the fact that no chemical reaction ever goes to 100% completion, a decision must be made as to which form of incompleteness is worse. In a steam-hydrocarbon reforming system, we must ask ourselves which is worse: excess (unreacted) steam at the outlet, or excess (unreacted) hydrocarbon at the outlet. Excess hydrocarbon content will “coke” the catalyst and heater tubes, which is very bad for the process over time. Excess steam merely results in a bit more operating energy loss, with no degradation to equipment life. The choice, then, is clear: it is better to operate this process “hydrocarbon-lean” (more steam than ideal) than “hydrocarbon-rich” (less steam than ideal).↩︎
999. This mixing of superheated steam and cold water happens in a specially-designed device called a desuperheater. The basic concept is that the water will absorb heat from the superheated steam, turning that injected water completely into steam and also reducing the temperature of the superheated steam. The result is a greater volume of steam than before, at a reduced temperature. So long as some amount of superheat remains, the de-superheated steam will still be “dry” (above its condensing temperature). The desuperheater control merely adds the appropriate amount of water until it achieves the desired superheat value.↩︎
1000. This statement is true only for self-regulating processes. Integrating and “runaway” processes require control systems to achieve stability even in the complete absence of any loads. However, since self-regulation typifies the vast majority of industrial processes, we may conclude that the fundamental purpose of most control systems is to counteract the effects of loads.↩︎
1001. The load variables I keep mentioning that influence a car’s speed constitute an incomplete list at best. Many other variables come into play, such as fuel quality, engine tuning, and tire pressure, just to name a few. In order for a purely feedforward (i.e. no feedback monitoring of the process variable) control system to work, every single load variable must be accurately monitored and factored into the system’s output signal. This is impractical or impossible for a great many applications, which is why we usually find feedforward control used in conjunction with feedback control, rather than feedforward control used alone.↩︎
1002. In fact, the only pure feedforward control strategies I have ever seen have been in cases where the process variable was nearly impossible to measure and could only be inferred from other variables.↩︎
1003. If the liquid level drops too low, there will be insufficient retention time in the vessel for the fluids to mix before they exit the product line at the bottom.↩︎
1004. The device or computer function performing the summation is shown in the P&ID as a bubble with “FY” as the label. The letter “F” denotes Flow, while the letter “Y” denotes a signal relay or transducer.↩︎
1005. Incidentally, this is a good example of an integrating mass-balance process, where the rate of process variable change over time is proportional to the imbalance of flow rates in and out of the process. Stated another way, total accumulated (or lost) mass in a mass-balance system such as this is the time-integral of the difference between incoming and outgoing mass flow rates: $$\Delta m = \int_0^T (W_{in} - W_{out}) \> dt$$.↩︎
1006. Residence time or Retention time is the average amount of time each liquid molecule spends inside the vessel. It is an important variable in chemical reaction processes, where adequate time must be given to the reactant molecules in order to ensure a complete reaction. It is also important for non-reactive mixing processes such as paint and food manufacturing, to ensure the ingredients are thoroughly mixed together and not stratified. For any given flow rate through a vessel, the residence time is directly proportional to the volume of liquid contained in that vessel: double the captive volume, and you double the residence time. For any given captive volume, the residence time is inversely proportional to the flow rate through the vessel: double the flow rate through the vessel, and you halve the residence time. In some mixing systems where residence time is critical to the thorough mixing of liquids, vessel level control may be coupled to measured flow rate, such that an increase in flow rate results in an increased level setpoint, thus maintaining a constant residence time despite changes in production rate.↩︎
1007. Energy demand is an example of what is called an inferred variable: a physical quantity that we cannot measure directly but instead calculate from measurements made of other variables.↩︎
1008. Most control systems’ feedforward function blocks are designed in such a way that both the feedback and the feedforward signal paths are disabled when the controller is placed into manual mode, in order to give the human operator 100% control over the final element (valve) in that mode. For the purpose of “tuning” the feedforward gain/bias function block, one must disable the feedback control only so feedforward action is still able to respond to load changes. If simply switching the feedback controller to manual mode is not an option (which it usually is not), one may achieve the equivalent result by setting the gain value of the feedback controller to zero and ensuring the PID equation is not the “parallel” type. If the PID equation is parallel, you will need to set all three terms (P, I, and D) at their minimum settings.↩︎
1009. This is why it was recommended to leave the feedback controller’s output at or near 50%. The goal is to have the feedforward action adjusted such that the feedback controller’s output is “neutral,” and has room to swing either direction if needed to provide necessary trim to the process.↩︎
1010. Tuning this gain/bias block is done with the pH controller in manual mode with its output at 50%. The gain value is adjusted such that step-changes in flocculant feed rate have little long-term effect on pH. The bias value is adjusted until the pH approaches setpoint (even with the pH controller in manual mode).↩︎
1011. This “thought experiment” assumes no compensating action on the part of the feedback pH controller for the sake of simplicity. However, even if we include the pH controller’s efforts, the problem does not go away. As pH rises due to the premature addition of extra lime, the controller will try to reduce the lime feed rate. This will initially reduce the degree to which pH deviates from setpoint, but then the reverse problem will occur when the increased flocculant enters the vessel 55 seconds later. Now, the pH will drop below setpoint, and the feedback controller will have to ramp up lime addition (to the amount it was before the additional lime reached the vessel) to achieve setpoint.↩︎
1012. Let me know if you are ever able to invent such a thing. I’ll even pay your transportation costs to Stockholm, Sweden so you can collect your Nobel prize. Of course, I will demand to see the prize before buying tickets for your travel, but with your time-travel device that should not be a problem for you.↩︎
1013. For a more detailed discussion of lag times and their meaning, see section 30.1.5 beginning on page .↩︎
1014. Knowing this allows us to avoid measuring the incoming cold oil temperature and just measure incoming cold oil flow rate as the feedforward variable. If the incoming oil’s temperature were known to vary substantially over time, we would be forced to measure it as well as flow rate, combining the two variables together to calculate the energy demand and use this inferred variable as the feedforward variable.↩︎
1015. Transport delay (dead time) in heat exchanger systems can be a thorny problem to overcome, as they they tend to change with flow rate! For reasons of simplicity in our illustration, we will treat this process as if it only possessed lag times, not dead times.↩︎
1016. Technically, two cascaded lag times is not the same as one large lag time, no matter the time constant values. Two first-order lags in series with one another create a second-order lag, which is a different effect. However imperfect as the added lag solution is, it is still better than nothing at all!↩︎
1017. I generally suggest keeping such limit values inaccessible to low-level operations personnel. This is especially true in cases such as this where the presence of a high temperature setpoint limit is intended for the longevity of the equipment. There is a strong tendency in manufacturing environments to “push the limits” of production beyond values considered safe or expedient by the engineers who designed the equipment. Limits are there for a reason, and should not be altered except by people with full understanding of and full responsibility over the consequences!↩︎
1018. Only the coolant flow control instruments and piping are shown in this diagram, for simplicity. In a real P&ID, there would be many more pipes, valves, and other apparatus shown surrounding this process vessel.↩︎
1019. In order to understand how this works, I advise you try a “thought experiment” for each function block network whereby you arbitrarily assign three different numerical values for A, B, and C, then see for yourself which of those three values becomes the output value.↩︎
1020. In FOUNDATION Fieldbus, each and every signal path not only carries the signal value, but also a “status” flag declaring it to be “Good,” “Bad,” or “Uncertain.” This status value gets propagated down the entire chain of connected function blocks, to alert dependent blocks of a possible signal integrity problem if one were to occur.↩︎
1021. This principle holds true even for systems with no function blocks “voting” between the redundant transmitters. Perhaps the installation consists of two transmitters with remote indications for a human operator to view. If the two displays substantially disagree, which one should the operator trust? A set of three indicators would be much better, providing the operator with enough information to make an intelligent decision on which display(s) to trust.↩︎
1022. In most applications this takes the form of an AC induction motor receiving power from a Variable Frequency Drive or VFD. Since the rotational speed of an induction motor is a function of frequency, the VFD achieves motor speed control by electronically converting the fixed-frequency line power into variable-frequency power to drive the motor.↩︎
1023. Some differential pressure transmitter manufacturers, such as Bailey, apply the same convention to denote the actions of a DP transmitter’s two pressure ports: using a “+” label to represent direct action (i.e. increasing pressure at this port drives the output signal up) and a “$$-$$” symbol to represent reverse action (i.e. increasing pressure at this port drives the output signal down).↩︎
1024. For that matter, it is impossible to eliminate all danger from life in general. Every thing you do (or don’t do) involves some level of risk. The question really should be, “how much risk is there in a given action, and how much risk am I willing to tolerate?” To illustrate, there does exist a non-zero probability that something you will read in this book is so shocking it will cause you to suffer a heart attack. However, the odds of you walking away from this book and never reading it again over concern of epiphany-induced cardiac arrest are just as slim.↩︎
1025. Also humorously referred to as the “belt and suspenders” school of engineering.↩︎
1026. Frangible roofs are a common design applied to liquid storage tanks harboring the potential for overpressure, such as sulfuric acid storage tanks which may generate accumulations of explosive hydrogen gas. Having the roof seam rupture from overpressure is a far less destructive event than having a side seam or floor seam rupture and consequently spill large volumes of acid. This technique of mitigating overpressure risk does not work to reduce pressure in the system, but it does reduce the risk of damage caused by overpressure in the system.↩︎
1027. Chemical corrosiveness, biohazardous substances, poisonous materials, and radiation are all examples of other types of industrial hazards not covered by the label “hazardous” in this context. This is not to understate the danger of these other hazards, but merely to focus our attention on the specific hazard of explosions and how to build instrument systems that will not trigger explosions due to electrical spark.↩︎
1028. Article 506 is a new addition to the NEC as of 2008. Prior to that, the only “zone”-based categories were those specified in Article 505.↩︎
1029. The final authority on Class and Division definitions is the National Electrical Code itself. The definitions presented here, especially with regard to Divisions, may not be precise enough for many applications. Article 500 of the NEC is quite specific for each Class and Division combination, and should be referred to for detailed information in any particular application.↩︎
1030. Once again, the final authority on this is the National Electrical Code, in this case Article 505. My descriptions of Zones and Divisions are for general information only, and may not be specific or detailed enough for many applications.↩︎
1031. Traditionally, the three elements of a “fire triangle” were fuel, oxidizer, and ignition source. However, this model fails to account for fuels not requiring oxygen as well as cases where a chemical inhibitor prevents a self-sustaining reaction even in the presence of fuel, oxidizer, and ignition source.↩︎
1032. To illustrate this concept in a different context, consider my own personal history of automobiles. For many years I drove an ugly and inexpensive truck which I joked had “intrinsic theft protection:” it was so ugly, no one would ever want to steal it. Due to this “intrinsic” property of my vehicle, I had no need to invest in an alarm system or any other protective measure to deter theft. Similarly, the components of an intrinsically safe system need not be located in explosion-proof or purged enclosures because the intrinsic energy limitation of the system is protection enough.↩︎
1033. Real passive barriers often used redundant zener diodes connected in parallel to ensure protection against excessive voltage even in the event of a zener diode failing open.↩︎
1034. Of course, transformers cannot be used to pass DC signals of any kind, which is why chopper/converter circuits are used before and after the signal transformer to convert each DC current signal into a form of chopped (AC) signal that can be fed through the transformer. This way, the information carried by each 4-20 mA DC current signal passes through the barrier, but electrical fault current cannot.↩︎
1035. To be honest, the coin could also land on its edge, which is a third possibility. However, that third possibility is so remote as to be negligible in the presence of the other two. Strictly speaking, $$P(\hbox{heads''}) + P(\hbox{tails''}) + P(\hbox{edge''}) = 1$$.↩︎
1036. In his excellent book, Reliability Theory and Practice, Igor Bazovsky describes the relationship between true probability ($$P$$) calculated from ideal values and estimated probability ($$\hat P$$) calculated from experimental trials as a limit function: $$P = \lim_{N \to \infty} \hat P$$, where $$N$$ is the number of trials.↩︎
1037. Most people can recall instances where a weather forecast proved to be completely false: a prediction for rainfall resulting in a completely dry day, or vice-versa. In such cases, one is tempted to blame the weather service for poor forecasting, but in reality it has more to do with the nature of probability, specifically the meaninglessness of probability calculations in predicting singular events.↩︎
1038. Here, “essential” means the system will fail if any of these identified components fails. Thus, Lusser’s Law implies a logical “AND” relationship between the components’ reliability values and the overall system reliability.↩︎
1039. According to Bazovsky (pp. 275-276), the first reliability principle adopted by the design team was that the system could be no more reliable than its least-reliable (weakest) component. While this is technically true, the mistake was to assume that the system would be as reliable as its weakest component (i.e. the “chain” would be exactly as strong as its weakest link). This proved to be too optimistic, as the system would still fail due to the failure of “stronger” components even when the “weaker” components happened to survive. After noting the influence of “stronger” components’ unreliabilities on overall system reliability, engineers somehow reached the bizarre conclusion that system reliability was equal to the mathematical average of the components’ reliabilities. Not surprisingly, this proved even less accurate than the “weakest link” principle. Finally, the designers were assisted by the mathematician Erich Pieruschka, who helped formulate Lusser’s Law.↩︎
1040. Here we have an example where dependability and security are lumped together into one “reliability” quantity.↩︎
1041. An easy way to remember what each of these terms mean in the context of a protective system is to associate $$D$$ (Dependability) with a dangerous scenario and $$S$$ (Security) with a safe scenario: $$D$$ expresses what the system or component will do when a dangerous condition presents itself to the protective system and it needs to act; $$S$$ expresses what the system or component will do when conditions are safe and there is no need to act.↩︎
1042. Since most high-quality industrial devices and systems are repairable for most faults, MTBF and MTTF are interchangeable terms.↩︎
1043. This does not mean the amount of time for all components to fail, but rather the amount of time to log a total number of failures equal to the total number of components tested. Some of those failures may be multiple for single components, while some other components in the batch might never fail within the MTBF time.↩︎
1044. The typically large values we see for MTBF and MTTF can be misleading, as they represent a theoretical time based on the failure rate seen over relatively short testing times where all components are “young.” In reality, the wear-out time of a component will be less than its MTBF. In the case of these control valves, they would likely all “die” of old age and wear long before reaching an age of 66.667 years!↩︎
1045. One could even imagine some theoretical component immune to wear-out, but still having finite values for failure rate and MTBF. Remember, $$\lambda_{useful}$$ and MTBF refer to chance failures, not the normal failures associated with age and extended use.↩︎
1046. Preventive maintenance is not the only example of such a dynamic. Modern society is filled with monetarily expensive programs and institutions existing for the ultimate purpose of avoiding greater costs, monetary and otherwise. Public education, health care, and national militaries are just a few that come to my mind. Not only is it a challenge to continue justifying the expense of a well-functioning cost-avoidance program, but it is also a challenge to detect and remove unnecessary expenses (waste) within that program. To extend the preventive maintenance example, an appeal by maintenance personnel to continue (or further) the maintenance budget may happen to be legitimate, but a certain degree of self-interest will always be present in the argument. Just because preventive maintenance is actually necessary to avoid greater expense due to failure, does not mean all preventive maintenance demands are economically justified! Proper funding of any such program depends on the financiers being fair in their judgment and the executors being honest in their requests. So long as both parties are human, this territory will remain contentious.↩︎
1047. Sustained vibrations can do really strange things to equipment. It is not uncommon to see threaded fasteners undone slowly over time by vibrations, as well as cracks forming in what appear to be extremely strong supporting elements such as beams, pipes, etc. Vibration is almost never good for mechanical (or electrical!) equipment, so it should be eliminated wherever reliability is a concern.↩︎
1048. On an anecdotal note, a friend of mine once destroyed his car’s engine, having never performed an oil or filter change on it since the day he purchased it. His poor car expired after only 70000 miles of driving – a mere fraction of its normal service life with regular maintenance. Given the type of car it was, he could have easily expected 200000 miles of service between engine rebuilds had he performed the recommended maintenance on it.↩︎
1049. Another friend of mine used to work as a traffic signal technician in a major American city. Since the light bulbs they replaced still had some service life remaining, they decided to donate the bulbs to a charity organization where the used bulbs would be freely given to low-income citizens. Incidentally, this same friend also instructed me on the proper method of inserting a new bulb into a socket: twisting the bulb just enough to maintain some spring tension on the base, rather than twisting the bulb until it will not turn farther (as most people do). Maintaining some natural spring tension on the metal leaf within the socket helps extend the socket’s useful life as well!↩︎
1050. Many components do not exhibit any relationship between load and lifespan. An electronic PID controller, for example, will last just as long controlling an “easy” self-regulating process as it will controlling a “difficult” unstable (“runaway”) process. The same might not be said for the other components of those loops, however! If the control valve in the self-regulating process rarely changes position, but the control valve in the runaway process continually moves in an effort to stabilize it at setpoint, the less active control valve will most likely enjoy a longer service life.↩︎
1051. This redundancy module has its own MTBF value, and so by including it in the system we are adding one more component that can fail. However, the MTBF rate of a simple diode network greatly exceeds that of an entire AC-to-DC power supply, and so we find ourselves at a greater level of reliability using this diode redundancy module than if we did not (and only had one power supply).↩︎
1052. Of course, this assumes good communication and proper planning between all parties involved. It is not uncommon for piping engineers and instrument engineers to mis-communicate during the crucial stages of process vessel design, so that the vessel turns out not to be configured as needed for redundant instruments.↩︎
1053. If a swirling fluid inside the vessel encounters a stationary baffle, it will tend to “pile up” on one side of that baffle, causing the liquid level to actually be greater in that region of the vessel than anywhere else inside the vessel. Any transmitter placed within this region will register a greater level, regardless of the measurement technology used.↩︎
1054. The father of a certain friend of mine has operated a used automobile business for many years. One of the tasks given to this friend when he was a young man, growing up helping his father in his business, was to regularly drive some of the cars on the lot which had not been driven for some time. If an automobile is left un-operated for many weeks, there is a marked tendency for batteries to fail and tires to lose their air pressure, among other things. The salespeople at this used car business jokingly referred to this as lot rot, and the only preventive measure was to routinely drive the cars so they would not “rot” in stagnation. Machines, like people, suffer if subjected to a lack of physical activity.↩︎
1055. A simple “memory trick” I use to correctly distinguish between relief and safety valves is to remember that a safety valve has snap action (both words beginning with the letter “s”).↩︎
1056. To illustrate, consider a (vertical) cylindrical storage tank 15 feet tall and 20 feet in diameter, with an internal gas pressure of 8 inches water column. The total force exerted radially on the walls of this tank from this very modest internal pressure would be in excess of 39000 pounds! The force exerted by the same pressure on the tank’s circular lid would exceed 13000 pounds (6.5 tons)!↩︎
1057. Think: a safety valve has snap action!↩︎
1058. This photograph courtesy of the National Transportation Safety Board’s report of the 1999 petroleum pipeline rupture in Bellingham, Washington. Improper setting of this relief valve pilot played a role in the pipeline rupture, the result of which was nearly a quarter-million gallons of gasoline spilling into a creek and subsequently igniting. One of the lessons to take from this event is the importance of proper instrument maintenance and configuration, and how such technical details concerning industrial components may have consequences reaching far beyond the industrial facility where those components are located.↩︎
1059. Many synonyms exist to describe the action of a safety system needlessly shutting down a process. The term “nuisance trip” is often (aptly) used to describe such events. Another (more charitable) label is “fail-to-safe,” meaning the failure brings the process to a safe condition, as opposed to a dangerous condition.↩︎
1060. Of course, there do exist industrial facilities operating at a financial loss for the greater public benefit (e.g. certain waste processing operations), but these are the exception rather than the rule. It is obviously the point of a business to turn a profit, and so the vast majority of industries simply cannot sustain a philosophy of safety at any cost. One could argue that a “paranoid” safety system even at a waste processing plant is unsustainable, because too many “false trips” result in inefficient processing of the waste, posing a greater public health threat the longer it remains unprocessed.↩︎
1061. As drawn, these valves happen to be ball-design, the first actuated by an electric motor and the second actuated by a pneumatic piston. As is often the case with redundant instruments, an effort is made to diversify the technology applied to the redundant elements in order to minimize the probability of common-cause failures. If both block valves were electrically actuated, a failure of the electric power supply would disable both valves. If both block valves were pneumatically actuated, a failure of the compressed air supply would disable both valves. The use of one electric valve and one pneumatic valve grants greater independence of operation to the double-block valve system.↩︎
1062. For what it’s worth, the ISA safety standard 84 defines this notation as “MooN,” but I have seen sufficient examples of the contrary (“NooM”) to question the authority of either label.↩︎
1063. For a general introduction to process switches, refer to chapter 9 beginning on page .↩︎
1064. Of course, the presence of some variation in a transmitter’s output over time is no guarantee of proper operation. Some failures may cause a transmitter to output a randomly “walking” signal when in fact it is not registering the process at all. However, being able to measure the continuous output of a process transmitter provides the instrument technician with far more data than is available with a discrete process switch. A safety transmitter’s output signal may be correlated against the output signal of another transmitter measuring the same process variable, perhaps even the transmitter used in the regulatory control loop. If two transmitters measuring the same process variable agree closely with one another over time, chances are extremely good are both functioning properly.↩︎
1065. It should be noted that the use of a single orifice plate and of common (parallel-connected) impulse lines represents a point of common-cause failure. A blockage at one or more of the orifice plate ports, or a closure of a manual block valve, would disable all three transmitters. As such, this might not be the best method of achieving high flow-measurement reliability.↩︎
1066. The best way to prove to yourself the median-selecting abilities of both function block networks is to perform a series of “thought experiments” where you declare three arbitrary transmitter signal values, then follow through the selection functions until you reach the output. For any three signal values you might choose, the result should always be the same: the median signal value is the one chosen by the voter.↩︎
1067. MTBF stands for Mean Time Between Failure, and represents the reliability of a large collection of components or systems. For any large batch of identical components or systems constantly subjected to ordinary stresses, MTBF is the theoretical length of time it will take for 63.2% of them to fail based on ordinary failure rates within the lifetime of those components or systems. Thus, MTBF may be thought of as the “time constant” ($$\tau$$) for failure within a batch of identical components or systems.↩︎
1068. This is assuming, of course, that there are no air leaks anywhere in the actuator, tubing, or solenoid which would cause the trapped pressure to decrease over time.↩︎
1069. Of course, if there is opportunity to fully stroke the safety valve to the point of process shutdown without undue interruption to production, this is the superior way of performing valve proof tests. Such “test-to-shutdown” proof testing may be scheduled at a time convenient to operations personnel, such as at the beginning of a planned process shutdown.↩︎
1070. Probability is a quantitative measure of a particular outcome’s likelihood. A probability value of 1, or 100%, means the outcome in question is certain to happen. A probability value of 0 (0%) means the outcome is impossible. A probability value of 0.3 (30%) means it will happen an average of three times out of ten.↩︎
1071. Lusser’s Law of Reliability states that the total reliability of a system dependent on the function of several independent components is the mathematical product of those components’ individual reliabilities. For example, a system with three essential components, each of those components having an individual reliability value of 70%, will exhibit a reliability of only 34.3% because $$0.7 \times 0.7 \times 0.7 = 0.343$$. This is why a safety function may utilize a pressure transmitter rated for use in SIL-3 applications, but exhibit a much lower total SIL rating due to the use of an ordinary final control element.↩︎
1072. Yes, maintenance and operations personnel alike are often tempted to bypass the purge time of a burner management system out of impatience and a desire to resume production. I have personally witnessed this in action, performed by an electrician with a screwdriver and a “jumper” wire, overriding the timing function of a flame safety system during a troubleshooting exercise simply to get the job done faster. The electrician’s rationale was that since the burner system was having problems lighting, and had been repeatedly purged in prior attempts, the purge cycle did not have to be full-length in subsequent attempts. I asked him if he would feel comfortable repeating those same words in court as part of the investigation of why the furnace exploded. He didn’t think this was funny.↩︎
1073. Boiling-water reactors (BWR), the other major design type in the United States, output saturated steam at the top rather than heated water. Control rods enter a BWR from the bottom of the pressure vessel, rather than from the top as is standard for PWRs.↩︎
1074. Other means of reactor shutdown exist, such as the purposeful injection of “neutron poisons” into the coolant system which act as neutron-absorbing control rods on a molecular level. The insertion of “scram” rods into the reactor, though, is by far the fastest method for quenching the chain-reaction.↩︎
1075. This appears courtesy of the Nuclear Regulatory Commission’s special inquiry group report following the accident at Three Mile Island, on page 159.↩︎
1076. The term isotope refers to differences in atomic mass for any chemical element. For example, the most common isotope of the element carbon (C) has six neutrons and six protons within each carbon atom nucleus, giving that isotope an atomic mass of twelve ($$^{12}$$C). A carbon atom having two more neutrons in its nucleus would be an example of the isotope $$^{14}$$C, which just happens to be radioactive: the nucleus is unstable, and will over time decay, emitting energy and particles and in the process change into another element.↩︎
1077. It is noteworthy that $$^{238}$$U can be converted into a different, fissile element called plutonium through the process of neutron bombardment. Likewise, naturally-occurring thorium 232 ($$^{232}$$Th) may be converted into $$^{233}$$U which is fissile. However, converting non-fissile uranium into fissile plutonium, or converting non-fissile thorium into fissile uranium, requires intense neutron bombardment at a scale only seen within the core of a nuclear reactor running on some other fuel such as $$^{235}$$U, which makes $$^{235}$$U the critical ingredient for any independent nuclear program.↩︎
1078. Power reactors using “heavy” water as the moderator (such as the Canadian “CANDU” design) are in fact able to use uranium at natural $$^{235}$$U concentration levels as fuel, but most of the power reactors in the world do not employ this design.↩︎
1079. The formula weight for UF$$_{6}$$ containing fissile $$^{235}$$U is 349 grams per mole, while the formula weight for UF$$_{6}$$ containing non-fissile $$^{238}$$U is only slightly higher: 352 grams per mole. Thus, the difference in mass between the two molecules is less than one percent.↩︎
1080. By some estimates, gas centrifuge enrichment is 40 to 50 times more energy efficient than gaseous diffusion enrichment.↩︎
1081. A typical gas centrifuge’s mass flow rating is on the order of milligrams per second. At their very low (vacuum) operating pressures, a typical centrifuge rotor will hold only a few grams of gas at any moment in time.↩︎
1082. Three major factors influence the efficiency of a gas centrifuge: rotor wall speed, rotor length, and gas temperature. Of these, rotor wall speed is the most influential. Higher speeds separate isotopes more effectively, because higher wall speeds result in greater amounts of radial acceleration, which increases the amount of centrifugal force experienced by the gas molecules. Longer rotors also separate isotopes more effectively because they provide more opportunity for the counter-flowing gas streams to separate lighter molecules toward the center and heavier molecules toward the wall. Higher temperatures reduce separation efficiency, because gas molecules at higher temperatures are more mobile and therefore diffuse (i.e. mix together) at higher rates. Therefore, the optimum gas centrifuge design will be long, spin as fast as possible, and operate as cool as possible.↩︎
1083. To give you an idea of just how long some gas centrifuge rotors are, the units built for the US Department of Energy facility in Ohio used rotors 40 feet in length!↩︎
1084. This means the hollow casing exists in a state of vacuum, with no air or other gases present. This is done in order to help thermally insulate the rotor from ambient conditions, as well as avoid generating heat from air friction against the rotor’s outside surface. Remember, elevated temperatures cause the gas to diffuse at a faster rate, which in turn causes the gas to randomly mix and therefore not separate into light and heavy isotopes as intended.↩︎
1085. The term zero-day in the digital security world refers to vulnerabilities that are unknown to the manufacturer of the software, as opposed to known vulnerabilities that have been on record with the manufacturer for some time. The fact that Stuxnet 1.x employed no less than four zero-day Windows exploits strongly suggests it was developed by an agency with highly sophisticated resources. In other words, Stuxnet 1.x wasn’t made by amateurs. This is literally world-class hacking in action!↩︎
1086. Consider what forms of sabotage striking employees might be willing to do in order to gain leverage at the bargaining table.↩︎
1087. Before you laugh at the idea of losing one’s own body, consider something as plausible as a fingerprint scanner programmed to accept the image of al fingers on one hand, and then that user suffering an injury to one of the fingers on that hand either obscuring the fingerprint or destroying the finger entirely.↩︎
1088. For the curious, iptables is an administration-level utility application for Linux operating systems, used to edit the ACL rulebase of the operating system’s built-in software firewall. Each line of text in these examples is a command that may be typed manually at the command-line interface of the operating system, or more commonly written to a script file to be automatically read and executed upon start-up of the computer. The -A option instructs iptables to Append a new rule to the ACL. These rules are organized into groups called “chains” which are given names such as INPUT and OUTPUT. While the specific format of ACL rules are unique to each firewall, they share many common features.↩︎
1089. No device connected directly to the internet should bear an IP address within any of these three ranges, and therefore any data packets received from devices with such an address is immediately suspect.↩︎
1090. If a TCP-capable device receives too many SYN (“synchronize”) messages in rapid succession, it may lock up and refuse to accept any others.↩︎
1091. These external computers are called clients, and in this network could include the office workstations as well as workstation PCs at corporate headquarters and the regional manager’s office.↩︎
1092. Data Historians have existed in Distributed Control Systems (DCSs) for many years, and in fact pre-date DMZs. Their purpose during those halcyon days prior to network security concerns was to provide operations and maintenance personnel with long-term data useful for running the process and diagnosing a range of problems. DCS controllers are typically limited in memory, and simply cannot archive the vast quantities of process data capable within a general-purpose computer. Their function in modern times as part of an industrial control system DMZ is simply an extension of their original purpose.↩︎
1093. Like all tools, VPN must be used with care. What follows is a cautionary tale. A controls engineer was hired to do PLC programming at an industrial facility, and the technical staff there insisted he connect his portable computer to the facility’s PLC network via a VPN so that he could work via the internet. This limited his need to be on-site by ensuring he could securely upload, edit, and download code to PLC systems from any location. After completing the job and traveling to a different client to do more PLC programming work, this engineer accidently logged into the old client’s VPN and placed one of their operating PLCs in Stop mode, causing a loss of control on a major process there, hundreds of miles away from where he was. Apart from the lesson of carefully checking login parameters when initiating a VPN connection, this example shows just how vulnerable some industrial control systems are and how over-confident some people are in tools such as VPN to protect their digital assets! Just because a VPN promises secure communication does not mean it is therefore safe to allow low-level access to control system components along public networks.↩︎
1094. An example of this strategy in action is an internet-connected personal computer system I once commissioned, running the Linux operating system from a DVD-ROM optical disk rather than a magnetic hard drive. The system would access the optical disk upon start-up to load the operating system kernel into its RAM memory, and then access the disk as needed for application executable files, shared library files, and other data. The principal use of this system was web browsing, and my intent was to make the computer as “hacker-proof” as I possibly could. Since the operating system files were stored on a read-only optical disk, it was impossible for an attacker to modify that data without having physical access to the machine. In order to thwart attacks on the data stored in the machine’s RAM memory, I configured the system to automatically shut down and re-start every day at an hour when no one would be using it. Every time the computer re-booted, its memory would be a tabula rasa (“clean slate”). Of course, this meant no one could permanently store downloaded files or other data on this machine from the internet, but from a security perspective that was the very point.↩︎
1095. Consider the very realistic scenario of logging in as administrator (or “root” in Unix systems) and then opening an email message which happens to carry an attached file infected with malware. Any file executed by a user is by default run at that user’s level of privilege because the operating system assumes that is the user’s intent.↩︎
1096. Telnet is a legacy software utility used to remotely access command-line computer operating systems. Inherently unsecure, telnet exchanges login credentials (user name and password) unencrypted over the network connection. A modern replacement for telnet is SSH (Secure SHell).↩︎
1097. I am reminded of an example from the world of “smart” mobile telephones, commonly equipped with accelerometer sensors for detecting physical orientation. Accelerometers detect the force of acceleration and of gravity, and are useful for a variety of convenient “apps” having nothing to do with telephony. Smart phone manufacturers include such sensors in their mobile devices and link those sensors to the phone’s operating system because doing so permits innovative applications, which in turn makes the product more desirable to application developers and ultimately consumers. It was discovered, though, that the signals generated by these accelerometers could be used to detect “keystrokes” made by the user, the sensors picking up vibrations made as the user taps their finger against the glass touch-screen of the smart phone. With the right signal processing, the accelerometers’ signals could be combined in such a way to identify which characters the user was tapping on the virtual keyboard, and thereby eavesdrop on their text-based communications!↩︎
1098. An example of this is where a piece of obsolete industrial software runs on the computer’s operating system, for example a data acquisition program or data-analysis program made by a company that no longer exists. If this specialized software was written to run on a particular operating system, and no others, future versions of that operating system might not permit proper function of that specialized software. I have seen such cases in industry, where industrial facilities continue to run obsolete (unsupported) operating systems in order to keep running some specialized industrial software (e.g. PLC programming editors), which is needed to operate or maintain some specialized piece of control hardware which itself is obsolete but still functions adequately for the task. In order to upgrade to a modern operating system on that computer (e.g. an obsolete version of Microsoft Windows), one must upgrade the specialized software (e.g. the PLC programming editor software), which in turn would mean upgrading the control hardware (e.g. the PLCs themselves). All of this requires time and money, much more than just what is required to upgrade the operating system software itself.↩︎
1099. As a case in point, there are still a great many industrial computers running Microsoft Windows XP at the time of this writing (2016), even though this operating system is no longer supported by Microsoft. This means no more Service Pack upgrades from Microsoft, security patches, or even research on vulnerabilities for this obsolete operating system. All users of Windows XP are “on their own” with regard to cyber-attacks.↩︎
1100. This raises a potential problem from the perspective of outside technical support, since such support often entails contracted or manufacturer-employed personnel entering the site and using their work computers to perform system configuration tasks. For any organization implementing a strong security access policy, this point will need to be negotiated into every service contract to ensure all the necessary pieces of hardware and software exist “in-house” for the service personnel to use while on the job.↩︎
1101. With $$R_2$$ dropping zero voltage, test point B is now essentially common to the node at the top of the bridge circuit. With test point A already common with the lower terminal of $$R_1$$ and now test point B common to the upper terminal of $$R_1$$, $$V_{out}$$ is exactly the same as $$V_{R1}$$.↩︎
1102. As before, the limiting case of a thermistor fault causes test points A and B to become synonymous with the terminals of one of the remaining resistors, in this case $$R_3$$. Since point A is already common with the upper terminal of $$R_3$$ and the shorted fault has now made point B common with the lower terminal of $$R_3$$, $$V_{out}$$ must be exactly the same as $$V_{R3}$$.↩︎
1103. Other possible tests include inspecting the LED status light on that PLC output card channel (a light indicates the HMI and PLC program are working correctly, and that the problem could lie within the output card or beyond to the motor) or measuring voltage at the drive output (voltage there indicates the problem must lie with the motor or the cable to the motor rather than further back).↩︎
1104. As a child, I often watched episodes of the American science-fiction television show Star Trek, in which the characters made frequent use of a diagnostic tool called a tricorder. Week after week the protagonists of this show would avoid trouble and solve problems using this nifty device. The sonic screwdriver was a similar tool in the British science-fiction television show Doctor Who. Little did I realize while growing up that my career would make just as frequent use of another diagnostic tool: the electrical multimeter.↩︎
1105. I honestly considered naming this section “Stupid Multimeter Tricks,” but changed my mind when I realized how confusing this could be for some of my readers not familiar with colloquial American English.↩︎
1106. I have personally measured “phantom” voltages in excess of 100 volts AC, in systems where the source voltage was 120 volts AC.↩︎
1107. Before there was such an accessory available, I used a 20 k$$\Omega$$ high-power resistor network connected in parallel with my DMM’s input terminals, which I fabricated myself. It was ugly and cumbersome, but it worked well. When I made this, I took great care in selecting resistors with power ratings high enough that accidental contact with a truly “live” AC power source (up to 600 volts) would not cause damage to them. A pre-manufactured device such as the Fluke SV225, however, is a much better option.↩︎
1108. These are AC voltages having frequencies that are integer-multiples of the fundamental powerline frequency. In the United States, where 60 Hz is standard, harmonic frequencies would be whole-number multiples of 60: 120 Hz, 180 Hz, 240 Hz, 300 Hz, etc.↩︎
1109. There is a design reason for this. Most digital multimeters are designed to be used on semiconductor circuits, where the minimum “turn-on” voltage of a silicon PN junction is approximately 500 to 700 millivolts. The diode-check function must output more than that, in order to force a PN junction into forward conduction. However, it is useful to be able to check ohmic resistance in a circuit without activating any PN junctions, and so the resistance measurement function typically uses test voltages less than 500 millivolts.↩︎
1110. Since we get to choose whatever $$k$$ value we need to make this an equality, we don’t have to keep $$k$$ inside the radicand, and so you will usually see the equation written as it is shown in the last step with $$k$$ outside the radicand.↩︎
1111. In engineering, this goes by the romantic name of swamping. We say that the overshadowing effect “swamps” out all others because of its vastly superior magnitude, and so it is safe (not to mention simpler!) to ignore the smaller effect(s). The most elegant cases of “swamping” are when an engineer intentionally designs a system so the desired effect is many times greater than the undesired effect(s), thereby forcing the system to behave more like the ideal. This application of swamping is prevalent in electrical engineering, where resistors are often added to circuits for the purpose of overshadowing the effects of stray (undesirable) resistance in wiring and components.↩︎
1112. To be sure, there are some gifted lecturers in the world. However, rather than rely on a human being’s live performance, it is better to capture the brilliance of an excellent presentation in static form where it may be peer-reviewed and edited to perfection, then placed into the hands of an unlimited number of students in perpetuity. In other words, if you think you’re great at explaining things, do us all a favor and translate that brilliance into a format capable of reaching more people!↩︎
1113. It would be arrogant of me to suggest my book is the best source of information for your students. Have them research information on instrumentation from other textbooks, from manufacturers’ literature, from whitepapers, from reference manuals, from encyclopedia sets, or whatever source(s) you deem most appropriate. If you possess knowledge that your students need to know that isn’t readily found in any book, publish it for everyone’s benefit!↩︎
1114. And multimedia resources, too! With all the advances in multimedia presentations, there is no reason why an instructor cannot build a library of videos, computer simulations, and other engaging resources to present facts and concepts to students outside of class time.↩︎
1115. Any instructor who can be replaced with a book or a video should be replaced by a book or a video!↩︎
1116. Of course, we had to have plenty of instruments to install in this loop system, and industrial instruments are not cheap. My point is that the infrastructure of control panel, trunk cabling, field wiring, terminal blocks, etc. was very low-cost. If an Instrumentation program already has an array of field instruments for students to work with in a lab setting, it will not cost much at all to integrate these instruments into a realistic multi-loop system as opposed to having students work with individual instruments on the benchtop or installed in dedicated “trainer” modules.↩︎
1117. When I built my first fully-fledged educational loop system in 2006 at Bellingham Technical College in Washington state (I built a crude prototype in 2003), I opted for Cooper B-Line metal strut because it seemed the natural choice for the application. It wasn’t until 2009 when I needed to expand and upgrade the loop system to accommodate more students that I happened to come up with the idea of using pallet racking as the framework material. Used pallet racking is plentiful, and very inexpensive compared to building a comparable structure out of metal strut. As these photographs show, I still used Cooper B-Line strut for some portions, but the bulk of the framework is simply pallet racking adapted for this unconventional application.↩︎
1118. One of the reasons diagnostic skill is so highly prized in industry is because so few people are actually good at it. This is a classic case of supply and demand establishing the value of a commodity. Demand for technicians who know how to troubleshoot will always be high, because technology will always break. Supply, however, is short because the skill is difficult to teach. This combination elevates the value of diagnostic skill to a very high level.↩︎
1119. Yes, I have actually heard people make this claim!↩︎
1120. The infamous “divide and conquer” strategy of troubleshooting where the technician works to divide the system into halves, isolating which half the problem is in, is but one particular procedure: merely one tool in the diagnostician’s toolbox, and does not constitute the whole of diagnostic method.↩︎
1121. Other things could be at fault. An “open” test lead on the multimeter for example could account for both the zero-current measurement and the zero-voltage measurement. This scientific concept eludes many people: it is far easier to disprove an hypothesis than it is to prove one. To quote Albert Einstein, “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”↩︎
1122. Jammed turbine wheel in flowmeter, failed pickup coil in flowmeter, open wire in cable FT-112 or pair 1 of cable 3 (assuming the flow controller’s display was not configured to register below 0% in an open-loop condition), etc.↩︎
1123. I must confess to having a lot of fun here. Sometimes I even try to describe the problem incorrectly. For instance, if the problem is a huge damping constant, I might tell the student that the instrument simply does not respond, because that it what it looks like it you do not take the time to watch it respond very slowly.↩︎
1124. The instructor may opt to step away from the group at this time and allow the student to proceed unsupervised for some time before returning to observe.↩︎
1125. I distinctly remember a time during my first assignment as an industrial instrument technician that I had to troubleshoot a problem in a loop where the transmitter was an oxygen analyzer. I had no idea how this particular analyzer functioned, but I realized from the loop documentation that it measured oxygen concentration and output a signal corresponding to the percentage concentration (0 to 21 percent) of O$$_{2}$$. By subjecting the analyzer to known concentrations of oxygen (ambient air for 21%, inert gas for 0%) I was able to determine the analyzer was responding quite well, and that the problem was somewhere else in the system. If the analyzer had failed my simple calibration test, I would have known there was something wrong with it, which would have led me to either get help from other technicians working at that facility or simply replace the analyzer with a new unit and try to learn about and repair the old unit in the shop. In other words, my ignorance of the transmitter’s specific workings did not prevent me from diagnosing the loop in general.↩︎
1126. Anyone can (eventually) find a fault if they check every detail of the system. Randomly probing wire connections or aimlessly searching through a digital instrument’s configuration is not troubleshooting. I have seen technicians waste incredible amounts of time on the job randomly searching for faults, when they could have proceeded much more efficiently by taking a few multimeter measurements and/or stimulating the system in ways revealing what and where the problem is. One of your tasks as a technical educator is to discourage this bad habit by refusing to tolerate random behavior during a troubleshooting exercise!↩︎
1127. It should be noted that some incentive ought to be built in to the mastery exams, or else students will tend to not study for them (knowing they can always retest with no penalty). This incentive may take the form of time (e.g. mastery re-takes compete for time needed to complete other coursework) and/or take the form of a percentage score awarded on each student’s first attempt on that exam.↩︎
1128. This latter concept is called the mesh hypothesis: that learning is enhanced when one’s learning style meshes well with instruction given in that style↩︎
1129. You cannot pass my original work to anyone else under different terms or conditions than the Attribution license. That is called sublicensing, and the Attribution license forbids it. In fact, any re-distribution of my original work must come with a notice to the Attribution license, so anyone receiving the book through you knows their rights.↩︎
• Share
Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License | 2021-04-13T19:27:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4803835451602936, "perplexity": 2469.2989798199987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038074941.13/warc/CC-MAIN-20210413183055-20210413213055-00345.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu3ast/sec_cu3ast_proc/ssec_cu3ast_proc_iter.html | # 3.4.5 Iteration strategy and convergence
Author(s): Alex Bombrun, David Hobbs
AGIS is a hybrid iterative solver with a ‘simple iteration’ (SI) scheme that was the starting point for a long development towards a fully functional scheme with much improved convergence properties. The main stages in this development were the ‘accelerated simple iteration’ (ASI), the conjugate gradients (CG), and finally the fully flexible ‘hybrid scheme’ (SI–CG) to be used in the final implementation of AGIS. As much of this development has at most historical interest, only a brief outline is given here.
Already in the very early implementation of the simple iteration scheme it was observed that convergence was slower than (naively) expected, and that after some iterations, the updates always seemed to go in the same direction, forming a geometrically (exponentially) decreasing series. This behaviour was very easily understood: the persistent pattern of updates is roughly proportional to the eigenvector of the largest eigenvalue of the iteration matrix, and the (nearly constant) ratio of the sizes of successive updates is the corresponding eigenvalue. From this realization it was natural to test an acceleration method based on a Richardson-type extrapolation of the updates. The idea is simply that if the updates in two successive iterations are roughly proportional to each other, $\boldsymbol{d}^{(k+1)}\simeq\lambda\boldsymbol{d}^{(k)}$, with $|\lambda|<1$, then we can infer that the next update is again a factor $\lambda$ smaller than $\boldsymbol{d}^{(k+1)}$, and so on. The sum of all the updates after iteration $k$ can therefore be estimated as $\boldsymbol{d}^{(k+1)}+\lambda\boldsymbol{d}^{(k+1)}+\lambda^{2}\boldsymbol{d}% ^{(k+1)}+\dots=(1-\lambda)^{-1}\boldsymbol{d}^{(k+1)}$. Thus, in iteration $k+1$ we apply an acceleration factor $1/(1-\lambda)$ based on the current estimate of the ratio $\lambda$. This accelerated simple iteration (ASI) scheme is seen to be a variant of the well-known successive over-relaxation method (Axelsson 1996). The factor $\lambda$ is estimated by statistical analysis of the parallax updates for a small fraction of the sources; the parallax updates are used for this analysis, since they are unaffected by a possible change in the frame orientation between successive iterations. With this simple device, the number of iterations for full convergence was reduced roughly by a factor 2.
Both the simple iteration and the accelerated simple iteration belongs to a much more general class of solution methods known as Krylov subspace approximations. The sequence of updates $\boldsymbol{d}^{(k)}$, $k=0\dots K-1$ generated by the first $K$ simple iterations constitute the basis for the $K$-dimensional subspace of the solution space, known as the Krylov subspace for the given matrix and right-hand side (e.g., Greenbaum (1997); van der Vorst (2003)). Krylov methods compute approximations that, in the $k$th iteration, belongs to the $k$-dimensional Krylov subspace. But whereas the simple and accelerated iteration schemes, in the $k$th iteration, use updates that are just proportional to the $k$th basis vector, more efficient algorithms generate approximations that are (in some sense) optimal linear combinations of all $k$ basis vectors. Conjugate gradients (CG) is one of the best-known such methods, and possibly the most efficient one for general symmetric positive-definite matrices (e.g., Axelsson (1996); Björck (1996); van der Vorst (2003)). Its implementation within the AGIS framework is more complicated, but has been considered in detail by Bombrun et al. (2012). As it provides significant advantages over the SI and ASI schemes in terms of convergence speed, this algorithm has been chosen as the baseline method for the astrometric core solution of Gaia (see below however). From practical experience, we have found that CG is roughly a factor 2 faster than ASI, or a factor 4 faster than the SI scheme. Like SI, the CG algorithm uses a preconditioner and can be formulated in terms of the S, A, C and G blocks, so the subsequent description of these blocks remains valid. In the terminology of Bombrun et al. (2012) the process of solving the preconditioner system $\boldsymbol{K}\boldsymbol{d}=\boldsymbol{b}$ is the kernel operation common to all these solution methods, which only differ in how the updates are applied according to the various iteration schemes. The main difference compared with the simple iteration scheme is that the updates suggested by the preconditioner are modified in view of the previous updates to optimize the convergence in a certain sense (for details, see Bombrun et al. (2012)).
The CG algorithm assumes that the normal matrix is constant in the course of the iterations. This is not strictly true if the observation weights are allowed to change as functions of the residuals, as will be required for efficient outlier elimination. Using the CG algorithm together with the weight-adjustment scheme described below could therefore lead to instabilities, i.e., a reduced convergence rate or even non-convergence. On the other hand, the SI scheme is extremely stable with respect to all such modifications in the course of the iterations, as can be expected from the interpretation of the SI scheme as the successive and independent application of the different solution blocks. The finally adopted algorithm is therefore a hybrid scheme combining SI (or ASI) and CG, where SI is used initially, until the weights have settled, after which CG is turned on. A temporary switch back to SI, with an optional re-adjustment of the weights, may be employed after a certain number of CG iterations; this could avoid some problems due to the accumulation of numerical rounding errors in CG.
The convergence can be controlled using a web based monitor looking at the distribution of the residuals, at the distribution of the excess noise and at the distribution of the updates. | 2018-10-19T20:06:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 20, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7375372648239136, "perplexity": 441.7263616252931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512434.71/warc/CC-MAIN-20181019191802-20181019213302-00154.warc.gz"} |
https://www.idea.int/node/310867 | # 41. Are there limits on the amount a candidate can spend? - New Zealand
Country:
New Zealand
Question:
41. Are there limits on the amount a candidate can spend? | 2021-10-25T11:34:10 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9424800276756287, "perplexity": 4814.932366996326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587659.72/warc/CC-MAIN-20211025092203-20211025122203-00132.warc.gz"} |
https://par.nsf.gov/biblio/10345893-beyond-standard-model | K → μ+μ− beyond the standard model
A bstract We analyze the New Physics sensitivity of a recently proposed method to measure the CP-violating $$\mathcal{B}$$ B ( K S → μ + μ − ) ℓ =0 decay rate using K S − K L interference. We present our findings both in a model-independent EFT approach as well as within several simple NP scenarios. We discuss the relation with associated observables, most notably $$\mathcal{B}$$ B ( K L → π 0 $$\nu \overline{\nu}$$ ν ν ¯ ). We find that simple NP models can significantly enhance $$\mathcal{B}$$ B ( K S → μ + μ − ) ℓ =0 , making this mode a very promising probe of physics beyond the standard model in the kaon sector.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10345893
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
3
ISSN:
1029-8479
1. A bstract We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe − e − amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $$p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k)$$ p p 1 ′ p p 2 ′ W − k , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ( NN ) scattering in the 1 S 0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing themore »
2. A bstract We present a search for the dark photon A ′ in the B 0 → A ′ A ′ decays, where A ′ subsequently decays to e + e − , μ + μ − , and π + π − . The search is performed by analyzing 772 × 10 6 $$B\overline{B}$$ B B ¯ events collected by the Belle detector at the KEKB e + e − energy-asymmetric collider at the ϒ(4 S ) resonance. No signal is found in the dark photon mass range 0 . 01 GeV /c 2 ≤ m A ′ ≤ 2 . 62 GeV /c 2 , and we set upper limits of the branching fraction of B 0 → A ′ A ′ at the 90% confidence level. The products of branching fractions, $$\mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right)\times \mathrm{\mathcal{B}}{\left(A\prime \to {e}^{+}{e}^{-}\right)}^2$$ ℬ B 0 → A ′ A ′ × ℬ A ′ → e + e − 2 and $$\mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right)\times \mathrm{\mathcal{B}}{\left(A\prime \to {\mu}^{+}{\mu}^{-}\right)}^2$$ ℬ B 0 → A ′ A ′ × ℬ A ′ → μ + μ − 2 , have limits of the order of 10 − 8 dependingmore »
3. A bstract This article presents differential measurements of the asymmetry between $${\varLambda}_b^0$$ Λ b 0 and $${\overline{\varLambda}}_b^0$$ Λ ¯ b 0 baryon production rates in proton-proton collisions at centre-of-mass energies of $$\sqrt{s}$$ s = 7 and 8 TeV collected with the LHCb experiment, corresponding to an integrated luminosity of 3 fb − 1 . The $${\varLambda}_b^0$$ Λ b 0 baryons are reconstructed through the inclusive semileptonic decay $${\varLambda}_b^0$$ Λ b 0 → $${\varLambda}_c^{+}$$ Λ c + μ − $$\overline{\nu}$$ ν ¯ μ X . The production asymmetry is measured both in intervals of rapidity in the range 2 . 15 < y < 4 . 10 and transverse momentum in 2 < p T < 27 GeV/ c . The results are found to be incompatible with symmetric production with a significance of 5.8 standard deviations for both $$\sqrt{s}$$ s = 7 and 8 TeV data, assuming no CP violation in the decay. There is evidence for a trend as a function of rapidity with a significance of 4 standard deviations. Comparisons to predictions from hadronisation models in P ythia and heavy-quark recombination aremore »
4. A bstract We present measurements of the branching fractions for the decays B → Kμ + μ − and B → Ke + e − , and their ratio ( R K ), using a data sample of 711 fb − 1 that contains 772 × 10 6 $$B\overline{B}$$ B B ¯ events. The data were collected at the ϒ(4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The ratio R K is measured in five bins of dilepton invariant-mass-squared ( q 2 ): q 2 ∈ (0 . 1 , 4 . 0) , (4 . 00 , 8 . 12) , (1 . 0 , 6 . 0), (10 . 2 , 12 . 8) and ( > 14 . 18) GeV 2 /c 4 , along with the whole q 2 region. The R K value for q 2 ∈ (1 . 0 , 6 . 0) GeV 2 /c 4 is $${1.03}_{-0.24}^{+0.28}$$ 1.03 − 0.24 + 0.28 ± 0 . 01. The first and second uncertainties listed are statistical and systematic, respectively. All results for R K are consistent with Standard Model predictions. Wemore »
We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu$$$B\to {D}^{\ast }\ell \nu$at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$${N}_{f}=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$$a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$$|{V}_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$$\left({V}_{\mathrm{cb}}\right)=\left(38.40±0.{68}_{\text{th}}±0.{34}_{\text{exp}}±0.{18}_{\text{EM}}\right)×{10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$${\chi }^{2}\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is inmore » | 2023-03-26T16:22:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8947688341140747, "perplexity": 1619.809874703131}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945473.69/warc/CC-MAIN-20230326142035-20230326172035-00244.warc.gz"} |
https://www.usgs.gov/center-news/ky-summer-2017-newsletter | Release Date:
Highlights of the USGS activities and water-related science going on at the Indiana-Kentucky Water Science Center and some of our amazing scientists that work for the USGS.
SAVE THE DATE.....The IN-KY WSC Annual Cooperators and Science Showcase will be October 24 in Indianapolis and October 26 in Louisville. Please plan to attend.
USGS’s FY2018 Budget
Just thought I would give you an update on our proposed budget for FY18. The President’s fiscal year (FY) 2018 budget request provides $922 million for USGS, a reduction of$163 million, or 15%, from our FY 2017 enacted level. The budget proposal reflects the new Administration’s commitment to reducing the size of the Federal Government and increasing efficiency to support national objectives and priorities. The budget proposal underscores a continuing commitment to our core mission that aligns with Administration priorities and focuses on conducting leading-edge research and providing impartial scientific data to stakeholders and decision-makers that promotes national health, safety, and prosperity. Scientific integrity is the USGS cornerstone, and we will maintain our commitment to excellence as we explore more efficient ways to do business. We will continue to work with our stakeholders and Congress to highlight the role USGS science plays in addressing a wide range of policy issues. It is important that we continue to educate policymakers about our mission and capabilities as they make decisions about the allocation of scarce resources. Funding reductions across the spectrum of our federal partners will very likely reduce reimbursable dollars the USGS receives.
The graph (to the left) shows the loss of buying power USGS funding has in present dollars and that our proposed budget is back to FY2002 levels. The USGS will continue to conduct studies and assessments for our Nation’s energy, minerals, water resources, natural hazards, and ecosystems to support economic growth, land and water stewardship, environmental protection, national security, and public safety.
Jeff Frey, IN-KY Deputy Director presenting Les with his USGS award at the Indianapolis office
USGS Award Winner
Congratulations to former Indiana Water Science Center employee Leslie D. Arihood who was selected for the U.S. Geological Survey’s Dallas Peck Outstanding Scientist Emeritus Award. This award recognizes significant contributions to the USGS mission by an individual while volunteering as a Scientist Emeritus. Les was co-author on the USGS report: “Maps of hydrogeologic information created from standardized water-well drillers’ records of the glaciated United States”: U.S. Geological Survey Scientific Investigations Report 2015–5105, 34 p.
Employee Spotlight
Angie Crain is a Hydrologist with the U.S. Geological Survey (USGS) Indiana-Kentucky Water Science Center (IN-KY) in Louisville, KY. Angie began her professional career with the USGS in 1995 as a student intern in the Louisville Office working on water- quality projects. Since that time, she has served as principal investigator of many water-quality projects at the national, state, and local levels.
In 2004, she began serving as the Water-Quality Specialist for the Kentucky Office and currently serves as the IN-KY QW Specialist for both the Indiana and Kentucky Offices. She also served 2 years with the USGS Office of Water Quality as the Acting USGS Water Science Field Team—Water- Quality Specialist providing technical assistance to water-quality projects throughout the southeastern United States.
Angie received a B.S. degree in Natural Resources and Environmental Science from Purdue University, and a M.S. degree in Aquatic Biology from the University of Louisville. Besides work activities, she enjoys participating in Boy Scout/Cub Scout activities with her sons, reading, and spending time with her family.
Molly Lott began working for the U.S. Geological Survey (USGS) in 2011 as an student intern at the Murray, KY field office. After graduating from Murray State University, with a degree in Environmental Geology, she accepted a full-time position as a Hydrologic Technician for the Indiana-Kentucky Water Science Center (IN-KY) Louisville, KY office.
Molly is the Field Team Lead for four “Super Gage” sites, as well as two National Water Quality Network (NWQN) sites, --Wabash River at New Harmony, Indiana and Ohio River at Cannelton, Indiana. Additionally, Molly oversees the installation, operation, management and data collection for Kentucky’s Continuous Water Quality network. Molly has been involved in the collection of discrete and continuous Water Quality and Surface Water data for projects outside of the gaging network that has allowed her to gain a wide range of field experience. Although Molly’s career focus has taken an emphasis in water quality, one of the things she loves most about working for the USGS is the variety of work and new challenges it constantly brings.
Moving forward, Molly wants to continue to develop her leadership skills and knowledge of water quality and quantity issues through data interpretation. She also plans to help increase public knowledge of the USGS and the important work we do through public outreach, volunteering in the local community and environmental education.
Katrina Gelwick has been a Hydrologic Technician at the Indiana-Kentucky Water Science Center (IN-KY), Indianapolis office since 2015.
Working in the Hydrologic Networks Section, she spends much of her time in the field gathering surface water data and maintaining Indiana’s world-class network of streamgages. During her time with IN-KY, she has been given many opportunities to expand her knowledge and skills in surface-water and groundwater monitoring and looks forward to learning more as her career advances.
Katrina began her career with the USGS in 2012 as an intern in the Volcano Hazards Program in Menlo Park, CA. Under the mentorship of Dr. Steve Ingebritsen, she participated in a monitoring campaign to gather long- term hydrothermal data at high-risk volcanoes throughout the Cascade Volcanic Arc. Her involvement in this project gave her invaluable experience in data management and analysis and introduced her to the joys of rigorous fieldwork. She wrapped up her internship in 2014 with her undergraduate thesis quantifying heat flow at California’s Medicine Lake Volcano.
After graduating, Katrina spent a year teaching students and supporting faculty in geographic information systems (GIS)-driven research at her alma mater, Oberlin College. From there, she found her way back to the USGS through the IN-KY Water Science Center, where she will be working until this summer.
Katrina will be relocating with her two cats in July 2017 to Lehigh University in Pennsylvania to begin her studies in a master's program in fluvial and tectonic geomorphology.
While she is sorry to be moving away from her IN-KY family, she is happy to be maintaining her personal ties with the Center and will continue to work remotely part-time as she completes her studies.
Dave Lampe has been a hydrologist in the Hydrologic Investigations Section at the Indiana-Kentucky Water Science Center (IN-KY) since 2003. Dave is the Center’s National Water Information System (NWIS) Database administrator. He currently leads a Great Lakes Restoration Initiative project that
is evaluating the water budget of “green infrastructure” designed to reduce the amount of stormwater contributed to sewers in Gary, Indiana. He coordinates the collection, quality assurance and reporting of water levels from the Indiana Volunteer Groundwater Monitoring Network in cooperation with partners at the Indiana Department of Natural Resources.
Originally from the St. Louis metro east area, Dave attended Belleville Area College (now Southwestern Illinois College) and earned an Associate degree in Pre–Engineering Science. Dave moved on to the University of Illinois at Urbana Champaign where he completed a Bachelor of Science degree in Geology. There he worked with the Illinois State Geological Survey Oil and Gas Section to develop a series of oil and gas well field maps. In 2001, Dave began his study of the geology and hydrology of Indiana in the Geology Department at Indiana University in Bloomington where he studied under Greg Olyphant. While at Indiana University, Dave worked at the Indiana Geological Survey’s Center for Geospatial Data Analysis. Dave graduated with his Master of Science degree in Geology in 2005.
Dave has used computer models to simulate the groundwater flow system and interactions with restored and natural wetlands and other surface water within the Indiana
Dunes National Lakeshore and adjacent areas. Those results are being used by the National Park Service and other agencies to understand how restored and modified wetlands, engineering modifications to groundwater and surface water drainage, and fluctuations of Lake Michigan levels affect groundwater levels and groundwater flooding in adjacent areas. He has completed reports to characterize the hydrostratigraphy of the Lake Michigan basin, compiled national-scale water quality datasets for the National Water Quality Assessment (NAWQA) Project Agricultural Chemical Transport (ACT) team, and managed data collection networks of groundwater monitoring wells within Indiana.
You can see more detail about Dave’s work at his USGS profile page.
National Water Quality Network Harmful Algal Bloom (HAB) Pilot Study
In collaboration with NWQN (National Water Quality Network) and the Kansas Water Science Center, the Indiana-Kentucky Water Science Center (IN-KY), Louisville Office will be collecting a series of discrete water quality samples this summer for a pilot study on HABS or Harmful Algal Blooms in large rivers. "Cyanobacterial harmful algal blooms (CyanoHABs) are increasingly a global concern because CyanoHABs pose a threat to human and ecosystem health and cause economic damages. Toxins produced by some species of cyanobacteria (cyanotoxins) can cause acute and chronic illnesses in humans. Human illnesses associated with cyanotoxins have most commonly occurred after exposure through recreational activities or drinking water. Recent national and regional assessments have shown that cyanotoxins are commonly detected in the Nation’s lakes, reservoirs, small streams, and wetlands. CyanoHAB events occur on large rivers. However, studies conducted on large rivers have been in response to CyanoHAB events and there has not been a comprehensive assessment of cyanotoxin occurrence in the Nation’s large rivers.
The specific objectives of the proposed pilot study are to:
• describe cyanotoxin occurrence
• "assess potential for CyanoHAB occurrence in the Nation’s large rivers using a combination of traditional and emerging approaches." – Graham, Rowe, & Dubrovsky
If the USGS sees significant budget cuts, unfortunately, this pilot study could be a very short-term assessment of the large river conditions.
For additional information on this topic, you may contact Molly Lott ([email protected]).
Indiana-Kentucky Water Science Center “Advancing the Science” using Unmanned Aerial Systems (UAS)
Subsurface agricultural drainage commonly referred to as “tile drains”, help to dry fields by providing a conduit through which soil water can rapidly move to nearby ditches or streams. This enables agricultural producers to access fields earlier in the spring and increases crop yields. Several counties report that subsurface drainage increased substantially around 2008 when corn prices were high. This increased drainage has the potential to significantly change local water-budgets by preventing soil-water from recharging groundwater. Additional concerns are the movement of nutrients and sediment to streams and changes to both the ecological and the human environment because of more rapid storm response and decreased baseflow in streams. However, the location and amount of tile drains installed remains a mystery as most tile systems are installed by farmers and remain undocumented. While visible imagery occasionally shows the tile drain network, planned data collection has proven more difficult and time consuming. The images (to the left), taken within 24 hours, indicate that thermal infrared imagery is successful at delineating the tile-drain network – clearly showing the subsurface drainage that can only be guessed at using the multi-spectral imagery. These images were used to ground truth the location of the tile drains and several tiles were found to have direct connections to the surface. These direct connections allow sediment and anything attached to the sediment such as phosphorus and pesticides to be rapidly transported to streams.
For additional information about the UAS program at the IN-KY WSC, contact Tanja Williamson ([email protected]) or Pete Cinotto ([email protected]).
Real-Time Groundwater Well Information expands in Indiana and Kentucky
The U.S. Geological Survey (USGS) measures more than 20,000 wells each year for a variety of objectives as part of federal programs and in cooperation with state and local agencies. Water- level data are collected using consistent data- collection and quality-control methods. A small subset of these wells meets the criteria necessary to be included in a “Climate Response Network” of wells designed to illustrate the response of the groundwater system to climate variations nationwide. In FY16, the Indiana-Kentucky Water Science Center (IN-KY WSC) added eight real-time sites to the Network supported by the USGS Groundwater Resources Program.
The primary purpose of the Climate Response Network is to portray the effect of climate on groundwater levels in unconfined aquifers or near surface confined aquifers that are minimally affected by pumping or other anthropogenic stresses. The Climate Response Network Web site, (https://groundwaterwatch.usgs.gov ) is the official USGS Web site for illustrating current ground-water conditions in the United States and Puerto Rico. The Climate Response Network “home” page provides a visual snapshot of the groundwater conditions across the Nation. Site locations and groundwater levels are depicted using color-coded symbols. The symbol defines the type of measurement (periodic, continuous, or real time), and the colors depict the relation between the most recent measurement and the monthly percentiles calculated from the long- term record for the well. Only symbols of wells having at least 10 years of measurements in a given month are color coded to ensure that the calculated percentiles are representative of historical conditions.
The USGS maintains a network of wells to monitor the effects of droughts and other climate variability on groundwater levels. The network consists of about 200 wells monitored that are fully funded by the USGS Groundwater and Streamflow Information Program, supplemented by funded wells in some states monitored from state, local, regional, and tribal partners with USGS Cooperative Matching Funds, or with funded wells from other federal partners.
The water-level changes in the Climate Response Network should primarily reflect climatic variability and not human influences. The climate variations of interest are those that affect recharge on monthly and longer time scales; not barometric or tidal influences.
New Real-Time Streamgages added to the IN-KY WSC Monitoring Network
Eight real-time streamgages were installed at several new locations across Indiana and Kentucky over the past 9 months. These new real-time streamgages were installed in cooperation with the Indiana Department of Transportation, Kentucky Division of Water (KDOW), and the U.S. Army Corps of Engineers (USACE).
Indiana
• 03360652 - Bee Hunter Ditch at Linton
• 033483827 - Big Duck Creek at 14th Street Park at Elwood
• 03361605 - Brandywine Creek at Greenfield
• 03348350 - Pipe Creek at Frankton
• 05523865 - Carpenter Creek at Remington
Kentucky
• 03299500 - Rolling Fork at New Haven
• 03435105 - Red River at Dot
• 03280790 - Trace Branch at Trace Branch Campground at Confluence
2017 IN-KY WSC Publication
• Bayless, E.R., Arihood, L.D., Reeves, H.W., Sperl, B.J.S., Qi, S.L., Stipe, V.E., and Bunch. A.R., 2017, Maps of hydrogeologic information created from standardized water- well drillers’ records of the glaciated United States: U.S. Geological Survey Scientific Investigations Report 2015– 5105, 34 p. [https://doi.org/10.3133/sir20155105]
• Fowler, K.K., 2017, Flood-inundation maps for the Big Blue River at Shelbyville, Indiana: U.S. Geological Survey Scientific Investigations Report 2016–5166, 11 p., [https://doi.org/10.3133/sir20165166]
• Lampe, D.C., and Unthank, M.D., 2016, Performance evaluation testing of wells in the gradient control system at a federally operated Confined Disposal Facility using single well aquifer tests, East Chicago, Indiana: U.S. Geological Survey Scientific Investigations Report 2016–5125, 50 p., [https://doi.org/10.3133/sir20165125]
• Martin, Z.W., 2017, Flood-inundation maps for the St. Joseph River at Elkhart, Indiana: U.S. Geological Survey Scientific Investigations Report 2016–5179, 10 p., [https://doi.org/10.3133/sir20165179]
• Risch, M.R., DeWild, J.F., Gay, D.A., Zhang, L., Boyer, E.W., and Krabbenhoft, D.P., 2017, Atmospheric Mercury Deposition to Forests in the Eastern USA: Environmental Pollution, v. 228, p. 8-18, [https://doi.org/10.1016/j.envpol.2017.05.004]
• Zhang, L.; Wu, Z.; Cheng, I.; Wright, L.P.; Olson, M.L.;Gay, D.; Risch, M.R.; Brooks, S.; Castro, M.S.; Conley, G.D.; Edgerton, E.S.; Holsen, T.M.; Luke, W.; Tordon, R.; and Weiss-Penzias, P., 2016, The estimated six-year mercury dry deposition across North America, Environmental Science and Technology, v. 50, no. 23, p. 12864-12873, [http://pubs.acs.org/doi/abs/10.1021/acs.est.6b04276] | 2020-02-28T03:24:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23061051964759827, "perplexity": 10851.088385778517}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146940.95/warc/CC-MAIN-20200228012313-20200228042313-00465.warc.gz"} |
http://dlmf.nist.gov/32.2 | # §32.2(i) Introduction
The six Painlevé equations $\mbox{P}_{\mbox{\scriptsize I}}$$\mbox{P}_{\mbox{\scriptsize VI}}$ are as follows:
32.2.1 $\frac{{d}^{2}w}{{dz}^{2}}=6w^{2}+z,$ Symbols: $\frac{df}{dx}$: derivative of $f$ with respect to $x$ and $z$: real Referenced by: §32.11(i), §32.11(i) Permalink: http://dlmf.nist.gov/32.2.E1 Encodings: TeX, pMML, png
32.2.2 $\frac{{d}^{2}w}{{dz}^{2}}=2w^{3}+zw+\alpha,$
32.2.3 $\frac{{d}^{2}w}{{dz}^{2}}=\frac{1}{w}\left(\frac{dw}{dz}\right)^{2}-\frac{1}{z% }\frac{dw}{dz}+\frac{\alpha w^{2}+\beta}{z}+\gamma w^{3}+\frac{\delta}{w},$
32.2.4 $\frac{{d}^{2}w}{{dz}^{2}}=\frac{1}{2w}\left(\frac{dw}{dz}\right)^{2}+\frac{3}{% 2}w^{3}+4zw^{2}+2(z^{2}-\alpha)w+\frac{\beta}{w},$
32.2.5 $\frac{{d}^{2}w}{{dz}^{2}}=\left(\frac{1}{2w}+\frac{1}{w-1}\right)\left(\frac{% dw}{dz}\right)^{2}-\frac{1}{z}\frac{dw}{dz}+\frac{(w-1)^{2}}{z^{2}}\left(% \alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1},$
32.2.6 $\frac{{d}^{2}w}{{dz}^{2}}=\frac{1}{2}\left(\frac{1}{w}+\frac{1}{w-1}+\frac{1}{% w-z}\right)\left(\frac{dw}{dz}\right)^{2}-\left(\frac{1}{z}+\frac{1}{z-1}+% \frac{1}{w-z}\right)\frac{dw}{dz}+\frac{w(w-1)(w-z)}{z^{2}(z-1)^{2}}\left(% \alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+\frac{\delta z(z-1)% }{(w-z)^{2}}\right),$
with $\alpha$, $\beta$, $\gamma$, and $\delta$ arbitrary constants. The solutions of $\mbox{P}_{\mbox{\scriptsize I}}$$\mbox{P}_{\mbox{\scriptsize VI}}$ are called the Painlevé transcendents. The six equations are sometimes referred to as the Painlevé transcendents, but in this chapter this term will be used only for their solutions.
Let
32.2.7 $\frac{{d}^{2}w}{{dz}^{2}}=F\left(z,w,\frac{dw}{dz}\right),$
be a nonlinear second-order differential equation in which $F$ is a rational function of $w$ and $\ifrac{dw}{dz}$, and is locally analytic in $z$, that is, analytic except for isolated singularities in $\Complex$. In general the singularities of the solutions are movable in the sense that their location depends on the constants of integration associated with the initial or boundary conditions. An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however.
There are fifty equations with the Painlevé property. They are distinct modulo Möbius (bilinear) transformations
32.2.8 $\displaystyle W(\zeta)$ $\displaystyle=\frac{a(z)w+b(z)}{c(z)w+d(z)},$ $\displaystyle\zeta$ $\displaystyle=\phi(z),$
in which $a(z)$, $b(z)$, $c(z)$, $d(z)$, and $\phi(z)$ are locally analytic functions. The fifty equations can be reduced to linear equations, solved in terms of elliptic functions (Chapters 22 and 23), or reduced to one of $\mbox{P}_{\mbox{\scriptsize I}}$$\mbox{P}_{\mbox{\scriptsize VI}}$.
For arbitrary values of the parameters $\alpha$, $\beta$, $\gamma$, and $\delta$, the general solutions of $\mbox{P}_{\mbox{\scriptsize I}}$$\mbox{P}_{\mbox{\scriptsize VI}}$ are transcendental, that is, they cannot be expressed in closed-form elementary functions. However, for special values of the parameters, equations $\mbox{P}_{\mbox{\scriptsize II}}$$\mbox{P}_{\mbox{\scriptsize VI}}$ have special solutions in terms of elementary functions, or special functions defined elsewhere in the DLMF.
# §32.2(ii) Renormalizations
If $\gamma\delta\neq 0$ in $\mbox{P}_{\mbox{\scriptsize III}}$, then set $\gamma=1$ and $\delta=-1$, without loss of generality, by rescaling $w$ and $z$ if necessary. If $\gamma=0$ and $\alpha\delta\neq 0$ in $\mbox{P}_{\mbox{\scriptsize III}}$, then set $\alpha=1$ and $\delta=-1$, without loss of generality. Lastly, if $\delta=0$ and $\beta\gamma\neq 0$, then set $\beta=-1$ and $\gamma=1$, without loss of generality.
If $\delta\neq 0$ in $\mbox{P}_{\mbox{\scriptsize V}}$, then set $\delta=-\tfrac{1}{2}$, without loss of generality.
# §32.2(iii) Alternative Forms
In $\mbox{P}_{\mbox{\scriptsize III}}$, if $w(z)=\zeta^{-1/2}u(\zeta)$ with $\zeta=z^{2}$, then
32.2.9 $\frac{{d}^{2}u}{{d\zeta}^{2}}=\frac{1}{u}\left(\frac{du}{d\zeta}\right)^{2}-% \frac{1}{\zeta}\frac{du}{d\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}+% \frac{\beta}{4\zeta}+\frac{\delta}{4u},$
which is known as $\mbox{P}^{\prime}_{\mbox{\scriptsize III}}$.
In $\mbox{P}_{\mbox{\scriptsize III}}$, if $w(z)=\mathop{\exp\/}\nolimits\!\left(-iu(z)\right)$, $\beta=-\alpha$, and $\delta=-\gamma$, then
32.2.10 $\frac{{d}^{2}u}{{dz}^{2}}+\frac{1}{z}\frac{du}{dz}=\frac{2\alpha}{z}\mathop{% \sin\/}\nolimits u+2\gamma\mathop{\sin\/}\nolimits\!\left(2u\right).$
In $\mbox{P}_{\mbox{\scriptsize IV}}$, if $w(z)=2\sqrt{2}(u(\zeta))^{2}$ with $\zeta=\sqrt{2}z$ and $\alpha=2\nu+1$, then
32.2.11 $\frac{{d}^{2}u}{{d\zeta}^{2}}=3u^{5}+2\zeta u^{3}+\left(\tfrac{1}{4}\zeta^{2}-% \nu-\tfrac{1}{2}\right)u+\frac{\beta}{32u^{3}}.$
When $\beta=0$ this is a nonlinear harmonic oscillator.
In $\mbox{P}_{\mbox{\scriptsize V}}$, if $w(z)=(\mathop{\coth\/}\nolimits u(\zeta))^{2}$ with $\zeta=\mathop{\ln\/}\nolimits z$, then
32.2.12 $\frac{{d}^{2}u}{{d\zeta}^{2}}=-\frac{\alpha\mathop{\cosh\/}\nolimits u}{2(% \mathop{\sinh\/}\nolimits u)^{3}}-\frac{\beta\mathop{\sinh\/}\nolimits u}{2(% \mathop{\cosh\/}\nolimits u)^{3}}-\tfrac{1}{4}\gamma e^{\zeta}\mathop{\sinh\/}% \nolimits\!\left(2u\right)-\tfrac{1}{8}\delta e^{2\zeta}\mathop{\sinh\/}% \nolimits\!\left(4u\right).$
See also Okamoto (1987c), McCoy et al. (1977), Bassom et al. (1992), Bassom et al. (1995), and Takasaki (2001).
# §32.2(iv) Elliptic Form
$\mbox{P}_{\mbox{\scriptsize VI}}$ can be written in the form
32.2.13 $z(1-z)I\left(\int_{\infty}^{w}\frac{dt}{\sqrt{t(t-1)(t-z)}}\right)=\sqrt{w(w-1% )(w-z)}\*\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(% \delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}}\right),$
where
32.2.14 $I=z(1-z)\frac{{d}^{2}}{{dz}^{2}}+(1-2z)\frac{d}{dz}-\frac{1}{4}.$
See Fuchs (1907), Painlevé (1906), Gromak et al. (2002, §42); also Manin (1998).
# §32.2(v) Symmetric Forms
Let
32.2.15 $\displaystyle\frac{df_{1}}{dz}+f_{1}(f_{2}-f_{3})+2\mu_{1}$ $\displaystyle=0,$ $\displaystyle\frac{df_{2}}{dz}+f_{2}(f_{3}-f_{1})+2\mu_{2}$ $\displaystyle=0,$ $\displaystyle\frac{df_{3}}{dz}+f_{3}(f_{1}-f_{2})+2\mu_{3}$ $\displaystyle=0,$
where $\mu_{1}$, $\mu_{2}$, $\mu_{3}$ are constants, $f_{1}$, $f_{2}$, $f_{3}$ are functions of $z$, with
32.2.16 $\mu_{1}+\mu_{2}+\mu_{3}=1,$ Symbols: $\mu_{j}$: constants Permalink: http://dlmf.nist.gov/32.2.E16 Encodings: TeX, pMML, png
32.2.17 $f_{1}(z)+f_{2}(z)+f_{3}(z)+2z=0.$ Symbols: $z$: real and $f_{j}(z)$: solutions Permalink: http://dlmf.nist.gov/32.2.E17 Encodings: TeX, pMML, png
Then $w(z)=f_{1}(z)$ satisfies $\mbox{P}_{\mbox{\scriptsize IV}}$ with
32.2.18 $(\alpha,\beta)=(\mu_{3}-\mu_{2},-2\mu_{1}^{2}).$
Next, let
32.2.19 $\displaystyle z\frac{df_{1}}{dz}$ $\displaystyle=f_{1}f_{3}(f_{2}-f_{4})+(\tfrac{1}{2}-\mu_{3})f_{1}+\mu_{1}f_{3},$ $\displaystyle z\frac{df_{2}}{dz}$ $\displaystyle=f_{2}f_{4}(f_{3}-f_{1})+(\tfrac{1}{2}-\mu_{4})f_{2}+\mu_{2}f_{4},$ $\displaystyle z\frac{df_{3}}{dz}$ $\displaystyle=f_{3}f_{1}(f_{4}-f_{2})+(\tfrac{1}{2}-\mu_{1})f_{3}+\mu_{3}f_{1},$ $\displaystyle z\frac{df_{4}}{dz}$ $\displaystyle=f_{4}f_{2}(f_{1}-f_{3})+(\tfrac{1}{2}-\mu_{2})f_{4}+\mu_{4}f_{2},$
where $\mu_{1}$, $\mu_{2}$, $\mu_{3}$, $\mu_{4}$ are constants, $f_{1}$, $f_{2}$, $f_{3}$, $f_{4}$ are functions of $z$, with
32.2.20 $\mu_{1}+\mu_{2}+\mu_{3}+\mu_{4}=1,$ Symbols: $\mu_{j}$: constants Permalink: http://dlmf.nist.gov/32.2.E20 Encodings: TeX, pMML, png
32.2.21 $f_{1}(z)+f_{3}(z)=\sqrt{z},$ Symbols: $z$: real and $f_{j}(z)$: solutions Permalink: http://dlmf.nist.gov/32.2.E21 Encodings: TeX, pMML, png
32.2.22 $f_{2}(z)+f_{4}(z)=\sqrt{z}.$ Symbols: $z$: real and $f_{j}(z)$: solutions Permalink: http://dlmf.nist.gov/32.2.E22 Encodings: TeX, pMML, png
Then $w(z)=1-(\sqrt{z}/f_{1}(z))$ satisfies $\mbox{P}_{\mbox{\scriptsize V}}$ with
32.2.23 $(\alpha,\beta,\gamma,\delta)=(\tfrac{1}{2}\mu_{1}^{2},-\tfrac{1}{2}\mu_{3}^{2}% ,\mu_{4}-\mu_{2},-\tfrac{1}{2}).$
$\mbox{P}_{\mbox{\scriptsize I}}$$\mbox{P}_{\mbox{\scriptsize V}}$ are obtained from $\mbox{P}_{\mbox{\scriptsize VI}}$ by a coalescence cascade:
32.2.24 $\begin{array}[]{ccccccc}\mbox{\mbox{P}_{\mbox{\scriptsize VI}}}&% \longrightarrow&\mbox{\mbox{P}_{\mbox{\scriptsize V}}}&\longrightarrow&\mbox% {\mbox{P}_{\mbox{\scriptsize IV}}}\\ &&\big\downarrow&&\big\downarrow\\ &&\mbox{\mbox{P}_{\mbox{\scriptsize III}}}&\longrightarrow&\mbox{\mbox{P}_{% \mbox{\scriptsize II}}}&\longrightarrow&\mbox{\mbox{P}_{\mbox{\scriptsize I}% }}\end{array}$ Permalink: http://dlmf.nist.gov/32.2.E24 Encodings: TeX, pMML, png
For example, if in $\mbox{P}_{\mbox{\scriptsize II}}$
32.2.25 $w(z;\alpha)=\epsilon W(\zeta)+\frac{1}{\epsilon^{5}},$
32.2.26 $\displaystyle z$ $\displaystyle=\epsilon^{2}\zeta-\frac{6}{\epsilon^{10}},$ $\displaystyle\alpha$ $\displaystyle=\frac{4}{\epsilon^{15}},$ Symbols: $z$: real and $\alpha$: arbitrary constant Permalink: http://dlmf.nist.gov/32.2.E26 Encodings: TeX, TeX, pMML, pMML, png, png
then
32.2.27 $\frac{{d}^{2}W}{{d\zeta}^{2}}=6W^{2}+\zeta+\epsilon^{6}(2W^{3}+\zeta W);$
thus in the limit as $\epsilon\to 0$, $W(\zeta)$ satisfies $\mbox{P}_{\mbox{\scriptsize I}}$ with $z=\zeta$.
If in $\mbox{P}_{\mbox{\scriptsize III}}$
32.2.28 $w(z;\alpha,\beta,\gamma,\delta)=1+2\epsilon W(\zeta;a),$
32.2.29 $\displaystyle z$ $\displaystyle=1+\epsilon^{2}\zeta,$ $\displaystyle\alpha$ $\displaystyle=-\tfrac{1}{2}\epsilon^{-6},$ $\displaystyle\beta$ $\displaystyle=\tfrac{1}{2}\epsilon^{-6}+2a\epsilon^{-3},$ $\displaystyle\gamma$ $\displaystyle=-\delta=\tfrac{1}{4}\epsilon^{-6},$
then as $\epsilon\to 0$, $W(\zeta;a)$ satisfies $\mbox{P}_{\mbox{\scriptsize II}}$ with $z=\zeta$, $\alpha=a$.
If in $\mbox{P}_{\mbox{\scriptsize IV}}$
32.2.30 $w(z;\alpha,\beta)=2^{2/3}\epsilon^{-1}W(\zeta;a)+\epsilon^{-3},$
32.2.31 $\displaystyle z$ $\displaystyle=2^{-2/3}\epsilon\zeta-\epsilon^{-3},$ $\displaystyle\alpha$ $\displaystyle=-2a-\tfrac{1}{2}\epsilon^{-6},$ $\displaystyle\beta$ $\displaystyle=-\tfrac{1}{2}\epsilon^{-12},$ Symbols: $z$: real, $\alpha$: arbitrary constant and $\beta$: arbitrary constant Permalink: http://dlmf.nist.gov/32.2.E31 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png
then as $\epsilon\to 0$, $W(\zeta;a)$ satisfies $\mbox{P}_{\mbox{\scriptsize II}}$ with $z=\zeta$, $\alpha=a$.
If in $\mbox{P}_{\mbox{\scriptsize V}}$
32.2.32 $w(z;\alpha,\beta,\gamma,\delta)=1+\epsilon\zeta W(\zeta;a,b,c,d),$
32.2.33 $\displaystyle z$ $\displaystyle=\zeta^{2},$ $\displaystyle\alpha$ $\displaystyle=\tfrac{1}{4}a\epsilon^{-1}+\tfrac{1}{8}c\epsilon^{-2},$ $\displaystyle\beta$ $\displaystyle=-\tfrac{1}{8}c\epsilon^{-2},$ $\displaystyle\gamma$ $\displaystyle=\tfrac{1}{4}\epsilon b,$ $\displaystyle\delta$ $\displaystyle=\tfrac{1}{8}\epsilon^{2}d,$
then as $\epsilon\to 0$, $W(\zeta;a,b,c,d)$ satisfies $\mbox{P}_{\mbox{\scriptsize III}}$ with $z=\zeta$, $\alpha=a$, $\beta=b$, $\gamma=c$, $\delta=d$.
If in $\mbox{P}_{\mbox{\scriptsize V}}$
32.2.34 $w(z;\alpha,\beta,\gamma,\delta)=\tfrac{1}{2}\sqrt{2}\epsilon W(\zeta;a,b),$
32.2.35 $\displaystyle z$ $\displaystyle=1+\sqrt{2}\epsilon\zeta,$ $\displaystyle\alpha$ $\displaystyle=\tfrac{1}{2}\epsilon^{-4},$ $\displaystyle\beta$ $\displaystyle=\tfrac{1}{4}b,$ $\displaystyle\gamma$ $\displaystyle=-\epsilon^{-4},$ $\displaystyle\delta$ $\displaystyle=a\epsilon^{-2}-\tfrac{1}{2}\epsilon^{-4},$
then as $\epsilon\to 0$, $W(\zeta;a,b)$ satisfies $\mbox{P}_{\mbox{\scriptsize IV}}$ with $z=\zeta$, $\alpha=a$, $\beta=b$.
Lastly, if in $\mbox{P}_{\mbox{\scriptsize VI}}$
32.2.36 $w(z;\alpha,\beta,\gamma,\delta)=W(\zeta;a,b,c,d),$
32.2.37 $\displaystyle z$ $\displaystyle=1+\epsilon\zeta,$ $\displaystyle\gamma$ $\displaystyle=c\epsilon^{-1}-d\epsilon^{-2},$ $\displaystyle\delta$ $\displaystyle=d\epsilon^{-2},$ Symbols: $z$: real, $\gamma$: arbitrary constant and $\delta$: arbitrary constant Permalink: http://dlmf.nist.gov/32.2.E37 Encodings: TeX, TeX, TeX, pMML, pMML, pMML, png, png, png
then as $\epsilon\to 0$, $W(\zeta;a,b,c,d)$ satisfies $\mbox{P}_{\mbox{\scriptsize V}}$ with $z=\zeta$, $\alpha=a$, $\beta=b$, $\gamma=c$, $\delta=d$. | 2015-08-02T02:19:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 398, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9975873827934265, "perplexity": 4397.669165829177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988930.94/warc/CC-MAIN-20150728002308-00176-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://lammps.sandia.gov/doc/pair_spin_neel.html | # pair_style spin/neel command
## Syntax
pair_style spin/neel cutoff
• cutoff = global cutoff pair (distance in metal units)
## Examples
pair_style spin/neel 4.0
pair_coeff * * neel 4.0 0.0048 0.234 1.168 2.6905 0.705 0.652
pair_coeff 1 2 neel 4.0 0.0048 0.234 1.168 0.0 0.0 1.0
## Description
Style spin/neel computes the Neel pair anisotropy model between pairs of magnetic spins:
where si and sj are two neighboring magnetic spins of two particles, rij = ri - rj is the inter-atomic distance between the two particles, eij = (ri - rj)/|ri-rj| is their normalized separation vector and g1, q1 and q2 are three functions defining the intensity of the dipolar and quadrupolar contributions, with:
With the functions g(rij) and q(rij) defined and fitted according to the same Bethe-Slater function used to fit the exchange interaction:
where a, b and d are the three constant coefficients defined in the associated “pair_coeff” command.
The coefficients a, b, and d need to be fitted so that the function above matches with the values of the magneto-elastic constant of the materials at stake.
Examples and more explanations about this function and its parameterization are reported in (Tranchida). More examples of parameterization will be provided in future work.
From this DM interaction, each spin i will be submitted to a magnetic torque omega and its associated atom to a force F (for spin-lattice calculations only).
More details about the derivation of these torques/forces are reported in (Tranchida).
## Restrictions
All the pair/spin styles are part of the SPIN package. These styles are only enabled if LAMMPS was built with this package, and if the atom_style “spin” was declared. See the Build package doc page for more info. | 2019-01-16T16:19:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6762651801109314, "perplexity": 3359.2268842070084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657555.87/warc/CC-MAIN-20190116154927-20190116180927-00223.warc.gz"} |
https://bison.inl.gov/Documentation/source/userobject/U3Si2TricubicInterpolationUserObject.aspx | # Uvar element = document.getElementById("moose-equation-7958823d-5f8c-4e54-b541-ccd9d4917ff5");katex.render("_3", element, {displayMode:false,throwOnError:false});Sivar element = document.getElementById("moose-equation-085463d1-4b5b-4656-b38b-45afa23bfd9c");katex.render("_2", element, {displayMode:false,throwOnError:false}); Tricubic Interpolation User Object
Performs tricubic interpolation in temperature, temperature gradient, and burnup (fission density) to determine the degradation to the thermal conductivity and gaseous swelling of U3Si2 fuel.
## Description
The U3Si2TricubicInterpolationUserObject performs tricubic interpolation using the data contained in the input comma separated value (.csv) files for calculations utilized by ThermalSilicideFuel and U3Si2VolumetricSwellingEigenstrain.
### Required CSV Files
The user must specify six input csv files for the algorithm.
The first three represent the grid points of the tricubic calculation for which values are known. These grid points are for temperature, temperature gradient, and fission density. These files must be in ROW format consisting of a single row of data with each column delimited. The units of the values in the files should be K for temperature, K/mm for temperature gradient and fissions/cm with the power of 10 removed (i.e., a fission density of 2.010 would be input as 2.0).
The last three files represent the values of grain boundary coverage (FCOV), gaseous swelling strain due to intragranular bubbles (GSWb), and total gaseous swelling (GSW) for a given combination of temperature, temperature gradient and fission density. These files must have as many rows as the product of the number of columns in the temperature_grid_points file and number of columns in the temperature_gradient_grid_points file. The number of columns in these three files should equal the number of columns in the fission_density_grid_points file.
## Example Input Syntax
[UserObjects]
type = U3Si2TricubicInterpolationUserObject
execute_on = 'initial nonlinear'
temperature_grid_points_file = temperature.csv
fission_density_grid_points_file = fission_density.csv
grain_boundary_coverage_file = fcov.csv
intragranular_gaseous_swelling_file = gswb.csv
total_gaseous_swelling_file = gsw.csv
[../]
[]
(test/tests/thermalSilicideFuel/thermalU3Si2_argonne.i)
## Input Parameters
• fission_density_grid_points_fileFile holding data for the fission density (burnup) grid points to be used with the tricubic interpolation. Units are fissions/cm^3 with the trailing 10^21 removed (i.e., 2.5e20^21 would be 2.5).
C++ Type:FileName
Description:File holding data for the fission density (burnup) grid points to be used with the tricubic interpolation. Units are fissions/cm^3 with the trailing 10^21 removed (i.e., 2.5e20^21 would be 2.5).
• intragranular_gaseous_swelling_fileFile holding data for the gaseous swelling strain due to intragranular bubbles (GSWb) to be used with the tricubic interpolation calculation.
C++ Type:FileName
Description:File holding data for the gaseous swelling strain due to intragranular bubbles (GSWb) to be used with the tricubic interpolation calculation.
• total_gaseous_swelling_fileFile holding data for the total gaseous swelling strain (GSW) to be used with the tricubic interpolation calculation.
C++ Type:FileName
Description:File holding data for the total gaseous swelling strain (GSW) to be used with the tricubic interpolation calculation.
• temperature_gradient_grid_points_fileFile holding data for the temperature gradient grid points to be used with the tricubic interpolation.
C++ Type:FileName
Description:File holding data for the temperature gradient grid points to be used with the tricubic interpolation.
• grain_boundary_coverage_fileFile holding data for the grain boundary converage (FCOV) to be used with the tricubic interpolation calculation.
C++ Type:FileName
Description:File holding data for the grain boundary converage (FCOV) to be used with the tricubic interpolation calculation.
• temperature_grid_points_fileFile holding data for temperature grid points to be used with the tricubic interpolation.
C++ Type:FileName
Description:File holding data for temperature grid points to be used with the tricubic interpolation.
### Required Parameters
• execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
### Optional Parameters
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• force_preauxFalseForces the GeneralUserObject to be executed in PREAUX
Default:False
C++ Type:bool
Description:Forces the GeneralUserObject to be executed in PREAUX | 2020-12-04T05:34:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3468247950077057, "perplexity": 5784.020243972205}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00342.warc.gz"} |
https://www.usgs.gov/media/images/spattering-was-occurring-three-locations-along-edge-l | # Spattering was occurring at three locations along the edge of the l...
## Detailed Description
Spattering was occurring at three locations along the edge of the lava lake during today's overflight. Spattering like this is common, can occur anywhere around the lake margin (though it most often occurs at the southeast edge), and repeatedly starts and stops. View is toward the southeast.
## Details
Image Dimensions: 1152 x 768
Date Taken: | 2020-06-06T04:37:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8016859292984009, "perplexity": 6036.325499885621}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348509972.80/warc/CC-MAIN-20200606031557-20200606061557-00349.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Agusein-zade.sabir-m | Compute Distance To:
Documents Indexed: 154 Publications since 1966, including 6 Books 2 Contributions as Editor Biographic References: 1 Publication Co-Authors: 58 Co-Authors with 119 Joint Publications 2,094 Co-Co-Authors
all top 5
### Co-Authors
37 single-authored 41 Ebeling, Wolfgang 28 Delgado, Felix 27 Campillo, Antonio 22 Melle-Hernández, Alejandro 21 Luengo, Ignacio 9 Varchenko, Alexander Nikolaevich 6 Arnol’d, Vladimir Igorevich 4 Ilyashenko, Yulij Sergeevich 3 Lando, Sergei K. 3 Natanzon, Sergei M. 3 Tsfasman, Michael A. 2 Nekhoroshev, Nikolaĭ Nikolaevich 2 Rauch, A.-M. Ya. 2 Rybnikov, Leonid Grigor’evich 2 Vasil’ev, Viktor Anatol’evich 1 Agrachev, Andreĭ Aleksandrovich 1 Aliev, Nihan A. 1 Anosov, Dmitriĭ Viktorovich 1 Arzhantsev, Ivan Vladimirovich 1 Bogaevskij, Il’ya Aleksandrovich 1 Bortakovskii, A. S. 1 Budak, A. B. 1 Bukhshtaber, Viktor Matveevich 1 Chubarikov, Vladimir Nikolaevich 1 Costa Gonzáles, Antonio Félix 1 Davydov, Alekseĭ Aleksandrovich 1 Duzhin, Fedor S. 1 Etingof, Pavel Il’ich 1 Gorsky, Eugene 1 Goryunov, Victor V. 1 Guliyeva, Arzu M. 1 Hernando, Fernando 1 Kazaryan, Maxim Eduardovich 1 Khanin, Konstantin M. 1 Khovanskiĭ, Askold Georgievich 1 Kozlov, Valeriĭ Vasil’evich 1 Krichever, Igor’ Moiseevich 1 Loktev, Sergey A. 1 Luengo, A. I. 1 Mamedova, F. I. 1 Manin, Yuri Ivanovich 1 Nadirashvili, Nikolai S. 1 Nogin, Dmitry Yu. 1 Novikov, Sergeĭ Petrovich 1 Orlov, Dmitri O. 1 Porteous, Hugh L. 1 Rybakov, Sergeĭ Yur’evich 1 Schwarzman, Ossip 1 Seade, Jose Antonio 1 Sedykh, Vyacheslav Dmitrievich 1 Shlosman, Senya B. 1 Siersma, Dirk 1 Sinaĭ, Yakov Grigor’evich 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Takahashi, Atsushi 1 Timashev, Dmitri A. 1 Treshchev, Dmitriĭ Valer’evich 1 Zarodov, V. R. 1 Zykin, A. I.
all top 5
### Serials
20 Functional Analysis and its Applications 10 Russian Mathematical Surveys 10 Moscow Mathematical Journal 5 Proceedings of the Steklov Institute of Mathematics 4 Bulletin of the London Mathematical Society 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Journal of Geometry and Physics 3 Funktsional’nyĭ Analiz i ego Prilozheniya 3 Mathematische Zeitschrift 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 International Journal of Mathematics 3 Journal of Mathematical Sciences (New York) 3 Revista Matemática Complutense 3 Journal of Singularities 2 Mathematical Notes 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Commentarii Mathematici Helvetici 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 St. Petersburg Mathematical Journal 2 Mathematical Research Letters 2 Monographs in Mathematics 2 Azerbaijan Journal of Mathematics 2 Modern Birkhäuser Classics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Matematicheskie Zametki 1 Arkiv för Matematik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematics of the USSR. Izvestiya 1 Michigan Mathematical Journal 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Topology and its Applications 1 IMRN. International Mathematics Research Notices 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 European Mathematical Society Newsletter 1 Doklady Mathematics 1 Advances in Theoretical and Mathematical Physics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of Algebra and its Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Pure and Applied Mathematics Quarterly 1 Functional Analysis and Other Mathematics 1 TWMS Journal of Pure and Applied Mathematics 1 Arnold Mathematical Journal 1 European Journal of Mathematics
all top 5
### Fields
91 Several complex variables and analytic spaces (32-XX) 87 Algebraic geometry (14-XX) 40 Manifolds and cell complexes (57-XX) 36 Global analysis, analysis on manifolds (58-XX) 13 Algebraic topology (55-XX) 12 Commutative algebra (13-XX) 9 Associative rings and algebras (16-XX) 8 $$K$$-theory (19-XX) 7 History and biography (01-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Category theory; homological algebra (18-XX) 3 Quantum theory (81-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
### Citations contained in zbMATH Open
110 Publications have been cited 1,063 times in 725 Documents Cited by Year
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
Intersection matrices for certain singularities of functions of two variables. Zbl 0304.14009
1974
The monodromy groups of isolated singularities of hypersurfaces. Zbl 0379.32013
1977
The Alexander polynomial of a plane curve singularity via the ring of functions on it. Zbl 1028.32013
2003
A power structure over the Grothendieck ring of varieties. Zbl 1063.14026
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2004
Poincaré series of a rational surface singularity. Zbl 1060.14054
2004
Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Zbl 1122.14003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Multi-index filtrations and generalized Poincaré series. Zbl 1111.14020
2007
The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic. Zbl 1056.14035
2003
On indices of 1-forms on determinantal singularities. Zbl 1202.32023
2009
Universal abelian covers of rational surface singularities and multi-index filtrations. Zbl 1156.14317
2008
On generators of the semigroup of a plane curve singularity. Zbl 0974.14020
1999
Dynkin diagrams for singularities of functions of two variables. Zbl 0309.14006
1974
Poincaré series for several plane divisorial valuations. Zbl 1083.14502
2003
Radial index and Euler obstruction of a 1-form on a singular variety. Zbl 1110.14004
2005
Zeta functions for germs of meromorphic functions, and Newton diagrams. Zbl 0933.32003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1998
On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions. Zbl 0967.14017
1999
Partial resolutions and the zeta-function of a singularity. Zbl 0901.32024
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1997
Saito duality between Burnside rings for invertible polynomials. Zbl 1298.32017
2012
Homological index for 1-forms and a Milnor number for isolated singularities. Zbl 1065.14003
2004
Indices of 1-forms on an isolated complete intersection singularity. Zbl 1039.32033
2003
On the index of a vector field at an isolated singularity. Zbl 0942.57024
1999
Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity. Zbl 1046.32007
2000
Integration with respect to the Euler characteristic and its applications. Zbl 1228.14005
2010
Singularities of differentiable mappings. Classification of critical points, caustics and wave fronts. (Osobennosti differentsiruemykh otobrazhenij. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov). Zbl 0513.58001
Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1982
The Alexander polynomial of plane curve singularities and rings of functions on curves. Zbl 0976.32017
1999
Equivariant Poincaré series of filtrations. Zbl 1276.14005
2013
Indices of vector fields and 1-forms on singular varieties. Zbl 1124.32012
2006
Singularities of differentiable mappings. Monodromy and asymptotics of integrals. (Osobennosti differentsiruemykh otobrazhenij. Monodromiya i asimptotiki integralov). Zbl 0545.58001
Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1984
Verlinde algebras and the intersection form on vanishing cycles. Zbl 0911.32044
1997
On Poincaré series of filtrations on equivariant functions of two variables. Zbl 1131.14007
2007
Orbifold Euler characteristics for dual invertible polynomials. Zbl 1319.14046
2012
On the power structure over the Grothendieck ring of varieties and its applications. Zbl 1222.14007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2007
The problem of choice and the optimal stopping rule for a sequence of independent trails. Zbl 0203.20405
1966
An equivariant Poincaré series of filtrations and monodromy zeta functions. Zbl 1327.14019
2015
Topology of meromorphic germs and its applications. Zbl 0972.32022
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2000
Singularities of type $$A_k$$ on plane curves of a chosen degree. Zbl 0980.32008
Gusein-Zade, S. M.; Nekhoroshev, N. N.
2000
The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors. Zbl 1203.14031
2010
Equivariant analogues of the Euler characteristic and Macdonald type equations. Zbl 1376.57039
2017
Integrals with respect to the Euler characteristic over spaces of functions and the Alexander polynomial. Zbl 1030.32021
2002
Equivariant indices of vector fields and 1-forms. Zbl 1336.14007
2015
Orbifold E-functions of dual invertible polynomials. Zbl 1379.32025
Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi
2016
Poincaré series of curves on rational surface singularities. Zbl 1075.14024
2005
An equivariant version of the monodromy zeta function. Zbl 1156.32016
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2008
On the pre-$$\lambda$$-ring structure on the Grothendieck ring of stacks and the power structures over it. Zbl 1272.14006
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2013
Poincaré series of collections of plane valuations. Zbl 1213.32013
2010
Indices of vector fields or 1-forms and characteristic numbers. Zbl 1086.32025
2005
Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristic. Zbl 1440.14187
2020
Orbifold zeta functions for dual invertible polynomials. Zbl 1360.14107
2017
Bifurcations and topology of meromorphic germs. Zbl 0991.32019
Gusein-Zade, Sabir; Luengo, Ignacio; Hernández, Alejandro Melle
2001
Quadratic forms for a 1-form on an isolated complete intersection singularity. Zbl 1089.32018
2006
On a game connected with a Wiener process. Zbl 0191.49702
1969
The extended semigroup of a plane curve singularity. Zbl 1048.58027
1998
On the zeta-function of a polynomial at infinity. Zbl 0970.32015
Gusein-Zade, Sabir M.; Luengo, Ignacio; Melle-Hernández, Alejandro
2000
Higher order generalized Euler characteristics and generating series. Zbl 1320.32029
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
Index of a singular point of a gradient vector field. Zbl 0555.32006
1984
Monodromies and Poincaré series of quasihomogeneous complete intersections. Zbl 1070.14004
2004
On the existence of deformations without critical points (the Teissier problem for functions of two variables). Zbl 0911.32046
1997
Grothendieck ring of varieties with actions of finite groups. Zbl 1454.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2019
On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groups. Zbl 1455.14078
2020
Equivariant versions of higher order orbifold Euler characteristics. Zbl 1382.55004
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2016
On the topological type of a set of plane valuations with symmetries. Zbl 1397.13009
2017
Hilbert function, generalized Poincaré series and topology of plane valuations. Zbl 1325.14010
2014
On adjacencies of singularities $$A_ k$$ to points of the $$\mu =const$$ stratum of a singularity. Zbl 0555.32008
Gusejn-Zade, S. M.; Nekhoroshev, N. N.
1983
Poincaré series and zeta function of the monodromy of a quasihomogeneous singularity. Zbl 1056.14003
2002
On the number of topological types of plane curves. Zbl 0915.57004
Gusein-Zade, S. M.; Duzhin, F. S.
1998
On the index of a holomorphic $$1$$-form on an isolated complete intersection singularity. Zbl 1086.32501
2001
Equivariant Poincaré series of filtrations and topology. Zbl 1317.14006
2014
Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function. Zbl 1350.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
On generating series of classes of equivariant Hilbert schemes of fat points. Zbl 1206.14014
Gusein-Zade, S.; Luengo, I.; Melle-Hernández, A.
2010
Orbifold Milnor lattice and orbifold intersection form. Zbl 1393.14056
2018
The universal Euler characteristic of $$V$$-manifolds. Zbl 1423.57042
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Method of real morsifications for complete intersection singularities. Zbl 0829.14022
1994
Chern obstructions for collections of 1-forms on singular varieties. Zbl 1130.32011
2007
Coxeter-Dynkin diagrams of the complete intersection singularities $$Z_ 9$$ and $$Z_{10}$$. Zbl 0834.14002
1995
Klein foams as families of real forms of Riemann surfaces. Zbl 1366.81270
Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2017
Higher-order spectra, equivariant Hodge-Deligne polynomials, and Macdonald-type equations. Zbl 1454.57020
2017
Multi-variable Poincaré series associated with Newton diagrams. Zbl 1302.32025
2010
On divisorial filtrations associated with Newton diagrams. Zbl 1292.32008
2011
On singularities from which an $$A_ 1$$ can be split off. Zbl 0793.32013
1993
A version of the Berglund-Hübsch-Henningson duality with non-abelian groups. Zbl 1479.14048
2021
Number of critical points for a quasiperiodic potential. Zbl 0711.58007
1989
On singularities admitting perturbations with a small number of critical values. Zbl 0626.32025
1987
On an equivariant version of the zeta function of a transformation. Zbl 1325.32030
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On the action of a circle on manifolds. Zbl 0235.57014
1972
U-actions of a circle and fixed points. Zbl 0248.57026
1972
Equivariant Poincaré series and topology of valuations. Zbl 1431.14004
2016
On indices of meromorphic 1-forms. Zbl 1060.32013
2004
On the zeta functions of a meromorphic germ in two variables. Zbl 1077.14039
2004
On the topology of quasiperiodic functions. Zbl 0959.58048
1999
Monodromiegruppen isolierter Singularitäten von Hyperflächen. Zbl 0363.32010
1977
On the monodromy at infinity of a plane curve and the Poincaré series of its coordinate ring. Zbl 1005.14012
1999
The Arf-invariant and the Arnold invariants of plane curves. Zbl 1076.57500
Gusein-Zade, S. M.; Natanzon, S. M.
1997
Dynkin diagrams of some complete intersections and real morsifications. Zbl 0882.32017
1995
On atypical values and local monodromies of meromorphic functions. Zbl 0990.32007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1999
Distinguished bases of simple singularities. Zbl 0484.32002
1981
Alexander polynomials and Poincaré series of sets of ideals. Zbl 1271.32032
2011
A version of the Berglund-Hübsch-Henningson duality with non-abelian groups. Zbl 1479.14048
2021
Dual invertible polynomials with permutation symmetries and the orbifold Euler characteristic. Zbl 1440.14187
2020
On the orbifold Euler characteristics of dual invertible polynomials with non-abelian symmetry groups. Zbl 1455.14078
2020
Grothendieck ring of varieties with actions of finite groups. Zbl 1454.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2019
Orbifold Milnor lattice and orbifold intersection form. Zbl 1393.14056
2018
The universal Euler characteristic of $$V$$-manifolds. Zbl 1423.57042
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Power structure over the Grothendieck ring of maps. Zbl 1423.14061
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2018
Equivariant analogues of the Euler characteristic and Macdonald type equations. Zbl 1376.57039
2017
Orbifold zeta functions for dual invertible polynomials. Zbl 1360.14107
2017
On the topological type of a set of plane valuations with symmetries. Zbl 1397.13009
2017
Klein foams as families of real forms of Riemann surfaces. Zbl 1366.81270
Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2017
Higher-order spectra, equivariant Hodge-Deligne polynomials, and Macdonald-type equations. Zbl 1454.57020
2017
On equivariant indices of 1-forms on varieties. Zbl 1398.32036
Gusein-Zade, S. M.; Mamedova, F. I.
2017
An equivariant version of the Euler obstruction. Zbl 1380.32011
2017
Orbifold E-functions of dual invertible polynomials. Zbl 1379.32025
Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi
2016
Equivariant versions of higher order orbifold Euler characteristics. Zbl 1382.55004
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2016
Equivariant Poincaré series and topology of valuations. Zbl 1431.14004
2016
An equivariant Poincaré series of filtrations and monodromy zeta functions. Zbl 1327.14019
2015
Equivariant indices of vector fields and 1-forms. Zbl 1336.14007
2015
Higher order generalized Euler characteristics and generating series. Zbl 1320.32029
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On an equivariant version of the zeta function of a transformation. Zbl 1325.32030
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2015
On Poincaré series of filtrations. Zbl 1406.13021
2015
Hilbert function, generalized Poincaré series and topology of plane valuations. Zbl 1325.14010
2014
Equivariant Poincaré series of filtrations and topology. Zbl 1317.14006
2014
Equivariant Poincaré series of filtrations. Zbl 1276.14005
2013
On the pre-$$\lambda$$-ring structure on the Grothendieck ring of stacks and the power structures over it. Zbl 1272.14006
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2013
Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol’d. Reprint of the 1985 hardback edition. Zbl 1290.58001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Singularities of differentiable maps, Volume 2. Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous and revised by the authors and James Montaldi. Reprint of the 1988 hardback edition. Zbl 1297.32001
Arnold, V. I.; Gusein-Zade, S. M.; Varchenko, A. N.
2012
Saito duality between Burnside rings for invertible polynomials. Zbl 1298.32017
2012
Orbifold Euler characteristics for dual invertible polynomials. Zbl 1319.14046
2012
On a Newton filtration for functions on a curve singularity. Zbl 1292.32009
2012
Equivariant Poincaré series and monodromy zeta functions of quasihomogeneous polynomials. Zbl 1255.32013
2012
On divisorial filtrations associated with Newton diagrams. Zbl 1292.32008
2011
Alexander polynomials and Poincaré series of sets of ideals. Zbl 1271.32032
2011
Klein foams. Zbl 1268.14027
Costas, Antonio F.; Gusein-Zade, Sabir M.; Natanzon, Sergey M.
2011
Monodromy of dual invertible polynomials. Zbl 1257.32028
2011
Integration with respect to the Euler characteristic and its applications. Zbl 1228.14005
2010
The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors. Zbl 1203.14031
2010
Poincaré series of collections of plane valuations. Zbl 1213.32013
2010
On generating series of classes of equivariant Hilbert schemes of fat points. Zbl 1206.14014
Gusein-Zade, S.; Luengo, I.; Melle-Hernández, A.
2010
Multi-variable Poincaré series associated with Newton diagrams. Zbl 1302.32025
2010
On indices of 1-forms on determinantal singularities. Zbl 1202.32023
2009
Universal abelian covers of rational surface singularities and multi-index filtrations. Zbl 1156.14317
2008
An equivariant version of the monodromy zeta function. Zbl 1156.32016
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2008
Multi-index filtrations and generalized Poincaré series. Zbl 1111.14020
2007
On Poincaré series of filtrations on equivariant functions of two variables. Zbl 1131.14007
2007
On the power structure over the Grothendieck ring of varieties and its applications. Zbl 1222.14007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2007
Chern obstructions for collections of 1-forms on singular varieties. Zbl 1130.32011
2007
Lectures on monodromy. Zbl 1135.32029
2007
Deformations of polynomials and their zeta-functions. Zbl 1194.32017
2007
Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Zbl 1122.14003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Indices of vector fields and 1-forms on singular varieties. Zbl 1124.32012
2006
Quadratic forms for a 1-form on an isolated complete intersection singularity. Zbl 1089.32018
2006
Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function. Zbl 1350.14023
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2006
Radial index and Euler obstruction of a 1-form on a singular variety. Zbl 1110.14004
2005
Poincaré series of curves on rational surface singularities. Zbl 1075.14024
2005
Indices of vector fields or 1-forms and characteristic numbers. Zbl 1086.32025
2005
A power structure over the Grothendieck ring of varieties. Zbl 1063.14026
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2004
Poincaré series of a rational surface singularity. Zbl 1060.14054
2004
Homological index for 1-forms and a Milnor number for isolated singularities. Zbl 1065.14003
2004
Monodromies and Poincaré series of quasihomogeneous complete intersections. Zbl 1070.14004
2004
On indices of meromorphic 1-forms. Zbl 1060.32013
2004
On the zeta functions of a meromorphic germ in two variables. Zbl 1077.14039
2004
The Alexander polynomial of a plane curve singularity via the ring of functions on it. Zbl 1028.32013
2003
The Alexander polynomial of a plane curve singularity and integrals with respect to the Euler characteristic. Zbl 1056.14035
2003
Poincaré series for several plane divisorial valuations. Zbl 1083.14502
2003
Indices of 1-forms on an isolated complete intersection singularity. Zbl 1039.32033
2003
Integrals with respect to the Euler characteristic over spaces of functions and the Alexander polynomial. Zbl 1030.32021
2002
Poincaré series and zeta function of the monodromy of a quasihomogeneous singularity. Zbl 1056.14003
2002
Bifurcations and topology of meromorphic germs. Zbl 0991.32019
Gusein-Zade, Sabir; Luengo, Ignacio; Hernández, Alejandro Melle
2001
On the index of a holomorphic $$1$$-form on an isolated complete intersection singularity. Zbl 1086.32501
2001
Integration with respect to the Euler characteristic over a function space and the Alexander polynomial of a plane curve singularity. Zbl 1046.32007
2000
Topology of meromorphic germs and its applications. Zbl 0972.32022
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
2000
Singularities of type $$A_k$$ on plane curves of a chosen degree. Zbl 0980.32008
Gusein-Zade, S. M.; Nekhoroshev, N. N.
2000
On the zeta-function of a polynomial at infinity. Zbl 0970.32015
Gusein-Zade, Sabir M.; Luengo, Ignacio; Melle-Hernández, Alejandro
2000
On generators of the semigroup of a plane curve singularity. Zbl 0974.14020
1999
On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions. Zbl 0967.14017
1999
On the index of a vector field at an isolated singularity. Zbl 0942.57024
1999
The Alexander polynomial of plane curve singularities and rings of functions on curves. Zbl 0976.32017
1999
On the topology of quasiperiodic functions. Zbl 0959.58048
1999
On the monodromy at infinity of a plane curve and the Poincaré series of its coordinate ring. Zbl 1005.14012
1999
On atypical values and local monodromies of meromorphic functions. Zbl 0990.32007
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1999
Zeta functions for germs of meromorphic functions, and Newton diagrams. Zbl 0933.32003
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1998
The extended semigroup of a plane curve singularity. Zbl 1048.58027
1998
On the number of topological types of plane curves. Zbl 0915.57004
Gusein-Zade, S. M.; Duzhin, F. S.
1998
Partial resolutions and the zeta-function of a singularity. Zbl 0901.32024
Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A.
1997
Verlinde algebras and the intersection form on vanishing cycles. Zbl 0911.32044
1997
On the existence of deformations without critical points (the Teissier problem for functions of two variables). Zbl 0911.32046
1997
The Arf-invariant and the Arnold invariants of plane curves. Zbl 1076.57500
Gusein-Zade, S. M.; Natanzon, S. M.
1997
Coxeter-Dynkin diagrams of the complete intersection singularities $$Z_ 9$$ and $$Z_{10}$$. Zbl 0834.14002
1995
Dynkin diagrams of some complete intersections and real morsifications. Zbl 0882.32017
1995
Method of real morsifications for complete intersection singularities. Zbl 0829.14022
1994
On singularities from which an $$A_ 1$$ can be split off. Zbl 0793.32013
1993
Number of critical points for a quasiperiodic potential. Zbl 0711.58007
1989
Singularities of differentiable maps. Volume II: Monodromy and asymptotics of integrals. Transl. from the Russian by Hugh Porteous. Zbl 0659.58002
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1988
On singularities admitting perturbations with a small number of critical values. Zbl 0626.32025
1987
Singularities of differentiable maps. Volume I: The classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, ed. by V. I. Arnol’d. Zbl 0554.58001
Arnol’d, V. I.; Gusejn-Zade, S. M.; Varchenko, A. N.
1985
Singularities of differentiable mappings. Monodromy and asymptotics of integrals. (Osobennosti differentsiruemykh otobrazhenij. Monodromiya i asimptotiki integralov). Zbl 0545.58001
Arnol’d, V. I.; Varchenko, A. N.; Gusejn-Zade, S. M.
1984
Index of a singular point of a gradient vector field. Zbl 0555.32006
1984
On adjacencies of singularities $$A_ k$$ to points of the $$\mu =const$$ stratum of a singularity. Zbl 0555.32008
Gusejn-Zade, S. M.; Nekhoroshev, N. N.
1983
...and 10 more Documents
all top 5
### Cited by 809 Authors
52 Gusein-Zade, Sabir M. 25 Ebeling, Wolfgang 16 Delgado, Felix 16 Némethi, András 14 Campillo, Antonio 12 Luengo, Ignacio 12 Melle-Hernández, Alejandro 10 Moyano Fernández, Julio José 9 Janeczko, Stanisław 9 Soares Ruas, Maria Aparecida 8 Vasil’ev, Viktor Anatol’evich 7 Izumiya, Shyuichi 7 Milanov, Todor E. 6 Bivià-Ausina, Carles 6 Greenblatt, Michael 6 Martín-Morales, Jorge 6 Nagy, János 6 Novikov, Dmitry 6 Seade, Jose Antonio 6 Takahashi, Atsushi 5 Albeverio, Sergio A. 5 Borodzik, Maciej 5 Davydov, Alekseĭ Aleksandrovich 5 de Góes Grulha, Nivaldo jun. 5 Dimca, Alexandru 5 Gorsky, Eugene 5 Goryunov, Victor V. 5 Ikromov, Isroil A. 5 László, Tamás 5 Maxim, Laurentiu G. 5 Shen, Yefeng 5 Siersma, Dirk 5 Takeuchi, Kiyoshi 5 Yakovenko, Sergei 5 Yamada, Yuichi 4 Astashov, Evgeniĭ Aleksandrovich 4 Esterov, Alexander I. 4 Galindo Pastor, Carlos 4 Hertling, Claus 4 Il’yuta, G. G. 4 Kamimoto, Joe 4 Monserrat, Francisco 4 Movasati, Hossein 4 Ricolfi, Andrea T. 4 Schürmann, Jörg 4 Shustin, Eugenii Isaakovich 4 Szendrői, Balázs 4 Varchenko, Alexander Nikolaevich 4 Veys, Willem 4 Zakalyukin, Vladimir M. 4 Zuber, Jean-Bernard 3 Allcock, Daniel Jonathan 3 Arnol’d, Vladimir Igorevich 3 Baryshnikov, Yuliy M. 3 Basalaev, Alexey 3 Binyamini, Gal 3 Challapa, Lizandro Sanchez 3 Chmutov, Sergei V. 3 D’Anna, Marco 3 Dubrovin, Boris Anatol’evich 3 Dunne, Gerald V. 3 Dutertre, Nicolas 3 Gaffney, Terence 3 Gómez-Mont, Xavier 3 Greuel, Gert-Martin 3 Hernando, Fernando 3 Ishikawa, Goo 3 Laza, Radu 3 Manh, Hy Duc 3 Mardešić, Pavao 3 Mazzucchi, Sonia 3 Micale, Vincenzo 3 Morrison, Andrew 3 Nakamura, Yayoi 3 Natanzon, Sergei M. 3 Nose, Toshihiro 3 Nuño-Ballesteros, Juan José 3 Proskurnin, Ivan Andreevich 3 Reeve, Graham Mark 3 Ruan, Yongbin 3 Sedykh, Vyacheslav Dmitrievich 3 Shende, Vivek Vijay 3 Villa, Manuel González 3 Weber, Andrzej 3 Zach, Matthias 3 Żołądek, Henryk 2 Aazami, Amir Babak 2 Abiev, Nurlan Abievich 2 A’Campo, Norbert 2 Aleksandrov, Aleksandr Grigor’evich 2 Alharbi, Fawaz 2 Ardentov, Andrei A. 2 Barbero-Liñán, María 2 Belavin, Aleksandr Abramovich 2 Bryan, Jim 2 Carlson, James A. 2 Ceresole, Anna 2 Chen, Hao 2 Chiodo, Alessandro 2 Cogolludo Agustín, José Ignacio ...and 709 more Authors
all top 5
### Cited in 200 Serials
36 Functional Analysis and its Applications 23 Advances in Mathematics 19 Proceedings of the Steklov Institute of Mathematics 18 Mathematische Zeitschrift 17 Journal of Mathematical Sciences (New York) 16 Journal of Geometry and Physics 16 Annales de l’Institut Fourier 16 Duke Mathematical Journal 16 Topology and its Applications 13 Transactions of the American Mathematical Society 12 Communications in Mathematical Physics 12 Mathematical Notes 12 Journal of High Energy Physics 11 Mathematische Annalen 10 Journal of Differential Equations 10 Manuscripta Mathematica 10 Revista Matemática Complutense 9 Inventiones Mathematicae 9 Journal of Algebra 9 Bulletin of the Brazilian Mathematical Society. New Series 9 Arnold Mathematical Journal 8 Israel Journal of Mathematics 8 Compositio Mathematica 8 Journal of Dynamical and Control Systems 8 Journal of Singularities 7 Journal of Mathematical Physics 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Nuclear Physics. B 7 Selecta Mathematica. New Series 7 Bulletin des Sciences Mathématiques 7 Geometry & Topology 6 Moscow University Mathematics Bulletin 6 Theoretical and Mathematical Physics 6 Journal of Pure and Applied Algebra 6 Journal of Algebraic Geometry 6 Algebraic & Geometric Topology 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Journal of Mathematical Analysis and Applications 5 Geometriae Dedicata 5 Journal of the Mathematical Society of Japan 5 Michigan Mathematical Journal 5 Monatshefte für Mathematik 5 Indagationes Mathematicae. New Series 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Russian Journal of Mathematical Physics 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Differential Geometry and its Applications 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 St. Petersburg Mathematical Journal 4 Doklady Mathematics 4 Annals of Mathematics. Second Series 4 Regular and Chaotic Dynamics 3 Archive for Rational Mechanics and Analysis 3 Communications in Algebra 3 Letters in Mathematical Physics 3 Nonlinearity 3 Rocky Mountain Journal of Mathematics 3 Reviews in Mathematical Physics 3 Bulletin of the London Mathematical Society 3 Osaka Journal of Mathematics 3 Proceedings of the American Mathematical Society 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Tôhoku Mathematical Journal. Second Series 3 Physica D 3 Journal of Symbolic Computation 3 Revista Matemática Iberoamericana 3 International Journal of Mathematics 3 Journal of Knot Theory and its Ramifications 3 Izvestiya: Mathematics 3 The Journal of Fourier Analysis and Applications 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Algebra and its Applications 3 Journal de l’École Polytechnique – Mathématiques 2 International Journal of Modern Physics A 2 Journal of Statistical Physics 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Demonstratio Mathematica 2 Glasgow Mathematical Journal 2 Journal of Combinatorial Theory. Series A 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Tokyo Journal of Mathematics 2 Advances in Applied Mathematics 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Discrete & Computational Geometry 2 Computational Mathematics and Mathematical Physics 2 Applicable Algebra in Engineering, Communication and Computing 2 Sbornik: Mathematics 2 Qualitative Theory of Dynamical Systems 2 Moscow Mathematical Journal 2 Mediterranean Journal of Mathematics 2 Functional Analysis and Other Mathematics 2 Analysis and Mathematical Physics 2 European Journal of Mathematics 1 Discrete Applied Mathematics 1 General Relativity and Gravitation 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique ...and 100 more Serials
all top 5
### Cited in 57 Fields
325 Algebraic geometry (14-XX) 243 Several complex variables and analytic spaces (32-XX) 119 Global analysis, analysis on manifolds (58-XX) 112 Manifolds and cell complexes (57-XX) 96 Differential geometry (53-XX) 67 Dynamical systems and ergodic theory (37-XX) 50 Quantum theory (81-XX) 44 Ordinary differential equations (34-XX) 42 Commutative algebra (13-XX) 40 Partial differential equations (35-XX) 30 Group theory and generalizations (20-XX) 23 Algebraic topology (55-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 19 Associative rings and algebras (16-XX) 17 Number theory (11-XX) 16 Combinatorics (05-XX) 16 Nonassociative rings and algebras (17-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Systems theory; control (93-XX) 11 Category theory; homological algebra (18-XX) 11 Functions of a complex variable (30-XX) 11 Probability theory and stochastic processes (60-XX) 11 Optics, electromagnetic theory (78-XX) 11 Relativity and gravitational theory (83-XX) 10 Operator theory (47-XX) 10 Mechanics of particles and systems (70-XX) 9 Real functions (26-XX) 9 Measure and integration (28-XX) 9 Convex and discrete geometry (52-XX) 7 $$K$$-theory (19-XX) 7 Approximations and expansions (41-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Numerical analysis (65-XX) 7 Fluid mechanics (76-XX) 6 Mechanics of deformable solids (74-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Topological groups, Lie groups (22-XX) 5 Integral transforms, operational calculus (44-XX) 5 Geometry (51-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 Field theory and polynomials (12-XX) 4 Operations research, mathematical programming (90-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Statistics (62-XX) 3 Information and communication theory, circuits (94-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Biology and other natural sciences (92-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-08-14T22:33:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6763270497322083, "perplexity": 2643.604902073403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572077.62/warc/CC-MAIN-20220814204141-20220814234141-00063.warc.gz"} |
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/58870bb8472d4a1fef81095d | ### How Newton Discovered Law of Gravitation:
The law of gravitation was discovered by Isaac Newton, which states that “Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” But have you ever wondered how Newton discovered this law? Watch this video to know! | 2019-12-10T03:43:23 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.820945680141449, "perplexity": 140.84097903721513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540525781.64/warc/CC-MAIN-20191210013645-20191210041645-00252.warc.gz"} |
https://par.nsf.gov/biblio/10044103-out-plane-chiral-domain-wall-spin-structures-ultrathin-plane-magnets | Out-of-plane chiral domain wall spin-structures in ultrathin in-plane magnets
Authors:
; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10044103
Journal Name:
Nature Communications
Volume:
8
Page Range or eLocation-ID:
15302
ISSN:
2041-1723
3. ABSTRACT Early-type galaxies – slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars – define a Fundamental Plane (FP) in the space of half-light radius Re, enclosed surface brightness Ie, and velocity dispersion σe. Since Ie and σe are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which Ie and σe can be used to estimate sizes Re. We show that: (1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in Re is $\sim 16{{\ \rm per\ cent}}$, of which only $\sim 9{{\ \rm per\ cent}}$ is intrinsic. Removing galaxies with M* < 1011 M⊙ further reduces the observed scatter to $\sim 13{{\ \rm per\ cent}}$ ($\sim 4{{\ \rm per\ cent}}$ intrinsic). The observed scatter increases to $\sim 25{{\ \rm per\ cent}}$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only 5 per cent orthogonal to the plane. (2) The structure within the FP is most easily understood as arising frommore » | 2023-02-08T11:42:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8459401726722717, "perplexity": 3079.7704531349736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500758.20/warc/CC-MAIN-20230208092053-20230208122053-00669.warc.gz"} |
https://beta11.pnnl.gov/news-media/pnnl-technologies-garner-six-rd-100-honors | October 2, 2020
News Release
## PNNL Technologies Garner Six R&D 100 Honors
Five PNNL inventions recognized in the global innovation competition
R&D 100 | WTWH Media
RICHLAND, Wash. A shoe scanner that would allow people to keep on their footwear as they pass through airport security and a cement that repairs itself are R&D 100 Award recipients. The scanner and self-healing cement are among five innovations developed at the U.S. Department of Energy’s Pacific Northwest National Laboratory (PNNL) that were bestowed six honors this week in the annual international research and development competition.
The R&D 100 Awards, now in its 58th year, recognize pioneers in science and technology from industry, the federal government, and academia. Including the most recent awardees, PNNL has garnered a total of 116 since the program’s inception.
## Millimeter-Wave Shoe Scanner
The Millimeter-Wave Shoe Scanner, which uses imaging to detect concealed objects in footwear, could potentially be integrated into the floor of a body-scanning portal. Anyone who travels can recognize the potential benefit: Passengers would not need to remove their shoes to pass through airport security, thus reducing a bottleneck in screenings. PNNL partnered with the U.S. Department of Homeland Security Science and Technology to build the shoe scanner. The scanner builds on PNNL's pioneering research in optical and acoustic holography dating back to the 1960s. Scientists and engineers determined how to use millimeter waves to penetrate clothing and scan for concealed objects, resulting in commercial body scanner systems. The shoe scanner was a winner in the IT/Electrical R&D 100 Award category.
## Self-Healing Cement
A winner in the R&D 100 Mechanical/Materials category, the self-healing cement can repair itself when cracked or damaged. The innovation also was bestowed a silver medal for the R&D 100 Award Green Tech category. PNNL’s self-healing cement has a restorative polymer component that migrates toward cracks, rebonds, and heals fractures within 24 hours. The polymer makes the material flexible, unlike conventional, brittle concrete. Cracking is a common, expensive problem with concrete, with an annual price tag for repairs of $18 billion to$21 billion. Cracked concrete is a persistent problem for the oil industry, which uses the construction material to build geothermal wells.
## Rapid Analytics for Disaster Response
Rapid Analytics for Disaster Response (RADR), software that can assess post-disaster structural damage, earned an R&D 100 Award in the Software/Services category. PNNL researchers developed RADR as a software suite that provides utilities, energy providers, disaster managers, first responders, and others with a damage assessment capability using image analytics. The software sizes up disasters with critical data within eight hours of an event three to six times faster than traditional methods.
## Shear Assisted Processing and Extrusion
Shear Assisted Processing and Extrusion (ShAPE), an energy-efficient manufacturing method that transforms and improves metals, earned an R&D 100 Award in the Process/Prototyping category. ShAPE transforms metal feedstocks such as ingots, powders, or recycled scrap into higher performing components in a single step. ShAPE a PNNL custom-designed machine uses less energy than conventional extrusion and delivers better products, enabling next-generation materials for a wide variety of high-tech industries.
## Amanzi–ATS
PNNL shared an R&D 100 Award with lead developer Los Alamos National Laboratory for the mapping software application, Amanzi–ATS: Modeling Environmental Systems across Scales.” In addition to PNNL, Oak Ridge National Laboratory and Lawrence Berkeley National Laboratory shared in the softwares development.
R&D 100 winners were announced over a three-day period this week, ending Thursday, in a virtual award presentation. R&D World magazine sponsors the worldwide competition which receives entries from nearly 20 countries or regions. This year’s awards will be presented online Nov. 5, 12 and 19 at the R&D 100 Conference.
###
Pacific Northwest National Laboratory draws on signature capabilities in chemistry, Earth sciences, and data analytics to advance scientific discovery and create solutions to the nation's toughest challenges in energy resiliency and national security. Founded in 1965, PNNL is operated by Battelle for the U.S. Department of Energy's Office of Science. DOE's Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit PNNL's News Center. Follow us on FacebookInstagramLinkedIn and Twitter.
Published: October 2, 2020 | 2021-04-19T13:10:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22323721647262573, "perplexity": 7070.527555087972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038879374.66/warc/CC-MAIN-20210419111510-20210419141510-00125.warc.gz"} |
https://googology.wikia.org/wiki/Largest_known_Fibonacci_prime | 10,954 Pages
The largest Fibonacci prime currently known as of March 2017 is F104,911, where F1 = F2 = 1. It is 21,925 digits long and was discovered in October 2015.[1]
The largest known Fibonacci prime candidate is F3,340,367, which is 698,096 digits long. It was discovered in March 2018.[2]
## Approximations
Notation Approximation
Scientific notation $$5.66\times10^{21\,924}$$
Arrow notation $$2\uparrow\uparrow5$$
BEAF $$\{2,5,2\}$$
Chained arrow notation $$2\rightarrow5\rightarrow2$$
Multivariable Ackermann $$Ack(4,2)$$
Fast-growing hierarchy $$f_2(f_2(13))$$
## Sources
Community content is available under CC-BY-SA unless otherwise noted. | 2021-07-25T23:01:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.880054771900177, "perplexity": 8712.391978018984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151866.98/warc/CC-MAIN-20210725205752-20210725235752-00170.warc.gz"} |
https://www.anl.gov/argonne-scientific-publications/pub/148342 | Publication
Monte Carlo calculation and verification of the geometrical factors for the NPDGamma experiment
Authors
Blyth, D.; Fry, J.; Fomin, N.; Alarcon, R.; Alonzi, L.; Askanazi, E.; Baeßler, S.; Balascuta, S.; Barron-Palos, L.; Barzilov, A.
Abstract
The NPDGamma experiment measures the parity-violating asymmetry in gamma-ray emission in the capture of polarized neutrons on liquid parahydrogen. The sensitivity to the asymmetry for each detector in the array is used as a parameter in the extraction of the physics asymmetry from the measured data. The detector array is approximately cylindrically symmetric around the target and a step-wise sinusoidal function has been used for the sensitivity in the previous iteration of the NPDGamma experiment, but deviations from cylindrical symmetry necessitate the use of a Monte Carlo model to determine corrections to the geometrical factors. For the calculations, source code modifications to MCNPX were done in order to calculate the sensitivity of each cesium iodide detector to the physics asymmetry. We describe the MCNPX model and results from calculations and how the results are validated through measurement of the parity violating asymmetry of gamma-rays from neutron capture on chlorine.
HEP
2018
Article | 2019-06-26T17:03:02 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9411695599555969, "perplexity": 2379.5305904627767}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000367.74/warc/CC-MAIN-20190626154459-20190626180459-00394.warc.gz"} |
https://www.usgs.gov/center-news/1940-was-a-momentous-year-mauna-loa-and-thomas-a-jaggar | # 1940 was a momentous year for Mauna Loa - and for Thomas A. Jaggar
Release Date:
April 2010 marks the 70th anniversary of Mauna Loa's third longest summit eruption in recorded history. The 134-day-long eruption in 1940 has been exceeded in duration only by summit eruptions in 1873-74 and in 1949, which lasted 560 days and 147 days, respectively.
The 1940 eruption began around 11:00 p.m., H.s.t., on April 7, as indicated by increased volcanic tremor recorded on Hawaiian Volcano Observatory (HVO) seismographs. Half an hour later, the first glow at the summit of Mauna Loa was observed by people in Kona.
In Hilo, only a faint crimson glow could be seen through overcast skies, but from Hawaii National Park (later renamed Hawaii Volcanoes National Park), the entire western sky was illuminated by the eruption. A park resident also heard a distinct roar but dismissed it as the sound of a distant car motor.
By 3:00 a.m., H.s.t., military planes from Hickam Field on Oahu were on their way to Hawaii Island. Following a flight over Mauna Loa, the Army Air Corp fliers landed in Hilo and provided the first eyewitness accounts of the eruption, which they described as "spectacular."
During the first few hours, lava fountains 20-60 m (65-200 ft) high erupted along a nearly continuous line of fissures about 5.5 km (3.5 mi) long. The fissures extended from near the center of Mokuaweoweo (Mauna Loa's summit caldera), through the southwest caldera rim, to an area down the southwest flank of the volcano.
Within Mokuaweoweo, floods of pahoehoe lava rapidly covered more than two-thirds of the caldera floor and partially filled North Bay (now called North Pit). Fissures outside the caldera erupted aa flows that advanced downslope about 2 km (1.2 mi) and spilled into three pit craters along Mauna Loa's upper southwest rift zone.
Volcanic gas emissions created a large column of fume that rose more than 3,050 m (10,000 ft) above the summit of Mauna Loa. The lava fountains also produced large quantities of Pele's hair, thin strands of volcanic glass, which were carried by wind and distributed over the entire southern part of the island.
Soon after receiving reports of the eruption, park rangers began ascending Mauna Loa. By the time they reached Mokuaweoweo on the evening of April 8, active vents were restricted to a fissure in the southwestern part of the caldera and remained there for the rest of the eruption. Activity outside the caldera lasted less than a day.
Lava fountains along the active fissure built a row of cinder-and-spatter cones that gradually coalesced to form a single elongate cone more than 100 m (330 ft) high. In 1984, an eruptive fissure cut through, and lava flows surrounded, the 1940 cone, but it remains a prominent landmark on the floor of Mokuaweoweo.
The 1940 eruption increased in intensity in mid-April, when lava fountains occasionally blasted spatter, pumice, and cinder to heights of 275 m (900 ft). Throughout May, June, and July, the volcanic activity was intermittent, with periods of seeming quiet lava effusion followed by eruptive outbursts. Lava fountains rarely reached heights greater than 30 m (100 ft), but fluid lava continued to cover almost the entire caldera floor. By the end of the eruption, the average depth of 1940 lava flows in Mokuaweoweo was 14 m (45 ft).
Following a brief burst of activity in mid-August, Mauna Loa's third longest summit eruption ended on the night of August 18.
The 1940 Mauna Loa eruption is also noteworthy in that it was Thomas A. Jaggar's last as HVO's Director. He retired from HVO on July 31 but continued his study of Hawaiian volcanoes as a Research Associate in Volcanology at the University of Hawaii.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
On Kīlauea's east rift zone, small breakouts remain active above Pulama pali and were visible from Kalapana by the beginning of the week. Despite the continued activity, the overall vigor of the surface flows seems lower than usual.
At Kīlauea's summit, a ponded, circulating lava surface deep within the collapse pit inset within the floor of Halemaumau Crater was visible much of the time via Webcam during the past week. Volcanic gas emissions remain elevated, resulting in high concentrations of sulfur dioxide downwind.
Two earthquakes beneath Hawai`i Island, both southwest of Waimea, were reported felt during the past week. A magnitude-2.1 earthquake occurred at 3:13 a.m., H.s.t., on Monday, March 29, 2010, and was located 6 km (4 miles) southwest of Waimea, at a depth of 8 km (5 miles). A magnitude-2.4 earthquake occurred at 1:59 p.m, on Tuesday, March 30, and was located 7 km (4 miles) southwest of Waimea, at a depth of 2 km (2 miles). | 2020-04-09T21:58:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2799340784549713, "perplexity": 4598.477533976771}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371876625.96/warc/CC-MAIN-20200409185507-20200409220007-00118.warc.gz"} |
https://ffxiclopedia.fandom.com/wiki/Talk:Modus_Veritas?diff=prev&oldid=1156415 | ## FANDOM
53,306 Pages
Ok now theoretically spoken if we got an alliance of 18 SCH and stick a 100 damage Helix onto a mob. Now we let the SCH all Modus Veritas onto that one, and assuming there will be at least 1 more tick we would look at a damage total of: $100$(initial) + $100*2^{18}$ = 100 + 26,214,400 damage
So you could even "1-Shot" AV just my 2 cent Nemumancer 15:59, 19 April 2008 (UTC)
Unless you got it within milliseconds of the next tick, you wouldn't be able to pull it off. That said, you certainly can get to the point where it would actually add damage using this strategy. Tahngarthortalk-contribs 16:15, 19 April 2008 (UTC)
Well, a tick for a helix spell is 10 seconds, so in theory you possibly could. Shentok 18:23, 19 October 2008 (UTC)
I did a little math on the helix discussion page, so if anyone wants to take a look at it, it'd be greatly appreciated. I believe it shows some nice information and theoretical capabilities of SCH as a DoT job. --- Elixer Of Quetz 14:27, 30 Nov 2008 (CST)
## Modus Veritas Merits
Is my understanding correct that merits in this reduce the duration reduction, such that a fully merited Modus Veritas does not reduce a Helix's duration at all? --Volkai 13:03, 9 September 2008 (UTC)
That's what it looks like. With all due respect, however, it's possible that it might merely reduce it by 10% of the reduction amount - never really know with SE sometimes. Of course, given the description, I believe that this assumption would be the most accurate and would REALLY up the damage potential of this - though some people think it would be worthless. I don't know.. if the base hit is 80-100 damage, and you use a fully merited Modus Veritas, that would be 160-200 damage per tick for ten ticks. So, in total, 1600-2000 damage in one minute's time.. of course, that's if it's not at all resisted and lasts for the entire time. Imagine what this could do, for damage reasons, if multiple SCHs would fully merit this and stack it upon an enemy. Indeed, this has great potential, if people are willing to merit it. --- Elixer_Of_Quetz 10:42, 9 Sep 2008 (CST)
The exact wording is that each level of merits increase the duration of Modus Veritas, as opposed to reducing the time reduction. Based on that wording, I would guess that it would increase the initial 50% duration, by 50%. So possibly a fully merited Modus Veritas would only reduce the duration of the helix spell by 25%, instead of 50%. This is only a guess of course, it will need much more testing. --FFXI-Setesh 01:50, 27 September 2008 (UTC)
## Modus Veritas "Ticks"
If I'm reading this right Modus doesn't lessen the damage done, it halves the time between "ticks" and does double the damage (without merits), so it wouldn't matter when however many Scholar's used Modus, because it'll just do more damage quicker?
• No Modus = xdmg every 10 seconds
• 1 Modus = 2xdmg every 5 seconds
• 2 Modus = 2^2xdmg every 2.5 seconds
• 3 Modus = 2^3xdmg every 1.25 seconds
• 4 Modus = 2^4xdmg every 0.625 seconds
• 5 Modus = 2^5xdmg every 0.3125 seconds
• 6 Modus = 2^6xdmg every 0.15625 seconds
If other Sch's in the ally can use it too
• 18 Modus - 2^18xdmg every 0.00003814697265625 seconds
I don't know if I'm reading the description wrong or not --Bikpik 16:50, 25 March 2009 (UTC)
The idea is that Modus Veritas (as I can personally verify) decreases total duration, but not time in-between individual 'ticks'. The time in-between the damage remains consistent, at least when Modus'd once.
Finally, Modus may be used even if you are not in the alliance, provided you can attack the target. (Such as Dynamis, or Call for Help.) --Taeria Saethori 05:22, 26 March 2009 (UTC)
Well if that's the case then this would be pretty much impossible to pull off, with lag and latency issues. If 1 "tick" is 10 seconds, and everyone waits until what they think is 9 seconds, then if 18 Schs fire off Modus then it would cause the next tick not to happen. The cut off point would be 6 Schs (maybe lucky with 7) 6 Modus would cut the duration to 1.5625 seconds (7 Modus would be 0.78125 seconds), but that still would do a nice chunk of damage. 100 dmg helix with 6 Schs would = 6400 (7 = 12.8k), so as you can see, it's nothing game breaking in either case.
--Bikpik 13:30, 26 March 2009 (UTC)
Someone managed to one shot a UFO using this: [1] --Sabishii 22:13, September 26, 2009 (UTC)
Well, they took it from us. Before we could even try anything real fun with it, like one-shotting AV. Shame, really, its not like it was easy to time or a fool-proof tactic to one-shotting hnms. As of the 11/9/09 update, Modus has been addressed by SE, making some mobs (almost definately AV although it hasnt been comfirmed yet) resistant to the effect and adding a time delay to the ability usage (unknown mechanics at this time). --Kravler 22:35, November 9, 2009 (UTC)
## Modus Veritas Glitched?
Since the 6/21/10 update has anyone been able to land Modus Veritas on mobs with any decent success rate?
Community content is available under CC-BY-SA unless otherwise noted. | 2020-05-29T05:10:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.70939040184021, "perplexity": 3262.7684944601647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347401260.16/warc/CC-MAIN-20200529023731-20200529053731-00315.warc.gz"} |
http://www.itl.nist.gov/div898/handbook/pmd/section6/pmd644.htm | 4. Process Modeling
4.6. Case Studies in Process Modeling
4.6.4. Thermal Expansion of Copper Case Study
4.6.4.4.
Q/Q Rational Function Model Starting Values Based on the procedure described in 4.6.4.2, we fit the model: $$y = A_0 + A_1 x + A_2 x^2 - B_1 x - B_2 x^2 + \varepsilon \, ,$$ using the following five representative points to generate the starting values for the Q/Q rational function.
Temp THERMEXP
---- --------
10 0
50 5
120 12
200 15
800 20
The coefficients from the preliminary linear fit of the five points are:
A0 = -3.005450
A1 = 0.368829
A2 = -0.006828
B1 = -0.011234
B2 = -0.000306
Nonlinear Fit Results The results for the nonlinear fit are shown below.
Parameter Estimate Stan. Dev t Value
A0 -8.028e+00 3.988e-01 -20.13
A1 5.083e-01 1.930e-02 26.33
A2 -7.307e-03 2.463e-04 -29.67
B1 -7.040e-03 5.235e-04 -13.45
B2 -3.288e-04 1.242e-05 -26.47
Residual standard deviation = 0.5501
Residual degrees of freedom = 231
The regression yields the following estimated model. $$\hat{y} = \frac{-8.028 + 0.508x - 0.007307x^{2}} {1 - 0.00704x - 0.0003288x^{2}}$$
Plot of Q/Q Rational Function Fit We generate a plot of the fitted rational function model with the raw data.
Looking at the fitted function with the raw data appears to show a reasonable fit.
6-Plot for Model Validation Although the plot of the fitted function with the raw data appears to show a reasonable fit, we need to validate the model assumptions. The 6-plot is an effective tool for this purpose.
The plot of the residuals versus the predictor variable temperature (row 1, column 2) and of the residuals versus the predicted values (row 1, column 3) indicate a distinct pattern in the residuals. This suggests that the assumption of random errors is badly violated.
Residual Plot We generate a full-sized residual plot in order to show more detail.
The full-sized residual plot clearly shows the distinct pattern in the residuals. When residuals exhibit a clear pattern, the corresponding errors are probably not random. | 2017-10-21T22:57:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.593851625919342, "perplexity": 1704.7868393169974}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00616.warc.gz"} |
http://dlmf.nist.gov/30.2 | # §30.2(i) Spheroidal Differential Equation
30.2.1 $\frac{d}{dz}\left((1-z^{2})\frac{dw}{dz}\right)+\left(\lambda+\gamma^{2}(1-z^{% 2})-\frac{\mu^{2}}{1-z^{2}}\right)w=0.$
This equation has regular singularities at $z=\pm 1$ with exponents $\pm\frac{1}{2}\mu$ and an irregular singularity of rank 1 at $z=\infty$ (if $\gamma\neq 0$). The equation contains three real parameters $\lambda$, $\gamma^{2}$, and $\mu$. In applications involving prolate spheroidal coordinates $\gamma^{2}$ is positive, in applications involving oblate spheroidal coordinates $\gamma^{2}$ is negative; see §§30.13, 30.14.
# §30.2(ii) Other Forms
The Liouville normal form of equation (30.2.1) is
30.2.2 $\frac{{d}^{2}g}{{dt}^{2}}+\left(\lambda+\frac{1}{4}+\gamma^{2}{\mathop{\sin\/}% \nolimits^{2}}t-\frac{\mu^{2}-\frac{1}{4}}{{\mathop{\sin\/}\nolimits^{2}}t}% \right)g=0,$
30.2.3 $\displaystyle z$ $\displaystyle=\mathop{\cos\/}\nolimits t,$ $\displaystyle w(z)$ $\displaystyle=(1-z^{2})^{-\frac{1}{4}}g(t).$
With $\zeta=\gamma z$ Equation (30.2.1) changes to
30.2.4 $(\zeta^{2}-\gamma^{2})\frac{{d}^{2}w}{{d\zeta}^{2}}+2\zeta\frac{dw}{d\zeta}+% \left(\zeta^{2}-\lambda-\gamma^{2}-\frac{\gamma^{2}\mu^{2}}{\zeta^{2}-\gamma^{% 2}}\right)w=0.$
# §30.2(iii) Special Cases
If $\gamma=0$, Equation (30.2.1) is the associated Legendre differential equation; see (14.2.2). If $\mu^{2}=\frac{1}{4}$, Equation (30.2.2) reduces to the Mathieu equation; see (28.2.1). If $\gamma=0$, Equation (30.2.4) is satisfied by spherical Bessel functions; see (10.47.1). | 2014-10-25T11:12:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 46, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9623265862464905, "perplexity": 1151.82906115991}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119648146.28/warc/CC-MAIN-20141024030048-00128-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S008T&home=sumtabM | # ${{\boldsymbol \pi}^{\pm}}$ MEAN LIFE INSPIRE search
Measurements with an error $>$ $0.02 \times 10^{-8}~$s have been omitted.
VALUE ($10^{-8}$ s) DOCUMENT ID TECN CHG COMMENT
$\bf{ 2.6033 \pm0.0005}$ OUR AVERAGE Error includes scale factor of 1.2.
$2.60361$ $\pm0.00052$ 1
1995
SPEC + Surface ${{\mathit \mu}^{+}}$'s
$2.60231$ $\pm0.00050$ $\pm0.00084$
1995
SPEC + Surface ${{\mathit \mu}^{+}}$'s
$2.609$ $\pm0.008$
1973
CNTR +
$2.602$ $\pm0.004$
1971
CNTR $\pm{}$
$2.604$ $\pm0.005$
1967
CNTR +
$2.602$ $\pm0.004$
1965
CNTR +
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.640$ $\pm0.008$ 2
1966
CNTR +
1 KOPTEV 1995 combines the statistical and systematic errors; the statistical error dominates.
2 Systematic errors in the calibration of this experiment are discussed by NORDBERG 1967 .
References:
KOPTEV 1995
JETPL 61 877 Measurement of ${{\mathit \pi}^{\pm}}$ and ${{\mathit K}^{\pm}}$ Lifetime
NUMAO 1995
PR D52 4855 A New ${{\mathit \pi}^{+}}$ Lifetime Measurement
DUNAITSEV 1973
SJNP 16 292 On Measuring the Mean Lifetime of ${{\mathit \pi}^{+}}$ Meson with a High Speed Multiray Scope
AYRES 1971
PR D3 1051 Measurements of the Lifetimes of Positive and Negative Pions
NORDBERG 1967
PL 24B 594 Remeasurement of the ${{\mathit \pi}^{+}}$ Lifetime
KINSEY 1966
PR 144 1132 Measurement of the Lifetime of the Positive Pion
ECKHAUSE 1965
PL 19 348 A New Measurement of the Lifetime of the Positive Pion | 2020-07-11T14:38:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7496859431266785, "perplexity": 9742.37734242268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655933254.67/warc/CC-MAIN-20200711130351-20200711160351-00266.warc.gz"} |
https://tianjara.net/blog/tags/law/ | # tianjara.net | Andrew Harvey's Blog
### Entries tagged "law".
12th November 2010
I've taken some time to look at the NearMap licenses (Community License, Free Commercial License) more closely. Here is some of my commentary of them. I'll use the terminology used in the licences so please excuse me for using their language and jargon. When I say free I mean free as in "free software", "free culture" and "free as in freedom". Also this is just my interpretation from reading them, I am not a lawyer. Hopefully I've interpreted them as NearMap intended.
## Derived Works
"ShareAlike is an imperfect solution to copyright restrictions, as it imposes one restriction of its own: a restriction against imposing any further restrictions. It's an attempt to use copyright against itself. As long as we live in a world wherein everything is copyrighted by default, I will use ShareAlike or some other Copyleft equivalent to attempt to maintain a "copyright-free zone" around my works. In a better world, there would be no automatic copyright and thus no need for me to use any license at all. Should that Utopia come about, I will remove all licenses from all my work. Meanwhile I attempt to limit other peoples' freedom to limit other peoples' freedom." -- http://questioncopyright.org/CC-branding-confusion
Another important observation that I previously overlooked is the fact that,
"You will own all Derived Works that you create. However, you may only distribute Derived Works to others on the terms of a Creative Commons Attribution Share Alike (CC-BY-SA) licence (and you may use any version of that licence you wish, whether localised for a particular country or not). For example, you may Use the Licensed PhotoMaps or Modified PhotoMaps to obtain information which you can then use, under the Creative Commons Attribution Share Alike (CC-BY-SA) licence, to populate or update community street mapping projects." -- http://www.nearmap.com/products/community-licence#clause5
Previously I had thought that any derived works that came from NearMap PhotoMaps used in OpenStreetMap needed to be attributed to NearMap. I guess I just incorrectly thought that all the information was CC BY-SA licensed by NearMap, but that is not the case. These works actually need to be attributed to the user who observed that information and turned it into a work by, for example, adding it into the OSM database. The works do not need to be attributed in any way to NearMap.1 This also means that any copyright that arises from any creativity in deciding what to trace, and any copyright that arises from the tracing being a derivative work can be treated as CC BY-SA licensed by that person or user. That person is the copyright holder but they are only allowed to distribute the work under a CC BY-SA license. This is a good thing! I'm glad that NearMap have not chosen to change the wording to make it compatible with the public-domain-like OpenStreetMap contributor terms, as (unless of course one has some other license from NearMap) it guarantees that this information remains free2.
The discussion and use of Yahoo imagery as a source of tracing for OpenStreetMap was before my time, but from http://wiki.openstreetmap.org/wiki/Yahoo it seems that strong legal foundations are lacking. In this respect I feel much safer tracing from NearMap. I know that my contributions can be licensed under the free CC BY-SA license and nothing can be done to unfree these works. Whereas the legalities of Yahoo imagery is, at least from my reading, very questionable and potentially a huge problem in the future.
## Modified Works
Another reason I took a closer look at the licenses was to make sure that the works I posted earlier which were modified PhotoMaps complied with all licensing requirements, both the NearMap and OpenStreetMap requirements. I have come to the conclusion that unfortunately I am most likely unable to satisfy both the Mapnik share-alike requirement and the NearMap share-alike requirement in coexistence.
The NearMap "free community licence" gives me the "right to use, copy, modify and distribute our PhotoMaps". The distribution to others clause says that I must give NearMap attribution for the distribution of any original or modified PhotoMaps, however the license also says "You may sublicense your rights to the Licensed PhotoMaps, Modified PhotoMaps or APIs to others on the same terms as this licence or our free commercial licence." I interpret this as if I modify a PhotoMap I need release it under the "NearMap free community license", that is it is share-alike.
On the other hand though, I also used the default OpenStreetMap Mapnik-style map images. My understanding is that like the data used to create these maps, the actual map images are copyrighted by all the OpenStreetMap contributors and released under the CC BY-SA license. The share-alike means that any derivative works (like overlaying NearMap terrain maps) must the released under a CC BY-SA compatible license, so you cannot impose non-commercial or non-government on it. However although the NearMap free community licence plus the NearMap free commercial license almost allow anyone to use or modify the work they don't meet CC BY-SA because they exclude government and exclude commercial use made in a "competing manner" and use that is "material to their business". This leaves me to believe that I cannot legally distribute any work that is a mash-up of OSM data/maps and NearMap PhotoMaps. Unless of course that it is only the default Mapnik tiles that are CC BY-SA, and that anyone can copyright map images made from OSM data. Because NearMap uses OSM data to create Mapnik tiles using their own map style. I assume then that it is only the OSM data that is CC BY-SA and someone is free to make a non-free map using their own style from this data. Then they would own the copyright to that map and hence you would be free to combine this with NearMap's PhotoMaps and release the product under their free community license. This could also explain why NearMap can overlay their transparent tiles based on OSM data over their non CC BY-SA imagery.
It is a shame, but I can totally understand NearMap restricting use of their PhotoMaps in a specific field of endeavor, namely the government. The government is central to their current revenue stream, without it they probably could not produce the volume of work they currently do under their almost free, community license. It is almost CC BY-SA, except they exclude three fields of endeavor, "Competing Manner", "Material to their business" and "Government Entities that use our PhotoMaps for their own governmental purposes". The first two exclusions make the PhotoMaps near CC BY-NC-SA, but the last clause means they cannot be compatible with any of the Creative Commons licenses.
Let me use the example case of distribution of original NearMap PhotoMaps. For instance say I download a bunch of imagery tiles and distribute them through BitTorrent, the key question here is do I need to enforce that this distribution is to non-government entities. If I am only allowed to distribute it to non-government, I cannot do that, so the freedoms that the license grants are not as broad as I thought. If on the other hand if I can distribute the works to government entities along with the free community license as a LICENSE file, but leave the responsibility and liability on the government to not use the works I make available, then this would be much better. Hopefully the latter is the case. This was almost touched on here, but which party the liability lies on was not mentioned.
## Termination
This is why I hate reading all this legal jargon, every word is important but has different interpretations. Code on the other hand has just one interpretation, and that is defined in the compiler... Anyway, at first I thought this termination clause meant NearMap could terminate the license grant at any time, however I missed the words "if the other party breaches this licence". I view this to mean that NearMap cannot terminate the license grant unless you breach the license. But even if such a case arose, derived information is safe. So NearMap can do nothing to prevent the CC BY-SA distribution of derived information. Although it appears all the other parts of the license grant can be subject to this clause.
1 However I still think that one should attribute NearMap regardless. In the OSM case, attribution using the source tag should be done for other reasons as well; like so people know where the data came from, hinting some clues of the quality of the data.
18th February 2010
Following up from my previous post, I have made improvements to the code, and I now have all the NPLAN data too. There are also some data files so you don't need to run the scraper and parser which hopefully this makes the data more usable and to a wider range of people. Now that I have the NPLAN data you can compare schools in terms of their (I assume the numbers are averages) test results. I was going to put in the repository some tables mashing together some of the data in the database, but I've had to research about a silly NSW law first. I'm not exactly sure what I can publish and what the implication of that would be (so best make your own league tables and possibly publish them if you want). The NSW law says,
A person must not, in a newspaper or other document that is publicly available in this State: (a) publish any ranking or other comparison of particular schools according to school results, or, (b) identify a school as being in a percentile of less than 90 per cent in relation to school results.
The folks at the Sydney Morning Herald seem to think that "Published online the same tables infringe no law; printed on these pages they are illegal." This is not what I interpret the law as. Publishing online means that the document is available for access from NSW. However I am confident I can get around this by not hosting anything myself and not hosting in Australia. For this I rely on the great services provided by wordpress.com (Automattic, Inc.) and/or github.com (GitHub, Inc.). Hopefully these US companies wouldn't cave into any threats from the Australian government.
This section of the law carries a maximum of 50 penalty units. Which is currently a fine of 5500, that is a large enough sum for me to take extra care. This is why I'm still not sure if I should put such lists like schools ordered by certain NPLAN results in the github repository. By the way, this censorship and damaging law raises the same questions and problems (problems for those that wish to avoid criminal or civil charges) about legal jurisdiction over the internet, the classic example is the "yahoo! nazi paraphernalia" debacle. Footnote: This SQL query should give you an ordered list of schools based on the 2009 year 9 NPLAN results (but I guess if you can load the database dump you can probably write your own queries...). SELECT s.name, n.score, sub.state FROM nplan n, school s, (SELECT distinct pcode, state FROM suburb) sub WHERE n.school = s.myschool_url AND s.postcode = sub.pcode AND n.year = 2009 AND n.grade = 9 AND n.area = 'numeracy' ORDER BY n.score DESC; Tags: education, law. 8th February 2010 I post these here for the purpose of future reference and use. ...for purpose of parody or satire ...for the purpose of, or is associated with, the reporting of news by means of a communication... ...for the purposes ... of a report of a judicial proceeding. They are "Acts not constituting infringements of copyright in works". So I'm just reminding myself of these rights so that any time I wish to use material covered by these, I can just grab the text and link from here and note it next to the copy. Of course this is not really relevant here because this blog is hosted by a US company, but it would be help if I were to one day decide to self host in Australia. Tags: law. 22nd January 2010 So I've started reading a book about networks, and to complement this I've been taking a closer look at my network traffic in Wireshark (really great tool, by the way.). So I pick an ftp site that I know, ftp://download.nvidia.com/ and see what happens in Wireshark when I visit it in Firefox. At the FTP application level this is what happens, ftpsite to me: 220 spftp/1.0.0000 Server [69.31.121.43]\r\n me to ftpsite: USER anonymous\r\n ftpsite to me: 331 Password required for USER.\r\n me to ftpsite: PASS [email protected]\r\n ftpsite to me: 230- \r\n 230- ---------------------------------------------------------------------------\r\n 230- WARNING: This is a restricted access system. If you do not have explicit\r\n 230- permission to access this system, please disconnect immediately!\r\n 230 ----------------------------------------------------------------------------\r\n But Firefox does not disconnect. So I did some more research and I found no references to "anonymous" users in either RFC 959 (FTP) or RFC 3659 (extensions to FTP). (Though there are references in latter RFCs, see RFC 2228). The thing I find disconcerting is that I don't think I have "explicit permission" to access this system. I (or rather Firefox) just guessed a username and password and they happened to let me in (what if I guessed a different username and password that wasn't anonymous and it let me in?). If the RFC specified that a user of anonymous requires no password, or any password, then I would assume that the FTP server is granting me permission, but I assume rather people just started using anonymous as the user and it caught on... The real problem here is that there are laws which govern such areas, and it doesn't help that that I don't understand what PART 6 - COMPUTER OFFENCES of the CRIMES ACT 1900 (NSW) is saying. Tags: computing, law. 4th January 2010 What happens when you mix a service like AustLii with version control system like Git with a wiki like editing system, and deliver it to the people through the web? Well I haven't tried, but it sounds like a good idea. You get a service that, • allows anyone to propose changes to laws (and work on branches) or draft and new laws, and • keeps track of the law and when it was changed (and which politicians/parties introduced those changes, who voted for them, etc...). Tags: law, politics. 19th September 2009 I try my best to be accurate, but I would not be surprised if I have made some errors here. Also this post is still a work in progress and I'll be making changes. # Week 1 & 2 ## Historical Origins of The Australian Legal System • Common Law Legal System • Australia has a "Common Law Legal System". The main feature of this that separates it from other Western legal systems is the degree that it relies on precedent (through the doctrine of precedent). Under this system laws either come from Parliament, called legislation, or Courts, called case law or common law. • I've come to realise that its not enough to just follow just the legislation as cases can provide extra details and insights into the legality of a matter. Furthermore you can rely on these precedents in court (although it seems they can go back on their decisions and make new precedents to override old ones, as seen with [2009] HCA 14.). • Institution Laws People parliament statute law members of parliament courts common law judges (most courts)/magistrates (in the local court) • Barristers are the ones in court arguing a case, eg. in litigation. Solicitors are the people you usually go to see first. They can arrange a barrister, draft wills, give legal advice, etc. • Norman Period • Australian Law stems from English law. English Law started out in the Norman Period. • Feudalism • It is a hierarchy where the king is at the top. The king own all the land and leases it out. This goes down a few levels where at the bottom you have people who are allowed to use the land if they share their crops and provide military service if necessary. • Trials by Ordeal and Trials by Battle. • Relied on "divine intervention" to determine the verdict. • The Writ System (court orders...) • Lead to Equity. • Equity -> eg. forced to comply with the contract. • Constitutionalism -> Can be thought of as 'guidelines for government' • Magna Carta • Just an old document. But an important clause was that no one could be detained without being charged, and right to trial. • allowing appeal against unlawful imprisonment. • Includes, • A right that a person can seek relief from the unlawful detention of him or herself, or of another person. • Westminster (Parliament) • Monarchy <-> Republic • House of Lords/House of Commons (Upper House/Lower House) • Parliament • Legislative Arm -> Creation of laws • Executive Arm -> Administration of laws • The Bill of Rights 1689 • Non-Partisan - Not affiliated with a political party • Security of Tenure of Judges - Protects from external pressure. ie. contractual right not to be sacked without just cause. • Trial by Jury • Originally (ages ago in England) the jury were locals, now they are impartial (and so are the judges) which means that they have no prior knowledge of the case. • Saxton's introduced compensation into the law # Week 3 ## Rule of Law The rule of law had origins in the Magna Carta but its not what we now consider "the rule of law". The key theme of the Rule of Law is everyone is subject to the law. Eight Ways to Make Law Fail (based on the allegory concerning Rex): • Failure to publicise law • Obscure law • Retroactive law • Contradictions in the law • Unable to comply with the law • Unstable daily amendments to the law • Differences between rules/laws as announced and their administration However at least some of these (if not all) are not law themselves. They are not in the constitution so there is nothing stopping a government from creating say retrospective law. ## Law, Land & Society Before 1788 Terra Nullius is a term used to describe be land belonging to no one. The British belied Australia to be Terra Nullius as they did not see the land as having an established legal system. # Week 4 ## Types of Legal Systems • Common Law • Adversarial System (this is the type of procedure practised in common law courts) • "relies on the skill of each advocate representing his or her party's positions and involves an impartial person, usually a jury, trying to determine the truth of the case." (Wikipedia.org, Adversarial System) • Mostly done orally in the court room. • Civil Law • "The Code" • No precedence (so there is no case law) • Inquisitive System (this is the type of procedure practised in civil law courts) • "has a judge (or a group of judges who work together) whose task is to investigate the case" (Wikipedia.org, Inquisitive System) • Mostly done through written submissions to the judge. • Judge actively steers routes of evidence investigation (compared with a common law system where the lawyers do this). • No jury (mostly). • Communist Law • Religious Law • Customary Law • eg. Aboriginal customary law • Never written down These legal systems "supposedly" all have the same aim. ## Separation of Powers Kept separate to balance power of any one: 1. Legislative Arm (Parliament) • Amends/Creates Laws 2. Executive Arm • Administrate Laws/Initiating Laws/Enforce laws • Government Departments, Governor General, Police... 3. Judicial Arm • Courts/Judges (High Court...) • Interpret laws Jurisdiction is the power of a court to exercise judgement. Three different types of jurisdiction, • State vs. Federal • Original vs. Appeal • Civil vs. Criminal # Week 5 ## Federation and Laws Made By Parliament • Australia Act 1986 (ie. federation) (according to the constitution) stipulates the number of senators and the distribution among the states. • It was not until the UK passed their statues did Australia become legally a federation. • Senate (Upper House) -> Scrutinise Bills • House of Reps (Lower House) -> Draft/Introduce Bills To get voted into the senate you need 1/6 + 1 of the votes. Once you reach this quota extra votes that would be used on you are distributed to the voters other preferences. Senators are only up for election every two elections (usually). • Senate -> Representative of the State • Reps -> Representative of the Country (Although its a little more detailed as they are really representative of the electorate. Because of this you can have a party with 49% of the votes but still get no members into the house of reps.) We generally get lots of independents in the senate because people rarely vote 1. Labor 2. Liberal. If someone supports party A where B is A's greatest competitor, most people will usually not vote for their opposition as 2, so they sometimes put some independents (remember once the quote is met, surplus votes are redistributed (either as the voter order their preferences, or if not chosen by the voter, how the party chooses)). • With regards to politicians voting on bills, a Conscious Vote is crossing the partly line (or whatever the party decided on how they would vote) vs. a Party Vote where you (the politician) vote as your party does regardless on what you think. Preferential Voting ensures a strong 2 party system. Passing a Law: (Repeated for each house) • 1st Reading • 2nd Reading - Purpose of the bill (Sometimes used by lawyers to interpret the law). • 3rd Reading The Australian Constitution stipulates which matters the Commonwealth have power to make laws over and which the states have power. # Week 6 ## Laws Made By Courts & Precedent An indictable offence is one where you can go to prison over it. A case begins in the local court with committal proceedings, except for the more serious cases which begin in the supreme court. But there are some exceptions, for example certain constitutional cases will go straight to the High Court. The different courts are listed http://www.austlii.edu.au/databases.html, although the list is not complete as you also have local courts in most states. Local court -> District Court -> Supreme Court -> High Court. [caption id="attachment_756" align="aligncenter" width="450" caption="Hierarchy of the Australian Courts"][/caption] • If you don't like the decision make by one court you can appeal to a higher one. • For a matter to be heard in court there must be "reasonable prospects of success". • Civil matters claiming over750 go straight to the supreme court.
In a criminal case beyond a reasonable doubt must be established, this is not the case in civil cases.
Because we have a common law legal system (adversarial), "the judge can only make a decision about what was herd in court and cannot make any other inquiries about the case"1.
"A judge will usually order that the costs of the successful party be paid by the unsuccessful party."1
• Ratio decidendi
• reason for judgement.
• meaning "the reason" or "the rationale for the decision."
• Unlike obiter dicta, the ratio decidendi is, as a general rule, binding on courts of lower jurisdiction—through the doctrine of precedent.
• Obiter dicta
• is a remark or observation made by a judge that, although included in the body of the court's opinion, does not form a necessary part of the court's decision.
• statements constituting obiter dicta are not binding (meaning cannot be used as argument for a precedent), although in some jurisdictions, they can be strongly persuasive.
• The High Court is the final court of appeal in Australia in matters of both State and Federal.
• Must rely on a precedent in a higher court (which implies that the precedents set by the high court are binding in all other courts).
• BUT the Full Court of the High Court is not bound by previous decisions made by the High Court, so the High Court can overrule itself.
• The Full Court of the High Court means all the judges (there are 7 and they are called justices) sit in and vote on the case, rather than just one judge per case.
• The full court of the Federal court means at least three judges sit in.
• Try mostly have an odd number of judges as when making a decision on a case, the majority prevails.
• If you don't like the precedents try to find differences that can distinguish the cases.
• If no precedent, you can look at obiter dicta, or you can look into other jurisdictions (these are not binding but can be persuasive).
# Week 7
## The Legal Profession
Barristers and Solicitors are distinct parties. They have different roles and have no relation. "Solicitors have more direct contact with the clients, whereas barristers often only become involved in a case once advocacy before a court is needed by the client. Barristers are also engaged by solicitors to provide specialist advice on points of law. Barristers are rarely instructed by clients directly (although this occurs frequently in tax matters). Instead, the client's solicitors will instruct a barrister on behalf of the client when appropriate." (Wikipedia.org, Barrister)
In Australia Barristers are always sole traders. The research for a case is done by the solicitor who gives a brief to the barrister before they appear in the court.
Attorneys are much the same as Solicitors. The term Attorney is used more commonly in the US.
# Week 9
• Negotiation
• Informal
• Voluntary
• Both parties meet privately and try to work out a resolution without needing to go to court.
• Can lead to a settlement.
• Private. Unlike adjudication which is public. Companies that don't want the media attention that may come from a court case, make take this option.
• Quick
• One negative for the public is that no precedent is set, so little people cannot rely on large corporations to set the precedents for them.
• Mediation
• Voluntary
• Mediator is present
• Outcome only accepted when both parties agree to it
• Individual may feel in control of the matter rather than their lawyer.
• Business relationships can be maintained
• Conciliation (only for some courts)
• Mandatory
• Mediator present, but cannot enforce/make a decision on the outcome
• Can be lengthy taking from months to years.
• Arbitration
• Tribunals
• Courts
• Legislation
• The government changes the law to make a certain dispute clear.
This is very much a scale. At the top the parties very much are in control of the outcome. Whereas at the bottom they don't have much control at all of the outcome (so long as the system is not corrupt). The top is informal, wheras the bottom is formal. At the top things are by agreement, whereas at the bottom things are much by imposition.
## Other Legal Institutions
• Tribunals are set up by laws.
• They are like courts but are less formal.
• Unlike courts the strict doctorine of precedent does not apply to tribunals.
The Administrative Decisions Tribunal (ADT) is one such tribunal (they are is the NSW jurisdiction). The Administrative Appeals Tribunal is another tribunal (federal jurisdiction). As per their website "The Administrative Appeals Tribunal (AAT) provides independent review of a wide range of administrative decisions made by the Australian government and some non-government bodies. The AAT aims to provide fair, impartial, high quality and prompt review with as little formality and technicality as possible. Both individuals and government agencies use the services of the AAT."
In most cases if you are unhappy with the tribunals decision you can appeal to a court, although there are conditions on this. For example as stated on the AAT's web site "If you disagree with the Tribunal's decision you may appeal to the Federal Court on a point of law. This means that the Court can only hear an appeal from the Tribunal decision if you or your adviser believe the Tribunal made a mistake in law in deciding your case. Because there are many rules about Federal Court appeals you may wish to get legal assistance."
# Week 10
## Contracts and Torts
### Contracts
• A contract is an agreement that is enforceable through the courts.
• Contracts can be written or verbal, but written contracts are easier to prove.
• For a contract to be valid there must be, (i.e. otherwise the contract is void, meaning its not legally binding)
• An intention by the parties to be legally bound by their promises,
• agreement by the parties on the terms of the contract,
• consideration from both sides.
• If the parties do not intend for a contract to be legally binding and there is agreement on that then the courts will honour this. (See Rose and Frank v Crompton [1923] 2 KB 261).
• When not expressly stated the courts will presume that, (but this can be rebutted, see Wakeling v Ripley (1951) 51 SR (NSW) 183)
• social, family or domestic agreements are not intended to be legally binding, and
• commercial agreements are intended to be legally binding.
### Agreement of a Contract
• As mentioned for a contract to be valid it must have agreement by the parties.
• Offer and Acceptance
• An offer is made by one party, and if accepted by the other, then the contract has agreement. (I think that means, if you make an offer they say okay, you cannot go back and not be bound by the contract.)
• An "invitation to treat" is not an offer.
• Lapse of an offer
• Acceptance
• Silence is not acceptance (Felthouse v Bindley (1862) 11 CB (NS) 869) (but an act can be)
• Acceptance must be in response to an offer for the contract to be valid (R v Clarke (1927) 40 CLR 227).
There is a bunch of related conditions regarding selling of goods. See the Trade Practices Act.
### Torts
• A tort is a civil wrong.
• Breach of Contract is a tort.
• Don't need to have a contract to commit a tort. eg. Tort of Negligence.
# Week 11
## Criminal Law
(work in progress)
Criminal Law is meant to cover matters concerning the state.
• There are sanctions for failing to abide by the law. But there is no capital punishment in Australia.
Reasons for sanctions,
• Retribution - "they ought to suffer"
• Deterrent
• Incapacitation - protect society by locking the criminal up in jail.
• Rehabilitation - try to change them so they won't re-offend.
Need,
1. proof of crime (actus reus)
2. criminal intent (mens rea) (although some "strict liability" crimes don't need this)
Two types of offences,
1. Summary offence -> Decided by a magistrate. No jury. Max 2 years imprisonment.
2. Indictable offence -> most cases have a jury.
• Prosecution need to prove defendant is guilty beyond a reasonable doubt.
• A hung jury is when the jury cannot come to a unanimous (although now they will accept one who votes different to everyone else) decision.
• A persons previous criminal history can only be made known at the sentencing (after a jury has decided if they are guilty or not).
• The jury decides the defendants guilt/innocence, the judge decides the sentencing.
Sentencing,
• Could be prison.
• Could be periodic or home detention.
• Could be community service.
• Could be a fine.
• Could be discharged on a good behaviour bond.
# References
[1] http://www.fedcourt.gov.au/videos/text_version/how_a_case_travels.html
Tags: genl2021, law.
12th September 2009
I've run into a little legal problem. By a problem I mean that if I were convicted for this I could face "a fine of not more than 550 penalty units or imprisonment for not more than 5 years, or both." Apparently one penalty unit is $110. So that means in the worst case a$60, 500 fine and 5 years imprisonment.
What's all this over? Well I thought I better check up on the Copyright Act 1968 (which I will refer to as The Act) and it is an indictable (meaning you can be sent to jail if found guilty) offence to do the following. (SECT 132AL, The Act)
(1) A person commits an offence if: (a) the person makes a device, intending it to be used for making an infringing copy of a work or other subject‑matter; and (b) copyright subsists in the work or other subject‑matter at the time of the making of the device. (2) A person commits an offence if: (a) the person possesses a device, intending it to be used for making an infringing copy of a work or other subject‑matter; and (b) copyright subsists in the work or other subject‑matter at the time of the possession. .... (11) In a prosecution for an offence against this section, it is not necessary to prove which particular work or other subject‑matter is intended to be, or will be, copied using the device.
And herein lies the problem. As a regular citizen this is too ambiguous, because people have different interpretations of what a "device" is. Case law can help here as it can give concrete examples of what is illegal and what is not, but someone always is going to be the first one to have to step up to the court to make the case law. Statute law should be clear enough on its own to be understood by the general public.
The term "infringing copy" could also be interpreted different ways, but the law actually explains what it means here (unlike for device which is to be interpreted as "includes a plate" where a "plate includes a stereotype, stone, block, mould, matrix, transfer, negative or other similar appliance." (The Act)).
Back to the actual problem that I'm referring to, I read the "Time-shifting" fact sheet from the Attorney-General's Department, http://www.ag.gov.au/www/agd/rwpattach.nsf/VAP/(CFD7369FCAE9B8F32F341DBE097801FF)~Copyright+Fact+Sheets+-+Time-shifting.pdf/file/Copyright+Fact+Sheets+-+Time-shifting.pdf (wow what an ugly URL!). It says that it is now legal to record a television or radio broadcast to watch or listen to at a more convenient time. However broadcast does not cover streaming of content online. As such ABC's iView and friends fall outside this scope. When you stream content from ABC's iView using an Adobe Flash player I'm not sure if any content is actually written to disk or not but it is definitely saved on various memories, however this "copy" would fall under SECT 111B of The Act and is legal. What would probably not fall under SECT 111B is there are tools, or what a court may call "devices", that are "intending it to be used for making an infringing copy of a work" (SECT 132AL, The Act). You can use these tools to store a permanent copy of material that ABC's transmits to you. My problem is I wrote a script which "helps" users make infringing copies of material published by SBS. Its not the part that actually copies the material (flvstreamer does that) but I can just imagine some lawyer convincing a judge and jury that they should send me to prison. Its way too confusing because you don't even need these scripts you just need your OS. tcpdump can be used to capture the traffic just like these tools do. Then there is the word "intending" which is open to interpretation to much. The computer is a copying machine, its not going to stop and check if the copy will be infringing or not. Sorry this has turned into a bit of a rant, but The Act really annoys me. Maybe its because I interpret it different to the people who wrote it, or the people who will use it to send me to prison or give me huge fines. Then there is the whole other thing of who is held liable. I wrote about the script on wordpress.com, and linked to its location on pastebin.com. Will they come after Automattic (the owner of wordpress.com) or me or the owners of pastebin.cem? But I'm (or maybe its not really me at all but Automattic) publishing all this in the US (I presume wordpress.com is hosted on servers in the US), so that makes all this Australian Copyright Act garbage useless. Oh and the other thing, under the current act, if you visit a web site most browsers will cache that to disk (I wouldn't call that a temporary copy "as part of a technical process of use", but I would call the copying of the data for the HTML document to registers, the processor cache and RAM a temporary copy, but this is not defined in The Act.). Are then web browsers a "device, intending it to be used for making an infringing copy of a work" because they ask for content from a web server, get given it and then save it to disk? (but it's no defence to say heaps of other people are breaking the law and you have singled me out so you can't charge me) Does it matter that the web server can send a "Cache-Control: no-cache" response header, if they don't does that mean that we are allowed to cache all this to disk? But that HTTP header and even the whole HTTP spec is just a W3C recommendation. This is just a little bit on my reasons why I have no respect at all for the Copyright Act. I don't want to have to worry about any of this legal stuff, but I must because if I don't the government can send me to prison or impose huge fines and I don't want to take a risk there. Oh and in my defence, the script that I linked to in this post, I would not classify as "device, intending it to be used for making an infringing copy of a work" if anything it would be flvstreamer, but then you cannot single those out. If publishing that script I linked to, or flvstreamer is illegal in this country then publishing an HTTP web browser, tcpdump, or an OS that interfaces with a network must also be devices that are intending it to be used for making an infringing copy of a work. Also something I've been wondering for ages, how can anyone ever be convicted of downloading copyright infringement mealy by downloading it over the internet? One cannot know if such material is protected by copyright (they don't even know what the data is until they have downloaded it), and one cannot know if the entity they are receiving the data from is the copyright holder who permits this use. A lawyer may come along and say that this is all true, but I wouldn't want to bet my life on the fact that the court will also agree (given the track record of the courts, see Cooper v Universal Music Australia Pty Ltd [2006] FCAFC 187). Anyway back to studying for my COMP courses. Tags: copyright, law. 8th September 2009 Say I know of a law (could be any law but I'll try to choose a recent one as the records don't go back all that far) and say its the FAIR WORK ACT 2009. I found this through AustLii, now I want to find the bill that this act was created from, as well as any bills that lead to amendments to this act. This information cannot be found in the Act itself. I could do a search on AustLii for the Act Name minus the year and the word Act, and add the word Bill, but because I don't know enough about parliamentary procedure I don't know if this is the rule and all acts must be named the same as the bill, or this is just something commonly done. Ideally there should be some references in the database that link bills to an act (if it has been passed). Now that I have located a Bill I can read the bill on AustLii, but I've heard that there are these things called "First Reading", "Second Reading" and so on that happen in parliament that give the reasons for the introduction of a bill. I want to find that information. So I head over to openaustralia.org, Because I'm not too familiar with parliamentary practice I don't know where these first and second readings fit in. So I do a search for "FAIR WORK BILL 2009" Second Reading". [caption id="attachment_746" align="aligncenter" width="450" caption="From the search results I manually look down the list to find the one that appears to be the second reading."][/caption] I have to manually look down the list for one that appears to be the second reading. Sure there may be technical reasons for this which may explain this but at first glance it seems that debates that are the Second Reading of a Bill appear to end with ": Second Reading". Perhaps an advanced search could use this to determine if a debate is a Second Reading of a Bill or not. Looking at the XML data provided by OpenAustralia for that day you can see that the debate has a minor-heading of "Second Reading", so sorting and searching by this attribute shouldn't be too hard. Admittedly I don't know enough about the way parliament works. Are these second readings mandatory or just customary? Tags: law, politics. 13th August 2009 I was going to answer all their questions, but after reading realised I haven't the time. So instead I'll repost it just because I can. Source: http://gov2.net.au/consultation/2009/07/23/towards-government-2-0-an-issues-paper-final/ ## Government 2.0 Issues Paper How you should use this Issues Paper We want to hear the arguments, information and stories that you have to tell us. The rest of this document is simply our way of helping you do that. It is not a template that you should feel obliged to follow, though we hope that this paper helps. There may be questions you wish to address that are not here, just as there may be questions we have raised you do not wish to address. Also, please note, our focus in this Issues Paper is on your making a written submission. You can find details about how to make a submission at Appendix 1. We also offer the option to make online submissions through our Consultation page at http://gov2.net.au/consultation. As you may be aware, there are other channels by which you can communicate with us. You can comment on our blog at http://gov2.net.au and members of both the Taskforce and its secretariat are attending various conferences and other activities where Government 2.0 will be discussed. You are welcome to attend. You can provide the Taskforce with feedback at any time, for instance through our blog, but we cannot promise to consider submissions on this paper which we receive after start of business Monday 24 August 2009. The Taskforce would like to thank those people, both from Australia and offshore, who contributed to this Issues Paper both by making comments on our blog and by making specific comments on this Issues Paper when it was issued in ‘Beta’ format a few days before finalisation. Our Job The Taskforce is charged with finding ways of accelerating the development of Government 2.0 to help government consult, and where possible actively collaborate with the community, to open up government and to maximise access to publicly funded information through the use of Web 2.0 techniques. We will do this with recommendations for government policy and also by funding projects which offer promise in accelerating the coming of Government 2.0. The Taskforce will be looking at the use of Web 2.0 both within government as well as in the government/public interface. The Terms of Reference of the Taskforce are at Appendix 2. Why Government 2.0? The aim of Government 2.0 is to make government information more accessible and useable, to make government more consultative, participatory and transparent, to build a culture of online innovation, and to promote collaboration across agencies in online and information initiatives. There are obvious benefits in moving in this direction to support, complement and strengthen existing engagement and consultation practices. Online engagement means citizens should be able to collaborate more readily with government and each other in developing and considering new policy ideas. It can give citizens greater insight into the policy making process and greater appreciation of the complexities of policy decisions. It makes possible an ongoing conversation amongst all who wish to participate in considering the effectiveness of existing government programs, laws and regulations and the scope for improvement. Government can use collaborative technologies to draw on the skills, knowledge and resources of the general community when developing policies or delivering services. Government agencies can receive feedback more rapidly, from more people at less cost. This in turn provides an opportunity for government to improve the way it delivers services to citizens. How will we achieve Government 2.0? Governments around the world and certainly our own governments have been relatively good at seizing many of the opportunities provided in the first incarnation of the internet, now often called Web 1.0, that is the use of the internet as a platform to distribute public material and solicit information from stakeholders by way of online ‘feedback forms’. Indeed in 2008 the internet became the most common way citizens last made contact with government . However a range of possibilities are emerging on the internet which have been dubbed Web 2.0. The revolutionary potential of Web 2.0 is apparent in websites like Google, Flickr, Facebook and Wikipedia. The central theme of Web 2.0 is moving away from point to point communications and towards many to many communication and collaboration. There is a buzz of Web 2.0 in the community and amongst enthusiasts who post to blogs and sites like Flickr and join online discussions. Governments across Australia have taken some interest in the applications of Web 2.0 to government. However compared with the speed of adoption of Web 2.0 tools and modes of operating in some quarters, progress in embracing Web 2.0 within government has been modest. A comment from our Beta consultation: This comes down to a fundamental view of what Government is for. If one is of the view that the purpose of Government is to shape society into some kind of ideal, where everyone is on the same page working to some kind of utopian goal, then Web2.0 has very little to offer. In that world view, the Government has already worked out what it’s going to do and the job of the citizen is to either help it get there (usually by means of constructive “submissions”, but only when “consulted”) or get out of the way and let the Government do its thing. If one is of the view that the role of the Government is to act as a kind of social lubricant to enable citizens to employ their own ideals in furtherance of their own goals, then that’s where Web2.0 is strong. Enabling that outcome requires the Government to be part of the conversation, so that it can see where obstacles are and apply its resources appropriately to smoothing the way for citizens without creating more problems than it solves. Government can be a remarkably blunt instrument, which needs to be wielded with care. I suspect that the slowness of Web2.0 adoption comes from the fact that those of us who support this initiative are in the latter mindset, while much of the Government and its accompanying bureaucracy are in the former mindset. Resolving this schism is, IMHO, one of the paramount challenges of Government 2.0. Mark Newton Key Questions On public sector information How can we build a culture within government which favours the disclosure of public sector information? What government information should be more freely available and what might be made of it? On digital engagement What are the major obstacles to fostering a culture of online engagement within government and how can they be tackled? How can government capture the imagination of citizens to encourage participation in policy development and collaboration between citizens and government? A comment from our Beta consultation: The primary obstacles that emerge in our research on this are very clear, they include: i) there is an inherent culture of risk aversion within government; ii) failing to integrate online engagement fully into the policy cycle means that people see little point in becoming engaged; iii) within government, engagement happens at too low a level; people want to see senior policy officials and ministers involved before they believe it has value; and iv) using the wrong kind of engagement tool; it’s not about fashion, it’s about choosing the right tool for the policy stage and audience. Andy Williamson Introduction A number of reviews and processes have pointed to the importance of greater dissemination and reuse of public sector information and greater online engagement with citizens/between governments/between governments and citizens. At the Australian Government level, for example, these include the Cutler Review into Innovation , and the Gershon Review into ICT use and management . Some State governments have also been making important strides. Most recently the Victorian Government has released its Report of the Economic Development and Infrastructure Committee on the Inquiry into Improving Access to Victorian Public Sector Information and Data, Parliamentary Paper No. 198 Session 2006-2009, June 2009. Proposed legislative change, including proposals for the establishment of an Office of the Information Commissioner and amendments to Freedom of Information legislation to impose a publication scheme on all agencies underpin an agenda of greater public access to government information. The proposed Office of the Information Commissioner will incorporate the existing Office of the Privacy Commissioner. Handling privacy well is important to generating the trust and confidence in the community necessary to optimise community engagement in Web 2.0 initiatives. Many government agencies are currently involved in aspects of information policy development. Many are also exploring the use of new tools and techniques to improve the way they work. The Taskforce seeks to build on this work and to accelerate this process of change to allow more open access to, and use of, the information created and/or funded by government. Equally important, the Taskforce will explore the issue of effective consultation, engagement and collaboration with citizens. This work will inform the framework for an Information Policy that can be applied across the Australian Government. In this paper we elaborate on issues relating to public sector information. We have covered these at greater length than other issues under reference because there has been greater policy development in this area compared with innovation and online engagement. The relatively smaller space devoted to the latter themes in this Issues Paper does not signal that we view them as being of lesser importance. OECD Principles for public sector information In April 2008 the Organisation of Economic Co-operation and Development (OECD) Council, adopted the Recommendation of the OECD Council for enhanced access and more effective use of public sector information. (Australia is a member of the OECD and was a participant in and a signatory to the Recommendation.) It recommends that member countries “in establishing or reviewing their policies regarding access and use of public sector information…take due account of and implement the following principles, which provide a general framework for the wider and more effective use of public sector information and content and the generation of new uses from it.” The Taskforce acknowledges these principles and intends to use them as a starting point for that part of our work relating to public sector information. Our focus then becomes how we realise those principles as fully as possible in the practical operations of government. 1. Openness. Maximising the availability of public sector information for use and re-use based upon presumption of openness as the default rule to facilitate access and re-use. Developing a regime of access principles or assuming openness in public sector information as a default rule wherever possible no matter what the model of funding is for the development and maintenance of the information. Defining grounds of refusal or limitations, such as for protection of national security interests, personal privacy, preservation of private interests for example where protected by copyright, or the application of national access legislation and rules. 2. Access and transparent conditions for re-use. Encouraging broad non-discriminatory competitive access and conditions for re-use of public sector information, eliminating exclusive arrangements, and removing unnecessary restrictions on the ways in which it can be accessed, used, re-used, combined or shared, so that in principle all accessible information would be open to re-use by all. Improving access to information over the Internet and in electronic form. Making available and developing automated on-line licensing systems covering re-use in those cases where licensing is applied, taking into account the copyright principle below. 3. Asset lists. Strengthening awareness of what public sector information is available for access and re-use. This could take the form of information asset lists and inventories, preferably published on-line, as well as clear presentation of conditions to access and re-use at access points to the information. 4. Quality. Ensuring methodical data collection and curation practices to enhance quality and reliability including through cooperation of various government bodies involved in the creation, collection, processing, storing and distribution of public sector information. 5. Integrity. Maximising the integrity and availability of information through the use of best practices in information management. Developing and implementing appropriate safeguards to protect information from unauthorised modification or from intentional or unintentional denial of authorised access to information. 6. New technologies and long-term preservation. Improving interoperable archiving, search and retrieval technologies and related research including research on improving access and availability of public sector information in multiple languages, and ensuring development of the necessary related skills. Addressing technological obsolescence and challenges of long term preservation and access. Finding new ways for the digitisation of existing public sector information and content, the development of born-digital public sector information products and data, and the implementation of cultural digitisation projects (public broadcasters, digital libraries, museums, etc.) where market mechanisms do not foster effective digitisation. 7. Copyright. Intellectual property rights should be respected. There is a wide range of ways to deal with copyrights on public sector information, ranging from governments or private entities holding copyrights, to public sector information being copyright-free. Exercising copyright in ways that facilitate re-use (including waiving copyright and creating mechanisms that facilitate waiving of copyright where copyright owners are willing and able to do so, and developing mechanisms to deal with orphan works), and where copyright holders are in agreement, developing simple mechanisms to encourage wider access and use (including simple and effective licensing arrangements), and encouraging institutions and government agencies that fund works from outside sources to find ways to make these works widely accessible to the public. 8. Pricing. When public sector information is not provided free of charge, pricing public sector information transparently and consistently within and, as far as possible, across different public sector organisations so that it facilitates access and re-use and ensures competition. Where possible, costs charged to any user should not exceed marginal costs of maintenance and distribution, and in special cases extra costs for example of digitisation. Basing any higher pricing on clearly expressed policy grounds. 9. Competition. Ensuring that pricing strategies take into account considerations of unfair competition in situations where both public and business users provide value added services. Pursuing competitive neutrality, equality and timeliness of access where there is potential for cross-subsidisation from other government monopoly activities or reduced charges on government activities. Requiring public bodies to treat their own downstream/value-added activities on the same basis as their competitors for comparable purposes, including pricing. Particular attention should be paid to single sources of information resources. Promoting non-exclusive arrangements for disseminating information so that public sector information is open to all possible users and re-users on non-exclusive terms. 10. Redress mechanisms: Providing appropriate transparent complaints and appeals processes. 11. Public private partnerships. Facilitating public-private partnerships where appropriate and feasible in making public sector information available, for example by finding creative ways to finance the costs of digitisation, while increasing access and re-use rights of third parties. 12. International access and use. Seeking greater consistency in access regimes and administration to facilitate cross-border use and implementing other measures to improve cross-border interoperability, including in situations where there have been restrictions on non-public users. Supporting international co-operation and co-ordination for commercial re-use and non-commercial use. Avoiding fragmentation and promote greater interoperability and facilitate sharing and comparisons of national and international datasets. Striving for interoperability and compatible and widely used common formats. 13. Best practices. Encouraging the wide sharing of best practices and exchange of information on enhanced implementation, educating users and re-users, building institutional capacity and practical measures for promoting re-use, cost and pricing models, copyright handling, monitoring performance and compliance, and their wider impacts on innovation, entrepreneurship, economic growth and social effects. Structure of paper The remainder of this paper discusses OECD principles and additional principles as they relate to online innovation and engagement. • Principles for openness and access (OECD principles 1-3, 6, 10) • Principles for quality and integrity of information (OECD Principles 4 and 5.) • Principles to maximise efficiency in production and distribution of information (OECD principles 7-9, 11-13) • Maximising the potential of Government 2.0 Principles for openness and access Open access to public sector information is generally agreed to be beneficial to our economy and society and to be the preferred approach. By openness and access, we refer to the making available of appropriate categories of public sector information on terms and in formats that permit and enable use and reuse of that information by any member of the public. However, we recognise that there are limits to this principle of open access, namely to respect privacy, confidentiality, security and possibly cost recovery concerns. For the purposes of this issues paper public sector information is taken to exclude personal information that would not be available for publication or reuse under Australian privacy laws, or other legislation. It might include such information if it were adequately transformed to address any concern, for instance by anonymising it. Another issue is how widely policies to optimise the openness of public sector information should apply across government. The recent Victorian Parliamentary inquiry proposed that public sector information policy should apply to government departments only, at least for an initial period, although it suggested that it may be appropriate to expand this coverage over time. We would be interested to hear arguments for and against restrictive and more expansive application of policies to optimise the openness of public sector information and, where a broader definition is supported, how this might relate to information that is commercially sensitive. Question 1: How widely should policy to optimise the openness of public sector information be applied? Should it be applied beyond government departments and, if so, to which bodies, for instance government business enterprises or statutory authorities? Openness (OECD principle 1) The OECD recommends that the presumption of openness should be the default rule, and this has been backed by recent moves in the Australian Government. Proposed changes to the Freedom of Information Act 1982 (FOI Act) aim to make it easier to obtain documents under FOI legislation, in part by emphasising the presumption of openness. FOI Act changes also aim to encourage the release of information through a publication scheme and otherwise outside that Act. Proposed changes to the Archives Act 1983 bring forward the time at which government records come available under that Act from 30 to 20 years. These changes are backed by the proposed creation of an Information Commissioner and Freedom of Information Commissioner. These legislative changes are a significant move in the direction of accessibility of government information. One of the major barriers to achieving greater accessibility has been the lack of a pro-disclosure culture within government. Privacy, national security and confidentiality issues will properly prevent the release of some information, but this should not inhibit the release of other non-sensitive government information. Question 2: What are the ways in which we build a culture within government which favours the disclosure of public sector information? What specific barriers exist that would restrict or complicate this and how should they be dealt with? Question 3: What government information would you like to see made more freely available? Question 4: What are the possible privacy, security, confidentiality or other implications that might arise in making public sector information available? What options are there for mitigating any potential risks? A comment from our Beta consultation: I believe that Question 2 is one of the most important problems we face in adoption of this goal. Broad cultural change is required across government that encourages innovation whilst providing a safety-net for those who try and fail. Leadership from the highest levels and generational change is required to make this a reality. The key is not to expect too much too soon as transparency is a terrifying concept for most government agencies and their officers. All of the technical, legal and logistical problems will be solvable, but worthless without real cultural change at all levels of government. David Heacock Access and transparent conditions for re-use (OECD principle 2) Government agencies currently make a large amount of information available on their websites, and much more could be made available freely on the internet. However, technological, copyright and licensing issues tend to restrict the way that this information can be made available and used by the public. Making government information accessible online, particularly in standard formats such as XML, CSV, ODF, RDF or RDFa etc allows those outside government, whether they are citizens, firms or third sector organisations, to combine, present and analyse this information in different ways, creating both public and private benefits. Question 5: What is needed to make the large volume of public sector information (a) searchable and (b) useable? And in each case, what do we do about legacy information in agencies? How might the licensing of on-line information be improved to facilitate greater re-use where appropriate? The Semantic Web The Semantic Web is a series of World Wide Web Consortium (W3C) standards that provides a framework to describe information about data. This information is called metadata. Providing sets of raw data without accompanying context may limit the ability of people to meaningfully re-use any information provided. For example, what does the data element ‘60’ represent? Is it someone’s age? A speed limit? When was the information collected? By whom? What are the units of measurement? Providing metadata in a standardised format also facilitates a precise search. For example, ‘What are the Commonwealth import duties for a lathe purchased from Germany?’ In Australia the Australian Government Locator Service (AGLS) Metadata Standard (AS 5044) has been endorsed by all Australian Governments as the standard for describing government resources (information and services) to support their discovery in a Web environment. AGLS is based on and extends the international resource discovery metadata standard, the Dublin Core Metadata Element Set. AGLS metadata can be expressed using RDF (Resource Description Framework) syntax and modelling, which is one of the recommendations of the Semantic Web. There are other relevant metadata standards as well for things like rights management, geospatial data, recordkeeping, digital preservation, etc, all of which can potentially be useful in a semantic web environment, but discoverability is the key requirement for which you need standardised metadata for the Semantic Web to work. There are of course costs associated with marking up data with semantic annotations. These costs increase with the degree of metadata provided for each element. A difficult-to-answer issue what be at what point do the costs of providing extra information exceed the benefits? Ensuring discoverability - asset lists (OECD principle 3) How could information be made more accessible? Question 6: How does government ensure that people, business, industry and other potential users of government information know about, and can readily find, information they may want to use, for example, the use of a consolidated directory or repository for public sector information? New technologies and long-term preservation (OECD principle 6) Publication in proprietary formats can represent a barrier to participation for citizens if the owner of intellectual property in the standard refuses to make it freely available. In addition, a requirement for government to maintain information in multiple formats represents a cost to government. Some national and sub-national governments have mandated that all information must be accessible and stored in formats that are publicly open standards. Thus such formats like Open Document Formats (ODF) have been preferred to proprietary formats such as DOC. Question 7: Should governments mandate that information should be only kept and stored in open and publicly documented standards? Could such a stipulation raise costs or reduce flexibility? It should be possible to share the benefits and knowledge gained from online and information initiatives across government. However, this largely depends on the interoperability of information and business architectures between government agencies and between them and their users. Interoperability in turn depends on a range of factors including the adoption of standards and definitions for recording information to enable it to be shared. Question 8: What approaches should the Government use to allow information to be easily shared? In addition, there are many online and information initiatives being trialled across government agencies. A variety of online tools, technologies and platforms are being tested and used. In the Web 2.0 sphere, these include the use by agencies of blogs, YouTube, Flickr and Facebook. Some additional principles outlined in an exploration of the issues relating to the use of Web 2.0 by Tim O’Reilly include the following: • Support lightweight programming models that allow for loosely coupled systems • Cooperate, Don’t Control • Design for hackability and remixability • Network Effects by Default • The Perpetual Beta Question 9: How can the initiatives and ideas of agencies be harnessed for the benefit of agencies across government? How can duplication of effort be avoided? Data.gov The US Government has recently established the Data.gov website to increase public access to high value, machine readable datasets generated by the Executive Branch of the Federal Government. Data.gov includes searchable data catalogues providing access to data in three ways: through the "raw" data catalogue, the tool catalogue and the geo-data catalogue. The raw data and the Geo-data catalogues are provided in CSV, XML, KML or SHP formats. The Tools Catalogue includes pre-packaged data sets such as look-up tables. The stated goal of Data.gov is to improve access to Federal data and expand creative use of those data beyond the walls of government by encouraging innovative ideas (e.g., web applications). Another objective is to make government more transparent by creating an unprecedented level of openness. Redress mechanisms (OECD principle 10) To ensure these principles are implemented sensibly we need effective mechanisms for hearing complaints about and redressing government’s inaction in the release of information. Conversely, making government information available online may increase the risk of unintentional or inappropriate release of information that may damage an individual or business. If that information is then re-used, it may lead to proliferation of the harm. Formal complaints and appeals processes already apply across the Australian Government. Depending on the specific circumstances, a person has redress, for example, to appeal mechanisms in the FOI Act, the complaints mechanisms in the Ombudsman Act 1976 or Privacy Act 1988, or judicial mechanisms in the Administration Decisions (Judicial Review) Act 1977. Question 10: Are these complaints and appeals processes sufficient? Are additional processes needed for government as it engages in the Web 2.0 world? Principles for quality and integrity of information Quality and integrity (OECD principles 4 and 5) All government agencies are engaged in the creation and collection of information and government’s online engagement with citizens is subject to the same information laws, such as the Freedom of Information Act 1982, the Archives Act 1983 and the Privacy Act 1988, as are the records of other interactions with citizens. The fundamental importance of good recordkeeping to ensure transparent and accountable government has been widely recognised, as has the part played by failures in recordkeeping in many inquiries and audit reports. Question 11: What should government do to foster a culture of compliance with information and records management policies and best practice? Question 12: What recordkeeping challenges are posed by both the re-use of government information, and in the mechanisms of development of government policy and practice through interactive citizen engagement? There is rich potential in this area for perverse outcomes. Agencies frequently cite concerns about the integrity of their information as a reason for their reluctance to release it. And the perfect can be the enemy of the good. On the one hand mandating the release of information might be one way of ensuring that agencies have an incentive to maintain its quality and integrity. On the other hand the release of some information (with an appropriate disclaimer as to quality) may often, but not necessarily always, be better than not releasing it at all. Question 13: How does government manage the costs and risks of publication of inaccurate information? An important aspect of quality (and integrity) is the provision of information (‘metadata’) that describes the quality of information, so that users can determine whether it is ‘fit for purpose’ in terms of their proposed use of the information. For example, knowing the source of the information, the checks the information has been subject to, and any other factors that might affect accuracy, can help users know how the information might be used appropriately and equally important, the hazards in using it improperly. Users may be able to interact with government information providers to better understand the information (and therefore increase the likelihood that the information will be used appropriately) or to express concerns about aspects of the information. Citizens expect government information to be of high quality and integrity but will also have an expectation of the responsiveness of government to deliver information. Timeliness Timeliness is a particularly important matter. From at least the late 1970s the ICT revolution has been driven by firms that have made felicitous tradeoffs between the quality of their offering and getting their product to market. Too early and the market could turn against a product for the number of bugs and other errors which frustrate users. Too late and the market has moved on. This was the case even before ‘Web 1.0’ as summarised in Steve Jobs arresting comment “True genius ships”. But it is particularly so in the world of Web 2.0 where it is now quite normal to provide users with comprehensive access to beta products and indeed to leave them designated as beta products for many years. Gmail only recently moved out of beta after five years as a mainstream consumer product. The issue raises its head particularly in the area of data where government agencies delay publication to ensure data integrity anxious either from a natural desire to do their job properly, or to minimise risk, or to meet standards internally mandated within government. In the meantime, as we saw in the case of the Victorian fires, valuable information however imperfect goes unpublished. Question 14: What criteria might we adopt in ensuring that agencies make data available in a reasonable time-frame? (And how might we define a “reasonable time-frame”?) Question 15: It often takes quite some time to compile and create consistent and reliable data – especially for large data sets. When is it appropriate to release limited and possibly less accurate data and where is it appropriate to wait for higher quality and more extensive data? Where various principles are in some tension with each other, for instance quality and cost or timeliness, how should trade-offs be made? The National Toilet Map As part of the National Continence Management Strategy, the Australian Government funded the development of the National Toilet Map website . The website shows the location of more than 14,000 public and private public toilet facilities across Australia. Details can also be found along major travel routes and for shorter journeys as well. Useful information is provided about each toilet, such as location, opening hours, availability of baby change rooms, accessibility for people with disabilities and the details of other nearby toilets. A number of organisations, commercial and not-for-profit, large and small, have requested access to the data in order to provide a range of innovative services. To date, such access has not been granted. The wider availability of this information, through sources other than the National Toilet Map website, appears to promote the objectives of the National Continence Management Strategy and is consistent with the OECD principles enunciated earlier in this Issues Paper. Principles to maximise efficiency in production and distribution of information Intellectual property (OECD principle 7) It is hoped that, through strategic management of copyright and new Web 2.0 licensing tools like Creative Commons and similar open licensing mechanisms for database material, we can more easily provide the necessary permission to promote better access to and reuse of public sector information. In the short term this means using current copyright law and practice to do a better job and in the longer term assessing the appropriateness of existing copyright law for a digital environment and any changes that should be made to address problems. Question 16: What can we do to better promote and co-ordinate initiatives in this area? How can we draw key departments together? Question 17: What sort of public sector information should be released under what form of copyright license? When should government continue to utilise its intellectual property rights? Apps for Democracy Competition The 2008 Apps for Democracy competition was an initiative of the District of Columbia’s Office of the Chief Information Officer. The competition involved members of the public making an application using data from the 277 datasets made available by the District of Columbia. There was a total ofUS20,000 in prize money on offer, spread over 60 cash prizes ranging from $US100 to$US2000. The competition ran for 30 days and received 47 entries including web, Facebook and iPhone applications. Entries were divided into two categories: entries by professional agencies, and “indie” entries by individuals and groups of individuals.
Entries included a large number of geospatial mash-up applications making use of available datasets. The competition was viewed as an unqualified success by the D.C. government, as it cost $US50,000 to run, but provided a claimed$US2.6 million in value to the city through the created applications.
Government is subject to additional obligations which seek to ensure that all levels of our community are able to access its services, whether online or offline. For online engagement, government must consider those citizens who are excluded for various reasons, e.g. lack of access to technology, disability, health barriers, lack of computer-literacy, lack of English, lack of literacy, etc. Many of these issues are currently not adequately addressed by commercially available and popular online platforms.
Pricing and Competition (OECD principles 8-9) There is currently a mixed approach across government to the pricing of information. In the electronic world, the marginal costs of providing information are lower than in a paper-based environment, which could suggest that different pricing approaches might be appropriate. Furthermore, information is often considered as a ‘public good’, which also might impact on thinking about appropriate pricing policies.
Question 18: When should agencies charge for access to information? Should agencies charge when they are providing value-added services? What might constitute ‘value added services’ (eg customisation of information)? In what circumstances should agencies be able to recover the costs of obtaining the information or providing access? A common model in the private sector is ‘freemium’ distribution whereby many, often most, users are supplied with some product or service for free whilst others pay for use in large scale commercial enterprise (for instance AVG anti-virus) or for some premium product (for instance Word Web). Are there similar models for public sector information and/or do they merit further consideration?
A comment from our Beta consultation:
Pricing should also take into account the economic value of information if released.
There are many cases where there is significant positive economic or social value in making data freely available – such as the sharing of emergency data between government agencies (which currently is often costed at a level that discourages usage and therefore reduces the effectiveness of emergency responses).
Charging for maintenance and distribution costs can cost significantly more in lost economic or social benefit than it achieves in cost recovery.
Craig Thomler
Public private partnerships (OECD principle 11) Public-private partnerships might provide a way to make public sector information more readily available, for example by financing the costs of digitisation.
Question 19: How can government take advantage of public private partnerships to increase access to public sector information without unduly constraining opportunities for third parties to use and reuse the information?
International access and use (OECD principle 12) Many government agencies are involved in cooperative international programs and liaison. There are advantages to government in guiding interoperability and compatibility in dataset formats so as to ensure the most efficient and effective use of information.
Question 20: What international activities relevant to this Taskforce should the Taskforce be considering and what needs to be done to improve cross-border use and interoperability of information?
Best practice (OECD principle 13)
Question 21: How can best practice be facilitated, identified, rewarded, and further propagated?
Maximising the potential of Government 2.0
Fostering more consultative and collaborative online engagement in Government
There are obvious benefits to government in using collaborative technologies to draw on the skills, knowledge and resources of the general community when developing policies or delivering services. In many situations, much of the expertise, experience and deep knowledge that governments need to make good decisions about increasingly complex or ‘wicked’ problems exists outside government. New possibilities are emerging to link highly distributed networks of knowledge and expertise quickly and securely to focus on shared opportunities or problems to be solved.
In harnessing the opportunities arising from Web 2.0 technologies there is a potential for individuals to hesitate or avoid contributing where they sense that the technology isn’t ‘safe’. For example, people may fear that information about them will fall out of their control or they may avoid situations where they have to fully identify themselves before engaging with collaborative technologies. In this regard, embedding good privacy practices into collaborative technologies will play an important role in garnering the trust and confidence of individuals who wish to participate.
But beyond that, online engagement creates at least the potential to ‘democratise’ public administration and policy development by offering a much richer mix of spaces in which people can talk, listen, debate, argue and contribute their ideas and aspirations to the public conversation.
Moderated online engagement offers the potential for people to learn from each other and to constructively find common ground.
Question 22: Have you engaged with the Australian government via a Web 2.0 channel? Which one/s? If so, why and what was your experience? If not, why not? What can be improved?
Go to where the people are
A major finding of the UK Power of Information reports is that Government consultation efforts can be greatly enhanced by consulting with existing interest groups in their online communities, such as netmums.com. A similar approach involves employing social networks and existing forums and blogs to target a different audience than would normally respond to a traditional government consultation. In Australia a recent example of this was the use of the Open Forum blog by Father Frank Brennan , the Chair of the Human Rights Consultative Committee to engage netizens on questions relating to the consultation.
Different combinations of public interaction methods suit different requirements and different audiences.
Increasingly agencies are combining traditional modes of consultation with Web 2.0 features and applications to enhance the visibility, promotion and interactivity of Government online consultation efforts. These include:
• promoting a consultation on social networks such as Facebook
• blogs
• using videos either hosted on the consultation site or on a third-party site such as YouTube
• including RSS feeds on the consultation site.
A comment from our Beta consultation:
Having responded to one consultation, a user may be more likely to respond to another consultation. A related consultation should be easily visible at the point of completion or commencement of a user’s response.
“Like this consultation? If you’re interested, we’d also like your feedback on consultation X!”
Gordon Grace
Inclusion
The benefits of online engagement will be realised best if as wide a range of citizens as possible are involved. However, some people may be uncomfortable with this type of interaction with government.
Question 23: How can government capture the imagination of citizens to encourage participation in policy development and collaboration between citizens and government?
Question 24: What sort of privacy issues might dissuade individuals from engaging with government via collaborative technologies? What sort of steps can we take to ensure that personal information is used appropriately? What options are there for mitigating any potential privacy risks?
Governments have generally mandated minimum accessibility standards which can create obstacles to using some of the leading Web 2.0 platforms where they do not conform with those standards.
Question 25: How can government make it easier for people to engage on policy and other issues and make sure the opportunities are as open and accessible as possible?
Question 26: What trade-offs must be considered between government using commercially available and popular online platforms and ensuring inclusive participation with all members of society and how should those tradeoffs be made?
Privacy
It is significant that the Government is in the process of introducing legislation that proposes to incorporate the Office of the Privacy Commissioner, together with a Freedom of Information Commissioner, in a proposed Office of the Information Commissioner. These initiatives illustrate the complex relationship and tension between protecting the privacy of individuals and opening access to public sector information.
A great deal of public sector information (PSI) is not on its face “personal information” as defined in the Privacy Act 1988. On the other hand there can still be privacy issues or risks associated with open access to PSI. Information from which only name and address has been removed, may still fall under the definition of “personal information,” as an individual’s identity may still be reasonably ascertainable from the information.
Re-identification of personal information is usually context-sensitive. An organisation’s capacity to re-identify data may depend critically on its particular resources, or changing priorities. Factors which may impact on the capacity for data to be re-identified include available data, new technologies, resources, and social or political imperatives for access to new or different types of data. Combining unrelated datasets, now or in the future, may create the environment for more intrusive profiling, data-linking or data-matching of individuals’ personal information.
There are also privacy risks and issues relating to digital engagement, particularly around moderation, consent to publish and anonymity. For example, in respect to post-moderation, there is the risk that a participant may identify and provide information about another individual, which is published without that individual’s knowledge or consent. This may constitute a breach of privacy by the relevant agency and provide grounds for a complaint to the Privacy Commissioner by the individual whose personal information has been disclosed. This risk is not different in kind to existing risks, but the immediacy and ubiquity of the internet increases its likelihood considerably.
Online engagement challenges for Government
Australian Government efforts in online engagement have been crafted to comply with the Australian Public Service values, set out in section 10 of the Public Service Act 1999. These require that public servants to act in an apolitical, impartial and professional way.
The Australian Public Service Commission also recently released interim protocols for online media participation by public servants . There are a number of other legislative restrictions on what information can be disclosed by public servants. This has an impact on how free government agencies and public servants are to experiment with online consultation, since agency websites must be impartial and apolitical. This may affect the extent to which they can enter into meaningful discussion with the public.
Question 27: How can public servants comply with the APS values and other protocols whilst still participating in online engagement? Should existing rules including legislation be changed and/or adapted to facilitate greater online engagement?
Moderation Government collaborative websites such as blogs generally require moderation. This involves time and labour cost. Third-party moderation tools and services are available. The process of moderation should be transparent, with the principles and parameters of the editorial control specified. This is good practice in all online jurisdictions.
Online consultations seeking input from the public can be at risk of agenda hijacking and the derailment of discussion although other forms of engagement are not immune from such possibilities. Thus for instance when the Obama Administration held online consultations on what the new Administration’s new priorities should be, the legalisation of marijuana was voted the most important priority. More recently one of the most prominent priorities has been the release of Barack Obama’s birth certificate.
While it is appropriate that views about which people feel strongly are aired, it is also important for there to be an ability to ‘agree to disagree’ and get on with the process of using the strengths of online engagement to improve policy development without being diverted by the attention given to symbolic issues or to lowest common denominators in policy.
Question 28: How does government provide sufficient room for personal debate and passionate dissent but still ensure appropriate levels of moderation in online forums? Should moderation be ‘outsourced’ and if so in what circumstances and how? How might volunteers from the commenting community be selected to moderate?
A comment from our Beta consultation:
… If legalization of marijuana comes out of Obama’s online consultations, perhaps he should have a legalization-of-marijuana policy that stakes out a position on the issue. Personally I couldn’t care less, but if it’s an issue that some folks think is important enough to get organized over, why shouldn’t it be on the agenda? Would it hurt to put out a position paper?
Mark Newton
Fostering a culture of online innovation within government
New collaborative technologies are emerging all the time. These new technologies can improve the efficiencies of Government internally and can also alter and (hopefully) improve external-facing relations, particularly government-citizen engagement.
Innovation challenges for Government
Governments face responsibilities that are not always shared by the private sector or members of the broader community. Their conduct is expected to be above reproach. They are expected to be a trustworthy source of information and/or advice and they face a number of self-imposed obligations to ensure access and equity. Recognising this, there are a number of potential challenges to Government making effective use of these new collaborative technologies:
• access to many of these platforms may be blocked or considerably constrained for public service officials
• the potential of these tools may conflict, in real or imagined ways, with the rules, policies and practices that apply to the public service
• the greater immediacy, transparency, accountability and informality they introduce into our communications may be directly contrary to the prevailing government practice
• public servants may be concerned about being ‘overwhelmed’ by the potential volume of activity that might arise from the new collaborative technologies, particularly when there is an expectation that governments will respond to all issues raised by citizens
• awareness of the new technologies and the opportunities that they offer may delay their adoption.
The use by government of collaborative platforms is a relatively new phenomenon and may require a rethink of applicable rules, policies and practices. It also requires the development of social and online norms in government-citizen relations. As one commentator noted in discussion about one blogging effort by the Australian Government:
"It’s probably worth remembering: as untried as government consultation blogs are at the federal level in Australia, so too are citizens unused to being able to engage with their government in this way. They may be new at it, but so are we - and both sides still have a lot to learn about the other.”
Cultural barriers may constrain the adoption of collaborative tools and the newness of the approach may generate trepidation and dissuade uptake within the public sector.
Question 29: What are the barriers to fostering a culture of online innovation within government? Which of those barriers should be maintained in any Government 2.0 initiatives? Which of those barriers should be removed? How should this be achieved? What different norms can or should apply to Government 2.0 efforts?
Question 30: To what extent can government assist the uptake of Government 2.0 by centrally providing standard business management guidance and tools to avoid agencies having to ‘reinvent the wheel’ when considering their own online engagement guidelines?
Question 31: How can government engage with individuals and stakeholders to support the development of innovative policies, programs, practices and service delivery? Are there good examples of where this is happening?
For profit firms often use the rich data they harvest from their existing information assets and their ongoing presence on the web to guide their own innovation, measuring consumer reactions to many small scale experiments and optimising operations, for instance the design of a website, in response to this feedback.
Question 32: To what extent can we promote such an approach in the public sector and are there any examples of emerging practice?
Risk management
It is a cliché that public sector managers – and possibly the Ministers to whom they report -- are risk averse. But often they are not so much risk averse as innovation averse. That is, there is a high ‘burden of proof’ against doing something differently even where it involves relatively low risks.
Sometimes this is because it is simply more comfortable to do things the way they’ve always been done. In other circumstances, some argue that specific professions can be set in their ways. There may be some wisdom in this given the complexity of existing systems and the possibility of unanticipated consequences, particularly where these consequences may be political. These decisions are often heavily influenced by experts.
Question 33: How can such expertise be governed so as not to unduly stifle innovation?
In comparison to many large commercial enterprises, public sector agencies in the main adopt quite restrictive practices in allowing staff access to Web 2.0 tools, social networking sites and even webmail. Most agencies simply ban access to these sites. One of the reasons often used to justify this position is the need to protect internal IT systems from exposure to threats from the internet. Highly prescriptive and centrally mandated security policies are often rigorously applied. Given the low risk culture of the public sector, it is difficult to see how agencies wishing to enter into the Web 2.0 world will be able to argue that the benefits to citizens, and to the operations of the agency, are of sufficient value to offset an exposure which cannot easily be assessed. Clearly the risks to agencies will vary depending on the nature of their business. It is unlikely that technology alone will solve this challenge.
Question 34: To what degree is the opportunity for Government agencies to participate in the Web 2.0 world inhibited, or severely compromised, by issues such as security? How might this problem be overcome, in general and by individual agencies, within current legal and policy parameters and how might these parameters be changed to assist in overcoming these problems?
Contractual and procurement issues
The use by government agencies of social networks and Web 2.0 applications and services may raise contractual and procurement issues for governments such as unacceptable indemnity clauses.
The United States Government, through the General Services Administration, negotiated whole of government agreements with Flickr, YouTube and other Web 2.0 providers with waivers of objectionable provisions. Similar agreements with Web 2.0 providers may be needed in Australia.
Proposed Information Commissioner
The Australian Government has proposed legislative reforms with the principal objects of promoting a pro-disclosure culture across the Government and building a stronger foundation for more openness in government. These reforms involve changes to the Freedom of Information Act 1982 and Archives Act 1983 and the establishment of an Office of the Information Commissioner (OIC).
The functions of the Information Commissioner are set out in Clause 9 of the exposure draft and require the Information Commissioner to report to the Minister on a broad range of policies and practices relating to the administration and management of government information.
This Taskforce, in its Terms of Reference , has been given the task of identifying policies and frameworks to assist the Information Commissioner (and other agencies) in encouraging the dissemination of government information.
The Information Commissioner functions set out in the proposed Exposure Draft will obviously encompass issues that touch on questions raised in this Issues Paper. One of these is which aspects of Government information could fall within the purview of the proposed OIC.
These include, but are not limited to, the information management standards, policies and guidelines that are the responsibility of the National Archives, the IT system issues that are the responsibility of the Australian Government Information Management Office, and the administration of copyright that is the responsibility of the Attorney-General’s Department.
These areas all have some impact on recommendations the Taskforce might make.
Question 35: What role could the proposed OIC play in encouraging the development of Government 2.0? Are there practical recommendations the Taskforce might make about how the OIC might best fulfil its functions in relation to optimising the dissemination of Government information?
Appendix 1
Making a Submission: Terms of Engagement
We welcome your written submissions. There is no set format required and submissions need not be formal documents.
Submissions in electronic format are preferred and can be emailed to us at [email protected].
If that isn’t possible, you can mail them to:
Government 2.0 Taskforce Secretariat Department of Finance and Deregulation John Gorton Building King Edward Terrace Parkes ACT 2600 Australia
We also offer the option to make online submissions through our Consultation page at http://gov2.net.au/consultation.
As a general principle all written submissions will be placed on the Government 2.0 website, as will discussion papers and other material developed as the Taskforce progresses.
Confidential submissions will be accepted from individuals where individuals can argue credibly that publication might compromise their ability to express their view freely. Pseudonymous submissions will also be accepted. Should you make a pseudonymous submission, it may not receive full consideration unless you remain contactable by e-mail should we wish to seek clarification or elaboration.
Please note that any request made under the Freedom of Information Act 1982 for access to any material marked confidential will be determined in accordance with that Act. Submissions must be received by start of business Monday 24 August 2009.
If you do not want to make a written submission but would still like to give us some feedback, you can communicate with us on our blog at http://gov2.net.au.
Appendix 2
Terms of reference
• make government information more accessible and usable — to establish a pro-disclosure culture around non-sensitive public sector information;
• make government more consultative, participatory and transparent — to maximise the extent to which government utilises the views, knowledge and resources of the general community;
• build a culture of online innovation within government — to ensure that government is receptive to the possibilities created by new collaborative technologies and uses them to advance its ambition to continually improve the way it operates;
• promote collaboration across agencies with respect to online and information initiatives — to ensure that efficiencies, innovations, knowledge and enthusiasm are shared on a platform of open standards; and
• identify and/or trial initiatives that may achieve or demonstrate how to accomplish the above objectives.
The Taskforce will advise government on structural barriers that prevent, and policies to promote, greater information disclosure, digital innovation and online engagement including the division of responsibilities for, and overall coordination of, these issues within government.
The Taskforce will work with the public, private, cultural and not for profit sectors to fund and develop seed projects that demonstrate the potential of proactive information disclosure and digital engagement for government. More information can be found on the Taskforce’s Project Fund page.
In particular the Taskforce will also identify policies and frameworks to assist the Information Commissioner and other agencies in:
• developing and managing a whole of government information publication scheme to encourage greater disclosure of public sector information;
• extending opportunities for the reuse of government information, and considering the terms of that use, to maximise the beneficial flow of that information and facilitate productive applications of government information to the greatest possible extent;
• encouraging effective online innovation, consultation and engagement by government, including by drawing on the lessons of the government’s online consultation trials and any initiatives undertaken by the Taskforce.
The Taskforce will meet regularly, consulting in an open and transparent manner and use online solutions for its engagement wherever possible.
The Taskforce will provide a final report on its activities to the Minister for Finance and Deregulation and the Cabinet Secretary by the end of 2009. The Taskforce will disband on completion of its final report.
Creative Commons: some rights reserved
Unless otherwise specified, posts are licensed under the Creative Commons Attribution licence, Australian variant 2.5.
The Taskforce does not hold copyright for the Government 2.0 logo which was designed by Ben Crothers of Catch Media but as a condition of entry to the design competition, the creator of the logo consented to its use under a Creative Commons Attribution Non Commercial Use license Australian variant 2.5 .
8th May 2009
## Patents
I think that is the most important thing I gathered from this lecture by two Freehills attorneys (Stuart Irvine & Ronelle Geldenhuys) about IP and software patents. Lecture slides here.
Monopoly vs. Secrecy. In order to get the monopoly you must give up the secrecy.
Patents protect functionality.
Patents can be used as a sword (legal action to get royalties or force the infringer to stop), shield (dissuade others from infringing), war chest (trade and negotiation).
A patent gives the patent owner an exclusive right to exclude others from exploiting (manufacturing or importing a patented product or using or importing a product made by a patented process) an invention in a particular country.
To enforce a patent, the patent owner must take the infringer to court.
Tests for patentability,
• Patentable subject matter
• Industrially applicable
• newness (any prior art?)
• obviousness
With regards to patenting mathematical algorithms,
"A method of calculating a value c, where c = ex x sin(t)" is not patentable however this is,
"A method of determining the length of a road (L) in metres by applying the formula $L = \cos \theta \times N \times g^2$ where $\theta$ is the gradient of the road, N is the number of litres of fuel used by a car travelling on the road, and g is the acceleration due to gravity”, According to APO, Manual of Practice and Procedure, Volume 2. Sounds a bit silly to me.
An example,
US Pat. 5356330 (via google) - Apparatus for simulating a "high five"
Self publication prior to filing does class as prior art, meaning you cannot get the patent.
To invalidate a patent you just need to find prior art. That is, find the idea published prior to the filing date of the patent. Lesson here, if you know you don't want to get a patent for something and you want it to remain free to the world publish your idea/concept. Remember you don't need something working in order to patent it. Just detail how it would work (that's easier than getting it to work right?).
US patent 5490216 (or via google) is interesting. Filed in 1993, its a System for software registration. Basically there is a demo mode and a full mode. To get the full mode you need a registration key. Thats the general gitz. I didn't read the whole thing.
There are other examples,
• IBM holds patent #4,965,765 which covers the use of different colours to distinguish the nesting level of nested expressions. (Filed: 1986)
• Patent #5,249,290 covers assignment of client requests to the server process having the least load. (Filed: 1991)
• Patent #4,941,125 covers using a digital camera in conjunction with character recognition software to store and index documents on a CD ROM. (Filed: 1984)
I don't know what to think. They seem trivial, simple and obvious, but they weren't published today. As most people would say, you need to ensure that trivial patents are not granted (problem here is how do you define trivial?), and that the term is not too long (20 years is too long in my opinion).
Patenting of illegal methods in not allowed, though you may patent a things which may be used illegally such as gun (heh, otherwise nothing would be patentable).
Interesting example. A safe design was patented and then a thief used the patents to work out how to break it.
-----------------------
In terms of software, copyrighting software only stops others from using the same implementation as you. They are free to use an alternate implementation to do the exact same thing.
You can copyright compiled machine code.
I have a lot to say about this (creative/computational universe, and the clouds that span derivative works). So much that I'll have to leave it till later.
-----------------------
## Registered Designs
Registered designs are interesting. There is a nice brochure from an Australian Law firm here.
A registered design provides a monopoly of a limited duration (max 10 years in Australia) granted by the government to an entity of a "concept" which determines the appearance of a product. I'm a little confused here as I though (its such a shame that the audio recoding from that lecture is corrupt) Geldenhuys said that registered designs are for a specific device. So if you register a design for an electronic device, anyone can use that design for say a paperweight. However in their lecture slides it says that registered designs protect appearance not functionality.
You will all probably recognise AU Registered Design 307210. Currently owned by Apple Inc. and must expire by Nov 23, 2015.
All registered designs must have a "Statement of Newness and Distinctiveness". AU RD 307210 says, "Newness and distinctiveness is claimed in the visual features shown in solid lines in the representations."
Registered designs must be renewed to stay protected. Though they have a max of 10 years, renewal fees get larger near the end of the designs protected life, either Irvine or Geldenhuys then added to this "governments don't like monopolies". Sorry but I strongly disagree with you there. If governments didn't like monopolies they would abolish crown copyright.
I won't say too much here. But here is a sample trade mark "thing"(?).
[caption id="attachment_517" align="aligncenter" width="450" caption="Trade Mark 1111537 (http://pericles.ipaustralia.gov.au/atmoss/Falcon_Details.Print_TM_Details?p_tm_number=1111537&p_ExtDisp=D&p_Detail=DETAILED&p_Search_No=2&p_Lastrecord=FALSE&p_Is_Internal=F)"][/caption]
You don't publish, you just swear everyone to secrecy (contracts). Does not protect against reverse engineering or independent formulation.
8th May 2009
I went to a Talk by a Patent Attorney (Stephen Fung) the other day (3rd April 2009) about Patents. It was quite interesting. Here are some notes I made.
• Patent examiners work for the government.
• Patent attorneys are not lawyers, they have a science or engineering qualification
A provisional patent can be rubbish, and you can still amend it before you try to get it turned into a full patent. Its used as documentation of the invention at a specific time so that you have evidence and proof that it existed at a specific time.
Patents are a commercial instrument.
Often the venture capitalist will tell the person or company they invest in to file some patents. These people then go to the patent attorney, tell them this is what I've done, just file anything.
An interesting thing about patentable material, using the example of say a compression algorithm, the mathematical foundations are not patentable, but if you incorporate that into say a chip, you can patent that and prevent others from implementing the algorithm into chips of their own.
If you have some new invention that you want to try to patent. You may speak with a patent attorney, go through Technology Transfer (eg. New South Innovations), do the patent yourself, do not disclose until you have filed something.
If you copyright your source code it only protects that "creative expression" of the code. So if someone wrote the exact same program in another programming language then you cannot hinder their distribution of that.
If you patent the underlying algorithm then no one can use of implement that algorithm.
"Patent It Yourself" is apparently a good book.
Tags: law.
8th May 2009
I was looking forward to this talk by David Vaile since his name keeps popping up everywhere I go. So here are some rough notes I took down (and then expanded on some points now). His full slides can be found here.
This slide gives a nice overview.
(David Vaile. Legal perspectives on system development)
Lawyers can speak for clients (i.e. on their behalf). So you may want to be careful of what they are saying for you.
Cases are often about motivation. Why you did something. Your intent. Its not a whole science. eg. murder/manslaughter. did you intentionally push someone in front of a train, or did you slip and accidentally push them in front of a train. This can make a difference in a trial.
Criminal --> Beyond reasonable doubt. Civil --> Probability. Does not need to be beyond reasonable doubt.
Lawyer's will generally say "with respect I think you are wrong" rather than the direct "you are wrong".
Law exists to regulate. "It won't just work out itself [if we don't have laws]".
Courts can be expensive and risky. Going to court may not always be the best idea.
ASIC, ACCC... can step in sometimes. This strips away the companies advantage (lots of 's and lawyers) in a case against an individual.
"If you make something accessible in another country is that publishing in that country?" One court case says yes. I find this surprising. If you publish something on a web server in your country and allow all IP's to access your web pages then another country considers you publishing in that country??? Unfortunately Vaile didn't give the case reference for this (UPDATE: This is the case and here is a list of law journal articles referring to the case. I'll probably make another post once I get a chance to take a closer look at it).
Due to the free trade agreement its now illegal to copy even when allowed if you break the DRM.
Suing your customers --> turns them against your company! This builds a coalition of difference to try to change the law. The turning point is if that coalition is large enough. Could this mean that to win the copyright fight we must get the film studios to sue as many people as possible? I would hope not, and rather hope that people become aware of the current problems on their own accord not through legal action against them.
Litigation risk may change over time. You may do something now that has a low risk of litigation but in a year or so that may change. That minimal risk does not increase your chances of winning the case.
This slide from Vaile's talk is enlightening for me.
(David Vaile. Legal perspectives on system development)
Mainly because its so easy to fall through the top one that you forget there are layers underneath. Copyright laws is so tough and stupid its hard to convince yourself that you should not break them. You loose faith in the law and begin to not worry about anything. But the law is just one standard. Professional standards and ethics come into play. Let me look at some example cases.
Liability Litigation Risk 'Professional' standards (will your peers & colleagues reject you?) Ethics (Will your children & friends reject you?) Murder Illegal High Yes (probably) Yes (probably) Copyright Infringement of a feature film to avoid paying Illegal Low Perhaps Perhaps Copyright Infringement of a feature film to transfer a purchased DVD to a portable device (prior to amendments) Illegal Very Low No (unlikely) No (unlikely)
I think its just as important, if not more important to consider the bottom two standards (professional standards and ethics) than the top two (liability and litigation risk). These bottom two are still important even if you can get away with the illegal act.
Privacy. There are two interests here, the individual and the government.
The Individual. "I want to be left alone." 242227954b0d84ba7550fd6e3d10b9d0 The Government. “What have you got to hide? Tell us.”
When a political party is trying to pass a law public interest/politics may come into play and cause a party to back down on a bill, even if they can get it passed and want it passed.
US Australia Upper House Senate Senate Lower House Congress House of Representatives
The Australian SPAM act has no private right to sue. Must rely on ACMA. The US CANSPAM act has private rights to sue.
Tags: ethics, law, seng4921.
11th April 2009
There are two sources of law.
• Statutory Law: In Australia Statutory Law is written law set down by parliament. Before a law can come into force, the Bill must pass through both Houses of Parliament.
• Common Law: “Common law refers to law and the corresponding legal system developed through decisions of courts and similar tribunals (called case law), rather than through legislative statutes or executive action. Common law is law created and refined by judges: a decision in a currently pending legal case depends on decisions in previous cases and affects the law to be applied in future cases. When there is no authoritative statement of the law, judges have the authority and duty to make law by creating precedent.” –Wikipedia
Statutory law trumps common law.
In Australia, the legal system can be broadly classified into 4 different jurisdictions:
• Criminal Jurisdiction
• Civil Jurisdiction
• Contract Law
• Tort Law
• Equity
Litigation refers to the process of a lawsuit (when you take someone to court).
• The burden is on the party bringing the action (the Plaintiff)
• Litigation can be costly and something to be avoided
• Consider mediation and arbitration for civil matters
Punitive damages (in contrast to compensatory damages) are damages not awarded in order to compensate the plaintiff, but in order to reform or deter the defendant and similar persons from pursuing a course of action such as that which damaged the plaintiff.
In the area of Contract Law, clicking an OKAY button on a webpage or during installation is legally binding!
In the lecture we took a look at the Microsoft Windows Vista License Agreement. Though I think the iPhone License Agreement is worth taking a look at too.
### References
Ho. Peter S. 2009. Introduction to Law and Contracts.
Tags: law, seng4921.
13th March 2009
I was just reading this (which coincidently seems much better written in terms of style and content than what I write here on my blog),
"In my opinion, copyright and patent laws are entirely suboptimal, especially with regard to the digital side of things. The concept of a patent is a noble one -- that is, it allows the inventor of some concept to be protected by the law for a certain amount of time in the production or implementation of that concept. Before patents, inventors would hold their ideas very close to their chests, so nobody could steal them. They'd make a killing selling whatever it was they invented, then take their secret to the grave. Obviously the loss of knowledge is regrettable, but there was no way to let future generations benefit from the invention without giving away its secrets (and thus, your rights). Enter patents. The concept behind patents is that they provide protection for the patent holder for a time, given that he describes it in enough detail for his idea to be replicated. This solves the problem at hand quite neatly: the inventor keeps a grip on his invention, and is given ample time to monopolise upon it. If the inventor were to pass away, the knowledge is retained and can be referred to in the future. The period during which the patent can be enforced is, in most cases, 20 years. But, wait -- if we're to apply such a law to computer programs... when was the last time you used a 20-year-old piece of software? When was the last time you used even a 7-year-old piece of software? Probably about six years ago. Patents are still a good idea in software, but the patent term needs to be drastically reduced for it to apply sanely. 18 months, at a maximum." --http://nornagon.livejournal.com/27709.html
It got me thinking, patent law was really designed for a different age where you invented things such as the telephone and the Rubik's Cube. Patents documented the inner workings of the invention and how to build it. Thus after the patent owner has made some money from their invention and it falls into the patent equivalent of the public domain anyone else can make it and build upon it. Enter the digital age where generally copyright is used to protect computer software rather than patents (I've heard of software patents, but they don't require submission of source code). Copyright was intended to protect creative works where there are no "inner workings" or "instructions" needed in order to build it. Given the fact that most (maybe not most, but lots of) software is written in programming languages that get compiled into machine code, computer software needs these "inner workings" and "instructions" i.e. the source code in order to build upon it once the original creators have made some money.
There are two problems here with the fact that software falls under copyright rather than patents.
1. When the protection expires there is no method to ensure that the source is published, and
2. secondly copyright laws currently last life + 70 years. In some cases this could be 160 years it takes for the copyright to expire. By then the technologies would have most certainly changed and the software would be of no use (even if the physical storage medium has survived that long (though I think laws now allow copying for backup)). As suggested in the quoted article above a reasonable protection length would need to be less. I think 2-3 years, but really an experienced team of worldwide economists would be able to come up with this figure much better than I could. This would, I think, push innovation forward as software creators would need to come up with new things in order to continue the income stream.
But what if the government's were to introduce some new patent laws that tried to put computer software under patent laws rather than copyright (yes I know that's a semantics issue, but I'm referring to the current laws). Well lets say that the law said that you will only have protection for your computer program if you give us the source which we will lock up and then release after a few years. Despite the fact that you would need to employ a lot of patent officers, I don't think this will work because,
1. its hard to tell if the source that was provided really was everything for the program (i.e. manual checking would be needed.)
2. you could argue that machine code is the source (i.e. say you wrote the program in machine code when you really used C++)
3. that creators will just say "okay we don't need protection from the law, we won't use patents, we'll just implement our own DRM and skip your patent laws". This is even worse as it locks up the program for as long as it takes to crack the DRM.
Another key thing is that even in the time of patents if you bought a product that was protected under patent law, you were still allowed to make changes to it. For example if you bought a Rubik's Cube and if it was protected by a patent, the law could not stop you for example pulling it apart to see what it looks like on the inside, or writing some numbers on the outside squares. However now in the digital age and particularly with the DMCA you cannot even do this (though I don't think Australia has any law that is equivalent to the DMCA that restricts you circumventing DRM). In these time it is apparently illegal for you to open up and change your own products that you have purchased and own.
3rd March 2009
So I just read the article over at ZDNET.com.au. Sadly this sounds all to common. I recommend you read the article for yourself.
This is terrible news.
I don't know the legal status of whether RailCorp would win if they went to court, but either way this in more evidence of Australia's poor Copyright laws. The fact that government created facts that are not creative works can be protected by copyright is absurd. Dispite numerous reviews (Crown Copyright Law Review 2005, Review of The Nation Innovation System (though the Government is still reviewing the findings of this one)) nothing has changed.
As the article states, "A 2005 inquiry by the Copyright Law Review Committee recommended relaxation of Crown copyright provisions to allow for more easy access to public interest information, but those changes have yet to be implemented and RailCorp is standing by its challenge.". This inquiry was done in 2005, it is now 2009 so its safe to assume that the Government is not willing to change the laws in light of the recommendations.
They say that they are using copyright laws to protect people from information that may be false. That is a poor argument. The public know this, they know that this is a service provided by a third party and that it may not be accurate. This works because if there are too many problems with it for what the consumer is happy to accept they will simply not use this. This is no excuse to stop people using/republishing/remixing facts.
I always thought that copyright laws were there in order to create incentive for the original creation of a creative work. Thought I think that this is more of a US constitutional or outdated view. I do not necessarily agree with this, and I don't think that is the sole reason we need copyright laws. But obviously that is not what the copyright laws are doing in this case.
I'm just hoping that the Department of Broadband, Communications and the Digital Economy fixes crown copyright soon before this mess continues.
22nd January 2009
In the past week (more like a month now) or so I've had a few requests asking me how I got access to my exam scripts (i.e. my exam responses) and how they (having just completed their HSC) could access theirs. In light of this I thought I would explain why I think exam scripts should be accessible to the student.
About a year ago I made a request for my HSC examination scripts under the Freedom of Information Act 1989 (NSW). The process for submitting a FOI request is documented by the Board here. I was granted copies of these documents[my exam scripts]. In the past people have requested things such as raw marks, I did request those too but that was denied for me. You should note that the Board may or may not grant access to these documents in the future.
Now to why I think students should have access to their scripts, which is mainly because it makes the whole process more transparent (even US President Obama is pressing this with his recent FOIA memo). There should be nothing to hide, students should be able to check what they wrote in the exam. They should be able to publish this along with how their response was marked so that it can be scrutinised and studied by future students. I'm not convinced that this is the best study approach in the long term but that is no excuse for disallowing access to scripts. It would also be great if students could also find out how their questions were marked on a question by question basis.
However I can see reasons why the Board would not want to release exam scripts. It is time and money consuming. Even if the process is automated it still costs money and some time. For this I would accept why the Board would charge a reasonable fee for giving you your scripts.
The Board of Studies is doing the right thing here, they did allow my FOI request so I cannot argue that they are hiding them. Kudos to them for this. I hope two things to happen now, more people become aware that they can get their scripts, and the Board continuing to allow these requests.
Tags: board of studies nsw, education, hsc, law.
17th January 2009
I see two ways (they can even be combined so that both methods are used) to allowing use or granting rights to a copyrighted work. Those two being licensing the work with a copyright license when the work is published, and/or opting for "All rights reserved." and granting rights on a case by case basis when contacted.
Let's say an organisation uses the latter method for licensing a work. If you were an individual who wanted to use say a small portion for non-commercial purposes then that organisation may for instance grant you those usage rights for free. But if you were a commercial company who wanted to use the work say as part of a commercial feature film the organisation may for instance charge a fee for the usage rights. This is the approach that anyone who wanted to use a copyrighted work which does not have a license would need to take (or if the license does not meet their needs).
I oppose this approach for several reasons,
• What if the original copyright was vested in a company that goes out of business. The work becomes an orphan work. (I'm not exactly sure what provisions in the laws allow for this though) A license allows these decisions that the organisation once made to continue to be made.
• It leaves all discrimination transparent to the public and hence more reachable to the Anti-Discrimination Act. For example the latter effective allows an organisation to grant rights to say a girls school to exhibit a film to its students for free but may demand a similar boys school to pay. This kind of discrimination would be difficult to notice. However with the former approach of a license at creation time it is clear from the license what can and cannot be done and by who.
Sure I can see why a company, organisation or individual would want to do it, because it gives them more control over how their work is used, and the latter method is probably better suited where the copyright owner would charge money for any use. I personally haven't used the latter approach, though I do favour the former more.
24th December 2008
In the past month or two I've been watching and listening some of Lawrence Lessig's presentations and I've got his books on my reading list. I could do a lot of blogging on those topics but I wanted to focus on one particular thing. As I was reading Code v2 it lead me to think about a copyright issue that is close to me. It deals with the fact that the Board of Studies NSW, a government organisation copyrights (with a very restrictive license) its syllabi. These syllabi document what students should learn as part of their secondary state education HSC courses. These syllabi are material that students use as part of their study.
For the purposes of review here is the license that the syllabi are provided under,
"© 2002 Copyright Board of Studies NSW for and on behalf of the Crown in right of the State of New South Wales. This document contains Material prepared by the Board of Studies NSW for and on behalf of the State of New South Wales. The Material is protected by Crown copyright. All rights reserved. No part of the Material may be reproduced in Australia or in any other country by any process, electronic or otherwise, in any material form or transmitted to any other person or stored electronically in any form without the prior written permission of the Board of Studies NSW, except as permitted by the Copyright Act 1968. School students in NSW and teachers in schools in NSW may copy reasonable portions of the Material for the purposes of bona fide research or study. Teachers in schools in NSW may make multiple copies, where appropriate, of sections of the HSC papers for classroom use under the provisions of the school's Copyright Agency Limited (CAL) licence. When you access the Material you agree:
• to use the Material for information purposes only
• to reproduce a single copy for personal bona fide study use only and not to reproduce any major extract or the entire Material without the prior permission of the Board of Studies NSW
• to acknowledge that the Material is provided by the Board of Studies NSW
• not to make any charge for providing the Material or any part of the Material to another person or in any way make commercial use of the Material without the prior written consent of the Board of Studies NSW and payment of the appropriate copyright fee
• not to modify the Material or any part of the Material without the express prior written permission of the Board of Studies NSW."
Board of Studies NSW
In my opinion this is absurd! This is depriving students access of material that they require for their studies. This is not a private education institution, this is a government public education system. Students need to know what to study, this document tells students what to study, and as this document is not distributed to students (as in students are not provided a hard copy) the only way they can access it is to copy it, but apparently this is illegal!
The above license does give some rights to school students in NSW ("School students in NSW and teachers in schools in NSW may copy reasonable portions of the Material for the purposes of bona fide research or study."), but why only school students in NSW, what about publishers who are providing material to help students in their studies (for example an annotated copy)? Also why limit the amount students can copy to "reasonable portions"? So basically students cannot make whole copies of this document to aid in their studies!
Also why can't anyone remix the document adding their own annotations or commentary and then publish this? And why only for "personal" use? What if I want to provide a remixed copy to anyone who wants it? If the Board is worried that someone may change the document then republish it and someone mistakes this as an official version, then they should not worry. People are not stupid they know that if they want to ensure the reliability of the document they will go to the source. This is not a valid reason for refusing copying of the document.
These documents should be licensed more freely. They should be in-near public domain allowing anyone to do whatever they want with it. I say "near public domain" because I can understand the Board wanting attribution. But apart from that I don't see any other legal constraint that needs to be placed on these documents. Board of Studies, please consider a license such as the Creative Commons Attribution-Share Alike 2.5 Australia License.
I welcome comments on this matter. | 2018-12-11T00:24:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18735861778259277, "perplexity": 2367.877690810052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823516.50/warc/CC-MAIN-20181210233803-20181211015303-00094.warc.gz"} |
https://pbn.nauka.gov.pl/pbn-report-web/pages/publication/id/56982edc810641ecf916c82e | Absorption features in the quasar HS 1603+3820 II. Distance to the absorber from photoionization modeling.
PBN-AR
Instytucja
Centrum Astronomiczne im. Mikołaja Kopernika Polskiej Akademii Nauk
##### Informacje podstawowe
Główny język publikacji
EN
Czasopismo
New Astronomy
ISSN
1384-1076
EISSN
Wydawca
DOI
URL
Rok publikacji
2014
Numer zeszytu
Strony od-do
70
Numer tomu
28
Identyfikator DOI
Liczba arkuszy
##### Autorzy
(liczba autorów: 7)
Pozostali autorzy
+ 4
##### Streszczenia
Język
angielski
Treść
We present the photoionisation modelling of the intrinsic absorber in the bright quasar HS 1603 + 3820. We constructed the broad-band spectral energy distribution using the optical/UV/X-ray observations from different instruments as inputs for the photoionisation calculations. The spectra from the Keck telescope show extremely high CIV to HI ratios, for the first absorber in system A, named A1. This value, together with high column density of CIV ion, place strong constraints on the photoionisation model. We used two photoionisation codes to derive the hydrogen number density at the cloud illuminated surface. By estimating bolometric luminosity of HS 1603 + 3820 using the typical formula for quasars, we calculated the distance to A1. We could find one photoionization solution, by assuming either a constant density cloud (which was modelled using CLOUDY), or a stratified cloud (which was modelled using TITAN), as well as the solar abundances. This model explained both the ionic column density of CIV and the high CIV to HI ratio. The location of A1 is 0.1 pc, and it is situated even closer to the nucleus than the possible location of the Broad Line Region in this object. The upper limit of the distance is sensitive to the adopted covering factor and the carbon abundance. Photoionisation modelling always prefers dense clouds with the number density n0 = 1010 - 1012 cm-3, which explains intrinsic absorption in HS 1603 + 3820. This number density is of the same order as that in the disk atmosphere at the implied distance of A1. Therefore, our results show that the disk wind that escapes from the outermost accretion disk atmosphere can build up dense absorber in quasars.
##### Inne
System-identifier
3220
Crossref
###### Cytowania
Liczba prac cytujących tę pracę
Brak danych
###### Referencje
Liczba prac cytowanych przez tę pracę
Brak danych | 2020-02-25T12:29:20 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8024554252624512, "perplexity": 5479.982953778332}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146066.89/warc/CC-MAIN-20200225110721-20200225140721-00250.warc.gz"} |
https://www.khanacademy.org/computing/computer-programming/programming-natural-simulations/programming-oscillations/a/trig-and-forces-the-pendulum | # Oscillations
Do you remember reading about Newton’s laws of motion from a couple sections back? We are just about ready to convert those laws into running code. After all, it’s been nice learning about triangles and tangents and waves, but really, the core of this course is about simulating the physics of moving bodies. Let’s take a look at how trigonometry can help us with this pursuit.
A pendulum is a bob suspended from a pivot. Obviously a real-world pendulum would live in a 3D space, but we’re going to look at a simpler scenario, a pendulum in a 2D space—the program canvas.
In the Forces section, we learned how a force (such as the force of gravity shown in the diagram above) causes an object to accelerate. F = M * A or A = F / M. In this case, however, the pendulum bob doesn’t simply fall to the ground because it is attached by an arm to the pivot point. And so, in order to determine its angular acceleration, we not only need to look at the force of gravity, but also the force at the angle of the pendulum’s arm (relative to a pendulum at rest with an angle of 0).
In the above case, since the pendulum’s arm is of fixed length, the only variable in the scenario is the angle. We are going to simulate the pendulum’s motion through the use of angular velocity and acceleration. The angular acceleration will be calculated using Newton’s second law with a little trigonometry twist.
Let’s zoom in on the right triangle from the pendulum diagram.
We can see that the force of the pendulum (F_p) should point perpendicular to the arm of the pendulum in the direction that the pendulum is swinging. After all, if there were no arm, the bob would just fall straight down. It’s the tension force of the arm that keeps the bob accelerating towards the pendulum’s rest state. Since the force of gravity (F_g) points downward, by making a right triangle out of these two vectors, we’ve accomplished something quite magnificent. We’ve made the force of gravity the hypotenuse of a right triangle and separated the vector into two components, one of which represents the force of the pendulum. Since sine equals opposite over hypotenuse, we have:
sine(\theta) = \frac{F_p}{F_g}
Therefore:
F_p = F_g \times sine(\theta)
Lest we forget, we’ve been doing all of this with a single question in mind: What is the angular acceleration of the pendulum? Once we have the angular acceleration, we’ll be able to apply our rules of motion to find the new angle for the pendulum.
angular velocity = angular velocity + angular acceleration
angle = angle + angular velocity
The good news is that with Newton’s second law, we know that there is a relationship between force and acceleration, namely F = M \times A, or A = F / M, and we can use that relationship with the formula above to figure out the angular acceleration. See if you can follow this:
Starting with:
pendulum force = force due to gravity * sine(θ)
Then we divide the right side by mass, to come up with the acceleration, based on Newton's second law:
pendulum angular acceleration = (force due to gravity * sine(θ)) / mass
Then we realize we can just divide the force due to gravity by mass, and that's the same thing as acceleration due to gravity, so we'll just substitute that:
pendulum angular acceleration = acceleration due to gravity * sine (θ)
Ta-da! We now have a way to calculate the angular acceleration.
This is a good time to remind ourselves that we’re ProcessingJS programmers and not physicists. Yes, we know that the acceleration due to gravity on earth is 9.8 meters per second squared. But this number isn’t relevant to us. What we have here is just an arbitrary constant (we’ll call it gravity), one that we can use to scale the acceleration to something that feels right.
angular acceleration = gravity * sine(θ)
Amazing. After all that, the formula is so simple. You might be wondering, why bother going through the derivation at all? I mean, learning is great and all, but we could have easily just said, "Hey, the angular acceleration of a pendulum is some constant times the sine of the angle." This is just another moment in which we remind ourselves that the purpose of the course is not to learn how pendulums swing or gravity works. The point is to think creatively about how things can move about the screen in a computationally based graphics system. The pendulum is just a case study. If you can understand the approach to programming a pendulum, then however you choose to design your onscreen world, you can apply the same techniques.
Of course, we’re not finished yet. We may be happy with our simple, elegant formula, but we still have to apply it in code. This is most definitely a good time to practice our object-oriented programming skills and create a Pendulum object. Let’s think about all the properties we’ve encountered in our pendulum discussion that the object will need to keep track of:
• arm length
• angle
• angular velocity
• angular acceleration
Plus we'll also want to specify where the pendulum is hanging from, so we could start with a constructor like this:
var Pendulum = function(origin, armLength) {
this.origin = origin;
this.armLength = armLength;
this.angle = PI/4;
this.aVelocity = 0.0;
this.aAcceleration = 0.0;
};
We’ll also need to write an update() method to update the pendulum’s angle according to our formula…
Pendulum.prototype.update = function() {
// Arbitrary constant
var gravity = 0.4;
// Calculate acceleration
this.aAcceleration = -1 * gravity * sin(this.angle);
// Increment velocity
this.aVelocity += this.aAcceleration;
// Increment angle
this.angle += this.aVelocity;
};
…as well as a display() method to draw the pendulum in the window. This begs the question: “Um, where do we draw the pendulum?” We know the angle and the arm length, but how do we know the x,y (Cartesian!) coordinates for both the pendulum’s pivot point (let’s call it origin) and bob location (let’s call it position)? This may be getting a little tiring, but the answer, yet again, is trigonometry. Let's reference the diagram to the left.
The origin is just something we make up, as is the arm length. Let’s say we construct our pendulum like so:
var p = new Pendulum(new PVector(100, 10), 125);
We're storing the current angle on the angle property. So relative to the origin, the pendulum’s position is a polar coordinate: (r,angle). And we need it to be Cartesian. Luckily for us, we spent some time in the Angles section deriving the formula for converting from polar to Cartesian. In that section, our angle was relative to the horizontal axis, but here, it's relative to the vertical axis, so we end up using sin() for the x position and cos() for the y position, instead of cos() and sin(), respectively. And so, we can calculate the position relative to the origin using that conversion formula, and then add the origin position to it:
this.position = new PVector(
this.armLength * sin(this.angle),
this.armLength * cos(this.angle));
stroke(0, 0, 0);
fill(175, 175, 175);
line(this.origin.x, this.origin.y, this.position.x, this.position.y);
ellipse(this.position.x, this.position.y, 16, 16);
Before we put everything together, there’s one last little detail I neglected to mention. Let’s think about the pendulum arm for a moment. Is it a metal rod? A string? A rubber band? How is it attached to the pivot point? How long is it? What is its mass? Is it a windy day? There are a lot of questions that we could continue to ask that would affect the simulation. We’re living, of course, in a fantasy world, one where the pendulum’s arm is some idealized rod that never bends and the mass of the bob is concentrated in a single, infinitesimally small point.
Nevertheless, even though we don’t want to worry ourselves with all of the questions, we should add one more variable to our calculation of angular acceleration. To keep things simple, in our derivation of the pendulum’s acceleration, we assumed that the length of the pendulum’s arm is 1. In fact, the length of the pendulum’s arm affects the acceleration greatly: the longer the arm, the slower the acceleration. To simulate a pendulum more accurately, we divide by that length, in this case armLength. For a more involved explanation, visit The Simple Pendulum website.
this.aAcceleration = (-1 * gravity / this.armLength) * sin(this.angle);
Finally, a real-world pendulum is going to experience some amount of friction (at the pivot point) and air resistance. With our code as is, the pendulum would swing forever, so to make it more realistic we can use a “damping” trick. I say trick because rather than model the resistance forces with some degree of accuracy (as we did in the Forces section), we can achieve a similar result by simply reducing the angular velocity during each cycle. The following code reduces the velocity by 1% (or multiplies it by 99%) during each frame of animation:
this.aVelocity *= this.damping;
Putting everything together, we have the following example. We've added a bit of functionality to make it easy to drag the bob and drop it from different heights, too. Try it out!
This "Natural Simulations" course is a derivative of "The Nature of Code" by Daniel Shiffman, used under a Creative Commons Attribution-NonCommercial 3.0 Unported License. | 2016-05-04T10:03:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7851929664611816, "perplexity": 555.2781991787314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860122902.86/warc/CC-MAIN-20160428161522-00063-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://www.itl.nist.gov/div898/handbook/apr/section1/apr164.htm | 8. Assessing Product Reliability
8.1. Introduction
8.1.6. What are the basic lifetime distribution models used for non-repairable populations?
## Lognormal
Lognormal Formulas and relationship to the normal distribution Formulas and Plots
The lognormal life distribution, like the Weibull, is a very flexible model that can empirically fit many types of failure data. The two-parameter form has parameters $$\sigma$$ is the shape parameter and $$T_{50}$$ is the median (a scale parameter).
Note: If time to failure, $$t_f$$, has a lognormal distribution, then the (natural) logarithm of time to failure has a normal distribution with mean $$\mu$$ = ln $$T_{50}$$ and standard deviation $$\sigma$$. This makes lognormal data convenient to work with; just take natural logarithms of all the failure times and censoring times and analyze the resulting normal data. Later on, convert back to real time and lognormal parameters using $$\sigma$$ as the lognormal shape and $$T_{50} = e^\mu$$ as the (median) scale parameter.
Below is a summary of the key formulas for the lognormal. $$\begin{array}{ll} \mbox{PDF:} & f(t) = \frac{1}{\sigma t \sqrt{2 \pi}} \, e^{- \left( \displaystyle{\frac{1}{2 \sigma^2}} \right) \left( \mbox{ln } \displaystyle{t} - \mbox{ln } \displaystyle{T_{50}} \right)^2 } \\ & \\ \mbox{CDF:} & F(t) = \int_{0}^{T} \frac{1}{\sigma t \sqrt{2 \pi}} \, e^{- \left( \displaystyle{\frac{1}{2 \sigma^2}} \right) \left( \mbox{ln } \displaystyle{t} - \mbox{ln } \displaystyle{T_{50}} \right)^2} dt \\ & \\ & F(t) = \Phi \left( \frac{\mbox{ln }t - \mbox{ln } T_{50}}{\sigma}\right) \\ & \\ & \Phi(z) \mbox{ denotes the standard normal CDF.}\\ & \\ \mbox{Reliability:} & R(t) = 1-F(t) \\ & \\ \mbox{Failure Rate:} & h(t) = \frac{f(t)}{R(t)} \\ & \\ \mbox{Mean:} & T_{50} \, e^{\frac{1}{2} \sigma^2} \\ & \\ \mbox{Median:} & T_{50} \\ & \\ \mbox{Variance:} & T_{50}^2 \, e^{\sigma^2} \left(e^{\sigma^2} -1 \right) \end{array}$$
Note: A more general three-parameter form of the lognormal includes an additional waiting time parameter $$\theta$$ (sometimes called a shift or location parameter). The formulas for the three-parameter lognormal are easily obtained from the above formulas by replacing $$t$$ by $$(t - \theta)$$ wherever $$t$$ appears. No failure can occur before $$\theta$$ hours, so the time scale starts at $$\theta$$ and not 0. If a shift parameter $$\theta$$ is known (based, perhaps, on the physics of the failure mode), then all you have to do is subtract $$\theta$$ from all the observed failure times and/or readout times and analyze the resulting shifted data with a two-parameter lognormal.
Examples of lognormal PDF and failure rate plots are shown below. Note that lognormal shapes for small sigmas are very similar to Weibull shapes when the shape parameter $$\gamma$$ is large and large sigmas give plots similar to small Weibull $$\gamma$$'s. Both distributions are very flexible and it is often difficult to choose which to use based on empirical fits to small samples of (possibly censored) data.
Lognormal data 'shapes'
Lognormal failure rate 'shapes'
A very flexible model that also can apply (theoretically) to many degradation process failure modes Uses of the Lognormal Distribution Model
1. As shown in the preceding plots, the lognormal PDF and failure rate shapes are flexible enough to make the lognormal a very useful empirical model. In addition, the relationship to the normal (just take natural logarithms of all the data and time points and you have "normal" data) makes it easy to work with mathematically, with many good software analysis programs available to treat normal data.
2. The lognormal model can be theoretically derived under assumptions matching many failure degradation processes common to electronic (semiconductor) failure mechanisms. Some of these are: corrosion, diffusion, migration, crack growth, electromigration, and, in general, failures resulting from chemical reactions or processes. That does not mean that the lognormal is always the correct model for these mechanisms, but it does perhaps explain why it has been empirically successful in so many of these cases.
3. A brief sketch of the theoretical arguments leading to a lognormal model follows.
Applying the Central Limit Theorem to small additive errors in the log domain and justifying a normal model is equivalent to justifying the lognormal model in real time when a process moves towards failure based on the cumulative effect of many small "multiplicative" shocks. More precisely, if at any instant in time a degradation process undergoes a small increase in the total amount of degradation that is proportional to the current total amount of degradation, then it is reasonable to expect the time to failure (i.e., reaching a critical amount of degradation) to follow a lognormal distribution (Kolmogorov, 1941).
A more detailed description of the multiplicative degradation argument appears in a later section.
Lognormal probability plot We generated 100 random numbers from a lognormal distribution with shape 0.5 and median life 20,000. To see how well these random lognormal data points are fit by a lognormal distribution, we generate the lognormal probability plot shown below. Points that line up approximately on a straight line indicates a good fit to a lognormal (with shape 0.5). The time that corresponds to the (normalized) $$x$$-axis $$T_{50}$$ of 1 is the estimated $$T_{50}$$ according to the data. In this case it is close to 20,000, as expected.
For a lognormal distribution at time $$T$$ = 5000 with $$\sigma$$ = 0.5 and $$T_{50}$$ = 20,000, the PDF value is 0.34175E-5, the CDF value is 0.002781, and the failure rate is 0.3427E-5.
Functions for computing lognormal distribution PDF values, CDF values, failure rates, and for producing probability plots, are found in both Dataplot code and R code. | 2016-12-04T18:25:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7681392431259155, "perplexity": 674.7603474776331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541361.65/warc/CC-MAIN-20161202170901-00458-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://mooseframework.inl.gov/source/kernels/InertialForce.html | # InertialForce
Calculates the residual for the interial force () and the contribution of mass dependent Rayleigh damping and HHT time integration scheme ($\eta \cdot M \cdot ((1+\alpha)velq2-\alpha \cdot vel-old)$)
## Description
This class computes the inertial force using a consistent mass matrix and also computes the mass proportional Rayleigh damping. More information about the residual calculation and usage can be found at Dynamics. Each InertialForce kernel calculates the force only along one coordinate direction. So, a separate InertialForce input block should be set up for each coordinate direction.
## Input Parameters
• variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on
### Required Parameters
• accelerationacceleration variable
C++ Type:std::vector
Options:
Description:acceleration variable
• densitydensityName of Material Property that provides the density
Default:density
C++ Type:MaterialPropertyName
Options:
Description:Name of Material Property that provides the density
• betabeta parameter for Newmark Time integration
C++ Type:double
Options:
Description:beta parameter for Newmark Time integration
• eta0Name of material property or a constant real number defining the eta parameter for the Rayleigh damping.
Default:0
C++ Type:MaterialPropertyName
Options:
Description:Name of material property or a constant real number defining the eta parameter for the Rayleigh damping.
• gammagamma parameter for Newmark Time integration
C++ Type:double
Options:
Description:gamma parameter for Newmark Time integration
• velocityvelocity variable
C++ Type:std::vector
Options:
Description:velocity variable
• alpha0alpha parameter for mass dependent numerical damping induced by HHT time integration scheme
Default:0
C++ Type:double
Options:
Description:alpha parameter for mass dependent numerical damping induced by HHT time integration scheme
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:True
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
• diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
• vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill
• extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
• matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime system time
Description:The tag for the matrices this Kernel should fill
• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill | 2018-12-12T16:12:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25250953435897827, "perplexity": 7514.173997480559}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824059.7/warc/CC-MAIN-20181212155747-20181212181247-00422.warc.gz"} |
http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/9_5node5.html | ##### Personal tools
•
You are here: Home Lecture 9: Convolution Using the DFT
# Lecture 9: Convolution Using the DFT
##### Document Actions
Schedule :: The DFT :: Aliasing & Leakage :: Examples :: The FFT :: Convolution
We have seen the convolution theorem over and over: convolution in time is the transform of multiplication in the frequency domain. By numerically computing the transform using the DFT, we can compute convolutions of sequences. There are some issues to be very careful of, however, since the DFT imposes certain requirements on the signals. We will worry later about this. For the moment, consider the computational complexity. Suppose I have a sequence of points and another sequence also of points. We know that the convolution will have points. Computation of each of the outputs requires approximately computations. The overall complexity for computing convolution is therefore .
But here is the neat thing: We compute the DFT of and the DFT of , multiply the points in the frequency domain, then transform back:
This sure seems like the long way around the barn! But, consider the number of computations if we do the DFTs using FFTs: Each transform requires operations, the multiplication is , and the inverse transform is . The overall computation is . (That's how orders are computed!). So it requires fewer computations (by far!) than straightforward convolution, at least of is large enough. This is, in fact, the way M ATLAB computes its convolutions. This is also the way that symbolic packages (such as Mathematica) compute their multiplications of large integers.
Now the issues regarding use of the DFT for convolution. Recall that the DFT always assumes that the signal is periodic . This is the key to understanding the convolution. The convolution is done on periodic signals, where the period is the number of points in the DFT, and the result of the convolution is periodic also. Suppose that we are dealing with -point DFTs. We can define a convolution which is periodic with period by
The notation is used to indicate that the difference is taken modulo . Suppose , and is a sequence 6 points long and is a sequence 10 points long. Draw sequences, and their 10-periodic extensions. Show graphically what the periodic convolution is. The periodic convolution is the convolution computed when DFTs are used.
Suppose we don't want the effects of the circular convolution; we just want regular linear convolution. What we need to do is zero pad. If is a sequence of length and is a sequence of length , then their convolution will have points. If we take a DFT with at least that many points, there will be no wrap around. Show pictures.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 07). Lecture 9: Convolution Using the DFT. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/9_5node5.html. This work is licensed under a Creative Commons License | 2017-12-17T23:27:19 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9414402842521667, "perplexity": 770.233950229877}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948599156.77/warc/CC-MAIN-20171217230057-20171218012057-00161.warc.gz"} |
https://www.anl.gov/cse/hydrogen-and-fuel-cell-materials | Argonne National Laboratory
Physical Sciences and Engineering
Hydrogen and Fuel Cell Materials
Hydrogen-fueled polymer electrolyte fuel cell (PEFC) systems are high efficiency alternatives to conventional power systems for transportation, portable power and stationary applications. PEFC systems enable energy resiliency and rapid refueling.
Hydrogen fuel can be produced from zero-carbon sources using the electrochemical process of water electrolysis coupled with renewable zero-carbon sources of electricity, such as wind, solar, and nuclear power. The advantage of PEFCs is their high efficiency in converting fuel to electricity with low emissions and at low operating temperatures. The fuel of choice for many PEFC power applications is hydrogen due to its high energy density per mass of fuel, high conversion efficiency and non-carbon-containing emissions. The major issues impeding the widespread implementation of hydrogen-fueled PEFC power systems are hydrogen fuel cost, hydrogen fueling infrastructure, hydrogen storage, and PEFC system cost and lifetime. The Hydrogen and Fuel Cell Materials group in CSE has active research projects to develop new materials and enable existing materials to overcome the major barriers to enable cost-competitive use of hydrogen and PEFCs in a variety of applications.
Hydrogen can play a key role in decarbonizing many sectors beyond transportation, such as residential and commercial electricity and steel and ammonia production. Hydrogen can be produced from zero-carbon sources and processes, such as electrolysis of water, using renewable or nuclear energy. To be widely adopted, however, hydrogen must be cost competitive with incumbent fuels. In 2021, the U.S. Department of Energy announced the first Energy Earth Shot aimed at addressing the main issues with production of hydrogen using electrolysis: cost. The Hydrogen Shot established the goal of reaching $1 per kilogram of hydrogen in one decade (“1,1,1”). The current projected cost of hydrogen by low-temperature water electrolysis using a polymer electrolyte electrolyzer is between 3 and 5 times higher than this target due to the cost of electricity and the capital cost of the precious metal catalysts. The Hydrogen and Fuel Cell Materials group has active research projects to develop new materials and enable existing materials to reach the Hydrogen Shot targets and to enable cost-competitive use of this promising technology in a variety of applications. This work is primarily funded by the Hydrogen and Fuel Cell Technologies Office (HFTO) in the Department of Energy’s (DOE) Office of Energy Efficiency and Renewable Energy. The focus of HFTO has historically been on the automotive application, where cost competitiveness with the incumbent internal combustion engine requires PEFCs with low loadings of costly platinum-based electrocatalyst. Recently, HFTO’s R&D emphasis has shifted to PEFC systems for heavy duty vehicles, such as long-haul trucks. In 2020 HFTO established a consortium of five core national laboratories to address PEFC performance and durability for heavy-duty applications called the Million Mile Fuel Cell Truck consortium (M2FCT). The emphasis here is on efficiency (i.e., current density at high voltages) and durability and less on cost. In 2020, HFTO also established another national laboratory consortium to address the cost, efficiency, and lifetime issues with the production of hydrogen from low and high-temperature electrolysis: Hydrogen from the Next Generation of Electrolyzers of Water (H2NEW). This consortium aims to reduce the cost of hydrogen produced by these processes to$2/kg by 2025 toward the ultimate Hydrogen Shot goal of \$1/kg by 2030.
In support of decarbonization efforts, DOE is also exploring processes to convert carbon dioxide into liquid fuels or chemicals. One such process converts captured carbon dioxide to fuels/chemicals such as methanol, ethanol, isopropanol, and acetone using direct electrochemical reduction. Along with water electrolysis to produce hydrogen, these electrochemical processes can serve as effective means to store and utilize the energy produced from intermittent, renewable sources such as solar and wind.
Our research addresses the main issues facing the widespread deployment of PEFC power systems for numerous applications: performance, durability and cost. The group’s research also addresses the use of fuel cells for transportation applications: lack of cost-effective hydrogen and suitable high-capacity hydrogen storage materials. Additionally, the group is also developing materials and supporting the development of cells for the electrochemical conversion of carbon dioxide to fuels/chemicals.
PGM Free Catalysts
A major cost contributor to PEFC power systems and low-temperature water electrolysis hydrogen production systems and one of the major sources of efficiency loss for both technologies are the platinum group metal oxygen reduction reaction and oxygen evolution reaction catalysts. To address this issue, the Hydrogen and Fuel Cell Materials group is developing platinum group metal-free (PGM-free) catalysts with the aim of maximizing the active site density, accessibility of the active sites, and the activity and durability of those sites. Among other tools, to achieve these goals, the group is utilizing high-throughput materials synthesis coupled with machine learning,1 characterization2 and equipment and methodologies development for performance evaluation.3 This research takes advantage of the capabilities within CSE’s high-throughput research laboratory. This activity is a cornerstone of the DOE’s ElectroCat consortium, which is co-led by Argonne and Los Alamos National Laboratory.
Platinum Alloy Electrocatalysts
Another of the group’s research areas focuses on developing novel platinum and platinum alloy catalysts and on achieving high performance from advanced platinum alloy electrocatalysts by tuning the electrode layer composition and structure. One such novel catalyst approach utilizes a PGM-free catalyst as a support for platinum alloy nanoparticles.4 The group also seeks to determine the performance and durability-limiting properties of platinum and platinum alloy catalysts, electrode layer precursor solutions, and electrodes utilizing a combination of in-cell diagnostics and structural analyses, ex situ time-resolved detection of catalyst degradation products, and X-ray scattering, spectroscopy, and tomography techniques at Argonne’s Advanced Photon Source.5,6 The information from these characterizations and the impact of electrode layer composition and precursor solution solvent on the performance and structure is used to inform the design of electrodes with technology-enabling performance and durability for the automotive and heavy duty vehicle applications. This work is part of the DOE Hydrogen and Fuel Cell Technologies Office’s Million Mile Fuel Cell Truck Consortium (M2FCT).
Our group is also addressing the limited durability of PEFCs by identifying the mechanisms of catalyst degradation and determining the catalyst, catalyst support properties and operating conditions that limit catalyst lifetime. This research utilizes ex situin situ, and operando X-ray absorption and scattering techniques at Argonne’s Advanced Photon Source, aqueous dissolution studies, modeling of platinum dissolution and de-alloying, and modeling of the effect of catalyst degradation on cell performance, in collaboration with Argonne’s Energy Systems and Infrastructure Analysis Division.7,8 This work is also part of M2FCT.
Hydrogen Production
Water electrolysis to form hydrogen represents one of the critical technologies for distributed hydrogen production. Barriers to widespread implementation of this hydrogen production technology are cost and lifetime/durability. Due to the sluggish kinetics of the oxygen evolution reaction (OER), high loadings of costly iridium are needed to achieve reasonable electrolyzer efficiency and durability. The group is developing PGM-free OER catalysts to address the cost and durability issues of iridium OER catalysts. These materials are based on porous, stable transition metal composites derived from, for example, cobalt metal organic frameworks incorporated into a 3-D nano-network architecture.9
The group is also part of the DOE-HFTO Hydrogen from the Next Generation of Electrolyzers of Water” consortium (H2NEW), which aims to lower the cost of hydrogen by improving existing designs and materials of proton exchange membrane and solid oxide water electrolyzers. The group’s roles in the consortium are to define catalyst, electrode design, and operating conditions to improve the performance and extend the lifetime of the electrolyzers. We are utilizing a combination of in situ and operando X-ray absorption spectroscopy and scattering coupled with on-line inductively-coupled plasma mass spectrometry techniques to determine the mechanisms of catalyst degradation, to link catalyst atomic structure with performance, and to define the interactions in the catalyst-ionomer ink determining electrode structure and performance.
Carbon Dioxide to Fuel
Our group, in collaboration with Northern Illinois University, is developing highly effective and selective transition metal-based catalysts for the direct electrochemical conversion of carbon dioxide to value-added, multi-carbon organic chemicals such as ethanol, acetone, and isopropanol.10, 11 In addition to supporting initiatives from DOE’s Advanced Manufacturing Office (AMO), we are also working on commercializing our CO2 reduction catalysts and electrolyzer technology with sponsorship from DOE’s Fossil Energy and Carbon Management Office (FECM). In collaboration with the National Renewable Energy Laboratory, the group is also providing critical information for the development of selective, high efficiency, high current density cells for the conversion of carbon dioxide to fuels, such as formaldehyde.12
Citations
1. M. Karim, M. Ferrandon, S. Medina, E. Sture, N. Kariuki, D.J. Myers, E.F. Holby, P. Zelenay, and T. Ahmed, ACS Applied Energy Materials, doi:10.1021/acsaem.0c01466 (2020).
2. Luigi Osmieri, Rajesh K. Ahluwalia, Xiaohua Wang, Hoon T. Chung, Xi Yin, A. Jeremy Kropf, Jaehyung Park, David A. Cullen, Karren L. More, Piotr Zelenay, Deborah J. Myers, and K.C. Neyerlin, Applied Catalysis B: Environmental, 257 (2019) 117929.
3. Jaehyung Park and Deborah J. Myers, Journal of Power Sources, 480 (2020) 228801-228810.
4. L. Chong, J. Wen, J. Kubal, F. Sen, J. Zou, J. Greeley, M. Chan, H. Barkholtz, W. Ding, D.-J. Liu, Science, 362 (2018) 1276-1281.
5. Min Wang, Jae Hyung Park, Sadia Kabir, K.C. Neyerlin, Nancy N. Kariuki, Haifeng Lv, Vojislav R. Stamenkovic, Deborah J. Myers, Michael Ulsh, and Scott Mauger, ACS Applied Energy Materials, 2 (2019) 6417-6427.
6. Firat C. Cetinbas, Rajesh K. Ahluwalia, Nancy N. Kariuki, Vincent De Andrade, and Deborah J. Myers, Journal of the Electrochemical Society, 167 (2020) 013508-013516.
7. Deborah J. Myers, Xiaoping Wang, Matt C. Smith, and Karren L. More, Journal of the Electrochemical Society, 165(6) (2018) F3178-F3190.
8. Rajesh K. Ahluwalia, Dionissios D. Papadias, Nancy N. Kariuki, Jui-Kun Peng, Xiaoping Wang, Yifen Tsai, Donald G. Graczyk, and Deborah J. Myers, Journal of the Electrochemical Society, 165(6) (2018) F3024-F3035.
9. Di-Jia Liu, Gang Wu, and Hui Xu, “PGM-free OER Catalysts for PEM Electrolyzer,” 2020 DOE Hydrogen and Fuel Cells Program Annual Merit Review and Peer Evaluation Meeting, https://www.hydrogen.energy.gov/pdfs/review20/p157_liu_2020_p.pdf.
10. Haiping Xu, Dominic Rebollar, Haiying He, Lina Chong, Yuzi Liu, Cong Liu, Cheng-Jun Sun, Tao Li, John V. Muntean, Randall E. Winans, Di-Jia Liu, and Tao Xu, Nature Energy, 5 (2020) 623-632.
11. Di-Jia Liu, Joule (2022) in press.
12. Yingying Chen, Ashlee Vise, Ellis Klein, Firat C. Cetinbas, Deborah J. Myers, Wilson A. Smith, Todd G. Deutsch, and K.C. Neyerlin, ACS Energy Letters, 5 (2020) 1825-1833. | 2023-02-08T10:10:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5137374401092529, "perplexity": 9354.644289573767}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500758.20/warc/CC-MAIN-20230208092053-20230208122053-00102.warc.gz"} |
http://dlmf.nist.gov/29.9 | # §29.9 Stability
The Lamé equation (29.2.1) with specified values of $k,h,\nu$ is called stable if all of its solutions are bounded on $\Real$; otherwise the equation is called unstable. If $\nu$ is not an integer, then (29.2.1) is unstable iff $h\leq\mathop{a^{0}_{\nu}\/}\nolimits\!\left(k^{2}\right)$ or $h$ lies in one of the closed intervals with endpoints $\mathop{a^{m}_{\nu}\/}\nolimits\!\left(k^{2}\right)$ and $\mathop{b^{m}_{\nu}\/}\nolimits\!\left(k^{2}\right)$, $m=1,2,\dots$. If $\nu$ is a nonnegative integer, then (29.2.1) is unstable iff $h\leq\mathop{a^{0}_{\nu}\/}\nolimits\!\left(k^{2}\right)$ or $h\in[\mathop{b^{m}_{\nu}\/}\nolimits\!\left(k^{2}\right),\mathop{a^{m}_{\nu}\/% }\nolimits\!\left(k^{2}\right)]$ for some $m=1,2,\dots,\nu$. | 2015-11-30T00:53:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 12, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8752942681312561, "perplexity": 116.21720079605876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398460519.28/warc/CC-MAIN-20151124205420-00226-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://dlmf.nist.gov/19.32 | # §19.32 Conformal Map onto a Rectangle
The function
19.32.1 $z(p)=\mathop{R_{F}\/}\nolimits\!\left(p-x_{1},p-x_{2},p-x_{3}\right),$
with $x_{1},x_{2},x_{3}$ real constants, has differential
19.32.2 $dz=-\frac{1}{2}\left(\prod_{j=1}^{3}(p-x_{j})^{-1/2}\right)dp,$ $\imagpart{p}>0$; $0<\mathop{\mathrm{ph}\/}\nolimits\!\left(p-x_{j}\right)<\pi$, $j=1,2,3$.
If
19.32.3 $x_{1}>x_{2}>x_{3},$ Permalink: http://dlmf.nist.gov/19.32.E3 Encodings: TeX, pMML, png
then $z(p)$ is a Schwartz–Christoffel mapping of the open upper-half $p$-plane onto the interior of the rectangle in the $z$-plane with vertices
19.32.4 $\displaystyle z(\infty)$ $\displaystyle=0,$ $\displaystyle z(x_{1})$ $\displaystyle=\mathop{R_{F}\/}\nolimits\!\left(0,x_{1}-x_{2},x_{1}-x_{3}\right% )\quad\text{(>0)},$ $\displaystyle z(x_{2})$ $\displaystyle=z(x_{1})+z(x_{3}),$ $\displaystyle z(x_{3})$ $\displaystyle=\mathop{R_{F}\/}\nolimits\!\left(x_{3}-x_{1},x_{3}-x_{2},0\right% )=-i\mathop{R_{F}\/}\nolimits\!\left(0,x_{1}-x_{3},x_{2}-x_{3}\right).$
As $p$ proceeds along the entire real axis with the upper half-plane on the right, $z$ describes the rectangle in the clockwise direction; hence $z(x_{3})$ is negative imaginary.
For further connections between elliptic integrals and conformal maps, see Bowman (1953, pp. 44–85). | 2016-07-28T22:20:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 30, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9424440264701843, "perplexity": 1266.7957502838246}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257829320.70/warc/CC-MAIN-20160723071029-00317-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://dergipark.gov.tr/hujms/issue/39860/471165 | | | | |
## The growth of generalized Hadamard product of entire axially monogenic functions
#### M. Abdalla [1] , M. Abul-Ez [2]
##### 18 41
In this article, we estimated upper bounds for the growth order and growth type of generalized Hadamard product entire axially monogenic functions. Also, some results concerning the linear substitution are discussed. The obtained results are the natural generalizations of those given in complex setting of one variable to higher dimensions of more than four.
Axially monogenic function, Hadamard product, Growth order, Growth type
• Abul-Ez. M, Hadamard product of bases of polynomials in Clifford analysis, Complex Vari- ables., 43, 109-128, 2000.
• Abul-Ez. M and Constales. D, Basic sets of polynomials in Clifford analysis, Complex Vari- ables., 14, 177-185, 1990.
• Abul-Ez. M and Constales. D, Linear substitution for basic sets of polynomials in Clifford analysis, Portugaliae Mathematica., 48, 143-154, 1991.
• Abul-Ez. M and Constales. D, On convergence properties of basic series representing special monogenic functions, Arch. Math., 81, 62-71, 2002.
• Abul-Ez. M and De Almeida. R, On the lower order and type of entire axially monogenic functions, Results. Math., 63, 1257-1275, 2013.
• Brackx. F, Delanghe. R and Sommen. F, Clifford analysis. Research Notes in Mathematics 76. London: London Pitman Books Ltd, 1982.
• Constales. D, De Almeida. R and Krausshar. R, On the relation between the growth and the Taylor coeffcients of entire solutions to the higher dimensional Cauchy-Riemann system in $R^{n+1}$, J. Math. Anal. Appl., 327, 763-775, 2007.
• Constales. D, De Almeida. R and Krausshar. R, On the growth type of entire monogenic functions, Arch. Math., 88, 153-163, 2007.
• Constales. D, De Almeida. R and Krausshar. R, Applications of the maximum term and the central index in the asymptotic growth analysis of entire solutions to higher dimensional polynomial Cauchy-Riemann equations, Complex Var. Elliptic Equ., 53, 195-213, 2008.
• De Almeida. R and Krausshar. R, Basics on growth orders of polymonogenic functions, Complex Var. Elliptic Equ., 60, 1-25, 2015.
• Delanghe. R, Sommen. F and Souccěk. V, Clifford algebra and spinor-valued function. Dor- drecht: Kluwer Academic Publishers, 1992.
• Dutta. R. K, On order of a function of several complex variables analytic in the unit polydisc, Krag. J. Math., 36, 163-174, 2012.
• Gol'dberg. A. A, Elementary remarks on the formulas defining the order and type entire functions in several variables, Dokl. Akad. Nauk Arm. SSR., 29, 145-151, 1959.
• Jae Hochoi. J and Kim. Y. C, Generalized Hadamard product functions with negative coefficients, J. Math. Anal. Appl., 199, 459-501, 1996.
• Kishka. Z, Abul-Ez. M, Saleem. M and Abd-Elmaged. H, On the order and type of entire matrix functions in complete Reinhardt domain, J. Mod. Meth. Numer. Math., 3, 31-40, 2012.
• Lounesto. P and Bergh. P, Axially symmetric vector fields and their complex potentials, Complex Variables., 2, 139- 150, 1983.
• Ronkin. L. I, Introduction to the theory of entire functions of several variables, Trans. Math. Monog., 44. Providence R.I., American Mathematical Society, VI, 1974.
• Sayyed. K, Metwally. M and Mohamed. M, Some order and type of generalized Hadamard product of entire functions, South. Asi. Bull. Math., 26, 121-132, 2002.
• Sommen. F, Plane elliptic systems and monogenic functions in symmetric domains, Suppl. Rend. Circ. Mat. Palermo., 6, 259-269, 1984.
• Srivastava. R. K and Kumar. V, On the order and type of integral functions of several complex variables, Compo. Math., 17, 161-166, 1966.
• Srivastava. G. S and Kumar. S, On the generalized order and generalized type of entire monogenic functions, Demon. Math., 46, 663-677, 2013.
Primary Language en Mathematics Mathematics Author: M. Abdalla (Primary Author)Institution: MATHEMATICS DEPARTMENT, FACULTY OF SCIENCE, KING KHALID UNIVERSITYCountry: United Arab Emirates Author: M. Abul-EzInstitution: MATHEMATICS DEPARTMENT, FACULTY OF SCIENCE, SOHAG UNIVERSITY,Country: Egypt
Bibtex @research article { hujms471165, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2018}, volume = {47}, pages = {1231 - 1239}, doi = {}, title = {The growth of generalized Hadamard product of entire axially monogenic functions}, key = {cite}, author = {Abdalla, M. and Abul-Ez, M.} } APA Abdalla, M , Abul-Ez, M . (2018). The growth of generalized Hadamard product of entire axially monogenic functions. Hacettepe Journal of Mathematics and Statistics, 47 (5), 1231-1239. Retrieved from http://dergipark.gov.tr/hujms/issue/39860/471165 MLA Abdalla, M , Abul-Ez, M . "The growth of generalized Hadamard product of entire axially monogenic functions". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1231-1239 Chicago Abdalla, M , Abul-Ez, M . "The growth of generalized Hadamard product of entire axially monogenic functions". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1231-1239 RIS TY - JOUR T1 - The growth of generalized Hadamard product of entire axially monogenic functions AU - M. Abdalla , M. Abul-Ez Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1231 EP - 1239 VL - 47 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics The growth of generalized Hadamard product of entire axially monogenic functions %A M. Abdalla , M. Abul-Ez %T The growth of generalized Hadamard product of entire axially monogenic functions %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 5 %R %U ISNAD Abdalla, M. , Abul-Ez, M. . "The growth of generalized Hadamard product of entire axially monogenic functions". Hacettepe Journal of Mathematics and Statistics 47 / 5 (October 2018): 1231-1239. | 2019-04-21T20:12:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.446588397026062, "perplexity": 6614.970112030287}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532882.36/warc/CC-MAIN-20190421195929-20190421221929-00182.warc.gz"} |
https://indico.fnal.gov/event/15949/contributions/34654/ | # 36th Annual International Symposium on Lattice Field Theory
Jul 22 – 28, 2018
Kellogg Hotel and Conference Center
EST timezone
## Semileptonic decays of $B_{(s)}$ mesons to light pseudoscalar mesons on four-flavor HISQ ensembles
Jul 27, 2018, 5:10 PM
20m
103 (Kellogg Hotel and Conference Center)
### 103
#### Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Weak Decays and Matrix Elements
### Speaker
Mr Zechariah Gelzer (University of Iowa)
### Description
We report the status of an ongoing lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$~mesons with both charged currents ($B\to\pi\ell\nu$, $B_s\to K\ell\nu$) and neutral currents ($B\to\pi\ell^+\ell^-$, $B\to K\ell^+\ell^-$). The results are important for constraining or revealing physics beyond the Standard Model. This work uses MILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light valence quarks and the clover action in the Fermilab interpretation for the $b$~quark. Simulations are carried out at three lattice spacings down to $0.088$~fm, with both physical and unphysical sea-quark masses. We present preliminary blinded results for the form factors $f_+(q^2)$, $f_0(q^2)$, and $f_T(q^2)$ (in terms of momentum transfer $q^2$), along with an examination of systematic errors. Our preliminary results include studies of $z$-expansion methods to extend the kinematic range.
### Primary author
Mr Zechariah Gelzer (University of Iowa)
### Co-authors
Prof. Aida El-Khadra (University of Illinois at Urbana-Champaign) Dr Andreas Kronfeld (Fermilab) Carleton DeTar (University of Utah) Prof. Claude Bernard (Washington University) Dr Elvira Gamiz (University of Granada) Dr James Simone (Fermilab) Dr Ruth Van de Water (Fermilab) Steven Gottlieb (Indiana Univ.) Yannick Meurice (U. of Iowa)
Slides | 2023-03-31T18:24:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8027833700180054, "perplexity": 13301.24824066973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949678.39/warc/CC-MAIN-20230331175950-20230331205950-00389.warc.gz"} |
https://pos.sissa.it/334/282/ | Volume 334 - The 36th Annual International Symposium on Lattice Field Theory (LATTICE2018) - Weak Decays and Matrix Elements
$B\rightarrow D^\ast\ell\nu$ at non-zero recoil
A. Vaquero,* C. DeTar, A.X. El-Khadra, A. Kronfeld, J. Laiho, R. Van de Water on behalf of Fermilab Lattice and MILC Collaborations
*corresponding author
Full text: pdf
Published on: May 29, 2019
Abstract
We present preliminary blinded results from our analysis of the form factors for $B\to D^\ast\ell\nu$ decay at non-zero recoil. Our analysis includes 15 MILC asqtad ensembles with $N_f=2+1$ flavors of sea quarks and lattice spacings ranging from $a\approx 0.15$ fm down to $0.045$ fm. The valence light quarks employ the asqtad action, whereas the $b$ and $c$ quarks are treated using the Fermilab action. We discuss the impact that our results will have on $\left|V_{cb}\right|$ and $R(D\ast)$.
DOI: https://doi.org/10.22323/1.334.0282
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-12-05T12:09:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30243465304374695, "perplexity": 3917.1845288841605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141747774.97/warc/CC-MAIN-20201205104937-20201205134937-00485.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2003.2003.623 | Article Contents
Article Contents
# Positivity preserving discrete model for the coupled ODE's modeling glycolysis
• We construct a nonstandard finite difference scheme for the two coupled ODE's that model glycolysis. The primary emphasis is having the scheme satisfy a positivity condition and also retain the limit-cycle behavior for certain values of the parameters. We show that this is possible and give a full discussion of the scheme along with some of its numerical properties.
Mathematics Subject Classification: Primary: 65L12, 92B99; Secondary: 92-08.
Citation:
Open Access Under a Creative Commons license
• on this site
/ | 2023-03-28T21:15:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.17293599247932434, "perplexity": 807.5096051072361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948871.42/warc/CC-MAIN-20230328201715-20230328231715-00163.warc.gz"} |
http://dergipark.gov.tr/jum/issue/35239/390881 | | | | |
## A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS
#### M. Guerrero [1] , M. García [2] , J. Soria [3] , O. Castillo [4]
##### 79 186
In this work we studied of the parameters of the Cuckoo Search Algorithm via Levy Flights (CS). The main goal of the paper is designing a novel hybrid approach for modifying the Cuckoo Search Algorithm using a Fuzzy Inference System of the Mamdani type for calculating the optimal parameter values independent of the benchmark problem, which we are calling Fuzzy Cuckoo Search (for its acronyms FCS). In this paper different variants of the FCS are presented and the difference is the number of parameters adjusted by the fuzzy control system and the number of rules. Results show that the FCS outperforms the original version of the CS algorithms and the OCS variant of the algorithm proposed by Zhao. The statistical test shows that using a type - 1 fuzzy system in conjunction with the cuckoo search algorithms provides the best solutions
Konular JA45MJ39NH Araştırma Makalesi Yazar: M. Guerrero Yazar: M. García Yazar: J. Soria Yazar: O. Castillo
Bibtex @ { jum390881, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {GÖKHAN ÇUVALCIOĞLU}, year = {2018}, volume = {1}, pages = {32 - 61}, doi = {}, title = {A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS}, key = {cite}, author = {Guerrero, M. and García, M. and Soria, J. and Castillo, O.} } APA Guerrero, M , García, M , Soria, J , Castillo, O . (2018). A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS. Journal of Universal Mathematics, 1 (1), 32-61. Retrieved from http://dergipark.gov.tr/jum/issue/35239/390881 MLA Guerrero, M , García, M , Soria, J , Castillo, O . "A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS". Journal of Universal Mathematics 1 (2018): 32-61 Chicago Guerrero, M , García, M , Soria, J , Castillo, O . "A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS". Journal of Universal Mathematics 1 (2018): 32-61 RIS TY - JOUR T1 - A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS AU - M. Guerrero , M. García , J. Soria , O. Castillo Y1 - 2018 PY - 2018 N1 - DO - T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 32 EP - 61 VL - 1 IS - 1 SN - 2618-5660-2618-5660 M3 - UR - Y2 - 2019 ER - EndNote %0 Journal of Universal Mathematics A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS %A M. Guerrero , M. García , J. Soria , O. Castillo %T A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS %D 2018 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 1 %N 1 %R %U ISNAD Guerrero, M. , García, M. , Soria, J. , Castillo, O. . "A NEW ALGORITHM BASED ON THE CUCKOO SEARCH WITH DYNAMIC ADAPTATION OF PARAMETERS USING FUZZY SYSTEMS". Journal of Universal Mathematics 1 / 1 (Ocak 2018): 32-61. | 2019-03-26T10:06:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45066037774086, "perplexity": 4196.474844626423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204969.39/warc/CC-MAIN-20190326095131-20190326121131-00514.warc.gz"} |
http://dlmf.nist.gov/3.1 | # §3.1 Arithmetics and Error Measures
## §3.1(i) Floating-Point Arithmetic
Computer arithmetic is described for the binary based system with base 2; another frequently used system is the hexadecimal system with base 16.
A nonzero normalized binary floating-point machine number is represented as
where is equal to 1 or 0, each , , is either 0 or 1, is the most significant bit, () is the number of significant bits , is the least significant bit, is an integer called the exponent, is the significand, and is the fractional part.
The set of machine numbers is the union of 0 and the set
with and all allowable choices of , , , and .
Let with and . For given values of , , and , the format width in bits of a computer word is the total number of bits: the sign (one bit), the significant bits ( bits), and the bits allocated to the exponent (the remaining bits). The integers , , and are characteristics of the machine. The machine epsilon , that is, the distance between 1 and the next larger machine number with is given by . The machine precision is . The lower and upper bounds for the absolute values of the nonzero machine numbers are given by
3.1.3
Underflow (overflow) after computing occurs when is smaller (larger) than ().
### ¶ IEEE Standard
The current standard is the ANSI/IEEE Standard 754; see IEEE (1985, §§1–4). In the case of normalized binary representation the memory positions for single precision (, , , ) and double precision (, , , ) are as in Figure 3.1.1. The respective machine precisions are and .
Figure 3.1.1: Floating-point arithmetic. Memory positions in single and double precision, in the case of binary representation.
### ¶ Rounding
Let be any positive number with
, and
Then rounding by chopping or rounding down of gives , with maximum relative error . Symmetric rounding or rounding to nearest of gives or , whichever is nearer to , with maximum relative error equal to the machine precision .
Negative numbers are rounded in the same way as .
For further information see Goldberg (1991) and Overton (2001).
## §3.1(ii) Interval Arithmetic
Interval arithmetic is intended for bounding the total effect of rounding errors of calculations with machine numbers. With this arithmetic the computed result can be proved to lie in a certain interval, which leads to validated computing with guaranteed and rigorous inclusion regions for the results.
Let be the set of closed intervals . The elementary arithmetical operations on intervals are defined as follows:
3.1.6,
where , with appropriate roundings of the end points of when machine numbers are being used. Division is possible only if the divisor interval does not contain zero.
A basic text on interval arithmetic and analysis is Alefeld and Herzberger (1983), and for applications and further information see Moore (1979) and Petković and Petković (1998). The last reference includes analogs for arithmetic in the complex plane .
## §3.1(iii) Rational Arithmetics
Computer algebra systems use exact rational arithmetic with rational numbers , where and are multi-length integers. During the calculations common divisors are removed from the rational numbers, and the final results can be converted to decimal representations of arbitrary length. For further information see Matula and Kornerup (1980).
## §3.1(iv) Level-Index Arithmetic
To eliminate overflow or underflow in finite-precision arithmetic numbers are represented by using generalized logarithms given by
with and the unique nonnegative integer such that . In level-index arithmetic is represented by (or for negative numbers). Also in this arithmetic generalized precision can be defined, which includes absolute error and relative precision (§3.1(v)) as special cases.
For further information see Clenshaw and Olver (1984) and Clenshaw et al. (1989). For applications see Lozier (1993).
For further references on level-index arithmetic (and also other arithmetics) see Anuta et al. (1996). See also Hayes (2009).
## §3.1(v) Error Measures
If is an approximation to a real or complex number , then the absolute error is
3.1.8
If , the relative error is
3.1.9
The relative precision is
3.1.10
where for real variables, and for complex variables (with the principal value of the logarithm).
The mollified error is
3.1.11
For error measures for complex arithmetic see Olver (1983). | 2013-05-26T08:46:51 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8992775678634644, "perplexity": 1198.63511856297}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706762669/warc/CC-MAIN-20130516121922-00031-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://dlmf.nist.gov/13.2 | # §13.2 Definitions and Basic Properties
## §13.2(i) Differential Equation
### Kummer’s Equation
13.2.1 $z\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(b-z)\frac{\mathrm{d}w}{\mathrm{d% }z}-aw=0.$ ⓘ Symbols: $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$: derivative of $f$ with respect to $x$ and $z$: complex variable A&S Ref: 13.1.1 Referenced by: §13.14(i), §13.14(v), §13.2(i), §13.2(v), §13.29(ii), §13.3(i), §13.3(i) Permalink: http://dlmf.nist.gov/13.2.E1 Encodings: TeX, pMML, png See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
This equation has a regular singularity at the origin with indices $0$ and $1-b$, and an irregular singularity at infinity of rank one. It can be regarded as the limiting form of the hypergeometric differential equation (§15.10(i)) that is obtained on replacing $z$ by $\ifrac{z}{b}$, letting $b\to\infty$, and subsequently replacing the symbol $c$ by $b$. In effect, the regular singularities of the hypergeometric differential equation at $b$ and $\infty$ coalesce into an irregular singularity at $\infty$.
### Standard Solutions
The first two standard solutions are:
13.2.2 $M\left(a,b,z\right)=\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}}{{\left(b% \right)_{s}}s!}z^{s}=1+\frac{a}{b}z+\frac{a(a+1)}{b(b+1)2!}z^{2}+\cdots,$ ⓘ Defines: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function Symbols: ${{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$: $=M\left(\NVar{a},\NVar{b},\NVar{z}\right)$ notation for the Kummer confluent hypergeometric function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $!$: factorial (as in $n!$), $s$: nonnegative integer and $z$: complex variable A&S Ref: 13.1.2 Referenced by: §13.14(i), §13.2(i), §13.29(i), §13.29(ii), §13.9(i) Permalink: http://dlmf.nist.gov/13.2.E2 Encodings: TeX, pMML, png See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
and
13.2.3 ${\mathbf{M}}\left(a,b,z\right)=\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}}{% \Gamma\left(b+s\right)s!}z^{s},$ ⓘ Defines: ${\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Olver’s confluent hypergeometric function Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $!$: factorial (as in $n!$), $s$: nonnegative integer and $z$: complex variable Referenced by: §13.2(i) Permalink: http://dlmf.nist.gov/13.2.E3 Encodings: TeX, pMML, png See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
except that $M\left(a,b,z\right)$ does not exist when $b$ is a nonpositive integer. In other cases
13.2.4 $M\left(a,b,z\right)=\Gamma\left(b\right){\mathbf{M}}\left(a,b,z\right).$
The series (13.2.2) and (13.2.3) converge for all $z\in\mathbb{C}$. $M\left(a,b,z\right)$ is entire in $z$ and $a$, and is a meromorphic function of $b$. ${\mathbf{M}}\left(a,b,z\right)$ is entire in $z$, $a$, and $b$.
Although $M\left(a,b,z\right)$ does not exist when $b=-n$, $n=0,1,2,\dots$, many formulas containing $M\left(a,b,z\right)$ continue to apply in their limiting form. In particular,
13.2.5 $\lim_{b\to-n}\frac{M\left(a,b,z\right)}{\Gamma\left(b\right)}={\mathbf{M}}% \left(a,-n,z\right)=\frac{{\left(a\right)_{n+1}}}{(n+1)!}z^{n+1}M\left(a+n+1,n% +2,z\right).$
When $a=-n$, $n=0,1,2,\dots$, ${\mathbf{M}}\left(a,b,z\right)$ is a polynomial in $z$ of degree not exceeding $n$; this is also true of $M\left(a,b,z\right)$ provided that $b$ is not a nonpositive integer.
Another standard solution of (13.2.1) is $U\left(a,b,z\right)$, which is determined uniquely by the property
13.2.6 $U\left(a,b,z\right)\sim z^{-a},$ $z\to\infty$, $|\operatorname{ph}z|\leq\frac{3}{2}\pi-\delta$, ⓘ Defines: $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function Symbols: $\sim$: asymptotic equality, $\pi$: the ratio of the circumference of a circle to its diameter, $\operatorname{ph}$: phase, $z$: complex variable and $\delta$: small positive constant Referenced by: §13.2(i), §13.2(iv) Permalink: http://dlmf.nist.gov/13.2.E6 Encodings: TeX, pMML, png See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
where $\delta$ is an arbitrary small positive constant. In general, $U\left(a,b,z\right)$ has a branch point at $z=0$. The principal branch corresponds to the principal value of $z^{-a}$ in (13.2.6), and has a cut in the $z$-plane along the interval $(-\infty,0]$; compare §4.2(i).
When $a=-m$, $m=0,1,2,\dots$, $U\left(a,b,z\right)$ is a polynomial in $z$ of degree $m$:
13.2.7 $U\left(-m,b,z\right)=(-1)^{m}{\left(b\right)_{m}}M\left(-m,b,z\right)=(-1)^{m}% \sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}{\left(b+s\right)_{m-s}}(-z)^{s}.$ ⓘ Symbols: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$: binomial coefficient, $m$: integer, $n$: nonnegative integer, $s$: nonnegative integer and $z$: complex variable Referenced by: §13.2(i), item Equation (13.2.7) Permalink: http://dlmf.nist.gov/13.2.E7 Encodings: TeX, pMML, png Addition (effective with 1.0.10): The equality $U\left(-m,b,z\right)=(-1)^{m}{\left(b\right)_{m}}M\left(-m,b,z\right)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation $a=-n$ has been changed to $a=-m$. See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
Similarly, when $a-b+1=-n$, $n=0,1,2,\ldots$,
13.2.8 $U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-n\right)_{n}}}{z^{a+n}}M\left% (-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{s}{\left(a% \right)_{s}}z^{-s}.$ ⓘ Symbols: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$: binomial coefficient, $n$: nonnegative integer, $s$: nonnegative integer and $z$: complex variable Referenced by: §13.2(i), item Equation (13.2.8) Permalink: http://dlmf.nist.gov/13.2.E8 Encodings: TeX, pMML, png Addition (effective with 1.0.10): The equality $U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-n\right)_{n}}}{z^{a+n}}M\left% (-n,1-a-n,z\right)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Suggested 2014-02-10 by Adri Olde Daalhuis See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
When $b=n+1$, $n=0,1,2,\dots$, and $a\neq 0,-1,-2,\dots$,
13.2.9 $U\left(a,n+1,z\right)=\frac{(-1)^{n+1}}{n!\Gamma\left(a-n\right)}\sum_{k=0}^{% \infty}\frac{{\left(a\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^{k}\left(\ln z+% \psi\left(a+k\right)-\psi\left(1+k\right)-\psi\left(n+k+1\right)\right)+\frac{% 1}{\Gamma\left(a\right)}\sum_{k=1}^{n}\frac{(k-1)!{\left(1-a+k\right)_{n-k}}}{% (n-k)!}z^{-k}.$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $\psi\left(\NVar{z}\right)$: psi (or digamma) function, $!$: factorial (as in $n!$), $\ln\NVar{z}$: principal branch of logarithm function, $n$: nonnegative integer and $z$: complex variable Referenced by: §13.2(i), §33.6, §6.6, 5th item Permalink: http://dlmf.nist.gov/13.2.E9 Encodings: TeX, pMML, png Clarification (effective with 1.0.12): The condition $a\neq 0,-1,-2,\dots$ that appeared below this equation now appears ahead of the equation. Suggested 2016-07-05 by Adri Olde Daalhuis See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
When $b=n+1$, $n=0,1,2,\dots$, and $a=-m$, $m=0,1,2,\dots$,
13.2.10 $U\left(-m,n+1,z\right)=(-1)^{m}{\left(n+1\right)_{m}}M\left(-m,n+1,z\right)=(-% 1)^{m}\sum_{s=0}^{m}\genfrac{(}{)}{0.0pt}{}{m}{s}{\left(n+s+1\right)_{m-s}}(-z% )^{s}.$ ⓘ Symbols: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, ${\left(\NVar{a}\right)_{\NVar{n}}}$: Pochhammer’s symbol (or shifted factorial), $\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}$: binomial coefficient, $m$: integer, $n$: nonnegative integer, $s$: nonnegative integer and $z$: complex variable Referenced by: §13.2(i), item Equation (13.2.10), 5th item Permalink: http://dlmf.nist.gov/13.2.E10 Encodings: TeX, pMML, png Clarification (effective with 1.0.12): . The condition $a=-m,m=0,1,2,\dots$ that appeared below this equation now appears ahead of the equation. Suggested 2016-07-05 by Adri Olde Daalhuis Addition (effective with 1.0.10): The equality $U\left(-m,n+1,z\right)=(-1)^{m}{\left(n+1\right)_{m}}M\left(-m,n+1,z\right)$ has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation $a=-m,m=0,1,2,\ldots$ has been introduced. Suggested 2015-02-10 by Adri Olde Daalhuis See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
When $b=-n$, $n=0,1,2,\dots$, the following equation can be combined with (13.2.9) and (13.2.10):
13.2.11 $U\left(a,-n,z\right)=z^{n+1}U\left(a+n+1,n+2,z\right).$ ⓘ Symbols: $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, $n$: nonnegative integer and $z$: complex variable Permalink: http://dlmf.nist.gov/13.2.E11 Encodings: TeX, pMML, png See also: Annotations for §13.2(i), §13.2(i), §13.2 and Ch.13
## §13.2(ii) Analytic Continuation
When $m\in\mathbb{Z}$,
13.2.12 $U\left(a,b,ze^{2\pi\mathrm{i}m}\right)=\frac{2\pi\mathrm{i}e^{-\pi\mathrm{i}bm% }\sin\left(\pi bm\right)}{\Gamma\left(1+a-b\right)\sin\left(\pi b\right)}{% \mathbf{M}}\left(a,b,z\right)+e^{-2\pi\mathrm{i}bm}U\left(a,b,z\right).$
Except when $z=0$ each branch of $U\left(a,b,z\right)$ is entire in $a$ and $b$. Unless specified otherwise, however, $U\left(a,b,z\right)$ is assumed to have its principal value.
## §13.2(iii) Limiting Forms as $z\to 0$
13.2.13 $M\left(a,b,z\right)=1+O\left(z\right).$
Next, in cases when $a=-n$ or $-n+b-1$, where $n$ is a nonnegative integer,
13.2.14 $U\left(-n,b,z\right)=(-1)^{n}{\left(b\right)_{n}}+O\left(z\right),$
13.2.15 $U\left(-n+b-1,b,z\right)=(-1)^{n}{\left(2-b\right)_{n}}z^{1-b}+O\left(z^{2-b}% \right).$
In all other cases
13.2.16 $\displaystyle U\left(a,b,z\right)$ $\displaystyle=\frac{\Gamma\left(b-1\right)}{\Gamma\left(a\right)}z^{1-b}+O% \left(z^{2-\Re b}\right),$ $\Re b\geq 2$, $b\not=2$, ⓘ Symbols: $O\left(\NVar{x}\right)$: order not exceeding, $\Gamma\left(\NVar{z}\right)$: gamma function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, $\Re$: real part and $z$: complex variable A&S Ref: 13.5.6 (with order estimate corrected) Permalink: http://dlmf.nist.gov/13.2.E16 Encodings: TeX, pMML, png See also: Annotations for §13.2(iii), §13.2 and Ch.13 13.2.17 $\displaystyle U\left(a,2,z\right)$ $\displaystyle=\frac{1}{\Gamma\left(a\right)}z^{-1}+O\left(\ln z\right),$ 13.2.18 $\displaystyle U\left(a,b,z\right)$ $\displaystyle=\frac{\Gamma\left(b-1\right)}{\Gamma\left(a\right)}z^{1-b}+\frac% {\Gamma\left(1-b\right)}{\Gamma\left(a-b+1\right)}+O\left(z^{2-\Re b}\right),$ $1\leq\Re b<2$, $b\not=1$, 13.2.19 $\displaystyle U\left(a,1,z\right)$ $\displaystyle=-\frac{1}{\Gamma\left(a\right)}\left(\ln z+\psi\left(a\right)+2% \gamma\right)+O\left(z\ln z\right),$ 13.2.20 $\displaystyle U\left(a,b,z\right)$ $\displaystyle=\frac{\Gamma\left(1-b\right)}{\Gamma\left(a-b+1\right)}+O\left(z% ^{1-\Re b}\right),$ $0<\Re b<1$, 13.2.21 $\displaystyle U\left(a,0,z\right)$ $\displaystyle=\frac{1}{\Gamma\left(a+1\right)}+O\left(z\ln z\right),$ 13.2.22 $\displaystyle U\left(a,b,z\right)$ $\displaystyle=\frac{\Gamma\left(1-b\right)}{\Gamma\left(a-b+1\right)}+O\left(z% \right),$ $\Re b\leq 0$, $b\not=0$.
## §13.2(iv) Limiting Forms as $z\to\infty$
Except when $a=0,-1,\dots$ (polynomial cases),
13.2.23 ${\mathbf{M}}\left(a,b,z\right)\sim\ifrac{e^{z}z^{a-b}}{\Gamma\left(a\right)},$ $\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-\delta$,
where $\delta$ is an arbitrary small positive constant.
For $U\left(a,b,z\right)$ see (13.2.6).
## §13.2(v) Numerically Satisfactory Solutions
Fundamental pairs of solutions of (13.2.1) that are numerically satisfactory (§2.7(iv)) in the neighborhood of infinity are
13.2.24 $U\left(a,b,z\right)$, $e^{z}U\left(b-a,b,e^{-\pi\mathrm{i}}z\right)$, $-\tfrac{1}{2}\pi\leq\operatorname{ph}{z}\leq\tfrac{3}{2}\pi$, 13.2.25 $U\left(a,b,z\right)$, $e^{z}U\left(b-a,b,e^{\pi\mathrm{i}}z\right)$, $-\tfrac{3}{2}\pi\leq\operatorname{ph}{z}\leq\tfrac{1}{2}\pi$.
A fundamental pair of solutions that is numerically satisfactory near the origin is
13.2.26 $M\left(a,b,z\right),\quad z^{1-b}M\left(a-b+1,2-b,z\right),$ $b\not\in\mathbb{Z}$.
When $b=n+1=1,2,3,\dots$, a fundamental pair that is numerically satisfactory near the origin is $M\left(a,n+1,z\right)$ and
13.2.27 $\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!{\left(1-a\right)_{k}}}z^{-k}-\sum_{k=0}^{% \infty}\frac{{\left(a\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^{k}\left(\ln z+% \psi\left(a+k\right)-\psi\left(1+k\right)-\psi\left(n+k+1\right)\right),$
if $a-n\neq 0,-1,-2,\dots$, or $M\left(a,n+1,z\right)$ and
13.2.28 $\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!{\left(1-a\right)_{k}}}z^{-k}-\sum_{k=0}^{% -a}\frac{{\left(a\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^{k}\left(\ln z+\psi% \left(1-a-k\right)-\psi\left(1+k\right)-\psi\left(n+k+1\right)\right)+(-1)^{1-% a}(-a)!\sum_{k=1-a}^{\infty}\frac{(k-1+a)!}{{\left(n+1\right)_{k}}k!}z^{k},$
if $a=0,-1,-2,\dots$, or $M\left(a,n+1,z\right)$ and
13.2.29 $\sum_{k=a}^{n}\frac{(k-1)!}{(n-k)!(k-a)!}z^{-k},$ ⓘ Symbols: $!$: factorial (as in $n!$), $n$: nonnegative integer and $z$: complex variable Permalink: http://dlmf.nist.gov/13.2.E29 Encodings: TeX, pMML, png See also: Annotations for §13.2(v), §13.2 and Ch.13
if $a=1,2,\dots,n$.
When $b=-n=0,-1,-2,\dots$, a fundamental pair that is numerically satisfactory near the origin is $z^{n+1}\*M\left(a+n+1,n+2,z\right)$ and
13.2.30 $\sum_{k=1}^{n+1}\frac{(n+1)!(k-1)!}{(n-k+1)!{\left(-a-n\right)_{k}}}z^{n-k+1}-% \sum_{k=0}^{\infty}\frac{{\left(a+n+1\right)_{k}}}{{\left(n+2\right)_{k}}k!}z^% {n+k+1}\left(\ln z+\psi\left(a+n+k+1\right)-\psi\left(1+k\right)-\psi\left(n+k% +2\right)\right),$
if $a\neq 0,-1,-2,\dots$, or $z^{n+1}M\left(a+n+1,n+2,z\right)$ and
13.2.31 $\sum_{k=1}^{n+1}\frac{(n+1)!(k-1)!}{(n-k+1)!{\left(-a-n\right)_{k}}}z^{n-k+1}-% \sum_{k=0}^{-a-n-1}\frac{{\left(a+n+1\right)_{k}}}{{\left(n+2\right)_{k}}k!}z^% {n+k+1}\left(\ln z+\psi\left(-a-n-k\right)-\psi\left(1+k\right)-\psi\left(n+k+% 2\right)\right)+(-1)^{n-a}{(-a-n-1)!}\sum_{k=-a-n}^{\infty}\frac{(k+a+n)!}{{% \left(n+2\right)_{k}}k!}z^{n+k+1},$
if $a=-n-1,-n-2,-n-3,\dots$, or $z^{n+1}M\left(a+n+1,n+2,z\right)$ and
13.2.32 $\sum_{k=a+n+1}^{n+1}\frac{(k-1)!}{(n-k+1)!(k-a-n-1)!}z^{n-k+1},$ ⓘ Symbols: $!$: factorial (as in $n!$), $n$: nonnegative integer and $z$: complex variable Referenced by: §13.2(v) Permalink: http://dlmf.nist.gov/13.2.E32 Encodings: TeX, pMML, png See also: Annotations for §13.2(v), §13.2 and Ch.13
if $a=0,-1,\dots,-n$.
## §13.2(vi) Wronskians
13.2.33 $\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),z^{1-b}{\mathbf{% M}}\left(a-b+1,2-b,z\right)\right\}$ $\displaystyle=\sin\left(\pi b\right)z^{-b}e^{z}/\pi,$ 13.2.34 $\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),U\left(a,b,z% \right)\right\}$ $\displaystyle=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a\right)},$ 13.2.35 $\displaystyle\mathscr{W}\left\{{\mathbf{M}}\left(a,b,z\right),e^{z}U\left(b-a,% b,e^{\pm\pi\mathrm{i}}z\right)\right\}$ $\displaystyle=\ifrac{e^{\mp b\pi\mathrm{i}}z^{-b}e^{z}}{\Gamma\left(b-a\right)},$ 13.2.36 $\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2-b,z\right),U% \left(a,b,z\right)\right\}$ $\displaystyle=-\ifrac{z^{-b}e^{z}}{\Gamma\left(a-b+1\right)},$ 13.2.37 $\displaystyle\mathscr{W}\left\{z^{1-b}{\mathbf{M}}\left(a-b+1,2-b,z\right),e^{% z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right)\right\}$ $\displaystyle=-\ifrac{z^{-b}e^{z}}{\Gamma\left(1-a\right)},$ 13.2.38 $\displaystyle\mathscr{W}\left\{U\left(a,b,z\right),e^{z}U\left(b-a,b,e^{\pm\pi% \mathrm{i}}z\right)\right\}$ $\displaystyle=e^{\pm(a-b)\pi\mathrm{i}}z^{-b}e^{z}.$
## §13.2(vii) Connection Formulas
### Kummer’s Transformations
13.2.39 $\displaystyle M\left(a,b,z\right)$ $\displaystyle=e^{z}M\left(b-a,b,-z\right),$ ⓘ Symbols: $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm and $z$: complex variable A&S Ref: 13.1.27 Referenced by: §13.12, §13.8(i), §13.9(ii), §18.17(vi) Permalink: http://dlmf.nist.gov/13.2.E39 Encodings: TeX, pMML, png See also: Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13 13.2.40 $\displaystyle U\left(a,b,z\right)$ $\displaystyle=z^{1-b}U\left(a-b+1,2-b,z\right).$ ⓘ Symbols: $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function and $z$: complex variable A&S Ref: 13.1.29 Referenced by: §13.8(iii) Permalink: http://dlmf.nist.gov/13.2.E40 Encodings: TeX, pMML, png See also: Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13
13.2.41 $\frac{1}{\Gamma\left(b\right)}M\left(a,b,z\right)=\frac{e^{\mp a\pi\mathrm{i}}% }{\Gamma\left(b-a\right)}U\left(a,b,z\right)+\frac{e^{\pm(b-a)\pi\mathrm{i}}}{% \Gamma\left(a\right)}e^{z}U\left(b-a,b,e^{\pm\pi\mathrm{i}}z\right).$
Also, when $b$ is not an integer
13.2.42 $U\left(a,b,z\right)=\frac{\Gamma\left(1-b\right)}{\Gamma\left(a-b+1\right)}M% \left(a,b,z\right)+\frac{\Gamma\left(b-1\right)}{\Gamma\left(a\right)}z^{1-b}M% \left(a-b+1,2-b,z\right).$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $M\left(\NVar{a},\NVar{b},\NVar{z}\right)$: $={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$ Kummer confluent hypergeometric function, $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function and $z$: complex variable A&S Ref: 13.1.3 (in different form) Referenced by: §13.14(vii), §13.2(ii), §13.6(v), §13.9(ii), §33.13 Permalink: http://dlmf.nist.gov/13.2.E42 Encodings: TeX, pMML, png See also: Annotations for §13.2(vii), §13.2(vii), §13.2 and Ch.13 | 2018-10-23T00:03:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 423, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9729174375534058, "perplexity": 5075.7076701008145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515555.58/warc/CC-MAIN-20181022222133-20181023003633-00044.warc.gz"} |
https://gea.esac.esa.int/archive/documentation/GDR2/Gaia_archive/chap_datamodel/sec_dm_external_catalogues/ssec_dm_hipparcos_newreduction.html | # 14.4.3 hipparcos_newreduction
Hipparcos New Reduction: The Astrometric Catalogue
‘Hipparcos, the new Reduction of the Raw data’ by F. van Leeuwen, A&A 474, 653 (2007); http://dx.doi.org/10.1051/0004-6361:20078357
A new reduction of the astrometric data as produced by the Hipparcos mission has been published, claiming accuracies for nearly all stars brighter than magnitude Hp=8 to be better, by up to a factor 4, than in the original catalogue. The new Hipparcos astrometric catalogue is checked for the quality of the data and the consistency of the formal errors as well as the possible presence of error correlations. The differences with the earlier publication are explained. Methods. The internal errors are followed through the reduction process, and the external errors are investigated on the basis of a comparison with radio observations of a small selection of stars, and the distribution of negative parallaxes. Error correlation levels are investigated and the reduction by more than a factor 10 as obtained in the new catalogue is explained. Results. The formal errors on the parallaxes for the new catalogue are confirmed. The presence of a small amount of additional noise, though unlikely, cannot be ruled out. Conclusions. The new reduction of the Hipparcos astrometric data provides an improvement by a factor 2.2 in the total weight compared to the catalogue published in 1997, and provides much improved data for a wide range of studies on stellar luminosities and local galactic kinematics.
Note that the covariance matrix is stored in a rather obscure form in this catalogue. The way to reconstruct it from the existing fields is described in Appendix B of https://ui.adsabs.harvard.edu/#abs/2014A&A...571A..85M/abstract
Columns description:
hip : Hipparcos identifier (int)
Hipparcos identifier
ic : Entry in one of the supplementary catalogues (int)
Entry in one of the supplementary catalogues
ra : Right Ascension in ICRS, Ep=1991.25 (double, Angle[deg])
Right Ascension in ICRS, Ep=1991.25
dec : Declination in ICRS, Ep=1991.25 (double, Angle[deg])
Declination in ICRS, Ep=1991.25
Right Ascension in ICRS, Ep=1991.25
Declination in ICRS, Ep=1991.25
plx : Parallax (double, Angle[mas])
Parallax
pm_ra : Proper motion in Right Ascension (double, Angular Velocity[mas/year])
Proper motion in Right Ascension
pm_de : Proper motion in Declination (double, Angular Velocity[mas/year])
Proper motion in Declination
e_plx : Formal error on parallax (double, Angle[mas])
Formal error on parallax
e_pm_ra : Formal error on pm_ra (double, Angular Velocity[mas/year])
Formal error on pm_ra
e_pm_de : Formal error on pm_de (double, Angular Velocity[mas/year])
Formal error on pm_de
f1 : Percentage rejected data (int, Dimensionless[percentage/100])
Percentage rejected data
f2 : Goodness of fit (double)
Goodness of fit
nc : Number of components (int)
Number of components
ntr : Number of field transits used (int)
Number of field transits used
u3 : Upper-triangular weight matrix element 3 (double)
Upper-triangular weight matrix element 3; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u4 : Upper-triangular weight matrix element 4 (double)
Upper-triangular weight matrix element 4; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u5 : Upper-triangular weight matrix element 5 (double)
Upper-triangular weight matrix element 5; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u6 : Upper-triangular weight matrix element 6 (double)
Upper-triangular weight matrix element 6; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u7 : Upper-triangular weight matrix element 7 (double)
Upper-triangular weight matrix element 7; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u8 : Upper-triangular weight matrix element 8 (double)
Upper-triangular weight matrix element 8; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u9 : Upper-triangular weight matrix element 9 (double)
Upper-triangular weight matrix element 9; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
sn : [0,159] Solution type new reduction (int)
[0,159] Solution type new reduction
The solution type is a number 10xd+s consisting of two parts d and s:
s describes the type of solution adopted:
1 = stochastic solution (dispersion is given in the ’var’ column)
3 = VIM solution (additional parameters in file hipvim.dat)
5 = 5-parameter solution (this file)
7 = 7-parameter solution (additional parameters in hip7p.dat)
9 = 9-parameter solution (additional parameters in hip9p.dat)
d describes peculiarities, as a combination of values:
0 = single star
1 = double star
2 = variable in the system with amplitude $>$ 0.2mag
4 = astrometry refers to the photocenter
8 = measurements concern the secondary (fainter) in the double system
so : [0,5] Solution type old reduction (int)
[0,5] Solution type old reduction
as follows: 0 = standard 5-parameter solution 1 = 7- or 9-parameter solution 2 = stochastic solution 3 = double and multiple stars 4 = orbital binary as resolved in the published catalog 5 = VIM (variability-induced mover) solution
var : Cosmic dispersion added (stochastic solution) (double)
u1 : Upper-triangular weight matrix element 1 (double)
Upper-triangular weight matrix element 1; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u2 : Upper-triangular weight matrix element 2 (double)
Upper-triangular weight matrix element 2; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u10 : Upper-triangular weight matrix element 10 (double)
Upper-triangular weight matrix element 10; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u11 : Upper-triangular weight matrix element 11 (double)
Upper-triangular weight matrix element 11; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u12 : Upper-triangular weight matrix element 12 (double)
Upper-triangular weight matrix element 12; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u13 : Upper-triangular weight matrix element 13 (double)
Upper-triangular weight matrix element 13; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u14 : Upper-triangular weight matrix element 14 (double)
Upper-triangular weight matrix element 14; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
u15 : Upper-triangular weight matrix element 15 (double)
Upper-triangular weight matrix element 15; see Hipparcos, the New Reduction of the Raw data, Appendix C (van Leeuwen, 2007).
The upper-triangular weight matrix U is related to the covariance matrix C by
${\rm C}^{-1}={\rm U}^{T}{\rm U}$
and the elements $U_{i}$ forming the upper triangular matrix are indexed as
$\left(\begin{array}[]{ccccc}U_{1}&U_{2}&U_{4}&U_{7}&U_{11}\\ 0&U_{3}&U_{5}&U_{8}&U_{12}\\ 0&0&U_{6}&U_{9}&U_{13}\\ 0&0&0&U_{10}&U_{14}\\ 0&0&0&0&U_{15}\\ \end{array}\right)$
on the astrometric parameters RA, Dec, parallax, proper motion in RA, proper motion in Dec (in the case of 5-parameter solutions as above) and derivatives of those proper motion components (in the case of 7- and 9-parameter solutions).
hp_mag : Hipparcos magnitude (double, Magnitude[mag])
Hipparcos magnitude
b_v : Colour index (double, Magnitude[mag])
Colour index
v_i : V-I colour index (double, Magnitude[mag])
V-I colour index
e_hp_mag : Error on mean Hpmag (double, Magnitude[mag])
Error on mean Hpmag
e_b_v : Formal error on colour index (double, Magnitude[mag])
Formal error on colour index
s_hp : Scatter of Hpmag (double, Magnitude[mag])
Scatter of Hpmag
va : [0,2] Reference to variability annex (int)
[0,2] Reference to variability annex | 2019-05-22T07:55:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 46, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7363488674163818, "perplexity": 3201.9426793830353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256764.75/warc/CC-MAIN-20190522063112-20190522085112-00065.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M195W&home=MXXX025 | #### ${{\boldsymbol Z}_{{c}}{(4430)}}$ WIDTH
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 181 \pm31}$ OUR AVERAGE
$172$ $\pm13$ ${}^{+37}_{-34}$ 1
2014 AG
LHCB ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \psi}{(2S)}}$
$200$ ${}^{+41}_{-46}$ ${}^{+26}_{-35}$ 1
2013
BELL ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \psi}{(2S)}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$107$ ${}^{+86}_{-43}$ ${}^{+74}_{-56}$ 2
2009
BELL ${{\mathit B}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{+}}{{\mathit \psi}{(2S)}}$
$45$ ${}^{+18}_{-13}$ ${}^{+30}_{-13}$ 3
2008
BELL ${{\mathit B}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{+}}{{\mathit \psi}{(2S)}}$
1 From a four-dimensional amplitude analysis.
2 From a Dalitz plot analysis. Superseded by CHILIKIN 2013 .
3 Superseded by MIZUK 2009 and CHILIKIN 2013 .
References:
AAIJ 2014AG
PRL 112 222002 Observation of the Resonant Character of the ${{\mathit Z}{(4430)}^{-}}$ State
CHILIKIN 2013
PR D88 074026 Experimental Constraints on the Spin and Parity of the ${{\mathit Z}{(4430)}^{+}}$
MIZUK 2009
PR D80 031104 Dalitz Analysis of ${{\mathit B}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{+}}{{\mathit \psi}^{\,'}}$ Decays and the ${{\mathit Z}{(4430)}^{+}}$
CHOI 2008
PRL 100 142001 Observation of a Resonance-Like Structure in the ${{\mathit \pi}^{\pm}}{{\mathit \psi}^{\,'}}$ Mass Distribution in Exclusive ${{\mathit B}}$ $\rightarrow$ ${{\mathit K}}{{\mathit \pi}^{\pm}}{{\mathit \psi}^{\,'}}$ Decays | 2022-01-18T19:54:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9363822937011719, "perplexity": 5150.471754222697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300997.67/warc/CC-MAIN-20220118182855-20220118212855-00686.warc.gz"} |
https://math-physics-problems.wikia.org/wiki/Current_Carrying_Wires | 267 Pages
## Problem
Consider two current-carrying wires, one with current $I_1$, and one with current $I_2$. Using the right-hand rule, one can determine the direction of the magnetic fields across each wire. The right-hand rule is also used to determine the direction of the magnetic forces exerted on each current-carrying wire. Try it!
Part 1: If the currents through each wire are travelling in the same direction, will the wires attract or repel?
Part 2: Determine the magnitude of the magnetic force density (magnetic force per unit length) exerted on each wire.
## Solution
Part 1
Refer to the diagram on the left. Using the right-hand rule, if the two currents are travelling in the same direction, the magnetic fields will be curling in the same direction (counter-clockwise in the diagram because both currents point up). Thus the generated forces are pointing towards each other, which means the wires will attract.
Part 2
First determine the magnitude of the magnetic field for each wire. One can use Ampere's Law.
$\oint_C \mathbf{B} \cdot d\boldsymbol{l} = \mu_0 I$
$|\mathbf{B_1}| 2\pi r = \mu_0 I_1$
$|\mathbf{B_1}| = \frac{\mu_0 I_1}{2\pi r}$
Similarly,
$|\mathbf{B_2}| = \frac{\mu_0 I_2}{2\pi r}$.
The magnetic force of a current-carrying wire is
$\mathbf{F} = I\boldsymbol{l} \times \mathbf{B}$.
The magnitude of the magnetic force is thus
$|\mathbf{F}| = |Il||B|\sin \theta$.
Therefore,
$|\mathbf{F}| = |I_1 l|\left|\frac{\mu_0 I_2}{2\pi r} \right|\sin {90}^{\circ}$
$\frac{|\mathbf{F}|}{l} = \frac{\mu_0 I_1 I_2}{2\pi r}$.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-11-29T02:24:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427387475967407, "perplexity": 456.16870709386325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195967.34/warc/CC-MAIN-20201129004335-20201129034335-00676.warc.gz"} |
https://large-numbers.fandom.com/wiki/Hyperfactorial | ## FANDOM
1,124 Pages
The hyperfactorial is defined as $$H(n) = \prod^{n}_{i = 1} i^i = 1^1 \cdot 2^2 \cdot 3^3 \cdot 4^4 \cdot \ldots \cdot n^n$$.[1]
The first few values of $$H(n)$$ for $$n = 1, 2, 3, 4, \ldots$$ are 1, 4, 108, 27,648, 86,400,000, 4,031,078,400,000, 3,319,766,398,771,200,000, 55,696,437,941,726,556,979,200,000, 21,577,941,222,941,856,209,168,026,828,800,000, ... (OEIS A002109). The sum of the reciprocals of these numbers is 2.2592954398150629..., which can be approximated as $$\sqrt[12]{17,688}$$, or more precisely as $$\sqrt[7]{\sqrt[7]{3^{4}\cdot67\cdot3,929\cdot10,371,376,751}}$$, a curious 18-decimal-place approximation where we have a double 7th root (7 is prime) of the product of seven prime factors.
## Sources Edit
1. Hyperfactorial from Wolfram MathWorld
Community content is available under CC-BY-SA unless otherwise noted. | 2020-07-09T05:10:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9228465557098389, "perplexity": 2774.469165496028}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00489.warc.gz"} |
http://pdglive.lbl.gov/Particle.action?node=B179&init=0&home=sumtabB | ${{\boldsymbol \Omega}}$ BARYONS($\boldsymbol S$ = $-3$, $\boldsymbol I$ = 0) ${{\mathit \Omega}^{-}}$ = ${\mathit {\mathit s}}$ ${\mathit {\mathit s}}$ ${\mathit {\mathit s}}$ INSPIRE search
# ${{\boldsymbol \Omega}{(2012)}^{-}}$ $I(J^P)$ = $0(?^{-})$
Seen in ${{\mathit \Xi}^{0}}{{\mathit K}^{-}}$ and ${{\mathit \Xi}^{-}}{{\mathit K}_S^0}$ decays with a combined significance of 8.3 standard deviations.
${{\mathit \Omega}{(2012)}^{-}}$ MASS $2012.4 \pm0.9$ MeV
${{\mathit \Omega}{(2012)}^{-}}$ WIDTH $6.4 {}^{+3.0}_{-2.6}$ MeV
$\Gamma_{1}$ ${{\mathit \Xi}^{0}}{{\mathit K}^{-}}$ seen 403
$\Gamma_{2}$ ${{\mathit \Xi}^{-}}{{\mathit K}^{0}}$ seen 392 | 2019-12-14T06:06:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.969998836517334, "perplexity": 1258.6560964659222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540584491.89/warc/CC-MAIN-20191214042241-20191214070241-00425.warc.gz"} |
https://dust.trainhub.eumetsat.int/docs/solution_1.html | # Solution 1¶
You are working for ENAIRE, the air navigation authority for Spain and western Africa. You know that the Canary Islands are prone to Saharan dust events and for this reason, ENAIRE monitors dust on a daily basis. You are the operations analyst for the week of 21-27 February 2020 and responsible for issuing alerts, and if necessary, to mandate required safety measures.
On 21 February 2020, you are in-charge of analysing the dust forecast and to monitor potential dust events for the coming days. With your new knowledge on aerosol and dust data, you should be able to do this.
1. Brainstorm
• What dust forecasts do you know about?
• How do they differ from each other?
• What satellite data do you know about that can be used for dust nowcasting?
• Which variables can be used to monitor and forecast dust?
3. Download the MSG SEVIRI Level 1.5 data and visualize the Dust RGB composite
• Based on the dust forecast for the next days - which day and hour would you choose for getting a near real-time monitoring of dust from the MSG SEVIRI instrument?
• Hint
4. Interpret the results
• Describe the dust forecast event in comparison with the near real-time monitoring from the satellite.
• What decision as ENAIRE operations analyst do you take? Would you issue an alert? Would you implement some safety measures?
import xarray as xr
import glob
from IPython.display import HTML
import matplotlib.pyplot as plt
import matplotlib.colors
from matplotlib.cm import get_cmap
from matplotlib import animation
from matplotlib.axes import Axes
import cartopy.crs as ccrs
from cartopy.mpl.gridliner import LONGITUDE_FORMATTER, LATITUDE_FORMATTER
import cartopy.feature as cfeature
from cartopy.mpl.geoaxes import GeoAxes
GeoAxes._pcolormesh_patched = Axes.pcolormesh
from satpy.scene import Scene
from satpy.composites import GenericCompositor
from satpy.writers import to_image
from satpy.resample import get_area_def
import pyresample
import warnings
warnings.simplefilter(action = "ignore", category = RuntimeWarning)
%run ../../functions.ipynb
### 1. Brainstorm¶
Model forecasts
Forecast models differ in their spatial and temporal resolution, but also spatial coverage and forecast period.
Satellite observations
• MSG SEVIRI Level 1 RGB composites
• Terra/Aqua MODIS Level 1 RGB composites
The following variables can be used to monitor and forecast dust:
• Dust Optical Depth
• Aerosol Optical Depth
The first step is to load a MONARCH forecast file. The data is disseminated in the netCDF format on a daily basis, with the forecast initialisation at 12:00 UTC. Load the MONARCH dust forecast of 21 February 2020. You can use the function open_dataset() from the xarray Python library.
Once loaded, you see that the data has three dimensions: lat, lon and time; and offers two data variables od550_dust and sconc_dust.
filepath = '../../eodata/case_study/sds_was/2020022112_3H_NMMB-BSC.nc'
file = xr.open_dataset(filepath)
file
<xarray.Dataset>
Dimensions: (lon: 307, lat: 211, time: 25)
Coordinates:
* lon (lon) float64 -31.0 -30.67 -30.33 -30.0 ... 70.33 70.67 71.0
* lat (lat) float64 -3.0 -2.667 -2.333 -2.0 ... 66.0 66.33 66.67 67.0
* time (time) datetime64[ns] 2020-02-21T12:00:00 ... 2020-02-24T12:0...
Data variables:
od550_dust (time, lat, lon) float32 ...
sconc_dust (time, lat, lon) float32 ...
Attributes:
CDI: Climate Data Interface version 1.5.4 (http://c...
Conventions: CF-1.2
history: Fri Feb 21 23:50:54 2020: cdo remapbil,regular...
_FillValue: -32767.0
missing_value: -32767.0
title: Regional Reanalysis 0.5x0.5 deg NMMB-BSC-Dust ...
History: Fri Feb 21 22:12:45 2020: ncrcat -F -O pout_re...
Grid_type: B-grid: vectors interpolated to scalar positions
Map_Proj: Rotated latitude longitude
NCO: 4.0.8
CDO: Climate Data Operators version 1.5.4 (http://c...
Let us then retrieve the data variable od550_dust, which is the dust optical depth at 550 nm.
od550_dust = file['od550_dust']
od550_dust
<xarray.DataArray 'od550_dust' (time: 25, lat: 211, lon: 307)>
[1619425 values with dtype=float32]
Coordinates:
* lon (lon) float64 -31.0 -30.67 -30.33 -30.0 ... 70.0 70.33 70.67 71.0
* lat (lat) float64 -3.0 -2.667 -2.333 -2.0 ... 66.0 66.33 66.67 67.0
* time (time) datetime64[ns] 2020-02-21T12:00:00 ... 2020-02-24T12:00:00
Attributes:
long_name: dust optical depth at 550 nm
units:
title: dust optical depth at 550 nm
Let us now have a closer look at the dimensions of the data. Let us first inspect the two coordinate dimensions lat and lon. You can simply access the dimension’s xarray.DataArray by specifying the name of the dimension. Below you see that the data has a 0.1 x 0.1 degrees resolution and have the following geographical bounds:
• Longitude: [-63., 101.9]
• Latitude: [-11., 71.4]
latitude = file.lat
longitude = file.lon
latitude, longitude
(<xarray.DataArray 'lat' (lat: 211)>
array([-3. , -2.666667, -2.333333, ..., 66.333326, 66.66666 , 66.999993])
Coordinates:
* lat (lat) float64 -3.0 -2.667 -2.333 -2.0 ... 66.0 66.33 66.67 67.0
Attributes:
standard_name: latitude
long_name: latitude
units: degrees_north
axis: Y,
<xarray.DataArray 'lon' (lon: 307)>
array([-31. , -30.666667, -30.333333, ..., 70.333323, 70.666657,
70.99999 ])
Coordinates:
* lon (lon) float64 -31.0 -30.67 -30.33 -30.0 ... 70.0 70.33 70.67 71.0
Attributes:
standard_name: longitude
long_name: longitude
units: degrees_east
axis: X)
Now, let us also inspect the time dimension. You see that one daily forecast file has 25 time steps, with three hourly forecast information up to 72 hours (3 days) in advance.
file.time
<xarray.DataArray 'time' (time: 25)>
array(['2020-02-21T12:00:00.000000000', '2020-02-21T15:00:00.000000000',
'2020-02-21T18:00:00.000000000', '2020-02-21T21:00:00.000000000',
'2020-02-22T00:00:00.000000000', '2020-02-22T03:00:00.000000000',
'2020-02-22T06:00:00.000000000', '2020-02-22T09:00:00.000000000',
'2020-02-22T12:00:00.000000000', '2020-02-22T15:00:00.000000000',
'2020-02-22T18:00:00.000000000', '2020-02-22T21:00:00.000000000',
'2020-02-23T00:00:00.000000000', '2020-02-23T03:00:00.000000000',
'2020-02-23T06:00:00.000000000', '2020-02-23T09:00:00.000000000',
'2020-02-23T12:00:00.000000000', '2020-02-23T15:00:00.000000000',
'2020-02-23T18:00:00.000000000', '2020-02-23T21:00:00.000000000',
'2020-02-24T00:00:00.000000000', '2020-02-24T03:00:00.000000000',
'2020-02-24T06:00:00.000000000', '2020-02-24T09:00:00.000000000',
'2020-02-24T12:00:00.000000000'], dtype='datetime64[ns]')
Coordinates:
* time (time) datetime64[ns] 2020-02-21T12:00:00 ... 2020-02-24T12:00:00
Attributes:
standard_name: time
You can define variables for the attributes of a variable. This can be helpful during data visualization, as the attributes long_name and units can be added as additional information to the plot. From the xarray.DataArray, you simply specify the name of the attribute of interest.
long_name=od550_dust.long_name
units= od550_dust.units
#### Visualize dust Aerosol Optical Depth¶
Now we have loaded all necessary information to be able to visualize the dust Aerosol Optical Depth for one specific time during the forecast run. Let us use the function visualize_pcolormesh() to visualize the data with the help of the plotting library matplotlib and Cartopy.
You have to specify the following keyword arguments:
• data_array: the
• longitude, latitude: longitude and latitude variables of the data variable
• projection: one of Cartopy’s projection options
• color_scale: one of matplotlib’s colormaps
• units: unit of the data parameter, preferably taken from the data array’s attributes
• long_name: longname of the data parameter is taken as title of the plot, preferably taken from the data array’s attributes
• vmin, vmax: minimum and maximum bounds of the color range
• set_global: False, if data is not global
• lonmin, lonmax, latmin, latmax: kwargs have to be specified, if set_global=False
Note: in order to have the time information as part of the title, we add the string of the datetime information to the long_name variable: long_name + ' ' + str(od_dust[##,:,:].time.data).
forecast_step=0
visualize_pcolormesh(data_array=od550_dust[forecast_step,:,:],
longitude=od550_dust.lon,
latitude=od550_dust.lat,
projection=ccrs.PlateCarree(),
color_scale='afmhot_r',
unit=units,
long_name=long_name + ' ' + str(od550_dust[forecast_step,:,:].time.data),
vmin=0,
vmax=1.5,
set_global=False,
lonmin=longitude.min().data,
lonmax=longitude.max().data,
latmin=latitude.min().data,
latmax=latitude.max().data)
(<Figure size 1440x720 with 2 Axes>,
<GeoAxesSubplot:title={'center':'dust optical depth at 550 nm 2020-02-21T12:00:00.000000000'}>)
#### Animate dust Aerosol Optical Depth forecasts¶
In the last step, you can animate the Dust Aerosol Optical Depth forecasts in order to see how the trace gas develops over a period of 3 days, from 20th Feb 12 UTC to 24th February 2021.
You can do animations with matplotlib’s function animation. Jupyter’s function HTML can then be used to display HTML and video content.
The animation function consists of 4 parts:
• Setting the initial state:
Here, you define the general plot your animation shall use to initialise the animation. You can also define the number of frames (time steps) your animation shall have.
• Functions to animate:
An animation consists of three functions: draw(), init() and animate(). draw() is the function where individual frames are passed on and the figure is returned as image. In this example, the function redraws the plot for each time step. init() returns the figure you defined for the initial state. animate() returns the draw() function and animates the function over the given number of frames (time steps).
• Create a animate.FuncAnimation object:
The functions defined before are now combined to build an animate.FuncAnimation object.
• Play the animation as video:
As a final step, you can integrate the animation into the notebook with the HTML class. You take the generate animation object and convert it to a HTML5 video with the to_html5_video function
# Setting the initial state:
# 1. Define figure for initial plot
fig, ax = visualize_pcolormesh(data_array=od550_dust[0,:,:],
longitude=od550_dust.lon,
latitude=od550_dust.lat,
projection=ccrs.PlateCarree(),
color_scale='afmhot_r',
unit=units,
long_name=long_name + ' ' + str(od550_dust[0,:,:].time.data),
vmin=0,
vmax=1.5,
lonmin=longitude.min().data,
lonmax=longitude.max().data,
latmin=latitude.min().data,
latmax=latitude.max().data,
set_global=False)
frames = 24
def draw(i):
img = plt.pcolormesh(od550_dust.lon,
od550_dust.lat,
od550_dust[i,:,:],
cmap='afmhot_r',
transform=ccrs.PlateCarree(),
vmin=0,
vmax=1.5,
ax.set_title(long_name + ' '+ str(od550_dust.time[i].data), fontsize=20, pad=20.0)
return img
def init():
return fig
def animate(i):
return draw(i)
ani = animation.FuncAnimation(fig, animate, frames, interval=800, blit=False,
init_func=init, repeat=True)
HTML(ani.to_html5_video())
plt.close(fig)
HTML(ani.to_html5_video())
### 3. Download the MSG SEVIRI Level 1.5 data and visualize the Dust RGB composite¶
From the EUMETSAT Data Store, we downloaded High Rate SEVIRI Level 1.5 Image data for 23 February 2020 at 18 UTC.
The data is downloaded as a zip archive. We already unzipped the file. Hence, in a next step we can specify the file path and create a variable with the name file_name.
file_name = glob.glob('../../eodata/case_study/meteosat/event/2020/02/23/MSG4-SEVI-MSG15-0100-NA-20200223181244.112000000Z-NA.nat')
file_name
['../../eodata/case_study/meteosat/event/2020/02/23/MSG4-SEVI-MSG15-0100-NA-20200223181244.112000000Z-NA.nat']
In a next step, we use the Scene constructor from the satpy library. Once loaded, a Scene object represents a single geographic region of data, typically at a single continuous time range.
You have to specify the two keyword arguments reader and filenames in order to successfully load a scene. As mentioned above, for MSG SEVIRI data in the Native format, you can use the seviri_l1b_native reader.
scn = Scene(reader="seviri_l1b_native",
filenames=file_name)
scn
<satpy.scene.Scene at 0x7f7c2c5fb340>
Load the RGB composite ID natural color
Let us define load the composite ID natural_color. This list variable can then be passed to the function load(). Per default, scenes are loaded with the north pole facing downwards. You can specify the keyword argument upper_right_corner=NE in order to turn the image around and have the north pole facing upwards.
composite_id = ["natural_color"]
A print of the Scene object scn shows you that one band is available: natural_color
print(scn)
<xarray.DataArray 'where-1eeee2327f1f52a84787d02280871d42' (bands: 3, y: 3712, x: 3712)>
dask.array<where, shape=(3, 3712, 3712), dtype=float32, chunksize=(1, 3712, 3712), chunktype=numpy.ndarray>
Coordinates:
crs object PROJCRS["unknown",BASEGEOGCRS["unknown",DATUM["unknown",E...
* y (y) float64 5.569e+06 5.566e+06 5.563e+06 ... -5.563e+06 -5.566e+06
* x (x) float64 -5.569e+06 -5.566e+06 ... 5.563e+06 5.566e+06
* bands (bands) <U1 'R' 'G' 'B'
Attributes:
end_time: 2020-02-23 18:15:11.171248
sun_earth_distance_correction_factor: 0.9787042740413612
start_time: 2020-02-23 18:00:11.057487
area: Area ID: msg_seviri_fes_3km\nDesc...
georef_offset_corrected: True
orbital_parameters: {'projection_longitude': 0.0, 'pr...
sensor: seviri
ancillary_variables: []
standard_name: natural_color
resolution: 3000.403165817
platform_name: Meteosat-11
sun_earth_distance_correction_applied: True
wavelength: None
optional_datasets: []
name: natural_color
_satpy_id: DataID(name='natural_color', reso...
prerequisites: [DataQuery(name='IR_016', modifie...
optional_prerequisites: []
mode: RGB
Generate a geographical subset over Canary Islands
Crop the data with x and y values in original projection unit (x_min, y_min, x_max, y_max). Below we apply the funcion crop() and use the keyword argument xy_bbox=(xmin, ymin, xmax, ymax) in order to crop the file based on an area in original projection unit. For the bbox information we use the following settings: xmin=-20E5, ymin=23E5, xmax=-5E5, ymax=35E5.
Then, let’s visualize the cropped image with the function show().
scn_cropped = scn.crop(xy_bbox=(-20E5, 23E5, -5E5, 35E5))
scn_cropped.show("natural_color")
Let us store the area definition as variable.
area = scn_cropped['natural_color'].attrs['area']
area
Next, use the area definition to resample the loaded Scene object. Afterwards, you can visualize the resampled image with the function show().
scn_resample_nc = scn.resample(area)
scn_resample_nc.show('natural_color')
Load, visualize and interpret the MSG SEVIRI Dust RGB composite
Let us reload the file with the Scene constructor.
scn2 = Scene(reader="seviri_l1b_native",
filenames=file_name)
scn2
<satpy.scene.Scene at 0x7f7d387b6bb0>
Let us define a composite ID for dust in a list. This list variable can then be passed to the function load(). Per default, scenes are loaded with the north pole facing downwards. You can specify the keyword argument upper_right_corner=NE in order to turn the image around and have the north pole facing upwards.
composite_id = ["dust"]
scn2_resample_nc = scn2.resample(area)
Afterwards, you can visualize the resampled image with the function show().
scn2_resample_nc.show('dust') | 2023-03-22T03:07:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41817089915275574, "perplexity": 12923.476019689248}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943749.68/warc/CC-MAIN-20230322020215-20230322050215-00313.warc.gz"} |
http://dlmf.nist.gov/13.31 | # §13.31 Approximations
## §13.31(i) Chebyshev-Series Expansions
Luke (1969b, pp. 35 and 25) provides Chebyshev-series expansions of and that include the intervals and , respectively, where is an arbitrary positive constant. | 2013-12-06T14:53:21 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.968262791633606, "perplexity": 8476.495626335814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163051986/warc/CC-MAIN-20131204131731-00091-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=M210M&home=sumtabM | # ${{\boldsymbol Z}_{{c}}{(3900)}}$ MASS INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT
$\bf{ 3888.4 \pm2.5}$ OUR AVERAGE Error includes scale factor of 1.7.
$3902.6$ ${}^{+5.2}_{-5.0}$ ${}^{+3.3}_{-1.4}$ 1
2019
D0 1.96 TeV ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$3895.0$ $\pm5.2$ ${}^{+4.0}_{-2.7}$ 502 2
2018 B
D0 1.96 TeV ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$3885.7$ ${}^{+4.3}_{-5.7}$ $\pm8.4$ 3
2015 AB
BES3 0 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}$( ${{\mathit D}}{{\overline{\mathit D}}^{*}}$) ${}^{0}$
$3881.7$ $\pm1.6$ $\pm1.6$ 1.2k 3
2015 AC
BES3 $\pm{}$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$( ${{\mathit D}}{{\overline{\mathit D}}^{*}}$) ${}^{-+}$
$3894.8$ $\pm2.3$ $\pm3.2$ 356 3
2015 U
BES3 0 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit J / \psi}}$
$3883.9$ $\pm1.5$ $\pm4.2$ 1.2k 3
2014 A
BES3 $\pm{}$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ ( ${{\mathit D}}{{\overline{\mathit D}}^{*}}$ )${}^{-+}$
$3899.0$ $\pm3.6$ $\pm4.9$ 307 3
2013 T
BES3 $\pm{}$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
$3894.5$ $\pm6.6$ $\pm4.5$ 159 3
2013 B
BELL $\pm{}$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
$3886$ $\pm4$ $\pm2$ 81 3, 4
2013 A
$\pm{}$ 4.17 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
$3904$ $\pm9$ $\pm5$ 25 3, 4
2013 A
0 4.17 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit J / \psi}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$3881.2$ $\pm4.2$ $\pm52.7$ 6k 5
2017 J
BES3 $\pm{}$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$
1 Measured in weak decays of ${{\mathit b}}$-flavored hadrons (nonprompt).
2 The signal of the ${{\mathit Z}_{{c}}{(3900)}}$ is correlated with a parent ${{\mathit J / \psi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ system in the invariant mass range $4.2 - 4.7$ GeV.
3 Neglecting interference between the ${{\mathit Z}_{{c}}{(3900)}}$ and non-resonant continuum.
4 For $\mathit M{}^{2}$( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ) $<$ 0.65 GeV${}^{2}$. Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration.
5 Pole mass obtained from a fit to a Flatte-like formula.
${{\mathit Z}_{{c}}{(3900)}}$ MASS (MeV)
References:
ABAZOV 2019
PR D100 012005 Properties of $Z_c^{\pm}(3900)$ produced in $p \bar p$ collision
ABAZOV 2018B
PR D98 052010 Evidence for $Z_c^{\pm}(3900)$ in semi-inclusive decays of $b$-flavored hadrons
ABLIKIM 2017J
PRL 119 072001 Determination of the Spin and Parity of the ${{\mathit Z}_{{c}}{(3900)}}$
ABLIKIM 2015AB
PRL 115 222002 Observation of a Neutral Structure near the ${{\mathit D}}{{\overline{\mathit D}}^{*}}$ Mass Threshold in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ (${{\mathit D}}{{\overline{\mathit D}}^{*}}){}^{0}{{\mathit \pi}^{0}}$ at $\sqrt {s }$ = 4.226 and 4.257 GeV
ABLIKIM 2015AC
PR D92 092006 Confirmation of a Charged CharmoniumLike State ${{\mathit Z}_{{c}}{(3885)}^{\mp}}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}$ (${{\mathit D}}{{\overline{\mathit D}}^{*}}){}^{\mp{}}$ with Double ${{\mathit D}}$ tag
ABLIKIM 2015U
PRL 115 112003 Observation of ${{\mathit Z}_{{c}}{(3900)}^{0}}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit J / \psi}}$
ABLIKIM 2014A
PRL 112 022001 Observation of a Charged (${{\mathit D}}{{\overline{\mathit D}}^{*}}){}^{+-}$ Mass Peak in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit D}}{{\overline{\mathit D}}^{*}}$ at $\sqrt {s }$ = 4.26 GeV
ABLIKIM 2013T
PRL 110 252001 Observation of a Charged Charmoniumlike Structure in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$ at $\sqrt {s }$ = 4.26 GeV
LIU 2013B
PRL 110 252002 Study of ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit J / \psi}}$ and Observation of a Charged Charmonium-like State at Belle
XIAO 2013A
PL B727 366 Observation of the Charged Hadron ${{\mathit Z}_{{c}}{(3900)}^{\pm}}$ and Evidence for the Neutral ${{\mathit Z}_{{c}}{(3900)}^{0}}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}{{\mathit J / \psi}}$ at $\sqrt {s }$ = 4170 MeV | 2021-03-09T07:04:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8631686568260193, "perplexity": 2253.059123148839}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389472.95/warc/CC-MAIN-20210309061538-20210309091538-00087.warc.gz"} |
Subsets and Splits