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https://math.stackexchange.com/questions/557709/find-a-permutation | # Find a permutation
For $x = (12)(34)$ and $y = (56)(13),$ find a permutation $a$ such that $a^{-1}xa = y$.
I written $a^{-1}xa = y$ as $xa = ay$ thus $(12)(34)a = a(56)(13)$ but I can't find the $a$?
Conjugation affects cycles like so: $\sigma(a_1~a_2~\cdots~a_r)\sigma^{-1}=(\sigma(a_1)~\sigma(a_2)~\cdots~\sigma(a_r))$.
• In particular: (1) do you understand what I've said so far? (2) can you extrapolate to figure out how conjugation explicitly affects a product of (disjoint) cycles? (3) so then (rearranging $a^{-1}xa=y$ $\Leftrightarrow x=aya^{-1}$) what does $a(56)(13)a^{-1}$ look like? and finally (4) what can you select $a$ to be to achieve $(12)(34)$? – anon Nov 13 '13 at 4:32
• $a^{-1}(12)(34)a = (56)(13)$. I am stuck in finding such an a. – user104235 Nov 13 '13 at 4:32 | {"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": 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": 0.9651116132736206, "perplexity": 433.13253088201037}, "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-2019-39/segments/1568514573832.23/warc/CC-MAIN-20190920050858-20190920072858-00179.warc.gz"} |
http://link.springer.com/article/10.1007%2FBF00911690 | , Volume 20, Issue 3, pp 333-337
# A calculation of the parameters of the high-speed jet formed in the collapse of a bubble
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## Abstract
As is known, the collapse of vapor bubbles in a liquid can cause the intensive destruction of solid boundary surfaces. Experimental and theoretical investigations of bubble collapse have led to the conclusion that the surface of a bubble can deform and a liquid jet directed toward the solid surface can form in the process [1, 2]. In the theoretical reports [3, 4] too low jet velocities were obtained, inadequate to explain the destruction of the surface in a single impact. In [5] it was found as a result of numerical calculations that the formation of jets possessing enormous velocities is possible. It was also found that two fundamentally different schemes of jet formation are possible in the collapse of a bubble near a wall. The transition from one scheme to the other occurs upon a relatively small change in the initial shape of the bubble. In the present report we investigate the case of sufficiently small initial deformations of a bubble when the region occupied by the bubble remains simply connected during the formation of the jet; i.e., the separation of a small bubble from the bubble does not occur. In the case of the second scheme of bubble collapse near a wall the connectedness of the free boundary is disrupted and a small bubble separates off during the formation of the jet.
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 94–99, May–June, 1979. | {"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": 0.8397111296653748, "perplexity": 583.3028378008062}, "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-2015-22/segments/1432207927245.60/warc/CC-MAIN-20150521113207-00180-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://www.baitstick.com/images/pdf.php?q=buy-Mathematical-Problems-in-Data-Science%3A-Theoretical-and-Practical-Methods/ | # Buy Mathematical Problems In Data Science: Theoretical And Practical Methods
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The space refers Getting a number that will be to determine the way that will customize the building with the complex adenosine. | {"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": 0.16977867484092712, "perplexity": 7436.407569559765}, "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/1606141184870.26/warc/CC-MAIN-20201125213038-20201126003038-00192.warc.gz"} |
https://socratic.org/questions/an-isosceles-triangle-has-sides-that-are-sqrt125-sqrt125-and-10-units-what-is-it | Geometry
Topics
# An isosceles triangle has sides that are sqrt125, sqrt125, and 10 units. What is its area?
Nov 21, 2015
$50 {\text{ units}}^{2}$
#### Explanation:
the area of a triangle is found through $A = \frac{1}{2} b h$. We have the base, but not the length of the height.
Imagine that an altitude is drawn down the center of the triangle, perpendicularly bisecting the base and bisecting the vertex angle. This creates two congruent right triangles inside the original isosceles triangle.
You know each of these triangles has a hypotenuse of $\sqrt{125}$ and a base of $5$, since they're half the original base.
We can use the Pythagorean theorem to figure out the length of the missing side, which is the height of the triangle.
${\left(5\right)}^{2} + {\left(h\right)}^{2} = {\left(\sqrt{125}\right)}^{2}$
$25 + {h}^{2} = 125$
${h}^{2} = 100$
$h = 10$
So, we now know that the base is $10$ units and the height is $10$ units.
Thus, $A = \frac{1}{2} \left(10\right) \left(10\right) = 50 {\text{ units}}^{2}$
##### Impact of this question
1285 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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": 0.8413199782371521, "perplexity": 355.43056466541}, "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-2022-27/segments/1656103322581.16/warc/CC-MAIN-20220626222503-20220627012503-00515.warc.gz"} |
https://www.physicsforums.com/threads/chain-rule-help.110398/ | # Chain rule help
1. Feb 12, 2006
### ussjt
f '(8)=5 g '(8)=3 f(4)=8 g(4)=10 g(4)=10 g(8)=2 f(8)=5
find (g o f)'(4)
how do I go about setting up these types of problem.
2. Feb 12, 2006
### AKG
What have you tried; where are you getting stuck?
3. Feb 12, 2006
### ussjt
have not tried because I don't know how to set up the problem...I don't really care about the answer I just want to know how you go about setting up these kinds of problems because I have a quiz tomorrow.
I figure the first step is g(f(x))
so g'(f(x))*f'(x)
g'(8)*f'(x)
3*f'(x)
Last edited: Feb 12, 2006
4. Feb 12, 2006
### AKG
(g o f)'(4)
= g'(f(4))*f'(4) by chain rule
= g'(8)*f'(4) since f(4) = 8
= 3*f'(4) since g'(8) = 3
And that's all you can do, since they don't tell you what f'(4) is. I suspect they do, and you just copied out the question wrong. Also, why have you given "g(4) = 10" twice?
Anyways, the way to setting up the problem is this:
Given a problem, "find X", write:
X
= A (by some theorem, or given fact, or logical inference)
= B (again, give justification)
= C (justification)
= D (justification)
until you get some answer D that you think the teacher will like, like an actual numeral. In this case, your X is (f o g)'(4), and your C is something like 3f'(4). You want a numeral for your D, but you can't get it yet from C because they haven't given you enough information (or you copied the question wrong).
5. Feb 12, 2006
### ussjt
For a given functionconsider the composite function Suppose we know that
Calculate f ' (x)
How do I go about setting up this type of problem?
6. Feb 13, 2006
### HallsofIvy
Staff Emeritus
You titled this thread "chain rule"! It ought to occur to you to use the chain rule!
If h(x)= f(2x3) then h'(x)= f '(2x3)(6x2).
You are given that h'(x)= 7x5.
You can easily solve f '(2x3)(6x2)= 7x5 for f '(2x3).
Now let y= 2x3. What is f(y)?
7. Feb 14, 2006
### ussjt
the way our TA showed up, the answer ought to be:
(7x^3/6)*(y/2)^(1/3)...but my answer must be in terms of x...so could someone please tell me if I went wrong somewhere or how to make it all in terms of x (by x I mean I can't have that "y"). Here are my steps:
f '(2x^3)(6x^2)= 7x^5
f '(2x^3)= (7x^5)/(6x^2)
f '(2x^3)= (7x^3)/6
~~~~~~~~~~~~
2x^3=y
x^3= y/2
x= (y/2)^(1/3)
~~~~~~~~~~
8. Feb 15, 2006
### VietDao29
It's fine up to here.
Now sub what you get in the expression:
f '(2x3)= (7x3)/6, we have:
f'(y) = 7y / 12.
So what's f'(x)?
Can you go from here?
9. Feb 15, 2006
### ussjt
where did the f'(y) come from?
10. Feb 15, 2006
### NateTG
In VietDao's post y is a place holder for $2x^3$
I don't know if this will make things any clearer for you:
The problem gives you
$$h(x)=f(z(x))$$
So, let's say we have some $a$ so that $x=z^{-1}(a)$ (provided that $z^{-1}$ actually exists). Then we can substitute that in
$$h(z^{-1}(a))=f(z(z^{-1}(a))$$
then simplify
$$h(z^{-1}(a))=f(a)$$
Now, we can take the derivative of both sides w.r.t. a
$$h'(z^{-1}(a)) \times \left(z^{-1}\right)' (a) = f'(a)$$
Now, since $h'$ and $z$ are both known, you should be able to work out what the left hand side of the equation is equal to. | {"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": 0.8814505338668823, "perplexity": 2305.9140626789217}, "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-2017-04/segments/1484560279915.8/warc/CC-MAIN-20170116095119-00523-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://jp.arxiv.org/list/cs.NA/pastweek?show=84 | # Numerical Analysis
## Authors and titles for recent submissions
[ total of 69 entries: 1-69 ]
[ showing up to 84 entries per page: fewer | more ]
### Thu, 26 May 2022
[1]
Title: Highly efficient energy-conserving moment method for the multi-dimensional Vlasov-Maxwell system
Subjects: Numerical Analysis (math.NA)
[2]
Title: On a large-stepsize integrator for charged-particle dynamics
Subjects: Numerical Analysis (math.NA); Plasma Physics (physics.plasm-ph)
[3]
Title: A systematic approach to Lyapunov analyses of continuous-time models in convex optimization
Authors: Céline Moucer (SIERRA, ENPC), Adrien Taylor (SIERRA), Francis Bach (SIERRA)
Subjects: Numerical Analysis (math.NA)
[4]
Title: Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
Subjects: Numerical Analysis (math.NA)
[5]
Title: A model of reactive settling of activated sludge: comparison with experimental data
Subjects: Numerical Analysis (math.NA)
[6]
Title: A Correlation Analysis and Visualization of Climate Change using Post-Disaster Heterogeneous Datasets
Subjects: Numerical Analysis (math.NA)
[7]
Title: Contour Integration for Eigenvector Nonlinearities
Subjects: Numerical Analysis (math.NA)
[8]
Title: Extensions and Analysis of an Iterative Solution of the Helmholtz Equation via the Wave Equation
Subjects: Numerical Analysis (math.NA)
[9]
Title: El-WaveHoltz: A Time-Domain Iterative Solver for Time-Harmonic Elastic Waves
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[10] arXiv:2205.12601 (cross-list from cs.LG) [pdf, other]
Title: Learning Distributions by Generative Adversarial Networks: Approximation and Generalization
Authors: Yunfei Yang
Comments: PhD Thesis. The contents are mainly from our previous works: arXiv:2105.13010, arXiv:2101.12353, arXiv:2201.09418 and arXiv:2005.11949
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)
[11] arXiv:2205.12457 (cross-list from math.FA) [pdf, other]
Title: Eigenvalues of the laplacian matrices of the cycles with one weighted edge
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[12] arXiv:2205.12313 (cross-list from physics.flu-dyn) [pdf, other]
Title: Numerical stability of solitary waves in flows with constant vorticity for the Euler equations
Subjects: Fluid Dynamics (physics.flu-dyn); Numerical Analysis (math.NA)
### Wed, 25 May 2022
[13]
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
[14]
Title: Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equation
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[15]
Title: Accelerated simulation of Boltzmann-BGK equations near the diffusive limit with asymptotic-preserving multilevel Monte Carlo
Comments: 26 page paper with 5 figures, 5 tables and 2 algorithms, 45 pages of additional supplementary material, submitted for peer review
Subjects: Numerical Analysis (math.NA)
[16]
Title: Construction and analysis of the quadratic finite volume methods on tetrahedral meshes
Journal-ref: SCIENCE CHINA Mathematics, 2022
Subjects: Numerical Analysis (math.NA)
[17]
Title: A divergence preserving cut finite element method for Darcy flow
Subjects: Numerical Analysis (math.NA)
[18]
Title: Testing interval arithmetic libraries, including their IEEE-1788 compliance
Subjects: Numerical Analysis (math.NA)
[19]
Title: On trajectories of complex-valued interior transmission eigenvalues
Subjects: Numerical Analysis (math.NA)
[20]
Title: On Computing Coercivity Constants in Linear Variational Problems Through Eigenvalue Analysis
Subjects: Numerical Analysis (math.NA)
[21]
Title: Windowed Green function method for wave scattering by periodic arrays of 2D obstacles
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Optics (physics.optics)
[22] arXiv:2205.12250 (cross-list from cs.LG) [pdf, other]
Title: Taming the sign problem of explicitly antisymmetrized neural networks via rough activation functions
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Quantum Physics (quant-ph)
### Tue, 24 May 2022
[23]
Title: Fractional SEIR Model and Data-Driven Predictions of COVID-19 Dynamics of Omicron Variant
Subjects: Numerical Analysis (math.NA); Physics and Society (physics.soc-ph); Populations and Evolution (q-bio.PE)
[24]
Title: Constraint Energy Minimizing Generalized Multiscale Finite Element Method for multi-continuum Richards equations
Comments: 22 pages, 7 figures, 4 tables, submitted to Journal of Computational Physics, fixed some typos and notation
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
[25]
Title: A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials
Subjects: Numerical Analysis (math.NA)
[26]
Title: Mixed finite elements for Bingham flow in a pipe
Subjects: Numerical Analysis (math.NA)
[27]
Title: Generalized Weak Galerkin Methods For Stokes Equations
Authors: W. Qi (1), P. Seshaiyer (2), J. Wang (3) ((1) School of Mathematics and Information Sciences, Henan Normal University, (2) Department of Mathematical Sciences, George Mason University (3) Division of Mathematical Sciences, National Science Foundation)
Subjects: Numerical Analysis (math.NA)
[28]
Title: Numerical method for the Fokker-Planck equation of Brownian motion subordinated by inverse tempered stable subordinator with drift
Subjects: Numerical Analysis (math.NA)
[29]
Title: A preconditioned deepest descent algorithm for a class of optimization problems involving the $p(x)$-Laplacian operator
Subjects: Numerical Analysis (math.NA); Functional Analysis (math.FA)
[30]
Title: A note on the probabilistic stability of randomized Taylor schemes
Authors: Tomasz Bochacik
Subjects: Numerical Analysis (math.NA)
[31]
Title: Mesh-free collocation for surface differential operators
Comments: 15 pages, 4 figures, 28 references
Subjects: Numerical Analysis (math.NA)
[32]
Title: A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation
Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG); Analysis of PDEs (math.AP)
[33]
Title: Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method
Authors: Thuy T. Le
Subjects: Numerical Analysis (math.NA)
[34]
Title: New quality measures for quadrilaterals and new discrete functionals for grid generation
Subjects: Numerical Analysis (math.NA)
[35]
Title: Unitarity of some barycentric rational approximants
Subjects: Numerical Analysis (math.NA)
[36]
Title: Spectral Neural Operators
Subjects: Numerical Analysis (math.NA)
[37] arXiv:2205.11466 (cross-list from math.OC) [pdf, other]
Title: Low-Rank Univariate Sum of Squares Has No Spurious Local Minima
Subjects: Optimization and Control (math.OC); Algebraic Geometry (math.AG); Numerical Analysis (math.NA)
[38] arXiv:2205.11404 (cross-list from cs.LG) [pdf, other]
Title: Variable-Input Deep Operator Networks
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)
[39] arXiv:2205.11396 (cross-list from physics.comp-ph) [pdf, other]
Title: Cross-mode Stabilized Stochastic Shallow Water Systems Using Stochastic Finite Element Methods
Subjects: Computational Physics (physics.comp-ph); Numerical Analysis (math.NA)
[40] arXiv:2205.11393 (cross-list from cs.LG) [pdf, ps, other]
Title: Generic bounds on the approximation error for physics-informed (and) operator learning
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA)
[41] arXiv:2205.11359 (cross-list from cs.LG) [pdf, other]
Title: Capacity Bounds for the DeepONet Method of Solving Differential Equations
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)
[42] arXiv:2205.11079 (cross-list from math.AP) [pdf, other]
Title: Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data
Authors: Mirella Aoun (LMRS), Olivier Guibé
Subjects: Analysis of PDEs (math.AP); Numerical Analysis (math.NA)
[43] arXiv:2205.11052 (cross-list from physics.comp-ph) [pdf, other]
Title: ALPINE: A set of performance portable plasma physics particle-in-cell mini-apps for exascale computing
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[44] arXiv:2205.11033 (cross-list from math.OC) [pdf, other]
Title: Augmented Newton Method for Optimization: Global Linear Rate and Momentum Interpretation
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA)
[45] arXiv:2205.11030 (cross-list from math.OC) [pdf, other]
Title: HessianFR: An Efficient Hessian-based Follow-the-Ridge Algorithm for Minimax Optimization
Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG); Numerical Analysis (math.NA)
[46] arXiv:2205.10879 (cross-list from cs.LG) [pdf, other]
Title: Fast Gaussian Process Posterior Mean Prediction via Local Cross Validation and Precomputation
Comments: 9 pages content, 4 figures, 3 tables
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML)
[47] arXiv:2205.10763 (cross-list from cs.LG) [pdf, other]
Title: A Deep Gradient Correction Method for Iteratively Solving Linear Systems
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA)
[48] arXiv:2205.10727 (cross-list from math.OC) [pdf, other]
Title: Regularization path-following methods with the trust-region updating strategy for linear complementarity problems
Subjects: Optimization and Control (math.OC); Computational Engineering, Finance, and Science (cs.CE); Mathematical Software (cs.MS); Dynamical Systems (math.DS); Numerical Analysis (math.NA)
### Mon, 23 May 2022
[49]
Title: Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation
Subjects: Numerical Analysis (math.NA)
[50]
Title: RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations
Subjects: Numerical Analysis (math.NA); Neural and Evolutionary Computing (cs.NE); Computational Physics (physics.comp-ph)
[51]
Title: An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients
Subjects: Numerical Analysis (math.NA)
[52]
Title: An efficient explicit jump HOC immersed interface approach for transient incompressible viscous flows
Subjects: Numerical Analysis (math.NA)
[53]
Title: pISTA: preconditioned Iterative Soft Thresholding Algorithm for Graphical Lasso
Subjects: Numerical Analysis (math.NA); Mathematical Software (cs.MS)
[54]
Title: Second-order uniformly asymptotic-preserving space-time-ImEx schemes for hyperbolic balance laws with stiff relaxation
Authors: Louis Reboul (CMAP), Teddy Pichard (CMAP), Marc Massot (CMAP)
Subjects: Numerical Analysis (math.NA)
[55]
Title: A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration
Subjects: Numerical Analysis (math.NA)
[56]
Title: B-spline velocity field level set topology optimization method for stress and buckling constraints based on discrete adjoint method
Subjects: Numerical Analysis (math.NA)
[57] arXiv:2205.10326 (cross-list from hep-th) [pdf, other]
Title: The Tensor Track VII: From Quantum Gravity to Artificial Intelligence
Comments: 23 pages, 7 figures, 1 table
Subjects: High Energy Physics - Theory (hep-th); Numerical Analysis (math.NA)
[58] arXiv:2205.09833 (cross-list from cs.LG) [pdf, other]
Title: Learning Interface Conditions in Domain Decomposition Solvers
Subjects: Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Discrete Mathematics (cs.DM); Numerical Analysis (math.NA)
[59] arXiv:2205.09779 (cross-list from physics.flu-dyn) [pdf, other]
Title: Residual Dynamic Mode Decomposition: Robust and verified Koopmanism
Subjects: Fluid Dynamics (physics.flu-dyn); Machine Learning (cs.LG); Dynamical Systems (math.DS); Numerical Analysis (math.NA); Spectral Theory (math.SP)
### Fri, 20 May 2022
[60]
Title: Multilevel Picard approximation algorithm for semilinear partial integro-differential equations and its complexity analysis
Subjects: Numerical Analysis (math.NA); Probability (math.PR)
[61]
Title: Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models
Comments: 25 pages, 9 figure; submitted to Computer Methods in Applied Mechanics and Engineering
Subjects: Numerical Analysis (math.NA)
[62]
Title: Geometric multigrid method for solving Poisson's equation on octree grids with irregular boundaries
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
[63]
Title: Strong approximation for fractional wave equation forced by fractional Brownian motion with Hurst parameter $H\in(0,\frac{1}{2})$
Authors: Xing Liu
Subjects: Numerical Analysis (math.NA)
[64] arXiv:2205.09724 (cross-list from math.DS) [pdf, other]
Title: Chemotactically induced search and defense strategies in a tritrophic system
Subjects: Dynamical Systems (math.DS); Numerical Analysis (math.NA)
[65] arXiv:2205.09588 (cross-list from cs.LG) [pdf, other]
Title: How catastrophic can catastrophic forgetting be in linear regression?
Journal-ref: 35th Annual Conference on Learning Theory (2022)
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA)
[66] arXiv:2205.09558 (cross-list from math.AP) [pdf, ps, other]
Title: Live load matrix recovery from scattering data in linear elasticity
Subjects: Analysis of PDEs (math.AP); Numerical Analysis (math.NA)
[67] arXiv:2205.09463 (cross-list from physics.comp-ph) [pdf, other]
Title: A fast dynamic smooth adaptive meshing scheme with applications to compressible flow | {"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": 0.6960854530334473, "perplexity": 18054.721437697863}, "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/1652662595559.80/warc/CC-MAIN-20220526004200-20220526034200-00533.warc.gz"} |
https://www.physicsforums.com/threads/uniform-circular-motion-of-a-particle.93044/ | # Uniform Circular Motion of a particle
1. Oct 8, 2005
### shawpeez
Im new at physics and have been looking at this question all day, any help would be greatly appreciated,
here it is
A particle moves along a cirular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.00s, it is at point (5.oom, 6.00m) with velocity (3.00 m/s)j and acceleration in the positive x direction. At time t2 = 10.0s, it has velocity (-3.00 m/s)i and acceleration in the positive y direction. What are the x and y coordinates of the centre of the circular path.
2. Oct 8, 2005
### mezarashi
1. The center of the circular motion
Draw out a diagram of a particle under circular motion. At each quarter circle, draw out the vectors for velocity and acceleration. Compare it to your questions problem.
The times give you a clue to finding the radius and subsequently the center of the motion. Within (10 - 4)seconds, the object moved from one part of the circle to another. You know d = vt. You also know that v^2/r defines acceleration in circular motion. A bit tricky, but I hope now you can start thinking about it.
3. Oct 8, 2005
### shawpeez
thanks for the post, but i'm still lost????
4. Oct 8, 2005
### mezarashi
Draw out a diagram of a particle under circular motion. At each quarter circle, draw out the vectors for velocity and acceleration. Compare it to your questions problem.
5. Oct 8, 2005
### shawpeez
from the diagram i see that at the first point its in the 2nd quarter and at the second point its in the 4th quarter( moving in a clockwise direction). Would the radius be the square root of (5^2 + 6^2). I still can't understand how this would relate to an xy centre coordinate(I thought the centre coordinate should be the origin of your plane).
6. Oct 8, 2005
### mezarashi
Aha, you're starting to understand a bit now. Your direction of motion is also correct. Not so fast about the radius just yet. You were drawing your own diagram based on the center of the motion being at 0,0. But in this case, the center isn't there, and you must find it. Can you find the corresponding point on the question's x-y coordinate for the first point? From there you can possibly estimate where the 2nd point would be, but you can't tell until you know the radius.
Now to finding this radius. You know that points 1 and 2 are separated by 3/4 of a circle, do you agree? Refer back to the diagram you drew. The circumference of a circle can be described as $$2\pi r$$. Now we know it took (10-4) seconds to make its way across three quarters of it, where d = vt. Getting closer?
7. Oct 8, 2005
### HallsofIvy
Staff Emeritus
You know that the circle passes through (5, 6) and that the vector 3.00j is tangent to the circle there. Since 3j is vertical, you know that (5,6) is at one end of a horizontal diameter. Further, you know that its speed, at any time, is 3 m/s. You also know that, 6 seconds later later, "it has velocity (-3.00 m/s)i and acceleration in the positive y direction. " so at that time, when it has moved 3(6)= 18 m, it is at the top of the vertical diameter. That appears to mean that it has moved 3/4 of the entire circle. What is the circumference of the circle? What is the diameter of the circle? Knowing the radius and that one end of a horizontal diameter is (5,6), it should be easy to find the coordinates of the center.
(Notice the word "appears". It is also possible that in those 6 seconds, it has gone completely around the circle and then one quarter of the circle.)
8. Oct 8, 2005
### shawpeez
so 3/4 of the trip was 18m , then the total circumference would be 24m , the diameter 7.6 and radius 3.8 m. Then the centre of the circle would be x = 8.8 y = 6 | {"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": 0.8126362562179565, "perplexity": 509.91427482693393}, "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-2017-04/segments/1484560281331.15/warc/CC-MAIN-20170116095121-00437-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/Sociable_number | # Sociable number
Sociable numbers are numbers whose aliquot sums form a cyclic sequence that begins and ends with the same number. They are generalizations of the concepts of amicable numbers and perfect numbers. The first two sociable sequences, or sociable chains, were discovered and named by the Belgian mathematician Paul Poulet in 1918.[1] In a set of sociable numbers, each number is the sum of the proper factors of the preceding number, i.e., the sum excludes the preceding number itself. For the sequence to be sociable, the sequence must be cyclic and return to its starting point.
The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle.
If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number—for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of order 2. There are no known sociable numbers of order 3, and searches for them have been made up to ${\displaystyle 5\times 10^{7}}$ as of 1970 [2].
It is an open question whether all numbers end up at either a sociable number or at a prime (and hence 1), or, equivalently, whether there exist numbers whose aliquot sequence never terminates, and hence grows without bound.
## Example
An example with period 4:
The sum of the proper divisors of ${\displaystyle 1264460}$ (${\displaystyle =2^{2}\cdot 5\cdot 17\cdot 3719}$) is:
1 + 2 + 4 + 5 + 10 + 17 + 20 + 34 + 68 + 85 + 170 + 340 + 3719 + 7438 + 14876 + 18595 + 37190 + 63223 + 74380 + 126446 + 252892 + 316115 + 632230 = 1547860
The sum of the proper divisors of ${\displaystyle 1547860}$ (${\displaystyle =2^{2}\cdot 5\cdot 193\cdot 401}$) is:
1 + 2 + 4 + 5 + 10 + 20 + 193 + 386 + 401 + 772 + 802 + 965 + 1604 + 1930 + 2005 + 3860 + 4010 + 8020 + 77393 + 154786 + 309572 + 386965 + 773930 = 1727636
The sum of the proper divisors of ${\displaystyle 1727636}$ (${\displaystyle =2^{2}\cdot 521\cdot 829}$) is:
1 + 2 + 4 + 521 + 829 + 1042 + 1658 + 2084 + 3316 + 431909 + 863818 = 1305184
The sum of the proper divisors of ${\displaystyle 1305184}$ (${\displaystyle =2^{5}\cdot 40787}$) is:
1 + 2 + 4 + 8 + 16 + 32 + 40787 + 81574 + 163148 + 326296 + 652592 = 1264460.
## List of known sociable numbers
The following categorizes all known sociable numbers as of July 2018 by the length of the corresponding aliquot sequence:
Sequence
length
Number of known
sequences
1 51
2 1225736919[3]
4 5398
5 1
6 5
8 4
9 1
28 1
It is conjectured that if n mod 4 = 3, then there are no such sequence with length n.
The smallest number of the only known 28-cycle is 14316.
## Searching for sociable numbers
The aliquot sequence can be represented as a directed graph, ${\displaystyle G_{n,s}}$, for a given integer ${\displaystyle n}$, where ${\displaystyle s(k)}$ denotes the sum of the proper divisors of ${\displaystyle k}$.[4] Cycles in ${\displaystyle G_{n,s}}$ represent sociable numbers within the interval ${\displaystyle [1,n]}$. Two special cases are loops that represent perfect numbers and cycles of length two that represent amicable pairs.
## Conjecture of the sum of sociable number cycles
As the number of sociable number cycles with length greater than 2 approaches infinity, the percentage of the sums of the sociable number cycles divisible by 10 approaches 100%. (sequence A292217 in the OEIS).
## References
1. ^ P. Poulet, #4865, L'Intermédiaire des Mathématiciens 25 (1918), pp. 100–101. (The full text can be found at ProofWiki: Catalan-Dickson Conjecture.)
2. ^ Bratley, Paul; Lunnon, Fred; McKay, John (1970). "Amicable numbers and their distribution". Mathematics of Computation. 24 (110): 431–432. doi:10.1090/S0025-5718-1970-0271005-8. ISSN 0025-5718.
3. ^ Sergei Chernykh Amicable pairs list
4. ^ Rocha, Rodrigo Caetano; Thatte, Bhalchandra (2015), Distributed cycle detection in large-scale sparse graphs, Simpósio Brasileiro de Pesquisa Operacional (SBPO), doi:10.13140/RG.2.1.1233.8640
• H. Cohen, On amicable and sociable numbers, Math. Comp. 24 (1970), pp. 423–429 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "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": 0.891385018825531, "perplexity": 334.86822658341873}, "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-2020-34/segments/1596439737238.53/warc/CC-MAIN-20200808021257-20200808051257-00044.warc.gz"} |
https://leanprover-community.github.io/archive/stream/217875-Is-there-code-for-X%3F/topic/Sums.20and.20products.20with.20multiplicative.2Fadditive.html | ## Stream: Is there code for X?
### Topic: Sums and products with multiplicative/additive
#### Yakov Pechersky (Mar 14 2021 at 14:48):
Do we have
import algebra.big_operators
open_locale big_operators
variables {α β γ δ : Type*} [comm_monoid γ] [add_comm_monoid δ]
(s : finset α) (f : α → γ) (g : α → δ)
lemma ex1 :
multiplicative.to_add (∏ i in s, multiplicative.of_add (g i)) = (∑ i in s, g i) :=
begin
sorry
end
lemma ex2 :
additive.to_mul (∑ i in s, additive.of_mul (f i)) = (∏ i in s, f i) :=
begin
sorry
end
#### Yakov Pechersky (Mar 14 2021 at 14:49):
Seems like #6045 maybe defines these: https://github.com/leanprover-community/mathlib/pull/6045/files#diff-85bc8aab8a979e8f901b4350d1f6334cabc79a77315ff84b4b4cd4f97240c3a9R51-R60
Or do they exist otherwise? I need them to try redefining nsmul/gsmul and porting some proofs.
#### Eric Wieser (Mar 14 2021 at 14:59):
refl closes those right now
Last updated: May 07 2021 at 19:12 UTC | {"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": 0.7940815091133118, "perplexity": 7645.785866359877}, "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-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00530.warc.gz"} |
http://acronymsmeanings.com/acronym-meanings/3068547/acronym-abbreviation-meaning-of-1 | # Acronym/Abbreviation meaning of 1"'-- (2)
The acronym 1"'--(2) means : 1
Acronyms, abbreviations and meanings similar to 1"'--
## Famous / Popular results for 1"'--
List of NBA champions
court in Games 1, 2, 6, and 7) during 1949, 1953–1955, and 1985–2013, in a 1111111 format during 1956 and 1971, and in a 1–2–2–11 format during
2019 Indian general election
rescheduled from 18 to 23 April. Vellore, Tamil Nadu: Over ₹11 crore (US$1.6 million) in cash was seized in Vellore from DMK leaders – a regional party UEFA Euro 2020 qualifying in question; If, after having applied criteria 1 to 4, teams still have an equal ranking, criteria 1 to 4 are reapplied exclusively to the matches between FIFA U-20 World Cup nations that have reached at least the semifinal in the U-20 World Cup finals. 1 As Yugoslavia. All continental confederations except for the OFC (Oceania) List of countries and dependencies by population inclusion within the list being primarily based on the ISO standard ISO 3166-1. For instance, the United Kingdom is considered as a single entity, while List of Stanley Cup champions 1 division title) The other two teams have relocated and have not made the Finals in either location: Atlanta Thrashers (11 seasons, 1 playoff, 1 division 1 1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or USB power): IEC 62680-1.1:2015 - Part 1-1: Common components - USB Battery Charging Specification, Revision 1.2 IEC 62680-1-2:2018 - Part 1-2: Common components Standard deviation 1%. A more accurate approximation is to replace N − 1.5 {\displaystyle N-1.5} above with N − 1.5 + 1 / ( 8 ( N − 1 ) ) {\displaystyle N-1.5+1/(8(N-1))} Normal distribution a + b = 1 1 a + 1 b = ( a − 1 + b − 1 ) − 1 . {\displaystyle {\frac {ab}{a+b}}={\frac {1}{{\frac {1}{a}}+{\frac {1}{b}}}}=(a^{-1}+b^{-1})^{-1}.} This List of NBA champions court in Games 1, 2, 6, and 7) during 1949, 1953–1955, and 1985–2013, in a 1111111 format during 1956 and 1971, and in a 1–2–2–11 format during UEFA Euro 2020 qualifying in question; If, after having applied criteria 1 to 4, teams still have an equal ranking, criteria 1 to 4 are reapplied exclusively to the matches between 2019 Indian general election rescheduled from 18 to 23 April. Vellore, Tamil Nadu: Over ₹11 crore (US$1.6 million) in cash was seized in Vellore from DMK leaders – a regional party
FIFA U-20 World Cup
nations that have reached at least the semifinal in the U-20 World Cup finals. 1 As Yugoslavia. All continental confederations except for the OFC (Oceania)
List of countries and dependencies by population
inclusion within the list being primarily based on the ISO standard ISO 3166-1. For instance, the United Kingdom is considered as a single entity, while
List of Stanley Cup champions
1 division title) The other two teams have relocated and have not made the Finals in either location: Atlanta Thrashers (11 seasons, 1 playoff, 1 division
USB
power): IEC 62680-1.1:2015 - Part 1-1: Common components - USB Battery Charging Specification, Revision 1.2 IEC 62680-1-2:2018 - Part 1-2: Common components
Normal distribution
a + b = 1 1 a + 1 b = ( a − 1 + b − 1 ) − 1 . {\displaystyle {\frac {ab}{a+b}}={\frac {1}{{\frac {1}{a}}+{\frac {1}{b}}}}=(a^{-1}+b^{-1})^{-1}.} This
1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or
Standard deviation
1%. A more accurate approximation is to replace N − 1.5 {\displaystyle N-1.5} above with N − 1.5 + 1 / ( 8 ( N − 1 ) ) {\displaystyle N-1.5+1/(8(N-1))}
## Meaning of LDA
LDA means: Linear Diode Array
## Meaning of SCLM
SCLM means: Scanning Confocal Laser Microscopy
## Meaning of PSL
PSL means: Propellant Seal
## Meaning of YGBSM
YGBSM means: You Gotta Be Sh*ttin' Me!
## Meaning of ROTM
ROTM means: Right On The Money | {"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": 0.6873824000358582, "perplexity": 11979.552006891021}, "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/1560628000044.37/warc/CC-MAIN-20190626013357-20190626035357-00528.warc.gz"} |
http://mathhelpforum.com/differential-equations/164609-wave-equation-polar-coordinates-print.html | # wave equation in polar coordinates
The wave equation is given to me as : $\frac{\partial^{2}u}{\partial t^{2}}=\nabla^{2}u$ and that $c^2=1$ | {"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": 2, "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": 0.9979020953178406, "perplexity": 247.05295487130195}, "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-2017-13/segments/1490218189686.56/warc/CC-MAIN-20170322212949-00645-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://gitlab.math.univ-paris-diderot.fr/beppe/occurrence-typing/-/commit/70a43e940bd50b32fcee63428d9df92b19c57c55 | Commit 70a43e94 by Giuseppe Castagna
### rewording
parent a06aa2ef
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... ... @@ -98,7 +98,7 @@ inference). Second, the result of our analysis can be used to infer intersection types for functions, even in the absence of precise type annotations such as the one in the definition of \code{foo} in~\eqref{foo2}: to put it simply, we are able to infer the type~\eqref{eq:inter} for the unannotated pure JavaScript code of \code{foo}. Third, we show how to combine occurrence typing with gradual typing, and in show how to combine occurrence typing with gradual typing, in particular how the former can be used to optimize the compilation of the latter. ... ... @@ -201,7 +201,7 @@ particular if the static type of $e'$ is an intersection of arrows). Additionally, we can repeat the reasoning for all subterms of $e'$ and $e''$ as long as they are applications, and deduce distinct types for all subexpressions of $e$ that form applications. How to do it precisely---not only for applications, but also for other terms such as pairs, projections, records etc---is explained in the rest of the paper but the key ideas are pretty simple and are explained next. the paper but the key ideas are pretty simple and are presented next. \subsection{Key ideas}\label{sec:ideas} ... ...
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https://www.researchgate.net/profile/Margareta-Halicka | # Margaréta HalickáComenius University Bratislava · Department of Applied Mathematics and Statistics
25
Publications
875
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
277
Citations
Introduction
Skills and Expertise
## Publications
Publications (25)
Article
In data envelopment analysis (DEA), non-radial graph models represent an important class characterized by the independent treatment of each input and output factor in the efficiency measurement. The extensive literature on this topic often analyses individual models in isolation, so much so that the same model may be known under different names due...
Article
The hyperbolic measure (HM) model is a radial, non-oriented model that is often used in Data Envelopment Analysis (DEA). It is formulated as a non-linear programming problem and hence the conventional linear programming methods, customarily used in DEA, cannot be applied to it in general. In this paper, we reformulate the hyperbolic measure model i...
Article
Full-text available
In data envelopment analysis for environmental performance measurement the undesirable outputs are taken into account. Ones of the standard approaches for dealing with the undesirable outputs are the hyperbolic and the directional distance measures. They both allow a simultaneous expansion of desirable outputs and a contraction of undesirable outpu...
Chapter
A one-dimensional free terminal time optimal control problem stemming from mathematical finance is studied. To find the optimal solution and prove its optimality the standard maximum principle procedure including Arrow’s sufficiency theorem is combined with specific properties of the problem. Certain unexpected features of the solution are pointed...
Article
Throughout its evolution, data envelopment analysis (DEA) has mostly relied on linear programming, particularly because of simple primal-dual relations and the existence of standard software for solving linear programs. Although also nonlinear models, such as Russell measure or hyperbolic measure models, have been introduced, their use in applicati...
Article
A model of sustainable economic growth in an economy with two types of exhaustible resources is analyzed. The resources are assumed to be perfect substitutes with marginal rate of substitution varying over time. The optimal control framework is used to characterize the optimal paths under the maximin criterion. It is shown that the resource with in...
Article
This paper studies limiting behaviour of infeasible weighted central paths in semidefinite programming under strict complementarity assumption. It is known that weighted central paths associated with the ‘Cholesky factor’ symmetrization of the μ-parameterized centring condition are well defined for some classes of weight matrices, and they are anal...
Article
Full-text available
It was recently shown in [4] that, unlike in linear optimization, the central path in semidefinite optimization (SDO) does not converge to the analytic center of the optimal set in general. In this paper we analyze the limiting behavior of the central path to explain this unexpected phenomenon. This is done by deriving a new necessary and sufficien...
Article
In this paper we study the limiting behavior of the central path for semidefinite programming (SDP). We show that the central path is an analytic function of the barrier parameter even at the limit point, provided that the semidefinite program has a strictly complementary solution. A consequence of this property is that the derivatives – of any ord...
Article
Full-text available
The central path in linear optimization always converges to the analytic center of the optimal set. This result was extended to semidefinite optimization in [D. Goldfarb and K. Scheinberg, SIAM J. Optim. 8, 871–886 (1998; Zbl 0914.90215)]. We show that this latter result is not correct in the absence of strict complementarity. We provide a countere...
Article
Several papers have appeared recently establishing the analyticity of the central path at the boundary point for both linear programming (LP) and linear complementarity problems (LCP). While the proofs for LP are long, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting of an applicat...
Article
In this paper we discuss results of Data Envelopment Analysis for the assessment of efficiency of a large structured network of bank branches. We focus on the problem of a suitable choice of efficiency measures and we show how these measures can influence results. As an underlying model we make use of the so-called normalized weighted additive mode...
Article
This note shows the incorrectness of several results concerning robustness measures introduced by M. S. Mahmoud (1996: Some robustness measures for a class of discretetime systems. IMA J. Math. Control & info . 13 , 117–128). Some confusing issues are discussed, and the correct forms of the corresponding results are provided.
Article
We study the properties of the weighted central paths in linear programming. We consider each path as the function of the parameter μ≥0 where the value at μ=0 corresponds to the limit point at the boundary of the feasible set. We calculate the recursive formulas for the central path derivatives of all orders valid at each μ≥0. We establish the geom...
Article
Full-text available
. In this paper a duality of transformation functions in the interior point method is treated. A dual pair of convex or linear programming problems is considered and the primal problem is transformed by the parametrized transformation function of a more general form than logarithmic is. The construction of the parametrized transformation function f...
Chapter
The stabilization problem of linear discrete-time large scale systems (LSS) is studied. Our recent results on stability robustness bound Halická and Rosinová (1992) are employed and a sufficient stability condition for LSS is developed which comprises different Lyapunov - type bounds as special cases. The obtained condition yields a decentralized s...
Article
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Project (1) | {"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": 0.9204496741294861, "perplexity": 670.6370983409723}, "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/1659882571056.58/warc/CC-MAIN-20220809155137-20220809185137-00213.warc.gz"} |
https://www.physicsforums.com/threads/is-there-an-intermediate-particle-to-pair-production.323530/ | # Is there an intermediate 'particle' to pair production?
1. Jul 6, 2009
### Rymer
This question was brought to mind while reading other threads. I didn't think it was appropriate to diverge those threads off their subjects, so I started a new one. (hope this is right).
I'm specifically thinking about the extremely rare event of the interaction of two gamma rays as the
pair production event. It would seem that there should be an intermediate 'combined' particle since the event can't be instantaneous. Does this particle have a name? What would its properties have to be?
(Is it spin 2 like a graviton?)
This is not my field, just interested. Thank you.
2. Jul 6, 2009
### malawi_glenn
in terms of Feynman diagrams, the intermediate particles are virtual electrons/positrons, but in the REAL interaction (Feynman diagrams are just mathematical remnants when we do perturbation theory - I don't think that Nature DOES perturbation theory), just as middle steps in our calculations when we calculate work etc.
Now, ask yourself WHY the event CAN NOT be instantaneous, why this bias?
3. Jul 6, 2009
### Rymer
The process involves finite constrained interaction -- as all must to some degree -- it cannot be instantaneous. Uncertainty Principle I thought. So what are the properties of the intermediate?
4. Jul 6, 2009
### malawi_glenn
You have confused with what we can now with a statistical certainty and how nature works. Also, when we approach nature, we can only apply our models and see if they make sense, we can never go "down there" and see how these things occur with our own eyes. In the language of QFT with perturbation theory, I don't think it makes sense to ask how long time it took for the intermediate virtual particle to propagate etc.
Also, why is the forming of this intermediate state NON-instantaneous?
Last edited: Jul 6, 2009
5. Jul 6, 2009
### Bob_for_short
You can think of a superposition of positronium states (positronium is a neutral system which can have spin 2 in excited states).
Last edited: Jul 6, 2009
6. Jul 6, 2009
Why??
7. Jul 6, 2009
### Rymer
I have not calculated it -- so I guess I don't understand it.
To me instantaneous and infinitesimal seem to be mathematical conveniences -- not scientific possibilities.
8. Jul 6, 2009
### malawi_glenn
But you argued that 2gamma's -> 1electron + 1positron can not be a instantaneous process, but that it should go though an intermediate state [with spin 2?? why not spin 1 or 0? ;-) ]
thus
2gamma's -> intermediate state ->1electron + 1positron
why is this cancelling the "instantaneous" "problem"?
9. Jul 6, 2009
### Rymer
Don't know. Only mentioned spin 2 because I understood spin 0 would be disallowed and spin 1 would not balance.
I was wondering if this could be related to the pair production reported near super-massive objects in the galactic core.
10. Jul 6, 2009
### malawi_glenn
why is spin0 dissalowed and spin1 not "balance"? define "balance"
We, as far as I know, do not know so much of that ep-prodution yet, but what is related to it? The "intermediate step mechanicsm" or?? why should it?
11. Jul 6, 2009
### Rymer
No idea why ... that was why the question.
I don't know the basics of how this interaction occurs. Are these photons both spin-up or down?
How are they 'approaching' each other ... a 'head-on' or at an angle?
How is the interaction occurring?
12. Jul 6, 2009
### malawi_glenn
do you even know ANY interaction in quantum field theory? "how" they occur, as I wrote, it all depends on what model you are using.
You can, in the lowest order in perturbation theory, write it as 2 real photons, exhanging virtual electrons/positrons with a spectator nucleus, giving rise to 1 real electron and 1 real positron. Then we can derive angular- and spin dependent cross section (probability function that the process occur - recall that we are in the quantum realm).
13. Jul 6, 2009
### Rymer
I know very little about it -- but have read that there is another reaction -- far more rare -- that does not require the presence of a 'spectator nucleus'. It was that interaction to which I was referring.
14. Jul 6, 2009
### malawi_glenn
But where did you read it? Maybe if you show us we can help you more :-)
Saying things like "I have read/heard" is not so good :-(
15. Jul 6, 2009
### Rymer
More than one place -- sorry I had thought it was 'common knowledge' in the field. But since, I know little about this field, I guess I'm wrong.
I'll do some checking and track it down.
16. Jul 6, 2009
### malawi_glenn
Well since you said you had little knowledge about this field, you should not assume what is common knowledge and not, just an advice for the future ;-)
17. Jul 6, 2009
### Rymer
My knowledge -- what little there is of it -- is 40 years old.
A quick internet search gave a reference to: http://prola.aps.org/abstract/PR/v155/i5/p1404_1
It seems to be from 'my era' so it may be passe now.
18. Jul 6, 2009
### malawi_glenn
ok it should just be a virtual particle exchange of an electron or a positron in lowest order perturbation theory.
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https://socratic.org/questions/how-does-intensity-affect-the-photoelectric-effect | Chemistry
Topics
# How does intensity affect the photoelectric effect?
##### 1 Answer
May 9, 2015
If the frequency of electromagnetic waves is higher than the extraction threshold of the metal and electrons are emitted from the metal surface, then an increase of light intensity will result in a proportional increase of electrical current of the electrical circuit where the emitted electrons are conveyed.
This is simply explained by the photon model of light. In that model an electromagnetic wave carries its energy not like a continuum, but as multitude of grains of energy which have the same individisible amount of energy. The indivisible grain of light energy, also called "light dart" by Einstein, and then electromagnetic energy quanta or photons is given by the Planck-Einstein's law:
${E}_{\text{photon" = h*f}}$
where $f$ is the frequency of light. For each single photon at the same frequency.
From the point of view of photons, a more intense light is not made of "higher waves", but of a higher number of photons.
Than is obvious that, if each photon is capable to expel an electron, the more intense is the light the more number of electrons will be expelled. If frequency is under the threshold, then even the higher intense light will be equally incapable to eject even a single electron.
It is impossible to explain these experimental outcomes with the wave model of light.
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https://www.physicsforums.com/threads/putting-a-satellite-into-orbit.129342/ | # Putting a satellite into orbit
1. Aug 21, 2006
### wizzart
Geez it's been ages since I last was here. Anyway, I was thinking a little on the subject below and remembered this place. It's probably ridiculously trivial, but still I wonder:
A satellite stays in orbit around the earth because it's falling at the same pace as the earth's surface curves, simply put. But that's a sattelite in stationary orbit. What happens if I release a sattelite in an orbit that's to high for it's speed? My guess: it falls back to earth and because it's angular momentum needs to be preserved it gradually picks up more tangential speed until it lands into a stationary orbit, wich would be somewhere between the orbit where it should've been and where it was released...
Correct or rubbish?
2. Aug 21, 2006
### DaveC426913
You've put it in an elliptical orbit. Its apogee (maximum altitude) is where you released it, its perigee (minimum altitude) will be where it is closest to the Earth (but moving fastest). Provided the perigee is still above Earth's atmospheric drag, it will remain in that stable, elliptical orbit.
BTW, ALL orbits are elliptical, though some have an eccentricity of nearly zero (meaning it is nearly circular).
Rubbish. See above.
There is no such thing as a "stationary orbit".
Last edited: Aug 21, 2006
3. Aug 21, 2006
### wizzart
hm...sounds plausible too
Well, quasi-stationary then...slowly spiralling down to earth.
4. Aug 21, 2006
### Farsight
The thing to note, wizzart, is that if you're in an orbiting spaceship and you want to get into a higher orbit, you put your foot on the gas and go faster.
You don't point the nose up and fire the rockets, because that doesn't give you the forward velocity that stretches your arc of fall into a bigger circle. It would just give you an eccentric orbit, like Dave says.
5. Aug 21, 2006
### BobG
I think your term, stationary, is wrong, making readers wonder what you mean. Do you mean stable orbit? Circular orbit?
Any object with any tangential velocity at all travels in an elliptical orbit. Some of those orbits just happen to intersect the Earth (a Roger Clemens fastball, for example).
If the satellite's trajectory misses the Earth and is high enough that it isn't affected by the Earth's atmosphere, the satellite's mechanical energy stays constant through the entire orbit. The balance between potential and kinetic energy just changes.
As DaveC explained, by time the satellite reaches perigee, it has enough kinetic energy that starts gaining altitude again and returns to the same point it started. The orbit is just as stable as a circular orbit. The orbit remains elliptical and never becomes circular.
The only way the satellite spirals down to Earth is if the satellite is low enough to be affected by the Earth's atmosphere. Generally, only satellites with an altitude lower than 1000 km are affected and circular orbits are affected more than elliptical orbits. In this case, atmospheric drag is decreasing the total mechanical energy rather than just changing the balance between potential and kinetic.
Edit: For an elliptical orbit where perigee is low enough to be affected by atmospheric drag, your assumption would be correct. If you slow a satellite at perigee due to atmospheric drag, it's not the perigee altitude that changes; it's the apogee altitude. As soon as the satellite was slowed, a new orbit was created and the satellite's current location has to be part of that new orbital ellipse. So atmospheric drag would slowly decrease the apogee height until you had a circular orbit, at which point the satellite would 'spiral' into the Earth's atmosphere.
Last edited: Aug 21, 2006
6. Aug 21, 2006
### WhyIsItSo
Did you mean Geo-Stationary?
7. Aug 21, 2006
### DaveC426913
There is no such thing as a quasi-stationary orbit. The words stationary and orbit used in conjunction with each other are very nearly an oxymoron. (The only combination that makes sense is geo-stationary orbit which is something completely different and has nothing to do with this thread.)
An orbit that is "slowly spiralling down to earth" is an orbit that is decaying. The only thing (within reason) that could be causing this is drag, sapping forward motion from the satellite.
I think the term you are looking for is stable orbit. Unless acted upon by an outside force (such as another gravitational body, or friction) (or, an inside force such as rockets), a satellite will remain in a stable elliptical orbit. Period. This is critical to your understanding of orbits.
Now, if you play with the adjustments carefully, you can get the satellite's orbit to have virtually zero eccentricity, meaning its orbit is circular, and meaning that it will move around while maintaining a constant altitude above the Earth.
Last edited: Aug 21, 2006
8. Aug 21, 2006
### DaveC426913
Look at the attached illo.
#### Attached Files:
• ###### PF060821orbits.gif
File size:
26.5 KB
Views:
80
9. Aug 21, 2006
### wizzart
Dang, it's right here in my 1st year Relativity book...need to critically review some of the old stuff I guess.
As for stationarity: stationary to me means nothing changes. For the orbiting object everything changes constantly, without drag the orbit itself (circle or ellipse) doesn't change shape, hence my use of the word stationary. If you prefer stable, I can see why.
10. Aug 21, 2006
### DaveC426913
:surprised :surprised You're in post-2ndary??:surprised :surprised
11. Aug 21, 2006
### wizzart
Dude, I'll make it a lil worse...I'm one subject away from my bachelors degree :P Did research on noise in Quantum Dots and all that.
The mechanics course was 5 years ago, and back then I didn't really get the whole orbit stuff (and the big point in the course was relativity, so I got away with it)...read through it again now and makes perfect sense. It's just one of those questions that pops into your head and you go "I'm pretty sure I should know this...but I don't".
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https://kampus.umcs.pl/course/index.php?categoryid=3309 | ### Animal physiology – an extensive course
During the course the following issues are discussed: phenomena related to the excitability of the body's cells, skeletal and smooth muscle physiology. | {"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": 0.3804102838039398, "perplexity": 8254.956793663932}, "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/1610703549416.62/warc/CC-MAIN-20210124141945-20210124171945-00554.warc.gz"} |
https://courses.mizzouk12.missouri.edu/courses/4130/assignments/syllabus | # Course Syllabus
## Syllabus Chemistry B
University of Missouri High School
SCI-1101B-GL | 1/2 Credit Science | Mizzou Academy Global Course
### Welcome
We are pleased that you selected this course to fulfill your unique educational needs. You are now a member of the Mizzou Academy's global student body.
Although the freedom to choose when and where to study is a privilege, it is also a responsibility that requires motivation and self-discipline. To succeed at learning, you will need to develop a study plan by setting realistic goals and working toward them.
This global course is designed through the individual sections to assist in your pacing.
#### MEGAN LILIEN
Megan Lilien is the Health and Science Division Chair for Mizzou Academy. She earned a bachelor’s degree in Biology from the University of Illinois and a Master’s degree in Teaching and Learning from Point Loma University. She lives in Columbia with her husband and three daughters. Before coming to Mizzou Academy, Megan worked as a high school biology and chemistry teacher in San Diego, California, and coached varsity girls’ lacrosse. Her favorite part of working with Mizzou Academy is the innovative and unique experiences she has working with students and teachers locally and internationally.
Megan Lilien
Teacher
Science and Health
#### ROGER BERGMAN
Roger Bergman is the Science Specialist from Mizzou Academy. He recently retired from the classroom after 31 years. He was at Southern Boone County R-1 in Ashland, Missouri for 11 years and then taught at Jefferson City High School in Jefferson City, Missouri for the other twenty years. Roger has taught Chemistry, Biology, Physics, Physical Science and Principles of Technology during that time.
Roger and his wife, Janet, currently live in rural Callaway county north of Jefferson City.
Roger Bergman
Teacher
Science
### Course Overview
In this second chemistry course, students will continue to explore chemistry and learn how it influences our daily lives. There will be eleven lessons in the course. Lessons focus on the States of Matter, Behavior of Gases, Aqueous Systems and Solutions, Chemical Reactions including heat and energy changes, reaction rates, acid/base reactions, oxidation/reduction reactions and organic chemistry. The final lesson will cover Nuclear Chemistry. Students will engage in both virtual experiments and ones that can be conducted at home.
Each lesson will consist of a reading assignment in the textbook, answering LessonCheck questions at the end of each section in the lessons (the text reading is usually broken into three or four sections), an end of lesson quiz consisting of 10 multiple choice questions and 10 short answer questions, and a Laboratory Activity report. At the end of each lesson in the text there are also review questions which have selected answers at the end of the book. These review questions are optional for the student but provide an opportunity for extra study and review of concepts.
### Course Description
In this introductory chemistry course, students will explore chemistry and learn how it influences our daily lives. Lessons focus on the scientific method, theories, and scientific laws; matter and change; scientific measurement; atomic structure and the periodic table; electrons in atoms; ionic, metallic, and covalent bonding; chemical names and formulas; and chemical quantities. Students will engage in both virtual experiments and ones that can be conducted at home.
### Course Objectives
At the end of this course, students should be able to accomplish the following:
1. Understand the Kinetic Theory and use it to explain states of matter and behavior of solids, liquids, and gases.
2. Understand and calculate the role energy changes play in chemical processes.
3. Understand and describe the role that reaction rates and equilibrium play in chemical processes.
4. Understand the processes of oxidation and reduction reactions
5. Explain the role of carbon in organic chemistry.
6. Understand and explain the difference between nuclear reactions and chemical reactions.
### Required Materials
Wilbraham, et al. Pearson Chemistry. Boston, MA: Pearson Education, 2012.
Lab Materials. Most items can be purchased at local stores. An Amazon Shopping List (Links to an external site.) is also provided at this link for your convenience.
### View all Lab materials
This list includes all of the materials necessary to complete all of the laboratory activities shown in the textbook and in the commentary in the course. Not all laboratory activities shown in the textbook are assigned for students to do or complete a Laboratory activity report on. Most items are easily found in stores. Use the Amazon Shopping List for harder to find items.
Lesson 1: Freezing Point of Water Lab
• Test tube (can use a small cup)
• Thermometer
• Container (glass or bowl to hold test tube)
• Table Salt (if a freezer is available, salt is not needed)
Lesson 2: Carbon Dioxide from Antacid Tablets Lab
• Effervescent Antacid tablets
• Balloons
• Medicine dropper (or something to transfer water)
• Watch/Timer
• Tape measure/ruler
Lesson 3: Separation of Mixtures Report
• No materials required
Lesson 4: Effect of Temperature on the Solubility of Sugar Lab
• thermometer
• plastic cups
• table sugar
• water of different temperatures
Lesson 5: Heat of Combustion of a Candle Lab
• 100-ml graduated cylinder or volume measuring device
• ruler
• candle
• aluminum foil
• balance
• soda can
• *balance
• *thermometer
Lesson 6: No submitted assignment
Lesson 7: Acid-Base Simulation
• No materials required
Lesson 8: Oxidizing Writing Assignment
• No materials required
Lesson 9: Electrochemistry Writing Assignment
• No materials required
Lesson 10: (Hydrocarbon Isomers is the assignment for this unit which requires a Laboratory Activity Report)
• Ball and stick molecular model (optional)
• Pencil and paper
• Toothpicks
• Modeling clay (or alternative material such as gum drops or grapes to make model)
• Pencil
• paper
Lesson 11: No submitted assignment
#### Optional Materials
Pearson Chemistry: Chemistry Skills and Math Workbook copyright 2012 Pearson Education, Inc. ISBN-13:978-0-13-320449-0, ISBN-10: 0-13-320449-9
Pearson Virtual ChemLab Copyright Pearson Education, Inc. Single User ISBN-10: 0-13-324214-5, Single User ISBN-13: 978-0-13-324214-0
### Technical Requirements
The most up-to-date requirements can be found here:
Additional requirements for the course are below:
• Student must download and use Logger Pro 3 Software. Software is distributed to students by Mizzou Academy upon course enrollment.
### Canvas and Technical Support
Canvas is the where course content, grades, and communication will reside for this course.
### Quizzes & Assignments
You should submit all assigned work in sequence (Lesson 1, then Lesson 2, etc.) Assignments for the course are listed at the bottom of this syllabus.
#### Quizzes
Quizzes are taken online. After you submit them, you’ll quickly receive a report on how you did. Unlike exams, you may use any assigned readings, your notes, and other course-related materials to complete graded quizzes and assignments.
#### Assignments
Assignments may require you to submit your completed work in the form of a file (such as a text document, image, audio or video recording, or multimedia presentation) or a hyperlink for grading.
#### Practice
There are PRACTICES throughout the course. These activities are ungraded and can be submitted multiple times.
After your work has been graded, you will receive a report that provides individualized feedback and comments on your work. Look carefully at what you missed and read any corresponding feedback. Then study the lesson materials to make certain that you can accomplish the associated learning objectives.
Each lesson provides step-by-step instructions on how to submit your work. Be sure to check submitted work carefully for errors (e.g. spelling, grammar, and punctuation) as they may result in points being deducted.
### Exams
You are required to take proctored exams for this course.
Your final grade will be based on the number of points you earn on assignments and exams.
Points Distribution
Source Available Points
Assignments 180
Quizzes 220
Midterm Exam 300
Final Exam 300
Total 1000
$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$$\frac{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}earned}{total\phantom{\rule{0ex}{0ex}}exam\phantom{\rule{0ex}{0ex}}points\phantom{\rule{0ex}{0ex}}possible}=exam\mathrm{%}$.
A 90–100
B 80–89
C 70–79
D 60–69
F 0–59
After completing the course, unofficial transcripts will be available in the Tiger Portal. See this page for information on requesting official transcripts.
### Canvas Overview
For more on navigating the Canvas interface, visit the Canvas Student Guide.
Here are some quick links to get you started:
### Mobile Apps
If you are on a mobile device, download the Canvas mobile apps. With the apps, you can access all your courses using the Canvas mobile app, "Canvas By Instructure." Go to Google Play to download the Android version and iTunes to download the iOS version.
View the mobile features by device
### Library, Writing, and Research Resources
#### Library Resources
Below are several useful library links. Click the images to go directly to the websites.
### Assignments
#### Assignment Formatting
You may use whichever style unless specifically requested by your instructor.
#### Submitting Assignments
How to submit assignments (without Turnitin)
View Canvas overview videos:
In this video, you will learn more about assignments: what they are and how to submit them through Canvas.
For more on uploading and viewing assignments, visit Assignments in the Canvas Student Guide.
### ~~Turnitin
#### How-To Instructions
How to submit a Turnitin assignment
View the above link for step-by-step instructions on submitting a Turnitin assignment.
#### Types of Turnitin Submissions
You can submit a file upload [1], input text [2], or select a file from Google Drive or Dropbox [3].
#### Turnitin Originality Report
Mizzou Academy uses Turnitin, which provides tools for assignments. One of these tools is the "originality check." Note that it is not called a "plagiarism detector." That is because ONLY an instructor can determine plagiarism.
For example, it could be that you get a 100% match (in red) on your submission. However, perhaps you are working in a group or your instructor had you submit something multiple times to different assignments within the same course. Or perhaps your class is filling out a worksheet, so all of the worksheet components would be "not original" but your content would be.
If you are concerned about any results that you are confused about, feel free to discuss this with your teacher.
Watch the video below which shows you how to use your Originality check tool. We hope you use this as a learning tool.
The University of Missouri has a license agreement with Turnitin.com, a service that helps detect plagiarism by comparing student papers with Turnitin's database and Internet sources. Students who take this course agree that all required papers may be submitted to Turnitin.com.
Students who submit papers to Turnitin retain the copyright to the work they created. A copy of submitted papers is retained in a Turnitin database archive to be compared with future submissions—a practice that helps protect and strengthen copyright ownership. Use of the Turnitin service is subject to the Terms and Conditions of Use posted on Turnitin's website at https://guides.turnitin.com/Privacy_and_Security#Terms_of_Service.
### Citing Sources
#### Citing Sources Interactive Module
The Citing Sources Interactive Tutorial to help you with learning how to cite your sources as well as inform you about what plagiarism is, what it isn't, and how to avoid it.
View the Citing Sources tutorial
See the OWL Resource Website for additional help in citing sources and avoiding plagiarism.
### How to Record and Submit Audio and Video
#### Recording and Submitting
There are many ways you can submit audio and video recordings for a Mizzou K–12 course in Canvas. Your course content may refer to Audacity. (Links to an external site.)However, you don't need to use Audacity to make an mp3 recording for your course. After all, there are many programs and apps on computers and mobile devices that will do just that!
Note: You can also submit assignments using files stored on third-party apps (e.g. Dropbox) on your mobile apps.
We do NOT allow you to submit .wav files.
### How to Shoot Quality Audio and Video
The only way for you to present quality speeches (and other multimedia) to your Mizzou teacher is by uploading a video of yourself. Therefore, it's incredibly important that the audio and video quality is good enough that your instructor can see and hear everything clearly. You might all be in different environments using various types of cameras, so rather than attempting to teach you about specific cameras, we're going to concentrate on things like lighting, background, setup and stabilization, and audio.
### Lighting and Background
• Use a distraction-free background
• Face windows with natural light
• Avoid overhead lights when indoors
• Use a lamp or two for additional lighting
• Watch back your video to see how it looks
• Keep trying, keep learning, and keep having fun
### Setup and Stabilization
• Don't shoot handheld
• Use anything that can safely hold the camera steady
• tripod and mount
• DIY solutions (picture stand, bean bag, binder clips)
• Place the camera level with your eyeline
### Audio
• Shoot video in the quietest room at the quietest time of day
• Turn everything off (cell phone, TV, radio, fans, etc.)
• Get closer to the camera
• Avoid noisy habits (hand rubbing, clapping, etc.)
• Use an external microphone
If you already have a Gmail account, then you have a YouTube account, but in case you don't, getting your account set up is the first step. Just go to gmail.com and create an account to get started. Work with a trusted adult or parent.
##### Creator Studio
On thing to note is that you can access all of your channel's videos and privacy settings through the Creator Studio. To locate this area in your account, click the icon in the upper right corner (where you logged in) and you should see the option for Creator Studio under your login name. Once you click this, you will be taken to the dashboard area for your account. There are a few different areas available you should be aware of:
##### Video Manager
This section houses all of the videos on your account. You can also create playlists (lists or groups of videos with a similar topic or theme).
##### Channel
Your content settings are located with the majority of your video and content settings. It is also where you can determine the privacy of your videos. If you click on Upload Defaults in this section, it will give you the options that you can set for all future uploads. Changing the privacy to Unlisted means that anyone with the link will be able to view your video but it won't be searchable to the public.
##### Create
This section isn't required, but it's good to be aware that this area provides a basic video editor where you can make minor adjustments to your videos as well as add copyright free background music.
• Click Upload in the upper right-hand corner of the screen
• Either drag & drop the video file into the box or click on the gray arrow to select it from your files. You will notice that the privacy box will already be set to unlisted based on your privacy settings
• This will automatically begin the upload once the file is selected, taking you to a new window:
• Make sure the title box is correctly filled out
• Descriptions and tags are usually left blank unless the video is public
• Thumbnails This is what viewers will see when they first pull up your video. You can choose from a few automatic image selections, or you can upload your image
• Once the video finishes uploading, processing, and you selected the titles/thumbnails, click "Done
If you are comfortable with recording video, transferring the file to your computer, and then uploading, this is the preferred method because some assignments (such as video journals) will have you recording multiple videos for one assignment. One problem you may run into is a camera that creates an incredibly large file. In such cases, you may need to convert the file to make it smaller.
### File Conversion
Some cameras record videos that create very large file sizes. Depending on your internet connection, these larger files might have problems uploading. In these cases, you might need to convert the video to a smaller version. Look for a free video converter like Any Video Converter or Format Factory to help you.
### Getting Your Videos Into the Course: Direct Recording
Canvas does allow you to record via webcam directly into Canvas. However, this will not be available when multiple videos are required. Another reason to shy away from this method is that if you have a hiccup in your internet connection or your computer freezes, your video will be lost, and you will have to rerecord everything. Just to save the hassle, it's better to either upload a file or provide a link to an unpublished YouTube video.
### Quizzes and Exams
In this video, we'll show you how to take a quiz/exam in Canvas.
For more on taking quizzes and exams, visit Quizzes in the Canvas Student Guide.
NOTE: Read your Syllabus and the Quiz and Exam instructions for your course so that you are aware of the policies and how a quiz and exam is setup. The Quizzes link may not be in the course navigation menu in your course and only accessible by clicking on Modules and clicking on the pertinent lesson.
### ~~Suggestions for Taking Objective Examinations
What is an "objective examination?" Objective means that there IS a right answer (or answers), and you either get things right or wrong. An example is a multiple-choice quiz or exam. This section is here to provide you with tips on how to take objective examinations, or "exams."
Many people worry about how to do well when taking objective examinations. What does What follows are some simple suggestions that should help you to do your best.
What do you do when you know the answer? Silly question, right? You mark it!
What do you do when you don’t know the answer? This is what you want to hear!
1. First, you need to remember that our quizzes and exams are based on the number of right answers out of the total possible. So you should answer every question, even if it’s a guess. There are four answer choices, so your odds when you guess are 1 in 4. That is, on average, you should get 1 out of every 4 guesses correct.
2. How do you narrow the odds, to make them more in your favor? If you are able to eliminate one or more of the answers as definitely wrong, you have done just that. When you are guessing which answer is correct out of 3, then you could get one-third of your guesses correct. When you are guessing between two, you could get half of them right.
3. What if you see an answer choice that you absolutely have never seen before? There is a very good chance it is a wrong answer, and you can eliminate it. Remember, you’ve read over and studied the material. Most of the time you will know if something doesn’t belong.
4. Does the answer make sense? A correct answer always makes sense. Incorrect choices may, or may not. So if a choice does not make sense in relation to the question, it is probably a wrong answer.
5. Do not spend a lot of time on a question that is giving you trouble. Move on, and come back to it later. Many times, you will find something in a later question or answer choice that helps you to select the answer to a question you skipped over. This is known as making the test work FOR YOU.
6. Above all, relax! You have been over the material. It is all in your head. Just take a deep breath and go at it. YOU CAN DO IT!
Many students develop their own tricks to help themselves on objective tests. What you see above can assist you. But you may also rely on whatever works for you.
### ~~Suggestions for Taking Essay Exams
#### What!? I’m going to have to write!?
It is not unusual for people to be nervous about taking an essay exam. You will have to decide what the question means, search through the memory banks of your brain, recall information that relates to the question, and then write something that is well organized and clear. What follows are some tips that just might make this process a little less scary.
An essay question may be fairly short, perhaps only one paragraph. They may also be longer, requiring several paragraphs to answer. No matter how short, or long, the essay needs to be, the process is the same. As an example, we’ll use a topic that is “medium.”
The framers of the Constitution of the United States established the Electoral College system, which provides an indirect method of electing the President. This system should be changed to permit the direct election of the President, so the candidate who receives the greatest number of the popular vote to win election. Agree or disagree.
#### Great! Now what?
This may seem pretty long. But you need to remember that you do not have to deal with everything in the statement. The first thing you need to do is identify what you have to answer, and what you can ignore. The question statement is reproduced below, with the parts you have to consider highlighted.
The framers of the Constitution of the United States established the Electoral College system, which provides an indirect method of electing the President. This system should be changed to permit the direct election of the President, so the candidate who receives the greatest number of the popular vote to win the election. Agree or disagree.
While everything else in the question is relevant to the topic, you are being asked to support the Electoral College system (indirect election) or the popular vote (direct election).
#### Next?
Write down a brief outline of what you need to do. It would be best if you did this in order.
• Introduction: State your position. Do you agree or disagree. Give a preview of why you have chosen your position.
• Body Paragraph: Explain your first reason for your position. You might also want to state why the method you did NOT choose falls short.
• Body Paragraph: Explain your second reason for your position. Again, you could state why the method you did NOT choose falls short.
• Body Paragraph: Explain your third reason, if you have one, along with why the method you did NOT choose falls short.
#### What are we saying here?
There is a very simple way to look at essay writing. No matter if the essay is one paragraph, or five, or ten. You do the same three things.
1. Tell the readers what you are going to tell them (introduction).
2. Tell them (body).
3. Tell the readers what you told them (conclusion).
#### And in conclusion….
This process can be very helpful. You need to remember: you are probably not going to be expected to respond to every word in the essay topic. That’s why it’s important to identify what you need to consider. While essays from different classes will look different, the approach to them is pretty much the same. You can even practice this skill on your own, creating topics on things with which you are familiar. The more you practice, the easier it becomes.
Good luck!
### ~~Examity
One of the options that is now available to you is to use Examity (Links to an external site.), a 100% online proctoring service. This means that instead of finding someone in-person that can proctor your test, you can instead choose Examity.
Examity does charge a fee. The Examity link located at the end of the Online Proctoring Resources module allows you to be automatically logged in to schedule your exam and pay for proctoring. If you scheduled to have your test proctored with Examity, you will also use that link to log in to Examity to begin your exam.
Next, you will need to read the detailed directions and requirements before using Examity. Examity use is not mandatory; it is only an option.
### Calendar
The calendar video introduces you to the Canvas Calendar and shows you how you can stay organized by scheduling your own events.
### Netiquette
Netiquette—short for "network etiquette" or "Internet etiquette"—is a set of guidelines for how to communicate appropriately on the web. As a Mizzou K–12 Online student, you will be expected to follow these guidelines in your interactions with your instructor and fellow students.
• Be respectful. Online, as in life, the Golden Rule applies: Treat others as you would like to be treated. There are effective ways to disagree with someone without being insulting. Keep in mind that sarcasm can sometimes be misinterpreted.
• Use appropriate language. Avoid foul language and rude or vulgar comments.
• Use proper grammar and spelling. Typos and spelling mistakes are bound to happen, but excessive errors are distracting. Use a browser with a built-in spell checker if you need help!
• Respect others' privacy. Do not quote or forward personal messages or information without the original author's permission.
• Avoid plagiarism. It is never acceptable to copy and paste the work of others and call it your own. Be sure to cite your sources correctly.
For more about appropriate online behavior, view Show Me Respect: Tips for Thwarting Cyberbullying, Cyber-Harassment, and Cyberstalking from the University of Missouri's Equity Office.
### Parent Registration and Student Observation
View how to create a parent account
The Canvas Parent app is the mobile version of Canvas that helps parents stay up-to-date with their student's courses. Download the Canvas Parent app on Android and iOS devices.
Canvas Parent Android Guide
Canvas Parent iOS Guide
Our academic integrity policy at Mizzou Academy is based on our values of ethical behavior, learning, and giving all stakeholders the benefit of the doubt. Collaboration, research, and technical literacy are vital 21st-century skills when combined with academic integrity.
#### Definitions
Mizzou Academy's academic integrity policy is aligned with the University of Missouri’s academic integrity policy. The definitions of what constitutes "cheating" and "plagiarism"are posted on the Provost’s Advising Council’s webpage which can be found here: https://advising.missouri.edu/policies/academic-integrity
#### Issues Involving Violations of Academic Integrity
If, when completing any of your assignments or exams for this course, you are found to have demonstrated cheating or plagiarism as defined above, this is a violation of academic integrity. At your teacher's discretion, violations of academic integrity may be subject to either or both of the following actions:
• receiving a zero for the assignment or exam
• receiving an F for the course
### Accessibility
If you anticipate barriers related to the format or requirements of this course, please let Mizzou Academy know as soon as possible. If disability-related accommodations are necessary (for example, a scribe, reader, extended time on exams, captioning), please contact Mizzou Academy.
*This section describes the policies of exams at Mizzou Academy. This section only applies if you have exams in your course. See the section above to see if you have exams.
During exams, unless otherwise noted, you are not allowed to navigate away from the exam or use any other resources. If you deviate from the exam guidelines without proper prior permission, it is considered cheating on an exam.
#### SCHEDULING EXAMS
##### Global Courses
First, request approval for your proctor. Allow enough time (2 weeks) for our office to receive your request and communicate with your chosen exam site and proctor. Mizzou Academy has approved exam sites throughout the United States and around the world.
Request Exam Date and Proctor Approval Form
• Choose a proctor and make arrangements for taking the exam.
• At least 2 weeks prior to taking your exam, submit your proctor information to Mizzou Academy
• You will be sent an email notice indicating if your chosen proctor has been approved or denied.
You can also schedule with an online proctor using Examity. Review the information in the "Getting Started Resources (Canvas and Other Resources)" section under the "Examity" panel. in the course syllabus.
##### Co-Teach Courses
If you are taking a co-teach course, work with your local teacher to identify your date of the exam and how you will be proctored. You do not need to request an exam date with the above form.
#### HOW TO PREPARE FOR EXAMS
• Complete and review all assignments.
• Review the learning objectives; make sure you can accomplish them.
• Be prepared to explain any key terms and concepts.
• Review all the lessons, exercises, and study questions.
• Review any feedback and/or comments on your assignments and previous exams; look up answers to any questions you missed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "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": 0.1562304049730301, "perplexity": 2814.2491245780443}, "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-2020-45/segments/1603107885059.50/warc/CC-MAIN-20201024223210-20201025013210-00040.warc.gz"} |
https://www.rosettacommons.org/category/category/scoring?page=4 | # Scoring
## Building loop extensions in a membrane protein with Remodel
Category:
Design
Scoring
Loop Modeling
Membrane
Hi All,
I was wondering whether Remodel is currently compatible with the RosettaMP framework? I have a designed membrane protein and I'm trying to alter the sequence of water-exposed loops, which involves a few insertions. I'm using Remodel to do this but haven't been able to run it using the franklin2019 scorefunction.
Here are the flags that I'm using:
Post Situation:
## mp_transform optimize with franklin2019 scoring
Category:
Design
Scoring
Enzyme Design
Membrane
Hi All,
I am running some flexible backbone design on a transmembrane four-helix bundle heme protein via RosettaScripts. I'm finding that the membrane residue is moving a lot during design, and I have to optimize the embedding with mp_transform post-design to reposition the mem residue. I have a few questions about this:
Post Situation:
## Setting output values using a database (with relax app)
Category:
Scoring
Hello all,
I noticed rosetta creates 23 tables in MySQL when using it as output backend in the RELAX application.
For my specific research I only need to hold the per-residue energies and the total energies... I don't need the atoms, topology or PDB data to be saved after each cycle, as it consumes a lot of memory.
Post Situation:
## Output "per-residue" energy score to database
Category:
Scoring
Hello all.
I noticed that when I output a relax cycle to a PDB, the residue scores are in the bottom of the PDB.
When I output the results to a database (MySQL), the table structure_scores holds the energy scores of the whole PDB, but I can't find the per-residue values anywhere.
Post Situation:
## BUG REPORT: MySql column protocol.protocol_id must have the AUTO_INCREMENT flag set
Category:
Scoring
I tried running relax compiled with MPI and MYSQL.
MySQL was configured properly. A test run without MPI successfully created tables and wrote data to MySQL.
The protocol file @relax.flags was created with the following options:
-list pdblist.txt
-relax:script relax.script
-relax:bb_move false
-score:output_residue_energies
-score:weights res2015
Post Situation:
## Relaxation vs minimisation
Category:
Structure prediction
Scoring
PyRosetta
Hi all,
I am very new to the computational structural biology community and I have tried to model a structure by using a software which runs MODELLER on the background. However, my result shows a number of steric clashes and a very high fa_rep when I calculate it with PyRosetta. I am therefore trying to improve the structure before moving on with the rest of my analysis.
Post Situation:
## dump_scored_pdb
Category:
Scoring
I am new to Pyrosetta and trying to dump the modified pose along with its total energy.
I have used pose.dump_score_pdb('model.pdb', scorefxn) to have the total score printed out with the PDB file.
However, this method prints out way more information. What would be the equivalent way of having the total score printed out (as the fileters work in the xml file at rosetta scripts)?
Post Situation:
## Distorted metal coordination geometry after relaxation (SetupMetalMover was used, fold tree and constraints were set manually)
Category:
Design
Scoring
Constraints
PyRosetta
Hello,
I am trying to relax Zn containing peptides like zinc fingers, but always got distorted geometries of the coordination site and much higher scores after the relax. Still, the rest of the peptide looks nice.
Post Situation:
## Working through tutorials: expected output scorces differ from calculated results
Category:
Scoring
Hi,
I'm new to Rosetta and currently working through the tutorials.
I often recognized that the the score values produced by the recent version "Rosetta 2019.47" on my computer differ from the ones cited in the tutorials and given expected_output.
e.g.:
in the Scoring Tutorial (subchapter "Changing the Score Function") the command
ROSETTA3/bin/score_jd2.linuxgccrelease @flag_docking
with flags
Post Situation:
## Compaing interface socre of different ligands with the same protein structure
Category:
Scoring
I am trying to dock molecules with the same parent core but different substitution groups into the same PDB structure using ROISE.
I tried to read through some published papers on ResettaLigand but still was not able to find out the answer for:
Since we are only allowed to include on ligand in each run, can we submit a few different runs and compare the interface score directly?
Post Situation: | {"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": 0.2926785349845886, "perplexity": 4767.28644295806}, "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-2021-39/segments/1631780057403.84/warc/CC-MAIN-20210922223752-20210923013752-00098.warc.gz"} |
https://ssconlineexam.com/onlinetest/ssc-cgl-tier-1/quantitative-aptitude/qa-test-76 | # ssc cgl tier 1 :: quantitative aptitude :: qa test 76
## Home ssc cgl tier 1 / quantitative aptitude Questions and Answers
1 .A watch company produces four different products. The sale of these products in lakhs during 2005 and 2010 are shown in The following bar diagram Study the graph and answer the question
The sales in percentage of wrist watch in 2010 more than the sales of table clock in 2010 was nearly by :
26.7%
27.7%
28.7%
21.7%
2 .
A number when divided by 10 gives a remainder 3. When the same number is divided 7, the remainder will be ?
3
4
1
can not be determined
3 .
In a division sum, divisor is 3 times the quotient and 6 times the remainder. If the remainder is 2, then the dividend is ?
48
28
36
50
4 .
Three numbers which are co-primes to one another are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is
75
81
85
89
5 .
A man's pension on retirement from service is equal to half the average salary during last 3 years of his service His salary from 1-1-1983 is Rs. 380 per month with increment of Rs. 40 due on 1-10-83, 1-10-84 and 1-10-85. If he retires on 1-1-86, what pension does he draw per month ?
Rs.205
Rs.215
Rs.225
Rs.230
6 .
If the $n^ {th}$ term of an A.P. is 2n+1 Find the sum of first n terms of A.P ?
n (n+2)
n(n+1)
$n^ 2$
n
7 .
A man has in all Rs. 640 in the denominations of one-rupee, five rupees and ten-rupees notes. The number of each type of note is equal. The total number of each type of notes he has ?
150
120
90
100
8 .
The numerator of number is increased by 62.5% and denominator is increased by 77.5% The new fraction becomes $13\over 25$ Find the original fraction?
53/50
69/25
52/49
71/125
9 .
In factory ratio of workers, lobourers and clerks is 8:5:1 and ratio between the wages of one worker, one labourer and one clerk is 5:2:3 If there are 20 labourers working in factory and total wages of the employees is Rs. 318. Find the daily wages of one employee of each category ?
7.5 , 3 , 4
7 , 3 , 4.5
7.5 , 3 , 4.5
7.5 , 4 , 4.5
10 .
One type of liquid contains 20% water in a mixture of milk and water and the second type of liquid contains 65% of milk in the same type of milk and water solution. A glass is filled with 10 parts of first liquid and 4 parts of second liquid. The water in the new mixture is ?
37 %
46 %
12$1\over 7$%
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https://blackhole12.blogspot.de/2013/05/ | ## May 30, 2013
### How To Complain About Men And Be Sexist At The Same Time
What if I told you about an article that complained about how social media and instant gratification has eroded away at our social fabric? How we don't take the time to pause and reflect on how we live our lives? How we fail to really work at making the world a better place, and instead waste time building websites to share cat photos on? I'd think that it raised several important issues about modern society.
What if I then told you that the entire article only applied this to men? What if it was titled, "Why Men Aren't Really Men Anymore"? Suddenly, things just got a lot more sexist. In fact, that entire article is built almost entirely out of gender stereotypes. It's that subtle, classy kind of sexism; bigotry that hides behind delicate prose, hiding it's true nature. If the article were rewritten so that it described these issues in gender-nuetral terms, I'd be liable to agree with it. Trolling, aggression, lack of human interaction, billions of dollars being spent on worthless startups that solve first world problems - these are all real issues. Yet, to imply that men are the ones with these problems, to imply that any class of problems belong to only one gender, is sexist.
The article is wonderfully subtle in its sexism. Just look at how it claims "real" men should treat women:
Real men are not selfish. Real men are just as concerned for the feelings, needs and minds of women as they are for their own — not just women’s bodies and their sexual usefulness. Real men have a well-defined code of ethics and respect that they follow.
Isn't that sweet? Except, oh wait, we have this disturbing sentence in the middle of the article:
Men have become lazy pussies. I don’t even want to use the word pussy because it brings to mind women, who nowadays have much more character than men.
Not to be outdone, the article's last paragraph contains this gem:
Some great women are settling for these fools and then finding that they themselves have no choice but to wear the pants in the family because their “man” is PMSing.
This is horribly sexist. These three sentences enforce multiple gender stereotypes and tell us a number of things:
1. Women want manly men. If they think they don't want a manly man, they just haven't found one manly enough yet.
2. Men are always the ones who should be wearing the pants in the family, because men always have to be the manly ones.
3. Women shouldn't have more character than men.
4. Women are allowed to be PMSing because they're women, and everyone knows women get emotional, but a man should never be emotional, because he's a man.
See, the reasoning behind all these is just "because men are men and women are women." That isn't a reason, it's sexism. It's bigotry. It's enforcing stereotypes and trying to tell people how they should live their lives based on a set of gender roles that society arbitrarily decided on. It simply assumes it knows what women want, and goes so far to imply that the only reason a women wouldn't want a "real" man is because they haven't seen one yet. This is exactly like those annoying little assholes who tell you "Oh you just haven't heard good dubstep! You'll like it then!" Inevitably, after you still don't like it, they just tell you that something is clearly wrong with you and you have no taste.
At no point do they entertain the notion that, maybe, just maybe, you actually don't like dubstep.
Our society suffers from the same tunnel vision. We assume that when a women is working overtime and the man is doing laundry that it's the man's fault for not being manly enough and the women has been forced to become the head of the household. If she had just married a man manly enough, she wouldn't have had to do that!
It never crosses their minds that maybe, just maybe, the women actually likes it this way. Maybe some men just don't want to be manly. Maybe some women like men who aren't manly. Maybe you can't fit every single human being into nice neat little gender boxes.
It is not a man's job to be manly simply because they are men. It is not a women's job to be PMSing or making you a sandwich. It is not society's place to tell anyone how they should live their lives. You do not know what they want and you should never pretend you do. We can make certain observations about genders, like men tend to be more aggressive, and women tend to be more emotional, but we should never assume that men should be more aggressive, or women should be more emotional. That is for the individual to decide, not society.
A human being is something precious, something complicated, something that can't be easily categorized. Stop trying to stuff them into square boxes.
## May 25, 2013
### Course Notes
It's standard procedure at the University of Washington to allow a single sheet of handwritten notes during a Mathematics exam. I started collecting these sheets after I realized how useful it was to have a reference that basically summarized all the useful parts of the course on a single sheet of paper. Now that I've graduated, it's easy for me to quickly forget all the things I'm not using. The problem is that, when I need to say, develop an algorithm for simulating turbulent airflow, I need to go back and re-learn vector calculus, differential equations and nonlinear dynamics. So I've decided to digitize all my notes and put them in one place where I can reference them. I've uploaded it here in case they come in handy to anyone else.
The earlier courses listed here had to be reconstructed from my class notes because I'd thrown my final notesheet away or otherwise lost it. The classes are not listed in the order I took them, but rather organized into related groups. This post may be updated later with expanded explanations for some concepts, but these are highly condensed notes for reference, and a lot of it won't make sense to someone who hasn't taken a related course.
Math 124 - Calculus I
lost
Math 125 - Calculus II
lost
Math 126 - Calculus III
lost
Math 324 - Multivariable Calculus I
$r^2 = x^2 + y^2$
$x= r\cos\theta$
$y=r\sin\theta$
$\iint\limits_R f(x,y)\,dA = \int_\alpha^\beta\int_a^b f(r\cos\theta,r\sin\theta)r\,dr\,d\theta=\int_\alpha^\beta\int_{h_1(\theta}^{h_2(\theta)} f(r\cos\theta,r\sin\theta)r\,dr\,d\theta$
$m=\iint\limits_D p(x,y)\,dA \begin{cases} M_x=\iint\limits_D y p(x,y)\,dA & \bar{x}=\frac{M_y}{m}=\frac{1}{m}\iint x p(x,y)\,dA \\ M_y=\iint\limits_D x p(x,y)\,dA & \bar{y}=\frac{M_x}{m}=\frac{1}{m}\iint y p(x,y)\,dA \end{cases}$
$Q = \iint\limits_D \sigma(x,y)\,dA$
$I_x = \iint\limits_D y^2 p(x,y)\,dA$
$I_y = \iint\limits_D x^2 p(x,y)\,dA$
$I_0 = \iint\limits_D (x^2 + y^2) p(x,y)\,dA$
$\iiint f(x,y,z) dV = \lim_{l,m,n\to\infty}\sum_{i=1}^l\sum_{j=1}^m\sum_{k=1}^n f(x_i,y_j,z_k) \delta V$
$\iiint\limits_B f(x,y,z)\,dV=\int_r^s\int_d^c\int_a^b f(x,y,z)\,dx\,dy\,dz = \int_a^b\int_r^s\int_d^c f(x,y,z)\,dy\,dz\,dx$
$E$ = general bounded region
Type 1: $E$ is between graphs of two continuous functions of $x$ and $y$.
$E=\{(x,y,z)|(x,y)\in D, u_1(x,y) \le z \le u_2(x,y)\}$
$D$ is the projection of E on to the xy-plane, where
$\iiint\limits_E f(x,y,z)\,dV = \iint\limits_D\left[\int_{u_1(x,y)}^{u_2(x,y)} f(x,y,z)\,dz \right]\,dA$
$D$ is a type 1 planar region:
$\iiint\limits_E f(x,y,z)\,dV = \int_a^b \int_{g_1(x)}^{g_2(x)} \int_{u_1(x,y)}^{u_2(x,y)} f(x,y,z)\,dz\,dy\,dx$
$D$ is a type 2 planar region:
$\iiint\limits_E f(x,y,z)\,dV = \int_d^c \int_{h_1(y)}^{h_2(y)} \int_{u_1(x,y)}^{u_2(x,y)} f(x,y,z)\,dz\,dx\,dy$
Type 2: $E$ is between $y$ and $z$, $D$ is projected on to $yz$-plane
$E=\{(x,y,z)|(y,z)\in D, u_1(y,z) \le x \le u_2(y,z)\}$
$\iiint\limits_E f(x,y,z)\,dV = \iint\limits_D\left[\int_{u_1(y,z)}^{u_2(y,z)} f(x,y,z)\,dx \right]\,dA$
Type 3: $E$ is between $x$ and $z$, $D$ is projected on to $xz$-plane
$E=\{(x,y,z)|(x,z)\in D, u_1(x,z) \le y \le u_2(x,z)\}$
$\iiint\limits_E f(x,y,z)\,dV = \iint\limits_D\left[\int_{u_1(x,z)}^{u_2(x,z)} f(x,y,z)\,dy \right]\,dA$
Mass
$m = \iiint\limits_E p(x,y,z)\,dV$
$\bar{x} = \frac{1}{m}\iiint\limits_E x p(x,y,z)\,dV$
$\bar{y} = \frac{1}{m}\iiint\limits_E y p(x,y,z)\,dV$
$\bar{z} = \frac{1}{m}\iiint\limits_E z p(x,y,z)\,dV$
Center of mass: $(\bar{x},\bar{y},\bar{z})$
$Q = \iiint\limits_E \sigma(x,y,z)\,dV$
$I_x = \iiint\limits_E (y^2 + z^2) p(x,y,z)\,dV$
$I_y = \iiint\limits_E (x^2 + z^2) p(x,y,z)\,dV$
$I_z = \iiint\limits_E (x^2 + y^2) p(x,y,z)\,dV$
Spherical Coordinates:
$z=p\cos\phi$
$r=p\sin\phi$
$dV=p^2\sin\phi$
$x=p\sin\phi\cos\theta$
$y=p\sin\phi\sin\theta$
$p^2 = x^2 + y^2 + z^2$
$\iiint\limits_E f(x,y,z)\,dV = \int_c^d\int_\alpha^\beta\int_a^b f(p\sin\phi\cos\theta,p\sin\phi\sin\theta,p\cos\phi) p^2\sin\phi\,dp\,d\theta\,d\phi$
Jacobian of a transformation $T$ given by $x=g(u,v)$ and $y=h(u,v)$ is:
$\frac{\partial (x,y)}{\partial (u,v)} = \begin{vmatrix} \frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} \end{vmatrix} = \frac{\partial x}{\partial u} \frac{\partial y}{\partial v} - \frac{\partial x}{\partial v} \frac{\partial y}{\partial u}$
Given a transformation T whose Jacobian is nonzero, and is one to one:
$\iint\limits_R f(x,y)\,dA = \iint\limits_S f\left(x(u,v),y(u,v)\right)\left|\frac{\partial (x,y)}{\partial (u,v)}\right|\,du\,dv$
Polar coordinates are just a special case:
$x = g(r,\theta)=r\cos\theta$
$y = h(r,\theta)=r\sin\theta$
$\frac{\partial (x,y)}{\partial (u,v)} = \begin{vmatrix} \frac{\partial x}{\partial r} & \frac{\partial x}{\partial \theta} \\ \frac{\partial y}{\partial r} & \frac{\partial y}{\partial \theta} \end{vmatrix} = \begin{vmatrix} \cos\theta & -r\sin\theta \\ \sin\theta & r\cos\theta \end{vmatrix} = r\cos^2\theta + r\sin^2\theta=r(\cos^2\theta + \sin^2\theta) = r$
$\iint\limits_R f(x,y)\,dx\,dy = \iint\limits_S f(r\cos\theta, r\sin\theta)\left|\frac{\partial (x,y)}{\partial (u,v)}\right|\,dr\,d\theta=\int_\alpha^\beta\int_a^b f(r\cos\theta,r\sin\theta)|r|\,dr\,d\theta$
For 3 variables this expands as you would expect: $x=g(u,v,w)$ $y=h(u,v,w)$ $z=k(u,v,w)$
$\frac{\partial (x,y,z)}{\partial (u,v,w)}=\begin{vmatrix} \frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} & \frac{\partial x}{\partial w} \\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} & \frac{\partial y}{\partial w} \\ \frac{\partial z}{\partial u} & \frac{\partial z}{\partial v} & \frac{\partial z}{\partial w} \end{vmatrix}$
$\iiint\limits_R f(x,y,z)\,dV = \iiint\limits_S f(g(u,v,w),h(u,v,w),k(u,v,w)) \left|\frac{\partial (x,y,z)}{\partial (u,v,w)} \right| \,du\,dv\,dw$
Line Integrals
Parameterize: $r(t)=\langle x(t),y(t),z(t) \rangle$ where $r'(t)=\langle x'(t),y'(t),z'(t) \rangle$ and $|r'(t)|=\sqrt{x'(t)^2 + y'(t)^2 + z'(t)^2}$
$\int_C f(x,y,z)\,ds = \int_a^b f(r(t))\cdot |r'(t)|\,dt = \int_a^b f(x(t),y(t),z(t))\cdot\sqrt{x'(t)^2 + y'(t)^2 + z'(t)^2}\,dt\;\;\;a<t<b$
For a vector function $\mathbf{F}$:
$\int_C \mathbf{F}\cdot dr = \int_a^b \mathbf{F}(r(t))\cdot r'(t)\,dt$
Surface Integrals
Parameterize: $r(u,v) = \langle x(u,v),y(u,v),z(u,v) \rangle$
$\begin{matrix} r_u=\frac{\partial x}{\partial u}\vec{\imath} + \frac{\partial y}{\partial u}\vec{\jmath} + \frac{\partial z}{\partial u}\vec{k} \\ r_v=\frac{\partial x}{\partial v}\vec{\imath} + \frac{\partial y}{\partial v}\vec{\jmath} + \frac{\partial z}{\partial v}\vec{k} \end{matrix}$
$r_u \times r_v = \begin{vmatrix} \vec{\imath} & \vec{\jmath} & \vec{k} \\ \frac{\partial x}{\partial u} & \frac{\partial y}{\partial u} & \frac{\partial z}{\partial u} \\ \frac{\partial x}{\partial v} & \frac{\partial y}{\partial v} & \frac{\partial z}{\partial v} \end{vmatrix}$
$\iint\limits_S f(x,y,z) dS = \iint\limits_D f(r(t))|r_u \times r_v|\,dA$
For a vector function $\mathbf{F}$:
$\iint\limits_S \mathbf{F}\cdot dr = \iint\limits_D \mathbf{F}(r(u,v))\cdot (r_u \times r_v)\,dA)$
Any surface $S$ with $z=g(x,y)$ is equivalent to $x=x$, $y=y$, and $z=g(x,y)$, so
$xy$ plane:
$\iint\limits_S f(x,y,z)\,dS = \iint\limits_D f(x,y,g(x,y))\sqrt{\left(\frac{\partial z}{\partial x}\right)^2+\left(\frac{\partial z}{\partial y}\right)^2+1}\,dA$
$yz$ plane:
$\iint\limits_S f(x,y,z)\,dS = \iint\limits_D f(x,h(x,z),z)\sqrt{\left(\frac{\partial y}{\partial x}\right)^2+\left(\frac{\partial y}{\partial z}\right)^2+1}\,dA$
$xz$ plane:
$\iint\limits_S f(x,y,z)\,dS = \iint\limits_D f(g(y,z),y,z)\sqrt{\left(\frac{\partial x}{\partial y}\right)^2+\left(\frac{\partial x}{\partial z}\right)^2+1}\,dA$
Flux:
$\iint\limits_S\mathbf{F}\cdot dS = \iint\limits_D\mathbf{F}\cdot (r_u \times r_v)\,dA$
The gradient of $f$ is the vector function $\nabla f$ defined by:
$\nabla f(x,y)=\langle f_x(x,y),f_y(x,y)\rangle = \frac{\partial f}{\partial x}\vec{\imath} + \frac{\partial f}{\partial y}\vec{\jmath}$
Directional Derivative:
$D_u\,f(x,y) = f_x(x,y)a + f_y(x,y)b = \nabla f(x,y)\cdot u \text{ where } u = \langle a,b \rangle$
$\int_C\,ds=\int_a^b |r'(t)|=L$
If $\nabla f$ is conservative, then:
$\int_{c_1} \nabla f\,dr=\int_{c_2} \nabla f\,dr$
This means that the line integral between two points will always be the same, no matter what curve is used to go between the two points - the integrals are path-independent and consequently only depend on the starting and ending positions in the conservative vector field.
A vector function is conservative if it can be expressed as the gradient of some potential function $\psi$: $\nabla \psi = \mathbf{F}$
$curl\,\mathbf{F} =\nabla\times\mathbf{F}$
$div\,\mathbf{F} =\nabla\cdot\mathbf{F}$
Math 326 - Multivariable Calculus II
$f(x,y)$ is continuous at a point $(x_0,y_0)$ if
$\lim\limits_{(x,y)\to(0,0)} f(x,y) = f(x_0,y_0)$
$f+g$ is continuous if $f$ and $g$ are continuous, as is $\frac{f}{g}$ if $g \neq 0$
A composite function of a continuous function is continuous
$\frac{\partial f}{\partial x} = f_x(x,y)$
$\frac{\partial f}{\partial x}\bigg|_{(x_0,y_0)}=\left(\frac{\partial f}{\partial x}\right)_{(x_0,y_0)}=f_x(x_0,y_0)$
To find $\frac{\partial z}{\partial x} F(x,y,z)$, differentiate $x$ as normal, hold y constant, and differentiate $z$ as a function (such that $z^2 = 2z \frac{\partial z}{\partial x}$ and $2z = 2 \frac{\partial z}{\partial x}$)
Ex:
$F(x,y,z) = \frac{x^2}{16} + \frac{y^2}{12} + \frac{z^2}{9} = 1$
$\frac{\partial z}{\partial x} F = \frac{2x}{16} + \frac{2z}{}\frac{\partial z}{\partial x} = 0$
The tangent plane of $S$ at $(a,b,c): z-c = f_x(a,b)(x-a) + f_y(a,b)(y-b)$ where $z=f(x,y)$, or $z =f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b)$
Note that
$f_x(a,b)=\frac{\partial z}{\partial x}\bigg|_{(a,b)}$
which enables you to find tangent planes implicitly.
Set $z=f(x,y)$. $f_x=f_y=0$ at a relative extreme $(a,b)$.
Distance from origin:
$D^2 = z^2 + y^2 + x^2 = f(a,b)^2 + y^2 + x^2$
Minimize $D$ to get point closest to the origin.
The differential of $f$ at $(x,y)$:
$df(x,y;dx,dy)=f_x(x,y)\,dx + f_y(x,y)\,dy$
$dz=\frac{\partial f}{\partial x}\,dx + \frac{\partial f}{\partial y}\,dy$
$f$ is called differentiable at $(x,y)$ if it $s$ defined for all points near $(x,y)$ and if there exists numbers $A$,$B$ such that
$\lim_{(n,k)\to(0,0)}\frac{|f(x+h,y+k) - f(x,y) - Ah - Bk|}{\sqrt{h^2 + k^2}}=0$
If $f$ is differentiable at $(x,y)$ it is continuous there.
$A = f_x(x,y)$
and
$B=f_y(x,y)$
If $F_x(x,y)$ and $F_y(x,y)$ are continuous at a point $(x_0,y_0)$ defined in $F$, then $F$ is differentiable there.
Ex: The differential of $f(x,y)=3x^2y+2xy^2+1$ at $(1,2)$ is $df(1,2;h,k)=20h+11k$
$d(u+v)=du+dv$
$d(uv)=u\,dv + v\,du$
$d\left(\frac{u}{v}\right)=\frac{v\,du -u\,dv}{v^2}$
Taylor Series:
$f^{(n)}(t)=\left[\left(h\frac{}{} + k\frac{}{})^n F(x,y) \right) \right]_{x=a+th,y=b+tk}$
Note:
$f''(t)=h^2 F_{xx} + 2hk F_{xy} + k^2 F_{yy}$
$\begin{matrix} x=f(u,v) \\ y=g(u,v) \end{matrix}$
$J=\frac{\partial(f,g)}{\partial(u,v)}$
$\begin{matrix} u=F(x,y) \\ v=G(x,y) \end{matrix}$
$j = J^{-1} = \frac{1}{\frac{\partial(f,g)}{\partial(u,v)}}$
$\begin{matrix} x = u-uv \\ y=uv \end{matrix}$
$\iint\limits_R\frac{dx\,dy}{x+y}$
R bounded by
$\begin{matrix} x+y=1 & x+y=4 \\ y=0 & x=0 \end{matrix}$
$\int_0^1\int_0^x \frac{du\,dv}{u-uv+ux}\left|\frac{\partial(x,y)}{\partial(u,v)}\right|$
$\frac{\partial(F,G)}{\partial(u,v)}=\begin{vmatrix} \frac{\partial F}{\partial u} & \frac{\partial F}{\partial v} \\ \frac{\partial G}{\partial u} & \frac{\partial G}{\partial v} \end{vmatrix}$
$\nabla f = \langle f_x, f_y, f_z \rangle$
$G_x(s_0,t_0) =F_x(a,b)f_x(s_0,t_0) + F_y(a,b)g_x(s_0,t_0)$
$U\times V = U_xV_y - U_yV_x \text{ or } A\times B = \left\langle \begin{vmatrix} a_y & a_z \\ b_y & b_z \end{vmatrix}, -\begin{vmatrix} a_x & a_z \\ b_x & b_z \end{vmatrix}, \begin{vmatrix} a_x & a_y \\ b_x & b_y \end{vmatrix} \right\rangle$
Given $G(s,t)=F(f(s,t),g(s,t))$, then:
$\begin{matrix} \frac{\partial G}{\partial s} = \frac{\partial F}{\partial x}\frac{\partial f}{\partial s} + \frac{\partial F}{\partial y}\frac{\partial g}{\partial s} \\ \frac{\partial G}{\partial t} = \frac{\partial F}{\partial x}\frac{\partial f}{\partial t} + \frac{\partial F}{\partial y}\frac{\partial g}{\partial t} \end{matrix}$
Alternatively, $u=F(x,y,z)=F(f(t),g(t),h(t))$ yields
$\frac{du}{dt}=\frac{\partial u}{\partial x}\frac{dx}{dt} + \frac{\partial u}{\partial y}\frac{dy}{dt} + \frac{\partial u}{\partial z}\frac{dz}{dt}$
Examine limit along line $y=mx$:
$\lim_{x\to 0} f(x,mx)$
If $g_x$ and $g_y$ are continuous, then $g$ is differentiable at that point (usually $0,0$).
Notice that if $f_x(0,0)=0$ and $f_y(0,0)=0$ then $df(0,0;h,l)=0h+0k=0$
The graph of $y(x,y)$ lies on a level surface $F(x,y,z)=c$ means $f(x,y(x,z),z)=c$. So then use the chain rule to figure out the result in terms of $F$ partials by considering $F$ a composite function $F(x,y(x,z),z)$.
Fundamental implicit function theorem: Let $F(x,y,z)$ be a function defined on an open set $S$ containing the point $(x_0,y_0,z_0)$. Suppose $F$ has continuous partial derivatives in $S$. Furthermore assume that: $F(x_0,y_0,z_0)=0, F_z(x_0,y_0,z_0)\neq 0$. Then $z=f(x,y)$ exists, is continuous, and has continuous first partial derivatives.
$f_x = -\frac{F_x}{F_z}$
$f_y = -\frac{F_y}{F_z}$
Alternatively, if
$\begin{vmatrix} F_x & F_y \\ G_x & G_y \end{vmatrix} \neq 0$
, then we can solve $x$ and $y$ as functions of $z$. Since the cross-product is made of these determinants, if the $x$ component is nonzero, you can solve $y,z$ as functions of $x$, and therefore graph it on the $x-axis$.
To solve level surface equations, let $F(x,y,z)=c$ and $G(x,y,z)=d$, then use the chain rule, differentiating by the remaining variable (e.g. $\frac{dy}{dx}$ and $\frac{dz}{dx}$ means do $x$)
$\begin{matrix} F_x + F_y y_x + F_z z_x = 0 \\ G_x + G_y y_x + G_z z_x = 0 \end{matrix}$
if you solve for $y_x$,$z_x$, you get
$\left[ \begin{matrix} F_y & F_z \\ G_y & G_z \end{matrix} \right] \left[ \begin{matrix} y_x \\ z_x \end{matrix} \right] = \left[\begin{matrix}F_x \\ G_x \end{matrix} \right]$
Mean value theorem:
$f(b) - f(a) = (b-a)f'(X)$
$a < X < b$
or:
$f(a+h)=f(a)+hf'(a + \theta h)$
$0 < \theta < 1$
xy-plane version:
$F(a+h,b+k)-F(a,b)=h F_x(a+\theta h,b+\theta k)+k F_y(a+\theta h, b+\theta k)$
$0 < \theta < 1$
Lagrange Multipliers: $\nabla f = \lambda\nabla g$ for some scale $\lambda$ if $(x,y,z)$ is a minimum:
$f_x=\lambda g_x$
$f_y=\lambda g_y$
$f_z=\lambda g_z$
Set $f=x^2 + y^2 + z^2$ for distance and let $g$ be given.
Math 307 - Introduction to Differential Equations
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Math 308 - Matrix Algebra
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Math 309 - Linear Analysis
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AMath 353 - Partial Differential Equations
Fourier Series:
$f(x)=b_0 + \sum_{n=1}^{\infty} \left(a_n \sin\frac{n\pi x}{L} + b_n\cos\frac{n\pi x}{L} \right)$
$b_0 = \frac{1}{2L}\int_{-L}^L f(y)\,dy$
$a_m \frac{1}{L}\int_{-L}^L f(y) \sin\frac{m\pi y}{L}\,dy$
$b_m = \frac{1}{L}\int_{-L}^L f(y)\cos\frac{m\pi y}{L}\,dy$
$m \ge 1$
$u_t=\alpha^2 u_{xx}$
$\alpha^2 = \frac{k}{pc}$
$u(x,t)=F(x)G(t)$
Dirichlet: $u(0,t)=u(L,t)=0$
Neumann:$u_x(0,t)=u_x(L,t)=0$
Robin:$a_1 u(0,t)+b_1 u_x(0,t) = a_2 u(L,t) + b_2 u_x(L,t) = 0$
Dirichlet:
$\lambda_n=\frac{n\pi}{L}\;\;\; n=1,2,...$
$u(x,t)=\sum_{n=1}^{\infty} A_n \sin\left(\frac{n\pi x}{L} \right)\exp\left(-\frac{n^2\alpha^2\pi^2 t}{L^2}\right)$
$A_n = \frac{2}{L} \int_0^L f(y) \sin\frac{n\pi y}{L}\,dy = 2 a_m\text{ for } 0\text{ to } L$
Neumann:
$\lambda_n=\frac{n\pi}{L}\;\;\; n=1,2,...$
$u(x,t)=B_0 + \sum_{n=1}^{\infty} B_n \cos\left(\frac{n\pi x}{L} \right)\exp\left(-\frac{n^2\alpha^2\pi^2 t}{L^2}\right)$
$B_0 = \frac{1}{L} \int_0^L f(y)\,dy$
$B_n = \frac{2}{L} \int_0^L f(y) \cos\frac{n\pi y}{L}\,dy = 2 b_m\text{ for } 0\text{ to } L$
Dirichlet/Neumann:
$\lambda_n=\frac{\pi}{2L}(2n + 1)\;\;\; n=0,1,2,...$
$u(x,t)=\sum_{n=0}^{\infty} A_n \sin\left(\lambda_n x\right) \exp\left(-\alpha^2 \lambda_n^2 t\right)$
$A_n = \frac{2}{L} \int_0^L f(y) \sin\left(\lambda_n y\right)\,dy$
Neumann/Dirichlet:
$\lambda_n=\frac{\pi}{2L}(2n + 1)\;\;\; n=0,1,2,...$
$u(x,t)=\sum_{n=0}^{\infty} B_n \cos\left(\lambda_n x\right) \exp\left(-\alpha^2 \lambda_n^2 t\right)$
$B_n = \frac{2}{L}\int_0^L f(y)\cos(\lambda_n y)\,dy$
$v_2(x,y)=\sum_{n=1}^{\infty} C_n(t)[\sin/\cos](\lambda_n x)$
Replace $[\sin/\cos]$ with whatever was used in $u(x,t)$
$C_n(t)=\int_0^t p_n(s) e^{\lambda_n^2\alpha^2 (s-t)}\,ds$
$p_n(t)=\frac{2}{L}\int_0^L p(y,t)[\sin/\cos](\lambda_n y)\,dy$
Replace $[\sin/\cos]$ with whatever was used in $u(x,t)$. Note that $\lambda_n$ for $C_n$ and $p_n(t)$ is the same as used for $u_1(x,t)$
Sturm-Liouville:
$p(x)\frac{d^2}{dx^2}+p'(x)\frac{d}{dx}+q(x)$
$a_2(x)\frac{d^2}{dx^2} + a_1(x)\frac{d}{dx} + a_0(x) \rightarrow p(x)=e^{\int\frac{a_1(x)}{a_2(x)}\,dx}$
$q(x)=p(x)\frac{a_0(x)}{a_2(x)}$
Laplace's Equation:
$\nabla^2 u=0$
$u=F(x)G(y)$
$\frac{F''(x)}{F(x)} = -\frac{G''(y)}{G(y)} = c$
for rectangular regions
$F_?(x)=A =\sinh(\lambda x) + B \cosh(\lambda x)$
use odd $\lambda_n$ if $F$ or $G$ equal a single $\cos$ term.
$G_?(y)=C =\sinh(\lambda y) + D \cosh(\lambda y)$
$u(x,?)=G(?)$
$u(?,y)=F(y)$
Part 1: All $u_?(x,?)=0$
$\lambda_n=\frac{n\pi}{L y}\text{ or }\frac{(2n+1)\pi}{2L y}$
$u_1(x,y)=\sum_{n=0}^{\infty}A_n F_1(x)G_1(y)$
$A_n = \frac{2}{L_y F_1(?)}\int_0^{L_y} u(?,y)G_1(y)\,dy$
$u(?,y)=h(y)$
$? = L_x\text{ or }0$
Part 2: All $u_?(?,y)=0$
$\lambda_n=\frac{n\pi}{L x}\text{ or }\frac{(2n+1)\pi}{2L x}$
$u_2(x,y)=\sum_{n=1}^{\infty}B_n F_2(x)G_2(y)$
$B_n = \frac{2}{L_x G_2(?)}\int_0^{L_x} u(x,?)F_2(x)\,dx$
$u(x,?)=q(x)$
$? = L_y\text{ or }0$
$u(x,y)=u_1(x,y)+u_2(x,y)$
Circular $\nabla^2 u$:
$u_{rr} + \frac{1}{r} u_r + \frac{1}{r^2}u_{\theta \theta} = 0$
$\frac{G''(\theta)}{G(\theta)}= - \frac{r^2 F''(r) + r F(r)}{F(r)} = c$
$\left\langle f,g \right\rangle = \int_a^b f(x) g(x)\,dx$
$\mathcal{L}_s=-p(x)\frac{d^2}{dx^2}-p'(x)\frac{d}{dx} + q(x)$
$\mathcal{L}_s\phi(x)=\lambda r(x) \phi(x)$
$\left\langle\mathcal{L}_s y_1,y_2 \right\rangle =\int_0^L \left(-[p y_1']'+q y_1\right)y_2\,dx$
$\mathcal{L}_s = f(x)$, then $\mathcal{L}_s^{\dagger} v(x) = 0$, where if $v=0$, $u(x)$ is unique, otherwise $v(x)$ exists only when forcing is orthogonal to all trivial solutions.
if $c=0$,
$G(\theta)=B$
$F(r)=C\ln r + D$
if $c=-\lambda^2 <0$,
$G(\theta)=A\sin(\lambda\theta) + B\cos(\lambda\theta)$
$F(r) = C\left(\frac{r}{R} \right)^n + D\left( \frac{r}{R} \right)^{-n}$
$u(r,\theta)=B_0 + \sum_{n=1}^{\infty} F(r) G(\theta) = B_0 + \sum_{n=1}^{\infty}F(r)[A_n\sin(\lambda\theta) + B_n\cos(\lambda\theta)]$
$A_n = \frac{1}{\pi}\int_0^{2\pi} f(\theta)\sin(n\theta)\,d\theta$
$B_n = \frac{1}{\pi}\int_0^{2\pi} f(\theta)\cos(n\theta)\,d\theta$
$B_0 = \frac{1}{2\pi}\int_0^{2\pi} f(\theta)\,d\theta$
Wave Equation:
$u_{tt}=c^2 u_{xx}$
$u = F(x)G(t)$
$\frac{F''(x)}{F(x)}=\frac{G''(t)}{G(t)}=k \text{ where } u(t,0)=F(0)=u(t,L)=F(L)=0$
$F(x) = A\sin(\lambda x) + B\cos(\lambda x)$
$u_t(x,0)=g(x)=\sum_{n=1}^{\infty} A_n\lambda_n c \sin(\lambda_n x)$
$A_n = \frac{2}{\lambda_n c L}\int_0^L g(y)\sin(\lambda_n y)\,dy$
$G(t) = C\sin(\lambda t) + D\cos(\lambda t)$
$u(x,0)=f(x)=\sum_{n=1}^{\infty}B_n\sin(\lambda_n x)$
$B_n = \frac{2}{L}\int_0^L f(y)\sin(\lambda_n y)\,dy$
$u(x,t)=\sum_{n=1}^{\infty}F(x)G(t)=\sum_{n=1}^{\infty}F(x)\left[C\sin(\lambda t) + D\cos(\lambda t)\right]$
$\lambda_n=\frac{n\pi}{L}\text{ or }\frac{(2n+1)\pi}{2L}$
Inhomogeneous:
$u(0,t)=F(0)=p(t)$
$u(L,t)=F(L)=q(t)$
$u(x,t)=v(x,t) + \phi(x)p(t) + \psi(x)q(t)$
Transform to forced:
$v(x,y) = \begin{cases} v_{tt}=c^2 v_{xx} - \phi(x)p''(x) - \psi(x)q''(t) = c^2 v_{xx} + R(x,t) & \phi(x)=1 - \frac{x}{L}\;\;\;\psi(x)=\frac{x}{L}\\ v(0,t)=v(L,t)=0 & t>0 \\ v(x,0)=f(x)-\phi(x)p(0) - \psi(x)q(0) & f(x)=u(x,0) \\ v_t(x,0)=g(x)-\phi(x)p'(0) - \psi(x)q'(0) & g(x)=u_t(x,0) \end{cases}$
Then solve as a forced equation.
Forced:
$u_{tt}=c^2 u_{xx} + R(x,t)$
$u(x,t)=u_1(x,t)+u_2(x,t)$
$u_1$ found by $R(x,t)=0$ and solving.
$u_2(x,t)=\sum_{n=1}^{\infty} C_n(t)\sin\left(\frac{n\pi x}{L}\right)$
where $\sin\frac{n\pi x}{L}$ are the eigenfunctions from solving $R(x,t)=0$
$R(x,t)=\sum_{n=1}^{\infty} R_n(t)\sin\left(\frac{n\pi x}{L}\right)$
$R_n(t)=\frac{2}{L}\int_0^L R(y,t)\sin\left(\frac{n\pi x}{L}\right)\,dy$
$C_n''(t) + k^2 C_n(t)=R_n(t)$
$C_n(t)=\alpha\sin(k t) + \beta\cos(k t) + sin(k t)\int_0^t R_n(s)\cos(k s)\,ds - \cos(k t)\int_0^t R_n(s)\sin(k s)\,ds$
where $C_n(0)=0$ and $c_n'(0)=0$
Fourier Transform:
$\mathcal{F}(f)=\hat{f}(k)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} f(\xi) e^{-i k \xi}\,d\xi$
$\mathcal{F}^{-1}(f)=f(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \hat{f}(k) e^{ikx}\,dk$
$\mathcal{F}(f+g)=\widehat{f+g}=\hat{f} + \hat{g}$
$\widehat{fg}\neq\hat{f}\hat{g}$
$\widehat{f'}=ik\hat{f}\text{ or }\widehat{f^{(n)}}=(ik)^n\hat{f}$
$\widehat{u_t} = \frac{\partial \hat{u}}{\partial t} = \hat{u}_t$
$\widehat{u_{tt}}=\frac{\partial^2\hat{u}}{\partial t^2}=\hat{u}_{tt}$
$\widehat{u_{xx}}=(ik)^2\hat{u}=-k^2\hat{u}$
$u(x,t)=\mathcal{F}^{-1}(\hat{u})=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \hat{f}(k) e^{\alpha^2 k^2 t} e^{ikx}\,dk$
$u(x,t)=\mathcal{F}^{-1}\left(\hat{f}(k) e^{-\alpha^2 k^2 t}\right)$
Semi-infinite:
$\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \hat{F}(k) e^{\alpha^2 k^2 t} e^{ikx}\,dk$
where
$\hat{F}(k)=-i\sqrt{\frac{2}{\pi}}\int_0^{\infty} f(\xi)\sin(k\xi)\,d\xi$
$f(x)$ $\hat{f}(k)$ $1\text{ if } -s < x < s, 0\text{ otherwise }$ $\sqrt{\frac{2}{\pi}}\frac{\sin(ks)}{k}$ $\frac{1}{x^2 + s^2}$ $\frac{1}{s}\sqrt{\frac{\pi}{2}}e^{-s|k|}$ $e^{-sx^2}$ $\frac{1}{\sqrt{2s}}e^{\frac{k^2}{4s}}$ $\frac{\sin(sx)}{x}$ $\sqrt{\frac{\pi}{2}}\text{ if } |k| AMath 402 - Dynamical Systems and Chaos Dimensionless time \[ \tau = \frac{t}{T}$
where T gets picked so that
$\frac{}{}$
and
$\frac{}{}$
are of order 1.
Fixed points of $x'=f(x)$: set $f(x)=0$ and solve for roots
Bifurcation: Given $x'=f(x,r)$, set $f(x,r)=0$ and solve for $r$, then plot $r$ on the $x-axis$ and $x$ on the $y-axis$.
Transcritical
Subcritical Pitchfork
Supercritical Pitchfork
$\begin{matrix} x'=ax+by \\ y'=cx+dy \end{matrix}$
$A=\begin{bmatrix} a & b \\ c & d \end{bmatrix}$
$\begin{vmatrix} a-\lambda & b \\ c & d-\lambda \end{vmatrix}=0$
$\begin{matrix} \lambda^2 - \tau\lambda + \delta=0 & \lambda = \frac{\tau \pm \sqrt{\tau^2 - 4\delta}}{2} \\ \tau = a+d & \delta=ad-bc \end{matrix}$
$x(t)=c_1 e^{\lambda_1 t}v_1 + c_2 e^{\lambda_2 t}v_2$
$v_1,v_2$ are eigenvectors.
Given $\tau = \lambda_1 + \lambda_2$ and $\delta=\lambda_1\lambda_2$:
if $\delta < 0$, the eigenvalues are real with opposite signs, so the fixed point is a saddle point.
otherwise, if $\tau^2-4\delta > 0$, its a node. This node is stable if $\tau < 0$ and unstable if $\tau > 0$
if $\tau^2-4\delta < 0$, its a spiral, which is stable if $\tau < 0$, unstable if $\tau > 0$, or a center if $\tau=0$
if $\tau^2-4\delta = 0$, its degenerate.
$\begin{bmatrix} x'=f(x,y) \\ y'=g(x,y) \end{bmatrix}$
Fixed points are found by solving for $x'=0$ and $y'=0$ at the same time.
nullclines are when either $x'=0$ or $y'=0$ and are drawn on the phase plane.
$\begin{bmatrix} \frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \\ \frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} \end{bmatrix}$
$\leftarrow$ For nonlinear equations, evaluate this matrix at each fixed point, then use the above linear classification scheme to classify the point.
A basin for a given fixed point is the area of all trajectories that eventually terminate at that fixed point.
Given $x'=f(x)$, $E(x)$ is a conserved quantity if $\frac{dE}{dt}=0$
A limit cycle is an isolated closed orbit in a nonlinear system. Limit cycles can only exist in nonlinear systems.
If a function can be written as $\vec{x}'=-\nabla V$, then its a gradient function and can't have closed orbits.
The Liapunov function $V(x)$ for a fixed point $x^*$ satisfies $V(x) > 0 \forall x \neq x^*, V(x^*)=0, V' < 0 \forall x \neq x^*$
A Hopf bifurcation occurs as the fixed points eigenvalues (in terms of $\mu$) cross the imaginary axis.
Math 300 - Introduction to Mathematical Reasoning
P Q $P \Rightarrow Q$ $\neg P \vee Q$ T T T T T F F F F T T T F F T T
All valid values of $x$ constitute the Domain.
$f(x)=y$ The range in which $y$ must fall is the codomain
The image is the set of $y$ values that are possible given all valid values of $x$
So, $\frac{1}{x}$ has a domain $\mathbb{R} - \{0\}$ and a codomain of $\mathbb{R}$. However, no value of $x$ can ever produce $f(x)=0$, so the Image is $\mathbb{R}-\{0\}$
Injective: No two values of $x$ yield the same result. $f(x_1)\neq f(x_2)$ if $x_1 \neq x_2$ for all $x$
Surjective: All values of $y$ in the codomain can be produced by $f(x)$. In other words, the codomain equals the image.
Bijective: A Bijective function is both Injective and Surjective - all values of $y$ are mapped to exactly one value of $x$. A simple way to prove this is to solve $f(x)$ for $x$. If this can be done without creating multiple solutions (a square root, for example, yields $\pm$, not a single answer), then it's a bijective function.
If $f(x)$ is a bijection, it is denumerable. Any set that is equivalent to the natural numbers is denumerable.
$\forall x \in \mathbb{R}$ means "for all $x$ in $\mathbb{R}$", where $\mathbb{R}$ can be replaced by any set.
$\exists y \in \mathbb{R}$ means "there exists a $y$ in $\mathbb{R}$", where $\mathbb{R}$ can be replaced by any set.
$A \vee B = A\text{ or }B$
$A \wedge B = A\text{ and }B$
$P \Leftrightarrow Q\text{ means }P \Rightarrow Q \wedge Q\Rightarrow P \text{ or } P\text{ iff }Q \text{ (if and only if)}$
$A \cup B$ = Union - All elements that are in either A or B, or both.
$\{x|x \in A \text{ or } x \in B \}$
$A \cap B$ = Intersection - All elements that are in both A and B
$\{x|x \in A \text{ and } x \in B \}$
$A\subseteq B$ = Subset - Indicates A is a subset of B, meaning that all elements in A are also in B.
$\{x \in A \Rightarrow x \in B \}$
$A \subset B$ = Strict Subset - Same as above, but does not allow A to be equal to B (which happens if A has all the elements of B, because then they are the exact same set).
$A-B$ = Difference - All elements in A that aren't also in B
$\{x|x \in A \text{ and } x \not\in B \}$
$A\times B$ = Cartesian Product - All possible ordered pairs of the elements in both sets:
$\{(x,y)|x \in A\text{ and }y\in B\}$
Proof We use induction on $n$ Base Case: [Prove $P(n_0)$] Inductive Step: Suppose now as inductive hypothesis that [$P(k)$ is true] for some integer $k$ such that $k \ge n_0$. Then [deduce that $P(k+1)$ is true]. This proves the inductive step. Conclusion: Hence, by induction, [$P(n)$ is true] for all integers $n \ge n_0$.
Proof We use strong induction on $n$ Base Case: [Prove $P(n_0)$, $P(n_1)$, ...] Inductive Step: Suppose now as inductive hypothesis that [$P(n)$ is true for all $n \le k$] for some positive integer $k$, then [deduce that $P(k+1)$ is true]. This proves the inductive step. Conclusion: Hence, by induction [$P(n)$ is true] for all positive integers $n$.
Proof: Suppose, for contradiction, that the statement $P$ is false. Then, [create a contradiction]. Hence our assumption that $P$ is false must be false. Thus, $P$ is true as required.
The composite of $f:X\rightarrow Y$ and $g:Y\rightarrow Z$ is $g\circ f: x\rightarrow Z$ or just $gf: X\rightarrow Z$. $g\circ f = g(f(x)) \forall x \in X$
$a\equiv b \bmod m \Leftrightarrow b\equiv a \bmod m$
If
$a \equiv b \bmod m\text{ and }b \equiv c \bmod m,\text{ then }a$
Negation of $P \Rightarrow Q$ is $P \wedge (\neg Q)$ or $P and (not Q)$
If $m$ is divisible by $a$, then $a b_1 \equiv a b_2 \bmod m \Leftrightarrow b_1 \equiv b_2 \bmod\left(\frac{m}{a} \right)$
Fermat's little theorem: If $p$ is a prime, and $a \in \mathbb{Z}^+$ which is not a multiple of $p$, then $a^{p-1}\equiv 1 \bmod p$.
Corollary 1: If $p$ is prime, then $\forall a \in \mathbb{Z}, a^p = a \bmod p$
Corollary 2: If $p$ is prime, then $(p-1)! \equiv -1 \bmod p$
Division theorem: $a,b \in \mathbb{Z}$, $b > 0$, then $a = bq+r$ where $q,r$ are unique integers, and $0 \le r < b$. Thus, for $a=bq+r$, $\gcd(a,b)=\gcd(b,r)$. Furthermore, $b$ divides $a$ if and only if $r=0$, and if $b$ divides $a$, $\gcd(b,a)=b$
Euclidean Algorithm: $\gcd(136,96)$
$136=96\cdot 1 + 40$
$290x\equiv 5\bmod 357 \rightarrow 290x + 357y = 5$
$96=40\cdot 2 + 16$
$ax\equiv b \bmod c \rightarrow ax+cy=b$
$40=16\cdot 2 + 8$
$16=8\cdot 2 + 0 \leftarrow$ stop here, since the remainder is now 0
$\gcd(136,96)=8$
Diophantine Equations (or linear combinations):
$140m + 63n = 35$ $m,n \in \mathbb{Z}$ exist for $am+bn=c$ iff $\gcd(a,b)$ divides $c$
$140=140\cdot 1 + 63\cdot 0$
$63=140\cdot 0 + 63\cdot 1$ dividing $am+bn=c$ by $\gcd(a,b)$ always yields coprime $m$ and $n$.
$14=140\cdot 1 - 63\cdot 2$
$7=63\cdot 1 - 14\cdot 4 = 63 - (140\cdot 1 - 63\cdot 2)\cdot 4 = 63 - 140\cdot 4 + 63\cdot 8 = 63\cdot 9 - 140\cdot 4$
$0=14 - 7\cdot 2 =140\cdot 1 - 63\cdot 2 - 2(63\cdot 9 - 140\cdot 4) = 140\cdot 9-63\cdot 20$
So $m=9$ and $n=-20$
Specific: $7=63\cdot 9 - 140\cdot 4 \rightarrow 140\cdot(-4)+63\cdot 9=7\rightarrow 140\cdot(-20)+63\cdot45=35$
So for $140m+63n=35, m=-20, n=45$
Homogeneous: $140m+63n=0 \; \gcd(140,63)=7 \; 20m + 9n = 0 \rightarrow 29m=-9n$
$m=9q, n=-20q$ for $q\in \mathbb{Z}$ or $am+bn=0 \Leftrightarrow (m,n)=(bq,-aq)$
General: To find all solutions to $140m+63n=35$, use the specific solution $m=-20, n=45$
$140(m+20) + 63(n-45) = 0$
$(m+20,n-45)=(9q,-20q)$ use the homogeneous result and set them equal.
$(m,n)=(9q-20,-20q+45)$ So $m=9q-20$ and $n=-20q+45$
$[a]_m = \{x\in \mathbb{Z}| x\equiv a \bmod m \} \Rightarrow \{ mq + a|q \in \mathbb{Z} \}$
$ax\equiv b \bmod m$ has a unique solution $\pmod{m}$ if $a$ and $m$ are coprime. If $\gcd(a,b)=1$, then $a$ and $b$ are coprime. $[a]_m$ is invertible if $\gcd(a,m)=0$.
Math 327 - Introduction to Real Analysis I
Cauchy Sequence: For all $\epsilon > 0$ there exists an integer $N$ such that if $n,m \ge N$, then $|a_n-a_m|<\epsilon$
Alternating Series: Suppose the terms of the series $\sum u_n$ are alternately positive and negative, that $|u_{n+1}| \le |u_n|$ for all $n$, and that $u_n \to 0$ as $n\to\infty$. Then the series $\sum u_n$ is convergent.
Bolzano-Weierstrass Theorem: If $S$ is a bounded, infinite set, then there is at least one point of accumulation of $S$.
$\sum u_n$ is absolutely convergent if $\sum|u_n|$ is convergent
If $\sum u_n$ is absolutely convergent, then $\sum u_n = \sum a_n - \sum b_n$ where both $\sum a_n$ and $\sum b_n$ are convergent. If $\sum u_n$ is conditionally convergent, both $\sum a_n$ and $\sum b_n$ are divergent.
$\sum u_n = U = u_0 + u_1 + u_2 + ...$
$w_0 = u_0 v_0$
$w_1 = u_0 v_1 + u_1 v_0$
$\sum v_n = V = v_0 + v_1 + v_2 + ...$
$w_n = u_0 v_n + u_1 v_{n-1} + ... + u_n v_0$
$\sum w_n = UV = w_0 + w_1 + w_2 + ...$
Provided
$\sum u_n, \sum v_n$
are absolutely convergent.
$\sum a_n x^n$ is either absolutely convergent for all $x$, divergent for all $x\neq 0$, or absolutely convergent if $-R < x < R$ (it may or may not converge for $x=\pm R$ ).
$-R < x < R$ is the interval of convergence. $R$ is the radius of convergence.
$R=\lim_{n \to \infty}\left|\frac{a_n}{a_{n+1}}\right|$
if the limit exists or is $+\infty$
Let the functions of the sequence $f_n(x)$ be defined on the interval $[a,b]$. If for each $\epsilon > 0$ there is an integer $N$ independent of x such that $|f_n(x) - f_m(x)| < \epsilon$ where $N \le m,n$.
You can't converge uniformly on any interval containing a discontinuity.
$|a|+|b|\le|a+b|$
$\lim_{n \to \infty}(1+\frac{k}{n})^n = e^k$
$lim_{n \to \infty} n^{\frac{1}{n}}=1$
$\sum_{k=0}^{\infty}=\frac{a}{1-r}$
if $|r| < 1$
$\sum a_n x^n$
$R = \lim_{n \to \infty}\left|\frac{a_n}{a_{n+1}} \right|$
if it exists or is $+\infty$. The interval of convergence is $-R < x < R$
$\sum^{\infty}\frac{x^2}{(1+x^2)^n} = x^2\sum\left(\frac{1}{1+x^2}\right)^n = x^2\left(\frac{1}{1-\frac{1}{1+x^2}}\right) = x^2\left( \frac{1+x^2}{1+x^2-1}\right) = x^2\left( \frac{1+x^2}{x^2} \right) = 1+x^2$
Math 427 - Complex Analysis
0 $\frac{\pi}{6}$ $\frac{\pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\sin$ 0 $\frac{1}{2}$ $\frac{\sqrt{2}}{2}$ $\frac{\sqrt{3}}{2}$ 1 $\cos$ 1 $\frac{\sqrt{3}}{2}$ $\frac{\sqrt{2}}{2}$ $\frac{1}{2}$ 0 $\tan$ 0 $\frac{1}{\sqrt{3}}$ 1 $\sqrt{3}$ $\varnothing$
$\frac{z_1}{z_2} = \frac{x_1 x_2 + y_1 y_2}{x_2^2 + y_2^2} + i\frac{y_1 x_1 - x_1 y_2}{x_2^2 + y_2^2}$
$|z| = \sqrt{x^2 + y^2}$
$\bar{z} = x-i y$
$|\bar{z}|=|z|$
$\text{Re}\,z=\frac{z+\bar{z}}{2}$
$\text{Im}\,z=\frac{z-\bar{z}}{2i}$
$\text{Arg}\,z=\theta\text{ for } -\pi < \theta < \pi$
$z=re^{i\theta}=r(\cos(\theta) + i\sin(\theta))$
$\lim_{z \to z_0} f(z) = w_0 \iff \lim_{x,y \to x_0,y_0} u(x,y) = u_0 \text{ and }\lim_{x,y \to x_0,y_0} v(x,y)=v_0 \text{ where } w_0=u_0+iv_0 \text{ and } z_0=x_0+iy+0$
$\lim_{z \to z_0} f(z) = \infty \iff \lim_{z \to z_0} \frac{1}{f(z)}=0$
$\lim_{z \to \infty} f(z) = w_0 \iff \lim_{z \to 0} f\left(\frac{1}{z}\right)=w_0$
$\text{Re}\,z\le |\text{Re}\,z|\le |z|$
$\text{Im}\,z\le |\text{Im}\,z| \le z$
$\lim_{z \to \infty} f(z) = \infty \iff \lim_{z\to 0}\frac{1}{f\left(\frac{1}{z}\right)}=0$
$\left| |z_1| - |z_2| \right| \le |z_1 + z_2| \le |z_1| + |z_2|$
Roots:
$z = \sqrt[n]{r_0} \exp\left[i\left(\frac{\theta_0}{n} + \frac{2k\pi}{n} \right)\right]$
Harmonic:
$f_{xx} + f_{yy} = 0 \text{ or } f_{xx}=-f_{yy}$
Cauchy-Riemann:
$f(z) = u(x,y)+iv(x,y)$
$\sinh(z)=\frac{e^z-e^{-z}}{2}=-i\sin(iz)$
$\frac{d}{dz}\sinh(z)=\cosh(z)$
$u_x = v_y$
$u_y = -v_x$
$\cosh(z) = \frac{e^z + e^{-z}}{2} = cos(iz)$
$\frac{d}{dz}\cosh(z)=\sinh(z)$
$f(z) = u(r,\theta)+iv(r,\theta)$
$\sin(z)=\frac{e^{iz}-e{-iz}}{2i}=i-\sinh(iz)=\sin(x)\cosh(y) + i\cos(x)\sinh(y)$
$r u_r = v_{\theta}$
$u_{\theta}=-r v_r$
$\cos(z)=\frac{e^{iz}+e^{-iz}}{2}=\cosh(iz)=\cos(x)\cosh(y) - i \sin(x)\sinh(y)$
$\sin(x)^2 + \sinh(y)^2 = 0$
$|\sin(z)|^2 = \sin(x)^2 + \sinh(y)^2$
$|\cos(z)|^2 = \cos(x)^2 + \sinh(y)^2$
$e^z$ and Log:
$e^z=e^{x+iy}=e^x e^{iy}=e^x(\cos(y) + i\sin(y))$
$e^x e^{iy} = \sqrt{2} e^{i\frac{\pi}{4}}$
$e^x = \sqrt{2}$
$y = \frac{\pi}{4} + 2k\pi$
$x = \ln\sqrt{2}$
So,
$z = \ln\sqrt{2} + i\pi\left(\frac{1}{4} + 2k\right)$
$\frac{d}{dz} log(f(z)) = \frac{f'(z)}{f(z)}$
Cauchy-Gourgat: If $f(z)$ is analytic at all points interior to and on a simple closed contour $C$, then
$\int_C f(z) \,dz=0$
$\int_C f(z) \,dz = \int_a^b f[z(t)] z'(t) \,dt$
$a \le t \le b$
$z(t)$ is a parameterization. Use $e^{i\theta}$ for circle!
Maximum Modulus Principle: If $f(z)$ is analytic and not constant in $D$, then $|f(z)|$ has no maximum value in $D$. That is, no point $z_0$ is in $D$ such that $|f(z)| \le |f(z_0)|$ for all $z$ in $D$.
Corollary: If $f(z)$ is continuous on a closed bounded region $R$ and analytic and not constant through the interior of $R$, then the maximum value of $|f(z)|$ in $R$ always exists on the boundary, never the interior.
Taylor's Theorem: Suppose $f(z)$ is analytic throughout a disk $|z-z_0|<R$. Then $f(z)$ has a power series of the form
$f(z) = \sum_{n=0}^{\infty}\frac{f^{(n)}(z_0)}{n!}(z-z_0)^n$
where $|z-z_0| < R_0$ and $n=0,1,2,...$
Alternatively,
$\sum_{n=0}^{\infty} a_n(z-z_0)^n \text{ where } a_n=\frac{f^{(n)}(z_0)}{n!}$
For $|z|<\infty$:
$e^z = \sum_{n=0}^{\infty}\frac{z^n}{n!}$
$\sin(z) = \sum_{n=0}^{\infty}(-1)^n\frac{z^{2n+1}}{(2n+1)!}$
$\cos(z) = \sum_{n=0}^{\infty}(-1)^n\frac{z^{2n}}{(2n)!}$
Note that
$\frac{1}{1 - \frac{1}{z}}=\sum_{n=0}^{\infty}\left(\frac{1}{z}\right)^n \text{ for } \left|\frac{1}{z}\right| < 1$
, which is really $1 < |z|$ or $|z| > 1$
For $|z| < 1$:
$\frac{1}{1-z} = \sum_{n=0}^{\infty} z^n$
$\frac{1}{1+z} = \sum_{n=0}^{\infty} (-1)^n z^n$
For $|z-1|<1$:
$\frac{1}{z} = \sum_{n=0}^{\infty} (-1)^n (z-1)^n$
Analytic: $f(z)$ is analytic at point $z_0$ if it has a derivative at each point in some neighborhood of $z_0$.
$f(z)=u(x,y)+iv(x,y)$ is analytic if and only if $v$ is a harmonic conjugate of $u$.
If $u(x,y)$ and $v(x,y)$ are harmonic functions such that $u_{xx}=-u{yy}$ and $v_{xx}=-v_{yy}$, and they satisfy the Cauchy-Reimann conditions, then $v$ is a harmonic conjugate of $u$.
Differentiable: $f(z)=u(x,y)+iv(x,y)$ is differentiable at a point $z_0$ if $f(z)$ is defined within some neighborhood of $z_0=x_0+iy_0$, $u_x$ $u_y$ $v_x$ and $v_y$ exist everywhere in the neighborhood, those first-order partial derivatives exist at $(x_0,y_0)$ and satisfy the Reimann-Cauchy conditions at $(x_0,y_0)$.
Cauchy Integral Formula:
$\int_C \frac{f(z)}{z-z_0}\,dz = 2\pi i f(z_0)$
where $z_0$ is any point interior to $C$ and $f(z)$ is analytic everywhere inside and on $C$ taken in the positive sense. Note that $f(z)$ here refers to the actual function $f(z)$, not $\frac{f(z)}{z-z_0}$
Generalized Cauchy Integral Formula:
$\int_C \frac{f(z)}{(z-z_0)^{n+1}}\,dz = \frac{2\pi i}{n!} f^{(n)}(z_0)$
(same conditions as above)
Remember, discontinuities that are roots can be calculated and factored:
$\frac{1}{z^2-w_0}=\frac{1}{(z-z_1)(z-z_2)}$
Residue at infinity:
$\def\res{\mathop{Res}\limits} \int_C f(z)\,dz = 2\pi i \,\res_{z=0}\left[\frac{1}{z^2} f\left(\frac{1}{z}\right) \right]$
A residue at $z_0$ is the $n=-1$ term of the Laurent series centered at $z_0$.
A point $z_0$ is an isolated singular point if $f(z_0)$ fails to be analytic, but is analytic at some point in every neighborhood of $z_0$, and there's a deleted neighborhood $0 < |z-z_0| < \epsilon$ of $z_0$ throughout which $f$ is analytic.
$\res_{z=z_0}\,f(z)=\frac{p(z_0)}{q'(z_0)}\text{ where }f(z) = \frac{p(z)}{q(z)}\text{ and } p(z_0)\neq 0$
$\int_C f(z)\,dz = 2\pi i \sum_{k=1}^n\,\res_{z=z_k}\,f(z)$
where $z_0$, $z_1$, $z_2$,... $z_k$ are all the singular points of $f(z)$ (which includes poles).
If a series has a finite number of $(z-z_0)^{-n}$ terms, its a pole ($\frac{1}{z^4}$ is a pole of order 3). If a function, when put into a series, has no $z^{-n}$ terms, it's a removable singularity. If it has an infinite number of $z^{-n}$ terms, its an essential singularity (meaning, you can't get rid of it).
AMath 401 - Vector Calculus and Complex Variables
$||\vec{x}||=\sqrt{x_1^2+x_2^2+ ...}$
$\vec{u}\cdot\vec{v} = ||\vec{u}||\cdot||\vec{v}|| \cos(\theta)=u_1v_1+u_2v_2+ ...$
$||\vec{u}\times\vec{v}|| = ||\vec{u}||\cdot||\vec{v}|| \sin(\theta) = \text{ area of a parallelogram}$
$\vec{u}\times\vec{v} = \begin{vmatrix} \vec{\imath} & \vec{\jmath} & \vec{k} \\ u_1 & u_2 & u_3 \\ v_1 & v_2 & v_3 \end{vmatrix}$
$\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad-bc$
$\vec{u}\cdot\vec{v}\times\vec{w} = \vec{u}\cdot(\vec{v}\times\vec{w})=\text{ volume of a parallelepiped}$
$h_?\equiv\left|\left|\frac{\partial\vec{r}}{\partial ?}\right|\right|$
$\hat{e}_r(\theta)=\frac{1}{h_r}\frac{\partial\vec{r}}{\partial r}$
$\hat{e}_r'(\theta)=\frac{d\hat{e}_r}{d\theta}=\hat{e}_{\theta}(\theta)$
$\vec{r}=r(t)\hat{e}_r(\theta(t))$
$\vec{r}'(t)=r'(t)\hat{e}_r + r(t)\frac{d\hat{e}_r}{dt}$
$\vec{r}'(t)=r'(t)\hat{e}_r + r(t)\frac{d\hat{e}_r}{d\theta}\frac{d\theta}{dt}=r'(t)\hat{e}_r + r(t)\hat{e}_{\theta} \theta'(t)$
Projection of $\vec{u}$ onto $\vec{v}$:
$||\vec{u}|| \cos(\theta) = \frac{\vec{u}\cdot\vec{v}}{||\vec{v}||}$
Arc Length:
$\int_a^b \left|\left| \frac{d\vec{r}}{dt} \right|\right| \,dt = \int_a^b ds$
Parametrization:
$s(t) = \int_a^t \left|\left|\frac{d\vec{r}}{dt}\right|\right| \,dt$
$\frac{dx}{dt}=x'(t)$
$dx = x'(t)\,dt$
$\oint x \,dy - y \,dx = \oint\left(x \frac{dy}{dt} - y \frac{dx}{dt}\right)\,dt = \oint x y'(t) - y x'(t) \,dt$
$\nabla = \frac{\partial}{\partial x}\vec{\imath} + \frac{\partial}{\partial y}\vec{\jmath} + \frac{\partial}{\partial z}\vec{k}$
$\nabla f = \left\langle \frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \right\rangle$
$D_{\vec{u}} f(\vec{P})=f'_{\vec{u}}=\nabla f \cdot \vec{u}$
$\nabla(fg)=f\nabla g + g \nabla f$
$\vec{F}(x,y,z)=F_1(x,y,z)\vec{\imath} + F_2(x,y,z)\vec{\jmath} + F_3(x,y,z)\vec{k}$
$\text{div}\, \vec{F} = \nabla \cdot \vec{F} = \frac{\partial F_1}{\partial x} + \frac{\partial F_2}{\partial y} + \frac{\partial F_3}{\partial z}$
$\text{curl}\, \vec{F} = \nabla \times \vec{F} = \left\langle \frac{\partial F_3}{\partial y} - \frac{\partial F_2}{\partial z}, \frac{\partial F_1}{\partial z} - \frac{\partial F_3}{\partial x}, \frac{\partial F_2}{\partial x} - \frac{\partial F_1}{\partial y} \right\rangle$
Line integral:
$\int_{\vec{r}(a)}^{\vec{r}(b)}\vec{F}\cdot \vec{r}'(t)\,dt = \int_{\vec{r}(a)}^{\vec{r}(b)}\vec{F}\cdot d\vec{r}$
Closed path:
$\oint \vec{F}\cdot d\vec{r}$
$d\vec{r} = \nabla\vec{r}\cdot \langle du_1,du_2,du_3 \rangle = h_1 du_1 \hat{e}_1 + h_2 du_2 \hat{e}_2 + h_3 du_3 \hat{e}_3$
$h_?= \left|\left| \frac{\partial\vec{r}}{\partial ?} \right|\right| = \frac{1}{||\partial ?||}$
$\hat{e}_?=\frac{1}{h_?}\frac{\partial\vec{r}}{\partial?}=h_?\nabla?(x,y,z)=\frac{\nabla?}{||\nabla?||}$
If $\vec{r}=\vec{r}(s)$ then
$\int_a^b\vec{F}\cdot \frac{d\vec{r}}{ds} \,ds = \int_a^b\vec{F}\cdot\vec{T} \,ds$
$\nabla f \cdot \hat{e}_?=\frac{1}{h_?}\frac{\partial f}{\partial ?}$
$\nabla f = (\nabla f \cdot \hat{e}_r)\hat{e}_r + (\nabla f \cdot \hat{e}_{\theta})\hat{e}_{\theta} = \frac{\partial f}{\partial r}\hat{e}_r + \frac{1}{r}\frac{\partial f}{\partial \theta}\hat{e}_{\theta}$
$ds = \sqrt{d\vec{r}\cdot d\vec{r}} = \left|\left| \frac{d\vec{r}}{dt}dt \right|\right| = \sqrt{h_1^2 du_1^2 + h_2^2 du_2^2+h_3^2 du_3^2}$
$Spherical: h_r=1, h_{\theta}=r, h_{\phi}=r\sin(\theta)$
$\vec{r}=\frac{\nabla f}{||\nabla f||}$
$\vec{r}=\vec{r}(u,v)$
$\vec{n}= \frac{\frac{\partial\vec{r}}{\partial u}\times\frac{\partial\vec{r}}{\partial v}}{\left|\left| \frac{\partial\vec{r}}{\partial u}\times\frac{\partial\vec{r}}{\partial v} \right|\right|}$
$\vec{F}$ is conservative if:
$\vec{F}=\nabla\phi$
$\nabla\times\vec{F}=0$
$\vec{F}=\nabla\phi \iff \nabla\times\vec{F}=0$
$\iint\vec{F}\cdot d\vec{S}$
$d\vec{S}=\left(\frac{\partial\vec{r}}{\partial u} \times \frac{\partial\vec{r}}{\partial v} \right)\,du\,dv$
$d\vec{S}=\vec{n}\,dS$
Surface Area:
$\iint \,dS$
Flux:
$\iint\vec{F}\cdot d\vec{S}$
Shell mass:
$\iint p\cdot dS$
Stokes:
$\iint(\nabla\times\vec{F})\cdot d\vec{S} = \oint\vec{F}\cdot d\vec{r}$
Divergence:
$\iiint\limits_V\nabla\cdot\vec{F}\,dV=\iint\limits_{\partial v} \vec{F}\cdot d\vec{S}$
If $z=f(x,y)$, then
$\vec{r}(x,y) = \langle x,y,f(x,y) \rangle$
$\nabla\cdot\vec{F}=\frac{1}{h_1 h_2 h_3}\left[\frac{\partial}{\partial u_1}(F_1 h_2 h_3) + \frac{\partial}{\partial u_2}(F_2 h_1 h_3) + \frac{\partial}{\partial u_3}(F_3 h_1 h_2) \right]$
$dV = \left| \frac{\partial\vec{r}}{\partial u_1}\cdot\left(\frac{\partial\vec{r}}{\partial u_2}\times\frac{\partial\vec{r}}{\partial u_3} \right) \right| du_1 du_2 du_3$
If orthogonal,
$I = \iiint\limits_V f(u_1,u_2,u_3)h_1 h_2 h_3\,du_1\,du_2\,du_3$
$(x-c_x)^2 + (y-c_y)^2 = r^2 \Rightarrow \vec{r}(t)=\langle c_x + r\cos(t),c_y+r\sin(t) \rangle$
Ellipse:
$\Rightarrow \vec{r}(t)=\langle c_x+a\cos(t), c_y+b\sin(t) \rangle$
For spherical, if $\theta$ is innermost, its max value is $\pi$, or if its on the z value.
$\vec{r}(\theta,\phi)=\langle \sin(\theta)\cos(\phi), \sin(\theta)\sin(\phi),\cos(\theta) \rangle$
Laplace Transform:
$\mathcal{L}\left[f(t)\right]=F(s)=\int_0^{\infty}e^{-st}f(t)\,dt$
$\mathcal{L}[f'(t)] = s\mathcal{L}[f(t)] - f(0) = s\cdot F(s)-f(0)$
$\mathcal{L}[f''(t)] = s^2\mathcal{L}[f(t)] - s\cdot f(0) - f'(0) = s^2\cdot F(s) - s\cdot f(0) - f'(0)$
$\mathcal{L}[0] = 0$
$\mathcal{L}[1] = \frac{1}{s}$
$\mathcal{L}[k] = \frac{k}{s}$
$\mathcal{L}[e^{at}] = \frac{1}{s-a}$
$\mathcal{L}[\cos(\omega t)] = \frac{s}{s^2 + \omega^2}$
$\mathcal{L}[\sin(\omega t)] = \frac{\omega}{s^2 + \omega^2}$
Math 461 - Combinatorial Theory I
General Pigeon: Let $n$,$m$, and $r$ be positive integers so that $n>rm$. Let us distribute $n$ balls into $m$ boxes. Then there will be at least 1 box in which we place at least $r+1$ balls.
Base Case: Prove $P(0)$ or $P(1)$ Inductive Step: Show that by assuming the inductive hypothesis $P(k)$, this implies that $P(k+1)$ must be true. Strong Induction: Show that $P(k+1)$ is true if $P(n)$ for all $n < k+1$ is true.
There are $n!$ permutations of an $n$-element set (or $n!$ linear orderings of $n$ objects)
$n$ objects sorted into $a,b,c,...$ groups have $\frac{n!}{a!b!c!...}$ permutations. This is also known as a $k$-element multiset of $n$.
Number of $k$-digit strings in an $n$-element alphabet: $n^k$. All subsets of an $n$-element set: $2^n$
Let $n$ and $k$ be positive integers such that $n \ge k$, then the number of $k$-digit strings over an $n$-element alphabet where no letter is used more than once is $\frac{n!}{(n-k)!}=(n)_k$
$\binom{n}{k} = \frac{n!}{k!(n-k)!} = \frac{(n)_k}{k!} \rightarrow$
This is the number of $k$-element subsets in $[n]$, where $[n]$ is an $n$-element set.
$\binom{n}{k} = \binom{n}{n-k}$
$\binom{n}{0} = \binom{n}{n} = \binom{0}{0} = 1$
Number of $k$-element multisets in $[n]$:
$\binom{n+k-1}{k}$
Binomial Theorem:
$(x+y)^n = \sum_{k=0}^n\binom{n}{k}x^k y^{n-k} \text{ for } n \ge 0$
Multinomial Theorem:
$(x_1 + x_2 + ... + x_k)^n = \sum_{a_1,a_2,...,a_k} \binom{n}{a_1,a_2,...,a_k} x_1^{a_1} x_2^{a_2} ... x_k^{a_k}$
$\binom{n}{k} + \binom{n}{k+1} = \binom{n+1}{k+1} \text{ for } n,k \ge 0$
$\binom{k}{k} + \binom{k+1}{k} + ... + \binom{n}{k} = \binom{n+1}{k+1} \text{ for } n,k \ge 0$
$\binom{n}{k} \le \binom{n}{k} \text{ if and only if } k \le \frac{n-1}{2} \text{ and } n=2k+1$
$\binom{n}{k} \ge \binom{n}{k} \text{ if and only if } k \ge \frac{n-1}{2} \text{ and } n=2k+1$
$\binom{n}{a_1,a_2,...,a_k} = \frac{n!}{a_1!a_2!...a_k!}$
$\binom{n}{a_1,a_2,...,a_k} = \binom{n}{a_1}\cdot \binom{n-a_1}{a_2} \cdot ... \cdot \binom{n-a_1-a_2-...-a_{k-1}}{a_k} \text{ if and only if } n=\sum_{i=1}^k a_i$
$\binom{m}{k} = \frac{m(m-1)...(m-k+1)}{k!} \text{ for any real number } m$
$(1+x)^m = \sum_{n\ge 0}^{\infty} \binom{m}{n}x^n$
$\sum_{k=0}^n (-1)^k\binom{n}{k} = 0 \text{ for } n \ge 0$
$2^n = \sum_{k=0}^n \binom{n}{k} = 0 \text{ for } n \ge 0$
$\sum_{k=1}^n k\binom{n}{k} = n 2^{n-1} \text{ for } n \ge 0$
$\binom{n+m}{k} = \sum_{i=0}^k \binom{n}{i} \binom{n}{k-i} \text{ for } n,m,k \ge 0$
$|E| = \frac{1}{2}\sum_{v\in V} deg(v)$
or, the number of edges in a graph is half the sum of its vertex degrees.
Compositions: $n$ identical objects $k$ distinct boxes $\binom{n-1}{k-1}$ $n$ identical objects any number of distinct boxes $2^{n-1}$ Weak Compositions: (empty boxes allowed) $n$ identical objects $k$ distinct boxes $\binom{n+k-1}{k-1}$ $n$ distinct objects $k$ distinct boxes $k^n$
Split $n$ people into $k$ groups of $\frac{n}{k}$:
Unordered:
$\frac{n!}{\left(\left(\frac{n}{k}\right)!\right)^k k!}$
Ordered:
$\frac{n!}{\left(\left(\frac{n}{k}\right)!\right)^k}$
Steps from (0,0) to (n,k) on a lattice:
$\binom{n+k}{k}$
Ways to roll $n$ dice so all numbers 1-6 show up at least once: $6^n - \binom{6}{5}5^n + \binom{6}{4}4^n + \binom{6}{3}3^n + \binom{6}{2}2^n + \binom{6}{1}$
The Sieve: $|A_1| + |A_2| - |A_1\cap A_2|$ or $|A_1| + |A_2| + |A_3| - |A_1\cap A_2| - |A_1\cap A_3| - |A_2\cap A_3| + |A_1\cap A_2\cap A_3|$
Also, $|S - (S_A\cap S_B\cap S_C)| = |S| - |S_A| - |S_B| - |S_C| + |S_A\cap S_B| + |S_A\cap S_C| + |S_B\cap S_C| - |S_A\cap S_B\cap S_C|$
Graphs: A simple graph has no loops (edges connecting a vertex to itself) or multiple edges between the same vertices. A walk is a path through a series of connected edges. A trail is a walk where no edge is traveled on more than once. A closed trail starts and stops on the same vertex. A Eulerian trail uses all edges in a graph. A trail that doesn't touch a vertex more than once is a path. $K_n$ is the complete graph on $n$-vertices.
If one can reach any vertex from any other on a graph $G$, then $G$ is a connected graph.
A connected graph has a closed Eulerian trail if and only if all its vertices have even degree. Otherwise, it has a Eulerian trail starting on S and ending on T if only S and T have odd degree.
In a graph without loops there are an even number of vertices of odd-degree. A cycle touches all vertices only once, except for the vertex it starts and ends on. A Hamiltonian cycle touches all vertices on a graph.
Let $G$ be a graph on $n \ge 3$ vertices, then $G$ has a Hamiltonian cycle if all vertices in $G$ have degree equal or greater than $n/2$. A complete graph $K_n$ has $\binom{n}{k}\frac{(k-1)!}{2}$ cycles of $k$-vertices.
Total Cycles:
$\sum_{k=3}^n\binom{n}{k}\frac{(k-1)!}{2}$
Hamiltonian cycles:
$\frac{(n-1)!}{2}$
Two graphs are the same if for any pair of vertices, the number of edges connecting them is the same in both graphs. If this holds when they are unlabeled, they are isomorphic.
A Tree is a minimally connected graph: Removing any edge yields a disconnected graph. Trees have no cycles, so any connected graph with no cycles is a tree.
All trees on $n$ vertices have $n-1$ edges, so any connected graph with $n-1$ edges is a tree.
Let $T$ be a tree on $n \ge 2$ vertices, then T has at least two vertices of degree 1.
Let $F$ be a forest on $n$ vertices with $k$ trees. Then F has $n-k$ edges.
Cayley's formula: The number of all trees with vertex set $[n]$ is $A_n = n^{n-2}$
A connected graph $G$ can be drawn on a plane so that no two edges intersect, then G is a planar graph.
A connected planar graph or convex polyhedron satisfies: Vertices + Faces = Edges + 2
$K_{3,3}$ and $K_5$ are not planar, nor is any graph with a subgraph that is edge-equivalent to them.
A convex Polyhedron with V vertices, E edges, and F faces satisfies: $3F \le 3E$, $3V \le 3E$, $E \le 3V-6$, $E \le 3F-6$, one face has at most 5 edges, and one vertex has at most degree 5.
$K_{3,3}$ has 6 vertices and 9 edges
A graph on $n$-vertices has $\binom{n}{2}$ possible edges.
If a graph is planar, then $E \le 3V - 6$. However, some non-planar graphs, like $K_{3,3}$, satisfy this too.
Prüfer code: Remove the smallest vertex from the graph, write down only its neighbor's value, repeat.
Math 462 - Combinatorial Theory II
All labeled graphs on $n$ vertices:
$2^{\binom{n}{2}}$
There are $(n-1)!$ ways to arrange $n$ elements in a cycle.
Given $h_n=3 h_{n-1} - 2 h_{n-2}$, change to $h_{n+2}=3 h_{n+1} - 2 h_n$, then $h_{n+2}$ is $n=2$ so multiply by $x^{n+2}$
$\sum h_{n+2}x^{n+2} = 3 \sum h_{n+1}x^{n+2} - 2 \sum h_n x^{n+2}$
Then normalize to
$\sum_{n=2}^{\infty}h_n x^n$
by subtracting $h_0$ and $h_1$
$\sum h_n x^n - x h_1 - h_0 = 3 x \sum h_{n+1}x^{n+1} - 2 x^2 \sum h_n x^n$
$G(x) - x h_1 - h_0 = 3 x (G(x)-h_0) - 2 x^2 G(x)$
Solve for:
$G(x) = \frac{1-x}{2x^2-3x+1} = \frac{1}{1-2x} = \sum (2x)^n$
$G(x) = \sum(2x)^n = \sum 2^n x^n = \sum h_n x^n \rightarrow h_n=2^n$
$\sum_{n=0}^{\infty} \frac{x^n}{n!} = e^x$
$\sum_{n=0}^{\infty} (cx)^n = \frac{1}{1-cx}$
Also,
$2e_1 + 5e_2 = n \rightarrow \sum h_n x^n = \sum x^{2e_1+5e_2} = \sum x^{2e_1} x^{5e_2} = \left(\sum^{\infty} x^{2e_1}\right)\left(\sum^{\infty} x^{5e_2}\right)=\frac{1}{(1-x^2)(1-x^5)}$
$S(n,k)$: A Stirling number of the second kind is the number of nonempty partitions of $[n]$ into k blocks where the order of the blocks doesn't matter. $S(n,k)=S(n-1,k-1)+k S(n-1,k)$, $S(n,n-2) = \binom{n}{3} + \frac{1}{2}\binom{k}{2}\binom{n+2}{2}$
Bell Numbers:
$B(n) = \sum_{i=0}^n S(n,i)$
, or the number of all partitions of $[n]$ into nonempty parts (order doesn't matter).
Catalan Number $C_n$:
$\frac{1}{n+1}\binom{2n}{n}$
derived from
$\sum_{n \ge 1} c_{n-1} x^n = x C(x) \rightarrow C(x) - 1 = x C(x)\cdot C(x) \rightarrow C(x) = \frac{1 - \sqrt{1-4x}}{2x}$
Products: Let $A(n) = \sum a_n x^n$ and $B(n) = \sum b_n x^n$. Then $A(x)B(x)=C(x)=\sum c_n x^n$ where
$c_n = \sum_{i=0}^n a_i b_{n-i}$
Cycles: The number of $n$-permuatations with $a_i$ cycles of length $i \in [n]$ is \frac{n!}{a_1!a_2!...a_n!1^{a_1}2^{a_2}...n^{a_n}}
The number of n-permutations with only one cycle is $(n-1)!$
$c(n,k)$: The number of $n$-permutations with $k$-cycles is called a signless stirling number of the first kind.
$c(n,k) = c(n-1,k-1) + (n-1) c(n-1,k)$
$c(n,n-2)= 2\binom{n}{3} + \frac{1}{2}\binom{n}{2}\binom{n-2}{2}$
$s(n,k) = (-1)^{n-k} c(n,k)$ and is called a signed stirling number of the first kind.
Let $i \in [n]$, then fro all $k \in [n]$, there are $(n-1)!$ permutations that contain $i$ in a $k$-cycle.
$T(n,k)=\frac{k-1}{2k}n^2 - \frac{r(k-r)}{2k}$
Let Graph $G$ have $n$ vertices and more than $T(n,k)$ edges. Then $G$ contains a $K_{k+1}$ subgraph, and is therefore not $k$-colorable.
$N(T)$ = all neighbors of the set of vertices $T$
$a_{s,d} = \{ s,s+d,s+2d,...,s+(n-1)d \}$
$\chi(H)$: Chromatic number of Graph $H$, or the smallest integer $k$ for which $H$ is $k$-colorable.
A 2-colorable graph is bipartite and can divide its vertices into two disjoint sets.
A graph is bipartite if and only if it does not contain a cycle of odd length.
A bipartite graph has at most $\frac{n^2}{4}$ edges if $n$ is even, and at most $\frac{n^2 - 1}{4}$ edges if $n$ is odd.
If graph $G$ is not an odd cycle nor complete, then $\chi(G) \le$ the largest vertex degree $\ge 3$.
A bipartite graph on $n$ vertices with a max degree of $k$ has at most $k\cdot (n-k)$ edges.
A tree is always bipartite (2-colorable).
Philip Hall's Theorem: Let a bipartite graph $G=(X,Y)$. Then $X$ has a perfect matching to $Y$ if and only if for all $T \subset X, |T| \le |N(T)|$
$R(k,l):$ The Ramsey Number $R(k,l)$ is the smallest integer such that any 2-coloring of a complete graph on $R(k,l)$ vertices will contain a red $k$-clique or blue $l$-clique. A $k$-clique is a complete subgraph on $k$ vertices.
$R(k,l) \le R(k,l-1) + R(k-1,l)$
$R(k,k) \le 4^{k-1}$
$R(k,l) \le \binom{k+l-2}{l-1}$
Let $P$ be a partially ordered set (a "poset"), then:
1) $\le$ is reflexive, so $x \le x$ for all $x \in P$
2) $\le$ is transitive, so that if $x \le y$ and $y \le z$ then $x \le z$
3) $\le$ is anti-symmetric, such that if $x\le y$ and $y \le x$, then $x=y$
Let $P$ be the set of all subsets of $[n]$, and let $A \le B$ if $A \subset B$. Then this forms a partially ordered set $B_n$, or a Boolean Algebra of degree $n$.
$E(X)=\sum_{i \in S} i\cdot P(X=i)$
A chain is a set with no two incomparable elements. An antichain has no comparable elements.
Real numbers are a chain. $\{ (2,3), (1,3), (3,4), (2,4) \}$ is an antichain in $B_4$, since no set contains another.
Dilworth: In a finite partially ordered set $P$, the size of any maximum antichain is equal to the number of chains in any chain cover.
Weak composition of n into 4 parts: $a_1 + a_2 + a_3 + a_4 = n$
Applying these rules to the above equation: $a_1 \le 2, a_2\text{ mod }2 \equiv 0, a_3\text{ mod }2 \equiv 1, a_3 \le 7, a_4 \ge 1$
Yields the following:
$a_1 + 2a_2 + (2a_3 + 1) + a_4 = n$
$(\sum_0^2 x^{a_1})(\sum_0^{\infty} x^{2a_2})(\sum_0^3 x^{2a_3 + 1})(\sum_1^{\infty} x^{a_4})=\frac{1+x+x^2}{1-x^2}(x+x^3+x^5+x^7)\left(\frac{1}{1-x} - 1\right)$
Math 394 - Probability I
both E and F:
$P(EF) = P(E\cap F)$
If E and F are independent, then
$P(E\cap F) = P(E)P(F)$
$P(F) = P(E) + P(E^c F)$ $P(E\cup F) = P(E) + P(F) - P(EF)$
$P(E\cup F \cup G) = P(E) + P(F) + P(G) - P(EF) - P(EG) - P(FG) + P(EFG)$
E occurs given F:
$P(E|F)=\frac{P(EF)}{P(F)}$
$P(EF)=P(FE)=P(E)P(F|E)$
Bayes formula:
$P(E)=P(EF)+P(EF^c)$
$P(E)=P(E|F)P(F) + P(E|F^c)P(F^c)$
$P(E)=P(E|F)P(F) + P(E|F^c)[1 - P(F)]$
$P(B|A)=P(A|B)\frac{P(B)}{P(A)}$
The odds of A:
$\frac{P(A)}{P(A^c)} = \frac{P(A)}{1-P(A)}$
$P[\text{Exactly } k \text{ successes}]=\binom{n}{k}p^k(1-p)^{n-k}$
$P(n \text{ successes followed by } m \text{ failures}) = \frac{p^{n-1}(1-q^m)}{p^{n-1}+q^{m-1}-p^{n-1}q^{m-1}}$
where $p$ is the probability of success, and $q=1-p$ for failure.
$\sum_{i=1}^{\infty}p(x_i)=1$
where $x_i$ is the $i^{\text{th}}$ value that $X$ can take on.
$E[X] = \sum_{x:p(x) > 0}x p(x) \text{ or }\sum_{i=1}^{\infty} x_i p(x_i)$
$E[g(x)]=\sum_i g(x_i)p(x_i)$
$E[X^2] = \sum_i x_i^2 p(x_i)$
$Var(X) = E[X^2] - (E[X])^2$
$Var(aX+b) = a^2 Var(X)$
for constant $a,b$
$SD(X) = \sqrt{Var(X)}$
Binomial random variable $(n,p)$:
$p(i)=\binom{n}{i}p^i(1-p)^{n-i}\; i=0,1,...,n$
where $p$ is the probability of success and $n$ is the number of trials.
Poisson:
$E[X] = np$
$E[X^2] = \lambda(\lambda + 1)$
$Var(X)=\lambda$
$P[N(t)=k)] = e^{-\lambda t}\frac{(\lambda t)^k}{k!} \: k=0,1,2,...$
where $N(t)=[s,s+t]$
$E[X] = \int_{-\infty}^{\infty} x f(x) \,dx$
$P\{X \le a \} = F(a) = \int_{-\infty}^a f(x) \,dx$
$\frac{d}{da} F(g(a))=g'(a)f(g(a))$
$E[g(X)]=\int_{-\infty}^{\infty} g(x) f(x) \,dx$
$P\{ a \le X \le b \} = \int_a^b f(x) \,dx$
Uniform:
$f(x) = \frac{1}{b-a} \text{ for } a\le x \le b$
$E[X] = \frac{a+b}{2}$
$Var(X) = \frac{(b-a)^2}{12}$
Normal:
$f(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \text{ for } -\infty \le x \le \infty$
$E[X] = \mu$
$Var(X) = \sigma^2$
$Z = \frac{X-\mu}{\sigma}$
$P\left[a \le X \le b\right] = P\left[ \frac{a - \mu}{\sigma} < \frac{X - \mu}{\sigma} < \frac{b - \mu}{\sigma}\right] = \phi\left(\frac{b-\mu}{\sigma}\right) - \phi\left(\frac{a-\mu}{\sigma}\right)$
$\phi(x) = GRAPH$
$P[X \le a]=\phi\left(\frac{a-\mu}{\sigma}\right)$
$P[Z > x] = P[Z \le -x]$
$\phi(-x)=1-\phi(x)$
$Y=f(X)$
$F_Y=P[Y\le a]= P[f(X) \le a] = P[X \le f^{-1}(a)]=F_x(f^{-1}(a))$
$f_Y=\frac{d}{da}(f^{-1}(a))f_x(f^{-1}(a))$
$Y = X^2$
$F_Y = P[Y \le a] = P[X^2 \le a] = P[-\sqrt{a} \le X \le \sqrt{a}] = \int_{-\sqrt{a}}^{\sqrt{a}} f_X(x) dx$
$f_Y = \frac{d}{da}(F_Y)$
$N(k) \ge x \rightarrow 1 - N(k) < x$
$P(A \cap N(k) \ge x) = P(A) - P(A \cap N(k) < x)$
Discrete:
$P(X=1) = P(X \le 1) - P(X < 1)$
Continuous:
$P(X \le 1) = P(X < 1)$
Exponential:
$f(x) = \lambda e^{-\lambda x} \text{ for } x \ge 0$
$E[X] = \frac{1}{\lambda}$
$Var(X) = \frac{1}{\lambda^2}$
Gamma:
$f(x) = \frac{\lambda e^{-\lambda x} (\lambda x)^{\alpha - 1}}{\Gamma(\alpha)}$
$\Gamma(\alpha)=\int_0^{\infty} e^{-x}x^{\alpha-1} \,dx$
$E[X] = \frac{\alpha}{\lambda}$
$Var(X) = \frac{\alpha}{\lambda^2}$
$E[X_iX_j] = P(X_i = k \cap X_j=k) = P(X_i = k)P(X_j = k|X_i=k)$
Stat 390 - Probability and Statistics for Engineers and Scientists
$p(x) = \text{categorical (discrete)}$
$f(x) = \text{continuous}$
$\mu_x=E[x]$ $\sigma_x^2 = V[x]$ Binomial $n\pi$ $n\pi (1-\pi)$ Normal $\mu$ $\sigma^2$ Poisson $\lambda$ $\lambda$ Exponential $\frac{1}{\lambda}$ $\frac{1}{\lambda^2}$ Uniform $\frac{b+a}{2}$ $\frac{(b-a)^2}{12}$
Binomial $p(x) = \binom{n}{x} \pi^x (1 - \pi)^{n-x}$ Poisson $p(x) = \frac{e^{-\lambda} \lambda^x}{x!}$ Normal $f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{1}{2} \left(\frac{x - \mu}{\sigma} \right)}$ Exponential $f(x) = \lambda e^{-\lambda x}$ Uniform $f(x) = \frac{1}{b-a}$
$\pi = p =$ proportion
$n\pi = C = \lambda =$ mean
$\mu = n \pi$
$\sigma^2 = n \pi (1 - \pi)$
Sample mean: $\bar{x} =$ $\frac{1}{n} \sum_{i=1}^n x_i$ Sample median: $\tilde{x} = \text{if } n \text{ is odd,} \left(\frac{n+1}{2}\right)^{\text{th}} \text{ value}$ $\text{if } n \text{ is even, average} \frac{n}{2} \text{ and } \frac{n}{2}+1$
Sample variance: $s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2 = \frac{S_{xx}}{n-1} = \sum x_i^2 - \frac{1}{n} \left( \sum x_i \right)^2$ Standard deviation: $s = \sqrt{s^2}$
low/high quartile: median of lower/upper half of data. If $n$ is odd, include median in both.
low = 1st quartile high = 3rd quartile median = 2nd quartile
IQR: high - low quartiles
range: max - min
Total of something: $\bar{x} n$
An outlier is any data point outside the range defined by IQR $\cdot 1.5$
An extreme is any data point outside the range defined by IQR $\cdot 3$
$\mu_{\bar{x}} = \mu = \bar{x}$
$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$
$\mu_p = p = \pi$
$\sigma_p = \sqrt{\frac{p(1-p)}{n}}$
$p(x)$ distribution [discrete] mean: $\mu_x = \sum x \cdot p(x) = E[x]$ variance: $\sigma_x^2 = \sum(x-\mu_x)^2 p(x) = V[x]$ $f(x)$ distribution [continuous] mean: $\mu_x = \int_{-\infty}^{\infty} x \cdot f(x)$ median: $\tilde{\mu} \rightarrow \int_{-\infty}^{\tilde{\mu}} f(x) = \int_0^{\tilde{\mu}} f(x) = 0.5$ variance: $\sigma^2 = \int_{-\infty}^{\infty} (x =\mu_x)\cdot f(x)$ Normal $k = \frac{\mu + k \sigma - \mu}{\sigma}$standardize: $\frac{x - \mu}{\sigma}$$-k = \frac{\mu - k \sigma - \mu}{\sigma}$upper quartile: $\mu + 0.675\sigma$lower quartile: $\mu - 0.675\sigma$ Exponential $-ln(c) \cdot \frac{1}{\lambda} \text{ where c is the quartile }(0.25,0.5,0.75)$
$S_{xx} = \sum x_i^2 - \frac{1}{n}\left(\sum x_i\right)^2 = \sum(x_i - \bar{x})^2$
$S_{yy} = \sum y_i^2 - \frac{1}{n}\left(\sum y_i\right)^2 = \sum(y_i - \bar{y})^2$
$S_{xy} = \sum{x_i y_i} - \frac{1}{n}\left(\sum x_i\right)\left(\sum y_i\right)$ $\text{SSResid} = \text{SSE (error sum of squares)} = \sum(y_i - \hat{y}_i)^2 = S_{yy} - b S_{xy}$
$\text{SSTo} = \text{SST} = S_{yy} = \text{Total sum of squares} = \text{SSRegr} + \text{SSE} = \text{SSTr} + \text{SSE} = \sum_i^k \sum_j^n (x_{ij} - \bar{\bar{x}})^2$
$\text{SSRegr} = \text{regression sum of squares}$
$r^2 = 1 - \frac{\text{SSE}}{\text{SST}} = \frac{\text{SSRegr}}{\text{SST}} = \text{coefficient of determination}$
$r = \frac{S_{xy}}{\sqrt{S_{xx}}\sqrt{S_{yy}}}$
$\hat{\beta} = \frac{S_{xy}}{S_{xx}}$
$\hat{\alpha} = \bar{y} - \beta\bar{x}$
prediction:
$\hat{\alpha} = \bar{y} - \beta\bar{x}$
Percentile ($\eta_p$):
$\int_{-\infty}^{\eta_p} f(x) = p$
MSE (Mean Square Error) =
$\frac{1}{n} SSE = \frac{1}{n}\sum (y_i-\hat{y}_i)^2 = \frac{1}{n} \sum (y_i - \alpha - \beta x_i)^2$
MSTr (Mean Square for treatments)
ANOVA
$SST = SS_{\text{explained}} + SSE$
$R^2 = 1 - \frac{SSE}{SST}$
$\sum(y_i - \bar{y})^2 = \sum(\hat{y}_i - \bar{y})^2 + \sum(y_i - \hat{y}_i)^2$
$s_e^2 = \frac{SSE}{n-2} \text{ or } \frac{SSE}{n-(k+1)}$
$R_{adj}^2 = 1-\frac{SSE(n-1)}{SST(n-(k+1))}$
$H_0: \mu_1 = \mu_2 = .. = \mu_k$
$\bar{\bar{x}} = \left(\frac{n_1}{n}\right)\bar{x}_1 + \left(\frac{n_2}{n}\right)\bar{x}_2 + ... + \left(\frac{n_k}{n}\right)\bar{x}_k$
$SSTr = n_1(\bar{x}_1 - \bar{\bar{x}})^2 + n_2(\bar{x}_2 - \bar{\bar{x}})^2 + ... + n_k(\bar{x}_k - \bar{\bar{x}})^2$
Sources df SS MS F Between Samples $k-1$ SSTr MSTr $\frac{\text{MSTr}}{\text{MSE}}$ Within Samples $n-k$ SSE MSE Total $n-1$ SST
One-sample t interval:
$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$
(CI)
Prediction interval:
$\bar{x} \pm t^* s\sqrt{1+\frac{1}{n}}$
(PI)
Tolerance interval:
$\bar{x} \pm k^* s$
Difference t interval:
$\bar{x}_1 - \bar{x}_2 \pm t^*\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$
$R^2 = 1 - \left(\frac{n-1}{n-(k+1)}\right) \frac{SSE}{SST}$
Type I error: Reject $H_0$ when true; If the F-test p-value is small, it's useful.
Type II error: Don't reject $H_0$ when false.
B(Type II) =
$z^* \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$
Simple linear regression: $y = \alpha + \beta x$
General multiple regression: $y = \alpha + \beta_1 x_1 + ... + \beta_k x_k$
Prediction error: $\hat{y} - y^* = \sqrt{s_{\hat{y}}^2 + s_e^2} \cdot t$
$t = \frac{\hat{y}-y^*}{\sqrt{s_{\hat{y}}^2 + s_e^2}}$
$P(\hat{y} - y^* > 11) = P\left(\sqrt{s_{\hat{y}}^2 + s_e^2} \cdot t > 11\right) = P\left(t > \frac{11}{\sqrt{s_{\hat{y}}^2 + s_e^2}}\right)$
$\mu_{\hat{x}_1 - \hat{x}_2} = \mu_{\hat{x}_1} - \mu_{\hat{x}_2} = \mu_1 - \mu_2$
$\sigma_{\hat{x}_1 - \hat{x}_2} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$
$\hat{x}_1 - \hat{x}_2 \pm z^* \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$
To test if $\mu_1 = \mu_2$, use a two-sample t test with $\delta = 0$
If you're looking for the true average, it's a CI, not the standard deviation about the regression.
A large n value may indicate a z--test, but you must think about whether or not its paired or not paired.
A hypothesis is only valid if it tests a population parameter. Do not extrapolate outside of a regression analysis unless you use a future predictor.
F-Test
$F = \frac{MSRegr}{MSE}$
$MSRegr = \frac{SSRegr}{k}$
$MSResid = \frac{SSE}{n - (k+1)}$
$H_0: \beta_1=\beta_2=...=\beta_k=0$
Chi-Squared ($\chi^2$)
$H_0: \pi_1 = \frac{\hat{n}_1}{n_1},\pi_2 = \frac{\hat{n}_2}{n_2}, ..., \pi_k = \frac{\hat{n}_k}{n_k}$
$\chi^2 = \sum_{i=1}^k \frac{(n_i - \hat{n}_i)^2}{\hat{n}_i} = \sum \left(\frac{\text{observed - expected}}{\text{expected}}\right)$
Linear Association Test
$H_0: p=0$
$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$
$\sigma_{\hat{y}} = \sigma \sqrt{\frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{xx}} }$
$\mu_{\hat{y}} = \hat{y} = \alpha + \beta x^*$
$\hat{y} \pm t^* s_{\hat{y}} df = n-2 \text{ for a mean y value (population)}$
$\hat{y} \pm t^* \sqrt{s_e^2 + s_{\hat{y}}^2} df=n-2 \text{ for single future y-values (PI)}$
Paired T-test
$\bar{d} = \bar{(x-y)}$
$t = \frac{\bar{d} - \delta}{\frac{s_d}{\sqrt{n}}}$
$\sigma_d = \sigma \text{ of x-y pairs } = s_d$
Large Sample:
$z = \frac{\bar{x} - 0.5}{\frac{s}{\sqrt{n}}}$
$\text{P-value } \le \alpha$
Small Sample:
$z = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$
$df = n-1$
Difference:
$H-0: \mu_1 - \mu_2 = \delta$
$t = \frac{\bar{x}_1 - \bar{x}_2 - \delta}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$
$df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)}{\frac{1}{n_1-1} \left(\frac{s_1^2}{n_1}\right)^2 + \frac{1}{n_2-1} \left(\frac{s_2^2}{n_2}\right)^2 }$ | {"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": 0.8216547966003418, "perplexity": 524.9026195716284}, "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/1512948567785.59/warc/CC-MAIN-20171215075536-20171215095536-00029.warc.gz"} |
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# New perspectives on spinal motor systems
## Key Points
• Traditionally, the spinal cord is assigned a subservient role during the production of movement. This review challenges this idea by presenting evidence that the spinal cord is an active participant in complex functions of motor control.
• Planning: In contrast to previous models, which suggest that the spinal cord only functions during the final execution of movement, recent experiments have shown that spinal cord neurons are also active during preparation for movement
• Plasticity: Recent work indicates that spinal motor systems contribute to the functional plasticity of movement. Both the acquisition and expression of motor adaptation require an interaction between spinal and supraspinal systems.
• Organization: Spinal motor systems have a high degree of organization, suggesting that supraspinal systems must take this organization into account when producing movement. A recent hypothesis is discussed that suggests that spinal motor systems are organized into a small number of behavioural subunits, or spinal modules', that can be flexibly combined by supraspinal systems to produce a range of movements.
• These new data are now prompting further investigations of the interaction between spinal and supraspinal systems, and their relative contributions to the complexities of movement.
## Abstract
The production and control of complex motor functions are usually attributed to central brain structures such as cortex, basal ganglia and cerebellum. In traditional schemes the spinal cord is assigned a subservient function during the production of movement, playing a predominantly passive role by relaying the commands dictated to it by supraspinal systems. This review challenges this idea by presenting evidence that the spinal motor system is an active participant in several aspects of the production of movement, contributing to functions normally ascribed to higher' brain regions.
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## References
1. 1
Maier, M. A., Perlmutter, S. I. & Fetz, E. E. Response patterns and force relations of monkey spinal interneurons during active wrist movement. J. Neurophysiol. 80, 2495–2513 (1998).
2. 2
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## Acknowledgements
We are grateful to Ole Kiehn for comments on an earlier version of this review. Work in the Bizzi laboratory is supported by the NIH.
Authors
## Glossary
INTERNAL MODEL
A representation used by the nervous system to account for the properties of the motor apparatus and the environment. Such properties could include features of the limbs, such as their lengths and their masses, and could also include features of an object to be manipulated.
SET-RELATED ACTIVITY
Neuronal activity that reflects the behavioural set' of the animal, which can include information about a planned movement or about the state of readiness of the animal.
PARALYSED DECEREBRATE PREPARATIONS
Eliminates movement of the animal. This mechanical stabilization can be accomplished by the application of paralytic agents. This paralysis is often accompanied by a precollicular decerebration in which all brain regions rostral to the superior colliculus are removed.
SUPRASPINAL SYSTEMS
The many regions of the brain that interact with the spinal cord. These systems either receive sensory information from the spinal cord or transmit information to the spinal cord.
DORSAL SPINOCEREBELLAR TRACT
A system of neurons located within the spinal cord, which receive, among other information, sensory information from muscle afferents in the limb and transmit this information to the cerebellum.
VISUALLY GUIDED REACHING
Movements of the arm that are regulated by visual feedback of the target and of the limb.
GLYCINE-MEDIATED INHIBITION
In the spinal cord, neuronal inhibition is largely mediated by the neurotransmitter glycine. This inhibition can be blocked by the neuroconvulsant strychnine.
MOTOR PERTURBATION
A procedure that results in the disturbance of the normal characteristics of movement. Such perturbations could be induced by the application of a torque pulse during the movement, an alteration in the visual feedback from the limb, or the denervation of a muscle.
KINEMATIC AND DYNAMIC PROPERTIES
Kinematic properties describe the visible aspects of the limb, such as the length of the links, the angles of the joints, or the position of the hand. Dynamic properties describe the forces and torques produced that underlie visible movement.
FEEDFORWARD ANTICIPATORY ACTIVATION
A movement or muscle activation pattern that corrects for a predicted perturbation before the actual perturbation. This is in contrast to a feedback activation which is a response to the sensory signals resulting from the perturbation.
SPINALIZATION
A surgical separation of the spinal cord from the rest of the brain.
SPINAL INTERNEURONAL SYSTEMS
The set of neurons within the spinal cord that are involved in processing information transmitted to the spinal cord, either from the periphery or from supraspinal systems.
UNIT BURST GENERATORS
Grillner's hypothesis for the spinal production of behaviour. Each spinal unit' is proposed to control a small set of synergist muscles acting around specific joints, which can be coupled in many ways to produce a range of rhythmic behaviours.
WIPING REFLEX
The scratch reflex in the frog in which an irritant is removed from different regions of the body by limb movements that wipe' the irritant off the skin.
VESTIBULAR STIMULATION
The vestibular system senses changes in head orientation, which are produced by head movements or changes in the position of the head with respect to gravity.
PRINCIPLE COMPONENTS
A computational analysis that can be used to assess the dimensionality of a data set.
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Bizzi, E., Tresch, M., Saltiel, P. et al. New perspectives on spinal motor systems. Nat Rev Neurosci 1, 101–108 (2000). https://doi.org/10.1038/35039000
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https://worldwidescience.org/topicpages/g/gray+image+encryption.html | #### Sample records for gray image encryption
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In optical encryption systems, speckle noise is one major challenge in obtaining high quality decrypted images. This problem can be addressed by employing a QR code based noise-free scheme. Previous works have been conducted for optically encrypting a few characters or a short expression employing QR codes. This paper proposes a practical scheme for optically encrypting and decrypting a gray-scale image based on QR codes for the first time. The proposed scheme is compatible with common QR code generators and readers. Numerical simulation results reveal the proposed method can encrypt and decrypt an input image correctly.
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Science.gov (United States)
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2015-12-01
Full Text Available The Steganography is an art and science of hiding information by embedding messages within other, seemingly harmless messages and lots of researches are working in it. Proposed system is using AES Algorithm and Lossy technique to overcome the limitation of previous work and increasing the process’s speed. The sender uses AES Algorithm to encrypt message and image, then using LSB technique to hide encrypted data in encrypted message. The receive get the original data using the keys that had been used in encryption process. The proposed system has been implemented in NetBeans 7.3 software uses image and data in different size to find the system’s speed.
11. Simultaneous transmission for an encrypted image and a double random-phase encryption key
Science.gov (United States)
Yuan, Sheng; Zhou, Xin; Li, Da-Hai; Zhou, Ding-Fu
2007-06-01
We propose a method to simultaneously transmit double random-phase encryption key and an encrypted image by making use of the fact that an acceptable decryption result can be obtained when only partial data of the encrypted image have been taken in the decryption process. First, the original image data are encoded as an encrypted image by a double random-phase encryption technique. Second, a double random-phase encryption key is encoded as an encoded key by the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. Then the amplitude of the encrypted image is modulated by the encoded key to form what we call an encoded image. Finally, the encoded image that carries both the encrypted image and the encoded key is delivered to the receiver. Based on such a method, the receiver can have an acceptable result and secure transmission can be guaranteed by the RSA cipher system.
12. A new chaotic algorithm for image encryption
International Nuclear Information System (INIS)
Gao Haojiang; Zhang Yisheng; Liang Shuyun; Li Dequn
2006-01-01
Recent researches of image encryption algorithms have been increasingly based on chaotic systems, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper presents a new nonlinear chaotic algorithm (NCA) which uses power function and tangent function instead of linear function. Its structural parameters are obtained by experimental analysis. And an image encryption algorithm in a one-time-one-password system is designed. The experimental results demonstrate that the image encryption algorithm based on NCA shows advantages of large key space and high-level security, while maintaining acceptable efficiency. Compared with some general encryption algorithms such as DES, the encryption algorithm is more secure
13. Image encryption using the fractional wavelet transform
International Nuclear Information System (INIS)
Vilardy, Juan M; Useche, J; Torres, C O; Mattos, L
2011-01-01
In this paper a technique for the coding of digital images is developed using Fractional Wavelet Transform (FWT) and random phase masks (RPMs). The digital image to encrypt is transformed with the FWT, after the coefficients resulting from the FWT (Approximation, Details: Horizontal, vertical and diagonal) are multiplied each one by different RPMs (statistically independent) and these latest results is applied an Inverse Wavelet Transform (IWT), obtaining the encrypted digital image. The decryption technique is the same encryption technique in reverse sense. This technique provides immediate advantages security compared to conventional techniques, in this technique the mother wavelet family and fractional orders associated with the FWT are additional keys that make access difficult to information to an unauthorized person (besides the RPMs used), thereby the level of encryption security is extraordinarily increased. In this work the mathematical support for the use of the FWT in the computational algorithm for the encryption is also developed.
14. Chaos-based image encryption algorithm
International Nuclear Information System (INIS)
Guan Zhihong; Huang Fangjun; Guan Wenjie
2005-01-01
In this Letter, a new image encryption scheme is presented, in which shuffling the positions and changing the grey values of image pixels are combined to confuse the relationship between the cipher-image and the plain-image. Firstly, the Arnold cat map is used to shuffle the positions of the image pixels in the spatial-domain. Then the discrete output signal of the Chen's chaotic system is preprocessed to be suitable for the grayscale image encryption, and the shuffled image is encrypted by the preprocessed signal pixel by pixel. The experimental results demonstrate that the key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior
15. Quantum Color Image Encryption Algorithm Based on A Hyper-Chaotic System and Quantum Fourier Transform
Science.gov (United States)
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-12-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
16. Chaotic Image Encryption Algorithm Based on Circulant Operation
Directory of Open Access Journals (Sweden)
Xiaoling Huang
2013-01-01
Full Text Available A novel chaotic image encryption scheme based on the time-delay Lorenz system is presented in this paper with the description of Circulant matrix. Making use of the chaotic sequence generated by the time-delay Lorenz system, the pixel permutation is carried out in diagonal and antidiagonal directions according to the first and second components. Then, a pseudorandom chaotic sequence is generated again from time-delay Lorenz system using all components. Modular operation is further employed for diffusion by blocks, in which the control parameter is generated depending on the plain-image. Numerical experiments show that the proposed scheme possesses the properties of a large key space to resist brute-force attack, sensitive dependence on secret keys, uniform distribution of gray values in the cipher-image, and zero correlation between two adjacent cipher-image pixels. Therefore, it can be adopted as an effective and fast image encryption algorithm.
17. A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system
Science.gov (United States)
Wang, Zhen; Huang, Xia; Li, Yu-Xia; Song, Xiao-Na
2013-01-01
We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.
18. Compressive sensing based ptychography image encryption
Science.gov (United States)
Rawat, Nitin
2015-09-01
A compressive sensing (CS) based ptychography combined with an optical image encryption is proposed. The diffraction pattern is recorded through ptychography technique further compressed by non-uniform sampling via CS framework. The system requires much less encrypted data and provides high security. The diffraction pattern as well as the lesser measurements of the encrypted samples serves as a secret key which make the intruder attacks more difficult. Furthermore, CS shows that the linearly projected few random samples have adequate information for decryption with a dramatic volume reduction. Experimental results validate the feasibility and effectiveness of our proposed technique compared with the existing techniques. The retrieved images do not reveal any information with the original information. In addition, the proposed system can be robust even with partial encryption and under brute-force attacks.
19. Integral transformations applied to image encryption
International Nuclear Information System (INIS)
Vilardy, Juan M.; Torres, Cesar O.; Perez, Ronal
2017-01-01
In this paper we consider the application of the integral transformations for image encryption through optical systems, a mathematical algorithm under Matlab platform using fractional Fourier transform (FrFT) and Random Phase Mask (RPM) for digital images encryption is implemented. The FrFT can be related to others integral transforms, such as: Fourier transform, Sine and Cosine transforms, Radial Hilbert transform, fractional Sine transform, fractional Cosine transform, fractional Hartley transform, fractional Wavelet transform and Gyrator transform, among other transforms. The encryption scheme is based on the use of the FrFT, the joint transform correlator and two RPMs, which provide security and robustness to the implemented security system. One of the RPMs used during encryption-decryption and the fractional order of the FrFT are the keys to improve security and make the system more resistant against security attacks. (paper)
20. A Survey of Image Encryption Algorithms
Science.gov (United States)
Kumari, Manju; Gupta, Shailender; Sardana, Pranshul
2017-12-01
Security of data/images is one of the crucial aspects in the gigantic and still expanding domain of digital transfer. Encryption of images is one of the well known mechanisms to preserve confidentiality of images over a reliable unrestricted public media. This medium is vulnerable to attacks and hence efficient encryption algorithms are necessity for secure data transfer. Various techniques have been proposed in literature till date, each have an edge over the other, to catch-up to the ever growing need of security. This paper is an effort to compare the most popular techniques available on the basis of various performance metrics like differential, statistical and quantitative attacks analysis. To measure the efficacy, all the modern and grown-up techniques are implemented in MATLAB-2015. The results show that the chaotic schemes used in the study provide highly scrambled encrypted images having uniform histogram distribution. In addition, the encrypted images provided very less degree of correlation coefficient values in horizontal, vertical and diagonal directions, proving their resistance against statistical attacks. In addition, these schemes are able to resist differential attacks as these showed a high sensitivity for the initial conditions, i.e. pixel and key values. Finally, the schemes provide a large key spacing, hence can resist the brute force attacks, and provided a very less computational time for image encryption/decryption in comparison to other schemes available in literature.
1. Watermarking patient data in encrypted medical images
Due to the advancement of technology, internet has become an ... area including important information and must be stored without any distortion. .... Although someone with the knowledge of encryption key can obtain a decrypted image and ... ical image management, in: Engineering in Medicine and Biology Society.
2. Optical encryption with selective computational ghost imaging
International Nuclear Information System (INIS)
2014-01-01
Selective computational ghost imaging (SCGI) is a technique which enables the reconstruction of an N-pixel image from N measurements or less. In this paper we propose an optical encryption method based on SCGI and experimentally demonstrate that this method has much higher security under eavesdropping and unauthorized accesses compared with previous reported methods. (paper)
3. Parallel image encryption algorithm based on discretized chaotic map
International Nuclear Information System (INIS)
Zhou Qing; Wong Kwokwo; Liao Xiaofeng; Xiang Tao; Hu Yue
2008-01-01
Recently, a variety of chaos-based algorithms were proposed for image encryption. Nevertheless, none of them works efficiently in parallel computing environment. In this paper, we propose a framework for parallel image encryption. Based on this framework, a new algorithm is designed using the discretized Kolmogorov flow map. It fulfills all the requirements for a parallel image encryption algorithm. Moreover, it is secure and fast. These properties make it a good choice for image encryption on parallel computing platforms
4. Suggested Method for Encryption and Hiding Image using LCG and LSB
Directory of Open Access Journals (Sweden)
Atheer Hussein Zyara
2017-12-01
Full Text Available Maintaining the confidentiality of the data of the very important areas in computer applications , Where many researchers work in the fields of concealment and encryption . So in this research we are working on the combining of the two methods , where confidential data is encrypted by using a proposed method , Then the cover is encrypted (regular image by LCG algorithm (which generates a series of random numbers to generate the encrypted cover (irregular image , After that ,we hide the encrypted data in encrypted cover by depending on the LSB technique, then we convert the irregular image into regular image and thereby getting hidden data in random locations in the cover image , This method is characterized by flexibility in terms of the possibility of hiding the different types of confidential data in different types of media , and durability as that data be hidden in random locations and this what distinguishes the proposed algorithm , and the results showed high security, because the data is hidden in random locations in encrypted image then convert to the original regular image For clarification of the proposed algorithm , it has been applied on a digital image of the gray type using MATLAB language by using the efficiency scales PSNR and MSE
5. Image Encryption and Chaotic Cellular Neural Network
Science.gov (United States)
Peng, Jun; Zhang, Du
Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.
6. Multi-image encryption based on synchronization of chaotic lasers and iris authentication
Science.gov (United States)
Banerjee, Santo; Mukhopadhyay, Sumona; Rondoni, Lamberto
2012-07-01
A new technique of transmitting encrypted combinations of gray scaled and chromatic images using chaotic lasers derived from Maxwell-Bloch's equations has been proposed. This novel scheme utilizes the general method of solution of a set of linear equations to transmit similar sized heterogeneous images which are a combination of monochrome and chromatic images. The chaos encrypted gray scaled images are concatenated along the three color planes resulting in color images. These are then transmitted over a secure channel along with a cover image which is an iris scan. The entire cryptology is augmented with an iris-based authentication scheme. The secret messages are retrieved once the authentication is successful. The objective of our work is briefly outlined as (a) the biometric information is the iris which is encrypted before transmission, (b) the iris is used for personal identification and verifying for message integrity, (c) the information is transmitted securely which are colored images resulting from a combination of gray images, (d) each of the images transmitted are encrypted through chaos based cryptography, (e) these encrypted multiple images are then coupled with the iris through linear combination of images before being communicated over the network. The several layers of encryption together with the ergodicity and randomness of chaos render enough confusion and diffusion properties which guarantee a fool-proof approach in achieving secure communication as demonstrated by exhaustive statistical methods. The result is vital from the perspective of opening a fundamental new dimension in multiplexing and simultaneous transmission of several monochromatic and chromatic images along with biometry based authentication and cryptography.
7. Test and Verification of AES Used for Image Encryption
Science.gov (United States)
Zhang, Yong
2018-03-01
In this paper, an image encryption program based on AES in cipher block chaining mode was designed with C language. The encryption/decryption speed and security performance of AES based image cryptosystem were tested and used to compare the proposed cryptosystem with some existing image cryptosystems based on chaos. Simulation results show that AES can apply to image encryption, which refutes the widely accepted point of view that AES is not suitable for image encryption. This paper also suggests taking the speed of AES based image encryption as the speed benchmark of image encryption algorithms. And those image encryption algorithms whose speeds are lower than the benchmark should be discarded in practical communications.
8. Optical image encryption using multilevel Arnold transform and noninterferometric imaging
Science.gov (United States)
Chen, Wen; Chen, Xudong
2011-11-01
Information security has attracted much current attention due to the rapid development of modern technologies, such as computer and internet. We propose a novel method for optical image encryption using multilevel Arnold transform and rotatable-phase-mask noninterferometric imaging. An optical image encryption scheme is developed in the gyrator transform domain, and one phase-only mask (i.e., phase grating) is rotated and updated during image encryption. For the decryption, an iterative retrieval algorithm is proposed to extract high-quality plaintexts. Conventional encoding methods (such as digital holography) have been proven vulnerably to the attacks, and the proposed optical encoding scheme can effectively eliminate security deficiency and significantly enhance cryptosystem security. The proposed strategy based on the rotatable phase-only mask can provide a new alternative for data/image encryption in the noninterferometric imaging.
9. A hash-based image encryption algorithm
Science.gov (United States)
Cheddad, Abbas; Condell, Joan; Curran, Kevin; McKevitt, Paul
2010-03-01
There exist several algorithms that deal with text encryption. However, there has been little research carried out to date on encrypting digital images or video files. This paper describes a novel way of encrypting digital images with password protection using 1D SHA-2 algorithm coupled with a compound forward transform. A spatial mask is generated from the frequency domain by taking advantage of the conjugate symmetry of the complex imagery part of the Fourier Transform. This mask is then XORed with the bit stream of the original image. Exclusive OR (XOR), a logical symmetric operation, that yields 0 if both binary pixels are zeros or if both are ones and 1 otherwise. This can be verified simply by modulus (pixel1, pixel2, 2). Finally, confusion is applied based on the displacement of the cipher's pixels in accordance with a reference mask. Both security and performance aspects of the proposed method are analyzed, which prove that the method is efficient and secure from a cryptographic point of view. One of the merits of such an algorithm is to force a continuous tone payload, a steganographic term, to map onto a balanced bits distribution sequence. This bit balance is needed in certain applications, such as steganography and watermarking, since it is likely to have a balanced perceptibility effect on the cover image when embedding.
10. Encryption of Stereo Images after Compression by Advanced Encryption Standard (AES
Directory of Open Access Journals (Sweden)
Marwah k Hussien
2018-04-01
Full Text Available New partial encryption schemes are proposed, in which a secure encryption algorithm is used to encrypt only part of the compressed data. Partial encryption applied after application of image compression algorithm. Only 0.0244%-25% of the original data isencrypted for two pairs of dif-ferent grayscale imageswiththe size (256 ´ 256 pixels. As a result, we see a significant reduction of time in the stage of encryption and decryption. In the compression step, the Orthogonal Search Algorithm (OSA for motion estimation (the dif-ferent between stereo images is used. The resulting disparity vector and the remaining image were compressed by Discrete Cosine Transform (DCT, Quantization and arithmetic encoding. The image compressed was encrypted by Advanced Encryption Standard (AES. The images were then decoded and were compared with the original images. Experimental results showed good results in terms of Peak Signal-to-Noise Ratio (PSNR, Com-pression Ratio (CR and processing time. The proposed partial encryption schemes are fast, se-cure and do not reduce the compression performance of the underlying selected compression methods
11. Image encryption based on a delayed fractional-order chaotic logistic system
International Nuclear Information System (INIS)
Wang Zhen; Li Ning; Huang Xia; Song Xiao-Na
2012-01-01
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security. (general)
12. Image encryption based on a delayed fractional-order chaotic logistic system
Science.gov (United States)
Wang, Zhen; Huang, Xia; Li, Ning; Song, Xiao-Na
2012-05-01
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security.
13. Quantum image encryption based on generalized affine transform and logistic map
Science.gov (United States)
Liang, Hao-Ran; Tao, Xiang-Yang; Zhou, Nan-Run
2016-07-01
Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.
14. An Image Encryption Approach Using a Shuffling Map
International Nuclear Information System (INIS)
Xiao Yongliang; Xia Limin
2009-01-01
A new image encryption approach is proposed. First, a sort transformation based on nonlinear chaotic algorithm is used to shuffle the positions of image pixels. Then the states of hyper-chaos are used to change the grey values of the shuffled image according to the changed chaotic values of the same position between the above nonlinear chaotic sequence and the sorted chaotic sequence. The experimental results demonstrate that the image encryption scheme based on a shuffling map shows advantages of large key space and high-level security. Compared with some encryption algorithms, the suggested encryption scheme is more secure. (general)
15. Analysis of S-box in Image Encryption Using Root Mean Square Error Method
Science.gov (United States)
2012-07-01
The use of substitution boxes (S-boxes) in encryption applications has proven to be an effective nonlinear component in creating confusion and randomness. The S-box is evolving and many variants appear in literature, which include advanced encryption standard (AES) S-box, affine power affine (APA) S-box, Skipjack S-box, Gray S-box, Lui J S-box, residue prime number S-box, Xyi S-box, and S8 S-box. These S-boxes have algebraic and statistical properties which distinguish them from each other in terms of encryption strength. In some circumstances, the parameters from algebraic and statistical analysis yield results which do not provide clear evidence in distinguishing an S-box for an application to a particular set of data. In image encryption applications, the use of S-boxes needs special care because the visual analysis and perception of a viewer can sometimes identify artifacts embedded in the image. In addition to existing algebraic and statistical analysis already used for image encryption applications, we propose an application of root mean square error technique, which further elaborates the results and enables the analyst to vividly distinguish between the performances of various S-boxes. While the use of the root mean square error analysis in statistics has proven to be effective in determining the difference in original data and the processed data, its use in image encryption has shown promising results in estimating the strength of the encryption method. In this paper, we show the application of the root mean square error analysis to S-box image encryption. The parameters from this analysis are used in determining the strength of S-boxes
16. A high performance hardware implementation image encryption with AES algorithm
Science.gov (United States)
2011-06-01
This paper describes implementation of a high-speed encryption algorithm with high throughput for encrypting the image. Therefore, we select a highly secured symmetric key encryption algorithm AES(Advanced Encryption Standard), in order to increase the speed and throughput using pipeline technique in four stages, control unit based on logic gates, optimal design of multiplier blocks in mixcolumn phase and simultaneous production keys and rounds. Such procedure makes AES suitable for fast image encryption. Implementation of a 128-bit AES on FPGA of Altra company has been done and the results are as follow: throughput, 6 Gbps in 471MHz. The time of encrypting in tested image with 32*32 size is 1.15ms.
17. Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain
Science.gov (United States)
Sui, Liansheng; Lu, Haiwei; Ning, Xiaojuan; Wang, Yinghui
2014-02-01
A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.
18. Performance Analysis of Chaotic Encryption Using a Shared Image ...
African Journals Online (AJOL)
Most of the secret key encryption algorithms in use today are designed based on either the feistel structure or the substitution-permutation structure. This paper focuses on data encryption technique using multi-scroll chaotic natures and a publicly shared image as a key. A key is generated from the shared image using a full ...
19. A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism
Science.gov (United States)
Ye, Ruisong
2011-10-01
This paper proposes a novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism, in which permuting the positions of image pixels incorporates with changing the gray values of image pixels to confuse the relationship between cipher-image and plain-image. In the permutation process, a generalized Arnold map is utilized to generate one chaotic orbit used to get two index order sequences for the permutation of image pixel positions; in the diffusion process, a generalized Arnold map and a generalized Bernoulli shift map are employed to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. The yielded gray value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack as well.
20. OCML-based colour image encryption
International Nuclear Information System (INIS)
Rhouma, Rhouma; Meherzi, Soumaya; Belghith, Safya
2009-01-01
The chaos-based cryptographic algorithms have suggested some new ways to develop efficient image-encryption schemes. While most of these schemes are based on low-dimensional chaotic maps, it has been proposed recently to use high-dimensional chaos namely spatiotemporal chaos, which is modelled by one-way coupled-map lattices (OCML). Owing to their hyperchaotic behaviour, such systems are assumed to enhance the cryptosystem security. In this paper, we propose an OCML-based colour image encryption scheme with a stream cipher structure. We use a 192-bit-long external key to generate the initial conditions and the parameters of the OCML. We have made several tests to check the security of the proposed cryptosystem namely, statistical tests including histogram analysis, calculus of the correlation coefficients of adjacent pixels, security test against differential attack including calculus of the number of pixel change rate (NPCR) and unified average changing intensity (UACI), and entropy calculus. The cryptosystem speed is analyzed and tested as well.
1. A novel algorithm for thermal image encryption.
Science.gov (United States)
Hussain, Iqtadar; Anees, Amir; Algarni, Abdulmohsen
2018-04-16
Thermal images play a vital character at nuclear plants, Power stations, Forensic labs biological research, and petroleum products extraction. Safety of thermal images is very important. Image data has some unique features such as intensity, contrast, homogeneity, entropy and correlation among pixels that is why somehow image encryption is trickier as compare to other encryptions. With conventional image encryption schemes it is normally hard to handle these features. Therefore, cryptographers have paid attention to some attractive properties of the chaotic maps such as randomness and sensitivity to build up novel cryptosystems. That is why, recently proposed image encryption techniques progressively more depends on the application of chaotic maps. This paper proposed an image encryption algorithm based on Chebyshev chaotic map and S8 Symmetric group of permutation based substitution boxes. Primarily, parameters of chaotic Chebyshev map are chosen as a secret key to mystify the primary image. Then, the plaintext image is encrypted by the method generated from the substitution boxes and Chebyshev map. By this process, we can get a cipher text image that is perfectly twisted and dispersed. The outcomes of renowned experiments, key sensitivity tests and statistical analysis confirm that the proposed algorithm offers a safe and efficient approach for real-time image encryption.
2. Two-dimensional DFA scaling analysis applied to encrypted images
Science.gov (United States)
Vargas-Olmos, C.; Murguía, J. S.; Ramírez-Torres, M. T.; Mejía Carlos, M.; Rosu, H. C.; González-Aguilar, H.
2015-01-01
The technique of detrended fluctuation analysis (DFA) has been widely used to unveil scaling properties of many different signals. In this paper, we determine scaling properties in the encrypted images by means of a two-dimensional DFA approach. To carry out the image encryption, we use an enhanced cryptosystem based on a rule-90 cellular automaton and we compare the results obtained with its unmodified version and the encryption system AES. The numerical results show that the encrypted images present a persistent behavior which is close to that of the 1/f-noise. These results point to the possibility that the DFA scaling exponent can be used to measure the quality of the encrypted image content.
3. Chaos-based image encryption algorithm [rapid communication
Science.gov (United States)
Guan, Zhi-Hong; Huang, Fangjun; Guan, Wenjie
2005-10-01
In this Letter, a new image encryption scheme is presented, in which shuffling the positions and changing the grey values of image pixels are combined to confuse the relationship between the cipher-image and the plain-image. Firstly, the Arnold cat map is used to shuffle the positions of the image pixels in the spatial-domain. Then the discrete output signal of the Chen's chaotic system is preprocessed to be suitable for the grayscale image encryption, and the shuffled image is encrypted by the preprocessed signal pixel by pixel. The experimental results demonstrate that the key space is large enough to resist the brute-force attack and the distribution of grey values of the encrypted image has a random-like behavior.
4. New modified map for digital image encryption and its performance
Science.gov (United States)
Suryadi, MT; Yus Trinity Irsan, Maria; Satria, Yudi
2017-10-01
Protection to classified digital data becomes so important in avoiding data manipulation and alteration. The focus of this paper is in data and information protection of digital images form. Protection is provided in the form of encrypted digital image. The encryption process uses a new map, {x}n+1=\\frac{rλ {x}n}{1+λ {(1-{x}n)}2}\\quad ({mod} 1), which is called MS map. This paper will show: the results of digital image encryption using MS map and how the performance is regarding the average time needed for encryption/decryption process; randomness of key stream sequence with NIST test, histogram analysis and goodness of fit test, quality of the decrypted image by PSNR, initial value sensitivity level, and key space. The results show that the average time of the encryption process is relatively same as the decryption process and it depends to types and sizes of the image. Cipherimage (encrypted image) is uniformly distributed since: it passes the goodness of fit test and also the histogram of the cipherimage is flat; key stream, that are generated by MS map, passes frequency (monobit) test, and runs test, which means the key stream is a random sequence; the decrypted image has same quality as the original image; and initial value sensitivity reaches 10-17, and key space reaches 3.24 × 10634. So, that encryption algorithm generated by MS map is more resistant to brute-force attack and known plaintext attack.
5. Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system
Science.gov (United States)
Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian
2018-06-01
In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.
6. A light weight secure image encryption scheme based on chaos & DNA computing
Directory of Open Access Journals (Sweden)
2017-10-01
Full Text Available This paper proposed a new light weight secure cryptographic scheme for secure image communication. In this scheme the plain image is permuted first using a sequence of pseudo random number (PRN and encrypted by DeoxyriboNucleic Acid (DNA computation. Two PRN sequences are generated by a Pseudo Random Number Generator (PRNG based on cross coupled chaotic logistic map using two sets of keys. The first PRN sequence is used for permuting the plain image whereas the second PRN sequence is used for generating random DNA sequence. The number of rounds of permutation and encryption may be variable to increase security. The scheme is proposed for gray label images but the scheme may be extended for color images and text data. Simulation results exhibit that the proposed scheme can defy any kind of attack.
7. A novel image encryption scheme based on spatial chaos map
International Nuclear Information System (INIS)
Sun Fuyan; Liu Shutang; Li Zhongqin; Lue Zongwang
2008-01-01
In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint
8. Perceptual security of encrypted images based on wavelet scaling analysis
Science.gov (United States)
Vargas-Olmos, C.; Murguía, J. S.; Ramírez-Torres, M. T.; Mejía Carlos, M.; Rosu, H. C.; González-Aguilar, H.
2016-08-01
The scaling behavior of the pixel fluctuations of encrypted images is evaluated by using the detrended fluctuation analysis based on wavelets, a modern technique that has been successfully used recently for a wide range of natural phenomena and technological processes. As encryption algorithms, we use the Advanced Encryption System (AES) in RBT mode and two versions of a cryptosystem based on cellular automata, with the encryption process applied both fully and partially by selecting different bitplanes. In all cases, the results show that the encrypted images in which no understandable information can be visually appreciated and whose pixels look totally random present a persistent scaling behavior with the scaling exponent α close to 0.5, implying no correlation between pixels when the DFA with wavelets is applied. This suggests that the scaling exponents of the encrypted images can be used as a perceptual security criterion in the sense that when their values are close to 0.5 (the white noise value) the encrypted images are more secure also from the perceptual point of view.
9. A Novel Image Encryption Algorithm Based on DNA Subsequence Operation
Directory of Open Access Journals (Sweden)
Qiang Zhang
2012-01-01
Full Text Available We present a novel image encryption algorithm based on DNA subsequence operation. Different from the traditional DNA encryption methods, our algorithm does not use complex biological operation but just uses the idea of DNA subsequence operations (such as elongation operation, truncation operation, deletion operation, etc. combining with the logistic chaotic map to scramble the location and the value of pixel points from the image. The experimental results and security analysis show that the proposed algorithm is easy to be implemented, can get good encryption effect, has a wide secret key's space, strong sensitivity to secret key, and has the abilities of resisting exhaustive attack and statistic attack.
10. Hardware Realization of Chaos Based Symmetric Image Encryption
KAUST Repository
Barakat, Mohamed L.
2012-01-01
This thesis presents a novel work on hardware realization of symmetric image encryption utilizing chaos based continuous systems as pseudo random number generators. Digital implementation of chaotic systems results in serious degradations
11. Color image encryption based on Coupled Nonlinear Chaotic Map
International Nuclear Information System (INIS)
2009-01-01
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
12. A novel image encryption scheme based on the ergodicity of baker map
Science.gov (United States)
Ye, Ruisong; Chen, Yonghong
2012-01-01
Thanks to the exceptionally good properties in chaotic systems, such as sensitivity to initial conditions and control parameters, pseudo-randomness and ergodicity, chaos-based image encryption algorithms have been widely studied and developed in recent years. A novel digital image encryption scheme based on the chaotic ergodicity of Baker map is proposed in this paper. Different from traditional encryption schemes based on Baker map, we permute the pixel positions by their corresponding order numbers deriving from the approximating points in one chaotic orbit. To enhance the resistance to statistical and differential attacks, a diffusion process is suggested as well in the proposed scheme. The proposed scheme enlarges the key space significantly to resist brute-force attack. Additionally, the distribution of gray values in the cipher-image has a random-like behavior to resist statistical analysis. The proposed scheme is robust against cropping, tampering and noising attacks as well. It therefore suggests a high secure and efficient way for real-time image encryption and transmission in practice.
13. 3-D Image Encryption Based on Rubik's Cube and RC6 Algorithm
Science.gov (United States)
Helmy, Mai; El-Rabaie, El-Sayed M.; Eldokany, Ibrahim M.; El-Samie, Fathi E. Abd
2017-12-01
A novel encryption algorithm based on the 3-D Rubik's cube is proposed in this paper to achieve 3D encryption of a group of images. This proposed encryption algorithm begins with RC6 as a first step for encrypting multiple images, separately. After that, the obtained encrypted images are further encrypted with the 3-D Rubik's cube. The RC6 encrypted images are used as the faces of the Rubik's cube. From the concepts of image encryption, the RC6 algorithm adds a degree of diffusion, while the Rubik's cube algorithm adds a degree of permutation. The simulation results demonstrate that the proposed encryption algorithm is efficient, and it exhibits strong robustness and security. The encrypted images are further transmitted over wireless Orthogonal Frequency Division Multiplexing (OFDM) system and decrypted at the receiver side. Evaluation of the quality of the decrypted images at the receiver side reveals good results.
14. Hardware Realization of Chaos Based Symmetric Image Encryption
KAUST Repository
Barakat, Mohamed L.
2012-06-01
This thesis presents a novel work on hardware realization of symmetric image encryption utilizing chaos based continuous systems as pseudo random number generators. Digital implementation of chaotic systems results in serious degradations in the dynamics of the system. Such defects are illuminated through a new technique of generalized post proceeding with very low hardware cost. The thesis further discusses two encryption algorithms designed and implemented as a block cipher and a stream cipher. The security of both systems is thoroughly analyzed and the performance is compared with other reported systems showing a superior results. Both systems are realized on Xilinx Vetrix-4 FPGA with a hardware and throughput performance surpassing known encryption systems.
15. Image Blocking Encryption Algorithm Based on Laser Chaos Synchronization
Directory of Open Access Journals (Sweden)
Shu-Ying Wang
2016-01-01
Full Text Available In view of the digital image transmission security, based on laser chaos synchronization and Arnold cat map, a novel image encryption scheme is proposed. Based on pixel values of plain image a parameter is generated to influence the secret key. Sequences of the drive system and response system are pretreated by the same method and make image blocking encryption scheme for plain image. Finally, pixels position are scrambled by general Arnold transformation. In decryption process, the chaotic synchronization accuracy is fully considered and the relationship between the effect of synchronization and decryption is analyzed, which has characteristics of high precision, higher efficiency, simplicity, flexibility, and better controllability. The experimental results show that the encryption algorithm image has high security and good antijamming performance.
16. Remote-sensing image encryption in hybrid domains
Science.gov (United States)
Zhang, Xiaoqiang; Zhu, Guiliang; Ma, Shilong
2012-04-01
Remote-sensing technology plays an important role in military and industrial fields. Remote-sensing image is the main means of acquiring information from satellites, which always contain some confidential information. To securely transmit and store remote-sensing images, we propose a new image encryption algorithm in hybrid domains. This algorithm makes full use of the advantages of image encryption in both spatial domain and transform domain. First, the low-pass subband coefficients of image DWT (discrete wavelet transform) decomposition are sorted by a PWLCM system in transform domain. Second, the image after IDWT (inverse discrete wavelet transform) reconstruction is diffused with 2D (two-dimensional) Logistic map and XOR operation in spatial domain. The experiment results and algorithm analyses show that the new algorithm possesses a large key space and can resist brute-force, statistical and differential attacks. Meanwhile, the proposed algorithm has the desirable encryption efficiency to satisfy requirements in practice.
17. Fractional Hartley transform applied to optical image encryption
Energy Technology Data Exchange (ETDEWEB)
Jimenez, C [Grupo GIFES. Universidad de La Guajira. Riohacha (Colombia); Torres, C; Mattos, L, E-mail: [email protected] [Grupo LOI. Universidad Popular del Cesar. Valledupar (Colombia)
2011-01-01
A new method for image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as addictional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. Computer simulations are also perfomed to confirm the possibility of proposed method.
18. Optical image encryption with redefined fractional Hartley transform
Science.gov (United States)
Zhao, Daomu; Li, Xinxin; Chen, Linfei
2008-11-01
A new method for optical image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as additional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.
19. Fractional Hartley transform applied to optical image encryption
Science.gov (United States)
Jimenez, C.; Torres, C.; Mattos, L.
2011-01-01
A new method for image encryption is introduced on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform We encrypt the image by two fractional orders and random phase codes. It has an advantage over Hartley transform, for its fractional orders can also be used as addictional keys, and that, of course, strengthens image security. Only when all of these keys are correct, can the image be well decrypted. Computer simulations are also perfomed to confirm the possibilty of proposed method.
20. Digital Image Encryption Algorithm Design Based on Genetic Hyperchaos
Directory of Open Access Journals (Sweden)
Jian Wang
2016-01-01
Full Text Available In view of the present chaotic image encryption algorithm based on scrambling (diffusion is vulnerable to choosing plaintext (ciphertext attack in the process of pixel position scrambling, we put forward a image encryption algorithm based on genetic super chaotic system. The algorithm, by introducing clear feedback to the process of scrambling, makes the scrambling effect related to the initial chaos sequence and the clear text itself; it has realized the image features and the organic fusion of encryption algorithm. By introduction in the process of diffusion to encrypt plaintext feedback mechanism, it improves sensitivity of plaintext, algorithm selection plaintext, and ciphertext attack resistance. At the same time, it also makes full use of the characteristics of image information. Finally, experimental simulation and theoretical analysis show that our proposed algorithm can not only effectively resist plaintext (ciphertext attack, statistical attack, and information entropy attack but also effectively improve the efficiency of image encryption, which is a relatively secure and effective way of image communication.
1. An Image Encryption Algorithm Based on Balanced Pixel and Chaotic Map
Directory of Open Access Journals (Sweden)
Jian Zhang
2014-01-01
Full Text Available Image encryption technology has been applied in many fields and is becoming the main way of protecting the image information security. There are also many ways of image encryption. However, the existing encryption algorithms, in order to obtain a better effect of encryption, always need encrypting several times. There is not an effective method to decide the number of encryption times, generally determined by the human eyes. The paper proposes an image encryption algorithm based on chaos and simultaneously proposes a balanced pixel algorithm to determine the times of image encryption. Many simulation experiments have been done including encryption effect and security analysis. Experimental results show that the proposed method is feasible and effective.
2. DATA HIDING IN ENCRYPTED IMAGES USING ARNOLD TRANSFORM
Directory of Open Access Journals (Sweden)
S. Siva Shankar
2016-08-01
Full Text Available Digital image steganography has several applications in information security and communication. Data hiding in encrypted images ensure that both the cover image and the secret message can be recovered at the receiver end. This work presents a novel data hiding and image encryption scheme using random diffusion and Two dimensional Arnold cat mapping transform. The secret message bits are placed in the least significant bit positions of the cover image. Then a shared key is used to generate random 8 bit random integer stream and is added to the stego image in the random diffusion step. Arnold cat mapping transformation is done to scramble the pixels. The two steps of random diffusion and Arnold transform mapping are done alternatively several times to completely encrypt the image contents. The process is reversed at the receiver end to get both the secret message and the cover image with little loss. The random diffusion step overcomes the limited period of the Arnold transform. The embedding capacity of one bit per pixel is achieved. Security analysis is carried out which shows that the encryption is highly secure. The number of collisions is low thus preventing brute force attacks. The original cover image is recoverable with minimal losses.
3. Research on Image Encryption Based on DNA Sequence and Chaos Theory
Science.gov (United States)
Tian Zhang, Tian; Yan, Shan Jun; Gu, Cheng Yan; Ren, Ran; Liao, Kai Xin
2018-04-01
Nowadays encryption is a common technique to protect image data from unauthorized access. In recent years, many scientists have proposed various encryption algorithms based on DNA sequence to provide a new idea for the design of image encryption algorithm. Therefore, a new method of image encryption based on DNA computing technology is proposed in this paper, whose original image is encrypted by DNA coding and 1-D logistic chaotic mapping. First, the algorithm uses two modules as the encryption key. The first module uses the real DNA sequence, and the second module is made by one-dimensional logistic chaos mapping. Secondly, the algorithm uses DNA complementary rules to encode original image, and uses the key and DNA computing technology to compute each pixel value of the original image, so as to realize the encryption of the whole image. Simulation results show that the algorithm has good encryption effect and security.
4. Image encryption using random sequence generated from generalized information domain
International Nuclear Information System (INIS)
Zhang Xia-Yan; Wu Jie-Hua; Zhang Guo-Ji; Li Xuan; Ren Ya-Zhou
2016-01-01
A novel image encryption method based on the random sequence generated from the generalized information domain and permutation–diffusion architecture is proposed. The random sequence is generated by reconstruction from the generalized information file and discrete trajectory extraction from the data stream. The trajectory address sequence is used to generate a P-box to shuffle the plain image while random sequences are treated as keystreams. A new factor called drift factor is employed to accelerate and enhance the performance of the random sequence generator. An initial value is introduced to make the encryption method an approximately one-time pad. Experimental results show that the random sequences pass the NIST statistical test with a high ratio and extensive analysis demonstrates that the new encryption scheme has superior security. (paper)
5. Efficient image or video encryption based on spatiotemporal chaos system
International Nuclear Information System (INIS)
Lian Shiguo
2009-01-01
In this paper, an efficient image/video encryption scheme is constructed based on spatiotemporal chaos system. The chaotic lattices are used to generate pseudorandom sequences and then encrypt image blocks one by one. By iterating chaotic maps for certain times, the generated pseudorandom sequences obtain high initial-value sensitivity and good randomness. The pseudorandom-bits in each lattice are used to encrypt the Direct Current coefficient (DC) and the signs of the Alternating Current coefficients (ACs). Theoretical analysis and experimental results show that the scheme has good cryptographic security and perceptual security, and it does not affect the compression efficiency apparently. These properties make the scheme a suitable choice for practical applications.
6. Fast encryption of image data using chaotic Kolmogorov flows
Science.gov (United States)
Scharinger, Josef
1998-04-01
To guarantee security and privacy in image and video archival applications, efficient bulk encryption techniques are necessary which are easily implementable in soft- and hardware and are able to cope with the vast amounts of data involved. Experience has shown that block-oriented symmetric product ciphers constitute an adequate design paradigm for resolving this task, since they can offer a very high level of security as well as very high encryption rates. In this contribution we introduce a new product cipher which encrypts large blocks of plain text by repeated intertwined application of substitution and permutation operations. While almost all of the current product ciphers use fixed permutation operations on small data blocks, our approach involves parametrizable permutations on large data blocks induced by specific chaotic systems. By combining these highly unstable dynamics with an adaption of a very fast shift register based pseudo-random number generator, we obtain a new class of computationally secure product ciphers which offer many features that make them superior to contemporary bulk encryption systems when aiming at efficient image and video data encryption.
7. A symmetrical image encryption scheme in wavelet and time domain
Science.gov (United States)
Luo, Yuling; Du, Minghui; Liu, Junxiu
2015-02-01
There has been an increasing concern for effective storages and secure transactions of multimedia information over the Internet. Then a great variety of encryption schemes have been proposed to ensure the information security while transmitting, but most of current approaches are designed to diffuse the data only in spatial domain which result in reducing storage efficiency. A lightweight image encryption strategy based on chaos is proposed in this paper. The encryption process is designed in transform domain. The original image is decomposed into approximation and detail components using integer wavelet transform (IWT); then as the more important component of the image, the approximation coefficients are diffused by secret keys generated from a spatiotemporal chaotic system followed by inverse IWT to construct the diffused image; finally a plain permutation is performed for diffusion image by the Logistic mapping in order to reduce the correlation between adjacent pixels further. Experimental results and performance analysis demonstrate the proposed scheme is an efficient, secure and robust encryption mechanism and it realizes effective coding compression to satisfy desirable storage.
8. Chaotic Dynamical State Variables Selection Procedure Based Image Encryption Scheme
Directory of Open Access Journals (Sweden)
Zia Bashir
2017-12-01
Full Text Available Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption.
9. Cryptanalysis of a chaos-based image encryption algorithm
International Nuclear Information System (INIS)
Cokal, Cahit; Solak, Ercan
2009-01-01
A chaos-based image encryption algorithm was proposed in [Z.-H. Guan, F. Huang, W. Guan, Phys. Lett. A 346 (2005) 153]. In this Letter, we analyze the security weaknesses of the proposal. By applying chosen-plaintext and known-plaintext attacks, we show that all the secret parameters can be revealed
10. Security Analysis of A Chaos-based Image Encryption Algorithm
OpenAIRE
Lian, Shiguo; Sun, Jinsheng; Wang, Zhiquan
2006-01-01
The security of Fridrich Image Encryption Algorithm against brute-force attack, statistical attack, known-plaintext attack and select-plaintext attack is analyzed by investigating the properties of the involved chaotic maps and diffusion functions. Based on the given analyses, some means are proposed to strengthen the overall performance of the focused cryptosystem.
11. Optical image encryption based on interference under convergent random illumination
International Nuclear Information System (INIS)
Kumar, Pramod; Joseph, Joby; Singh, Kehar
2010-01-01
In an optical image encryption system based on the interference principle, two pure phase masks are designed analytically to hide an image. These two masks are illuminated with a plane wavefront to retrieve the original image in the form of an interference pattern at the decryption plane. Replacement of the plane wavefront with convergent random illumination in the proposed scheme leads to an improvement in the security of interference based encryption. The proposed encryption scheme retains the simplicity of an interference based method, as the two pure masks are generated with an analytical method without any iterative algorithm. In addition to the free-space propagation distance and the two pure phase masks, the convergence distance and the randomized lens phase function are two new encryption parameters to enhance the system security. The robustness of this scheme against occlusion of the random phase mask of the randomized lens phase function is investigated. The feasibility of the proposed scheme is demonstrated with numerical simulation results
12. Image encryption based on nonlinear encryption system and public-key cryptography
Science.gov (United States)
Zhao, Tieyu; Ran, Qiwen; Chi, Yingying
2015-03-01
Recently, optical asymmetric cryptosystem (OACS) has became the focus of discussion and concern of researchers. Some researchers pointed out that OACS was not tenable because of misunderstanding the concept of asymmetric cryptosystem (ACS). We propose an improved cryptosystem using RSA public-key algorithm based on existing OACS and the new system conforms to the basic agreement of public key cryptosystem. At the beginning of the encryption process, the system will produce an independent phase matrix and allocate the input image, which also conforms to one-time pad cryptosystem. The simulation results show that the validity of the improved cryptosystem and the high robustness against attack scheme using phase retrieval technique.
13. Images Encryption Method using Steganographic LSB Method, AES and RSA algorithm
Science.gov (United States)
2017-03-01
Vulnerability of communication of digital images is an extremely important issue nowadays, particularly when the images are communicated through insecure channels. To improve communication security, many cryptosystems have been presented in the image encryption literature. This paper proposes a novel image encryption technique based on an algorithm that is faster than current methods. The proposed algorithm eliminates the step in which the secrete key is shared during the encryption process. It is formulated based on the symmetric encryption, asymmetric encryption and steganography theories. The image is encrypted using a symmetric algorithm, then, the secret key is encrypted by means of an asymmetrical algorithm and it is hidden in the ciphered image using a least significant bits steganographic scheme. The analysis results show that while enjoying the faster computation, our method performs close to optimal in terms of accuracy.
14. Secure image encryption algorithm design using a novel chaos based S-Box
International Nuclear Information System (INIS)
Çavuşoğlu, Ünal; Kaçar, Sezgin; Pehlivan, Ihsan; Zengin, Ahmet
2017-01-01
Highlights: • A new chaotic system is developed for creating S-Box and image encryption algorithm. • Chaos based random number generator is designed with the help of the new chaotic system. NIST tests are run on generated random numbers to verify randomness. • A new S-Box design algorithm is developed to create the chaos based S-Box to be utilized in encryption algorithm and performance tests are made. • The new developed S-Box based image encryption algorithm is introduced and image encryption application is carried out. • To show the quality and strong of the encryption process, security analysis are performed and compared with the AES and chaos algorithms. - Abstract: In this study, an encryption algorithm that uses chaos based S-BOX is developed for secure and speed image encryption. First of all, a new chaotic system is developed for creating S-Box and image encryption algorithm. Chaos based random number generator is designed with the help of the new chaotic system. Then, NIST tests are run on generated random numbers to verify randomness. A new S-Box design algorithm is developed to create the chaos based S-Box to be utilized in encryption algorithm and performance tests are made. As the next step, the new developed S-Box based image encryption algorithm is introduced in detail. Finally, image encryption application is carried out. To show the quality and strong of the encryption process, security analysis are performed. Proposed algorithm is compared with the AES and chaos algorithms. According to tests results, the proposed image encryption algorithm is secure and speed for image encryption application.
15. An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm
Directory of Open Access Journals (Sweden)
Yuping Hu
2014-01-01
Full Text Available An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack.
16. Hardware realization of chaos based block cipher for image encryption
KAUST Repository
Barakat, Mohamed L.; Radwan, Ahmed G.; Salama, Khaled N.
2011-01-01
Unlike stream ciphers, block ciphers are very essential for parallel processing applications. In this paper, the first hardware realization of chaotic-based block cipher is proposed for image encryption applications. The proposed system is tested for known cryptanalysis attacks and for different block sizes. When implemented on Virtex-IV, system performance showed high throughput and utilized small area. Passing successfully in all tests, our system proved to be secure with all block sizes. © 2011 IEEE.
17. Hardware realization of chaos based block cipher for image encryption
KAUST Repository
Barakat, Mohamed L.
2011-12-01
Unlike stream ciphers, block ciphers are very essential for parallel processing applications. In this paper, the first hardware realization of chaotic-based block cipher is proposed for image encryption applications. The proposed system is tested for known cryptanalysis attacks and for different block sizes. When implemented on Virtex-IV, system performance showed high throughput and utilized small area. Passing successfully in all tests, our system proved to be secure with all block sizes. © 2011 IEEE.
18. A new color image encryption scheme using CML and a fractional-order chaotic system.
Directory of Open Access Journals (Sweden)
Xiangjun Wu
Full Text Available The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks.
19. Reversible Integer Wavelet Transform for the Joint of Image Encryption and Watermarking
Directory of Open Access Journals (Sweden)
Bin Wang
2015-01-01
Full Text Available In recent years, signal processing in the encrypted domain has attracted considerable research interest, especially embedding watermarking in encrypted image. In this work, a novel joint of image encryption and watermarking based on reversible integer wavelet transform is proposed. Firstly, the plain-image is encrypted by chaotic maps and reversible integer wavelet transform. Then the lossless watermarking is embedded in the encrypted image by reversible integer wavelet transform and histogram modification. Finally an encrypted image containing watermarking is obtained by the inverse integer wavelet transform. What is more, the original image and watermarking can be completely recovered by inverse process. Numerical experimental results and comparing with previous works show that the proposed scheme possesses higher security and embedding capacity than previous works. It is suitable for protecting the image information.
20. A new optical encryption system for image transformation
Science.gov (United States)
Yao, Shuyu; Chen, Linfei; Chang, Guojun; He, Bingyu
2017-12-01
This paper introduces a new optical image encryption system based on Fresnel diffraction and phase iterative algorithm, which can realize the conversion between different images. The method is based on the optical system of free space transmission, and uses the iterative phase retrieval algorithm to encode an image into two phase masks and a ciphertext. Unlike the existed methods, the ciphertext is a visible image, which can be used to achieve the conversion of one image to another image. In order to enhance the security, two phase masks are combined into a wide-scale phase mask by the double image cross pixel scrambling approach. In the decryption process, the wide-scale phase mask is re-decrypted into two random phase masks using a random shift matrix. The ciphertext and the first phase mask are placed on the input plane and the second random phase mask is placed on the transformation plane. The Fresnel diffraction principle can be used to obtain the plaintext information on the output plane. Theoretical analysis and simulation results show that the encryption system is feasible and quite safe.
1. Hiding a Covert Digital Image by Assembling the RSA Encryption Method and the Binary Encoding Method
OpenAIRE
Kuang Tsan Lin; Sheng Lih Yeh
2014-01-01
The Rivest-Shamir-Adleman (RSA) encryption method and the binary encoding method are assembled to form a hybrid hiding method to hide a covert digital image into a dot-matrix holographic image. First, the RSA encryption method is used to transform the covert image to form a RSA encryption data string. Then, all the elements of the RSA encryption data string are transferred into binary data. Finally, the binary data are encoded into the dot-matrix holographic image. The pixels of the dot-matri...
2. An image encryption approach based on chaotic maps
International Nuclear Information System (INIS)
Zhang Linhua; Liao Xiaofeng; Wang Xuebing
2005-01-01
It is well-known that images are different from texts in many aspects, such as highly redundancy and correlation, the local structure and the characteristics of amplitude-frequency. As a result, the methods of conventional encryption cannot be applicable to images. In this paper, we improve the properties of confusion and diffusion in terms of discrete exponential chaotic maps, and design a key scheme for the resistance to statistic attack, differential attack and grey code attack. Experimental and theoretical results also show that our scheme is efficient and very secure
3. Batch Image Encryption Using Generated Deep Features Based on Stacked Autoencoder Network
Directory of Open Access Journals (Sweden)
Fei Hu
2017-01-01
Full Text Available Chaos-based algorithms have been widely adopted to encrypt images. But previous chaos-based encryption schemes are not secure enough for batch image encryption, for images are usually encrypted using a single sequence. Once an encrypted image is cracked, all the others will be vulnerable. In this paper, we proposed a batch image encryption scheme into which a stacked autoencoder (SAE network was introduced to generate two chaotic matrices; then one set is used to produce a total shuffling matrix to shuffle the pixel positions on each plain image, and another produces a series of independent sequences of which each is used to confuse the relationship between the permutated image and the encrypted image. The scheme is efficient because of the advantages of parallel computing of SAE, which leads to a significant reduction in the run-time complexity; in addition, the hybrid application of shuffling and confusing enhances the encryption effect. To evaluate the efficiency of our scheme, we compared it with the prevalent “logistic map,” and outperformance was achieved in running time estimation. The experimental results and analysis show that our scheme has good encryption effect and is able to resist brute-force attack, statistical attack, and differential attack.
4. Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing
Science.gov (United States)
Zhou, Nanrun; Pan, Shumin; Cheng, Shan; Zhou, Zhihong
2016-08-01
Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.
5. Secure Image Steganography Algorithm Based on DCT with OTP Encryption
Directory of Open Access Journals (Sweden)
2017-04-01
Full Text Available Rapid development of Internet makes transactions message even easier and faster. The main problem in the transactions message is security, especially if the message is private and secret. To secure these messages is usually done with steganography or cryptography. Steganography is a way to hide messages into other digital content such as images, video or audio so it does not seem nondescript from the outside. While cryptography is a technique to encrypt messages so that messages can not be read directly. In this paper have proposed combination of steganography using discrete cosine transform (DCT and cryptography using the one-time pad or vernam cipher implemented on a digital image. The measurement method used to determine the quality of stego image is the peak signal to noise ratio (PSNR and ormalize cross Correlation (NCC to measure the quality of the extraction of the decrypted message. Of steganography and encryption methods proposed obtained satisfactory results with PSNR and NCC high and resistant to JPEG compression and median filter. Keywords—Image Steganography, Discrete Cosine Transform (DCT, One Time Pad, Vernam, Chiper, Image Cryptography
6. Optical multiple-image encryption based on multiplane phase retrieval and interference
International Nuclear Information System (INIS)
Chen, Wen; Chen, Xudong
2011-01-01
In this paper, we propose a new method for optical multiple-image encryption based on multiplane phase retrieval and interference. An optical encoding system is developed in the Fresnel domain. A phase-only map is iteratively extracted based on a multiplane phase retrieval algorithm, and multiple plaintexts are simultaneously encrypted. Subsequently, the extracted phase-only map is further encrypted into two phase-only masks based on a non-iterative interference algorithm. During image decryption, the advantages and security of the proposed optical cryptosystem are analyzed. Numerical results are presented to demonstrate the validity of the proposed optical multiple-image encryption method
7. An Efficient Secret Key Homomorphic Encryption Used in Image Processing Service
Directory of Open Access Journals (Sweden)
Pan Yang
2017-01-01
Full Text Available Homomorphic encryption can protect user’s privacy when operating on user’s data in cloud computing. But it is not practical for wide using as the data and services types in cloud computing are diverse. Among these data types, digital image is an important personal data for users. There are also many image processing services in cloud computing. To protect user’s privacy in these services, this paper proposed a scheme using homomorphic encryption in image processing. Firstly, a secret key homomorphic encryption (IGHE was constructed for encrypting image. IGHE can operate on encrypted floating numbers efficiently to adapt to the image processing service. Then, by translating the traditional image processing methods into the operations on encrypted pixels, the encrypted image can be processed homomorphically. That is, service can process the encrypted image directly, and the result after decryption is the same as processing the plain image. To illustrate our scheme, three common image processing instances were given in this paper. The experiments show that our scheme is secure, correct, and efficient enough to be used in practical image processing applications.
8. Optical image encryption scheme with multiple light paths based on compressive ghost imaging
Science.gov (United States)
Zhu, Jinan; Yang, Xiulun; Meng, Xiangfeng; Wang, Yurong; Yin, Yongkai; Sun, Xiaowen; Dong, Guoyan
2018-02-01
An optical image encryption method with multiple light paths is proposed based on compressive ghost imaging. In the encryption process, M random phase-only masks (POMs) are generated by means of logistic map algorithm, and these masks are then uploaded to the spatial light modulator (SLM). The collimated laser light is divided into several beams by beam splitters as it passes through the SLM, and the light beams illuminate the secret images, which are converted into sparse images by discrete wavelet transform beforehand. Thus, the secret images are simultaneously encrypted into intensity vectors by ghost imaging. The distances between the SLM and secret images vary and can be used as the main keys with original POM and the logistic map algorithm coefficient in the decryption process. In the proposed method, the storage space can be significantly decreased and the security of the system can be improved. The feasibility, security and robustness of the method are further analysed through computer simulations.
9. Implementation of digital image encryption algorithm using logistic function and DNA encoding
Science.gov (United States)
2018-03-01
Cryptography is a method to secure information that might be in form of digital image. Based on past research, in order to increase security level of chaos based encryption algorithm and DNA based encryption algorithm, encryption algorithm using logistic function and DNA encoding was proposed. Digital image encryption algorithm using logistic function and DNA encoding use DNA encoding to scramble the pixel values into DNA base and scramble it in DNA addition, DNA complement, and XOR operation. The logistic function in this algorithm used as random number generator needed in DNA complement and XOR operation. The result of the test show that the PSNR values of cipher images are 7.98-7.99 bits, the entropy values are close to 8, the histogram of cipher images are uniformly distributed and the correlation coefficient of cipher images are near 0. Thus, the cipher image can be decrypted perfectly and the encryption algorithm has good resistance to entropy attack and statistical attack.
10. A novel image encryption algorithm based on a 3D chaotic map
Science.gov (United States)
Kanso, A.; Ghebleh, M.
2012-07-01
Recently [Solak E, Çokal C, Yildiz OT Biyikoǧlu T. Cryptanalysis of Fridrich's chaotic image encryption. Int J Bifur Chaos 2010;20:1405-1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259-1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich's algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749-761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.
11. Hiding a Covert Digital Image by Assembling the RSA Encryption Method and the Binary Encoding Method
Directory of Open Access Journals (Sweden)
Kuang Tsan Lin
2014-01-01
Full Text Available The Rivest-Shamir-Adleman (RSA encryption method and the binary encoding method are assembled to form a hybrid hiding method to hide a covert digital image into a dot-matrix holographic image. First, the RSA encryption method is used to transform the covert image to form a RSA encryption data string. Then, all the elements of the RSA encryption data string are transferred into binary data. Finally, the binary data are encoded into the dot-matrix holographic image. The pixels of the dot-matrix holographic image contain seven groups of codes used for reconstructing the covert image. The seven groups of codes are identification codes, covert-image dimension codes, covert-image graylevel codes, pre-RSA bit number codes, RSA key codes, post-RSA bit number codes, and information codes. The reconstructed covert image derived from the dot-matrix holographic image and the original covert image are exactly the same.
12. Color Image Encryption Algorithm Based on TD-ERCS System and Wavelet Neural Network
Directory of Open Access Journals (Sweden)
Kun Zhang
2015-01-01
Full Text Available In order to solve the security problem of transmission image across public networks, a new image encryption algorithm based on TD-ERCS system and wavelet neural network is proposed in this paper. According to the permutation process and the binary XOR operation from the chaotic series by producing TD-ERCS system and wavelet neural network, it can achieve image encryption. This encryption algorithm is a reversible algorithm, and it can achieve original image in the rule inverse process of encryption algorithm. Finally, through computer simulation, the experiment results show that the new chaotic encryption algorithm based on TD-ERCS system and wavelet neural network is valid and has higher security.
13. A chaos-based image encryption algorithm with variable control parameters
International Nuclear Information System (INIS)
Wang Yong; Wong, K.-W.; Liao Xiaofeng; Xiang Tao; Chen Guanrong
2009-01-01
In recent years, a number of image encryption algorithms based on the permutation-diffusion structure have been proposed. However, the control parameters used in the permutation stage are usually fixed in the whole encryption process, which favors attacks. In this paper, a chaos-based image encryption algorithm with variable control parameters is proposed. The control parameters used in the permutation stage and the keystream employed in the diffusion stage are generated from two chaotic maps related to the plain-image. As a result, the algorithm can effectively resist all known attacks against permutation-diffusion architectures. Theoretical analyses and computer simulations both confirm that the new algorithm possesses high security and fast encryption speed for practical image encryption.
14. A fast image encryption algorithm based on chaotic map
Science.gov (United States)
Liu, Wenhao; Sun, Kehui; Zhu, Congxu
2016-09-01
Derived from Sine map and iterative chaotic map with infinite collapse (ICMIC), a new two-dimensional Sine ICMIC modulation map (2D-SIMM) is proposed based on a close-loop modulation coupling (CMC) model, and its chaotic performance is analyzed by means of phase diagram, Lyapunov exponent spectrum and complexity. It shows that this map has good ergodicity, hyperchaotic behavior, large maximum Lyapunov exponent and high complexity. Based on this map, a fast image encryption algorithm is proposed. In this algorithm, the confusion and diffusion processes are combined for one stage. Chaotic shift transform (CST) is proposed to efficiently change the image pixel positions, and the row and column substitutions are applied to scramble the pixel values simultaneously. The simulation and analysis results show that this algorithm has high security, low time complexity, and the abilities of resisting statistical analysis, differential, brute-force, known-plaintext and chosen-plaintext attacks.
15. Steganographic optical image encryption system based on reversible data hiding and double random phase encoding
Science.gov (United States)
Chuang, Cheng-Hung; Chen, Yen-Lin
2013-02-01
This study presents a steganographic optical image encryption system based on reversible data hiding and double random phase encoding (DRPE) techniques. Conventional optical image encryption systems can securely transmit valuable images using an encryption method for possible application in optical transmission systems. The steganographic optical image encryption system based on the DRPE technique has been investigated to hide secret data in encrypted images. However, the DRPE techniques vulnerable to attacks and many of the data hiding methods in the DRPE system can distort the decrypted images. The proposed system, based on reversible data hiding, uses a JBIG2 compression scheme to achieve lossless decrypted image quality and perform a prior encryption process. Thus, the DRPE technique enables a more secured optical encryption process. The proposed method extracts and compresses the bit planes of the original image using the lossless JBIG2 technique. The secret data are embedded in the remaining storage space. The RSA algorithm can cipher the compressed binary bits and secret data for advanced security. Experimental results show that the proposed system achieves a high data embedding capacity and lossless reconstruction of the original images.
16. A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations
International Nuclear Information System (INIS)
Zhang Li-Min; Sun Ke-Hui; Liu Wen-Hao; He Shao-Bo
2017-01-01
In this paper, Adomian decomposition method (ADM) with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear (PWL) hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks. (paper)
17. A novel hybrid color image encryption algorithm using two complex chaotic systems
Science.gov (United States)
Wang, Leyuan; Song, Hongjun; Liu, Ping
2016-02-01
Based on complex Chen and complex Lorenz systems, a novel color image encryption algorithm is proposed. The larger chaotic ranges and more complex behaviors of complex chaotic systems, which compared with real chaotic systems could additionally enhance the security and enlarge key space of color image encryption. The encryption algorithm is comprised of three step processes. In the permutation process, the pixels of plain image are scrambled via two-dimensional and one-dimensional permutation processes among RGB channels individually. In the diffusion process, the exclusive-or (XOR for short) operation is employed to conceal pixels information. Finally, the mixing RGB channels are used to achieve a multilevel encryption. The security analysis and experimental simulations demonstrate that the proposed algorithm is large enough to resist the brute-force attack and has excellent encryption performance.
18. Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion
Science.gov (United States)
Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.
2018-04-01
The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.
19. Optical image transformation and encryption by phase-retrieval-based double random-phase encoding and compressive ghost imaging
Science.gov (United States)
Yuan, Sheng; Yang, Yangrui; Liu, Xuemei; Zhou, Xin; Wei, Zhenzhuo
2018-01-01
An optical image transformation and encryption scheme is proposed based on double random-phase encoding (DRPE) and compressive ghost imaging (CGI) techniques. In this scheme, a secret image is first transformed into a binary image with the phase-retrieval-based DRPE technique, and then encoded by a series of random amplitude patterns according to the ghost imaging (GI) principle. Compressive sensing, corrosion and expansion operations are implemented to retrieve the secret image in the decryption process. This encryption scheme takes the advantage of complementary capabilities offered by the phase-retrieval-based DRPE and GI-based encryption techniques. That is the phase-retrieval-based DRPE is used to overcome the blurring defect of the decrypted image in the GI-based encryption, and the CGI not only reduces the data amount of the ciphertext, but also enhances the security of DRPE. Computer simulation results are presented to verify the performance of the proposed encryption scheme.
20. Separable and Error-Free Reversible Data Hiding in Encrypted Image with High Payload
Directory of Open Access Journals (Sweden)
Zhaoxia Yin
2014-01-01
Full Text Available This paper proposes a separable reversible data-hiding scheme in encrypted image which offers high payload and error-free data extraction. The cover image is partitioned into nonoverlapping blocks and multigranularity encryption is applied to obtain the encrypted image. The data hider preprocesses the encrypted image and randomly selects two basic pixels in each block to estimate the block smoothness and indicate peak points. Additional data are embedded into blocks in the sorted order of block smoothness by using local histogram shifting under the guidance of the peak points. At the receiver side, image decryption and data extraction are separable and can be free to choose. Compared to previous approaches, the proposed method is simpler in calculation while offering better performance: larger payload, better embedding quality, and error-free data extraction, as well as image recovery.
1. MR imaging of heterotopic gray matter
International Nuclear Information System (INIS)
Kryst-Widzgowska, T.; Kozlowski, P.; Poniatowska, R.
1994-01-01
Six patients with heterotopic gray matter were evaluated with MR. 5 patients had history of seizures. 4 cases were suspected of the cerebral tumor. In the MR examination areas of heterotopic gray matter were found along the posterior horn of the lateral ventricle on the one side in 4 cases and bilateraly in 2 cases. In 3 cases another brain abnormalities were also detected including: hypoplasia of corpus callosum, hypoplasia of brain hemisphere, cavum septi pellucidi. MR is a modality of choice in the assessment of abnormal gray matter migration. (author)
2. Multiple image encryption scheme based on pixel exchange operation and vector decomposition
Science.gov (United States)
Xiong, Y.; Quan, C.; Tay, C. J.
2018-02-01
We propose a new multiple image encryption scheme based on a pixel exchange operation and a basic vector decomposition in Fourier domain. In this algorithm, original images are imported via a pixel exchange operator, from which scrambled images and pixel position matrices are obtained. Scrambled images encrypted into phase information are imported using the proposed algorithm and phase keys are obtained from the difference between scrambled images and synthesized vectors in a charge-coupled device (CCD) plane. The final synthesized vector is used as an input in a random phase encoding (DRPE) scheme. In the proposed encryption scheme, pixel position matrices and phase keys serve as additional private keys to enhance the security of the cryptosystem which is based on a 4-f system. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed encryption scheme.
3. A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos
Directory of Open Access Journals (Sweden)
Chunyan Song
2015-10-01
Full Text Available DNA computing based image encryption is a new, promising field. In this paper, we propose a novel image encryption scheme based on DNA encoding and spatiotemporal chaos. In particular, after the plain image is primarily diffused with the bitwise Exclusive-OR operation, the DNA mapping rule is introduced to encode the diffused image. In order to enhance the encryption, the spatiotemporal chaotic system is used to confuse the rows and columns of the DNA encoded image. The experiments demonstrate that the proposed encryption algorithm is of high key sensitivity and large key space, and it can resist brute-force attack, entropy attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack.
4. Privacy-Aware Image Encryption Based on Logistic Map and Data Hiding
Science.gov (United States)
Sun, Jianglin; Liao, Xiaofeng; Chen, Xin; Guo, Shangwei
The increasing need for image communication and storage has created a great necessity for securely transforming and storing images over a network. Whereas traditional image encryption algorithms usually consider the security of the whole plain image, region of interest (ROI) encryption schemes, which are of great importance in practical applications, protect the privacy regions of plain images. Existing ROI encryption schemes usually adopt approximate techniques to detect the privacy region and measure the quality of encrypted images; however, their performance is usually inconsistent with a human visual system (HVS) and is sensitive to statistical attacks. In this paper, we propose a novel privacy-aware ROI image encryption (PRIE) scheme based on logistical mapping and data hiding. The proposed scheme utilizes salient object detection to automatically, adaptively and accurately detect the privacy region of a given plain image. After private pixels have been encrypted using chaotic cryptography, the significant bits are embedded into the nonprivacy region of the plain image using data hiding. Extensive experiments are conducted to illustrate the consistency between our automatic ROI detection and HVS. Our experimental results also demonstrate that the proposed scheme exhibits satisfactory security performance.
5. Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform
Science.gov (United States)
Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun
2018-07-01
Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.
6. Bit-level plane image encryption based on coupled map lattice with time-varying delay
Science.gov (United States)
Lv, Xiupin; Liao, Xiaofeng; Yang, Bo
2018-04-01
Most of the existing image encryption algorithms had two basic properties: confusion and diffusion in a pixel-level plane based on various chaotic systems. Actually, permutation in a pixel-level plane could not change the statistical characteristics of an image, and many of the existing color image encryption schemes utilized the same method to encrypt R, G and B components, which means that the three color components of a color image are processed three times independently. Additionally, dynamical performance of a single chaotic system degrades greatly with finite precisions in computer simulations. In this paper, a novel coupled map lattice with time-varying delay therefore is applied in color images bit-level plane encryption to solve the above issues. Spatiotemporal chaotic system with both much longer period in digitalization and much excellent performances in cryptography is recommended. Time-varying delay embedded in coupled map lattice enhances dynamical behaviors of the system. Bit-level plane image encryption algorithm has greatly reduced the statistical characteristics of an image through the scrambling processing. The R, G and B components cross and mix with one another, which reduces the correlation among the three components. Finally, simulations are carried out and all the experimental results illustrate that the proposed image encryption algorithm is highly secure, and at the same time, also demonstrates superior performance.
7. Hardware stream cipher with controllable chaos generator for colour image encryption
KAUST Repository
Barakat, Mohamed L.; Mansingka, Abhinav S.; Radwan, Ahmed Gomaa; Salama, Khaled N.
2014-01-01
This study presents hardware realisation of chaos-based stream cipher utilised for image encryption applications. A third-order chaotic system with signum non-linearity is implemented and a new post processing technique is proposed to eliminate
8. A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing
Directory of Open Access Journals (Sweden)
Taiyong Li
2017-01-01
Full Text Available In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.
9. Cryptanalysis on an image block encryption algorithm based on spatiotemporal chaos
International Nuclear Information System (INIS)
Wang Xing-Yuan; He Guo-Xiang
2012-01-01
An image block encryption scheme based on spatiotemporal chaos has been proposed recently. In this paper, we analyse the security weakness of the proposal. The main problem of the original scheme is that the generated keystream remains unchanged for encrypting every image. Based on the flaws, we demonstrate a chosen plaintext attack for revealing the equivalent keys with only 6 pairs of plaintext/ciphertext used. Finally, experimental results show the validity of our attack. (general)
10. Cryptanalysis of "an improvement over an image encryption method based on total shuffling"
Science.gov (United States)
Akhavan, A.; Samsudin, A.; Akhshani, A.
2015-09-01
In the past two decades, several image encryption algorithms based on chaotic systems had been proposed. Many of the proposed algorithms are meant to improve other chaos based and conventional cryptographic algorithms. Whereas, many of the proposed improvement methods suffer from serious security problems. In this paper, the security of the recently proposed improvement method for a chaos-based image encryption algorithm is analyzed. The results indicate the weakness of the analyzed algorithm against chosen plain-text.
11. A joint asymmetric watermarking and image encryption scheme
Science.gov (United States)
Boato, G.; Conotter, V.; De Natale, F. G. B.; Fontanari, C.
2008-02-01
Here we introduce a novel watermarking paradigm designed to be both asymmetric, i.e., involving a private key for embedding and a public key for detection, and commutative with a suitable encryption scheme, allowing both to cipher watermarked data and to mark encrypted data without interphering with the detection process. In order to demonstrate the effectiveness of the above principles, we present an explicit example where the watermarking part, based on elementary linear algebra, and the encryption part, exploiting a secret random permutation, are integrated in a commutative scheme.
12. Optical image encryption using QR code and multilevel fingerprints in gyrator transform domains
Science.gov (United States)
Wei, Yang; Yan, Aimin; Dong, Jiabin; Hu, Zhijuan; Zhang, Jingtao
2017-11-01
A new concept of GT encryption scheme is proposed in this paper. We present a novel optical image encryption method by using quick response (QR) code and multilevel fingerprint keys in gyrator transform (GT) domains. In this method, an original image is firstly transformed into a QR code, which is placed in the input plane of cascaded GTs. Subsequently, the QR code is encrypted into the cipher-text by using multilevel fingerprint keys. The original image can be obtained easily by reading the high-quality retrieved QR code with hand-held devices. The main parameters used as private keys are GTs' rotation angles and multilevel fingerprints. Biometrics and cryptography are integrated with each other to improve data security. Numerical simulations are performed to demonstrate the validity and feasibility of the proposed encryption scheme. In the future, the method of applying QR codes and fingerprints in GT domains possesses much potential for information security.
13. Fast ghost imaging and ghost encryption based on the discrete cosine transform
International Nuclear Information System (INIS)
2013-01-01
We introduce the discrete cosine transform as an advanced compression tool for images in computational ghost imaging. A novel approach to fast imaging and encryption, the discrete cosine transform, promotes the security level of ghost images and reduces the image retrieval time. To discuss the advantages of this technique we compare experimental outcomes with simulated ones. (paper)
14. Underwater Image Enhancement by Adaptive Gray World and Differential Gray-Levels Histogram Equalization
Directory of Open Access Journals (Sweden)
WONG, S.-L.
2018-05-01
Full Text Available Most underwater images tend to be dominated by a single color cast. This paper presents a solution to remove the color cast and improve the contrast in underwater images. However, after the removal of the color cast using Gray World (GW method, the resultant image is not visually pleasing. Hence, we propose an integrated approach using Adaptive GW (AGW and Differential Gray-Levels Histogram Equalization (DHE that operate in parallel. The AGW is applied to remove the color cast while DHE is used to improve the contrast of the underwater image. The outputs of both chromaticity components of AGW and intensity components of DHE are combined to form the enhanced image. The results of the proposed method are compared with three existing methods using qualitative and quantitative measures. The proposed method increased the visibility of underwater images and in most cases produces better quantitative scores when compared to the three existing methods.
15. Noise removing in encrypted color images by statistical analysis
Science.gov (United States)
Islam, N.; Puech, W.
2012-03-01
Cryptographic techniques are used to secure confidential data from unauthorized access but these techniques are very sensitive to noise. A single bit change in encrypted data can have catastrophic impact over the decrypted data. This paper addresses the problem of removing bit error in visual data which are encrypted using AES algorithm in the CBC mode. In order to remove the noise, a method is proposed which is based on the statistical analysis of each block during the decryption. The proposed method exploits local statistics of the visual data and confusion/diffusion properties of the encryption algorithm to remove the errors. Experimental results show that the proposed method can be used at the receiving end for the possible solution for noise removing in visual data in encrypted domain.
16. An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm
Science.gov (United States)
Zhang, B.; Sang, Jun; Alam, Mohammad S.
2013-03-01
An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.
17. Optical image encryption method based on incoherent imaging and polarized light encoding
Science.gov (United States)
Wang, Q.; Xiong, D.; Alfalou, A.; Brosseau, C.
2018-05-01
We propose an incoherent encoding system for image encryption based on a polarized encoding method combined with an incoherent imaging. Incoherent imaging is the core component of this proposal, in which the incoherent point-spread function (PSF) of the imaging system serves as the main key to encode the input intensity distribution thanks to a convolution operation. An array of retarders and polarizers is placed on the input plane of the imaging structure to encrypt the polarized state of light based on Mueller polarization calculus. The proposal makes full use of randomness of polarization parameters and incoherent PSF so that a multidimensional key space is generated to deal with illegal attacks. Mueller polarization calculus and incoherent illumination of imaging structure ensure that only intensity information is manipulated. Another key advantage is that complicated processing and recording related to a complex-valued signal are avoided. The encoded information is just an intensity distribution, which is advantageous for data storage and transition because information expansion accompanying conventional encryption methods is also avoided. The decryption procedure can be performed digitally or using optoelectronic devices. Numerical simulation tests demonstrate the validity of the proposed scheme.
18. Optical stream-cipher-like system for image encryption based on Michelson interferometer.
Science.gov (United States)
Yang, Bing; Liu, Zhengjun; Wang, Bo; Zhang, Yan; Liu, Shutian
2011-01-31
A novel optical image encryption scheme based on interference is proposed. The original image is digitally encoded into one phase-only mask by employing an improved Gerchberg-Saxton phase retrieval algorithm together with another predefined random phase mask which serves as the encryption key. The decryption process can be implemented optically based on Michelson interferometer by using the same key. The scheme can be regarded as a stream-cipher-like encryption system, the encryption and decryption keys are the same, however the operations are different. The position coordinates and light wavelength can also be used as additional keys during the decryption. Numerical simulations have demonstrated the validity and robustness of the proposed method.
19. A Novel Image Encryption Scheme Based on Self-Synchronous Chaotic Stream Cipher and Wavelet Transform
Directory of Open Access Journals (Sweden)
Chunlei Fan
2018-06-01
Full Text Available In this paper, a novel image encryption scheme is proposed for the secure transmission of image data. A self-synchronous chaotic stream cipher is designed with the purpose of resisting active attack and ensures the limited error propagation of image data. Two-dimensional discrete wavelet transform and Arnold mapping are used to scramble the pixel value of the original image. A four-dimensional hyperchaotic system with four positive Lyapunov exponents serve as the chaotic sequence generator of the self-synchronous stream cipher in order to enhance the security and complexity of the image encryption system. Finally, the simulation experiment results show that this image encryption scheme is both reliable and secure.
20. Image encryption using fingerprint as key based on phase retrieval algorithm and public key cryptography
Science.gov (United States)
Zhao, Tieyu; Ran, Qiwen; Yuan, Lin; Chi, Yingying; Ma, Jing
2015-09-01
In this paper, a novel image encryption system with fingerprint used as a secret key is proposed based on the phase retrieval algorithm and RSA public key algorithm. In the system, the encryption keys include the fingerprint and the public key of RSA algorithm, while the decryption keys are the fingerprint and the private key of RSA algorithm. If the users share the fingerprint, then the system will meet the basic agreement of asymmetric cryptography. The system is also applicable for the information authentication. The fingerprint as secret key is used in both the encryption and decryption processes so that the receiver can identify the authenticity of the ciphertext by using the fingerprint in decryption process. Finally, the simulation results show the validity of the encryption scheme and the high robustness against attacks based on the phase retrieval technique.
1. A Colour Image Encryption Scheme Using Permutation-Substitution Based on Chaos
Directory of Open Access Journals (Sweden)
Xing-Yuan Wang
2015-06-01
Full Text Available An encryption scheme for colour images using a spatiotemporal chaotic system is proposed. Initially, we use the R, G and B components of a colour plain-image to form a matrix. Then the matrix is permutated by using zigzag path scrambling. The resultant matrix is then passed through a substitution process. Finally, the ciphered colour image is obtained from the confused matrix. Theoretical analysis and experimental results indicate that the proposed scheme is both secure and practical, which make it suitable for encrypting colour images of any size.
2. Optical image encryption using fresnel zone plate mask based on fast walsh hadamard transform
Science.gov (United States)
Khurana, Mehak; Singh, Hukum
2018-05-01
A new symmetric encryption technique using Fresnel Zone Plate (FZP) based on Fast Walsh Hadamard Transform (FWHT) is proposed for security enhancement. In this technique, bits of plain image is randomized by shuffling the bits randomly. The obtained scrambled image is then masked with FZP using symmetric encryption in FWHT domain to obtain final encrypted image. FWHT has been used in the cryptosystem so as to protect image data from the quantization error and for reconstructing the image perfectly. The FZP used in proposed scheme increases the key space and makes it robust to many traditional attacks. The effectiveness and robustness of the proposed cryptosystem has been analyzed on the basis of various parameters by simulating on MATLAB 8.1.0 (R2012b). The experimental results are provided to highlight suitability of the proposed cryptosystem and prove that the system is secure.
3. An image encryption scheme based on three-dimensional Brownian motion and chaotic system
International Nuclear Information System (INIS)
Chai Xiu-Li; Yuan Ke; Gan Zhi-Hua; Lu Yang; Chen Yi-Ran
2017-01-01
At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. (paper)
4. A symmetric image encryption scheme based on 3D chaotic cat maps
International Nuclear Information System (INIS)
Chen Guanrong; Mao Yaobin; Chui, Charles K.
2004-01-01
Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. Due to the exceptionally desirable properties of mixing and sensitivity to initial conditions and parameters of chaotic maps, chaos-based encryption has suggested a new and efficient way to deal with the intractable problem of fast and highly secure image encryption. In this paper, the two-dimensional chaotic cat map is generalized to 3D for designing a real-time secure symmetric encryption scheme. This new scheme employs the 3D cat map to shuffle the positions (and, if desired, grey values as well) of image pixels and uses another chaotic map to confuse the relationship between the cipher-image and the plain-image, thereby significantly increasing the resistance to statistical and differential attacks. Thorough experimental tests are carried out with detailed analysis, demonstrating the high security and fast encryption speed of the new scheme
5. A fast image encryption algorithm based on only blocks in cipher text
Science.gov (United States)
Wang, Xing-Yuan; Wang, Qian
2014-03-01
In this paper, a fast image encryption algorithm is proposed, in which the shuffling and diffusion is performed simultaneously. The cipher-text image is divided into blocks and each block has k ×k pixels, while the pixels of the plain-text are scanned one by one. Four logistic maps are used to generate the encryption key stream and the new place in the cipher image of plain image pixels, including the row and column of the block which the pixel belongs to and the place where the pixel would be placed in the block. After encrypting each pixel, the initial conditions of logistic maps would be changed according to the encrypted pixel's value; after encrypting each row of plain image, the initial condition would also be changed by the skew tent map. At last, it is illustrated that this algorithm has a faster speed, big key space, and better properties in withstanding differential attacks, statistical analysis, known plaintext, and chosen plaintext attacks.
6. A fast image encryption algorithm based on only blocks in cipher text
International Nuclear Information System (INIS)
Wang Xing-Yuan; Wang Qian
2014-01-01
In this paper, a fast image encryption algorithm is proposed, in which the shuffling and diffusion is performed simultaneously. The cipher-text image is divided into blocks and each block has k ×k pixels, while the pixels of the plain-text are scanned one by one. Four logistic maps are used to generate the encryption key stream and the new place in the cipher image of plain image pixels, including the row and column of the block which the pixel belongs to and the place where the pixel would be placed in the block. After encrypting each pixel, the initial conditions of logistic maps would be changed according to the encrypted pixel's value; after encrypting each row of plain image, the initial condition would also be changed by the skew tent map. At last, it is illustrated that this algorithm has a faster speed, big key space, and better properties in withstanding differential attacks, statistical analysis, known plaintext, and chosen plaintext attacks
7. A Novel Image Encryption Based on Algebraic S-box and Arnold Transform
Science.gov (United States)
2017-09-01
Recent study shows that substitution box (S-box) only cannot be reliably used in image encryption techniques. We, in this paper, propose a novel and secure image encryption scheme that utilizes the combined effect of an algebraic substitution box along with the scrambling effect of the Arnold transform. The underlying algorithm involves the application of S-box, which is the most imperative source to create confusion and diffusion in the data. The speciality of the proposed algorithm lies, firstly, in the high sensitivity of our S-box to the choice of the initial conditions which makes this S-box stronger than the chaos-based S-boxes as it saves computational labour by deploying a comparatively simple and direct approach based on the algebraic structure of the multiplicative cyclic group of the Galois field. Secondly the proposed method becomes more secure by considering a combination of S-box with certain number of iterations of the Arnold transform. The strength of the S-box is examined in terms of various performance indices such as nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. We prove through the most significant techniques used for the statistical analyses of the encrypted image that our image encryption algorithm satisfies all the necessary criteria to be usefully and reliably implemented in image encryption applications.
8. Image encryption based on permutation-substitution using chaotic map and Latin Square Image Cipher
Science.gov (United States)
Panduranga, H. T.; Naveen Kumar, S. K.; Kiran, HASH(0x22c8da0)
2014-06-01
In this paper we presented a image encryption based on permutation-substitution using chaotic map and Latin square image cipher. The proposed method consists of permutation and substitution process. In permutation process, plain image is permuted according to chaotic sequence generated using chaotic map. In substitution process, based on secrete key of 256 bit generate a Latin Square Image Cipher (LSIC) and this LSIC is used as key image and perform XOR operation between permuted image and key image. The proposed method can applied to any plain image with unequal width and height as well and also resist statistical attack, differential attack. Experiments carried out for different images of different sizes. The proposed method possesses large key space to resist brute force attack.
9. Analysis and improvement of a chaos-based image encryption algorithm
International Nuclear Information System (INIS)
Xiao Di; Liao Xiaofeng; Wei Pengcheng
2009-01-01
The security of digital image attracts much attention recently. In Guan et al. [Guan Z, Huang F, Guan W. Chaos-based image encryption algorithm. Phys Lett A 2005; 346: 153-7.], a chaos-based image encryption algorithm has been proposed. In this paper, the cause of potential flaws in the original algorithm is analyzed in detail, and then the corresponding enhancement measures are proposed. Both theoretical analysis and computer simulation indicate that the improved algorithm can overcome these flaws and maintain all the merits of the original one.
10. Image Encryption Scheme Based on Balanced Two-Dimensional Cellular Automata
Directory of Open Access Journals (Sweden)
Xiaoyan Zhang
2013-01-01
Full Text Available Cellular automata (CA are simple models of computation which exhibit fascinatingly complex behavior. Due to the universality of CA model, it has been widely applied in traditional cryptography and image processing. The aim of this paper is to present a new image encryption scheme based on balanced two-dimensional cellular automata. In this scheme, a random image with the same size of the plain image to be encrypted is first generated by a pseudo-random number generator with a seed. Then, the random image is evoluted alternately with two balanced two-dimensional CA rules. At last, the cipher image is obtained by operating bitwise XOR on the final evolution image and the plain image. This proposed scheme possesses some advantages such as very large key space, high randomness, complex cryptographic structure, and pretty fast encryption/decryption speed. Simulation results obtained from some classical images at the USC-SIPI database demonstrate the strong performance of the proposed image encryption scheme.
11. Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms
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Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya
2017-01-01
In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.
12. Image encryption with chaotic map and Arnold transform in the gyrator transform domains
Science.gov (United States)
Sang, Jun; Luo, Hongling; Zhao, Jun; Alam, Mohammad S.; Cai, Bin
2017-05-01
An image encryption method combing chaotic map and Arnold transform in the gyrator transform domains was proposed. Firstly, the original secret image is XOR-ed with a random binary sequence generated by a logistic map. Then, the gyrator transform is performed. Finally, the amplitude and phase of the gyrator transform are permutated by Arnold transform. The decryption procedure is the inverse operation of encryption. The secret keys used in the proposed method include the control parameter and the initial value of the logistic map, the rotation angle of the gyrator transform, and the transform number of the Arnold transform. Therefore, the key space is large, while the key data volume is small. The numerical simulation was conducted to demonstrate the effectiveness of the proposed method and the security analysis was performed in terms of the histogram of the encrypted image, the sensitiveness to the secret keys, decryption upon ciphertext loss, and resistance to the chosen-plaintext attack.
13. Comment on ‘A technique for image encryption using digital signature’
Science.gov (United States)
Hernández Encinas, L.; Peinado Domínguez, A.
2006-12-01
The security of a recently proposed technique for encryption images by Sinha and Singh [A. Sinha, K. Singh, Opt. Commun. 218 (2003) 229], based on the use of digital signatures and error correcting codes, is analyzed. The proposed cryptosystem is shown to have some weakness. In fact, the secret key and the original image can be recovered efficiently by a brute force attack.
14. High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique
Science.gov (United States)
Zhao, Shengmei; Wang, Le; Liang, Wenqiang; Cheng, Weiwen; Gong, Longyan
2015-10-01
In this paper, we propose a high performance optical encryption (OE) scheme based on computational ghost imaging (GI) with QR code and compressive sensing (CS) technique, named QR-CGI-OE scheme. N random phase screens, generated by Alice, is a secret key and be shared with its authorized user, Bob. The information is first encoded by Alice with QR code, and the QR-coded image is then encrypted with the aid of computational ghost imaging optical system. Here, measurement results from the GI optical system's bucket detector are the encrypted information and be transmitted to Bob. With the key, Bob decrypts the encrypted information to obtain the QR-coded image with GI and CS techniques, and further recovers the information by QR decoding. The experimental and numerical simulated results show that the authorized users can recover completely the original image, whereas the eavesdroppers can not acquire any information about the image even the eavesdropping ratio (ER) is up to 60% at the given measurement times. For the proposed scheme, the number of bits sent from Alice to Bob are reduced considerably and the robustness is enhanced significantly. Meantime, the measurement times in GI system is reduced and the quality of the reconstructed QR-coded image is improved.
15. Digital double random amplitude image encryption method based on the symmetry property of the parametric discrete Fourier transform
Science.gov (United States)
2018-03-01
We propose a real-to-real image encryption method. It is a double random amplitude encryption method based on the parametric discrete Fourier transform coupled with chaotic maps to perform the scrambling. The main idea behind this method is the introduction of a complex-to-real conversion by exploiting the inherent symmetry property of the transform in the case of real-valued sequences. This conversion allows the encrypted image to be real-valued instead of being a complex-valued image as in all existing double random phase encryption methods. The advantage is to store or transmit only one image instead of two images (real and imaginary parts). Computer simulation results and comparisons with the existing double random amplitude encryption methods are provided for peak signal-to-noise ratio, correlation coefficient, histogram analysis, and key sensitivity.
16. A fast image encryption system based on chaotic maps with finite precision representation
International Nuclear Information System (INIS)
Kwok, H.S.; Tang, Wallace K.S.
2007-01-01
In this paper, a fast chaos-based image encryption system with stream cipher structure is proposed. In order to achieve a fast throughput and facilitate hardware realization, 32-bit precision representation with fixed point arithmetic is assumed. The major core of the encryption system is a pseudo-random keystream generator based on a cascade of chaotic maps, serving the purpose of sequence generation and random mixing. Unlike the other existing chaos-based pseudo-random number generators, the proposed keystream generator not only achieves a very fast throughput, but also passes the statistical tests of up-to-date test suite even under quantization. The overall design of the image encryption system is to be explained while detail cryptanalysis is given and compared with some existing schemes
17. Optical image encryption system using nonlinear approach based on biometric authentication
Science.gov (United States)
Verma, Gaurav; Sinha, Aloka
2017-07-01
A nonlinear image encryption scheme using phase-truncated Fourier transform (PTFT) and natural logarithms is proposed in this paper. With the help of the PTFT, the input image is truncated into phase and amplitude parts at the Fourier plane. The phase-only information is kept as the secret key for the decryption, and the amplitude distribution is modulated by adding an undercover amplitude random mask in the encryption process. Furthermore, the encrypted data is kept hidden inside the face biometric-based phase mask key using the base changing rule of logarithms for secure transmission. This phase mask is generated through principal component analysis. Numerical experiments show the feasibility and the validity of the proposed nonlinear scheme. The performance of the proposed scheme has been studied against the brute force attacks and the amplitude-phase retrieval attack. Simulation results are presented to illustrate the enhanced system performance with desired advantages in comparison to the linear cryptosystem.
18. Image encryption based on fractal-structured phase mask in fractional Fourier transform domain
Science.gov (United States)
Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-04-01
We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.
19. A NEW TECHNIQUE BASED ON CHAOTIC STEGANOGRAPHY AND ENCRYPTION TEXT IN DCT DOMAIN FOR COLOR IMAGE
Directory of Open Access Journals (Sweden)
2013-10-01
Full Text Available Image steganography is the art of hiding information into a cover image. This paper presents a new technique based on chaotic steganography and encryption text in DCT domain for color image, where DCT is used to transform original image (cover image from spatial domain to frequency domain. This technique used chaotic function in two phases; firstly; for encryption secret message, second; for embedding in DCT cover image. With this new technique, good results are obtained through satisfying the important properties of steganography such as: imperceptibility; improved by having mean square error (MSE, peak signal to noise ratio (PSNR and normalized correlation (NC, to phase and capacity; improved by encoding the secret message characters with variable length codes and embedding the secret message in one level of color image only.
20. Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain
Science.gov (United States)
Vilardy, Juan M.; Millán, María S.; Pérez-Cabré, Elisabet
2017-02-01
A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption-decryption scheme.
1. A proposed security technique based on watermarking and encryption for digital imaging and communications in medicine
Directory of Open Access Journals (Sweden)
Mohamed M. Abd-Eldayem
2013-03-01
Full Text Available Nowadays; modern Hospital Data Management Systems (HDMSs are applied in a computer network; in addition medicinal equipments produce medical images in a digital form. HDMS must store and exchange these images in a secured environment to provide image integrity and patient privacy. The reversible watermarking techniques can be used to provide the integrity and the privacy. In this paper, a security technique based on watermarking and encryption is proposed to be used for Digital Imaging and Communications in Medicine (DICOM. It provides patient authentication, information confidentiality and integrity based on reversible watermark. To achieve integrity service at the sender side; a hash value based on encrypted MD5 is determined from the image. And to satisfy the reversible feature; R–S-Vector is determined from the image and is compressed based on a Huffman compression algorithm. After that to provide confidentiality and authentication services: the compressed R–S-Vector, the hash value and patient ID are concatenated to form a watermark then this watermark is encrypted using AES encryption technique, finally the watermark is embedded inside the medical image. Experimental results prove that the proposed technique can provide patient authentication services, image integrity service and information confidentiality service with excellent efficiency. Concluded results for all tested DICOM medical images and natural images show the following: BER equals 0, both of SNR and PSNR are consistent and have large values, and MSE has low value; the average values of SNR, PSNR and MSE are 52 dB, 57 dB and 0.12 respectively. Therefore, watermarked images have high imperceptibility, invisibility and transparency. In addition, the watermark extracted from the image at the receiver side is identical to the watermark embedded into the image in the sender side; as a result, the proposed technique is totally reversible, and the embedded watermark does not
2. Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution
International Nuclear Information System (INIS)
Chen, Wen; Chen, Xudong; Sheppard, Colin J R
2012-01-01
We propose a new phase retrieval algorithm for optical image encryption in three-dimensional (3D) space. The two-dimensional (2D) plaintext is considered as a series of particles distributed in 3D space, and an iterative phase retrieval algorithm is developed to encrypt the series of particles into phase-only masks. The feasibility and effectiveness of the proposed method are demonstrated by a numerical experiment, and the advantages and security of the proposed optical cryptosystems are also analyzed and discussed. (paper)
3. An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps
Directory of Open Access Journals (Sweden)
Xiaojun Tong
2015-01-01
Full Text Available This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently.
4. Devil’s Vortex Phase Structure as Frequency Plane Mask for Image Encryption Using the Fractional Mellin Transform
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Sunanda Vashisth
2014-01-01
Full Text Available A frequency plane phase mask based on Devil’s vortex structure has been used for image encryption using the fractional Mellin transform. The phase key for decryption is obtained by an iterative phase retrieval algorithm. The proposed scheme has been validated for grayscale secret target images, by numerical simulation. The efficacy of the scheme has been evaluated by computing mean-squared-error between the secret target image and the decrypted image. Sensitivity analysis of the decryption process to variations in various encryption parameters has been carried out. The proposed encryption scheme has been seen to exhibit reasonable robustness against occlusion attack.
5. Encryption and watermark-treated medical image against hacking disease-An immune convention in spatial and frequency domains.
Science.gov (United States)
Lakshmi, C; Thenmozhi, K; Rayappan, John Bosco Balaguru; Amirtharajan, Rengarajan
2018-06-01
Digital Imaging and Communications in Medicine (DICOM) is one among the significant formats used worldwide for the representation of medical images. Undoubtedly, medical-image security plays a crucial role in telemedicine applications. Merging encryption and watermarking in medical-image protection paves the way for enhancing the authentication and safer transmission over open channels. In this context, the present work on DICOM image encryption has employed a fuzzy chaotic map for encryption and the Discrete Wavelet Transform (DWT) for watermarking. The proposed approach overcomes the limitation of the Arnold transform-one of the most utilised confusion mechanisms in image ciphering. Various metrics have substantiated the effectiveness of the proposed medical-image encryption algorithm. Copyright © 2018 Elsevier B.V. All rights reserved.
6. Design of an image encryption scheme based on a multiple chaotic map
Science.gov (United States)
Tong, Xiao-Jun
2013-07-01
In order to solve the problem that chaos is degenerated in limited computer precision and Cat map is the small key space, this paper presents a chaotic map based on topological conjugacy and the chaotic characteristics are proved by Devaney definition. In order to produce a large key space, a Cat map named block Cat map is also designed for permutation process based on multiple-dimensional chaotic maps. The image encryption algorithm is based on permutation-substitution, and each key is controlled by different chaotic maps. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to the proposed scheme with AES, DES and Logistic encryption methods, we come to the conclusion that the image encryption method solves the problem of low precision of one dimensional chaotic function and has higher speed and higher security.
7. Chaotic image encryption based on running-key related to plaintext.
Science.gov (United States)
Guanghui, Cao; Kai, Hu; Yizhi, Zhang; Jun, Zhou; Xing, Zhang
2014-01-01
In the field of chaotic image encryption, the algorithm based on correlating key with plaintext has become a new developing direction. However, for this kind of algorithm, some shortcomings in resistance to reconstruction attack, efficient utilization of chaotic resource, and reducing dynamical degradation of digital chaos are found. In order to solve these problems and further enhance the security of encryption algorithm, based on disturbance and feedback mechanism, we present a new image encryption scheme. In the running-key generation stage, by successively disturbing chaotic stream with cipher-text, the relation of running-key to plaintext is established, reconstruction attack is avoided, effective use of chaotic resource is guaranteed, and dynamical degradation of digital chaos is minimized. In the image encryption stage, by introducing random-feedback mechanism, the difficulty of breaking this scheme is increased. Comparing with the-state-of-the-art algorithms, our scheme exhibits good properties such as large key space, long key period, and extreme sensitivity to the initial key and plaintext. Therefore, it can resist brute-force, reconstruction attack, and differential attack.
8. Chaotic Image Encryption Based on Running-Key Related to Plaintext
Directory of Open Access Journals (Sweden)
Cao Guanghui
2014-01-01
Full Text Available In the field of chaotic image encryption, the algorithm based on correlating key with plaintext has become a new developing direction. However, for this kind of algorithm, some shortcomings in resistance to reconstruction attack, efficient utilization of chaotic resource, and reducing dynamical degradation of digital chaos are found. In order to solve these problems and further enhance the security of encryption algorithm, based on disturbance and feedback mechanism, we present a new image encryption scheme. In the running-key generation stage, by successively disturbing chaotic stream with cipher-text, the relation of running-key to plaintext is established, reconstruction attack is avoided, effective use of chaotic resource is guaranteed, and dynamical degradation of digital chaos is minimized. In the image encryption stage, by introducing random-feedback mechanism, the difficulty of breaking this scheme is increased. Comparing with the-state-of-the-art algorithms, our scheme exhibits good properties such as large key space, long key period, and extreme sensitivity to the initial key and plaintext. Therefore, it can resist brute-force, reconstruction attack, and differential attack.
9. An authenticated image encryption scheme based on chaotic maps and memory cellular automata
Science.gov (United States)
Bakhshandeh, Atieh; Eslami, Ziba
2013-06-01
This paper introduces a new image encryption scheme based on chaotic maps, cellular automata and permutation-diffusion architecture. In the permutation phase, a piecewise linear chaotic map is utilized to confuse the plain-image and in the diffusion phase, we employ the Logistic map as well as a reversible memory cellular automata to obtain an efficient and secure cryptosystem. The proposed method admits advantages such as highly secure diffusion mechanism, computational efficiency and ease of implementation. A novel property of the proposed scheme is its authentication ability which can detect whether the image is tampered during the transmission or not. This is particularly important in applications where image data or part of it contains highly sensitive information. Results of various analyses manifest high security of this new method and its capability for practical image encryption.
10. An Improved Image Encryption Algorithm Based on Cyclic Rotations and Multiple Chaotic Sequences: Application to Satellite Images
Directory of Open Access Journals (Sweden)
2017-10-01
Full Text Available In this paper, a new satellite image encryption algorithm based on the combination of multiple chaotic systems and a random cyclic rotation technique is proposed. Our contribution consists in implementing three different chaotic maps (logistic, sine, and standard combined to improve the security of satellite images. Besides enhancing the encryption, the proposed algorithm also focuses on advanced efficiency of the ciphered images. Compared with classical encryption schemes based on multiple chaotic maps and the Rubik's cube rotation, our approach has not only the same merits of chaos systems like high sensitivity to initial values, unpredictability, and pseudo-randomness, but also other advantages like a higher number of permutations, better performances in Peak Signal to Noise Ratio (PSNR and a Maximum Deviation (MD.
11. A Novel Image Encryption Scheme Based on Clifford Attractor and Noisy Logistic Map for Secure Transferring Images in Navy
Directory of Open Access Journals (Sweden)
2017-04-01
In this paper, we first give a brief introduction into chaotic image encryption and then we investigate some important properties and behaviour of the logistic map. The logistic map, aperiodic trajectory, or random-like fluctuation, could not be obtained with some choice of initial condition. Therefore, a noisy logistic map with an additive system noise is introduced. The proposed scheme is based on the extended map of the Clifford strange attractor, where each dimension has a specific role in the encryption process. Two dimensions are used for pixel permutation and the third dimension is used for pixel diffusion. In order to optimize the Clifford encryption system we increase the space key by using the noisy logistic map and a novel encryption scheme based on the Clifford attractor and the noisy logistic map for secure transfer images is proposed. This algorithm consists of two parts: the noisy logistic map shuffle of the pixel position and the pixel value. We use times for shuffling the pixel position and value then we generate the new pixel position and value by the Clifford system. To illustrate the efficiency of the proposed scheme, various types of security analysis are tested. It can be concluded that the proposed image encryption system is a suitable choice for practical applications.
12. Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme
Science.gov (United States)
Li, Xianye; Meng, Xiangfeng; Yang, Xiulun; Wang, Yurong; Yin, Yongkai; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi
2018-03-01
A multiple-image encryption method via lifting wavelet transform (LWT) and XOR operation is proposed, which is based on a row scanning compressive ghost imaging scheme. In the encryption process, the scrambling operation is implemented for the sparse images transformed by LWT, then the XOR operation is performed on the scrambled images, and the resulting XOR images are compressed in the row scanning compressive ghost imaging, through which the ciphertext images can be detected by bucket detector arrays. During decryption, the participant who possesses his/her correct key-group, can successfully reconstruct the corresponding plaintext image by measurement key regeneration, compression algorithm reconstruction, XOR operation, sparse images recovery, and inverse LWT (iLWT). Theoretical analysis and numerical simulations validate the feasibility of the proposed method.
13. Improved Image Encryption for Real-Time Application over Wireless Communication Networks using Hybrid Cryptography Technique
Directory of Open Access Journals (Sweden)
2016-12-01
Full Text Available Advances in communication networks have enabled organization to send confidential data such as digital images over wireless networks. However, the broadcast nature of wireless communication channel has made it vulnerable to attack from eavesdroppers. We have developed a hybrid cryptography technique, and we present its application to digital images as a means of improving the security of digital image for transmission over wireless communication networks. The hybrid technique uses a combination of a symmetric (Data Encryption Standard and asymmetric (Rivest Shamir Adleman cryptographic algorithms to secure data to be transmitted between different nodes of a wireless network. Three different image samples of type jpeg, png and jpg were tested using this technique. The results obtained showed that the hybrid system encrypt the images with minimal simulation time, and high throughput. More importantly, there is no relation or information between the original images and their encrypted form, according to Shannon’s definition of perfect security, thereby making the system much more secure.
14. Simultaneous optical image compression and encryption using error-reduction phase retrieval algorithm
International Nuclear Information System (INIS)
Liu, Wei; Liu, Shutian; Liu, Zhengjun
2015-01-01
We report a simultaneous image compression and encryption scheme based on solving a typical optical inverse problem. The secret images to be processed are multiplexed as the input intensities of a cascaded diffractive optical system. At the output plane, a compressed complex-valued data with a lot fewer measurements can be obtained by utilizing error-reduction phase retrieval algorithm. The magnitude of the output image can serve as the final ciphertext while its phase serves as the decryption key. Therefore the compression and encryption are simultaneously completed without additional encoding and filtering operations. The proposed strategy can be straightforwardly applied to the existing optical security systems that involve diffraction and interference. Numerical simulations are performed to demonstrate the validity and security of the proposal. (paper)
15. Differences in quantitative assessment of myocardial scar and gray zone by LGE-CMR imaging using established gray zone protocols.
Science.gov (United States)
Mesubi, Olurotimi; Ego-Osuala, Kelechi; Jeudy, Jean; Purtilo, James; Synowski, Stephen; Abutaleb, Ameer; Niekoop, Michelle; Abdulghani, Mohammed; Asoglu, Ramazan; See, Vincent; Saliaris, Anastasios; Shorofsky, Stephen; Dickfeld, Timm
2015-02-01
Late gadolinium enhancement cardiac magnetic resonance (LGE-CMR) imaging is the gold standard for myocardial scar evaluation. Heterogeneous areas of scar ('gray zone'), may serve as arrhythmogenic substrate. Various gray zone protocols have been correlated to clinical outcomes and ventricular tachycardia channels. This study assessed the quantitative differences in gray zone and scar core sizes as defined by previously validated signal intensity (SI) threshold algorithms. High quality LGE-CMR images performed in 41 cardiomyopathy patients [ischemic (33) or non-ischemic (8)] were analyzed using previously validated SI threshold methods [Full Width at Half Maximum (FWHM), n-standard deviation (NSD) and modified-FWHM]. Myocardial scar was defined as scar core and gray zone using SI thresholds based on these methods. Scar core, gray zone and total scar sizes were then computed and compared among these models. The median gray zone mass was 2-3 times larger with FWHM (15 g, IQR: 8-26 g) compared to NSD or modified-FWHM (5 g, IQR: 3-9 g; and 8 g. IQR: 6-12 g respectively, p zone extent (percentage of total scar that was gray zone) also varied significantly among the three methods, 51 % (IQR: 42-61 %), 17 % (IQR: 11-21 %) versus 38 % (IQR: 33-43 %) for FWHM, NSD and modified-FWHM respectively (p zone and scar core. Infarct core and total myocardial scar mass also differ using these methods. Further evaluation of the most accurate quantification method is needed.
16. Image Encryption Using Stream Cipher Based on Nonlinear Combination Generator with Enhanced Security
Directory of Open Access Journals (Sweden)
Belmeguenaï Aîssa
2013-03-01
Full Text Available The images are very largely used in our daily life; the security of their transfer became necessary. In this work a novel image encryption scheme using stream cipher algorithm based on nonlinear combination generator is developed. The main contribution of this work is to enhance the security of encrypted image. The proposed scheme is based on the use the several linear feedback shifts registers whose feedback polynomials are primitive and of degrees are all pairwise coprimes combined by resilient function whose resiliency order, algebraic degree and nonlinearity attain Siegenthaler’s and Sarkar, al.’s bounds. This proposed scheme is simple and highly efficient. In order to evaluate performance, the proposed algorithm was measured through a series of tests. These tests included visual test and histogram analysis, key space analysis, correlation coefficient analysis, image entropy, key sensitivity analysis, noise analysis, Berlekamp-Massey attack, correlation attack and algebraic attack. Experimental results demonstrate the proposed system is highly key sensitive, highly resistance to the noises and shows a good resistance against brute-force, statistical attacks, Berlekamp-Massey attack, correlation attack, algebraic attack and a robust system which makes it a potential candidate for encryption of image.
17. Fourier-Mellin moment-based intertwining map for image encryption
Science.gov (United States)
Kaur, Manjit; Kumar, Vijay
2018-03-01
In this paper, a robust image encryption technique that utilizes Fourier-Mellin moments and intertwining logistic map is proposed. Fourier-Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier-Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.
18. A novel image encryption algorithm based on chaos maps with Markov properties
Science.gov (United States)
Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang
2015-02-01
In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.
19. A Novel Image Encryption Scheme Based on Intertwining Chaotic Maps and RC4 Stream Cipher
Science.gov (United States)
Kumari, Manju; Gupta, Shailender
2018-03-01
As the systems are enabling us to transmit large chunks of data, both in the form of texts and images, there is a need to explore algorithms which can provide a higher security without increasing the time complexity significantly. This paper proposes an image encryption scheme which uses intertwining chaotic maps and RC4 stream cipher to encrypt/decrypt the images. The scheme employs chaotic map for the confusion stage and for generation of key for the RC4 cipher. The RC4 cipher uses this key to generate random sequences which are used to implement an efficient diffusion process. The algorithm is implemented in MATLAB-2016b and various performance metrics are used to evaluate its efficacy. The proposed scheme provides highly scrambled encrypted images and can resist statistical, differential and brute-force search attacks. The peak signal-to-noise ratio values are quite similar to other schemes, the entropy values are close to ideal. In addition, the scheme is very much practical since having lowest time complexity then its counterparts.
20. QR code-based non-linear image encryption using Shearlet transform and spiral phase transform
Science.gov (United States)
Kumar, Ravi; Bhaduri, Basanta; Hennelly, Bryan
2018-02-01
In this paper, we propose a new quick response (QR) code-based non-linear technique for image encryption using Shearlet transform (ST) and spiral phase transform. The input image is first converted into a QR code and then scrambled using the Arnold transform. The scrambled image is then decomposed into five coefficients using the ST and the first Shearlet coefficient, C1 is interchanged with a security key before performing the inverse ST. The output after inverse ST is then modulated with a random phase mask and further spiral phase transformed to get the final encrypted image. The first coefficient, C1 is used as a private key for decryption. The sensitivity of the security keys is analysed in terms of correlation coefficient and peak signal-to noise ratio. The robustness of the scheme is also checked against various attacks such as noise, occlusion and special attacks. Numerical simulation results are shown in support of the proposed technique and an optoelectronic set-up for encryption is also proposed.
1. Combination of Sharing Matrix and Image Encryption for Lossless $(k,n)$ -Secret Image Sharing.
Science.gov (United States)
Bao, Long; Yi, Shuang; Zhou, Yicong
2017-12-01
This paper first introduces a (k,n) -sharing matrix S (k, n) and its generation algorithm. Mathematical analysis is provided to show its potential for secret image sharing. Combining sharing matrix with image encryption, we further propose a lossless (k,n) -secret image sharing scheme (SMIE-SIS). Only with no less than k shares, all the ciphertext information and security key can be reconstructed, which results in a lossless recovery of original information. This can be proved by the correctness and security analysis. Performance evaluation and security analysis demonstrate that the proposed SMIE-SIS with arbitrary settings of k and n has at least five advantages: 1) it is able to fully recover the original image without any distortion; 2) it has much lower pixel expansion than many existing methods; 3) its computation cost is much lower than the polynomial-based secret image sharing methods; 4) it is able to verify and detect a fake share; and 5) even using the same original image with the same initial settings of parameters, every execution of SMIE-SIS is able to generate completely different secret shares that are unpredictable and non-repetitive. This property offers SMIE-SIS a high level of security to withstand many different attacks.
2. Optical image encryption using password key based on phase retrieval algorithm
Science.gov (United States)
Zhao, Tieyu; Ran, Qiwen; Yuan, Lin; Chi, Yingying; Ma, Jing
2016-04-01
A novel optical image encryption system is proposed using password key based on phase retrieval algorithm (PRA). In the encryption process, a shared image is taken as a symmetric key and the plaintext is encoded into the phase-only mask based on the iterative PRA. The linear relationship between the plaintext and ciphertext is broken using the password key, which can resist the known plaintext attack. The symmetric key and the retrieved phase are imported into the input plane and Fourier plane of 4f system during the decryption, respectively, so as to obtain the plaintext on the CCD. Finally, we analyse the key space of the password key, and the results show that the proposed scheme can resist a brute force attack due to the flexibility of the password key.
3. Color Image Encryption Using Three-Dimensional Sine ICMIC Modulation Map and DNA Sequence Operations
Science.gov (United States)
Liu, Wenhao; Sun, Kehui; He, Yi; Yu, Mengyao
Derived from Sine map and iterative chaotic map with infinite collapse (ICMIC), a three-dimensional hyperchaotic Sine ICMIC modulation map (3D-SIMM) is proposed based on a close-loop modulation coupling (CMC) method. Based on this map, a novel color image encryption algorithm is designed by employing a hybrid model of multidirectional circular permutation and deoxyribonucleic acid (DNA) masking. In this scheme, the pixel positions of image are scrambled by multidirectional circular permutation, and the pixel values are substituted by DNA sequence operations. The simulation results and security analysis show that the algorithm has good encryption effect and strong key sensitivity, and can resist brute-force, statistical, differential, known-plaintext and chosen-plaintext attacks.
4. Optical image encryption with silhouette removal based on interference and phase blend processing
Science.gov (United States)
Wang, Qu
2012-10-01
To completely eliminate the silhouette problem that inherently exists in the earlier interference-based encryption scheme with two phase-only masks (POMs), we propose a simple new encryption method based on optical interference of one random POM and two analytically obtained POMs. Different from the previous methods which require time-consuming iterative computation or postprocessing of the POMs for silhouette removal, our method can resolve the problem during the production of the POMs based on interference principle. Information associated with the original image is smoothed away by modulation of the random POM. Illegal deciphers cannot retrieve the primitive image using only one or two of the POMs. Incorporated with the linear phase blend operation, our method can provide higher robustness against brute force attacks. Simulation results are presented to support the validity and feasibility of our method.
5. Optical image encryption using chaos-based compressed sensing and phase-shifting interference in fractional wavelet domain
Science.gov (United States)
Liu, Qi; Wang, Ying; Wang, Jun; Wang, Qiong-Hua
2018-02-01
In this paper, a novel optical image encryption system combining compressed sensing with phase-shifting interference in fractional wavelet domain is proposed. To improve the encryption efficiency, the volume data of original image are decreased by compressed sensing. Then the compacted image is encoded through double random phase encoding in asymmetric fractional wavelet domain. In the encryption system, three pseudo-random sequences, generated by three-dimensional chaos map, are used as the measurement matrix of compressed sensing and two random-phase masks in the asymmetric fractional wavelet transform. It not only simplifies the keys to storage and transmission, but also enhances our cryptosystem nonlinearity to resist some common attacks. Further, holograms make our cryptosystem be immune to noises and occlusion attacks, which are obtained by two-step-only quadrature phase-shifting interference. And the compression and encryption can be achieved in the final result simultaneously. Numerical experiments have verified the security and validity of the proposed algorithm.
6. An Image Encryption Method Based on Bit Plane Hiding Technology
Institute of Scientific and Technical Information of China (English)
LIU Bin; LI Zhitang; TU Hao
2006-01-01
A novel image hiding method based on the correlation analysis of bit plane is described in this paper. Firstly, based on the correlation analysis, different bit plane of a secret image is hided in different bit plane of several different open images. And then a new hiding image is acquired by a nesting "Exclusive-OR" operation on those images obtained from the first step. At last, by employing image fusion technique, the final hiding result is achieved. The experimental result shows that the method proposed in this paper is effective.
7. A wavelet domain adaptive image watermarking method based on chaotic encryption
Science.gov (United States)
Wei, Fang; Liu, Jian; Cao, Hanqiang; Yang, Jun
2009-10-01
A digital watermarking technique is a specific branch of steganography, which can be used in various applications, provides a novel way to solve security problems for multimedia information. In this paper, we proposed a kind of wavelet domain adaptive image digital watermarking method using chaotic stream encrypt and human eye visual property. The secret information that can be seen as a watermarking is hidden into a host image, which can be publicly accessed, so the transportation of the secret information will not attract the attention of illegal receiver. The experimental results show that the method is invisible and robust against some image processing.
8. Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System
Directory of Open Access Journals (Sweden)
Guangya Peng
2018-01-01
Full Text Available The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.
9. Enhancement of security using structured phase masked in optical image encryption on Fresnel transform domain
Science.gov (United States)
2018-05-01
To enhance the security in optical image encryption system and to protect it from the attackers, this paper proposes new digital spiral phase mask based on Fresnel Transform. In this cryptosystem the Spiral Phase Mask (SPM) used is a hybrid of Fresnel Zone Plate (FZP) and Radial Hilbert Mask (RHM) which makes the key strong and enhances the security. The different keys used for encryption and decryption purposed make the system much more secure. Proposed scheme uses various structured phase mask which increases the key space also it increases the number of parameters which makes it difficult for the attackers to exactly find the key to recover the original image. We have also used different keys for encryption and decryption purpose to make the system much more secure. The strength of the proposed cryptosystem has been analyzed by simulating on MATLAB 7.9.0(R2008a). Mean Square Errors (MSE) and Peak Signal to Noise Ratio (PSNR) are calculated for the proposed algorithm. The experimental results are provided to highlight the effectiveness and sustainability of proposed cryptosystem and to prove that the cryptosystem is secure for usage.
10. A novel algorithm for image encryption based on mixture of chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Mahmodi, H.; Akhavan, A.
2008-01-01
Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet
11. Hierarchical multiple binary image encryption based on a chaos and phase retrieval algorithm in the Fresnel domain
International Nuclear Information System (INIS)
Wang, Zhipeng; Hou, Chenxia; Lv, Xiaodong; Wang, Hongjuan; Gong, Qiong; Qin, Yi
2016-01-01
Based on the chaos and phase retrieval algorithm, a hierarchical multiple binary image encryption is proposed. In the encryption process, each plaintext is encrypted into a diffraction intensity pattern by two chaos-generated random phase masks (RPMs). Thereafter, the captured diffraction intensity patterns are partially selected by different binary masks and then combined together to form a single intensity pattern. The combined intensity pattern is saved as ciphertext. For decryption, an iterative phase retrieval algorithm is performed, in which a support constraint in the output plane and a median filtering operation are utilized to achieve a rapid convergence rate without a stagnation problem. The proposed scheme has a simple optical setup and large encryption capacity. In particular, it is well suited for constructing a hierarchical security system. The security and robustness of the proposal are also investigated. (letter)
12. A joint image encryption and watermarking algorithm based on compressive sensing and chaotic map
International Nuclear Information System (INIS)
Xiao Di; Cai Hong-Kun; Zheng Hong-Ying
2015-01-01
In this paper, a compressive sensing (CS) and chaotic map-based joint image encryption and watermarking algorithm is proposed. The transform domain coefficients of the original image are scrambled by Arnold map firstly. Then the watermark is adhered to the scrambled data. By compressive sensing, a set of watermarked measurements is obtained as the watermarked cipher image. In this algorithm, watermark embedding and data compression can be performed without knowing the original image; similarly, watermark extraction will not interfere with decryption. Due to the characteristics of CS, this algorithm features compressible cipher image size, flexible watermark capacity, and lossless watermark extraction from the compressed cipher image as well as robustness against packet loss. Simulation results and analyses show that the algorithm achieves good performance in the sense of security, watermark capacity, extraction accuracy, reconstruction, robustness, etc. (paper)
13. Secure Image Encryption Based On a Chua Chaotic Noise Generator
Directory of Open Access Journals (Sweden)
A. S. Andreatos
2013-10-01
Full Text Available This paper presents a secure image cryptography telecom system based on a Chua's circuit chaotic noise generator. A chaotic system based on synchronised Master–Slave Chua's circuits has been used as a chaotic true random number generator (CTRNG. Chaotic systems present unpredictable and complex behaviour. This characteristic, together with the dependence on the initial conditions as well as the tolerance of the circuit components, make CTRNGs ideal for cryptography. In the proposed system, the transmitter mixes an input image with chaotic noise produced by a CTRNG. Using thresholding techniques, the chaotic signal is converted to a true random bit sequence. The receiver must be able to reproduce exactly the same chaotic noise in order to subtract it from the received signal. This becomes possible with synchronisation between the two Chua's circuits: through the use of specific techniques, the trajectory of the Slave chaotic system can be bound to that of the Master circuit producing (almost identical behaviour. Additional blocks have been used in order to make the system highly parameterisable and robust against common attacks. The whole system is simulated in Matlab. Simulation results demonstrate satisfactory performance, as well as, robustness against cryptanalysis. The system works with both greyscale and colour jpg images.
14. A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism
Science.gov (United States)
Chen, Jun-xin; Zhu, Zhi-liang; Fu, Chong; Yu, Hai; Zhang, Li-bo
2015-03-01
In recent years, a variety of chaos-based image cryptosystems have been investigated to meet the increasing demand for real-time secure image transmission. Most of them are based on permutation-diffusion architecture, in which permutation and diffusion are two independent procedures with fixed control parameters. This property results in two flaws. (1) At least two chaotic state variables are required for encrypting one plain pixel, in permutation and diffusion stages respectively. Chaotic state variables produced with high computation complexity are not sufficiently used. (2) The key stream solely depends on the secret key, and hence the cryptosystem is vulnerable against known/chosen-plaintext attacks. In this paper, a fast chaos-based image encryption scheme with a dynamic state variables selection mechanism is proposed to enhance the security and promote the efficiency of chaos-based image cryptosystems. Experimental simulations and extensive cryptanalysis have been carried out and the results prove the superior security and high efficiency of the scheme.
15. An Efficient Diffusion Scheme for Chaos-Based Digital Image Encryption
Directory of Open Access Journals (Sweden)
Jun-xin Chen
2014-01-01
Full Text Available In recent years, amounts of permutation-diffusion architecture-based image cryptosystems have been proposed. However, the key stream elements in the diffusion procedure are merely depending on the secret key that is usually fixed during the whole encryption process. Cryptosystems of this type suffer from unsatisfactory encryption speed and are considered insecure upon known/chosen plaintext attacks. In this paper, an efficient diffusion scheme is proposed. This scheme consists of two diffusion procedures, with a supplementary diffusion procedure padded after the normal diffusion. In the supplementary diffusion module, the control parameter of the selected chaotic map is altered by the resultant image produced after the normal diffusion operation. As a result, a slight difference in the plain image can be transferred to the chaotic iteration and bring about distinct key streams, and hence totally different cipher images will be produced. Therefore, the scheme can remarkably accelerate the diffusion effect of the cryptosystem and will effectively resist known/chosen plaintext attacks. Theoretical analyses and experimental results prove the high security performance and satisfactory operation efficiency of the proposed scheme.
16. Phase-Image Encryption Based on 3D-Lorenz Chaotic System and Double Random Phase Encoding
Science.gov (United States)
Sharma, Neha; Saini, Indu; Yadav, AK; Singh, Phool
2017-12-01
In this paper, an encryption scheme for phase-images based on 3D-Lorenz chaotic system in Fourier domain under the 4f optical system is presented. The encryption scheme uses a random amplitude mask in the spatial domain and a random phase mask in the frequency domain. Its inputs are phase-images, which are relatively more secure as compared to the intensity images because of non-linearity. The proposed scheme further derives its strength from the use of 3D-Lorenz transform in the frequency domain. Although the experimental setup for optical realization of the proposed scheme has been provided, the results presented here are based on simulations on MATLAB. It has been validated for grayscale images, and is found to be sensitive to the encryption parameters of the Lorenz system. The attacks analysis shows that the key-space is large enough to resist brute-force attack, and the scheme is also resistant to the noise and occlusion attacks. Statistical analysis and the analysis based on correlation distribution of adjacent pixels have been performed to test the efficacy of the encryption scheme. The results have indicated that the proposed encryption scheme possesses a high level of security.
17. An image encryption scheme based on the MLNCML system using DNA sequences
Science.gov (United States)
Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Jia; Chi, Ze-Lin
2016-07-01
We propose a new image scheme based on the spatiotemporal chaos of the Mixed Linear-Nonlinear Coupled Map Lattices (MLNCML). This spatiotemporal chaotic system has more cryptographic features in dynamics than the system of Coupled Map Lattices (CML). In the proposed scheme, we employ the strategy of DNA computing and one time pad encryption policy, which can enhance the sensitivity to the plaintext and resist differential attack, brute-force attack, statistical attack and plaintext attack. Simulation results and theoretical analysis indicate that the proposed scheme has superior high security.
18. Bluetooth Based Chaos Synchronization Using Particle Swarm Optimization and Its Applications to Image Encryption
Directory of Open Access Journals (Sweden)
Tzu-Hsiang Hung
2012-06-01
Full Text Available This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.
19. Encryption and display of multiple-image information using computer-generated holography with modified GS iterative algorithm
Science.gov (United States)
Xiao, Dan; Li, Xiaowei; Liu, Su-Juan; Wang, Qiong-Hua
2018-03-01
In this paper, a new scheme of multiple-image encryption and display based on computer-generated holography (CGH) and maximum length cellular automata (MLCA) is presented. With the scheme, the computer-generated hologram, which has the information of the three primitive images, is generated by modified Gerchberg-Saxton (GS) iterative algorithm using three different fractional orders in fractional Fourier domain firstly. Then the hologram is encrypted using MLCA mask. The ciphertext can be decrypted combined with the fractional orders and the rules of MLCA. Numerical simulations and experimental display results have been carried out to verify the validity and feasibility of the proposed scheme.
20. A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator
Science.gov (United States)
Tong, Xiaojun; Cui, Minggen; Wang, Zhu
2009-07-01
The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.
1. An enhanced chaotic key-based RC5 block cipher adapted to image encryption
Science.gov (United States)
Faragallah, Osama S.
2012-07-01
RC5 is a block cipher that has several salient features such as adaptability to process different word lengths with a variable block size, a variable number of rounds and a variable-length secret key. However, RC5 can be broken with various attacks such as correlation attack, timing attack, known plaintext correlation attack and differential attacks, revealing weak security. We aimed to enhance the RC5 block cipher to be more secure and efficient for real-time applications while preserving its advantages. For this purpose, this article introduces a new approach based on strengthening both the confusion and diffusion operations by combining chaos and cryptographic primitive operations to produce round keys with better pseudo-random sequences. Comparative security analysis and performance evaluation of the enhanced RC5 block cipher (ERC5) with RC5, RC6 and chaotic block cipher algorithm (CBCA) are addressed. Several test images are used for inspecting the validity of the encryption and decryption algorithms. The experimental results show the superiority of the suggested enhanced RC5 (ERC5) block cipher to image encryption algorithms such as RC5, RC6 and CBCA from the security analysis and performance evaluation points of view.
2. A novel image encryption algorithm using chaos and reversible cellular automata
Science.gov (United States)
Wang, Xingyuan; Luan, Dapeng
2013-11-01
In this paper, a novel image encryption scheme is proposed based on reversible cellular automata (RCA) combining chaos. In this algorithm, an intertwining logistic map with complex behavior and periodic boundary reversible cellular automata are used. We split each pixel of image into units of 4 bits, then adopt pseudorandom key stream generated by the intertwining logistic map to permute these units in confusion stage. And in diffusion stage, two-dimensional reversible cellular automata which are discrete dynamical systems are applied to iterate many rounds to achieve diffusion on bit-level, in which we only consider the higher 4 bits in a pixel because the higher 4 bits carry almost the information of an image. Theoretical analysis and experimental results demonstrate the proposed algorithm achieves a high security level and processes good performance against common attacks like differential attack and statistical attack. This algorithm belongs to the class of symmetric systems.
3. A two layer chaotic encryption scheme of secure image transmission for DCT precoded OFDM-VLC transmission
Science.gov (United States)
Wang, Zhongpeng; Chen, Fangni; Qiu, Weiwei; Chen, Shoufa; Ren, Dongxiao
2018-03-01
In this paper, a two-layer image encryption scheme for a discrete cosine transform (DCT) precoded orthogonal frequency division multiplexing (OFDM) visible light communication (VLC) system is proposed. Firstly, in the proposed scheme the transmitted image is first encrypted by a chaos scrambling sequence,which is generated from the hybrid 4-D hyper- and Arnold map in the upper-layer. After that, the encrypted image is converted into digital QAM modulation signal, which is re-encrypted by chaos scrambling sequence based on Arnold map in physical layer to further enhance the security of the transmitted image. Moreover, DCT precoding is employed to improve BER performance of the proposed system and reduce the PAPR of OFDM signal. The BER and PAPR performances of the proposed system are evaluated by simulation experiments. The experiment results show that the proposed two-layer chaos scrambling schemes achieve image secure transmission for image-based OFDM VLC. Furthermore, DCT precoding can reduce the PAPR and improve the BER performance of OFDM-based VLC.
4. Synchronization of Markovian jumping inertial neural networks and its applications in image encryption.
Science.gov (United States)
Prakash, M; Balasubramaniam, P; Lakshmanan, S
2016-11-01
This study is mainly concerned with the problem on synchronization criteria for Markovian jumping time delayed bidirectional associative memory neural networks and their applications in secure image communications. Based on the variable transformation method, the addressed second order differential equations are transformed into first order differential equations. Then, by constructing a suitable Lyapunov-Krasovskii functional and based on integral inequalities, the criteria which ensure the synchronization between the uncontrolled system and controlled system are established through designed feedback controllers and linear matrix inequalities. Further, the proposed results proved that the error system is globally asymptotically stable in the mean square. Moreover, numerical illustrations are provided to validate the effectiveness of the derived analytical results. Finally, the application of addressed system is explored via image encryption/decryption process. Copyright © 2016 Elsevier Ltd. All rights reserved.
5. Hardware stream cipher with controllable chaos generator for colour image encryption
KAUST Repository
Barakat, Mohamed L.
2014-01-01
This study presents hardware realisation of chaos-based stream cipher utilised for image encryption applications. A third-order chaotic system with signum non-linearity is implemented and a new post processing technique is proposed to eliminate the bias from the original chaotic sequence. The proposed stream cipher utilises the processed chaotic output to mask and diffuse input pixels through several stages of XORing and bit permutations. The performance of the cipher is tested with several input images and compared with previously reported systems showing superior security and higher hardware efficiency. The system is experimentally verified on XilinxVirtex 4 field programmable gate array (FPGA) achieving small area utilisation and a throughput of 3.62 Gb/s. © The Institution of Engineering and Technology 2013.
6. Fuzzy Matching Based on Gray-scale Difference for Quantum Images
Science.gov (United States)
Luo, GaoFeng; Zhou, Ri-Gui; Liu, XingAo; Hu, WenWen; Luo, Jia
2018-05-01
Quantum image processing has recently emerged as an essential problem in practical tasks, e.g. real-time image matching. Previous studies have shown that the superposition and entanglement of quantum can greatly improve the efficiency of complex image processing. In this paper, a fuzzy quantum image matching scheme based on gray-scale difference is proposed to find out the target region in a reference image, which is very similar to the template image. Firstly, we employ the proposed enhanced quantum representation (NEQR) to store digital images. Then some certain quantum operations are used to evaluate the gray-scale difference between two quantum images by thresholding. If all of the obtained gray-scale differences are not greater than the threshold value, it indicates a successful fuzzy matching of quantum images. Theoretical analysis and experiments show that the proposed scheme performs fuzzy matching at a low cost and also enables exponentially significant speedup via quantum parallel computation.
7. A Fingerprint Image Encryption Scheme Based on Hyperchaotic Rössler Map
Directory of Open Access Journals (Sweden)
F. Abundiz-Pérez
2016-01-01
Full Text Available Currently, biometric identifiers have been used to identify or authenticate users in a biometric system to increase the security in access control systems. Nevertheless, there are several attacks on the biometric system to steal and recover the user’s biometric trait. One of the most powerful attacks is extracting the fingerprint pattern when it is transmitted over communication lines between modules. In this paper, we present a novel fingerprint image encryption scheme based on hyperchaotic Rössler map to provide high security and secrecy in user’s biometric trait, avoid identity theft, and increase the robustness of the biometric system. A complete security analysis is presented to justify the secrecy of the biometric trait by using our proposed scheme at statistical level with 100% of NPCR, low correlation, and uniform histograms. Therefore, it can be used in secure biometric access control systems.
8. On the security of 3D Cat map based symmetric image encryption scheme
International Nuclear Information System (INIS)
Wang Kai; Pei, W.-J.; Zou, Liuhua; Song Aiguo; He Zhenya
2005-01-01
A 3D Cat map based symmetric image encryption algorithm, which significantly increases the resistance against statistical and differential attacks, has been proposed recently. It employs a 3D Cat map to shuffle the positions of image pixels and uses the Logistic map to diffuse the relationship between the cipher-image and the plain-image. Based on the factor that it is sufficient to break this cryptosystem only with the equivalent control parameters, some fundamental weaknesses of the cryptosystem are pointed out. With the knowledge of symbolic dynamics and some specially designed plain-images, we can calculate the equivalent initial condition of diffusion process and rebuild a valid equivalent 3D Cat matrix. In this Letter, we will propose a successful chosen-plain-text cryptanalytic attack, which is composed of two mutually independent procedures: the cryptanalysis of the diffusion process and the cryptanalysis of the spatial permutation process. Both theoretical and experimental results show that the lack of security discourages the use of these cryptosystems for practical applications
9. Optimal voxel size for measuring global gray and white matter proton metabolite concentrations using chemical shift imaging
DEFF Research Database (Denmark)
Hanson, Lars Peter Grüner; Adalsteinsson, E; Pfefferbaum, A
2000-01-01
Quantification of gray and white matter levels of spectroscopically visible metabolites can provide important insights into brain development and pathological conditions. Chemical shift imaging offers a gain in efficiency for estimation of global gray and white matter metabolite concentrations co...
10. GUI implementation of image encryption and decryption using Open CV-Python script on secured TFTP protocol
Science.gov (United States)
Reddy, K. Rasool; Rao, Ch. Madhava
2018-04-01
Currently safety is one of the primary concerns in the transmission of images due to increasing the use of images within the industrial applications. So it's necessary to secure the image facts from unauthorized individuals. There are various strategies are investigated to secure the facts. In that encryption is certainly one of maximum distinguished method. This paper gives a sophisticated Rijndael (AES) algorithm to shield the facts from unauthorized humans. Here Exponential Key Change (EKE) concept is also introduced to exchange the key between client and server. The things are exchange in a network among client and server through a simple protocol is known as Trivial File Transfer Protocol (TFTP). This protocol is used mainly in embedded servers to transfer the data and also provide protection to the data if protection capabilities are integrated. In this paper, implementing a GUI environment for image encryption and decryption. All these experiments carried out on Linux environment the usage of Open CV-Python script.
11. Encryption of QR code and grayscale image in interference-based scheme with high quality retrieval and silhouette problem removal
Science.gov (United States)
Qin, Yi; Wang, Hongjuan; Wang, Zhipeng; Gong, Qiong; Wang, Danchen
2016-09-01
In optical interference-based encryption (IBE) scheme, the currently available methods have to employ the iterative algorithms in order to encrypt two images and retrieve cross-talk free decrypted images. In this paper, we shall show that this goal can be achieved via an analytical process if one of the two images is QR code. For decryption, the QR code is decrypted in the conventional architecture and the decryption has a noisy appearance. Nevertheless, the robustness of QR code against noise enables the accurate acquisition of its content from the noisy retrieval, as a result of which the primary QR code can be exactly regenerated. Thereafter, a novel optical architecture is proposed to recover the grayscale image by aid of the QR code. In addition, the proposal has totally eliminated the silhouette problem existing in the previous IBE schemes, and its effectiveness and feasibility have been demonstrated by numerical simulations.
12. A Novel Image Authentication with Tamper Localization and Self-Recovery in Encrypted Domain Based on Compressive Sensing
Directory of Open Access Journals (Sweden)
Rui Zhang
2018-01-01
Full Text Available This paper proposes a novel tamper detection, localization, and recovery scheme for encrypted images with Discrete Wavelet Transformation (DWT and Compressive Sensing (CS. The original image is first transformed into DWT domain and divided into important part, that is, low-frequency part, and unimportant part, that is, high-frequency part. For low-frequency part contains the main information of image, traditional chaotic encryption is employed. Then, high-frequency part is encrypted with CS to vacate space for watermark. The scheme takes the processed original image content as watermark, from which the characteristic digest values are generated. Comparing with the existing image authentication algorithms, the proposed scheme can realize not only tamper detection and localization but also tamper recovery. Moreover, tamper recovery is based on block division and the recovery accuracy varies with the contents that are possibly tampered. If either the watermark or low-frequency part is tampered, the recovery accuracy is 100%. The experimental results show that the scheme can not only distinguish the type of tamper and find the tampered blocks but also recover the main information of the original image. With great robustness and security, the scheme can adequately meet the need of secure image transmission under unreliable conditions.
13. A chaos-based digital image encryption scheme with an improved diffusion strategy.
Science.gov (United States)
Fu, Chong; Chen, Jun-jie; Zou, Hao; Meng, Wei-hong; Zhan, Yong-feng; Yu, Ya-wen
2012-01-30
Chaos-based image cipher has been widely investigated over the last decade or so to meet the increasing demand for real-time secure image transmission over public networks. In this paper, an improved diffusion strategy is proposed to promote the efficiency of the most widely investigated permutation-diffusion type image cipher. By using the novel bidirectional diffusion strategy, the spreading process is significantly accelerated and hence the same level of security can be achieved with fewer overall encryption rounds. Moreover, to further enhance the security of the cryptosystem, a plain-text related chaotic orbit turbulence mechanism is introduced in diffusion procedure by perturbing the control parameter of the employed chaotic system according to the cipher-pixel. Extensive cryptanalysis has been performed on the proposed scheme using differential analysis, key space analysis, various statistical analyses and key sensitivity analysis. Results of our analyses indicate that the new scheme has a satisfactory security level with a low computational complexity, which renders it a good candidate for real-time secure image transmission applications.
14. New Encrypted Steganography Approach
Directory of Open Access Journals (Sweden)
Saba Mohammed Husain
2017-12-01
Full Text Available The proposed research Provides an approach for hiding an encrypted text in side a digital image. Where the text is encrypted in a complex manner used method of PlayFair to encrypt clear text and to increase security put lettering ciphertext on the geometric shape clockwise and then we write the ciphertext output in the form of lines, taken new ciphertext and converted to Ascii code and then to binary and hidden text in bits least importance in the picture. The results were good by PNSR scale
15. Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding
International Nuclear Information System (INIS)
Chen, Jun-Xin; Fu, Chong; Zhu, Zhi-Liang; Zhang, Li-Bo; Zhang, Yushu
2014-01-01
In this paper, we evaluate the security of an enhanced double random phase encoding (DRPE) image encryption scheme (2013 J. Lightwave Technol. 31 2533). The original system employs a chaotic Baker map prior to DRPE to provide more protection to the plain image and hence promote the security level of DRPE, as claimed. However, cryptanalysis shows that this scheme is vulnerable to a chosen-plaintext attack, and the ciphertext can be precisely recovered. The corresponding improvement is subsequently reported upon the basic premise that no extra equipment or computational complexity is required. The simulation results and security analyses prove its effectiveness and security. The proposed achievements are suitable for all cryptosystems under permutation and, following that, the DRPE architecture, and we hope that our work can motivate the further research on optical image encryption. (paper)
16. Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding
Science.gov (United States)
Chen, Jun-Xin; Zhu, Zhi-Liang; Fu, Chong; Zhang, Li-Bo; Zhang, Yushu
2014-12-01
In this paper, we evaluate the security of an enhanced double random phase encoding (DRPE) image encryption scheme (2013 J. Lightwave Technol. 31 2533). The original system employs a chaotic Baker map prior to DRPE to provide more protection to the plain image and hence promote the security level of DRPE, as claimed. However, cryptanalysis shows that this scheme is vulnerable to a chosen-plaintext attack, and the ciphertext can be precisely recovered. The corresponding improvement is subsequently reported upon the basic premise that no extra equipment or computational complexity is required. The simulation results and security analyses prove its effectiveness and security. The proposed achievements are suitable for all cryptosystems under permutation and, following that, the DRPE architecture, and we hope that our work can motivate the further research on optical image encryption.
17. Optical image encryption based on real-valued coding and subtracting with the help of QR code
Science.gov (United States)
Deng, Xiaopeng
2015-08-01
A novel optical image encryption based on real-valued coding and subtracting is proposed with the help of quick response (QR) code. In the encryption process, the original image to be encoded is firstly transformed into the corresponding QR code, and then the corresponding QR code is encoded into two phase-only masks (POMs) by using basic vector operations. Finally, the absolute values of the real or imaginary parts of the two POMs are chosen as the ciphertexts. In decryption process, the QR code can be approximately restored by recording the intensity of the subtraction between the ciphertexts, and hence the original image can be retrieved without any quality loss by scanning the restored QR code with a smartphone. Simulation results and actual smartphone collected results show that the method is feasible and has strong tolerance to noise, phase difference and ratio between intensities of the two decryption light beams.
18. Spread spectrum image data hiding in the encrypted discrete cosine transform coefficients
Science.gov (United States)
Zhang, Xiaoqiang; Wang, Z. Jane
2013-10-01
Digital watermarking and data hiding are important tools for digital rights protection of media data. Spread spectrum (SS)-based watermarking and data-hiding approaches are popular due to their outstanding robustness, but their security might not be sufficient. To improve the security of SS, a SS-based image data-hiding approach is proposed by encrypting the discrete cosine transform coefficients of the host image with the piecewise linear chaotic map, before the operation of watermark embedding. To evaluate the performance of the proposed approach, simulations and analyses of its robustness and security are carried out. The average bit-error-rate values on 100 real images from the Berkeley segmentation dataset under the JPEG compression, additive Gaussian noise, salt and pepper noise, and cropping attacks are reported. Experimental results show that the proposed approach can maintain the high robustness of traditional SS schemes and, meanwhile, also improve the security. The proposed approach can extend the key space of traditional SS schemes from 10 to 10 and thus can resist brute-force attack and unauthorized detection watermark attack.
19. MIA - a free and open source software for gray scale medical image analysis
OpenAIRE
Wöllny, Gert; Kellman, Peter; Ledesma Carbayo, María Jesús; Skinner, Matthew M.; Hublin, Jean-Jaques; Hierl, Thomas
2013-01-01
Background Gray scale images make the bulk of data in bio-medical image analysis, and hence, the main focus of many image processing tasks lies in the processing of these monochrome images. With ever improving acquisition devices, spatial and temporal image resolution increases, and data sets become very large. Various image processing frameworks exists that make the development of new algorithms easy by using high level programming languages or visual programming. These frameworks are also a...
20. A novel image encryption algorithm based on synchronized random bit generated in cascade-coupled chaotic semiconductor ring lasers
Science.gov (United States)
Li, Jiafu; Xiang, Shuiying; Wang, Haoning; Gong, Junkai; Wen, Aijun
2018-03-01
In this paper, a novel image encryption algorithm based on synchronization of physical random bit generated in a cascade-coupled semiconductor ring lasers (CCSRL) system is proposed, and the security analysis is performed. In both transmitter and receiver parts, the CCSRL system is a master-slave configuration consisting of a master semiconductor ring laser (M-SRL) with cross-feedback and a solitary SRL (S-SRL). The proposed image encryption algorithm includes image preprocessing based on conventional chaotic maps, pixel confusion based on control matrix extracted from physical random bit, and pixel diffusion based on random bit stream extracted from physical random bit. Firstly, the preprocessing method is used to eliminate the correlation between adjacent pixels. Secondly, physical random bit with verified randomness is generated based on chaos in the CCSRL system, and is used to simultaneously generate the control matrix and random bit stream. Finally, the control matrix and random bit stream are used for the encryption algorithm in order to change the position and the values of pixels, respectively. Simulation results and security analysis demonstrate that the proposed algorithm is effective and able to resist various typical attacks, and thus is an excellent candidate for secure image communication application.
1. Generalized double-humped logistic map-based medical image encryption
Directory of Open Access Journals (Sweden)
Samar M. Ismail
2018-03-01
Full Text Available This paper presents the design of the generalized Double Humped (DH logistic map, used for pseudo-random number key generation (PRNG. The generalized parameter added to the map provides more control on the map chaotic range. A new special map with a zooming effect of the bifurcation diagram is obtained by manipulating the generalization parameter value. The dynamic behavior of the generalized map is analyzed, including the study of the fixed points and stability ranges, Lyapunov exponent, and the complete bifurcation diagram. The option of designing any specific map is made possible through changing the general parameter increasing the randomness and controllability of the map. An image encryption algorithm is introduced based on pseudo-random sequence generation using the proposed generalized DH map offering secure communication transfer of medical MRI and X-ray images. Security analyses are carried out to consolidate system efficiency including: key sensitivity and key-space analyses, histogram analysis, correlation coefficients, MAE, NPCR and UACI calculations. System robustness against noise attacks has been proved along with the NIST test ensuring the system efficiency. A comparison between the proposed system with respect to previous works is presented.
2. Image Steganography of Multiple File Types with Encryption and Compression Algorithms
Directory of Open Access Journals (Sweden)
Ernest Andreigh C. Centina
2017-05-01
Full Text Available The goals of this study were to develop a system intended for securing files through the technique of image steganography integrated with cryptography by utilizing ZLIB Algorithm for compressing and decompressing secret files, DES Algorithm for encryption and decryption, and Least Significant Bit Algorithm for file embedding and extraction to avoid compromise on highly confidential files from exploits of unauthorized persons. Ensuing to this, the system is in acc ordance with ISO 9126 international quality standards. Every quality criteria of the system was evaluated by 10 Information Technology professionals, and the arithmetic Mean and Standard Deviation of the survey were computed. The result exhibits that m ost of them strongly agreed that the system is excellently effective based on Functionality, Reliability, Usability, Efficiency, Maintainability and Portability conformance to ISO 9126 standards. The system was found to be a useful tool for both governmen t agencies and private institutions for it could keep not only the message secret but also the existence of that particular message or file et maintaining the privacy of highly confidential and sensitive files from unauthorized access.
3. Securing SIFT: Privacy-preserving Outsourcing Computation of Feature Extractions Over Encrypted Image Data.
Science.gov (United States)
Hu, Shengshan; Wang, Qian; Wang, Jingjun; Qin, Zhan; Ren, Kui
2016-05-13
Advances in cloud computing have greatly motivated data owners to outsource their huge amount of personal multimedia data and/or computationally expensive tasks onto the cloud by leveraging its abundant resources for cost saving and flexibility. Despite the tremendous benefits, the outsourced multimedia data and its originated applications may reveal the data owner's private information, such as the personal identity, locations or even financial profiles. This observation has recently aroused new research interest on privacy-preserving computations over outsourced multimedia data. In this paper, we propose an effective and practical privacy-preserving computation outsourcing protocol for the prevailing scale-invariant feature transform (SIFT) over massive encrypted image data. We first show that previous solutions to this problem have either efficiency/security or practicality issues, and none can well preserve the important characteristics of the original SIFT in terms of distinctiveness and robustness. We then present a new scheme design that achieves efficiency and security requirements simultaneously with the preservation of its key characteristics, by randomly splitting the original image data, designing two novel efficient protocols for secure multiplication and comparison, and carefully distributing the feature extraction computations onto two independent cloud servers. We both carefully analyze and extensively evaluate the security and effectiveness of our design. The results show that our solution is practically secure, outperforms the state-of-theart, and performs comparably to the original SIFT in terms of various characteristics, including rotation invariance, image scale invariance, robust matching across affine distortion, addition of noise and change in 3D viewpoint and illumination.
4. SecSIFT: Privacy-preserving Outsourcing Computation of Feature Extractions Over Encrypted Image Data.
Science.gov (United States)
Hu, Shengshan; Wang, Qian; Wang, Jingjun; Qin, Zhan; Ren, Kui
2016-05-13
Advances in cloud computing have greatly motivated data owners to outsource their huge amount of personal multimedia data and/or computationally expensive tasks onto the cloud by leveraging its abundant resources for cost saving and flexibility. Despite the tremendous benefits, the outsourced multimedia data and its originated applications may reveal the data owner's private information, such as the personal identity, locations or even financial profiles. This observation has recently aroused new research interest on privacy-preserving computations over outsourced multimedia data. In this paper, we propose an effective and practical privacy-preserving computation outsourcing protocol for the prevailing scale-invariant feature transform (SIFT) over massive encrypted image data. We first show that previous solutions to this problem have either efficiency/security or practicality issues, and none can well preserve the important characteristics of the original SIFT in terms of distinctiveness and robustness. We then present a new scheme design that achieves efficiency and security requirements simultaneously with the preservation of its key characteristics, by randomly splitting the original image data, designing two novel efficient protocols for secure multiplication and comparison, and carefully distributing the feature extraction computations onto two independent cloud servers. We both carefully analyze and extensively evaluate the security and effectiveness of our design. The results show that our solution is practically secure, outperforms the state-of-theart, and performs comparably to the original SIFT in terms of various characteristics, including rotation invariance, image scale invariance, robust matching across affine distortion, addition of noise and change in 3D viewpoint and illumination.
5. A semi-symmetric image encryption scheme based on the function projective synchronization of two hyperchaotic systems.
Directory of Open Access Journals (Sweden)
Xiaoqiang Di
Full Text Available Both symmetric and asymmetric color image encryption have advantages and disadvantages. In order to combine their advantages and try to overcome their disadvantages, chaos synchronization is used to avoid the key transmission for the proposed semi-symmetric image encryption scheme. Our scheme is a hybrid chaotic encryption algorithm, and it consists of a scrambling stage and a diffusion stage. The control law and the update rule of function projective synchronization between the 3-cell quantum cellular neural networks (QCNN response system and the 6th-order cellular neural network (CNN drive system are formulated. Since the function projective synchronization is used to synchronize the response system and drive system, Alice and Bob got the key by two different chaotic systems independently and avoid the key transmission by some extra security links, which prevents security key leakage during the transmission. Both numerical simulations and security analyses such as information entropy analysis, differential attack are conducted to verify the feasibility, security, and efficiency of the proposed scheme.
6. Improving the Calibration of Image Sensors Based on IOFBs, Using Differential Gray-Code Space Encoding
Directory of Open Access Journals (Sweden)
Carlos Luna Vázquez
2012-07-01
Full Text Available This paper presents a fast calibration method to determine the transfer function for spatial correspondences in image transmission devices with Incoherent Optical Fiber Bundles (IOFBs, by performing a scan of the input, using differential patterns generated from a Gray code (Differential Gray-Code Space Encoding, DGSE. The results demonstrate that this technique provides a noticeable reduction in processing time and better quality of the reconstructed image compared to other, previously employed techniques, such as point or fringe scanning, or even other known space encoding techniques.
7. Phase-only optical encryption based on the zeroth-order phase-contrast technique
Science.gov (United States)
Pizolato, José Carlos; Neto, Luiz Gonçalves
2009-09-01
A phase-only encryption/decryption scheme with the readout based on the zeroth-order phase-contrast technique (ZOPCT), without the use of a phase-changing plate on the Fourier plane of an optical system based on the 4f optical correlator, is proposed. The encryption of a gray-level image is achieved by multiplying the phase distribution obtained directly from the gray-level image by a random phase distribution. The robustness of the encoding is assured by the nonlinearity intrinsic to the proposed phase-contrast method and the random phase distribution used in the encryption process. The experimental system has been implemented with liquid-crystal spatial modulators to generate phase-encrypted masks and a decrypting key. The advantage of this method is the easy scheme to recover the gray-level information from the decrypted phase-only mask applying the ZOPCT. An analysis of this decryption method was performed against brute force attacks.
8. A Parallel Algorithm for Connected Component Labelling of Gray-scale Images on Homogeneous Multicore Architectures
International Nuclear Information System (INIS)
Niknam, Mehdi; Thulasiraman, Parimala; Camorlinga, Sergio
2010-01-01
Connected component labelling is an essential step in image processing. We provide a parallel version of Suzuki's sequential connected component algorithm in order to speed up the labelling process. Also, we modify the algorithm to enable labelling gray-scale images. Due to the data dependencies in the algorithm we used a method similar to pipeline to exploit parallelism. The parallel algorithm method achieved a speedup of 2.5 for image size of 256 x 256 pixels using 4 processing threads.
9. Local gray level S-curve transformation - A generalized contrast enhancement technique for medical images.
Science.gov (United States)
Gandhamal, Akash; Talbar, Sanjay; Gajre, Suhas; Hani, Ahmad Fadzil M; Kumar, Dileep
2017-04-01
10. Single-beam image encryption using spatially separated ciphertexts based on interference principle in the Fresnel domain
Science.gov (United States)
Wang, Qu; Guo, Qing; Lei, Liang; Zhou, Jinyun
2014-12-01
A new optical security system for image encryption based on optical interference principle and translation property of Fresnel transform (FrT) has been proposed in this article. The algorithm of this proposal is specially designed for single-beam optical decryption and can thoroughly resolve the silhouette problem existing in the previous interference-based scheme. Different from earlier schemes using interference of phase-only masks (POMs), the inverse FrT of primitive image is digitally decomposed into a random POM and a complex field distribution. Information associated with the primitive images can be completely smoothed away by the modulation of this random POM. Through the translation property of FrT, two linear phase-only terms are then used to modulate the obtained random POM and the complex distribution, respectively. Two complex ciphertexts are generated by performing digital inverse FrT again. One cannot recover any visible information of secret image using only one ciphertext. Moreover, to recover the primitive image correctly, the correct ciphertexts must be placed in the certain positions of input plane of decryption system, respectively. As additional keys, position center coordinates of ciphertexts can increase the security strength of this encryption system against brute force attacks greatly. Numerical simulations have been given to verify the performance and feasibility of this proposal. To further enhance the application value of this algorithm, an alternative approach based on Fourier transform has also been discussed briefly.
11. Diffusion-tensor MR imaging of gray and white matter development during normal human brain maturation.
Science.gov (United States)
Mukherjee, Pratik; Miller, Jeffrey H; Shimony, Joshua S; Philip, Joseph V; Nehra, Deepika; Snyder, Abraham Z; Conturo, Thomas E; Neil, Jeffrey J; McKinstry, Robert C
2002-10-01
Conventional MR imaging findings of human brain development are thought to result from decreasing water content, increasing macromolecular concentration, and myelination. We use diffusion-tensor MR imaging to test theoretical models that incorporate hypotheses regarding how these maturational processes influence water diffusion in developing gray and white matter. Experimental data were derived from diffusion-tensor imaging of 167 participants, ages 31 gestational weeks to 11 postnatal years. An isotropic diffusion model was applied to the gray matter of the basal ganglia and thalamus. A model that assumes changes in the magnitude of diffusion while maintaining cylindrically symmetric anisotropy was applied to the white matter of the corpus callosum and internal capsule. Deviations of the diffusion tensor from the ideal model predictions, due to measurement noise, were estimated by using Monte Carlo simulations. Developing gray matter of the basal ganglia and developing white matter of the internal capsule and corpus callosum largely conformed to theory, with only small departures from model predictions in older children. However, data from the thalamus substantially diverged from predicted values, with progressively larger deviations from the model with increasing participant age. Changes in water diffusion during maturation of central gray and white matter structures can largely be explained by theoretical models incorporating simple assumptions regarding the influence of brain water content and myelination, although deviations from theory increase as the brain matures. Diffusion-tensor MR imaging is a powerful method for studying the process of brain development, with both scientific and clinical applications.
12. 3D shape recovery from image focus using gray level co-occurrence matrix
Science.gov (United States)
2018-04-01
Recovering a precise and accurate 3-D shape of the target object utilizing robust 3-D shape recovery algorithm is an ultimate objective of computer vision community. Focus measure algorithm plays an important role in this architecture which convert the color values of each pixel of the acquired 2-D image dataset into corresponding focus values. After convolving the focus measure filter with the input 2-D image dataset, a 3-D shape recovery approach is applied which will recover the depth map. In this document, we are concerned with proposing Gray Level Co-occurrence Matrix along with its statistical features for computing the focus information of the image dataset. The Gray Level Co-occurrence Matrix quantifies the texture present in the image using statistical features and then applies joint probability distributive function of the gray level pairs of the input image. Finally, we quantify the focus value of the input image using Gaussian Mixture Model. Due to its little computational complexity, sharp focus measure curve, robust to random noise sources and accuracy, it is considered as superior alternative to most of recently proposed 3-D shape recovery approaches. This algorithm is deeply investigated on real image sequences and synthetic image dataset. The efficiency of the proposed scheme is also compared with the state of art 3-D shape recovery approaches. Finally, by means of two global statistical measures, root mean square error and correlation, we claim that this approach -in spite of simplicity generates accurate results.
13. Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition
Science.gov (United States)
Kumar, Ravi; Bhaduri, Basanta; Nishchal, Naveen K.
2018-01-01
In this study, we propose a quick response (QR) code based nonlinear optical image encryption technique using spiral phase transform (SPT), equal modulus decomposition (EMD) and singular value decomposition (SVD). First, the primary image is converted into a QR code and then multiplied with a spiral phase mask (SPM). Next, the product is spiral phase transformed with particular spiral phase function, and further, the EMD is performed on the output of SPT, which results into two complex images, Z 1 and Z 2. Among these, Z 1 is further Fresnel propagated with distance d, and Z 2 is reserved as a decryption key. Afterwards, SVD is performed on Fresnel propagated output to get three decomposed matrices i.e. one diagonal matrix and two unitary matrices. The two unitary matrices are modulated with two different SPMs and then, the inverse SVD is performed using the diagonal matrix and modulated unitary matrices to get the final encrypted image. Numerical simulation results confirm the validity and effectiveness of the proposed technique. The proposed technique is robust against noise attack, specific attack, and brutal force attack. Simulation results are presented in support of the proposed idea.
14. Image feature extraction in encrypted domain with privacy-preserving SIFT.
Science.gov (United States)
Hsu, Chao-Yung; Lu, Chun-Shien; Pei, Soo-Chang
2012-11-01
Privacy has received considerable attention but is still largely ignored in the multimedia community. Consider a cloud computing scenario where the server is resource-abundant, and is capable of finishing the designated tasks. It is envisioned that secure media applications with privacy preservation will be treated seriously. In view of the fact that scale-invariant feature transform (SIFT) has been widely adopted in various fields, this paper is the first to target the importance of privacy-preserving SIFT (PPSIFT) and to address the problem of secure SIFT feature extraction and representation in the encrypted domain. As all of the operations in SIFT must be moved to the encrypted domain, we propose a privacy-preserving realization of the SIFT method based on homomorphic encryption. We show through the security analysis based on the discrete logarithm problem and RSA that PPSIFT is secure against ciphertext only attack and known plaintext attack. Experimental results obtained from different case studies demonstrate that the proposed homomorphic encryption-based privacy-preserving SIFT performs comparably to the original SIFT and that our method is useful in SIFT-based privacy-preserving applications.
15. Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map
Directory of Open Access Journals (Sweden)
Jian-feng Zhao
2017-01-01
Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks.
16. Determining the Number of Colors or Gray Levels in an Image Using Approximate Bayes Factors: The Pseudolikelihood Information Criterion (PLIC)
National Research Council Canada - National Science Library
Stanford, Derek C; Raftery, Adrian E
2001-01-01
.... This is motivated by medical and satellite image segmentation, and may also be useful for color and gray scale image quantization, the display and storage of computer-generated holograms, and the use...
17. Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption
Science.gov (United States)
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.
18. Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption
Science.gov (United States)
Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min
2016-01-01
Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196
19. Multifractal analysis of 2D gray soil images
Science.gov (United States)
González-Torres, Ivan; Losada, Juan Carlos; Heck, Richard; Tarquis, Ana M.
2015-04-01
Soil structure, understood as the spatial arrangement of soil pores, is one of the key factors in soil modelling processes. Geometric properties of individual and interpretation of the morphological parameters of pores can be estimated from thin sections or 3D Computed Tomography images (Tarquis et al., 2003), but there is no satisfactory method to binarized these images and quantify the complexity of their spatial arrangement (Tarquis et al., 2008, Tarquis et al., 2009; Baveye et al., 2010). The objective of this work was to apply a multifractal technique, their singularities (α) and f(α) spectra, to quantify it without applying any threshold (Gónzalez-Torres, 2014). Intact soil samples were collected from four horizons of an Argisol, formed on the Tertiary Barreiras group of formations in Pernambuco state, Brazil (Itapirema Experimental Station). The natural vegetation of the region is tropical, coastal rainforest. From each horizon, showing different porosities and spatial arrangements, three adjacent samples were taken having a set of twelve samples. The intact soil samples were imaged using an EVS (now GE Medical. London, Canada) MS-8 MicroCT scanner with 45 μm pixel-1 resolution (256x256 pixels). Though some samples required paring to fit the 64 mm diameter imaging tubes, field orientation was maintained. References Baveye, P.C., M. Laba, W. Otten, L. Bouckaert, P. Dello, R.R. Goswami, D. Grinev, A. Houston, Yaoping Hu, Jianli Liu, S. Mooney, R. Pajor, S. Sleutel, A. Tarquis, Wei Wang, Qiao Wei, Mehmet Sezgin. Observer-dependent variability of the thresholding step in the quantitative analysis of soil images and X-ray microtomography data. Geoderma, 157, 51-63, 2010. González-Torres, Iván. Theory and application of multifractal analysis methods in images for the study of soil structure. Master thesis, UPM, 2014. Tarquis, A.M., R.J. Heck, J.B. Grau; J. Fabregat, M.E. Sanchez and J.M. Antón. Influence of Thresholding in Mass and Entropy Dimension of 3-D
20. Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem
Directory of Open Access Journals (Sweden)
Zeyu Liu
2018-01-01
Full Text Available A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC. Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.
1. Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption.
Science.gov (United States)
Chen, Wu-Hua; Luo, Shixian; Zheng, Wei Xing
2016-12-01
This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.
2. A novel quantum LSB-based steganography method using the Gray code for colored quantum images
Science.gov (United States)
2017-10-01
As one of the prevalent data-hiding techniques, steganography is defined as the act of concealing secret information in a cover multimedia encompassing text, image, video and audio, imperceptibly, in order to perform interaction between the sender and the receiver in which nobody except the receiver can figure out the secret data. In this approach a quantum LSB-based steganography method utilizing the Gray code for quantum RGB images is investigated. This method uses the Gray code to accommodate two secret qubits in 3 LSBs of each pixel simultaneously according to reference tables. Experimental consequences which are analyzed in MATLAB environment, exhibit that the present schema shows good performance and also it is more secure and applicable than the previous one currently found in the literature.
3. The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression
Energy Technology Data Exchange (ETDEWEB)
Bradley, J.N.; Brislawn, C.M. [Los Alamos National Lab., NM (United States); Hopper, T. [Federal Bureau of Investigation, Washington, DC (United States)
1993-05-01
The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBIs Integrated Automated Fingerprint Identification System.
4. The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression
Energy Technology Data Exchange (ETDEWEB)
Bradley, J.N.; Brislawn, C.M. (Los Alamos National Lab., NM (United States)); Hopper, T. (Federal Bureau of Investigation, Washington, DC (United States))
1993-01-01
The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBI's Integrated Automated Fingerprint Identification System.
5. Hand Vein Images Enhancement Based on Local Gray-level Information Histogram
Directory of Open Access Journals (Sweden)
Jun Wang
2015-06-01
Full Text Available Based on the Histogram equalization theory, this paper presents a novel concept of histogram to realize the contrast enhancement of hand vein images, avoiding the lost of topological vein structure or importing the fake vein information. Firstly, we propose the concept of gray-level information histogram, the fundamental characteristic of which is that the amplitudes of the components can objectively reflect the contribution of the gray levels and information to the representation of image information. Then, we propose the histogram equalization method that is composed of an automatic histogram separation module and an intensity transformation module, and the histogram separation module is a combination of the proposed prompt multiple threshold procedure and an optimum peak signal-to-noise (PSNR calculation to separate the histogram into small-scale detail, the use of the intensity transformation module can enhance the vein images with vein topological structure and gray information preservation for each generated sub-histogram. Experimental results show that the proposed method can achieve extremely good contrast enhancement effect.
6. Logic Encryption
Science.gov (United States)
2014-02-01
encryption can also be performed non-iteratively by using a fault simulator that supports multiple stuck-at fault models. 8. REFERENCES [1] KPMG ...www.agmaglobal.org/press_events/press_docs/Counterfeit_WhitePaper_Final.pdf [2] SEMI. (2008) Innovation is at risk as semiconductor equipment and materials
7. LSB-based Steganography Using Reflected Gray Code for Color Quantum Images
Science.gov (United States)
Li, Panchi; Lu, Aiping
2018-02-01
At present, the classical least-significant-bit (LSB) based image steganography has been extended to quantum image processing. For the existing LSB-based quantum image steganography schemes, the embedding capacity is no more than 3 bits per pixel. Therefore, it is meaningful to study how to improve the embedding capacity of quantum image steganography. This work presents a novel LSB-based steganography using reflected Gray code for colored quantum images, and the embedding capacity of this scheme is up to 4 bits per pixel. In proposed scheme, the secret qubit sequence is considered as a sequence of 4-bit segments. For the four bits in each segment, the first bit is embedded in the second LSB of B channel of the cover image, and and the remaining three bits are embedded in LSB of RGB channels of each color pixel simultaneously using reflected-Gray code to determine the embedded bit from secret information. Following the transforming rule, the LSB of stego-image are not always same as the secret bits and the differences are up to almost 50%. Experimental results confirm that the proposed scheme shows good performance and outperforms the previous ones currently found in the literature in terms of embedding capacity.
8. Holographic memories with encryption-selectable function
Science.gov (United States)
Su, Wei-Chia; Lee, Xuan-Hao
2006-03-01
Volume holographic storage has received increasing attention owing to its potential high storage capacity and access rate. In the meanwhile, encrypted holographic memory using random phase encoding technique is attractive for an optical community due to growing demand for protection of information. In this paper, encryption-selectable holographic storage algorithms in LiNbO 3 using angular multiplexing are proposed and demonstrated. Encryption-selectable holographic memory is an advance concept of security storage for content protection. It offers more flexibility to encrypt the data or not optionally during the recording processes. In our system design, the function of encryption and non-encryption storage is switched by a random phase pattern and a uniform phase pattern. Based on a 90-degree geometry, the input patterns including the encryption and non-encryption storage are stored via angular multiplexing with reference plane waves at different incident angles. Image is encrypted optionally by sliding the ground glass into one of the recording waves or removing it away in each exposure. The ground glass is a key for encryption. Besides, it is also an important key available for authorized user to decrypt the encrypted information.
9. Histogram and gray level co-occurrence matrix on gray-scale ultrasound images for diagnosing lymphocytic thyroiditis.
Science.gov (United States)
Shin, Young Gyung; Yoo, Jaeheung; Kwon, Hyeong Ju; Hong, Jung Hwa; Lee, Hye Sun; Yoon, Jung Hyun; Kim, Eun-Kyung; Moon, Hee Jung; Han, Kyunghwa; Kwak, Jin Young
2016-08-01
The objective of the study was to evaluate whether texture analysis using histogram and gray level co-occurrence matrix (GLCM) parameters can help clinicians diagnose lymphocytic thyroiditis (LT) and differentiate LT according to pathologic grade. The background thyroid pathology of 441 patients was classified into no evidence of LT, chronic LT (CLT), and Hashimoto's thyroiditis (HT). Histogram and GLCM parameters were extracted from the regions of interest on ultrasound. The diagnostic performances of the parameters for diagnosing and differentiating LT were calculated. Of the histogram and GLCM parameters, the mean on histogram had the highest Az (0.63) and VUS (0.303). As the degrees of LT increased, the mean decreased and the standard deviation and entropy increased. The mean on histogram from gray-scale ultrasound showed the best diagnostic performance as a single parameter in differentiating LT according to pathologic grade as well as in diagnosing LT. Copyright © 2016 Elsevier Ltd. All rights reserved.
10. Comparison of 12-bit and 8-bit gray scale resolution in MR imaging of the CNS
International Nuclear Information System (INIS)
Smith, H.J.; Bakke, S.J.; Smevik, B.; Hald, J.K.; Moen, G.; Rudenhed, B.; Abildgaard, A.
1992-01-01
A reduction in gray scale resolution of digital images from 12 to 8 bits per pixel usually means halving the storage space needed for the images. Theoretically, important diagnostic information may be lost in the process. We compared the sensitivity and specificity achieved by 4 radiologists in reading laser-printed films of original 12-bit MR images and cathode ray tube displays of the same images which had been compressed to 8 bits per pixel using a specially developed computer program. Receiver operating characteristics (ROC) curves showed no significant differences between film reading and screen reading. A paired 2-tailed t-test, applied on the data for actually positive cases, showed that the combined, average performance of the reviewers was significantly better at screen reading than at film reading. No such differences were found for actually negative cases. Some individual differences were found, but it is concluded that gray scale resolution of MR images may be reduced from 12 to 8 bits per pixel without any significant reduction in diagnostic information. (orig.)
11. Automatic adjustment of display window (gray-level condition) for MR images using neural networks
International Nuclear Information System (INIS)
Ohhashi, Akinami; Nambu, Kyojiro.
1992-01-01
We have developed a system to automatically adjust the display window width and level (WWL) for MR images using neural networks. There were three main points in the development of our system as follows: 1) We defined an index for the clarity of a displayed image, and called 'EW'. EW is a quantitative measure of the clarity of an image displayed in a certain WWL, and can be derived from the difference between gray-level with the WWL adjusted by a human expert and with a certain WWL. 2) We extracted a group of six features from a gray-level histogram of a displayed image. We designed two neural networks which are able to learn the relationship between these features and the desired output (teaching signal), 'EQ', which is normalized to 0 to 1.0 from EW. Two neural networks were used to share the patterns to be learned; one learns a variety of patterns with less accuracy, and the other learns similar patterns with accuracy. Learning was performed using a back-propagation method. As a result, the neural networks after learning are able to provide a quantitative measure, 'Q', of the clarity of images displayed in the designated WWL. 3) Using the 'Hill climbing' method, we have been able to determine the best possible WWL for a displaying image. We have tested this technique for MR brain images. The results show that this system can adjust WWL comparable to that adjusted by a human expert for the majority of test images. The neural network is effective for the automatic adjustment of the display window for MR images. We are now studying the application of this method to MR images of another regions. (author)
12. Robust information encryption diffractive-imaging-based scheme with special phase retrieval algorithm for a customized data container
Science.gov (United States)
Qin, Yi; Wang, Zhipeng; Wang, Hongjuan; Gong, Qiong; Zhou, Nanrun
2018-06-01
The diffractive-imaging-based encryption (DIBE) scheme has aroused wide interesting due to its compact architecture and low requirement of conditions. Nevertheless, the primary information can hardly be recovered exactly in the real applications when considering the speckle noise and potential occlusion imposed on the ciphertext. To deal with this issue, the customized data container (CDC) into DIBE is introduced and a new phase retrieval algorithm (PRA) for plaintext retrieval is proposed. The PRA, designed according to the peculiarity of the CDC, combines two key techniques from previous approaches, i.e., input-support-constraint and median-filtering. The proposed scheme can guarantee totally the reconstruction of the primary information despite heavy noise or occlusion and its effectiveness and feasibility have been demonstrated with simulation results.
13. Reconstructing the CT number array from gray-level images and its application in PACS
Science.gov (United States)
Chen, Xu; Zhuang, Tian-ge; Wu, Wei
2001-08-01
Although DICOM compliant computed tomography has been prevailing in medical fields nowadays, there are some incompliant ones, from which we could hardly get the raw data and make an apropos interpretation due to the proprietary image format. Under such condition, one usually uses frame grabbers to capture CT images, the results of which could not be freely adjusted by radiologists as the original CT number array could. To alleviate the inflexibility, a new method is presented in this paper to reconstruct the array of CT number from several gray-level images acquired under different window settings. Its feasibility is investigated and a few tips are put forward to correct the errors caused respectively by 'Border Effect' and some hardware problems. The accuracy analysis proves it a good substitution for original CT number array acquisition. And this method has already been successfully used in our newly developing PACS and accepted by the radiologists in clinical use.
14. A Fixed-Pattern Noise Correction Method Based on Gray Value Compensation for TDI CMOS Image Sensor.
Science.gov (United States)
Liu, Zhenwang; Xu, Jiangtao; Wang, Xinlei; Nie, Kaiming; Jin, Weimin
2015-09-16
In order to eliminate the fixed-pattern noise (FPN) in the output image of time-delay-integration CMOS image sensor (TDI-CIS), a FPN correction method based on gray value compensation is proposed. One hundred images are first captured under uniform illumination. Then, row FPN (RFPN) and column FPN (CFPN) are estimated based on the row-mean vector and column-mean vector of all collected images, respectively. Finally, RFPN are corrected by adding the estimated RFPN gray value to the original gray values of pixels in the corresponding row, and CFPN are corrected by subtracting the estimated CFPN gray value from the original gray values of pixels in the corresponding column. Experimental results based on a 128-stage TDI-CIS show that, after correcting the FPN in the image captured under uniform illumination with the proposed method, the standard-deviation of row-mean vector decreases from 5.6798 to 0.4214 LSB, and the standard-deviation of column-mean vector decreases from 15.2080 to 13.4623 LSB. Both kinds of FPN in the real images captured by TDI-CIS are eliminated effectively with the proposed method.
15. Optical voice encryption based on digital holography.
Science.gov (United States)
Rajput, Sudheesh K; Matoba, Osamu
2017-11-15
We propose an optical voice encryption scheme based on digital holography (DH). An off-axis DH is employed to acquire voice information by obtaining phase retardation occurring in the object wave due to sound wave propagation. The acquired hologram, including voice information, is encrypted using optical image encryption. The DH reconstruction and decryption with all the correct parameters can retrieve an original voice. The scheme has the capability to record the human voice in holograms and encrypt it directly. These aspects make the scheme suitable for other security applications and help to use the voice as a potential security tool. We present experimental and some part of simulation results.
16. Dynamic encryption method
DEFF Research Database (Denmark)
2013-01-01
algorithm for on provision of a specific key, decrypting cipher data and reproduce plain data; encrypting the first data package comprising plain data, using a first encryption program implementing the first encryption algorithm of said first encryption technique, creating a first encrypted data package...... comprising cipher data; obtaining a first decryption program; and transmitting said first decryption program and said first encrypted data package to a receiver, wherein the first decryption, upon provision of the specific key and the first encrypted data package, will decrypt the cipher data in the first...
17. A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiuping, E-mail: [email protected]; Min, Lequan, E-mail: [email protected]; Wang, Xue, E-mail: [email protected] [Schools of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083 (China)
2015-05-15
This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2{sup 1345}. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.
18. A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.
Science.gov (United States)
Yang, Xiuping; Min, Lequan; Wang, Xue
2015-05-01
This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.
19. A Novel Image Encryption Algorithm Based on the Two-Dimensional Logistic Map and the Latin Square Image Cipher
Science.gov (United States)
Machkour, M.; Saaidi, A.; Benmaati, M. L.
2015-12-01
In this paper, we introduce a new hybrid system consisting of a permutation-substitution network based on two different encryption techniques: chaotic systems and the Latin square. This homogeneity between the two systems allows us to provide the good properties of confusion and diffusion, robustness to the integration of noise in decryption. The security analysis shows that the system is secure enough to resist brute-force attack, differential attack, chosen-plaintext attack, known-plaintext attack and statistical attack. Therefore, this robustness is proven and justified.
20. An end to end secure CBIR over encrypted medical database.
Science.gov (United States)
Bellafqira, Reda; Coatrieux, Gouenou; Bouslimi, Dalel; Quellec, Gwenole
2016-08-01
In this paper, we propose a new secure content based image retrieval (SCBIR) system adapted to the cloud framework. This solution allows a physician to retrieve images of similar content within an outsourced and encrypted image database, without decrypting them. Contrarily to actual CBIR approaches in the encrypted domain, the originality of the proposed scheme stands on the fact that the features extracted from the encrypted images are themselves encrypted. This is achieved by means of homomorphic encryption and two non-colluding servers, we however both consider as honest but curious. In that way an end to end secure CBIR process is ensured. Experimental results carried out on a diabetic retinopathy database encrypted with the Paillier cryptosystem indicate that our SCBIR achieves retrieval performance as good as if images were processed in their non-encrypted form.
1. Analysis on imaging features of mammography in computer radiography and investigation on gray scale transform and energy subtraction
International Nuclear Information System (INIS)
Feng Shuli
2003-01-01
In this dissertation, a novel transform method based on human visual response features for gray scale mammographic imaging in computer radiography (CR) is presented. The parameters for imaging quality on CR imaging for mammography were investigated experimentally. In addition, methods for image energy subtraction and a novel method of image registration for mammography of CR imaging are presented. Because the images are viewed and investigated by humans, the method of displaying differences in gray scale images is more convenient if the gray scale differences are displayed in a manner commensurate with human visual response principles. Through transformation of image gray scale with this method, the contrast of the image will be enhanced and the capability for humans to extract the useful information from the image will be increased. Tumors and microcalcifications are displayed in a form for humans to view more simply after transforming the image. The method is theoretically and experimentally investigated. Through measurement of the parameters of a geometrically blurred image, MTF, DQE, and ROC on CR imaging, and also comparison with the imaging quality of screen-film systems, the results indicate that CR imaging qualities in DQE and ROC are better than those of screen-film systems. In geometric blur of the image and MTF, the differences in image quality between CR and the screen-film system are very small. The results suggest that the CR system can replace the screen-film system for mammography imaging. In addition, the results show that the optimal imaging energy for CR mammography is about 24 kV. This condition indicates that the imaging energy of the CR system is lower than that of the screen-film system and, therefore, the x-ray dose to the patient for mammography with the CR system is lower than that with the screen-film system. Based on the difference of penetrability of x ray with different wavelength, and the fact that the part of the x-ray beam will pass
2. Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption
Directory of Open Access Journals (Sweden)
Hongjuan Liu
2014-01-01
Full Text Available A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.
3. Low gray scale values of computerized images of carotid plaques associated with increased levels of triglyceride-rich lipoproteins and with increased plaque lipid content
DEFF Research Database (Denmark)
Grønholdt, Marie-Louise M.; Nordestgaard, Børge; Weibe, Britt M.
1997-01-01
Relatioin between low gray scale values in computerized images of carotid plaques and 1) plasma levels of triglyceride-rich lipoproteins and 2) plaque lipid content......Relatioin between low gray scale values in computerized images of carotid plaques and 1) plasma levels of triglyceride-rich lipoproteins and 2) plaque lipid content...
4. MIA - A free and open source software for gray scale medical image analysis.
Science.gov (United States)
Wollny, Gert; Kellman, Peter; Ledesma-Carbayo, María-Jesus; Skinner, Matthew M; Hublin, Jean-Jaques; Hierl, Thomas
2013-10-11
Gray scale images make the bulk of data in bio-medical image analysis, and hence, the main focus of many image processing tasks lies in the processing of these monochrome images. With ever improving acquisition devices, spatial and temporal image resolution increases, and data sets become very large.Various image processing frameworks exists that make the development of new algorithms easy by using high level programming languages or visual programming. These frameworks are also accessable to researchers that have no background or little in software development because they take care of otherwise complex tasks. Specifically, the management of working memory is taken care of automatically, usually at the price of requiring more it. As a result, processing large data sets with these tools becomes increasingly difficult on work station class computers.One alternative to using these high level processing tools is the development of new algorithms in a languages like C++, that gives the developer full control over how memory is handled, but the resulting workflow for the prototyping of new algorithms is rather time intensive, and also not appropriate for a researcher with little or no knowledge in software development.Another alternative is in using command line tools that run image processing tasks, use the hard disk to store intermediate results, and provide automation by using shell scripts. Although not as convenient as, e.g. visual programming, this approach is still accessable to researchers without a background in computer science. However, only few tools exist that provide this kind of processing interface, they are usually quite task specific, and don't provide an clear approach when one wants to shape a new command line tool from a prototype shell script. The proposed framework, MIA, provides a combination of command line tools, plug-ins, and libraries that make it possible to run image processing tasks interactively in a command shell and to prototype by
5. QR code optical encryption using spatially incoherent illumination
Science.gov (United States)
Cheremkhin, P. A.; Krasnov, V. V.; Rodin, V. G.; Starikov, R. S.
2017-02-01
Optical encryption is an actively developing field of science. The majority of encryption techniques use coherent illumination and suffer from speckle noise, which severely limits their applicability. The spatially incoherent encryption technique does not have this drawback, but its effectiveness is dependent on the Fourier spectrum properties of the image to be encrypted. The application of a quick response (QR) code in the capacity of a data container solves this problem, and the embedded error correction code also enables errorless decryption. The optical encryption of digital information in the form of QR codes using spatially incoherent illumination was implemented experimentally. The encryption is based on the optical convolution of the image to be encrypted with the kinoform point spread function, which serves as an encryption key. Two liquid crystal spatial light modulators were used in the experimental setup for the QR code and the kinoform imaging, respectively. The quality of the encryption and decryption was analyzed in relation to the QR code size. Decryption was conducted digitally. The successful decryption of encrypted QR codes of up to 129 × 129 pixels was demonstrated. A comparison with the coherent QR code encryption technique showed that the proposed technique has a signal-to-noise ratio that is at least two times higher.
6. Local Directional Probability Optimization for Quantification of Blurred Gray/White Matter Junction in Magnetic Resonance Image
Directory of Open Access Journals (Sweden)
Xiaoxia Qu
2017-09-01
Full Text Available The blurred gray/white matter junction is an important feature of focal cortical dysplasia (FCD lesions. FCD is the main cause of epilepsy and can be detected through magnetic resonance (MR imaging. Several earlier studies have focused on computing the gradient magnitude of the MR image and used the resulting map to model the blurred gray/white matter junction. However, gradient magnitude cannot quantify the blurred gray/white matter junction. Therefore, we proposed a novel algorithm called local directional probability optimization (LDPO for detecting and quantifying the width of the gray/white matter boundary (GWB within the lesional areas. The proposed LDPO method mainly consists of the following three stages: (1 introduction of a hidden Markov random field-expectation-maximization algorithm to compute the probability images of brain tissues in order to obtain the GWB region; (2 generation of local directions from gray matter (GM to white matter (WM passing through the GWB, considering the GWB to be an electric potential field; (3 determination of the optimal local directions for any given voxel of GWB, based on iterative searching of the neighborhood. This was then used to measure the width of the GWB. The proposed LDPO method was tested on real MR images of patients with FCD lesions. The results indicated that the LDPO method could quantify the GWB width. On the GWB width map, the width of the blurred GWB in the lesional region was observed to be greater than that in the non-lesional regions. The proposed GWB width map produced higher F-scores in terms of detecting the blurred GWB within the FCD lesional region as compared to that of FCD feature maps, indicating better trade-off between precision and recall.
7. A New Chaos-Based Color Image Encryption Scheme with an Efficient Substitution Keystream Generation Strategy
Directory of Open Access Journals (Sweden)
Chong Fu
2018-01-01
Full Text Available This paper suggests a new chaos-based color image cipher with an efficient substitution keystream generation strategy. The hyperchaotic Lü system and logistic map are employed to generate the permutation and substitution keystream sequences for image data scrambling and mixing. In the permutation stage, the positions of colored subpixels in the input image are scrambled using a pixel-swapping mechanism, which avoids two main problems encountered when using the discretized version of area-preserving chaotic maps. In the substitution stage, we introduce an efficient keystream generation method that can extract three keystream elements from the current state of the iterative logistic map. Compared with conventional method, the total number of iterations is reduced by 3 times. To ensure the robustness of the proposed scheme against chosen-plaintext attack, the current state of the logistic map is perturbed during each iteration and the disturbance value is determined by plain-pixel values. The mechanism of associating the keystream sequence with plain-image also helps accelerate the diffusion process and increase the degree of randomness of the keystream sequence. Experimental results demonstrate that the proposed scheme has a satisfactory level of security and outperforms the conventional schemes in terms of computational efficiency.
8. MR imaging of heterotopic gray matter; Heterotopia istoty szarej mozgu w obrazie MR
Energy Technology Data Exchange (ETDEWEB)
Kryst-Widzgowska, T.; Kozlowski, P.; Poniatowska, R. [Instytut Psychiatrii i Neurologii, Warsaw (Poland)
1994-12-31
Six patients with heterotopic gray matter were evaluated with MR. 5 patients had history of seizures. 4 cases were suspected of the cerebral tumor. In the MR examination areas of heterotopic gray matter were found along the posterior horn of the lateral ventricle on the one side in 4 cases and bilateraly in 2 cases. In 3 cases another brain abnormalities were also detected including: hypoplasia of corpus callosum, hypoplasia of brain hemisphere, cavum septi pellucidi. MR is a modality of choice in the assessment of abnormal gray matter migration. (author). 6 refs, 4 figs.
9. A New Image Encryption Technique Combining Hill Cipher Method, Morse Code and Least Significant Bit Algorithm
Science.gov (United States)
Nofriansyah, Dicky; Defit, Sarjon; Nurcahyo, Gunadi W.; Ganefri, G.; Ridwan, R.; Saleh Ahmar, Ansari; Rahim, Robbi
2018-01-01
Cybercrime is one of the most serious threats. Efforts are made to reduce the number of cybercrime is to find new techniques in securing data such as Cryptography, Steganography and Watermarking combination. Cryptography and Steganography is a growing data security science. A combination of Cryptography and Steganography is one effort to improve data integrity. New techniques are used by combining several algorithms, one of which is the incorporation of hill cipher method and Morse code. Morse code is one of the communication codes used in the Scouting field. This code consists of dots and lines. This is a new modern and classic concept to maintain data integrity. The result of the combination of these three methods is expected to generate new algorithms to improve the security of the data, especially images.
10. Color encryption scheme based on adapted quantum logistic map
Science.gov (United States)
Zaghloul, Alaa; Zhang, Tiejun; Amin, Mohamed; Abd El-Latif, Ahmed A.
2014-04-01
This paper presents a new color image encryption scheme based on quantum chaotic system. In this scheme, a new encryption scheme is accomplished by generating an intermediate chaotic key stream with the help of quantum chaotic logistic map. Then, each pixel is encrypted by the cipher value of the previous pixel and the adapted quantum logistic map. The results show that the proposed scheme has adequate security for the confidentiality of color images.
11. Hiding Techniques for Dynamic Encryption Text based on Corner Point
Science.gov (United States)
Abdullatif, Firas A.; Abdullatif, Alaa A.; al-Saffar, Amna
2018-05-01
Hiding technique for dynamic encryption text using encoding table and symmetric encryption method (AES algorithm) is presented in this paper. The encoding table is generated dynamically from MSB of the cover image points that used as the first phase of encryption. The Harris corner point algorithm is applied on cover image to generate the corner points which are used to generate dynamic AES key to second phase of text encryption. The embedded process in the LSB for the image pixels except the Harris corner points for more robust. Experimental results have demonstrated that the proposed scheme have embedding quality, error-free text recovery, and high value in PSNR.
12. A Novel 1D Hybrid Chaotic Map-Based Image Compression and Encryption Using Compressed Sensing and Fibonacci-Lucas Transform
Directory of Open Access Journals (Sweden)
Tongfeng Zhang
2016-01-01
Full Text Available A one-dimensional (1D hybrid chaotic system is constructed by three different 1D chaotic maps in parallel-then-cascade fashion. The proposed chaotic map has larger key space and exhibits better uniform distribution property in some parametric range compared with existing 1D chaotic map. Meanwhile, with the combination of compressive sensing (CS and Fibonacci-Lucas transform (FLT, a novel image compression and encryption scheme is proposed with the advantages of the 1D hybrid chaotic map. The whole encryption procedure includes compression by compressed sensing (CS, scrambling with FLT, and diffusion after linear scaling. Bernoulli measurement matrix in CS is generated by the proposed 1D hybrid chaotic map due to its excellent uniform distribution. To enhance the security and complexity, transform kernel of FLT varies in each permutation round according to the generated chaotic sequences. Further, the key streams used in the diffusion process depend on the chaotic map as well as plain image, which could resist chosen plaintext attack (CPA. Experimental results and security analyses demonstrate the validity of our scheme in terms of high security and robustness against noise attack and cropping attack.
13. Vehicle security encryption based on unlicensed encryption
Science.gov (United States)
Huang, Haomin; Song, Jing; Xu, Zhijia; Ding, Xiaoke; Deng, Wei
2018-03-01
The current vehicle key is easy to be destroyed and damage, proposing the use of elliptical encryption algorithm is improving the reliability of vehicle security system. Based on the encryption rules of elliptic curve, the chip's framework and hardware structure are designed, then the chip calculation process simulation has been analyzed by software. The simulation has been achieved the expected target. Finally, some issues pointed out in the data calculation about the chip's storage control and other modules.
14. Imaging the functional connectivity of the Periaqueductal Gray during genuine and sham electroacupuncture treatment
Directory of Open Access Journals (Sweden)
Tu Peichi
2010-11-01
Full Text Available Abstract Background Electroacupuncture (EA is currently one of the most popular acupuncture modalities. However, the continuous stimulation characteristic of EA treatment presents challenges to the use of conventional functional Magnetic Resonance Imaging (fMRI approaches for the investigation of neural mechanisms mediating treatment response because of the requirement for brief and intermittent stimuli in event related or block designed task paradigms. A relatively new analysis method, functional connectivity fMRI (fcMRI, has great potential for studying continuous treatment modalities such as EA. In a previous study, we found that, compared with sham acupuncture, EA can significantly reduce Periaqueductal Gray (PAG activity when subsequently evoked by experimental pain. Given the PAG's important role in mediating acupuncture analgesia, in this study we investigated functional connectivity with the area of the PAG we previously identified and how that connectivity was affected by genuine and sham EA. Results Forty-eight subjects, who were randomly assigned to receive either genuine or sham EA paired with either a high or low expectancy manipulation, completed the study. Direct comparison of each treatment mode's functional connectivity revealed: significantly greater connectivity between the PAG, left posterior cingulate cortex (PCC, and precuneus for the contrast of genuine minus sham; significantly greater connectivity between the PAG and right anterior insula for the contrast of sham minus genuine; no significant differences in connectivity between different contrasts of the two expectancy levels. Conclusions Our findings indicate the intrinsic functional connectivity changes among key brain regions in the pain matrix and default mode network during genuine EA compared with sham EA. We speculate that continuous genuine EA stimulation can modify the coupling of spontaneous activity in brain regions that play a role in modulating pain
15. An efficient and secure partial image encryption for wireless multimedia sensor networks using discrete wavelet transform, chaotic maps and substitution box
Science.gov (United States)
2017-03-01
Wireless Sensor Networks (WSN) is widely deployed in monitoring of some physical activity and/or environmental conditions. Data gathered from WSN is transmitted via network to a central location for further processing. Numerous applications of WSN can be found in smart homes, intelligent buildings, health care, energy efficient smart grids and industrial control systems. In recent years, computer scientists has focused towards findings more applications of WSN in multimedia technologies, i.e. audio, video and digital images. Due to bulky nature of multimedia data, WSN process a large volume of multimedia data which significantly increases computational complexity and hence reduces battery time. With respect to battery life constraints, image compression in addition with secure transmission over a wide ranged sensor network is an emerging and challenging task in Wireless Multimedia Sensor Networks. Due to the open nature of the Internet, transmission of data must be secure through a process known as encryption. As a result, there is an intensive demand for such schemes that is energy efficient as well as highly secure since decades. In this paper, discrete wavelet-based partial image encryption scheme using hashing algorithm, chaotic maps and Hussain's S-Box is reported. The plaintext image is compressed via discrete wavelet transform and then the image is shuffled column-wise and row wise-wise via Piece-wise Linear Chaotic Map (PWLCM) and Nonlinear Chaotic Algorithm, respectively. To get higher security, initial conditions for PWLCM are made dependent on hash function. The permuted image is bitwise XORed with random matrix generated from Intertwining Logistic map. To enhance the security further, final ciphertext is obtained after substituting all elements with Hussain's substitution box. Experimental and statistical results confirm the strength of the anticipated scheme.
16. Towards Symbolic Encryption Schemes
DEFF Research Database (Denmark)
Ahmed, Naveed; Jensen, Christian D.; Zenner, Erik
2012-01-01
, namely an authenticated encryption scheme that is secure under chosen ciphertext attack. Therefore, many reasonable encryption schemes, such as AES in the CBC or CFB mode, are not among the implementation options. In this paper, we report new attacks on CBC and CFB based implementations of the well......Symbolic encryption, in the style of Dolev-Yao models, is ubiquitous in formal security models. In its common use, encryption on a whole message is specified as a single monolithic block. From a cryptographic perspective, however, this may require a resource-intensive cryptographic algorithm......-known Needham-Schroeder and Denning-Sacco protocols. To avoid such problems, we advocate the use of refined notions of symbolic encryption that have natural correspondence to standard cryptographic encryption schemes....
17. Contrast Enhancement Method Based on Gray and Its Distance Double-Weighting Histogram Equalization for 3D CT Images of PCBs
Directory of Open Access Journals (Sweden)
Lei Zeng
2016-01-01
Full Text Available Cone beam computed tomography (CBCT is a new detection method for 3D nondestructive testing of printed circuit boards (PCBs. However, the obtained 3D image of PCBs exhibits low contrast because of several factors, such as the occurrence of metal artifacts and beam hardening, during the process of CBCT imaging. Histogram equalization (HE algorithms cannot effectively extend the gray difference between a substrate and a metal in 3D CT images of PCBs, and the reinforcing effects are insignificant. To address this shortcoming, this study proposes an image enhancement algorithm based on gray and its distance double-weighting HE. Considering the characteristics of 3D CT images of PCBs, the proposed algorithm uses gray and its distance double-weighting strategy to change the form of the original image histogram distribution, suppresses the grayscale of a nonmetallic substrate, and expands the grayscale of wires and other metals. The proposed algorithm also enhances the gray difference between a substrate and a metal and highlights metallic materials. The proposed algorithm can enhance the gray value of wires and other metals in 3D CT images of PCBs. It applies enhancement strategies of changing gray and its distance double-weighting mechanism to adapt to this particular purpose. The flexibility and advantages of the proposed algorithm are confirmed by analyses and experimental results.
18. Image Steganography In Securing Sound File Using Arithmetic Coding Algorithm, Triple Data Encryption Standard (3DES) and Modified Least Significant Bit (MLSB)
Science.gov (United States)
Nasution, A. B.; Efendi, S.; Suwilo, S.
2018-04-01
The amount of data inserted in the form of audio samples that use 8 bits with LSB algorithm, affect the value of PSNR which resulted in changes in image quality of the insertion (fidelity). So in this research will be inserted audio samples using 5 bits with MLSB algorithm to reduce the number of data insertion where previously the audio sample will be compressed with Arithmetic Coding algorithm to reduce file size. In this research will also be encryption using Triple DES algorithm to better secure audio samples. The result of this research is the value of PSNR more than 50dB so it can be concluded that the image quality is still good because the value of PSNR has exceeded 40dB.
19. The role of gray and white matter segmentation in quantitative proton MR spectroscopic imaging.
Science.gov (United States)
Tal, Assaf; Kirov, Ivan I; Grossman, Robert I; Gonen, Oded
2012-12-01
Since the brain's gray matter (GM) and white matter (WM) metabolite concentrations differ, their partial volumes can vary the voxel's ¹H MR spectroscopy (¹H-MRS) signal, reducing sensitivity to changes. While single-voxel ¹H-MRS cannot differentiate between WM and GM signals, partial volume correction is feasible by MR spectroscopic imaging (MRSI) using segmentation of the MRI acquired for VOI placement. To determine the magnitude of this effect on metabolic quantification, we segmented a 1-mm³ resolution MRI into GM, WM and CSF masks that were co-registered with the MRSI grid to yield their partial volumes in approximately every 1 cm³ spectroscopic voxel. Each voxel then provided one equation with two unknowns: its i- metabolite's GM and WM concentrations C(i) (GM) , C(i) (WM) . With the voxels' GM and WM volumes as independent coefficients, the over-determined system of equations was solved for the global averaged C(i) (GM) and C(i) (WM) . Trading off local concentration differences offers three advantages: (i) higher sensitivity due to combined data from many voxels; (ii) improved specificity to WM versus GM changes; and (iii) reduced susceptibility to partial volume effects. These improvements made no additional demands on the protocol, measurement time or hardware. Applying this approach to 18 volunteered 3D MRSI sets of 480 voxels each yielded N-acetylaspartate, creatine, choline and myo-inositol C(i) (GM) concentrations of 8.5 ± 0.7, 6.9 ± 0.6, 1.2 ± 0.2, 5.3 ± 0.6 mM, respectively, and C(i) (WM) concentrations of 7.7 ± 0.6, 4.9 ± 0.5, 1.4 ± 0.1 and 4.4 ± 0.6mM, respectively. We showed that unaccounted voxel WM or GM partial volume can vary absolute quantification by 5-10% (more for ratios), which can often double the sample size required to establish statistical significance. Copyright © 2012 John Wiley & Sons, Ltd.
20. Distributed Searchable Symmetric Encryption
NARCIS (Netherlands)
Bösch, C.T.; Peter, Andreas; Leenders, Bram; Lim, Hoon Wei; Tang, Qiang; Wang, Huaxiong; Hartel, Pieter H.; Jonker, Willem
Searchable Symmetric Encryption (SSE) allows a client to store encrypted data on a storage provider in such a way, that the client is able to search and retrieve the data selectively without the storage provider learning the contents of the data or the words being searched for. Practical SSE schemes
1. Key management of the double random-phase-encoding method using public-key encryption
Science.gov (United States)
Saini, Nirmala; Sinha, Aloka
2010-03-01
Public-key encryption has been used to encode the key of the encryption process. In the proposed technique, an input image has been encrypted by using the double random-phase-encoding method using extended fractional Fourier transform. The key of the encryption process have been encoded by using the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. The encoded key has then been transmitted to the receiver side along with the encrypted image. In the decryption process, first the encoded key has been decrypted using the secret key and then the encrypted image has been decrypted by using the retrieved key parameters. The proposed technique has advantage over double random-phase-encoding method because the problem associated with the transmission of the key has been eliminated by using public-key encryption. Computer simulation has been carried out to validate the proposed technique.
2. Hot Spots Detection of Operating PV Arrays through IR Thermal Image Using Method Based on Curve Fitting of Gray Histogram
Directory of Open Access Journals (Sweden)
Jiang Lin
2016-01-01
Full Text Available The overall efficiency of PV arrays is affected by hot spots which should be detected and diagnosed by applying responsible monitoring techniques. The method using the IR thermal image to detect hot spots has been studied as a direct, noncontact, nondestructive technique. However, IR thermal images suffer from relatively high stochastic noise and non-uniformity clutter, so the conventional methods of image processing are not effective. The paper proposes a method to detect hotspots based on curve fitting of gray histogram. The result of MATLAB simulation proves the method proposed in the paper is effective to detect the hot spots suppressing the noise generated during the process of image acquisition.
3. SD LMS L-Filters for Filtration of Gray Level Images in Timespatial Domain Based on GLCM Features
Directory of Open Access Journals (Sweden)
Robert Hudec
2008-01-01
Full Text Available In this paper, the new kind of adaptive signal-dependent LMS L-filter for suppression of a mixed noise in greyscale images is developed. It is based on the texture parameter measurement as modification of spatial impulse detector structure. Moreover, the one of GLCM (Gray Level Co-occurrence Matrix features, namely, the contrast or inertia adjusted by threshold as switch between partial filters is utilised. Finally, at the positions of partial filters the adaptive LMS versions of L-filters are chosen.
4. The Design and Its Application in Secure Communication and Image Encryption of a New Lorenz-Like System with Varying Parameter
Directory of Open Access Journals (Sweden)
Lilian Huang
2016-01-01
Full Text Available A new Lorenz-like chaotic system with varying parameter is proposed by adding a state feedback function. The structure of the new designed system is simple and has more complex dynamic behaviors. The chaos behavior of the new system is studied by theoretical analysis and numerical simulation. And the bifurcation diagram shows a chaos-cycle-chaos evolution when the new parameter changes. Then a new synchronization scheme by a single state variable drive is given based on the new system and a chaotic parameter modulation digital secure communication system is also constructed. The results of simulation demonstrate that the new proposed system could be well applied in secure communication. Otherwise, based on the new system, the encryption and decryption of image could be achieved also.
5. Application of Mean of Absolute Deviation Method for the Selection of Best Nonlinear Component Based on Video Encryption
Science.gov (United States)
2013-07-01
The aim of this work is to make use of the mean of absolute deviation (MAD) method for the evaluation process of substitution boxes used in the advanced encryption standard. In this paper, we use the MAD technique to analyze some popular and prevailing substitution boxes used in encryption processes. In particular, MAD is applied to advanced encryption standard (AES), affine power affine (APA), Gray, Lui J., Residue Prime, S8 AES, SKIPJACK, and Xyi substitution boxes.
6. Homomorphic encryption and applications
CERN Document Server
Yi, Xun; Bertino, Elisa
2014-01-01
This book introduces the fundamental concepts of homomorphic encryption. From these foundations, applications are developed in the fields of private information retrieval, private searching on streaming data, privacy-preserving data mining, electronic voting and cloud computing. The content is presented in an instructional and practical style, with concrete examples to enhance the reader's understanding. This volume achieves a balance between the theoretical and the practical components of modern information security. Readers will learn key principles of homomorphic encryption as well as their
7. Key-space analysis of double random phase encryption technique
Science.gov (United States)
Monaghan, David S.; Gopinathan, Unnikrishnan; Naughton, Thomas J.; Sheridan, John T.
2007-09-01
We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.
8. Illuminant direction estimation for a single image based on local region complexity analysis and average gray value.
Science.gov (United States)
Yi, Jizheng; Mao, Xia; Chen, Lijiang; Xue, Yuli; Compare, Angelo
2014-01-10
Illuminant direction estimation is an important research issue in the field of image processing. Due to low cost for getting texture information from a single image, it is worthwhile to estimate illuminant direction by employing scenario texture information. This paper proposes a novel computation method to estimate illuminant direction on both color outdoor images and the extended Yale face database B. In our paper, the luminance component is separated from the resized YCbCr image and its edges are detected with the Canny edge detector. Then, we divide the binary edge image into 16 local regions and calculate the edge level percentage in each of them. Afterward, we use the edge level percentage to analyze the complexity of each local region included in the luminance component. Finally, according to the error function between the measured intensity and the calculated intensity, and the constraint function for an infinite light source model, we calculate the illuminant directions of the luminance component's three local regions, which meet the requirements of lower complexity and larger average gray value, and synthesize them as the final illuminant direction. Unlike previous works, the proposed method requires neither all of the information of the image nor the texture that is included in the training set. Experimental results show that the proposed method works better at the correct rate and execution time than the existing ones.
9. Encrypted Data Storage in EGEE
CERN Document Server
Frohner, Ákos
2006-01-01
The medical community is routinely using clinical images and associated medical data for diagnosis, intervention planning and therapy follow-up. Medical imaging is producing an increasing number of digital images for which computerized archiving, processing and analysis are needed. Grids are promising infrastructures for managing and analyzing the huge medical databases. Given the sensitive nature of medical images, practiotionners are often reluctant to use distributed systems though. Security if often implemented by isolating the imaging network from the outside world inside hospitals. Given the wide scale distribution of grid infrastructures and their multiple administrative entities, the level of security for manipulating medical data should be particularly high. In this presentation we describe the architecture of a solution, the gLite Encrypted Data Storage (EDS), which was developed in the framework of Enabling Grids for E-sciencE (EGEE), a project of the European Commission (contract number INFSO--508...
10. Evaluation of cost functions for gray value matching of two-dimensional images in radiotherapy
NARCIS (Netherlands)
Dekker, Niels; Ploeger, Lennert S.; van Herk, Marcel
2003-01-01
In external beam radiotherapy, portal imaging is applied for verification of the patient setup. Current automatic methods for portal image registration, which are often based on segmentation of anatomical structures, are especially successful for images of the pelvic region. For portal images of
11. [Research on K-means clustering segmentation method for MRI brain image based on selecting multi-peaks in gray histogram].
Science.gov (United States)
Chen, Zhaoxue; Yu, Haizhong; Chen, Hao
2013-12-01
To solve the problem of traditional K-means clustering in which initial clustering centers are selected randomly, we proposed a new K-means segmentation algorithm based on robustly selecting 'peaks' standing for White Matter, Gray Matter and Cerebrospinal Fluid in multi-peaks gray histogram of MRI brain image. The new algorithm takes gray value of selected histogram 'peaks' as the initial K-means clustering center and can segment the MRI brain image into three parts of tissue more effectively, accurately, steadily and successfully. Massive experiments have proved that the proposed algorithm can overcome many shortcomings caused by traditional K-means clustering method such as low efficiency, veracity, robustness and time consuming. The histogram 'peak' selecting idea of the proposed segmentootion method is of more universal availability.
12. Algoritmi selektivnog šifrovanja - pregled sa ocenom performansi / Selective encryption algorithms: Overview with performance evaluation
Directory of Open Access Journals (Sweden)
Boriša Ž. Jovanović
2010-10-01
13. System for Information Encryption Implementing Several Chaotic Orbits
Directory of Open Access Journals (Sweden)
Jiménez-Rodríguez Maricela
2015-07-01
Full Text Available This article proposes a symmetric encryption algorithm that takes, as input value, the original information of length L, that when encoded, generates the ciphertext of greater length LM. A chaotic discrete system (logistic map is implemented to generate 3 different orbits: the first is used for applying a diffusion technique in order to mix the original data, the second orbit is combined with the mixed information and increases the length of L to LM, and with the third orbit, the confusion technique is implemented. The encryption algorithm was applied to encode an image which is then totally recovered by the keys used to encrypt and his respective, decrypt algorithm. The algorithm can encode any information, just dividing into 8 bits, it can cover the requirements for high level security, it uses 7 keys to encrypt and provides good encryption speed
14. 基于计算全息的串联式三随机相位板图像加密%Image encryption technology of three random phase based on computer generated hologram
Institute of Scientific and Technical Information of China (English)
席思星; 孙欣; 刘兵; 田巍; 云茂金; 孔伟金; 张文飞; 梁键
2011-01-01
本文提出一种串联式三随机相位板图像加密的新方法，该方法充分运用计算全息记录复值光场的特性以记录加密图像，在传统的双随机相位加密系统基础上，置人第三个随机相位板在输出平面上，对输出的计算全息图进行相位调制加密，引入了新的密钥，获得很好的双密钥效果!同时由于计算全息周再现的多频特性，解密须正确提取单元频谱，进一步提高了图像传输的安全性。%A new image encryption technology of three random phase plates is proposed.Recording the encrypted image by CGH with it＇s features of Recording the value of optical field in this method,the third random phase plate was placed on the output plane in the 4f double random phase encryption system to modulate and encrypt the phase of the CGH,there are new keys,the third random phase plate,the exact drawing of the spectrum uint with the multi-frequency characteristics of CGH,which further improve the image transmission security.
15. H-1 chemical shift imaging of the brain in guanidino methyltransferase deficiency, a creatine deficiency syndrome; guanidinoacetate accumulation in the gray matter
NARCIS (Netherlands)
Sijens, PE; Verbruggen, KT; Meiners, LC; Soorani-Lunsing, RJ; Rake, JP; Oudkerk, M
MR spectroscopy results in a mild case of guanidinoacetate methyltransferase (GAMT) deficiency are presented. The approach differs from previous MRS studies in the acquisition of a chemical shift imaging spectral map showing gray and white matter with the corresponding spectra in one overview. MR
16. Late effects of high-dose adjuvant chemotherapy on white and gray matter in breast cancer survivors: Converging results from multimodal magnetic resonance imaging
NARCIS (Netherlands)
de Ruiter, Michiel B.; Reneman, Liesbeth; Boogerd, Willem; Veltman, Dick J.; Caan, Matthan; Douaud, Gwenaëlle; Lavini, Cristina; Linn, Sabine C.; Boven, Epie; van Dam, Frits S. A. M.; Schagen, Sanne B.
2012-01-01
The neural substrate underlying cognitive impairments after chemotherapy is largely unknown. Here, we investigated very late (>9 years) effects of adjuvant high-dose chemotherapy on brain white and gray matter in primary breast cancer survivors (n = 17) with multimodal magnetic resonance imaging
17. Separable Reversible Data Hiding in Encrypted Signals with Public Key Cryptography
Directory of Open Access Journals (Sweden)
Wei-Liang Tai
2018-01-01
Full Text Available We propose separable reversible data hiding in an encrypted signal with public key cryptography. In our separable framework, the image owner encrypts the original image by using a public key. On receipt of the encrypted signal, the data-hider embeds data in it by using a data-hiding key. The image decryption and data extraction are independent and separable at the receiver side. Even though the receiver, who has only the data-hiding key, does not learn about the decrypted content, he can extract data from the received marked encrypted signal. However, the receiver who has only the private key cannot extract the embedded data, but he can directly decrypt the received marked encrypted signal to obtain the original image without any error. Compared with other schemes using a cipher stream to encrypt the image, the proposed scheme is more appropriate for cloud services without degrading the security level.
18. Gender classification from face images by using local binary pattern and gray-level co-occurrence matrix
Science.gov (United States)
Uzbaş, Betül; Arslan, Ahmet
2018-04-01
Gender is an important step for human computer interactive processes and identification. Human face image is one of the important sources to determine gender. In the present study, gender classification is performed automatically from facial images. In order to classify gender, we propose a combination of features that have been extracted face, eye and lip regions by using a hybrid method of Local Binary Pattern and Gray-Level Co-Occurrence Matrix. The features have been extracted from automatically obtained face, eye and lip regions. All of the extracted features have been combined and given as input parameters to classification methods (Support Vector Machine, Artificial Neural Networks, Naive Bayes and k-Nearest Neighbor methods) for gender classification. The Nottingham Scan face database that consists of the frontal face images of 100 people (50 male and 50 female) is used for this purpose. As the result of the experimental studies, the highest success rate has been achieved as 98% by using Support Vector Machine. The experimental results illustrate the efficacy of our proposed method.
19. The fast encryption package
Science.gov (United States)
Bishop, Matt
1988-01-01
The organization of some tools to help improve passwork security at a UNIX-based site is described along with how to install and use them. These tools and their associated library enable a site to force users to pick reasonably safe passwords (safe being site configurable) and to enable site management to try to crack existing passworks. The library contains various versions of a very fast implementation of the Data Encryption Standard and of the one-way encryption functions used to encryp the password.
20. Using Chaotic System in Encryption
Science.gov (United States)
Findik, Oğuz; Kahramanli, Şirzat
In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.
1. Global gray matter changes in posterior cortical atrophy: A serial imaging study
NARCIS (Netherlands)
Lehmann, M.; Barnes, J.; Ridgway, G.R.; Ryan, N.S.; Warrington, E.K.; Crutch, S.J.; Fox, N.C.
2012-01-01
Background: Posterior cortical atrophy (PCA) is a neurodegenerative condition predominantly associated with Alzheimer's disease (AD) pathology. Cross-sectional imaging studies have shown different atrophy patterns in PCA patients compared with typical amnestic Alzheimer's disease (tAD) patients,
2. The effects of gray scale image processing on digital mammography interpretation performance.
Science.gov (United States)
Cole, Elodia B; Pisano, Etta D; Zeng, Donglin; Muller, Keith; Aylward, Stephen R; Park, Sungwook; Kuzmiak, Cherie; Koomen, Marcia; Pavic, Dag; Walsh, Ruth; Baker, Jay; Gimenez, Edgardo I; Freimanis, Rita
2005-05-01
To determine the effects of three image-processing algorithms on diagnostic accuracy of digital mammography in comparison with conventional screen-film mammography. A total of 201 cases consisting of nonprocessed soft copy versions of the digital mammograms acquired from GE, Fischer, and Trex digital mammography systems (1997-1999) and conventional screen-film mammograms of the same patients were interpreted by nine radiologists. The raw digital data were processed with each of three different image-processing algorithms creating three presentations-manufacturer's default (applied and laser printed to film by each of the manufacturers), MUSICA, and PLAHE-were presented in soft copy display. There were three radiologists per presentation. Area under the receiver operating characteristic curve for GE digital mass cases was worse than screen-film for all digital presentations. The area under the receiver operating characteristic for Trex digital mass cases was better, but only with images processed with the manufacturer's default algorithm. Sensitivity for GE digital mass cases was worse than screen film for all digital presentations. Specificity for Fischer digital calcifications cases was worse than screen film for images processed in default and PLAHE algorithms. Specificity for Trex digital calcifications cases was worse than screen film for images processed with MUSICA. Specific image-processing algorithms may be necessary for optimal presentation for interpretation based on machine and lesion type.
3. Chaos based encryption system for encrypting electroencephalogram signals.
Science.gov (United States)
Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De
2014-05-01
In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.
4. Measures of Morphological Complexity of Gray Matter on Magnetic Resonance Imaging for Control Age Grouping
OpenAIRE
Pham, Tuan; Abe, Taishi; Oka, Ryuichi; Chen, Yung-Fu
2015-01-01
Current brain-age prediction methods using magnetic resonance imaging (MRI) attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the p...
5. Photon-counting multifactor optical encryption and authentication
International Nuclear Information System (INIS)
Pérez-Cabré, E; Millán, M S; Mohammed, E A; Saadon, H L
2015-01-01
The multifactor optical encryption authentication method [Opt. Lett., 31 721-3 (2006)] reinforces optical security by allowing the simultaneous authentication of up to four factors. In this work, the photon-counting imaging technique is applied to the multifactor encrypted function so that a sparse phase-only distribution is generated for the encrypted data. The integration of both techniques permits an increased capacity for signal hiding with simultaneous data reduction for better fulfilling the general requirements of protection, storage and transmission. Cryptanalysis of the proposed method is carried out in terms of chosen-plaintext and chosen-ciphertext attacks. Although the multifactor authentication process is not substantially altered by those attacks, its integration with the photon-counting imaging technique prevents from possible partial disclosure of any encrypted factor, thus increasing the security level of the overall process. Numerical experiments and results are provided and discussed. (paper)
6. Page segmentation and text extraction from gray-scale images in microfilm format
Science.gov (United States)
Yuan, Qing; Tan, Chew Lim
2000-12-01
The paper deals with a suitably designed system that is being used to separate textual regions from graphics regions and locate textual data from textured background. We presented a method based on edge detection to automatically locate text in some noise infected grayscale newspaper images with microfilm format. The algorithm first finds the appropriate edges of textual region using Canny edge detector, and then by edge merging it makes use of edge features to do block segmentation and classification, afterwards feature aided connected component analysis was used to group homogeneous textual regions together within the scope of its bounding box. We can obtain an efficient block segmentation with reduced memory size by introducing the TLC. The proposed method has been used to locate text in a group of newspaper images with multiple page layout. Initial results are encouraging, we would expand the experiment data to over 300 microfilm images with different layout structures, promising result is anticipated with corresponding modification on the prototype of former algorithm to make it more robust and suitable to different cases.
7. Measures of Morphological Complexity of Gray Matter on Magnetic Resonance Imaging for Control Age Grouping
Directory of Open Access Journals (Sweden)
Tuan D. Pham
2015-12-01
Full Text Available Current brain-age prediction methods using magnetic resonance imaging (MRI attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the phylogenetic tree reconstruction and measures of information complexity. Experimental results carried out on a public MRI database suggest the feasibility of the proposed concept.
8. Encryption is Useless!?
CERN Multimedia
IT Department
2011-01-01
This week FTP (the file transfer protocol) celebrated its 40th birthday - and will hopefully retire soon! While a nice and simple means of transferring files, it is totally insecure: both the transferred contents and the authentication password are transfered unencrypted. FTP is not the only protocol that transfers data unencrypted: standard web traffic (“HTTP”) and e-mail (“SMTP”) are not encrypted either. Not an issue? Think again! Nowadays, we all use wireless Ethernet from our laptops and mobile phones. This means that your traffic can be intercepted by anyone*… What if I could your web browsing history, read your last e-mail to your boyfriend/girlfriend, or see which commands you’ve just executed? I could easily intercept your Facebook session… If this worries you, check for secrecy and encryption. Usually this is shown by an “S” in your communication protocol: · “HTTPS&...
9. The end of encryption
CERN Multimedia
Computer Security Team
2013-01-01
Sigh! Pandora’s box has been opened (once again). Recent documents leaked by whistle-blower Edward Snowden have revealed that the NSA project “Bullrun” is intruding deeply into the confidentiality of our documents and the privacy of our lives. In their continuous effort to kill privacy on the Internet, the US National Security Agency (NSA) and the British Government Communications Headquarters (GCHQ) have made significant progress in breaking almost every basic encryption protocol or have developed the means to bypass them. “US and British intelligence agencies have successfully cracked much of the online encryption relied upon by hundreds of millions of people to protect the privacy of their personal data, online transactions and e-mails.” - The Guardian So what’s left? With “Prism” and “Tempora”, our public communication on the Internet was already filtered and analysed (see our Bulletin ar...
10. Searchable Encryption in Cloud Storage
OpenAIRE
Ren-Junn Hwang; Chung-Chien Lu; Jain-Shing Wu
2014-01-01
Cloud outsource storage is one of important services in cloud computing. Cloud users upload data to cloud servers to reduce the cost of managing data and maintaining hardware and software. To ensure data confidentiality, users can encrypt their files before uploading them to a cloud system. However, retrieving the target file from the encrypted files exactly is difficult for cloud server. This study proposes a protocol for performing multikeyword searches for encrypted cloud data by applying ...
11. Video Encryption-A Survey
OpenAIRE
Jolly Shah; Vikas Saxena
2011-01-01
Multimedia data security is becoming important with the continuous increase of digital communications on internet. The encryption algorithms developed to secure text data are not suitable for multimedia application because of the large data size and real time constraint. In this paper, classification and description of various video encryption algorithms are presented. Analysis and Comparison of these algorithms with respect to various parameters like visual degradation, encryption ratio, spe...
12. Analysis of double random phase encryption from a key-space perspective
Science.gov (United States)
Monaghan, David S.; Situ, Guohai; Ryle, James; Gopinathan, Unnikrishnan; Naughton, Thomas J.; Sheridan, John T.
2007-09-01
The main advantage of the double random phase encryption technique is its physical implementation however to allow us to analyse its behaviour we perform the encryption/decryption numerically. A typically strong encryption scheme will have an extremely large key-space, which will make the probable success of any brute force attack on that algorithm miniscule. Traditionally, designers of optical image encryption systems only demonstrate how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. We analyse this algorithm from a key-space perspective. The key-space of an encryption algorithm can be defined as the set of possible keys that can be used to encode data using that algorithm. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute force attack.
13. A New Measurement Method of Iimage Encryption
International Nuclear Information System (INIS)
Yu, X Y; Zhang, J; Ren, H E; Li, S; Zhang, X D
2006-01-01
Image scrambling transformation is applied widely in the digital watermarking and image encryption. Although more and more scrambling algorithms appear, they lack a method to evaluate the image scrambling degree. According to the relative differences of a point and adjacent point in scrambling front and back, a new method which judges the scrambling degree is proposed. Not only it can evaluate the change of each pixel's position, but also evaluate the change of adjacent pixel's value. Apply Matlab to the simulation experiment, the result indicated that this method can evaluate image scrambling degree well, and it accorded with people's vision too
14. Imaging of olfactory bulb and gray matter volumes in brain areas associated with olfactory function in patients with Parkinson's disease and multiple system atrophy
Energy Technology Data Exchange (ETDEWEB)
Chen, Shun, E-mail: [email protected] [Department of Neurology, The First Affiliated Hospital of Guangzhou Medical College (China); Tan, Hong-yu, E-mail: [email protected] [Department of Neurology, The First Affiliated Hospital of Guangzhou Medical College (China); Wu, Zhuo-hua, E-mail: [email protected] [Department of Neurology, The First Affiliated Hospital of Guangzhou Medical College (China); Sun, Chong-peng, E-mail: [email protected] [Imaging Center, The First Affiliated Hospital of Guangzhou Medical College (China); He, Jian-xun, E-mail: [email protected] [Imaging Center, The First Affiliated Hospital of Guangzhou Medical College (China); Li, Xin-chun, E-mail: [email protected] [Imaging Center, The First Affiliated Hospital of Guangzhou Medical College (China); Shao, Ming, E-mail: [email protected] [Department of Neurology, The First Affiliated Hospital of Guangzhou Medical College (China)
2014-03-15
We explored if magnetic resonance imaging sequences might aid in the clinical differential diagnosis of idiopathic Parkinson's disease (IPD) and multiple system atrophy (MSA). We measured the volumes of the olfactory bulb, the olfactory tract, and olfaction-associated cortical gray matter in 20 IPD patients, 14 MSA patients, and 12 normal subjects, using high-resolution magnetic resonance imaging sequences in combination with voxel-based statistical analysis. We found that, compared to normal subjects and MSA patients, the volumes of the olfactory bulb and tract were significantly reduced in IPD patients. The gray matter volume of IPD patients decreased in the following order: the olfactory area to the right of the piriform cortex, the right amygdala, the left entorhinal cortex, and the left occipital lobe. Further, the total olfactory bulb volume of IPD patients was associated with the duration of disease. The entorhinal cortical gray matter volume was negatively associated with the UPDRS III score. Conclusion: Structural volumes measured by high-resolution magnetic resonance imaging may potentially be used for differential diagnosis of IPD from MSA.
15. Imaging of olfactory bulb and gray matter volumes in brain areas associated with olfactory function in patients with Parkinson's disease and multiple system atrophy
International Nuclear Information System (INIS)
Chen, Shun; Tan, Hong-yu; Wu, Zhuo-hua; Sun, Chong-peng; He, Jian-xun; Li, Xin-chun; Shao, Ming
2014-01-01
We explored if magnetic resonance imaging sequences might aid in the clinical differential diagnosis of idiopathic Parkinson's disease (IPD) and multiple system atrophy (MSA). We measured the volumes of the olfactory bulb, the olfactory tract, and olfaction-associated cortical gray matter in 20 IPD patients, 14 MSA patients, and 12 normal subjects, using high-resolution magnetic resonance imaging sequences in combination with voxel-based statistical analysis. We found that, compared to normal subjects and MSA patients, the volumes of the olfactory bulb and tract were significantly reduced in IPD patients. The gray matter volume of IPD patients decreased in the following order: the olfactory area to the right of the piriform cortex, the right amygdala, the left entorhinal cortex, and the left occipital lobe. Further, the total olfactory bulb volume of IPD patients was associated with the duration of disease. The entorhinal cortical gray matter volume was negatively associated with the UPDRS III score. Conclusion: Structural volumes measured by high-resolution magnetic resonance imaging may potentially be used for differential diagnosis of IPD from MSA
16. Hologram production and representation for corrected image
Science.gov (United States)
Jiao, Gui Chao; Zhang, Rui; Su, Xue Mei
2015-12-01
In this paper, a CCD sensor device is used to record the distorted homemade grid images which are taken by a wide angle camera. The distorted images are corrected by using methods of position calibration and correction of gray with vc++ 6.0 and opencv software. Holography graphes for the corrected pictures are produced. The clearly reproduced images are obtained where Fresnel algorithm is used in graph processing by reducing the object and reference light from Fresnel diffraction to delete zero-order part of the reproduced images. The investigation is useful in optical information processing and image encryption transmission.
17. An Optical Encryption and Decryption Method and System
DEFF Research Database (Denmark)
2000-01-01
The invention relates to securing of information utilising optical imaging technologies and more specifically to phase encryption and decryption of images. An image is encrypted into a mask having a plurality of mask resolution elements (Xm, Ym) by encoding the image using e.g. a phase mask with ...... modulator resolution elements, the decrypting phase value phi d (Xd, Yd) and the decrypting amplitude value ad (Xd, Yd) respectively, of a modulator resolution element (Xd, Yd) being substantially equal to - phi c (Xm, Ym) and ac (Xm, Ym)....
18. Attribute-based encryption with encryption and decryption outsourcing
NARCIS (Netherlands)
Asim, M.; Petkovic, M.; Ignatenko, T.
2014-01-01
In this paper we propose a new scheme for ciphertext-policy attribute-based encryption that allows outsourcing of computationally expensive encryption and decryption steps. The scheme constitutes an important building block for mobile applications where both the host and users use mobile devices
19. Gray and white matter asymmetries in healthy individuals aged 21-29 years: a voxel-based morphometry and diffusion tensor imaging study.
Science.gov (United States)
Takao, Hidemasa; Abe, Osamu; Yamasue, Hidenori; Aoki, Shigeki; Sasaki, Hiroki; Kasai, Kiyoto; Yoshioka, Naoki; Ohtomo, Kuni
2011-10-01
The hemispheres of the human brain are functionally and structurally asymmetric. The study of structural asymmetries provides important clues to the neuroanatomical basis of lateralized brain functions. Previous studies have demonstrated age-related changes in morphology and diffusion properties of brain tissue. In this study, we simultaneously explored gray and white matter asymmetry using voxel-based morphometry (VBM) and diffusion tensor imaging (DTI) in 109 young healthy individuals (58 females and 51 males). To eliminate the potential confounding effects of aging and handedness, we restricted the study to right-handed subjects aged 21-29 years. VBM and voxel-based analysis of fractional anisotropy (FA) maps derived from DTI revealed a number of gray matter volume asymmetries (including the right frontal and left occipital petalias and leftward asymmetry of the planum temporale) and white matter FA asymmetries (including leftward asymmetry of the arcuate fasciculus, cingulum, and corticospinal tract). There was no significant effect of sex on gray and white matter asymmetry. Leftward volume asymmetry of the planum temporale and leftward FA asymmetry of the arcuate fasciculus were simultaneously demonstrated. Post hoc analysis showed that the gray matter volume of the planum temporale and FA of the arcuate fasciculus were positively related (Pearson correlation coefficient, 0.43; P < 0.0001). The results of our study demonstrate gray and white matter asymmetry in right-handed healthy young adults and suggest that leftward volume asymmetry of the planum temporale and leftward FA asymmetry of the arcuate fasciculus may be related. Copyright © 2010 Wiley-Liss, Inc.
20. Homomorphic encryption and secure comparison
NARCIS (Netherlands)
Damgard, Ivan; Geisler, M.; Kroigaard, M.
2008-01-01
We propose a protocol for secure comparison of integers based on homomorphic encryption.We also propose a homomorphic encryption scheme that can be used in our protocol, makes it more efficient than previous solutions, and can also be used as the basis of efficient and general secure Multiparty
1. Can homomorphic encryption be practical?
NARCIS (Netherlands)
Lauter, K.; Naehrig, M.; Vaikuntanathan, V.
2011-01-01
The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns for individuals and businesses alike. The privacy concerns can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption scheme is
2. Substring-Searchable Symmetric Encryption
Directory of Open Access Journals (Sweden)
Chase Melissa
2015-06-01
Full Text Available In this paper, we consider a setting where a client wants to outsource storage of a large amount of private data and then perform substring search queries on the data – given a data string s and a search string p, find all occurrences of p as a substring of s. First, we formalize an encryption paradigm that we call queryable encryption, which generalizes searchable symmetric encryption (SSE and structured encryption. Then, we construct a queryable encryption scheme for substring queries. Our construction uses suffix trees and achieves asymptotic efficiency comparable to that of unencrypted suffix trees. Encryption of a string of length n takes O(λn time and produces a ciphertext of size O(λn, and querying for a substring of length m that occurs k times takes O(λm+k time and three rounds of communication. Our security definition guarantees correctness of query results and privacy of data and queries against a malicious adversary. Following the line of work started by Curtmola et al. (ACM CCS 2006, in order to construct more efficient schemes we allow the query protocol to leak some limited information that is captured precisely in the definition. We prove security of our substring-searchable encryption scheme against malicious adversaries, where the query protocol leaks limited information about memory access patterns through the suffix tree of the encrypted string.
3. Matrix Encryption Scheme
Directory of Open Access Journals (Sweden)
Abdelhakim Chillali
2017-05-01
Full Text Available In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. In this work, we proposed a new problem applicable to the public key cryptography, based on the Matrices, called “Matrix discrete logarithm problem”, it uses certain elements formed by matrices whose coefficients are elements in a finite field. We have constructed an abelian group and, for the cryptographic part in this unreliable group, we then perform the computation corresponding to the algebraic equations, Returning the encrypted result to a receiver. Upon receipt of the result, the receiver can retrieve the sender’s clear message by performing the inverse calculation.
4. An Anti-Cheating Visual Cryptography Scheme Based on Chaotic Encryption System
Science.gov (United States)
Han, Yanyan; Xu, Zhuolin; Ge, Xiaonan; He, Wencai
By chaotic encryption system and introducing the trusted third party (TTP), in this paper, an anti-cheating visual cryptography scheme (VCS) is proposed. The scheme solved the problem of dishonest participants and improved the security of chaotic encryption system. Simulation results and analysis show that the recovery image is acceptable, the system can detect the cheating in participants effectively and with high security.
KAUST Repository
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
6. Security analysis of optical encryption
OpenAIRE
Frauel, Yann; Castro, Albertina; Naughton, Thomas J.; Javidi, Bahram
2005-01-01
This paper analyzes the security of amplitude encoding for double random phase encryption. We describe several types of attack. The system is found to be resistant to brute-force attacks but vulnerable to chosen and known plaintext attacks.
7. Security analysis of optical encryption
Science.gov (United States)
Frauel, Yann; Castro, Albertina; Naughton, Thomas J.; Javidi, Bahram
2005-10-01
This paper analyzes the security of amplitude encoding for double random phase encryption. We describe several types of attack. The system is found to be resistant to brute-force attacks but vulnerable to chosen and known plaintext attacks.
8. Stream Deniable-Encryption Algorithms
Directory of Open Access Journals (Sweden)
N.A. Moldovyan
2016-04-01
Full Text Available A method for stream deniable encryption of secret message is proposed, which is computationally indistinguishable from the probabilistic encryption of some fake message. The method uses generation of two key streams with some secure block cipher. One of the key streams is generated depending on the secret key and the other one is generated depending on the fake key. The key streams are mixed with the secret and fake data streams so that the output ciphertext looks like the ciphertext produced by some probabilistic encryption algorithm applied to the fake message, while using the fake key. When the receiver or/and sender of the ciphertext are coerced to open the encryption key and the source message, they open the fake key and the fake message. To disclose their lie the coercer should demonstrate possibility of the alternative decryption of the ciphertext, however this is a computationally hard problem.
9. The Lure of Wireless Encryption
CERN Multimedia
Computer Security Team
2013-01-01
Following our article entitled “Jekyll or Hyde? Better browse securely” in the last issue of the Bulletin, some people wondered why the CERN wireless network is not encrypted… There are many arguments why it is not. The simplest is usability: the communication and management of the corresponding access keys would be challenging given the sheer number of wireless devices the CERN network hosts. Keys would quickly become public, e.g. at conferences, and might be shared, written on whiteboards, etc. Then there are all the devices which cannot be easily configured to use encryption protocols - a fact which would create plenty of calls to the CERN Service Desk… But our main argument is that wireless encryption is DECEPTIVE. Wireless encryption is deceptive as it only protects the wireless network against unauthorised access (and the CERN network already has other means to protect against that). Wireless encryption however, does not really help you. You ...
10. Quantum computing on encrypted data.
Science.gov (United States)
Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J
2014-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.
11. An algorithm for automatic detection of chromosome aberrations induced by radiation using features of gray level profile across the main axis of chromosome image
International Nuclear Information System (INIS)
Kawashima, Hironao; Imai, Katsuhiro; Fukuoka, Hideya; Yamamoto, Mikio; Hayata, Isamu.
1990-01-01
A simple algorithm for detecting chromosome aberrations induced by radiation is developed. Microscopic images of conventional Giemsa stained chromosomes of rearranged chromosomes (abnormal chromosomes) including dicentric chromosomes, ordinary acentric fragments, small acentric fragments, and acentric rings are used as samples. Variation of width along the main axis and gray level profile across the main axis of the chromosome image are used as features for classification. In 7 microscopic images which include 257 single chromosomes, 90.0% (231 chromosomes) are correctly classified into 6 categories and 23 of 26 abnormal chromosomes are correctly identified. As a result of discrimination between a normal and an abnormal chromosome, 95.3% of abnormal chromosomes are detected. (author)
12. White and gray matter abnormalities in idiopathic rapid eye movement sleep behavior disorder: a diffusion-tensor imaging and voxel-based morphometry study.
Science.gov (United States)
Scherfler, Christoph; Frauscher, Birgit; Schocke, Michael; Iranzo, Alex; Gschliesser, Viola; Seppi, Klaus; Santamaria, Joan; Tolosa, Eduardo; Högl, Birgit; Poewe, Werner
2011-02-01
We applied diffusion-tensor imaging (DTI) including measurements of mean diffusivity (MD), a parameter of brain tissue integrity, fractional anisotropy (FA), a parameter of neuronal fiber integrity, as well as voxel-based morphometry (VBM), a measure of gray and white matter volume, to detect brain tissue changes in patients with idiopathic rapid eye movement (REM) sleep behavior disorder (iRBD). Magnetic resonance imaging (MRI) was performed in 26 patients with iRBD (mean disease duration, 9.2 ± 6.4 years) and 14 age-matched healthy control subjects. Statistical parametric mapping (SPM) was applied to objectively identify focal changes of MRI parameters throughout the entire brain volume. SPM localized significant decreases of FA in the tegmentum of the midbrain and rostral pons and increases of MD within the pontine reticular formation overlapping with a cluster of decreased FA in the midbrain (p < 0.001). VBM revealed increases of gray matter densities in both hippocampi of iRBD patients (p < 0.001). The observed changes in the pontomesencephalic brainstem localized 2 areas harboring key neuronal circuits believed to be involved in the regulation of REM sleep and overlap with areas of structural brainstem damage causing symptomatic RBD in humans. Bilateral increases in gray matter density of the hippocampus suggest functional neuronal reorganization in this brain area in iRBD. This study indicates that DTI detects distinct structural brainstem tissue abnormalities in iRBD in the regions where REM is modulated. Further studies should explore the relationship between MRI pathology and the risk of patients with iRBD of developing alpha-synuclein-related neurodegenerative diseases like Parkinson disease. Copyright © 2010 American Neurological Association.
13. Encryption Technology based on Human Biometrics
Directory of Open Access Journals (Sweden)
Wei Yang
2017-08-01
Full Text Available The research progress of encryption technologies based on human biometrics is reviewed in this paper.The technologies that utilize human biometrics to make information encryption and identity authentication,and the technologies which combine biometrics encryption with optical encryption methods are introduced in detail.The advantages and disadvantages of these encryption systems are discussed,and the obstacles in practical applications are pointed out.Finally,the prospect of the new encryption technologies that are based on human biometrics are predicted.
14. Security encryption for video-on-radio devices
Science.gov (United States)
Perrone, Antonio L.; Basti, Gianfranco
2002-03-01
In this paper we present an encryption module included in the Subsidiary Communication Channel (SCC) System we are developing for video-on-FM radio broadcasting. This module is aimed to encrypt by symmetric key the video image archive and real-time database of the broadcaster, and by asymmetric key the video broadcasting to final users. The module includes our proprietary Techniteia Encryption Library (TEL), that is already successfully running and securing several e-commerce portals in Europe. TEL is written in C-ANSI language for its easy exportation onto all main platforms and it is optimized for real-time applications. It is based on the blowfish encryption algorithm and it is characterized by a physically separated sub-module for the automatic generation/recovering of the variable sub-keys of the blowfish algorithm. In this way, different parts of the database are encrypted by different keys, both in space and in time, for granting an optimal security.
15. A Gray-code-based color image representation method using TSNAM%TSNAM彩色图像的格雷码表示
Institute of Scientific and Technical Information of China (English)
郑运平; 张佳婧
2012-01-01
为了提高彩色图像模式的表示效率,借助于三角形和正方形布局问题的思想,将格雷码和位平面分解方法应用到彩色图像的三角形和正方形NAM表示方法(TSNAM)中,提出了一种基于格雷码的TSNAM彩色图像表示方法(GTSNAM).给出了GTSNAM表示算法的形式化描述,并对其存储结构、总数据量和时空复杂性进行了分析.理论分析和实验结果表明,与最新提出的TSNAM表示方法和经典的线性四元树(LQT)表示方法相比,GTSNAM表示方法具有更少的子模式数(或节点数),能够更有效地减少数据存储空间,因而是一种有效的彩色图像表示方法.%Inspired by an idea obtained from the triangle and the square packing problems, a new Gray-code-based color image representation method using a non-symmetry and anti-packing pattern representation model with the triangle and the square subpatterns (TSNAM) , also called the GTSNAM representation method, was proposed to improve the representation efficiency of color images by applying the Gray code and the bit-plane decomposition method. Also, a concrete algorithm of GTSNAM for color images was presented, and the storage structure, the total data amount, and the time and space complexities of the proposed algorithm were analyzed. By comparing the GTSNAM algorithm with those of the classic linear quadtree (LQT) and the latest TSNAM, which is not based on the Gray code, the theoretical and experimental results show that the former can greatly reduce the number of subpatterns or nodes and simultaneously save the storage space much more effectively than the latter ones. The GTSNAM algorithm is therefore shown to be a better method to represent color images.
16. Real-time and encryption efficiency improvements of simultaneous fusion, compression and encryption method based on chaotic generators
Science.gov (United States)
Jridi, Maher; Alfalou, Ayman
2018-03-01
In this paper, enhancement of an existing optical simultaneous fusion, compression and encryption (SFCE) scheme in terms of real-time requirements, bandwidth occupation and encryption robustness is proposed. We have used and approximate form of the DCT to decrease the computational resources. Then, a novel chaos-based encryption algorithm is introduced in order to achieve the confusion and diffusion effects. In the confusion phase, Henon map is used for row and column permutations, where the initial condition is related to the original image. Furthermore, the Skew Tent map is employed to generate another random matrix in order to carry out pixel scrambling. Finally, an adaptation of a classical diffusion process scheme is employed to strengthen security of the cryptosystem against statistical, differential, and chosen plaintext attacks. Analyses of key space, histogram, adjacent pixel correlation, sensitivity, and encryption speed of the encryption scheme are provided, and favorably compared to those of the existing crypto-compression system. The proposed method has been found to be digital/optical implementation-friendly which facilitates the integration of the crypto-compression system on a very broad range of scenarios.
17. Parallel data encryption with RSA algorithm
OpenAIRE
Неретин, А. А.
2016-01-01
In this paper a parallel RSA algorithm with preliminary shuffling of source text was presented.Dependence of an encryption speed on the number of encryption nodes has been analysed, The proposed algorithm was implemented on C# language.
18. Towards Provably Secure Efficiently Searchable Encryption
NARCIS (Netherlands)
Sedghi, S.
2012-01-01
Traditional encryption systems are designed in such a way that either the whole data is decrypted, if the encryption and decryption keys match, or nothing is decrypted otherwise. However, there are applications that require a more flexible encryption system which supports decrypting data partially.
19. A Survey of Provably Secure Searchable Encryption
NARCIS (Netherlands)
Bösch, C.T.; Hartel, Pieter H.; Jonker, Willem; Peter, Andreas
We survey the notion of provably secure Searchable Encryption (SE) by giving a complete and comprehensive overview of the two main SE techniques: Searchable Symmetric Encryption (SSE) and Public Key Encryption with Keyword Search (PEKS). Since the pioneering work of Song, Wagner and Perrig (IEEE S&P
20. Selective Document Retrieval from Encrypted Database
NARCIS (Netherlands)
Bösch, C.T.; Tang, Qiang; Hartel, Pieter H.; Jonker, Willem
We propose the concept of selective document retrieval (SDR) from an encrypted database which allows a client to store encrypted data on a third-party server and perform efficient search remotely. We propose a new SDR scheme based on the recent advances in fully homomorphic encryption schemes. The
1. Encryption and decryption using FPGA
Science.gov (United States)
Nayak, Nikhilesh; Chandak, Akshay; Shah, Nisarg; Karthikeyan, B.
2017-11-01
In this paper, we are performing multiple cryptography methods on a set of data and comparing their outputs. Here AES algorithm and RSA algorithm are used. Using AES Algorithm an 8 bit input (plain text) gets encrypted using a cipher key and the result is displayed on tera term (serially). For simulation a 128 bit input is used and operated with a 128 bit cipher key to generate encrypted text. The reverse operations are then performed to get decrypted text. In RSA Algorithm file handling is used to input plain text. This text is then operated on to get the encrypted and decrypted data, which are then stored in a file. Finally the results of both the algorithms are compared.
2. Experimental protocol for packaging and encrypting multiple data
International Nuclear Information System (INIS)
Barrera, John Fredy; Trejos, Sorayda; Tebaldi, Myrian; Torroba, Roberto
2013-01-01
We present a novel single optical packaging and encryption (SOPE) procedure for multiple inputs. This procedure is based on a merging of a 2f scheme with a digital holographic technique to achieve efficient handling of multiple data. Through the 2f system with a random phase mask attached in its input plane, and the holographic technique, we obtain each processed input. A posteriori filtering and repositioning protocol on each hologram followed by an addition of all processed data, allows storing these data to form a single package. The final package is digitally multiplied by a second random phase mask acting as an encryption mask. In this way, the final user receives only one encrypted information unit and a single key, instead of a conventional multiple-image collecting method and several keys. Processing of individual images is cast into an optimization problem. The proposed optimization aims to simplify the handling and recovery of images while packing all of them into a single unit. The decoding process does not have the usual cross-talk or noise problems involved in other methods, as filtering and repositioning precedes the encryption step. All data are recovered in just one step at the same time by applying a simple Fourier transform operation and the decoding key. The proposed protocol takes advantage of optical processing and the versatility of the digital format. Experiments have been conducted using a Mach–Zehnder interferometer. An application is subsequently demonstrated to illustrate the feasibility of the SOPE procedure. (paper)
3. Selectively Encrypted Pull-Up Based Watermarking of Biometric data
Science.gov (United States)
Shinde, S. A.; Patel, Kushal S.
2012-10-01
Biometric authentication systems are becoming increasingly popular due to their potential usage in information security. However, digital biometric data (e.g. thumb impression) are themselves vulnerable to security attacks. There are various methods are available to secure biometric data. In biometric watermarking the data are embedded in an image container and are only retrieved if the secrete key is available. This container image is encrypted to have more security against the attack. As wireless devices are equipped with battery as their power supply, they have limited computational capabilities; therefore to reduce energy consumption we use the method of selective encryption of container image. The bit pull-up-based biometric watermarking scheme is based on amplitude modulation and bit priority which reduces the retrieval error rate to great extent. By using selective Encryption mechanism we expect more efficiency in time at the time of encryption as well as decryption. Significant reduction in error rate is expected to be achieved by the bit pull-up method.
4. Homomorphic encryption and secure comparison
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Geisler, Martin; Krøigaard, Mikkel
2008-01-01
Computation (MPC). We show how our comparison protocol can be used to improve security of online auctions, and demonstrate that it is efficient enough to be used in practice. For comparison of 16 bits numbers with security based on 1024 bits RSA (executed by two parties), our implementation takes 0.28 sec......We propose a protocol for secure comparison of integers based on homomorphic encryption.We also propose a homomorphic encryption scheme that can be used in our protocol, makes it more efficient than previous solutions, and can also be used as the basis of efficient and general secure Multiparty...
5. Influence of a perturbation in the Gyrator domain for a joint transform correlator-based encryption system
Science.gov (United States)
Vilardy, Juan M.; Millán, María. S.; Pérez-Cabré, Elisabet
2017-08-01
We present the results of the noise and occlusion tests in the Gyrator domain (GD) for a joint transform correlator-based encryption system. This encryption system was recently proposed and it was implemented by using a fully phase nonzero-order joint transform correlator (JTC) and the Gyrator transform (GT). The decryption system was based on two successive GTs. In this paper, we make several numerical simulations in order to test the performance and robustness of the JTC-based encryption-decryption system in the GD when the encrypted image is corrupted by noise or occlusion. The encrypted image is affected by additive and multiplicative noise. We also test the effect of data loss due to partial occlusion of the encrypted information. Finally, we evaluate the performance and robustness of the encryption-decryption system in the GD by using the metric of the root mean square error (RMSE) between the original image and the decrypted image when the encrypted image is degraded by noise or modified by occlusion.
6. Multivariate imaging-genetics study of MRI gray matter volume and SNPs reveals biological pathways correlated with brain structural differences in Attention Deficit Hyperactivity Disorder
Directory of Open Access Journals (Sweden)
2016-07-01
7. Improved decryption quality and security of a joint transform correlator-based encryption system
Science.gov (United States)
Vilardy, Juan M.; Millán, María S.; Pérez-Cabré, Elisabet
2013-02-01
Some image encryption systems based on modified double random phase encoding and joint transform correlator architecture produce low quality decrypted images and are vulnerable to a variety of attacks. In this work, we analyse the algorithm of some reported methods that optically implement the double random phase encryption in a joint transform correlator. We show that it is possible to significantly improve the quality of the decrypted image by introducing a simple nonlinear operation in the encrypted function that contains the joint power spectrum. This nonlinearity also makes the system more resistant to chosen-plaintext attacks. We additionally explore the system resistance against this type of attack when a variety of probability density functions are used to generate the two random phase masks of the encryption-decryption process. Numerical results are presented and discussed.
8. Improved Encrypted-Signals-Based Reversible Data Hiding Using Code Division Multiplexing and Value Expansion
Directory of Open Access Journals (Sweden)
Xianyi Chen
2018-01-01
Full Text Available Compared to the encrypted-image-based reversible data hiding (EIRDH method, the encrypted-signals-based reversible data hiding (ESRDH technique is a novel way to achieve a greater embedding rate and better quality of the decrypted signals. Motivated by ESRDH using signal energy transfer, we propose an improved ESRDH method using code division multiplexing and value expansion. At the beginning, each pixel of the original image is divided into several parts containing a little signal and multiple equal signals. Next, all signals are encrypted by Paillier encryption. And then a large number of secret bits are embedded into the encrypted signals using code division multiplexing and value expansion. Since the sum of elements in any spreading sequence is equal to 0, lossless quality of directly decrypted signals can be achieved using code division multiplexing on the encrypted equal signals. Although the visual quality is reduced, high-capacity data hiding can be accomplished by conducting value expansion on the encrypted little signal. The experimental results show that our method is better than other methods in terms of the embedding rate and average PSNR.
9. Encrypted IP video communication system
Science.gov (United States)
Bogdan, Apetrechioaie; Luminiţa, Mateescu
2010-11-01
Digital video transmission is a permanent subject of development, research and improvement. This field of research has an exponentially growing market in civil, surveillance, security and military aplications. A lot of solutions: FPGA, ASIC, DSP have been used for this purpose. The paper presents the implementation of an encrypted, IP based, video communication system having a competitive performance/cost ratio .
10. Mediated Encryption: Analysis and Design
Directory of Open Access Journals (Sweden)
I. Elashry1
2015-01-01
Full Text Available Boneh, Ding and Tsudik presented identity-based mediated RSA encryption and signature systems in which the users are not allowed to decrypt/sign messages without the authorisation of a security mediator.We show that ID-MRSA is not secure and we present a secure modified version of it which is as efficient as the original system. We also propose a generic mediated encryption that translates any identity based encryption to a mediated version of this IBE. It envelops an IBE encrypted message using a user’s identity into an IBE envelope using the identity of the SEM. We present two security models based on the role of the adversary whether it is a revoked user or a hacked SEM. We prove that GME is as secure as the SEM’s IBE against a revoked user and as secure as the user’s IBE against a hacked SEM. We also present two implementations of GME based on Boneh-Franklin FullIBE system which is a pairing-based system and Boneh, Gentry and Hamburg (BGH system which is pairing-free system.
11. Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform
International Nuclear Information System (INIS)
Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid
2014-01-01
We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)
12. SETI-EC: SETI Encryption Code
Science.gov (United States)
Heller, René
2018-03-01
The SETI Encryption code, written in Python, creates a message for use in testing the decryptability of a simulated incoming interstellar message. The code uses images in a portable bit map (PBM) format, then writes the corresponding bits into the message, and finally returns both a PBM image and a text (TXT) file of the entire message. The natural constants (c, G, h) and the wavelength of the message are defined in the first few lines of the code, followed by the reading of the input files and their conversion into 757 strings of 359 bits to give one page. Each header of a page, i.e. the little-endian binary code translation of the tempo-spatial yardstick, is calculated and written on-the-fly for each page.
13. Experimental color encryption in a joint transform correlator architecture
International Nuclear Information System (INIS)
Tebaldi, Myrian; Amaya, Dafne; Torroba, Roberto; Horrillo, Sergi; Perez-Cabre, Elisabet; Millan, Maria S; Bolognini, Nestor
2011-01-01
We present an experimental color image encryption by using a photorefractive crystal and a joint transform correlator (JTC) architecture. We achieve the color storing by changing the illumination wavelength. One JTC aperture has the input image information corresponding to a determined color channel bonded to a random phase mask (object aperture), and the other JTC aperture contains the key code mask. The joint power spectrum is stored in a photorefractive crystal. Each color data is stored as a modulation of birefringence in this photosensitive medium. The adequate wavelength change produces a corresponding power spectrum modification that avoids image encryption cross talk in the read out step. An analysis in terms of the sensitivity of the photorefractive silenite crystal for different recording wavelengths is carried out. It should be highlighted that the multiplexed power spectrum shows neither the multiplexing operation nor the amount of stored information increasing the system security. We present experimental results that support our approach
14. The Techniques for Arbitrary Secure Quering to Encrypted Cloud Database Using Fully Homomorphic Encryption
Directory of Open Access Journals (Sweden)
Filipp B. Burtyka
2017-06-01
Full Text Available The processing of queries to an encrypted database without its decryption has been actively investigated recently by both cryptographers and database researchers. Such a work is allowed by various types of so-called Processable encryption (PE, as well as special architectures of database management systems (DBMS which use these types of encryption. The most known types of PEs are order-preserving encryption, homomorphic encryption, functional encryption, searchable encryption, and property-preserving encryption. Based on these types of encryption, various DBMSs are built, the most famous of which are CryptDB, Mo- nomi, Arx and DBMS by researchers from Novosibirsk. These DBMSs are built on the basis of various types of PEs, for example order-preserving encryption, homomorphic encryption and traditional block encryption. However, this approach can cause privacy problems. The best approach from the security viewpoint is to build a cryptographic database using only homomorphic encryption. An obstacle to this is insufficient efficiency of the existing homomorphic encryption schemes and incomplete solution of a set of issues related to ensuring the confidentiality of decisions making in an untrusted environment. In this paper, we propose the techniques for solving these problems, in particular for organization of execution arbitrary secure query to the encrypted relational database using fully homomorphic encryption. Also we propose a model of query condition that splits query into atomic predicates and linking condition. One of roposed technique is aimed at ensuring the security of linking condition of queries, others keep security of atomic predicates. The parameters of the proposed techniques make it possible to implement them using the already existing homomorphic encryption schemes. The proposed techniques can be a basis for building secure cryptographic cloud databases.
15. Toward privacy-preserving JPEG image retrieval
Science.gov (United States)
Cheng, Hang; Wang, Jingyue; Wang, Meiqing; Zhong, Shangping
2017-07-01
This paper proposes a privacy-preserving retrieval scheme for JPEG images based on local variance. Three parties are involved in the scheme: the content owner, the server, and the authorized user. The content owner encrypts JPEG images for privacy protection by jointly using permutation cipher and stream cipher, and then, the encrypted versions are uploaded to the server. With an encrypted query image provided by an authorized user, the server may extract blockwise local variances in different directions without knowing the plaintext content. After that, it can calculate the similarity between the encrypted query image and each encrypted database image by a local variance-based feature comparison mechanism. The authorized user with the encryption key can decrypt the returned encrypted images with plaintext content similar to the query image. The experimental results show that the proposed scheme not only provides effective privacy-preserving retrieval service but also ensures both format compliance and file size preservation for encrypted JPEG images.
16. Developing a nomogram based on multiparametric magnetic resonance imaging for forecasting high-grade prostate cancer to reduce unnecessary biopsies within the prostate-specific antigen gray zone.
Science.gov (United States)
Niu, Xiang-Ke; Li, Jun; Das, Susant Kumar; Xiong, Yan; Yang, Chao-Bing; Peng, Tao
2017-02-01
17. Secret Sharing Schemes and Advanced Encryption Standard
Science.gov (United States)
2015-09-01
25 4.7 Computational Example . . . . . . . . . . . . . . . . . . . . . 26 5 Side-Channel Effect on Advanced Encryption Standard ( AES ) 31...improvements, and to build upon them to discuss the side-channel effects on the Advanced Encryption Standard ( AES ). The following questions are asked...secret sharing scheme? • Can the improvements to the current secret sharing scheme prove to be beneficial in strengthening/weakening AES encryption
18. Computing on Encrypted Data: Theory and Application
Science.gov (United States)
2016-01-01
permits short ciphertexts – e.g., encrypted using AES – to be de-compressed to longer ciphertexts that permit homomorphic operations. Bootstrapping...allows us to save memory by storing data encrypted in the compressed form – e.g., under AES . Here, we revisit bootstrapping, viewing it as an...COMPUTING ON ENCRYPTED DATA: THEORY AND APPLICATION MASSACHUSETTS INSTITUTE OF TECHNOLOGY JANUARY 2016 FINAL TECHNICAL REPORT
19. Secure Cloud Computing Using Homomorphic Encryption
Directory of Open Access Journals (Sweden)
Alexander Olegovich Zhirov
2013-02-01
Full Text Available The question of cloud security has become more significant with growing popularity of cloud computing. This article is dedicated to fully homomorphic encryption which is one of the most promising methods to reach the necessary level of privacy. In this article we consider the basic ideas on homomorphic encryption proposed by C. Gentry, make generalization of them and propose three new fully homomorphic encryption schemes based on polynomial rings.
20. Continuous QKD and high speed data encryption
Science.gov (United States)
Zbinden, Hugo; Walenta, Nino; Guinnard, Olivier; Houlmann, Raphael; Wen, Charles Lim Ci; Korzh, Boris; Lunghi, Tommaso; Gisin, Nicolas; Burg, Andreas; Constantin, Jeremy; Legré, Matthieu; Trinkler, Patrick; Caselunghe, Dario; Kulesza, Natalia; Trolliet, Gregory; Vannel, Fabien; Junod, Pascal; Auberson, Olivier; Graf, Yoan; Curchod, Gilles; Habegger, Gilles; Messerli, Etienne; Portmann, Christopher; Henzen, Luca; Keller, Christoph; Pendl, Christian; Mühlberghuber, Michael; Roth, Christoph; Felber, Norbert; Gürkaynak, Frank; Schöni, Daniel; Muheim, Beat
2013-10-01
We present the results of a Swiss project dedicated to the development of high speed quantum key distribution and data encryption. The QKD engine features fully automated key exchange, hardware key distillation based on finite key security analysis, efficient authentication and wavelength division multiplexing of the quantum and the classical channel and one-time pas encryption. The encryption device allows authenticated symmetric key encryption (e.g AES) at rates of up to 100 Gb/s. A new quantum key can uploaded up to 1000 times second from the QKD engine.
Science.gov (United States)
McMahan, Sherry S.
The use of encryption on satellite links is discussed. Advanced technology exists to provide transmission security for large earth station with data rates up to 50 megabits per second. One of the major concerns in the use of encryption equipment with very small aperture terminals (VSAT) is the key management issue and the related operational costs. The low cost requirement and the lack of physical protection of remote VSATs place severe constraints on the design of encryption equipment. Encryption may be accomplished by embedding a tamper proof encryption module into the baseband unit of each VSAT. VSAT networks are usually star networks where there is a single large earth station that serves as a hub and all satellite communications takes place between each VSAT and the hub earth station. The hub earth station has the secret master key of each VSAT. These master keys are used to downline load encrypted session keys to each VSAT. A more secure alternative is to use public key techniques where each embedded VSAT encryption module internally generates its own secret and public numbers. The secret number never leaves the module while the public number is sent to the hub at the time of initialization of the encryption module into the VSAT. Physical access control to encryption modules of VSAT systems can be implemented using passwords, smart cards or biometrics.
2. Choice of optical system is critical for the security of double random phase encryption systems
Science.gov (United States)
Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Cassidy, Derek; Zhao, Liang; Ryle, James P.; Healy, John J.; Sheridan, John T.
2017-06-01
The linear canonical transform (LCT) is used in modeling a coherent light-field propagation through first-order optical systems. Recently, a generic optical system, known as the quadratic phase encoding system (QPES), for encrypting a two-dimensional image has been reported. In such systems, two random phase keys and the individual LCT parameters (α,β,γ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfy some dynamic security properties. We, therefore, examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform-based double random phase encryption (DRPE) systems. The results show that the LCT-based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel-based encryption systems.
3. Radiation-induced changes in normal-appearing gray matter in patients with nasopharyngeal carcinoma: a magnetic resonance imaging voxel-based morphometry study
International Nuclear Information System (INIS)
Lv, Xiao-Fei; Zheng, Xiao-Li; Zhang, Wei-Dong; Liu, Li-Zhi; Zhang, You-Ming; Chen, Ming-Yuan; Li, Li
2014-01-01
4. Henry Gray, plagiarist.
Science.gov (United States)
Richardson, Ruth
2016-03-01
The first edition of Anatomy Descriptive and Surgical (1858) was greeted with accolades, but also provoked serious controversy concerning Henry Gray's failure to acknowledge the work of earlier anatomists. A review in the Medical Times (1859) accused Gray of intellectual theft. The journal took the unusual step of substantiating its indictment by publishing twenty parallel texts from Gray and from a pre-existing textbook, Quain's Anatomy. At the recent "Vesalius Continuum" conference in Zakynthos, Greece (2014) Professor Brion Benninger disputed the theft by announcing from the floor the results of a computer analysis of both texts, which he reported exonerated Gray by revealing no evidence of plagiarism. The analysis has not been forthcoming, however, despite requests. Here the historian of Gray's Anatomy supplements the argument set out in the Medical Times 150 years ago with data suggesting unwelcome personality traits in Henry Gray, and demonstrating the utility of others' work to his professional advancement. Fair dealing in the world of anatomy and indeed the genuineness of the lustre of medical fame are important matters, but whether quantitative evidence has anything to add to the discussion concerning Gray's probity can be assessed only if Benninger makes public his computer analysis. © 2015 Wiley Periodicals, Inc.
5. Retrospective analysis of cytopathology using gray level co-occurrence matrix algorithm for thyroid malignant nodules in the ultrasound imaging
Energy Technology Data Exchange (ETDEWEB)
Kim, Yeong Ju; Lee, Jin Soo [Dept. of Radiology, Inje University Haeundae Paik Hospital, Busan (Korea, Republic of); Kang, Se Sik; Kim, Chang Soo [Dept. of Radiological Science, College of Health Sciences, Catholic University of Pusan, Busan (Korea, Republic of)
2017-06-15
This study evaluated the applicability of computer-aided diagnosis by retrospective analysis of GLCM algorithm based on cytopathological diagnosis of normal and malignant nodules in thyroid ultrasound images. In the experiment, the recognition rate and ROC curve of thyroid malignant nodule were analyzed using 6 parameters of GLCM algorithm. Experimental results showed 97% energy, 93% contrast, 92% correlation, 92% homogeneity, 100% entropy and 100% variance. Statistical analysis showed that the area under the curve of each parameter was more than 0.947 (p = 0 .001) in t he ROC curve, which was s ignificant in the recognition of thyroid malignant nodules. In the GLCM, the cut-off value of each parameter can be used to predict the disease through analysis of quantitative computer-aided diagnosis.
6. Non-invasive Estimation of Temperature during Physiotherapeutic Ultrasound Application Using the Average Gray-Level Content of B-Mode Images: A Metrological Approach.
Science.gov (United States)
Alvarenga, André V; Wilkens, Volker; Georg, Olga; Costa-Félix, Rodrigo P B
2017-09-01
7. Linked alterations in gray and white matter morphology in adults with high-functioning autism spectrum disorder: A multimodal brain imaging study
Directory of Open Access Journals (Sweden)
Takashi Itahashi
2015-01-01
Full Text Available Growing evidence suggests that a broad range of behavioral anomalies in people with autism spectrum disorder (ASD can be linked with morphological and functional alterations in the brain. However, the neuroanatomical underpinnings of ASD have been investigated using either structural magnetic resonance imaging (MRI or diffusion tensor imaging (DTI, and the relationships between abnormalities revealed by these two modalities remain unclear. This study applied a multimodal data-fusion method, known as linked independent component analysis (ICA, to a set of structural MRI and DTI data acquired from 46 adult males with ASD and 46 matched controls in order to elucidate associations between different aspects of atypical neuroanatomy of ASD. Linked ICA identified two composite components that showed significant between-group differences, one of which was significantly correlated with age. In the other component, participants with ASD showed decreased gray matter (GM volumes in multiple regions, including the bilateral fusiform gyri, bilateral orbitofrontal cortices, and bilateral pre- and post-central gyri. These GM changes were linked with a pattern of decreased fractional anisotropy (FA in several white matter tracts, such as the bilateral inferior longitudinal fasciculi, bilateral inferior fronto-occipital fasciculi, and bilateral corticospinal tracts. Furthermore, unimodal analysis for DTI data revealed significant reductions of FA along with increased mean diffusivity in those tracts for ASD, providing further evidence of disrupted anatomical connectivity. Taken together, our findings suggest that, in ASD, alterations in different aspects of brain morphology may co-occur in specific brain networks, providing a comprehensive view for understanding the neuroanatomy of this disorder.
8. Using wavefront coding technique as an optical encryption system: reliability analysis and vulnerabilities assessment
Science.gov (United States)
Konnik, Mikhail V.
2012-04-01
Wavefront coding paradigm can be used not only for compensation of aberrations and depth-of-field improvement but also for an optical encryption. An optical convolution of the image with the PSF occurs when a diffractive optical element (DOE) with a known point spread function (PSF) is placed in the optical path. In this case, an optically encoded image is registered instead of the true image. Decoding of the registered image can be performed using standard digital deconvolution methods. In such class of optical-digital systems, the PSF of the DOE is used as an encryption key. Therefore, a reliability and cryptographic resistance of such an encryption method depends on the size and complexity of the PSF used for optical encoding. This paper gives a preliminary analysis on reliability and possible vulnerabilities of such an encryption method. Experimental results on brute-force attack on the optically encrypted images are presented. Reliability estimation of optical coding based on wavefront coding paradigm is evaluated. An analysis of possible vulnerabilities is provided.
9. Quantum Fully Homomorphic Encryption with Verification
DEFF Research Database (Denmark)
Alagic, Gorjan; Dulek, Yfke; Schaffner, Christian
2017-01-01
Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, e...
10. Secure Hybrid Encryption from Weakened Key Encapsulation
NARCIS (Netherlands)
D. Hofheinz (Dennis); E. Kiltz (Eike); A. Menezes
2007-01-01
textabstractWe put forward a new paradigm for building hybrid encryption schemes from constrained chosen-ciphertext secure (CCCA) key-encapsulation mechanisms (KEMs) plus authenticated symmetric encryption. Constrained chosen-ciphertext security is a new security notion for KEMs that we propose. It
KAUST Repository
Abdulwahed, Naif B.
2013-01-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores
12. A secure approach for encrypting and compressing biometric information employing orthogonal code and steganography
Science.gov (United States)
Islam, Muhammad F.; Islam, Mohammed N.
2012-04-01
The objective of this paper is to develop a novel approach for encryption and compression of biometric information utilizing orthogonal coding and steganography techniques. Multiple biometric signatures are encrypted individually using orthogonal codes and then multiplexed together to form a single image, which is then embedded in a cover image using the proposed steganography technique. The proposed technique employs three least significant bits for this purpose and a secret key is developed to choose one from among these bits to be replaced by the corresponding bit of the biometric image. The proposed technique offers secure transmission of multiple biometric signatures in an identification document which will be protected from unauthorized steganalysis attempt.
13. Secure image retrieval with multiple keys
Science.gov (United States)
Liang, Haihua; Zhang, Xinpeng; Wei, Qiuhan; Cheng, Hang
2018-03-01
This article proposes a secure image retrieval scheme under a multiuser scenario. In this scheme, the owner first encrypts and uploads images and their corresponding features to the cloud; then, the user submits the encrypted feature of the query image to the cloud; next, the cloud compares the encrypted features and returns encrypted images with similar content to the user. To find the nearest neighbor in the encrypted features, an encryption with multiple keys is proposed, in which the query feature of each user is encrypted by his/her own key. To improve the key security and space utilization, global optimization and Gaussian distribution are, respectively, employed to generate multiple keys. The experiments show that the proposed encryption can provide effective and secure image retrieval for each user and ensure confidentiality of the query feature of each user.
14. A Survey on Principal Aspects of Secure Image Transmission
OpenAIRE
Ali Soleymani; Zulkarnain Md Ali; Md Jan Nordin
2012-01-01
This paper is a review on the aspects and approaches of design an image cryptosystem. First a general introduction given for cryptography and images encryption and followed by different techniques in image encryption and related works for each technique surveyed. Finally, general security analysis methods for encrypted images are mentioned.
15. Easy encryption for CERN laptops
CERN Multimedia
Computer Security Team
2014-01-01
The number of laptops stolen from or lost by CERN staff and users is not negligible. On average, four to five devices are reported lost or stolen to the CERN Fire Brigade every month. The real number might be even higher as not everyone is aware that such thefts/losses should be reported in this way. Along with each laptop, private e-mails and personal documents, as well as MARS forms, contracts, NDAs, etc. are also lost. Fortunately, CERN has not lost any sensitive data so far (unlike other companies). In parallel with the approval by the Enlarged Directorate at its latest session of the development of a CERN-wide Data Protection Policy, the IT Department has prepared measures allowing you to protect the data on your laptop using full hard-disk encryption. While the word “encryption” might sounds complicated, the IT Department has fully automated the encryption process. For centrally managed Windows PCs, you just have to install the corresponding CMF package (“M...
16. An encryption scheme for a secure policy updating
NARCIS (Netherlands)
Ibraimi, L.; Asim, M.; Petkovic, M.; Obaidat, M.S.; Tsihrintzis, G.A.; Filipe, J.
2012-01-01
Ciphertext policy attribute based encryption is an encryption technique where the data is encrypted according to an access policy over attributes. Users who have a secret key associated with a set of attributes which satisfy the access policy can decrypt the encrypted data. However, one of the
17. Radiation-induced changes in normal-appearing gray matter in patients with nasopharyngeal carcinoma: a magnetic resonance imaging voxel-based morphometry study
Energy Technology Data Exchange (ETDEWEB)
Lv, Xiao-Fei; Zheng, Xiao-Li; Zhang, Wei-Dong; Liu, Li-Zhi; Zhang, You-Ming [State Key Laboratory of Oncology in South China, Collaborative Innovation Center for Cancer Medicine, Guangzhou (China); Sun Yat-sen University Cancer Center, Department of Medical Imaging and Interventional Radiology, Guangzhou (China); Chen, Ming-Yuan [Sun Yat-sen University Cancer Center, Department of Nasopharyngeal Carcinoma, Guangzhou (China); Li, Li [Sun Yat-sen University Cancer Center, Department of Medical Imaging and Interventional Radiology, Guangzhou (China)
2014-05-15
18. Improved decryption quality and security of a joint transform correlator-based encryption system
International Nuclear Information System (INIS)
Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet
2013-01-01
Some image encryption systems based on modified double random phase encoding and joint transform correlator architecture produce low quality decrypted images and are vulnerable to a variety of attacks. In this work, we analyse the algorithm of some reported methods that optically implement the double random phase encryption in a joint transform correlator. We show that it is possible to significantly improve the quality of the decrypted image by introducing a simple nonlinear operation in the encrypted function that contains the joint power spectrum. This nonlinearity also makes the system more resistant to chosen-plaintext attacks. We additionally explore the system resistance against this type of attack when a variety of probability density functions are used to generate the two random phase masks of the encryption–decryption process. Numerical results are presented and discussed. (paper)
19. HOMOMORPHIC ENCRYPTION: CLOUD COMPUTING SECURITY AND OTHER APPLICATIONS (A SURVEY
Directory of Open Access Journals (Sweden)
A. I. Trubei
2015-01-01
Full Text Available Homomorphic encryption is a form of encryption which allows specific types of computations to be carried out on cipher text and to obtain an encrypted result which matches the result of operations performed on the plain text. The article presents a basic concept of the homomorphic encryption and various encryption algorithms in accordance with the fundamental properties of the homomorphic encryption. The examples of various principles and properties of homomorphic encryption, some homomorphic algorithms using asymmetric key systems such as RSA, ElGamal, Paillier algorithms as well as various homomorphic encryption schemes are given. Prospects of homomorphic encryption application in the field of secure cloud computing, electronic voting, cipher text searching, encrypted mail filtering, mobile cipher and secure feedback systems are considered.
20. A Novel Image Cryptosystem Based on S-AES and Chaotic Map
Directory of Open Access Journals (Sweden)
Bai Lan
2015-01-01
Full Text Available This paper proposes a novel scheme based on simplified advanced encryption standard (S-AES for image encryption. Modified Arnold Map applied as diffusion technique for an image, and the key and dynamic S-box of encryption is generated by PWLCM. The goal is to balance rapidity and security of encryption. Experimental implementation has been done. This light encryption scheme shows resistance against chosen-plaintext attack and is suitable for sensor networks and IoT.
1. Video Encryption and Decryption on Quantum Computers
Science.gov (United States)
Yan, Fei; Iliyasu, Abdullah M.; Venegas-Andraca, Salvador E.; Yang, Huamin
2015-08-01
A method for video encryption and decryption on quantum computers is proposed based on color information transformations on each frame encoding the content of the encoding the content of the video. The proposed method provides a flexible operation to encrypt quantum video by means of the quantum measurement in order to enhance the security of the video. To validate the proposed approach, a tetris tile-matching puzzle game video is utilized in the experimental simulations. The results obtained suggest that the proposed method enhances the security and speed of quantum video encryption and decryption, both properties required for secure transmission and sharing of video content in quantum communication.
2. Encryption protection for communication satellites
Science.gov (United States)
Sood, D. R.; Hoernig, O. W., Jr.
In connection with the growing importance of the commercial communication satellite systems and the introduction of new technological developments, users and operators of these systems become increasingly concerned with aspects of security. The user community is concerned with maintaining confidentiality and integrity of the information being transmitted over the satellite links, while the satellite operators are concerned about the safety of their assets in space. In response to these concerns, the commercial satellite operators are now taking steps to protect the communication information and the satellites. Thus, communication information is being protected by end-to-end encryption of the customer communication traffic. Attention is given to the selection of the NBS DES algorithm, the command protection systems, and the communication protection systems.
3. Henry Gray's Anatomy.
Science.gov (United States)
Pearce, J M S
2009-04-01
Little is generally known of Henry Gray, the author of Gray's Anatomy, and even less of his colleague Henry Vandyke Carter, who played a vital role in the dissections and illustrations leading to the production of the first volume in 1859. This essay attempts to sketch briefly the salient, know aspects of these two men and their divergent careers. It traces succinctly the subsequent fate of the unique anatomy book that has influenced and instructed almost every student of medicine. (c) 2009 Wiley-Liss, Inc.
4. Quantum Secure Dialogue with Quantum Encryption
International Nuclear Information System (INIS)
Ye Tian-Yu
2014-01-01
How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice. (general)
5. Cracking Advanced Encryption Standard-A Review
Directory of Open Access Journals (Sweden)
Jashnil Kumar
2017-07-01
Full Text Available Password protection is a major security concern the world is facing today. While there are many publications available that discuss ways to protect passwords and data how widely user from around the world adhere to these rules are unknown. The novelty of this study is that this is the first time a review is done on software tools that can be used to crack Advanced Encryption Standards. Firstly the study does a review on top 10 software tools that are available to crack Advanced Encryption Standards. After which an analysis on two software tools was performed to see how long each software tool took to crack a password. The result of the study gives Advanced Encryption Standard researcher Network security researcher and the general public helpful information on how to strengthen advanced encryption standards and strengthen passwords that are hard for the software tools discussed above to crack.
6. Quantum key distribution via quantum encryption
CERN Document Server
Yong Sheng Zhang; Guang Can Guo
2001-01-01
A quantum key distribution protocol based on quantum encryption is presented in this Brief Report. In this protocol, the previously shared Einstein-Podolsky-Rosen pairs act as the quantum key to encode and decode the classical cryptography key. The quantum key is reusable and the eavesdropper cannot elicit any information from the particle Alice sends to Bob. The concept of quantum encryption is also discussed. (21 refs).
7. Dual-Layer Video Encryption using RSA Algorithm
Science.gov (United States)
2015-04-01
This paper proposes a video encryption algorithm using RSA and Pseudo Noise (PN) sequence, aimed at applications requiring sensitive video information transfers. The system is primarily designed to work with files encoded using the Audio Video Interleaved (AVI) codec, although it can be easily ported for use with Moving Picture Experts Group (MPEG) encoded files. The audio and video components of the source separately undergo two layers of encryption to ensure a reasonable level of security. Encryption of the video component involves applying the RSA algorithm followed by the PN-based encryption. Similarly, the audio component is first encrypted using PN and further subjected to encryption using the Discrete Cosine Transform. Combining these techniques, an efficient system, invulnerable to security breaches and attacks with favorable values of parameters such as encryption/decryption speed, encryption/decryption ratio and visual degradation; has been put forth. For applications requiring encryption of sensitive data wherein stringent security requirements are of prime concern, the system is found to yield negligible similarities in visual perception between the original and the encrypted video sequence. For applications wherein visual similarity is not of major concern, we limit the encryption task to a single level of encryption which is accomplished by using RSA, thereby quickening the encryption process. Although some similarity between the original and encrypted video is observed in this case, it is not enough to comprehend the happenings in the video.
8. Encryption and validation of multiple signals for optical identification systems
Energy Technology Data Exchange (ETDEWEB)
Perez-Cabre, E [Universitat PoliteGcnica de Catalunya, Department Optica i Optometria, Violinista Vellsola 37, 08222 Terrassa (Spain); Millan, M S [Universitat PoliteGcnica de Catalunya, Department Optica i Optometria, Violinista Vellsola 37, 08222 Terrassa (Spain); Javidi, B [University of Connecticut, Electrical and Computer Engineering Department, 371 Fairfield Road, CT 06269 Storrs (United States)
2007-07-15
Multifactor encryption-authentication technique reinforces optical security by allowing the simultaneous A N D-verification of more than one primary image. Instead of basing the identification on a unique signature or piece of information, our goal is to authenticate a given person, object, vehicle by the simultaneous recognition of several factors. Some of them are intrinsic to the person and object or vehicle under control. Other factors, act as keys of the authentication step. Such a system is proposed for situations such as the access control to restricted areas, where the demand of security is high. The multifactor identification method involves double random-phase encoding, fully phase-based encryption and a combined nonlinear joint transform correlator and a classical 4f-correlator for simultaneous recognition and authentication of multiple images. The encoded signal fulfils the general requirements of invisible content, extreme difficulty in counterfeiting and real-time automatic verification. Four reference double-phase encoded images are compared with the retrieved input images obtained in situ from the person or the vehicle whose authentication is wanted and from a database. A recognition step based on the correlation between the signatures and the stored references determines the authentication or rejection of the person and object under surveillance.
9. Encryption and validation of multiple signals for optical identification systems
International Nuclear Information System (INIS)
Perez-Cabre, E; Millan, M S; Javidi, B
2007-01-01
Multifactor encryption-authentication technique reinforces optical security by allowing the simultaneous A N D-verification of more than one primary image. Instead of basing the identification on a unique signature or piece of information, our goal is to authenticate a given person, object, vehicle by the simultaneous recognition of several factors. Some of them are intrinsic to the person and object or vehicle under control. Other factors, act as keys of the authentication step. Such a system is proposed for situations such as the access control to restricted areas, where the demand of security is high. The multifactor identification method involves double random-phase encoding, fully phase-based encryption and a combined nonlinear joint transform correlator and a classical 4f-correlator for simultaneous recognition and authentication of multiple images. The encoded signal fulfils the general requirements of invisible content, extreme difficulty in counterfeiting and real-time automatic verification. Four reference double-phase encoded images are compared with the retrieved input images obtained in situ from the person or the vehicle whose authentication is wanted and from a database. A recognition step based on the correlation between the signatures and the stored references determines the authentication or rejection of the person and object under surveillance
10. Gray matter heterotopias: MR and clinical features
International Nuclear Information System (INIS)
Moon, Tae Myung; Yoon, Jeong Hee; Chung, Chun Phil
1995-01-01
To evaluate types of gray matter heterotopias, associated brain anomalies, and its correlation with the patterns of seizure. We evaluated retrospectively 19 patients (male:female=10:9, mean age 21 years) with gray matter heterotopias on brain MRI. Using 1.0T superconducting MR unit, spin echo T1-, proton -density and T2-weighted images in axial, coronal and sagittal planes were obtained. Types of gray matter heterotopias were single subependymal in four patients, multiple subependymal in one, focal subcortical in eight, diffuse subcortical in two, mixed multiple subependymal and focal subcortical in four. Associated anomalies were seen in 11 patients: other neuronal migration anomalies in eight patients, corpus callosum agenesis in two, and combined holoprosencephaly and Dandy-Walker malformation in one. Fifteen patients had seizure. The patterns of seizure were not correlated with the types of heterotopias. In addition to subependymal, focal subcortical, and diffuse subcortical types, gray matter heterotopias included mixed variant of multiple subependymal and subcortical type. Schizencephaly was the most common form of accompanying anomalies, and patterns of seizure were not correlated with types of gray matter heterotopias, even though main clinical manifestation was seizure
11. Homomorphic encryption-based secure SIFT for privacy-preserving feature extraction
Science.gov (United States)
Hsu, Chao-Yung; Lu, Chun-Shien; Pei, Soo-Chang
2011-02-01
Privacy has received much attention but is still largely ignored in the multimedia community. Consider a cloud computing scenario, where the server is resource-abundant and is capable of finishing the designated tasks, it is envisioned that secure media retrieval and search with privacy-preserving will be seriously treated. In view of the fact that scale-invariant feature transform (SIFT) has been widely adopted in various fields, this paper is the first to address the problem of secure SIFT feature extraction and representation in the encrypted domain. Since all the operations in SIFT must be moved to the encrypted domain, we propose a homomorphic encryption-based secure SIFT method for privacy-preserving feature extraction and representation based on Paillier cryptosystem. In particular, homomorphic comparison is a must for SIFT feature detection but is still a challenging issue for homomorphic encryption methods. To conquer this problem, we investigate a quantization-like secure comparison strategy in this paper. Experimental results demonstrate that the proposed homomorphic encryption-based SIFT performs comparably to original SIFT on image benchmarks, while preserving privacy additionally. We believe that this work is an important step toward privacy-preserving multimedia retrieval in an environment, where privacy is a major concern.
12. Gray matter alterations and correlation of nutritional intake with the gray matter volume in prediabetes
Science.gov (United States)
Hou, Yi-Cheng; Lai, Chien-Han; Wu, Yu-Te; Yang, Shwu-Huey
2016-01-01
Abstract The neurophysiology of prediabetes plays an important role in preventive medicine. The dysregulation of glucose metabolism is likely linked to changes in neuron-related gray matter. Therefore, we designed this study to investigate gray matter alterations in medication-naive prediabetic patients. We expected to find alterations in the gray matter of prediabetic patients. A total of 64 prediabetic patients and 54 controls were enrolled. All subjects received T1 scans using a 3-T magnetic resonance imaging machine. Subjects also completed nutritional intake records at the 24-hour and 3-day time points to determine their carbohydrate, protein, fat, and total calorie intake. We utilized optimized voxel-based morphometry to estimate the gray matter differences between the patients and controls. In addition, the preprandial serum glucose level and the carbohydrate, protein, fat, and total calorie intake levels were tested to determine whether these parameters were correlated with the gray matter volume. Prediabetic patients had lower gray matter volumes than controls in the right anterior cingulate gyrus, right posterior cingulate gyrus, left insula, left super temporal gyrus, and left middle temporal gyrus (corrected P prediabetic patients. PMID:27336893
13. A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.
2007-01-01
In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security
14. Anti-Forensic Tool Using Double Encryption Scheme
OpenAIRE
Singh, Avtar; Singh, Kuldip
2009-01-01
In this paper we are implementing an Anti- Forensic tool that is used in data hiding approaches of the Anti-Forensic technology. This tool will encrypt a secret file twice: firstly it is encrypted with the XOR and then by the powerful AES (Advance Encryption Standard). To make XOR strong we have used three files that are selected by user. These files will create a mess with the plain text before encryption making the cipher text more secure and harder to break.
15. Quantum Encryption Minimising Key Leakage under Known Plaintext Attacks
DEFF Research Database (Denmark)
Pedersen, Thomas Brochmann
2006-01-01
, or interactive encryption schemes, where the interaction does not need to occur online. In our model we show that the amount of key leaked under a known plaintext attack can be made arbitrarily small even in non-interactive encryption schemes. We also give an encryption scheme where eavesdropping can be detected....... In this encryption scheme the entire key can be safely recycled when no eavesdropping is detected....
16. Transparent Data Encryption -- Solution for Security of Database Contents
OpenAIRE
Deshmukh, Dr. Anwar Pasha; Qureshi, Dr. Riyazuddin
2013-01-01
The present study deals with Transparent Data Encryption which is a technology used to solve the problems of security of data. Transparent Data Encryption means encrypting databases on hard disk and on any backup media. Present day global business environment presents numerous security threats and compliance challenges. To protect against data thefts and frauds we require security solutions that are transparent by design. Transparent Data Encryption provides transparent, standards-based secur...
17. Hybrid cryptosystem for image file using elgamal and double playfair cipher algorithm
Science.gov (United States)
Hardi, S. M.; Tarigan, J. T.; Safrina, N.
2018-03-01
In this paper, we present an implementation of an image file encryption using hybrid cryptography. We chose ElGamal algorithm to perform asymmetric encryption and Double Playfair for the symmetric encryption. Our objective is to show that these algorithms are capable to encrypt an image file with an acceptable running time and encrypted file size while maintaining the level of security. The application was built using C# programming language and ran as a stand alone desktop application under Windows Operating System. Our test shows that the system is capable to encrypt an image with a resolution of 500×500 to a size of 976 kilobytes with an acceptable running time.
18. Towards an Information Theoretic Analysis of Searchable Encryption (Extended Version)
NARCIS (Netherlands)
Sedghi, S.; Doumen, J.M.; Hartel, Pieter H.; Jonker, Willem
2008-01-01
Searchable encryption is a technique that allows a client to store data in encrypted form on a curious server, such that data can be retrieved while leaking a minimal amount of information to the server. Many searchable encryption schemes have been proposed and proved secure in their own
19. Towards an Information Theoretic Analysis of Searchable Encryption
NARCIS (Netherlands)
Sedghi, S.; Doumen, J.M.; Hartel, Pieter H.; Jonker, Willem
2008-01-01
Searchable encryption is a technique that allows a client to store data in encrypted form on a curious server, such that data can be retrieved while leaking a minimal amount of information to the server. Many searchable encryption schemes have been proposed and proved secure in their own
20. Generic Adaptively Secure Searchable Phrase Encryption
Directory of Open Access Journals (Sweden)
Kissel Zachary A.
2017-01-01
Full Text Available In recent years searchable symmetric encryption has seen a rapid increase in query expressiveness including keyword, phrase, Boolean, and fuzzy queries. With this expressiveness came increasingly complex constructions. Having these facts in mind, we present an efficient and generic searchable symmetric encryption construction for phrase queries. Our construction is straightforward to implement, and is proven secure under adaptively chosen query attacks (CQA2 in the random oracle model with an honest-but-curious adversary. To our knowledge, this is the first encrypted phrase search system that achieves CQA2 security. Moreover, we demonstrate that our document collection preprocessing algorithm allows us to extend a dynamic SSE construction so that it supports phrase queries. We also provide a compiler theorem which transforms any CQA2-secure SSE construction for keyword queries into a CQA2-secure SSE construction that supports phrase queries.
1. Comb to Pipeline: Fast Software Encryption Revisited
DEFF Research Database (Denmark)
Bogdanov, Andrey; Lauridsen, Martin Mehl; Tischhauser, Elmar Wolfgang
2015-01-01
AES-NI, or Advanced Encryption Standard New Instructions, is an extension of the x86 architecture proposed by Intel in 2008. With a pipelined implementation utilizing AES-NI, parallelizable modes such as AES-CTR become extremely efficient. However, out of the four non-trivial NIST......-recommended encryption modes, three are inherently sequential: CBC, CFB, and OFB. This inhibits the advantage of using AES-NI significantly. Similar observations apply to CMAC, CCM and a great deal of other modes. We address this issue by proposing the comb scheduler – a fast scheduling algorithm based on an efficient....... We observe a drastic speed-up of factor 5 for NIST’s CBC, CFB, OFB and CMAC performing around 0.88 cpb. Surprisingly, contrary to the entire body of previous performance analysis, the throughput of the authenticated encryption (AE) mode CCM gets very close to that of GCM and OCB3, with about 1.64 cpb...
2. Improvement of One Quantum Encryption Scheme
Science.gov (United States)
Cao, Zhengjun; Liu, Lihua
2012-01-01
Zhou et al. proposed a quantum encryption scheme based on quantum computation in 2006 [N. Zhou et al., Physica A362 (2006) 305]. Each qubit of the ciphertext is constrained to two pairs of conjugate states. So, its implementation is feasible with the existing technology. But it is inefficient since it entails six key bits to encrypt one message bit, and the resulting ciphertext for one message bit consists of three qubits. In addition, its security cannot be directly reduced to the well-known BB84 protocol. In this paper, we improve it using the technique developed in BB84 protocol. The new scheme entails only two key bits to encrypt one message bit. The resulting ciphertext is just composed of two qubits. It saves about a half cost without the loss of security. Moreover, the new scheme is probabilistic instead of deterministic.
3. Frontpage and Dreamweaver users must use encryption
CERN Multimedia
Web Services Team
2006-01-01
In order to ensure document confidentiality and protect users from the possible theft of their passwords, all web authoring actions will be required to use encryption as of 15 February 2006. Most Frontpage and Dreamweaver users will have to slightly change the way they connect to their web sites in order to enable encryption. Please note that only the initial connection to the web site from Frontpage or Dreamweaver is affected: there is no change in the use of these applications after the initial connection, and the web site itself is not affected. Further details, as well as instructions on how to enable encryption, are available at: http://cern.ch/web/docs/AuthDoc/SecureAuthoring. In case of problems, please contact the computer helpdesk or [email protected]. The Web Services Team
4. Protect sensitive data with lightweight memory encryption
Science.gov (United States)
Zhou, Hongwei; Yuan, Jinhui; Xiao, Rui; Zhang, Kai; Sun, Jingyao
2018-04-01
Since current commercial processor is not able to deal with the data in the cipher text, the sensitive data have to be exposed in the memory. It leaves a window for the adversary. To protect the sensitive data, a direct idea is to encrypt the data when the processor does not access them. On the observation, we have developed a lightweight memory encryption, called LeMe, to protect the sensitive data in the application. LeMe marks the sensitive data in the memory with the page table entry, and encrypts the data in their free time. LeMe is built on the Linux with a 3.17.6 kernel, and provides four user interfaces as dynamic link library. Our evaluations show LeMe is effective to protect the sensitive data and incurs an acceptable performance overhead.
5. A Spatiotemporal-Chaos-Based Encryption Having Overall Properties Considerably Better than Advanced Encryption Standard
Science.gov (United States)
Wang, Shi-Hong; Ye, Wei-Ping; Lü, Hua-Ping; Kuang, Jin-Yu; Li, Jing-Hua; Luo, Yun-Lun; Hu, Gang
2003-07-01
Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES). The project supported by National Natural Science Foundation of China under Grant No. 10175010 and the Special Funds for Major State Basic Research Projects under Grant No. G2000077304
6. Symmetric encryption algorithms using chaotic and non-chaotic generators: A review.
Science.gov (United States)
Radwan, Ahmed G; AbdElHaleem, Sherif H; Abd-El-Hafiz, Salwa K
2016-03-01
This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold's cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper.
7. Selective encryption for H.264/AVC video coding
Science.gov (United States)
Shi, Tuo; King, Brian; Salama, Paul
2006-02-01
Due to the ease with which digital data can be manipulated and due to the ongoing advancements that have brought us closer to pervasive computing, the secure delivery of video and images has become a challenging problem. Despite the advantages and opportunities that digital video provide, illegal copying and distribution as well as plagiarism of digital audio, images, and video is still ongoing. In this paper we describe two techniques for securing H.264 coded video streams. The first technique, SEH264Algorithm1, groups the data into the following blocks of data: (1) a block that contains the sequence parameter set and the picture parameter set, (2) a block containing a compressed intra coded frame, (3) a block containing the slice header of a P slice, all the headers of the macroblock within the same P slice, and all the luma and chroma DC coefficients belonging to the all the macroblocks within the same slice, (4) a block containing all the ac coefficients, and (5) a block containing all the motion vectors. The first three are encrypted whereas the last two are not. The second method, SEH264Algorithm2, relies on the use of multiple slices per coded frame. The algorithm searches the compressed video sequence for start codes (0x000001) and then encrypts the next N bits of data.
8. A Memory Efficient Network Encryption Scheme
Science.gov (United States)
El-Fotouh, Mohamed Abo; Diepold, Klaus
In this paper, we studied the two widely used encryption schemes in network applications. Shortcomings have been found in both schemes, as these schemes consume either more memory to gain high throughput or low memory with low throughput. The need has aroused for a scheme that has low memory requirements and in the same time possesses high speed, as the number of the internet users increases each day. We used the SSM model [1], to construct an encryption scheme based on the AES. The proposed scheme possesses high throughput together with low memory requirements.
9. Information encryption systems based on Boolean functions
Directory of Open Access Journals (Sweden)
Aureliu Zgureanu
2011-02-01
Full Text Available An information encryption system based on Boolean functions is proposed. Information processing is done using multidimensional matrices, performing logical operations with these matrices. At the basis of ensuring high level security of the system the complexity of solving the problem of building systems of Boolean functions that depend on many variables (tens and hundreds is set. Such systems represent the private key. It varies both during the encryption and decryption of information, and during the transition from one message to another.
10. Cracking Advanced Encryption Standard-A Review
OpenAIRE
Jashnil Kumar; Mohammed Farik
2017-01-01
Password protection is a major security concern the world is facing today. While there are many publications available that discuss ways to protect passwords and data how widely user from around the world adhere to these rules are unknown. The novelty of this study is that this is the first time a review is done on software tools that can be used to crack Advanced Encryption Standards. Firstly the study does a review on top 10 software tools that are available to crack Advanced Encryption Sta...
11. Multimedia encryption and authentication techniques and applications
CERN Document Server
Furht, Borko
2006-01-01
Intellectual property owners must continually exploit new ways of reproducing, distributing, and marketing their products. However, the threat of piracy looms as a major problem with digital distribution and storage technologies. Multimedia Encryption and Authentication Techniques and Applications covers current and future trends in the design of modern systems that use encryption and authentication to protect multimedia content. Containing the works of contributing authors who are worldwide experts in their fields, this volume is intended for researchers and practitioners, as well as for thos
12. The experiments and analysis of several selective video encryption methods
Science.gov (United States)
Zhang, Yue; Yang, Cheng; Wang, Lei
2013-07-01
This paper presents four methods for selective video encryption based on the MPEG-2 video compression,including the slices, the I-frames, the motion vectors, and the DCT coefficients. We use the AES encryption method for simulation experiment for the four methods on VS2010 Platform, and compare the video effects and the processing speed of each frame after the video encrypted. The encryption depth can be arbitrarily selected, and design the encryption depth by using the double limit counting method, so the accuracy can be increased.
13. Error function attack of chaos synchronization based encryption schemes.
Science.gov (United States)
Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu
2004-03-01
Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.
14. The Internet And Gray Marketing
OpenAIRE
2010-01-01
The purpose of this conceptual paper is to investigate the nature, extent, and outcomes of gray marketing on the Internet. We examined the current state of Internet-based gray marketing in several product categories and found the phenomenon to be on the rise. Next, we developed a series of propositions to address evolving trends in online gray marketing, regarding actions of intermediaries and manufacturers, response by consumers, and outcomes on marketing strategy.
15. Blood oxygen level-dependent magnetic resonance imaging for detecting pathological patterns in patients with lupus nephritis: a preliminary study using gray-level co-occurrence matrix analysis.
Science.gov (United States)
Shi, Huilan; Jia, Junya; Li, Dong; Wei, Li; Shang, Wenya; Zheng, Zhenfeng
2018-01-01
Objective Blood oxygen level-dependent magnetic resonance imaging (BOLD MRI) is a noninvasive technique useful in patients with renal disease. The current study was performed to determine whether BOLD MRI can contribute to the diagnosis of renal pathological patterns. Methods BOLD MRI was used to obtain functional magnetic resonance parameter R2* values. Gray-level co-occurrence matrixes (GLCMs) were generated for gray-scale maps. Several GLCM parameters were calculated and used to construct algorithmic models for renal pathological patterns. Results Histopathology and BOLD MRI were used to examine 12 patients. Two GLCM parameters, including correlation and energy, revealed differences among four groups of renal pathological patterns. Four Fisher's linear discriminant formulas were constructed using two variables, including the correlation at 45° and correlation at 90°. A cross-validation test showed that the formulas correctly predicted 28 of 36 samples, and the rate of correct prediction was 77.8%. Conclusions Differences in the texture characteristics of BOLD MRI in patients with lupus nephritis may be detected by GLCM analysis. Discriminant formulas constructed using GLCM parameters may facilitate prediction of renal pathological patterns.
16. Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications
Directory of Open Access Journals (Sweden)
Wafaa S. Sayed
2017-01-01
Full Text Available Chaotic systems appear in many applications such as pseudo-random number generation, text encryption, and secure image transfer. Numerical solutions of these systems using digital software or hardware inevitably deviate from the expected analytical solutions. Chaotic orbits produced using finite precision systems do not exhibit the infinite period expected under the assumptions of infinite simulation time and precision. In this paper, digital implementation of the generalized logistic map with signed parameter is considered. We present a fixed-point hardware realization of a Pseudo-Random Number Generator using the logistic map that experiences a trade-off between computational efficiency and accuracy. Several introduced factors such as the used precision, the order of execution of the operations, parameter, and initial point values affect the properties of the finite precision map. For positive and negative parameter cases, the studied properties include bifurcation points, output range, maximum Lyapunov exponent, and period length. The performance of the finite precision logistic map is compared in the two cases. A basic stream cipher system is realized to evaluate the system performance for encryption applications for different bus sizes regarding the encryption key size, hardware requirements, maximum clock frequency, NIST and correlation, histogram, entropy, and Mean Absolute Error analyses of encrypted images.
17. Anonymous Credential Schemes with Encrypted Attributes
NARCIS (Netherlands)
Guajardo Merchan, J.; Mennink, B.; Schoenmakers, B.
2011-01-01
In anonymous credential schemes, users obtain credentials on certain attributes from an issuer, and later show these credentials to a relying party anonymously and without fully disclosing the attributes. In this paper, we introduce the notion of (anonymous) credential schemes with encrypted
18. Innovative hyperchaotic encryption algorithm for compressed video
Science.gov (United States)
Yuan, Chun; Zhong, Yuzhuo; Yang, Shiqiang
2002-12-01
It is accepted that stream cryptosystem can achieve good real-time performance and flexibility which implements encryption by selecting few parts of the block data and header information of the compressed video stream. Chaotic random number generator, for example Logistics Map, is a comparatively promising substitute, but it is easily attacked by nonlinear dynamic forecasting and geometric information extracting. In this paper, we present a hyperchaotic cryptography scheme to encrypt the compressed video, which integrates Logistics Map with Z(232 - 1) field linear congruential algorithm to strengthen the security of the mono-chaotic cryptography, meanwhile, the real-time performance and flexibility of the chaotic sequence cryptography are maintained. It also integrates with the dissymmetrical public-key cryptography and implements encryption and identity authentification on control parameters at initialization phase. In accord with the importance of data in compressed video stream, encryption is performed in layered scheme. In the innovative hyperchaotic cryptography, the value and the updating frequency of control parameters can be changed online to satisfy the requirement of the network quality, processor capability and security requirement. The innovative hyperchaotic cryprography proves robust security by cryptoanalysis, shows good real-time performance and flexible implement capability through the arithmetic evaluating and test.
19. ML Confidential : machine learning on encrypted data
NARCIS (Netherlands)
Graepel, T.; Lauter, K.; Naehrig, M.; Kwon, T.; Lee, M.-K.; Kwon, D.
2013-01-01
We demonstrate that, by using a recently proposed leveled homomorphic encryption scheme, it is possible to delegate the execution of a machine learning algorithm to a computing service while retaining con¿dentiality of the training and test data. Since the computational complexity of the homomorphic
20. ML Confidential : machine learning on encrypted data
NARCIS (Netherlands)
Graepel, T.; Lauter, K.; Naehrig, M.
2012-01-01
We demonstrate that by using a recently proposed somewhat homomorphic encryption (SHE) scheme it is possible to delegate the execution of a machine learning (ML) algorithm to a compute service while retaining confidentiality of the training and test data. Since the computational complexity of the
1. Public-key encryption with chaos
Science.gov (United States)
Kocarev, Ljupco; Sterjev, Marjan; Fekete, Attila; Vattay, Gabor
2004-12-01
We propose public-key encryption algorithms based on chaotic maps, which are generalization of well-known and commercially used algorithms: Rivest-Shamir-Adleman (RSA), ElGamal, and Rabin. For the case of generalized RSA algorithm we discuss in detail its software implementation and properties. We show that our algorithm is as secure as RSA algorithm.
2. Dynamic Rule Encryption for Mobile Payment
Directory of Open Access Journals (Sweden)
Emir Husni
2017-01-01
Full Text Available The trend of financial transactions by using a mobile phone or mobile payment increases. By using the mobile payment service, users can save money on mobile phone (handset and separate from the pulse. For protecting users, mobile payment service providers must complete the mobile payment service with the transaction security. One way to provide transaction security is to utilize a secure mobile payment application. This research provides a safety feature used for an Android-based mobile payment application. This security feature is making encryption rules dynamically named Dynamic Rule Encryption (DRE. DRE has the ability to protect data by means of encrypting data with dynamic rules, and DRE also has a token function for an authentication. DRE token raised with dynamic time-based rules. Here, the time is used as a reference with the order of the day in the year (day of the year. The processes of the DRE’s encryption, decryption, and the DRE’s functionality as the token are discussed in this paper. Here, the Hamming distance metric is employed for having maximum differences between plaintext and ciphertext.
3. A Verifiable Secret Shuffle of Homomorphic Encryptions
DEFF Research Database (Denmark)
Groth, Jens
2003-01-01
We show how to prove in honest verifier zero-knowledge the correctness of a shuffle of homomorphic encryptions (or homomorphic commitments.) A shuffle consists in a rearrangement of the input ciphertexts and a reencryption of them so that the permutation is not revealed....
4. Efficient Tree Search in Encrypted Data
NARCIS (Netherlands)
Brinkman, R.; Feng, L.; Doumen, J.M.; Hartel, P.H.; Jonker, W.
Sometimes there is a need to store sensitive data on an untrusted database server. Song, Wagner and Perrig have introduced a way to search for the existence of a word in an encrypted textual document. The search speed is linear in the size of the document. It does not scale well for a large
5. 47 CFR 90.553 - Encryption.
Science.gov (United States)
2010-10-01
... January 23, 2001, Telecommunications Industry Association, ANSI/TIA/EIA-102.AAAA-A-2001. (c) The Director... 47 Telecommunication 5 2010-10-01 2010-10-01 false Encryption. 90.553 Section 90.553 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PRIVATE LAND...
6. Hybrid Approach To Steganography System Based On Quantum Encryption And Chaos Algorithms
Directory of Open Access Journals (Sweden)
ZAID A. ABOD
2018-01-01
Full Text Available A hybrid scheme for secretly embedding image into a dithered multilevel image is presented. This work inputs both a cover image and secret image, which are scrambling and divided into groups to embedded together based on multiple chaos algorithms (Lorenz map, Henon map and Logistic map respectively. Finally, encrypt the embedded images by using one of the quantum cryptography mechanisms, which is quantum one time pad. The experimental results show that the proposed hybrid system successfully embedded images and combine with the quantum cryptography algorithms and gives high efficiency for secure communication.
7. Gray Matter Is Targeted in First-Attack Multiple Sclerosis
Energy Technology Data Exchange (ETDEWEB)
Schutzer, Steven E.; Angel, Thomas E.; Liu, Tao; Schepmoes, Athena A.; Xie, Fang; Bergquist, Jonas P.; Vecsei, Lazlo' ; Zadori, Denes; Camp, David G.; Holland, Bart K.; Smith, Richard D.; Coyle, Patricia K.
2013-09-10
The cause of multiple sclerosis (MS), its driving pathogenesis at the earliest stages, and what factors allow the first clinical attack to manifest remain unknown. Some imaging studies suggest gray rather than white matter may be involved early, and some postulate this may be predictive of developing MS. Other imaging studies are in conflict. To determine if there was objective molecular evidence of gray matter involvement in early MS we used high-resolution mass spectrometry to identify proteins in the cerebrospinal fluid (CSF) of first-attack MS patients (two independent groups) compared to established relapsing remitting (RR) MS and controls. We found that the CSF proteins in first-attack patients were differentially enriched for gray matter components (axon, neuron, synapse). Myelin components did not distinguish these groups. The results support that gray matter dysfunction is involved early in MS, and also may be integral for the initial clinical presentation.
8. FPGA BASED HARDWARE KEY FOR TEMPORAL ENCRYPTION
Directory of Open Access Journals (Sweden)
B. Lakshmi
2010-09-01
Full Text Available In this paper, a novel encryption scheme with time based key technique on an FPGA is presented. Time based key technique ensures right key to be entered at right time and hence, vulnerability of encryption through brute force attack is eliminated. Presently available encryption systems, suffer from Brute force attack and in such a case, the time taken for breaking a code depends on the system used for cryptanalysis. The proposed scheme provides an effective method in which the time is taken as the second dimension of the key so that the same system can defend against brute force attack more vigorously. In the proposed scheme, the key is rotated continuously and four bits are drawn from the key with their concatenated value representing the delay the system has to wait. This forms the time based key concept. Also the key based function selection from a pool of functions enhances the confusion and diffusion to defend against linear and differential attacks while the time factor inclusion makes the brute force attack nearly impossible. In the proposed scheme, the key scheduler is implemented on FPGA that generates the right key at right time intervals which is then connected to a NIOS – II processor (a virtual microcontroller which is brought out from Altera FPGA that communicates with the keys to the personal computer through JTAG (Joint Test Action Group communication and the computer is used to perform encryption (or decryption. In this case the FPGA serves as hardware key (dongle for data encryption (or decryption.
9. Grays Harbor Paper
Energy Technology Data Exchange (ETDEWEB)
Quigg, B. [Grays Harbor Paper, Hoquiam, WA (United States)
2009-07-01
Wood waste biomass boilers are used at Grays Harbor Paper in Hoquiam, Washington. This presentation showed that large volumes of biomass are left after a traditional clearcut. The opportunities and challenges of collecting branches, tops and stumps from this wet coastal climate were outlined. The paper described some of the low-tech methods for picking up branches, stumps and woody debris. It included several photographs of custom logging machines for timber harvest, including a brush grapple slasher, a shearer shovel, chippers, grinders, slicesaws, trucks, trailers and caterpillar log loaders for handling slash. The slash recovery program relies on innovative harvesting machines that convert scattered logging slash into bundles that can be easily collected, transported, and stored for use in existing facilities that utilize wood fiber for fuel. figs.
10. Why Does Hair Turn Gray?
Science.gov (United States)
... out, but people with naturally lighter hair are just as likely to go gray. From the time a person notices a few gray hairs, it may take more than 10 years for all of that person's hair to turn ... really believe that this happens. Just in case, try not to freak out your ...
11. Novel Amdovirus in Gray Foxes
Science.gov (United States)
Li, Linlin; Pesavento, Patricia A.; Woods, Leslie; Clifford, Deana L.; Luff, Jennifer; Wang, Chunlin
2011-01-01
We used viral metagenomics to identify a novel parvovirus in tissues of a gray fox (Urocyon cinereoargenteus). Nearly full genome characterization and phylogenetic analyses showed this parvovirus (provisionally named gray fox amdovirus) to be distantly related to Aleutian mink disease virus, representing the second viral species in the Amdovirus genus. PMID:22000359
12. Cognitive Implications of Deep Gray Matter Iron in Multiple Sclerosis.
Science.gov (United States)
Fujiwara, E; Kmech, J A; Cobzas, D; Sun, H; Seres, P; Blevins, G; Wilman, A H
2017-05-01
Deep gray matter iron accumulation is increasingly recognized in association with multiple sclerosis and can be measured in vivo with MR imaging. The cognitive implications of this pathology are not well-understood, especially vis-à-vis deep gray matter atrophy. Our aim was to investigate the relationships between cognition and deep gray matter iron in MS by using 2 MR imaging-based iron-susceptibility measures. Forty patients with multiple sclerosis (relapsing-remitting, n = 16; progressive, n = 24) and 27 healthy controls were imaged at 4.7T by using the transverse relaxation rate and quantitative susceptibility mapping. The transverse relaxation rate and quantitative susceptibility mapping values and volumes (atrophy) of the caudate, putamen, globus pallidus, and thalamus were determined by multiatlas segmentation. Cognition was assessed with the Brief Repeatable Battery of Neuropsychological Tests. Relationships between cognition and deep gray matter iron were examined by hierarchic regressions. Compared with controls, patients showed reduced memory ( P processing speed ( P = .02) and smaller putamen ( P deep gray matter iron accumulation in the current multiple sclerosis cohort. Atrophy and iron accumulation in deep gray matter both have negative but separable relationships to cognition in multiple sclerosis. © 2017 by American Journal of Neuroradiology.
13. Spinal Cord Gray Matter Atrophy in Amyotrophic Lateral Sclerosis.
Science.gov (United States)
2018-01-01
There is an emerging need for biomarkers to better categorize clinical phenotypes and predict progression in amyotrophic lateral sclerosis. This study aimed to quantify cervical spinal gray matter atrophy in amyotrophic lateral sclerosis and investigate its association with clinical disability at baseline and after 1 year. Twenty-nine patients with amyotrophic lateral sclerosis and 22 healthy controls were scanned with 3T MR imaging. Standard functional scale was recorded at the time of MR imaging and after 1 year. MR imaging data were processed automatically to measure the spinal cord, gray matter, and white matter cross-sectional areas. A statistical analysis assessed the difference in cross-sectional areas between patients with amyotrophic lateral sclerosis and controls, correlations between spinal cord and gray matter atrophy to clinical disability at baseline and at 1 year, and prediction of clinical disability at 1 year. Gray matter atrophy was more sensitive to discriminate patients with amyotrophic lateral sclerosis from controls ( P = .004) compared with spinal cord atrophy ( P = .02). Gray matter and spinal cord cross-sectional areas showed good correlations with clinical scores at baseline ( R = 0.56 for gray matter and R = 0.55 for spinal cord; P amyotrophic lateral sclerosis. © 2018 by American Journal of Neuroradiology.
14. Attribute-Based Proxy Re-Encryption with Keyword Search
Science.gov (United States)
Shi, Yanfeng; Liu, Jiqiang; Han, Zhen; Zheng, Qingji; Zhang, Rui; Qiu, Shuo
2014-01-01
Keyword search on encrypted data allows one to issue the search token and conduct search operations on encrypted data while still preserving keyword privacy. In the present paper, we consider the keyword search problem further and introduce a novel notion called attribute-based proxy re-encryption with keyword search (), which introduces a promising feature: In addition to supporting keyword search on encrypted data, it enables data owners to delegate the keyword search capability to some other data users complying with the specific access control policy. To be specific, allows (i) the data owner to outsource his encrypted data to the cloud and then ask the cloud to conduct keyword search on outsourced encrypted data with the given search token, and (ii) the data owner to delegate other data users keyword search capability in the fine-grained access control manner through allowing the cloud to re-encrypted stored encrypted data with a re-encrypted data (embedding with some form of access control policy). We formalize the syntax and security definitions for , and propose two concrete constructions for : key-policy and ciphertext-policy . In the nutshell, our constructions can be treated as the integration of technologies in the fields of attribute-based cryptography and proxy re-encryption cryptography. PMID:25549257
15. Attribute-based proxy re-encryption with keyword search.
Science.gov (United States)
Shi, Yanfeng; Liu, Jiqiang; Han, Zhen; Zheng, Qingji; Zhang, Rui; Qiu, Shuo
2014-01-01
Keyword search on encrypted data allows one to issue the search token and conduct search operations on encrypted data while still preserving keyword privacy. In the present paper, we consider the keyword search problem further and introduce a novel notion called attribute-based proxy re-encryption with keyword search (ABRKS), which introduces a promising feature: In addition to supporting keyword search on encrypted data, it enables data owners to delegate the keyword search capability to some other data users complying with the specific access control policy. To be specific, ABRKS allows (i) the data owner to outsource his encrypted data to the cloud and then ask the cloud to conduct keyword search on outsourced encrypted data with the given search token, and (ii) the data owner to delegate other data users keyword search capability in the fine-grained access control manner through allowing the cloud to re-encrypted stored encrypted data with a re-encrypted data (embedding with some form of access control policy). We formalize the syntax and security definitions for ABRKS, and propose two concrete constructions for ABRKS: key-policy ABRKS and ciphertext-policy ABRKS. In the nutshell, our constructions can be treated as the integration of technologies in the fields of attribute-based cryptography and proxy re-encryption cryptography.
16. Double random phase spread spectrum spread space technique for secure parallel optical multiplexing with individual encryption key
Science.gov (United States)
Hennelly, B. M.; Javidi, B.; Sheridan, J. T.
2005-09-01
A number of methods have been recently proposed in the literature for the encryption of 2-D information using linear optical systems. In particular the double random phase encoding system has received widespread attention. This system uses two Random Phase Keys (RPK) positioned in the input spatial domain and the spatial frequency domain and if these random phases are described by statistically independent white noises then the encrypted image can be shown to be a white noise. Decryption only requires knowledge of the RPK in the frequency domain. The RPK may be implemented using a Spatial Light Modulators (SLM). In this paper we propose and investigate the use of SLMs for secure optical multiplexing. We show that in this case it is possible to encrypt multiple images in parallel and multiplex them for transmission or storage. The signal energy is effectively spread in the spatial frequency domain. As expected the number of images that can be multiplexed together and recovered without loss is proportional to the ratio of the input image and the SLM resolution. Many more images may be multiplexed with some loss in recovery. Furthermore each individual encryption is more robust than traditional double random phase encoding since decryption requires knowledge of both RPK and a lowpass filter in order to despread the spectrum and decrypt the image. Numerical simulations are presented and discussed.
17. The gray cortex: an early sign of stress fracture
Energy Technology Data Exchange (ETDEWEB)
Mulligan, M.E. [Dept. of Radiology, Univ. of Maryland Medical Center, Baltimore, MD (United States)
1995-04-01
The purpose of this report is to describe an early radiographic sign of stress fracture, the gray cortex. The imaging findings in three patients with tibial stress fractures were reviewed. The gray cortex` sign was evident on the initial conventional radiographs in all three cases. It was prospectively reported as a sign of stress fracture in two patients and was evident on the initial radiographs (taken elsewhere) of the third patient, who was referred for additional workup of a possible neoplasm. Special imaging studies (technetium-99m bone scan, computed tomography, and magnetic resonance imaging) confirmed the diagnosis in all three cases. (orig.)
18. The ''gray cortex'': an early sign of stress fracture
International Nuclear Information System (INIS)
Mulligan, M.E.
1995-01-01
The purpose of this report is to describe an early radiographic sign of stress fracture, the ''gray cortex.'' The imaging findings in three patients with tibial stress fractures were reviewed. The ''gray cortex'' sign was evident on the initial conventional radiographs in all three cases. It was prospectively reported as a sign of stress fracture in two patients and was evident on the initial radiographs (taken elsewhere) of the third patient, who was referred for additional workup of a possible neoplasm. Special imaging studies (technetium-99m bone scan, computed tomography, and magnetic resonance imaging) confirmed the diagnosis in all three cases. (orig.)
19. Encryption in Chaotic Systems with Sinusoidal Excitations
Directory of Open Access Journals (Sweden)
G. Obregón-Pulido
2014-01-01
Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.
20. Efficient Dynamic Searchable Encryption with Forward Privacy
Directory of Open Access Journals (Sweden)
2018-01-01
Full Text Available Searchable symmetric encryption (SSE enables a client to perform searches over its outsourced encrypted files while preserving privacy of the files and queries. Dynamic schemes, where files can be added or removed, leak more information than static schemes. For dynamic schemes, forward privacy requires that a newly added file cannot be linked to previous searches. We present a new dynamic SSE scheme that achieves forward privacy by replacing the keys revealed to the server on each search. Our scheme is efficient and parallelizable and outperforms the best previous schemes providing forward privacy, and achieves competitive performance with dynamic schemes without forward privacy. We provide a full security proof in the random oracle model. In our experiments on the Wikipedia archive of about four million pages, the server takes one second to perform a search with 100,000 results.
1. Tape SCSI monitoring and encryption at CERN
Science.gov (United States)
Laskaridis, Stefanos; Bahyl, V.; Cano, E.; Leduc, J.; Murray, S.; Cancio, G.; Kruse, D.
2017-10-01
CERN currently manages the largest data archive in the HEP domain; over 180PB of custodial data is archived across 7 enterprise tape libraries containing more than 25,000 tapes and using over 100 tape drives. Archival storage at this scale requires a leading edge monitoring infrastructure that acquires live and lifelong metrics from the hardware in order to assess and proactively identify potential drive and media level issues. In addition, protecting the privacy of sensitive archival data is becoming increasingly important and with it the need for a scalable, compute-efficient and cost-effective solution for data encryption. In this paper, we first describe the implementation of acquiring tape medium and drive related metrics reported by the SCSI interface and its integration with our monitoring system. We then address the incorporation of tape drive real-time encryption with dedicated drive hardware into the CASTOR [1] hierarchical mass storage system.
2. Practical quantum computing on encrypted data
OpenAIRE
Marshall, Kevin; Jacobsen, Christian S.; Schafermeier, Clemens; Gehring, Tobias; Weedbrook, Christian; Andersen, Ulrik L.
2016-01-01
The ability to perform computations on encrypted data is a powerful tool for protecting a client's privacy, especially in today's era of cloud and distributed computing. In terms of privacy, the best solutions that classical techniques can achieve are unfortunately not unconditionally secure in the sense that they are dependent on a hacker's computational power. Here we theoretically investigate, and experimentally demonstrate with Gaussian displacement and squeezing operations, a quantum sol...
3. Gray Matter Concentration Abnormality in Brains of Narcolepsy Patients
Energy Technology Data Exchange (ETDEWEB)
Joo, Eun Yeon; Tae, Woo Suk; Kim, Sung Tae; Hong, Seung Bong [Samsung Medical Center, Sungkyunkwan University School of Medicine, Seoul (Korea, Republic of)
2009-12-15
To investigate gray matter concentration changes in the brains of narcoleptic patients. Twenty-nine narcoleptic patient with cataplexy and 29 age and sex-matched normal subjects (mean age, 31 years old) underwent volumetric MRIs. The MRIs were spatially normalized to a standard T1 template and subdivided into gray matter, white matter, and cerebrospinal fluid (CSF). These segmented images were then smoothed using a 12-mm full width at half maximum (FWHM) isotropic Gaussian kernel. An optimized voxel-based morphometry protocol was used to analyze brain tissue concentrations using SPM2 (statistical parametric mapping). A one-way analysis of variance was applied to the concentration analysis of gray matter images. Narcoleptics with cataplexy showed reduced gray matter concentration in bilateral thalami, left gyrus rectus, bilateral frontopolar gyri, bilateral short insular gyri, bilateral superior frontal gyri, and right superior temporal and left inferior temporal gyri compared to normal subjects (uncorrected p < 0.001). Furthermore, small volume correction revealed gray matter concentration reduction in bilateral nuclei accumbens, hypothalami, and thalami (false discovery rate corrected p < 0.05). Gray matter concentration reductions were observed in brain regions related to excessive daytime sleepiness, cognition, attention, and memory in narcoleptics with cataplexy
4. Gray Matter Concentration Abnormality in Brains of Narcolepsy Patients
International Nuclear Information System (INIS)
Joo, Eun Yeon; Tae, Woo Suk; Kim, Sung Tae; Hong, Seung Bong
2009-01-01
To investigate gray matter concentration changes in the brains of narcoleptic patients. Twenty-nine narcoleptic patient with cataplexy and 29 age and sex-matched normal subjects (mean age, 31 years old) underwent volumetric MRIs. The MRIs were spatially normalized to a standard T1 template and subdivided into gray matter, white matter, and cerebrospinal fluid (CSF). These segmented images were then smoothed using a 12-mm full width at half maximum (FWHM) isotropic Gaussian kernel. An optimized voxel-based morphometry protocol was used to analyze brain tissue concentrations using SPM2 (statistical parametric mapping). A one-way analysis of variance was applied to the concentration analysis of gray matter images. Narcoleptics with cataplexy showed reduced gray matter concentration in bilateral thalami, left gyrus rectus, bilateral frontopolar gyri, bilateral short insular gyri, bilateral superior frontal gyri, and right superior temporal and left inferior temporal gyri compared to normal subjects (uncorrected p < 0.001). Furthermore, small volume correction revealed gray matter concentration reduction in bilateral nuclei accumbens, hypothalami, and thalami (false discovery rate corrected p < 0.05). Gray matter concentration reductions were observed in brain regions related to excessive daytime sleepiness, cognition, attention, and memory in narcoleptics with cataplexy
5. A privacy-preserving parallel and homomorphic encryption scheme
Directory of Open Access Journals (Sweden)
Min Zhaoe
2017-04-01
Full Text Available In order to protect data privacy whilst allowing efficient access to data in multi-nodes cloud environments, a parallel homomorphic encryption (PHE scheme is proposed based on the additive homomorphism of the Paillier encryption algorithm. In this paper we propose a PHE algorithm, in which plaintext is divided into several blocks and blocks are encrypted with a parallel mode. Experiment results demonstrate that the encryption algorithm can reach a speed-up ratio at about 7.1 in the MapReduce environment with 16 cores and 4 nodes.
6. Key exchange using biometric identity based encryption for sharing encrypted data in cloud environment
Science.gov (United States)
Hassan, Waleed K.; Al-Assam, Hisham
2017-05-01
The main problem associated with using symmetric/ asymmetric keys is how to securely store and exchange the keys between the parties over open networks particularly in the open environment such as cloud computing. Public Key Infrastructure (PKI) have been providing a practical solution for session key exchange for loads of web services. The key limitation of PKI solution is not only the need for a trusted third partly (e.g. certificate authority) but also the absent link between data owner and the encryption keys. The latter is arguably more important where accessing data needs to be linked with identify of the owner. Currently available key exchange protocols depend on using trusted couriers or secure channels, which can be subject to man-in-the-middle attack and various other attacks. This paper proposes a new protocol for Key Exchange using Biometric Identity Based Encryption (KE-BIBE) that enables parties to securely exchange cryptographic keys even an adversary is monitoring the communication channel between the parties. The proposed protocol combines biometrics with IBE in order to provide a secure way to access symmetric keys based on the identity of the users in unsecure environment. In the KE-BIOBE protocol, the message is first encrypted by the data owner using a traditional symmetric key before migrating it to a cloud storage. The symmetric key is then encrypted using public biometrics of the users selected by data owner to decrypt the message based on Fuzzy Identity-Based Encryption. Only the selected users will be able to decrypt the message by providing a fresh sample of their biometric data. The paper argues that the proposed solution eliminates the needs for a key distribution centre in traditional cryptography. It will also give data owner the power of finegrained sharing of encrypted data by control who can access their data.
7. The Gray whale: Eschrichtius robustus
National Research Council Canada - National Science Library
Jones, Mary Lou; Leatherwood, Stephen; Swartz, Steven L
1984-01-01
.... Section II documents historical aspects of gray whale exploitation and the economic importance of these whales to humans, beginning with aboriginal societies in Asia and North America, and leading...
8. Niobium in gray cast iron
International Nuclear Information System (INIS)
Castello Branco, C.H.; Beckert, E.A.
1984-03-01
The potential for utilization of niobium in gray cast iron is appraised and reviewed. Experiments described in literature indicate that niobium provides structural refinement of the eutectic cells and also promotes pearlite formation. (Author) [pt
9. Additively homomorphic encryption with a double decryption mechanism, revisited
NARCIS (Netherlands)
Peter, Andreas; Kronberg, M.; Trei, W.; Katzenbeisser, S.
We revisit the notion of additively homomorphic encryption with a double decryption mechanism (DD-PKE), which allows for additions in the encrypted domain while having a master decryption procedure that can decrypt all properly formed ciphertexts by using a special master secret. This type of
10. 48 CFR 352.239-71 - Standard for encryption language.
Science.gov (United States)
2010-10-01
... language. 352.239-71 Section 352.239-71 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES... Standard for encryption language. As prescribed in 339.101(d)(2), the Contracting Officer shall insert the following clause: Standard for Encryption Language (January 2010) (a) The Contractor shall use Federal...
11. Efficient reversible data hiding in encrypted H.264/AVC videos
Science.gov (United States)
Xu, Dawen; Wang, Rangding
2014-09-01
Due to the security and privacy-preserving requirements for cloud data management, it is sometimes desired that video content is accessible in an encrypted form. Reversible data hiding in the encrypted domain is an emerging technology, as it can perform data hiding in encrypted videos without decryption, which preserves the confidentiality of the content. Furthermore, the original cover can be losslessly restored after decryption and data extraction. An efficient reversible data hiding scheme for encrypted H.264/AVC videos is proposed. During H.264/AVC encoding, the intraprediction mode, motion vector difference, and the sign bits of the residue coefficients are encrypted using a standard stream cipher. Then, the data-hider who does not know the original video content, may reversibly embed secret data into the encrypted H.264/AVC video by using a modified version of the histogram shifting technique. A scale factor is utilized for selecting the embedding zone, which is scalable for different capacity requirements. With an encrypted video containing hidden data, data extraction can be carried out either in the encrypted or decrypted domain. In addition, real reversibility is realized so that data extraction and video recovery are free of any error. Experimental results demonstrate the feasibility and efficiency of the proposed scheme.
12. Securing Voice over IP Conferencing with Decentralized Group Encryption
Science.gov (United States)
2007-09-04
exchanged using 1024 bit RSA encryption. Moreover, Skype allows encrypted conferences to take place as well. On this basis, Skype has a number of...32] Internet Engineering Task Force (IETF). RFC 768 : “User Datagram Protocol,” Aug 1980. [33] Internet Engineering Task Force (IETF). RFC 791
13. A novel chaotic encryption scheme based on arithmetic coding
International Nuclear Information System (INIS)
Mi Bo; Liao Xiaofeng; Chen Yong
2008-01-01
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
14. A Contents Encryption Mechanism Using Reused Key in IPTV
Science.gov (United States)
Jeong, Yoon-Su; Kim, Yong-Tae; Cho, Young-Bok; Lee, Ki-Jeong; Park, Gil-Cheol; Lee, Sang-Ho
Recently IPTV is being spotlighted as a new stream service to stably provide video, audio and control signals to subscribers through the application of IP protocol. However, the IPTV system is facing more security threats than the traditional TV. This study proposes a multicasting encryption mechanism for secure transmission of the contents of IPTV by which the content provider encrypts their contents and send the encrypted contents and the key used for encryption of the contents to the user. In order to reduce the time and cost of Head-End, the proposed mechanism encrypts the media contents at the Head-End, embeds the code of the IPTV terminal used at the Head-End in the media contents for user tracking, and performs desynchronization for protection of the media contents from various attacks.
15. Discrete-Time Biomedical Signal Encryption
Directory of Open Access Journals (Sweden)
Victor Grigoraş
2017-12-01
Full Text Available Chaotic modulation is a strong method of improving communication security. Analog and discrete chaotic systems are presented in actual literature. Due to the expansion of digital communication, discrete-time systems become more efficient and closer to actual technology. The present contribution offers an in-depth analysis of the effects chaos encryption produce on 1D and 2D biomedical signals. The performed simulations show that modulating signals are precisely recovered by the synchronizing receiver if discrete systems are digitally implemented and the coefficients precisely correspond. Channel noise is also applied and its effects on biomedical signal demodulation are highlighted.
16. Prefrontal gray matter volume mediates genetic risks for obesity.
Science.gov (United States)
Opel, N; Redlich, R; Kaehler, C; Grotegerd, D; Dohm, K; Heindel, W; Kugel, H; Thalamuthu, A; Koutsouleris, N; Arolt, V; Teuber, A; Wersching, H; Baune, B T; Berger, K; Dannlowski, U
2017-05-01
Genetic and neuroimaging research has identified neurobiological correlates of obesity. However, evidence for an integrated model of genetic risk and brain structural alterations in the pathophysiology of obesity is still absent. Here we investigated the relationship between polygenic risk for obesity, gray matter structure and body mass index (BMI) by the use of univariate and multivariate analyses in two large, independent cohorts (n=330 and n=347). Higher BMI and higher polygenic risk for obesity were significantly associated with medial prefrontal gray matter decrease, and prefrontal gray matter was further shown to significantly mediate the effect of polygenic risk for obesity on BMI in both samples. Building on this, the successful individualized prediction of BMI by means of multivariate pattern classification algorithms trained on whole-brain imaging data and external validations in the second cohort points to potential clinical applications of this imaging trait marker.
17. Medial frontal white and gray matter contributions to general intelligence.
Directory of Open Access Journals (Sweden)
Toshiyuki Ohtani
Full Text Available The medial orbitofrontal cortex (mOFC and rostral anterior cingulate cortex (rACC are part of a wider neural network that plays an important role in general intelligence and executive function. We used structural brain imaging to quantify magnetic resonance gray matter volume and diffusion tensor white matter integrity of the mOFC-rACC network in 26 healthy participants who also completed neuropsychological tests of intellectual abilities and executive function. Stochastic tractography, the most effective Diffusion Tensor Imaging method for examining white matter connections between adjacent gray matter regions, was employed to assess the integrity of mOFC-rACC pathways. Fractional anisotropy (FA, which reflects the integrity of white matter connections, was calculated. Results indicated that higher intelligence correlated with greater gray matter volumes for both mOFC and rACC, as well as with increased FA for left posterior mOFC-rACC connectivity. Hierarchical regression analyses revealed that DTI-derived FA of left posterior mOFC-rACC uniquely accounted for 29%-34% of the variance in IQ, in comparison to 11%-16% uniquely explained by gray matter volume of the left rACC. Together, left rACC gray matter volume and white matter connectivity between left posterior mOFC and rACC accounted for up to 50% of the variance in general intelligence. This study is to our knowledge the first to examine white matter connectivity between OFC and ACC, two gray matter regions of interests that are very close in physical proximity, and underscores the important independent contributions of variations in rACC gray matter volume and mOFC-rACC white matter connectivity to individual differences in general intelligence.
18. Optical image security using Stokes polarimetry of spatially variant polarized beam
Science.gov (United States)
Fatima, Areeba; Nishchal, Naveen K.
2018-06-01
We propose a novel security scheme that uses vector beam characterized by the spatially variant polarization distribution. A vector beam is so generated that its helical components carry tailored phases corresponding to the image/images that is/are to be encrypted. The tailoring of phase has been done by employing the modified Gerchberg-Saxton algorithm for phase retrieval. Stokes parameters for the final vector beam is evaluated and is used to construct the ciphertext and one of the keys. The advantage of the proposed scheme is that it generates real ciphertext and keys which are easier to transmit and store than complex quantities. Moreover, the known plaintext attack is not applicable to this system. As a proof-of-concept, simulation results have been presented for securing single and double gray-scale images.
19. Advanced gray rod control assembly
Science.gov (United States)
Drudy, Keith J; Carlson, William R; Conner, Michael E; Goldenfield, Mark; Hone, Michael J; Long, Jr., Carroll J; Parkinson, Jerod; Pomirleanu, Radu O
2013-09-17
An advanced gray rod control assembly (GRCA) for a nuclear reactor. The GRCA provides controlled insertion of gray rod assemblies into the reactor, thereby controlling the rate of power produced by the reactor and providing reactivity control at full power. Each gray rod assembly includes an elongated tubular member, a primary neutron-absorber disposed within the tubular member said neutron-absorber comprising an absorber material, preferably tungsten, having a 2200 m/s neutron absorption microscopic capture cross-section of from 10 to 30 barns. An internal support tube can be positioned between the primary absorber and the tubular member as a secondary absorber to enhance neutron absorption, absorber depletion, assembly weight, and assembly heat transfer characteristics.
20. Grays River Watershed Geomorphic Analysis
Energy Technology Data Exchange (ETDEWEB)
Geist, David R
2005-04-30
This investigation, completed for the Pacific Northwest National Laboratory (PNNL), is part of the Grays River Watershed and Biological Assessment commissioned by Bonneville Power Administration under project number 2003-013-00 to assess impacts on salmon habitat in the upper Grays River watershed and present recommendations for habitat improvement. This report presents the findings of the geomorphic assessment and is intended to support the overall PNNL project by evaluating the following: The effects of historical and current land use practices on erosion and sedimentation within the channel network The ways in which these effects have influenced the sediment budget of the upper watershed The resulting responses in the main stem Grays River upstream of State Highway 4 The past and future implications for salmon habitat.
1. Structural imaging of the brain reveals decreased total brain and total gray matter volumes in obese but not in lean women with polycystic ovary syndrome compared to body mass index-matched counterparts.
Science.gov (United States)
Ozgen Saydam, Basak; Has, Arzu Ceylan; Bozdag, Gurkan; Oguz, Kader Karli; Yildiz, Bulent Okan
2017-07-01
To detect differences in global brain volumes and identify relations between brain volume and appetite-related hormones in women with polycystic ovary syndrome (PCOS) compared to body mass index-matched controls. Forty subjects participated in this study. Cranial magnetic resonance imaging and measurements of fasting ghrelin, leptin and glucagon-like peptide 1 (GLP-1), as well as GLP-1 levels during mixed-meal tolerance test (MTT), were performed. Total brain volume and total gray matter volume (GMV) were decreased in obese PCOS compared to obese controls (p lean PCOS and controls did not show a significant difference. Secondary analyses of regional brain volumes showed decreases in GMV of the caudate nucleus, ventral diencephalon and hippocampus in obese PCOS compared to obese controls (p lean patients with PCOS had lower GMV in the amygdala than lean controls (p PCOS, suggests volumetric reductions in global brain areas in obese women with PCOS. Functional studies with larger sample size are needed to determine physiopathological roles of these changes and potential effects of long-term medical management on brain structure of PCOS.
2. Chaotic Image Scrambling Algorithm Based on S-DES
International Nuclear Information System (INIS)
Yu, X Y; Zhang, J; Ren, H E; Xu, G S; Luo, X Y
2006-01-01
With the security requirement improvement of the image on the network, some typical image encryption methods can't meet the demands of encryption, such as Arnold cat map and Hilbert transformation. S-DES system can encrypt the input binary flow of image, but the fixed system structure and few keys will still bring some risks. However, the sensitivity of initial value that Logistic chaotic map can be well applied to the system of S-DES, which makes S-DES have larger random and key quantities. A dual image encryption algorithm based on S-DES and Logistic map is proposed. Through Matlab simulation experiments, the key quantities will attain 10 17 and the encryption speed of one image doesn't exceed one second. Compared to traditional methods, it has some merits such as easy to understand, rapid encryption speed, large keys and sensitivity to initial value
3. Symmetric weak ternary quantum homomorphic encryption schemes
Science.gov (United States)
Wang, Yuqi; She, Kun; Luo, Qingbin; Yang, Fan; Zhao, Chao
2016-03-01
Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general 3 × 3 unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled X (GCX(m,n)) gate was constructed and further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.
4. Hybrid Obfuscation Using Signals and Encryption
Directory of Open Access Journals (Sweden)
2018-01-01
Full Text Available Obfuscation of software and data is one of the subcategories of software security. Hence, the outlines of the obfuscation problem and its various methods have been studied in this article. This paper proposes a hybrid of two signals and encryption obfuscation to hide the behaviour program and prevent reconstruction of the normal code by hackers. The usual signal method is strong enough for obfuscation, but its problem is the high complexity because of a lot of call and return instructions. In this study, a new dispatcher was added to the source code to reconstruct the original control flow graph from the hidden one to solve the problem of the signal method. This dispatcher code is encrypted to preclude access by the hacker. In this paper, the potency that makes the obfuscation strong has been increased and the resilience that makes the obfuscation poor has been decreased. The results of a comparison of the similarity among the ambiguous data with its original code and with available efficient methods present a performance advantage of the proposed hybrid obfuscation algorithm.
5. PDES, Fips Standard Data Encryption Algorithm
Energy Technology Data Exchange (ETDEWEB)
Nessett, D N [Lawrence Livermore National Laboratory (United States)
1991-03-26
Description of program or function: PDES performs the National Bureau of Standards FIPS Pub. 46 data encryption/decryption algorithm used for the cryptographic protection of computer data. The DES algorithm is designed to encipher and decipher blocks of data consisting of 64 bits under control of a 64-bit key. The key is generated in such a way that each of the 56 bits used directly by the algorithm are random and the remaining 8 error-detecting bits are set to make the parity of each 8-bit byte of the key odd, i. e. there is an odd number of '1' bits in each 8-bit byte. Each member of a group of authorized users of encrypted computer data must have the key that was used to encipher the data in order to use it. Data can be recovered from cipher only by using exactly the same key used to encipher it, but with the schedule of addressing the key bits altered so that the deciphering process is the reverse of the enciphering process. A block of data to be enciphered is subjected to an initial permutation, then to a complex key-dependent computation, and finally to a permutation which is the inverse of the initial permutation. Two PDES routines are included; both perform the same calculation. One, identified as FDES.MAR, is designed to achieve speed in execution, while the other identified as PDES.MAR, presents a clearer view of how the algorithm is executed
6. PDES, Fips Standard Data Encryption Algorithm
International Nuclear Information System (INIS)
Nessett, D.N.
1991-01-01
Description of program or function: PDES performs the National Bureau of Standards FIPS Pub. 46 data encryption/decryption algorithm used for the cryptographic protection of computer data. The DES algorithm is designed to encipher and decipher blocks of data consisting of 64 bits under control of a 64-bit key. The key is generated in such a way that each of the 56 bits used directly by the algorithm are random and the remaining 8 error-detecting bits are set to make the parity of each 8-bit byte of the key odd, i. e. there is an odd number of '1' bits in each 8-bit byte. Each member of a group of authorized users of encrypted computer data must have the key that was used to encipher the data in order to use it. Data can be recovered from cipher only by using exactly the same key used to encipher it, but with the schedule of addressing the key bits altered so that the deciphering process is the reverse of the enciphering process. A block of data to be enciphered is subjected to an initial permutation, then to a complex key-dependent computation, and finally to a permutation which is the inverse of the initial permutation. Two PDES routines are included; both perform the same calculation. One, identified as FDES.MAR, is designed to achieve speed in execution, while the other identified as PDES.MAR, presents a clearer view of how the algorithm is executed
7. Wireless Networks Speed Depending on the Encryption using Windows 8.1 x64 Operating System
Directory of Open Access Journals (Sweden)
Tamás Krausz
2014-12-01
Full Text Available We can use variety of encryption standards to encrypt data traffic to ensure the safety of wireless networks. The question is to what extent the security of the network affects network performance. For answering this question, experiments were performed without data encryption, and the use of various encryption standards.
8. Storage and Retrieval of Encrypted Data Blocks with In-Line Message Authentication Codes
NARCIS (Netherlands)
Bosch, H.G.P.; McLellan Jr, Hubert Rae; Mullender, Sape J.
2007-01-01
Techniques are disclosed for in-line storage of message authentication codes with respective encrypted data blocks. In one aspect, a given data block is encrypted and a message authentication code is generated for the encrypted data block. A target address is determined for storage of the encrypted
9. Mapping Gray Matter Development: Implications for Typical Development and Vulnerability to Psychopathology
Science.gov (United States)
Gogtay, Nitin; Thompson, Paul M.
2010-01-01
Recent studies with brain magnetic resonance imaging (MRI) have scanned large numbers of children and adolescents repeatedly over time, as their brains develop, tracking volumetric changes in gray and white matter in remarkable detail. Focusing on gray matter changes specifically, here we explain how earlier studies using lobar volumes of specific…
10. Regional Gray Matter Volume Deficits in Adolescents with First-Episode Psychosis
Science.gov (United States)
Janssen, Joost; Parellada, Mara; Moreno, Dolores; Graell, Montserrat; Fraguas, David; Zabala, Arantzazu; Vazquez, Veronica Garcia; Desco, Manuel; Arango, Celso
2008-01-01
The regional gray matter volumes of adolescents with first-episode psychosis are compared with those of a control group. Magnetic resonance imaging was conducted on 70 patients with early onset FEP and on 51 individuals without FEP. Findings revealed that volume deficits in the left medial frontal gray matter were common in individuals with…
11. Computed gray levels in multislice and cone-beam computed tomography.
Science.gov (United States)
Azeredo, Fabiane; de Menezes, Luciane Macedo; Enciso, Reyes; Weissheimer, Andre; de Oliveira, Rogério Belle
2013-07-01
Gray level is the range of shades of gray in the pixels, representing the x-ray attenuation coefficient that allows for tissue density assessments in computed tomography (CT). An in-vitro study was performed to investigate the relationship between computed gray levels in 3 cone-beam CT (CBCT) scanners and 1 multislice spiral CT device using 5 software programs. Six materials (air, water, wax, acrylic, plaster, and gutta-percha) were scanned with the CBCT and CT scanners, and the computed gray levels for each material at predetermined points were measured with OsiriX Medical Imaging software (Geneva, Switzerland), OnDemand3D (CyberMed International, Seoul, Korea), E-Film (Merge Healthcare, Milwaukee, Wis), Dolphin Imaging (Dolphin Imaging & Management Solutions, Chatsworth, Calif), and InVivo Dental Software (Anatomage, San Jose, Calif). The repeatability of these measurements was calculated with intraclass correlation coefficients, and the gray levels were averaged to represent each material. Repeated analysis of variance tests were used to assess the differences in gray levels among scanners and materials. There were no differences in mean gray levels with the different software programs. There were significant differences in gray levels between scanners for each material evaluated (P <0.001). The software programs were reliable and had no influence on the CT and CBCT gray level measurements. However, the gray levels might have discrepancies when different CT and CBCT scanners are used. Therefore, caution is essential when interpreting or evaluating CBCT images because of the significant differences in gray levels between different CBCT scanners, and between CBCT and CT values. Copyright © 2013 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.
12. Altered Gray Matter Volume and Resting-State Connectivity in Individuals With Internet Gaming Disorder: A Voxel-Based Morphometry and Resting-State Functional Magnetic Resonance Imaging Study
Science.gov (United States)
Seok, Ji-Woo; Sohn, Jin-Hun
2018-01-01
Neuroimaging studies on the characteristics of individuals with Internet gaming disorder (IGD) have been accumulating due to growing concerns regarding the psychological and social problems associated with Internet use. However, relatively little is known about the brain characteristics underlying IGD, such as the associated functional connectivity and structure. The aim of this study was to investigate alterations in gray matter (GM) volume and functional connectivity during resting state in individuals with IGD using voxel-based morphometry and a resting-state connectivity analysis. The participants included 20 individuals with IGD and 20 age- and sex-matched healthy controls. Resting-state functional and structural images were acquired for all participants using 3 T magnetic resonance imaging. We also measured the severity of IGD and impulsivity using psychological scales. The results show that IGD severity was positively correlated with GM volume in the left caudate (p < 0.05, corrected for multiple comparisons), and negatively associated with functional connectivity between the left caudate and the right middle frontal gyrus (p < 0.05, corrected for multiple comparisons). This study demonstrates that IGD is associated with neuroanatomical changes in the right middle frontal cortex and the left caudate. These are important brain regions for reward and cognitive control processes, and structural and functional abnormalities in these regions have been reported for other addictions, such as substance abuse and pathological gambling. The findings suggest that structural deficits and resting-state functional impairments in the frontostriatal network may be associated with IGD and provide new insights into the underlying neural mechanisms of IGD. PMID:29636704
13. Altered Gray Matter Volume and Resting-State Connectivity in Individuals With Internet Gaming Disorder: A Voxel-Based Morphometry and Resting-State Functional Magnetic Resonance Imaging Study
Directory of Open Access Journals (Sweden)
Ji-Woo Seok
2018-03-01
Full Text Available Neuroimaging studies on the characteristics of individuals with Internet gaming disorder (IGD have been accumulating due to growing concerns regarding the psychological and social problems associated with Internet use. However, relatively little is known about the brain characteristics underlying IGD, such as the associated functional connectivity and structure. The aim of this study was to investigate alterations in gray matter (GM volume and functional connectivity during resting state in individuals with IGD using voxel-based morphometry and a resting-state connectivity analysis. The participants included 20 individuals with IGD and 20 age- and sex-matched healthy controls. Resting-state functional and structural images were acquired for all participants using 3 T magnetic resonance imaging. We also measured the severity of IGD and impulsivity using psychological scales. The results show that IGD severity was positively correlated with GM volume in the left caudate (p < 0.05, corrected for multiple comparisons, and negatively associated with functional connectivity between the left caudate and the right middle frontal gyrus (p < 0.05, corrected for multiple comparisons. This study demonstrates that IGD is associated with neuroanatomical changes in the right middle frontal cortex and the left caudate. These are important brain regions for reward and cognitive control processes, and structural and functional abnormalities in these regions have been reported for other addictions, such as substance abuse and pathological gambling. The findings suggest that structural deficits and resting-state functional impairments in the frontostriatal network may be associated with IGD and provide new insights into the underlying neural mechanisms of IGD.
14. An Efficient Quantum Somewhat Homomorphic Symmetric Searchable Encryption
Science.gov (United States)
Sun, Xiaoqiang; Wang, Ting; Sun, Zhiwei; Wang, Ping; Yu, Jianping; Xie, Weixin
2017-04-01
In 2009, Gentry first introduced an ideal lattices fully homomorphic encryption (FHE) scheme. Later, based on the approximate greatest common divisor problem, learning with errors problem or learning with errors over rings problem, FHE has developed rapidly, along with the low efficiency and computational security. Combined with quantum mechanics, Liang proposed a symmetric quantum somewhat homomorphic encryption (QSHE) scheme based on quantum one-time pad, which is unconditional security. And it was converted to a quantum fully homomorphic encryption scheme, whose evaluation algorithm is based on the secret key. Compared with Liang's QSHE scheme, we propose a more efficient QSHE scheme for classical input states with perfect security, which is used to encrypt the classical message, and the secret key is not required in the evaluation algorithm. Furthermore, an efficient symmetric searchable encryption (SSE) scheme is constructed based on our QSHE scheme. SSE is important in the cloud storage, which allows users to offload search queries to the untrusted cloud. Then the cloud is responsible for returning encrypted files that match search queries (also encrypted), which protects users' privacy.
15. The Picture of Dorian Gray
NARCIS (Netherlands)
Wilde, Oscar
2005-01-01
On its first publication The Picture of Dorian Gray was regarded as dangerously modern in its depiction of fin-de-sicle decadence. In this updated version of the Faust story, the tempter is Lord Henry Wotton, who lives selfishly for amoral pleasure; Dorian's good angel is the portrait painter Basil
16. Paulette Gray, Ph.D.
Science.gov (United States)
Paulette S. Gray, Ph.D. is the Director for the Division of Extramural Activities (DEA). As the director of the division, she is responsible for the overall scientific, fiscal, and administrative management of the division, including broad strategic planning, development, implementation, and evaluation.
17. Tsenseerimata Dorian Gray? / Udo Uibo
Index Scriptorium Estoniae
Uibo, Udo, 1956-
2011-01-01
Harvardi ülikooli kirjastus üllitas 2011. a. kevadel Oscar Wilde'i ainsaks jäänud romaani "Dorian Gray portree" esialgse versiooni, mis on varustatud toimetaja Nicholas Frankeli põhjalike kommentaaridega ja kus eessõna manifesteerib jõuliselt autori esteetilisi vaateid
18. A Review Of Encryption Algorithms-RSA And Diffie-Hellman
Directory of Open Access Journals (Sweden)
Nilesh A. Lal
2017-07-01
Full Text Available Network security is protecting data and message from cybercrime. Cryptography system is designed freely to communicate over a computer network. It is a process where sender sends encrypted message to the recipient. Symmetric encryption is known as the single key encryption. RSA algorithm is a symmetric key encryption.it uses public key and private key. Diffie Hellman cryptography is where both parties exchange secrets keys to encrypt message.
19. Simple Multi-Authority Attribute-Based Encryption for Short Messages
OpenAIRE
Viktoria I. Villanyi
2016-01-01
Central authority free multi-authority attribute based encryption scheme for short messages will be presented. Several multi-authority attribute based encryption schemes were recently proposed. We can divide these schemes into two groups, one of them are the ciphertext-policy attribute based encryption schemes (CP-ABE), the another one are the key-policy attribute based encryption schemes (KP-ABE). In our new multi-authority attribute based encryption scheme we combine them: the access struct...
20. Longitudinal Study of Gray Matter Changes in Parkinson Disease.
Science.gov (United States)
Jia, X; Liang, P; Li, Y; Shi, L; Wang, D; Li, K
2015-12-01
The pathology of Parkinson disease leads to morphological brain volume changes. So far, the progressive gray matter volume change across time specific to patients with Parkinson disease compared controls remains unclear. Our aim was to investigate the pattern of gray matter changes in patients with Parkinson disease and to explore the progressive gray matter volume change specific to patients with Parkinson disease with disease progression by using voxel-based morphometry analysis. Longitudinal cognitive assessment and structural MR imaging of 89 patients with Parkinson disease (62 men) and 55 healthy controls (33 men) were from the Parkinson's Progression Markers Initiative data base, including the initial baseline and 12-month follow-up data. Two-way analysis of covariance was performed with covariates of age, sex, years of education, imaging data from multiple centers, and total intracranial volume by using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra tool from SPM8 software. Gray matter volume changes for patients with Parkinson disease were detected with decreased gray matter volume in the frontotemporoparietal areas and the bilateral caudate, with increased gray matter volume in the bilateral limbic/paralimbic areas, medial globus pallidus/putamen, and the right occipital cortex compared with healthy controls. Progressive gray matter volume decrease in the bilateral caudate was found for both patients with Parkinson disease and healthy controls, and this caudate volume was positively associated with cognitive ability for both groups. The progressive gray matter volume increase specific to the patients with Parkinson disease was identified close to the left ventral lateral nucleus of thalamus, and a positive relationship was found between the thalamic volume and the tremor scores in a subgroup with tremor-dominant patients with Parkinson disease. The observed progressive changes in gray matter volume in Parkinson disease may provide
1. Complementary Metal-Oxide-Silicon (CMOS)-Memristor Hybrid Nanoelectronics for Advanced Encryption Standard (AES) Encryption
Science.gov (United States)
2016-04-01
were built in-house at the SUNY Poly-technic Institute’s Center for Semiconductor Research ( CSR ); however, the initial devices for materials screening...A code that models the sweep-mode behavior of the bipolar ReRAM device that is initially in HRS. ............................................ 15...Standard (AES). AES is one of the most important encryption systems and is widely used in military and commercial systems. Based on an iterative
2. Multiple Lookup Table-Based AES Encryption Algorithm Implementation
Science.gov (United States)
Gong, Jin; Liu, Wenyi; Zhang, Huixin
Anew AES (Advanced Encryption Standard) encryption algorithm implementation was proposed in this paper. It is based on five lookup tables, which are generated from S-box(the substitution table in AES). The obvious advantages are reducing the code-size, improving the implementation efficiency, and helping new learners to understand the AES encryption algorithm and GF(28) multiplication which are necessary to correctly implement AES[1]. This method can be applied on processors with word length 32 or above, FPGA and others. And correspondingly we can implement it by VHDL, Verilog, VB and other languages.
3. System for processing an encrypted instruction stream in hardware
Science.gov (United States)
Griswold, Richard L.; Nickless, William K.; Conrad, Ryan C.
2016-04-12
A system and method of processing an encrypted instruction stream in hardware is disclosed. Main memory stores the encrypted instruction stream and unencrypted data. A central processing unit (CPU) is operatively coupled to the main memory. A decryptor is operatively coupled to the main memory and located within the CPU. The decryptor decrypts the encrypted instruction stream upon receipt of an instruction fetch signal from a CPU core. Unencrypted data is passed through to the CPU core without decryption upon receipt of a data fetch signal.
4. Message Encryption in Robot Operating System: Collateral Effects of Hardening Mobile Robots
Directory of Open Access Journals (Sweden)
Francisco J. Rodríguez-Lera
2018-03-01
Full Text Available In human–robot interaction situations, robot sensors collect huge amounts of data from the environment in order to characterize the situation. Some of the gathered data ought to be treated as private, such as medical data (i.e., medication guidelines, personal, and safety information (i.e., images of children, home habits, alarm codes, etc.. However, most robotic software development frameworks are not designed for securely managing this information. This paper analyzes the scenario of hardening one of the most widely used robotic middlewares, Robot Operating System (ROS. The study investigates a robot’s performance when ciphering the messages interchanged between ROS nodes under the publish/subscribe paradigm. In particular, this research focuses on the nodes that manage cameras and LIDAR sensors, which are two of the most extended sensing solutions in mobile robotics, and analyzes the collateral effects on the robot’s achievement under different computing capabilities and encryption algorithms (3DES, AES, and Blowfish to robot performance. The findings present empirical evidence that simple encryption algorithms are lightweight enough to provide cyber-security even in low-powered robots when carefully designed and implemented. Nevertheless, these techniques come with a number of serious drawbacks regarding robot autonomy and performance if they are applied randomly. To avoid these issues, we define a taxonomy that links the type of ROS message, computational units, and the encryption methods. As a result, we present a model to select the optimal options for hardening a mobile robot using ROS.
5. Evaluation of Subependymal Gray Matter Heterotopias on Fetal MRI.
Science.gov (United States)
Nagaraj, U D; Peiro, J L; Bierbrauer, K S; Kline-Fath, B M
2016-04-01
Subependymal grey matter heterotopias are seen in a high proportion of children with Chiari II malformation and are potentially clinically relevant. However, despite its growing use, there is little in the literature describing its detection on fetal MRI. Our aim was to evaluate the accuracy in diagnosing subependymal gray matter heterotopias in fetuses with spinal dysraphism on fetal MR imaging. This study is a retrospective analysis of 203 fetal MRIs performed at a single institution for spinal dysraphism during a 10-year period. Corresponding obstetric sonography, postnatal imaging, and clinical/operative reports were reviewed. Of the fetal MRIs reviewed, 95 fetuses were included in our analysis; 23.2% (22/95) were suspected of having subependymal gray matter heterotopias on fetal MR imaging prospectively. However, only 50% (11/22) of these cases were confirmed on postnatal brain MR imaging. On postnatal brain MR imaging, 28.4% (27/95) demonstrated imaging findings consistent with subependymal gray matter heterotopia. Only 40.7% (11/27) of these cases were prospectively diagnosed on fetal MR imaging. Fetal MR imaging is limited in its ability to identify subependymal gray matter heterotopias in fetuses with spinal dysraphism. It is believed that this limitation relates to a combination of factors, including artifacts from fetal motion, the very small size of fetal neuroanatomy, differences in imaging techniques, and, possibly, irregularity related to denudation of the ependyma/subependyma in the presence of spinal dysraphism and/or stretching of the germinal matrix in ventriculomegaly. © 2016 by American Journal of Neuroradiology.
International Nuclear Information System (INIS)
Wong, R.L.
1991-01-01
Description of program or function: CNVUFAC, the General Dynamics heat-transfer radiation view program, was adapted for use on the LLNL computer system. The input and output were modified, and a node incrementing logic added for compatibility with TRUMP (NESC 771) thermal analyzer and related codes. The program performs the multiple integration necessary to evaluate the geometric black-body radiation node to node view factors. CNVUFAC uses an elemental area summation scheme to evaluate the multiple integrals. The program permits shadowing and self-shadowing. The basic configuration shapes that can be considered are cylinders, cones, spheres, ellipsoids, flat plates, disks, toroids, and polynomials of revolution. Portions of these shapes can also be considered. Card-image output containing node number and view factor information is generated for input to GRAY, a related code. GRAY performs the matrix manipulations necessary to convert black-body radiation heat-transfer view factors to gray-body view factors as required by thermal analyzer codes. The black-body view factors contain only geometric relationships. GRAY allows the effects of multiple gray-body reflections to be included. The resulting effective gray-body view factors can then be used with the corresponding fourth-power temperature differences to obtain the net radiative heat flux. GRAY accepts a matrix input or the card-image output generated by CNVUFAC. The resulting card-image GRAY output is in a form usable by TRUMP
7. A Layered Searchable Encryption Scheme with Functional Components Independent of Encryption Methods
Science.gov (United States)
Luo, Guangchun; Qin, Ke
2014-01-01
Searchable encryption technique enables the users to securely store and search their documents over the remote semitrusted server, which is especially suitable for protecting sensitive data in the cloud. However, various settings (based on symmetric or asymmetric encryption) and functionalities (ranked keyword query, range query, phrase query, etc.) are often realized by different methods with different searchable structures that are generally not compatible with each other, which limits the scope of application and hinders the functional extensions. We prove that asymmetric searchable structure could be converted to symmetric structure, and functions could be modeled separately apart from the core searchable structure. Based on this observation, we propose a layered searchable encryption (LSE) scheme, which provides compatibility, flexibility, and security for various settings and functionalities. In this scheme, the outputs of the core searchable component based on either symmetric or asymmetric setting are converted to some uniform mappings, which are then transmitted to loosely coupled functional components to further filter the results. In such a way, all functional components could directly support both symmetric and asymmetric settings. Based on LSE, we propose two representative and novel constructions for ranked keyword query (previously only available in symmetric scheme) and range query (previously only available in asymmetric scheme). PMID:24719565
8. Efficient KDM-CCA Secure Public-Key Encryption via Auxiliary-Input Authenticated Encryption
Directory of Open Access Journals (Sweden)
Shuai Han
2017-01-01
Full Text Available KDM[F]-CCA security of public-key encryption (PKE ensures the privacy of key-dependent messages f(sk which are closely related to the secret key sk, where f∈F, even if the adversary is allowed to make decryption queries. In this paper, we study the design of KDM-CCA secure PKE. To this end, we develop a new primitive named Auxiliary-Input Authenticated Encryption (AIAE. For AIAE, we introduce two related-key attack (RKA security notions, including IND-RKA and weak-INT-RKA. We present a generic construction of AIAE from tag-based hash proof system (HPS and one-time secure authenticated encryption (AE and give an instantiation of AIAE under the Decisional Diffie-Hellman (DDH assumption. Using AIAE as an essential building block, we give two constructions of efficient KDM-CCA secure PKE based on the DDH and the Decisional Composite Residuosity (DCR assumptions. Specifically, (i our first PKE construction is the first one achieving KDM[Faff]-CCA security for the set of affine functions and compactness of ciphertexts simultaneously. (ii Our second PKE construction is the first one achieving KDM[Fpolyd]-CCA security for the set of polynomial functions and almost compactness of ciphertexts simultaneously. Our PKE constructions are very efficient; in particular, they are pairing-free and NIZK-free.
9. Anonymity-Preserving Public-Key Encryption
DEFF Research Database (Denmark)
Kohlweiss, Markulf; Maurer, Ueli; Onete, Cristina
2013-01-01
security properties have been proposed. We investigate constructions as well as limitations for preserving receiver anonymity when using public-key encryption (PKE). We use the constructive cryptography approach by Maurer and Renner and interpret cryptographic schemes as constructions of a certain ideal...... literature (IND-CCA, key-privacy, weak robustness). We also show that a desirable stronger variant, preventing the adversary from selective ”trial-deliveries” of messages, is unfortunately unachievable by any PKE scheme, no matter how strong. The constructive approach makes the guarantees achieved...... by applying a cryptographic scheme explicit in the constructed (ideal) resource; this specifies the exact requirements for the applicability of a cryptographic scheme in a given context. It also allows to decide which of the existing security properties of such a cryptographic scheme are adequate...
10. Optical encryption using pseudorandom complex spatial modulation.
Science.gov (United States)
2012-12-01
In this paper we propose a new (to our knowledge) complex spatial modulation method to encode data pages applicable in double random phase encryption (DRPE) to make the system more resistant to brute-force attack. The proposed modulation method uses data page pixels with random phase and amplitude values with the condition that the intensity of the interference of light from two adjacent pixels should correspond to the encoded information. A differential phase contrast technique is applied to recover the data page at the output of the system. We show that the proposed modulation method can enhance the robustness of the DRPE technique using point spread function analysis. Key space expansion is determined by numeric model calculations.
11. Evaluating the Performance of Rijndael Encryption
Directory of Open Access Journals (Sweden)
Bogdan CIOBANU
2012-01-01
Full Text Available In this paper we present a a comparative analysis of the performance of the Rijndael algorithm, developed with the help of two programming languages, namely C and Matlab. The main goal is to get a full, detailed picture about the functioning of this algorithm. In order to evaluate the performances of the Rijndael algorithm for the two different implementations, we took into account establishing the variable factors within each type of implementation so as to avoid the reasons that might lead to running differences (for instance, the comparison of the two implementations will be performed for the situation in which the encryption key length is the same. We chose to use the traditional algorithm for both types of implementation, in which the input is transformed into 4 blocks of 4 bytes, followed by the handling of each byte from each individual column
12. A Novel Method for Generating Encryption Keys
Directory of Open Access Journals (Sweden)
Dascalescu Ana Cristina
2009-12-01
Full Text Available The development of the informational society, which has led to an impressive growth of the information volume circulating in the computer networks, has accelerated the evolution and especially the use of modern cryptography instruments. Today, the commercial products use standard cryptographic libraries that implement certified and tested cryptographic algorithms. Instead, the fragility ofencryption algorithms is given by compositional operations like key handling or key generation. In this sense, the article proposes an innovative method to generate pseudorandom numbers which can be used for the construction of secure stream encryption keys. The proposed method is based on the mathematical complements based on the algebra of the finite fields and uses a particularized structure of the linear feedback shift registers.
13. Novel optical scanning cryptography using Fresnel telescope imaging.
Science.gov (United States)
Yan, Aimin; Sun, Jianfeng; Hu, Zhijuan; Zhang, Jingtao; Liu, Liren
2015-07-13
We propose a new method called modified optical scanning cryptography using Fresnel telescope imaging technique for encryption and decryption of remote objects. An image or object can be optically encrypted on the fly by Fresnel telescope scanning system together with an encryption key. For image decryption, the encrypted signals are received and processed with an optical coherent heterodyne detection system. The proposed method has strong performance through use of secure Fresnel telescope scanning with orthogonal polarized beams and efficient all-optical information processing. The validity of the proposed method is demonstrated by numerical simulations and experimental results.
14. Evaluation of Four Encryption Algorithms for Viability, Reliability and ...
African Journals Online (AJOL)
Akorede
power utilization of each of these algorithms. KEYWORDS: ... business, military, power, health and so on. .... During data transmission, the sender encrypts the plain text with the ..... Schemes in Wireless Devices Unpublished Thesis, university.
15. Key Generation for Fast Inversion of the Paillier Encryption Function
Science.gov (United States)
Hirano, Takato; Tanaka, Keisuke
We study fast inversion of the Paillier encryption function. Especially, we focus only on key generation, and do not modify the Paillier encryption function. We propose three key generation algorithms based on the speeding-up techniques for the RSA encryption function. By using our algorithms, the size of the private CRT exponent is half of that of Paillier-CRT. The first algorithm employs the extended Euclidean algorithm. The second algorithm employs factoring algorithms, and can construct the private CRT exponent with low Hamming weight. The third algorithm is a variant of the second one, and has some advantage such as compression of the private CRT exponent and no requirement for factoring algorithms. We also propose the settings of the parameters for these algorithms and analyze the security of the Paillier encryption function by these algorithms against known attacks. Finally, we give experimental results of our algorithms.
16. Video encryption using chaotic masks in joint transform correlator
Science.gov (United States)
Saini, Nirmala; Sinha, Aloka
2015-03-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.
17. Video encryption using chaotic masks in joint transform correlator
International Nuclear Information System (INIS)
Saini, Nirmala; Sinha, Aloka
2015-01-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest–Shamir–Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique. (paper)
18. Hardware Realization of Chaos-based Symmetric Video Encryption
KAUST Repository
2013-05-01
This thesis reports original work on hardware realization of symmetric video encryption using chaos-based continuous systems as pseudo-random number generators. The thesis also presents some of the serious degradations caused by digitally implementing chaotic systems. Subsequently, some techniques to eliminate such defects, including the ultimately adopted scheme are listed and explained in detail. Moreover, the thesis describes original work on the design of an encryption system to encrypt MPEG-2 video streams. Information about the MPEG-2 standard that fits this design context is presented. Then, the security of the proposed system is exhaustively analyzed and the performance is compared with other reported systems, showing superiority in performance and security. The thesis focuses more on the hardware and the circuit aspect of the system’s design. The system is realized on Xilinx Vetrix-4 FPGA with hardware parameters and throughput performance surpassing conventional encryption systems.
19. Cryptanalysis of a discrete-time synchronous chaotic encryption system
International Nuclear Information System (INIS)
Arroyo, David; Alvarez, Gonzalo; Li Shujun; Li Chengqing; Nunez, Juana
2008-01-01
Recently a chaotic cryptosystem based on discrete-time synchronization has been proposed. Some weaknesses of that new encryption system are addressed and exploited in order to successfully cryptanalyze the system
20. Hardware Realization of Chaos-based Symmetric Video Encryption
KAUST Repository
2013-01-01
This thesis reports original work on hardware realization of symmetric video encryption using chaos-based continuous systems as pseudo-random number generators. The thesis also presents some of the serious degradations caused by digitally
1. UMPHE: A Library for Effective Computing On Encrypted Data
Directory of Open Access Journals (Sweden)
Philipp Borisovich Burtyka
2016-03-01
Full Text Available The paper describes the design and implementation of a new software library that implements fully homomorphic encryption schemes based on unilateral matrix polynomials. The library is written in C++ using the NTL mathematical library and has multilayer structure. The main focus is on optimizations and batching techniques. The paper presents novel encryption and key generation algorithms for matrix polynomial based cryptosystems and techniques for data movement between the slots of the ciphertext.
2. Gray Code for Cayley Permutations
Directory of Open Access Journals (Sweden)
J.-L. Baril
2003-10-01
Full Text Available A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p . In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list differ at most in two positions.
3. Dynamic video encryption algorithm for H.264/AVC based on a spatiotemporal chaos system.
Science.gov (United States)
Xu, Hui; Tong, Xiao-Jun; Zhang, Miao; Wang, Zhu; Li, Ling-Hao
2016-06-01
Video encryption schemes mostly employ the selective encryption method to encrypt parts of important and sensitive video information, aiming to ensure the real-time performance and encryption efficiency. The classic block cipher is not applicable to video encryption due to the high computational overhead. In this paper, we propose the encryption selection control module to encrypt video syntax elements dynamically which is controlled by the chaotic pseudorandom sequence. A novel spatiotemporal chaos system and binarization method is used to generate a key stream for encrypting the chosen syntax elements. The proposed scheme enhances the resistance against attacks through the dynamic encryption process and high-security stream cipher. Experimental results show that the proposed method exhibits high security and high efficiency with little effect on the compression ratio and time cost.
4. Batch Attribute-Based Encryption for Secure Clouds
Directory of Open Access Journals (Sweden)
Chen Yang
2015-10-01
Full Text Available Cloud storage is widely used by organizations due to its advantage of allowing universal access with low cost. Attribute-based encryption (ABE is a kind of public key encryption suitable for cloud storage. The secret key of each user and the ciphertext are associated with an access policy and an attribute set, respectively; in addition to holding a secret key, one can decrypt a ciphertext only if the associated attributes match the predetermined access policy, which allows one to enforce fine-grained access control on outsourced files. One issue in existing ABE schemes is that they are designed for the users of a single organization. When one wants to share the data with the users of different organizations, the owner needs to encrypt the messages to the receivers of one organization and then repeats this process for another organization. This situation is deteriorated with more and more mobile devices using cloud services, as the ABE encryption process is time consuming and may exhaust the power supplies of the mobile devices quickly. In this paper, we propose a batch attribute-based encryption (BABE approach to address this problem in a provably-secure way. With our approach, the data owner can outsource data in batches to the users of different organizations simultaneously. The data owner is allowed to decide the receiving organizations and the attributes required for decryption. Theoretical and experimental analyses show that our approach is more efficient than traditional encryption implementations in computation and communication.
5. Parallel Algorithm for Wireless Data Compression and Encryption
Directory of Open Access Journals (Sweden)
Qin Jiancheng
2017-01-01
Full Text Available As the wireless network has limited bandwidth and insecure shared media, the data compression and encryption are very useful for the broadcasting transportation of big data in IoT (Internet of Things. However, the traditional techniques of compression and encryption are neither competent nor efficient. In order to solve this problem, this paper presents a combined parallel algorithm named “CZ algorithm” which can compress and encrypt the big data efficiently. CZ algorithm uses a parallel pipeline, mixes the coding of compression and encryption, and supports the data window up to 1 TB (or larger. Moreover, CZ algorithm can encrypt the big data as a chaotic cryptosystem which will not decrease the compression speed. Meanwhile, a shareware named “ComZip” is developed based on CZ algorithm. The experiment results show that ComZip in 64 b system can get better compression ratio than WinRAR and 7-zip, and it can be faster than 7-zip in the big data compression. In addition, ComZip encrypts the big data without extra consumption of computing resources.
6. A Fingerprint Encryption Scheme Based on Irreversible Function and Secure Authentication
Directory of Open Access Journals (Sweden)
Yijun Yang
2015-01-01
Full Text Available A fingerprint encryption scheme based on irreversible function has been designed in this paper. Since the fingerprint template includes almost the entire information of users’ fingerprints, the personal authentication can be determined only by the fingerprint features. This paper proposes an irreversible transforming function (using the improved SHA1 algorithm to transform the original minutiae which are extracted from the thinned fingerprint image. Then, Chinese remainder theorem is used to obtain the biokey from the integration of the transformed minutiae and the private key. The result shows that the scheme has better performance on security and efficiency comparing with other irreversible function schemes.
7. Correlation between white matter damage and gray matter lesions in multiple sclerosis patients
Directory of Open Access Journals (Sweden)
Xue-mei Han
2017-01-01
Full Text Available We observed the characteristics of white matter fibers and gray matter in multiple sclerosis patients, to identify changes in diffusion tensor imaging fractional anisotropy values following white matter fiber injury. We analyzed the correlation between fractional anisotropy values and changes in whole-brain gray matter volume. The participants included 20 patients with relapsing-remitting multiple sclerosis and 20 healthy volunteers as controls. All subjects underwent head magnetic resonance imaging and diffusion tensor imaging. Our results revealed that fractional anisotropy values decreased and gray matter volumes were reduced in the genu and splenium of corpus callosum, left anterior thalamic radiation, hippocampus, uncinate fasciculus, right corticospinal tract, bilateral cingulate gyri, and inferior longitudinal fasciculus in multiple sclerosis patients. Gray matter volumes were significantly different between the two groups in the right frontal lobe (superior frontal, middle frontal, precentral, and orbital gyri, right parietal lobe (postcentral and inferior parietal gyri, right temporal lobe (caudate nucleus, right occipital lobe (middle occipital gyrus, right insula, right parahippocampal gyrus, and left cingulate gyrus. The voxel sizes of atrophic gray matter positively correlated with fractional anisotropy values in white matter association fibers in the patient group. These findings suggest that white matter fiber bundles are extensively injured in multiple sclerosis patients. The main areas of gray matter atrophy in multiple sclerosis are the frontal lobe, parietal lobe, caudate nucleus, parahippocampal gyrus, and cingulate gyrus. Gray matter atrophy is strongly associated with white matter injury in multiple sclerosis patients, particularly with injury to association fibers.
8. Digital color image encoding and decoding using a novel chaotic random generator
International Nuclear Information System (INIS)
Nien, H.H.; Huang, C.K.; Changchien, S.K.; Shieh, H.W.; Chen, C.T.; Tuan, Y.Y.
2007-01-01
This paper proposes a novel chaotic system, in which variables are treated as encryption keys in order to achieve secure transmission of digital color images. Since the dynamic response of chaotic system is highly sensitive to the initial values of a system and to the variation of a parameter, and chaotic trajectory is so unpredictable, we use elements of variables as encryption keys and apply these to computer internet communication of digital color images. As a result, we obtain much higher communication security. We adopt one statistic method involving correlation coefficient γ and FIPS PUB 140-1 to test on the distribution of distinguished elements of variables for continuous-time chaotic system, and accordingly select optimal encryption keys to use in secure communication of digital color images. At the transmitter end, we conduct RGB level decomposition on digital color images, and encrypt them with chaotic keys, and finally transmit them through computer internet. The same encryption keys are used to decrypt and recover the original images at the receiver end. Even if the encrypted images are stolen in the public channel, an intruder is not able to decrypt and recover the original images because of the lack of adequate encryption keys. Empirical example shows that the chaotic system and encryption keys applied in the encryption, transmission, decryption, and recovery of digital color images can achieve higher communication security and best recovered images
9. Analyzing and improving a chaotic encryption method
International Nuclear Information System (INIS)
Wu Xiaogang; Hu Hanping; Zhang Baoliang
2004-01-01
To resist the return map attack [Phys. Rev. Lett. 74 (1995) 1970] presented by Perez and Cerdeira, Shouliang Bu and Bing-Hong Wang proposed a simple method to improve the security of the chaotic encryption by modulating the chaotic carrier with an appropriately chosen scalar signal in [Chaos, Solitons and Fractals 19 (2004) 919]. They maintained that this modulating strategy not only preserved all appropriate information required for synchronizing chaotic systems but also destroyed the possibility of the phase space reconstruction of the sender dynamics such as a return map. However, a critical defect does exist in this scheme. This paper gives a zero-point autocorrelation method, which can recover the parameters of the scalar signal from the modulated signal. Consequently, the messages will be extracted from the demodulated chaotic carrier by using return map. Based on such a fact, an improved scheme is presented to obtain higher security, and the numerical simulation indicates the improvement of the synchronizing performance as well
10. Universal Intelligent Data Encryption Standards: A Review
Directory of Open Access Journals (Sweden)
Renjith V Ravi
2014-06-01
Full Text Available -The most challenging aspects in the word of electronic communication is nothing but the data security. The significance of the exchanged data over the internet and other media types are increasing. One of the most interesting subjects in the security related communities is the hunt for the best solution to offer an essential protection against the data intruders’ attacks together with providing these services in time. Cryptography is the one of the main category of data security which converts information from its original form into an unreadable form. There are two main uniqueness to distinguish an encryption system from another are its ability to secure the protected data against cryptanalytic attacks and its speed and efficiency in the process.Cryptographic research has a common objective to design protocols that offer a confidential and authenticated transmission channel for messages over an insecure network. If a cryptographic algorithm is said to be computationally secured, it cannot be broken with typical resources, either present or future and apart from the algorithm, key distribution is also more important to make an proficient cryptographic system.
11. Robustness against attacks of dual polarization encryption using the Stokes–Mueller formalism
International Nuclear Information System (INIS)
Dubreuil, Matthieu; Alfalou, Ayman; Brosseau, Christian
2012-01-01
The security of our recently proposed dual polarization encryption scheme of images is evaluated by numerical simulations. This consists of testing the resistance of the scheme against brute force, known-plaintext, chosen-plaintext and video sequence attacks. While some attacks are ineffective (brute force, video sequence) others are effective (known-plaintext, chosen-plaintext), but only under certain assumptions. An optimization of the setup, which is based on a regular rotation of polarization optics angles (polarizers, wave plates), is proposed associating the use of a high dynamic range for the key image, or the use of a phase-only spatial light modulator in the target and in the key image channel. The possibility of the attacker decrypting an unknown image is thus strongly reduced. The precision required for optical specifications is also evaluated, in order to ensure a good decryption for an authorized user. (paper)
12. Robustness against attacks of dual polarization encryption using the Stokes-Mueller formalism
Science.gov (United States)
Dubreuil, Matthieu; Alfalou, Ayman; Brosseau, Christian
2012-09-01
The security of our recently proposed dual polarization encryption scheme of images is evaluated by numerical simulations. This consists of testing the resistance of the scheme against brute force, known-plaintext, chosen-plaintext and video sequence attacks. While some attacks are ineffective (brute force, video sequence) others are effective (known-plaintext, chosen-plaintext), but only under certain assumptions. An optimization of the setup, which is based on a regular rotation of polarization optics angles (polarizers, wave plates), is proposed associating the use of a high dynamic range for the key image, or the use of a phase-only spatial light modulator in the target and in the key image channel. The possibility of the attacker decrypting an unknown image is thus strongly reduced. The precision required for optical specifications is also evaluated, in order to ensure a good decryption for an authorized user.
13. Correlation among body height, intelligence, and brain gray matter volume in healthy children.
Science.gov (United States)
Taki, Yasuyuki; Hashizume, Hiroshi; Sassa, Yuko; Takeuchi, Hikaru; Asano, Michiko; Asano, Kohei; Kotozaki, Yuka; Nouchi, Rui; Wu, Kai; Fukuda, Hiroshi; Kawashima, Ryuta
2012-01-16
A significant positive correlation between height and intelligence has been demonstrated in children. Additionally, intelligence has been associated with the volume of gray matter in the brains of children. Based on these correlations, we analyzed the correlation among height, full-scale intelligence quotient (IQ) and gray matter volume applying voxel-based morphometry using data from the brain magnetic resonance images of 160 healthy children aged 5-18 years of age. As a result, body height was significantly positively correlated with brain gray matter volume. Additionally, the regional gray matter volume of several regions such as the bilateral prefrontal cortices, temporoparietal region, and cerebellum was significantly positively correlated with body height and that the gray matter volume of several of these regions was also significantly positively correlated with full-scale intelligence quotient (IQ) scores after adjusting for age, sex, and socioeconomic status. Our results demonstrate that gray and white matter volume may mediate the correlation between body height and intelligence in healthy children. Additionally, the correlations among gray and white matter volume, height, and intelligence may be at least partially explained by the effect of insulin-like growth factor-1 and growth hormones. Given the importance of the effect of environmental factors, especially nutrition, on height, IQ, and gray matter volume, the present results stress the importance of nutrition during childhood for the healthy maturation of body and brain. Copyright © 2011 Elsevier Inc. All rights reserved.
14. Differential regional gray matter volumes in patients with on-line game addiction and professional gamers
Science.gov (United States)
Han, Doug Hyun; Lyoo, In Kyoon; Renshaw, Perry F.
2015-01-01
Patients with on-line game addiction (POGA) and professional video game players play video games for extended periods of time, but experience very different consequences for their on-line game play. Brain regions consisting of anterior cingulate, thalamus and occpito-temporal areas may increase the likelihood of becoming a pro-gamer or POGA. Twenty POGA, seventeen pro-gamers, and eighteen healthy comparison subjects (HC) were recruited. All magnetic resonance imaging (MRI) was performed on a 1.5 Tesla Espree MRI scanner (SIEMENS, Erlangen, Germany). Voxel-wise comparisons of gray matter volume were performed between the groups using the two-sample t-test with statistical parametric mapping (SPM5). Compared to HC, the POGA group showed increased impulsiveness and perseverative errors, and volume in left thalamus gray matter, but decreased gray matter volume in both inferior temporal gyri, right middle occipital gyrus, and left inferior occipital gyrus, compared with HC. Pro-gamers showed increased gray matter volume in left cingulate gyrus, but decreased gray matter volume in left middle occipital gyrus and right inferior temporal gyrus compared with HC. Additionally, the pro-gamer group showed increased gray matter volume in left cingulate gyrus and decreased left thalamus gray matter volume compared with the POGA group. The current study suggests that increased gray matter volumes of the left cingulate gyrus in pro-gamers and of the left thalamus in POGA may contribute to the different clinical characteristics of pro-gamers and POGA. PMID:22277302
15. Comparable Encryption Scheme over Encrypted Cloud Data in Internet of Everything
Directory of Open Access Journals (Sweden)
Qian Meng
2017-01-01
Full Text Available User authentication has been widely deployed to prevent unauthorized access in the new era of Internet of Everything (IOE. When user passes the legal authentication, he/she can do series of operations in database. We mainly concern issues of data security and comparable queries over ciphertexts in IOE. In traditional database, a Short Comparable Encryption (SCE scheme has been widely used by authorized users to conduct comparable queries over ciphertexts, but existing SCE schemes still incur high storage and computational overhead as well as economic burden. In this paper, we first propose a basic Short Comparable Encryption scheme based on sliding window method (SCESW, which can significantly reduce computational and storage burden as well as enhance work efficiency. Unfortunately, as the cloud service provider is a semitrusted third party, public auditing mechanism needs to be furnished to protect data integrity. To further protect data integrity and reduce management overhead, we present an enhanced SCESW scheme based on position-aware Merkle tree, namely, PT-SCESW. Security analysis proves that PT-SCESW and SCESW schemes can guarantee completeness and weak indistinguishability in standard model. Performance evaluation indicates that PT-SCESW scheme is efficient and feasible in practical applications, especially for smarter and smaller computing devices in IOE.
16. 75 FR 36481 - Encryption Export Controls: Revision of License Exception ENC and Mass Market Eligibility...
Science.gov (United States)
2010-06-25
.... Upon effectiveness of this rule, BIS will send encryption SNAP-R submissions to the ENC Encryption... fire alarm, HVAC); automotive, aviation, and other transportation systems; LCD TV, Blu-ray/DVD, video...
17. 77 FR 67290 - Basic Service Tier Encryption Compatibility Between Cable Systems and Consumer Electronics Equipment
Science.gov (United States)
2012-11-09
...-126] Basic Service Tier Encryption Compatibility Between Cable Systems and Consumer Electronics... between consumer electronics equipment (such as digital television sets) and newly encrypted cable service... Act''), Congress sought to make sure that consumer electronics equipment could receive cable...
18. Searchable Data Vault: Encrypted Queries in Secure Distributed Cloud Storage
Directory of Open Access Journals (Sweden)
Geong Sen Poh
2017-05-01
Full Text Available Cloud storage services allow users to efficiently outsource their documents anytime and anywhere. Such convenience, however, leads to privacy concerns. While storage providers may not read users’ documents, attackers may possibly gain access by exploiting vulnerabilities in the storage system. Documents may also be leaked by curious administrators. A simple solution is for the user to encrypt all documents before submitting them. This method, however, makes it impossible to efficiently search for documents as they are all encrypted. To resolve this problem, we propose a multi-server searchable symmetric encryption (SSE scheme and construct a system called the searchable data vault (SDV. A unique feature of the scheme is that it allows an encrypted document to be divided into blocks and distributed to different storage servers so that no single storage provider has a complete document. By incorporating the scheme, the SDV protects the privacy of documents while allowing for efficient private queries. It utilizes a web interface and a controller that manages user credentials, query indexes and submission of encrypted documents to cloud storage services. It is also the first system that enables a user to simultaneously outsource and privately query documents from a few cloud storage services. Our preliminary performance evaluation shows that this feature introduces acceptable computation overheads when compared to submitting documents directly to a cloud storage service.
19. Clinical and Morphological Aspects of Gray Matter Heterotopia Type Developmental Malformations
International Nuclear Information System (INIS)
Zając-Mnich, Monika; Kostkiewicz, Agnieszka; Guz, Wiesław; Dziurzyńska-Białek, Ewa; Solińska, Anna; Stopa, Joanna; Kucharska-Miąsik, Iwona
2014-01-01
Gray matter heterotopia (GMH) is a malformation of the central nervous system characterized by interruption of normal neuroblasts migration between the 7 th and 16 th week of fetal development. The aim of the study was the analysis of clinical symptoms, prevalence rate and the most common concurrent central nervous system (CNS) developmental disorders as well as assessment of characteristic morphological changes of gray matter heterotopia in children hospitalized in our institution between the year 2001 and 2012. We performed a retrospective analysis of patients’ data who were hospitalized in our institution between the year 2001 and 2012. We assessed clinical data and imaging exams in children diagnosed with gray matter heterotopia confirmed in MRI (magnetic resonance imaging). GMH occurred in 26 children hospitalized in our institution between the year 2001 and 2012. Among children with gray matter heterotopia most common clinical symptoms were: epilepsy, intellectual disability and hemiparesis. The commonest location of heterotopic gray matter were fronto-parietal areas of brain parenchyma, mostly subependymal region. Gray matter heterotopia occurred with other developmental disorders of the central nervous system rather than solely and in most cases it was bilateral. Schizencephaly and abnormalities of the corpus callosum were the most often developmental disorders accompanying GMH. 1. Subependymal gray matter heterotopia was more common than subcortical GMH. Subependymal GMH showed tendency to localize in the region of the bodies of the lateral ventricles. The least common was laminar GMH. 2. Gray matter heterotopia occurred more often with other developmental disorders of the central nervous system rather than solely. The most frequent concurrent disorders of the central nervous system were: schizencephaly, developmental abnormalities of the corpus callosum, arachnoid cyst, abnormalities of the septum pellucidum and the fornix. 3. GMH foci were more often
20. New Encryption Scheme of One-Time Pad Based on KDC
Science.gov (United States)
Xie, Xin; Chen, Honglei; Wu, Ying; Zhang, Heng; Wu, Peng
As more and more leakage incidents come up, traditional encryption system has not adapted to the complex and volatile network environment, so, there should be a new encryption system that can protect information security very well, this is the starting point of this paper. Based on DES and RSA encryption system, this paper proposes a new scheme of one time pad, which really achieves "One-time pad" and provides information security a new and more reliable encryption method. | {"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": 0.5189328193664551, "perplexity": 2821.1257085017482}, "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-2018-39/segments/1537267162385.84/warc/CC-MAIN-20180925202648-20180925223048-00166.warc.gz"} |
https://checkit.clontz.org/banks/tbil-la/V9/ | V9 - Homogeneous systems
Example 1 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} & & & & x_{3} & & &+& x_{5} &=& 0 \\-x_{1} &-& 5 \, x_{2} &+& 5 \, x_{3} &+& 2 \, x_{4} &+& 7 \, x_{5} &=& 0 \\x_{1} &+& 5 \, x_{2} &-& x_{3} &-& 2 \, x_{4} &-& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & -5 & 5 & 2 & 7 & 0 \\ 1 & 5 & -1 & -2 & -3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 5 & 0 & -2 & -2 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -5 \, a + 2 \, b + 2 \, c \\ a \\ -c \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -5 \\ 1 \\ 0 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ 0 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ 0 \\ -1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 2 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} 3 \, x_{1} &+& 7 \, x_{2} &-& 9 \, x_{3} &+& 7 \, x_{4} &=& 0 \\4 \, x_{1} &+& 9 \, x_{2} &-& 10 \, x_{3} &+& 6 \, x_{4} &=& 0 \\-2 \, x_{1} &-& 5 \, x_{2} &+& 7 \, x_{3} &-& 6 \, x_{4} &=& 0 \\-x_{1} & & &+& x_{3} &-& 3 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 3 & 7 & -9 & 7 & 0 \\ 4 & 9 & -10 & 6 & 0 \\ -2 & -5 & 7 & -6 & 0 \\ -1 & 0 & 1 & -3 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & -2 & 0 \\ 0 & 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ 2 \, a \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 2 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 3 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &+& x_{2} &-& 2 \, x_{3} &+& 7 \, x_{4} &=& 0 \\x_{1} &-& x_{2} &-& 5 \, x_{3} &+& 9 \, x_{4} &=& 0 \\ &-& 3 \, x_{2} &-& 5 \, x_{3} &+& 4 \, x_{4} &=& 0 \\ & & 2 \, x_{2} &-& x_{3} &+& 6 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & 1 & -2 & 7 & 0 \\ 1 & -1 & -5 & 9 & 0 \\ 0 & -3 & -5 & 4 & 0 \\ 0 & 2 & -1 & 6 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 2 & 0 \\ 0 & 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ -2 \, a \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ -2 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 4 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 4 \, x_{1} &-& 6 \, x_{2} &-& 6 \, x_{3} &=& 0 \\4 \, x_{1} &-& 11 \, x_{2} &-& x_{3} &=& 0 \\ & & 4 \, x_{2} &-& 4 \, x_{3} &=& 0 \\x_{1} &-& x_{2} &-& 2 \, x_{3} &=& 0 \\-5 \, x_{1} &+& 12 \, x_{2} &+& 3 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 4 & -6 & -6 & 0 \\ 4 & -11 & -1 & 0 \\ 0 & 4 & -4 & 0 \\ 1 & -1 & -2 & 0 \\ -5 & 12 & 3 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -3 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 3 \, a \\ a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 3 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 5 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &-& 5 \, x_{2} &+& 6 \, x_{3} &=& 0 \\x_{1} & & &+& x_{3} &=& 0 \\4 \, x_{1} &+& x_{2} &+& 3 \, x_{3} &=& 0 \\-5 \, x_{1} &+& 4 \, x_{2} &-& 9 \, x_{3} &=& 0 \\ & & 2 \, x_{2} &-& 2 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & -5 & 6 & 0 \\ 1 & 0 & 1 & 0 \\ 4 & 1 & 3 & 0 \\ -5 & 4 & -9 & 0 \\ 0 & 2 & -2 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 6 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} & & x_{2} & & &-& 2 \, x_{4} &+& 2 \, x_{5} &=& 0 \\-x_{1} &-& x_{2} &+& 3 \, x_{3} &+& 9 \, x_{4} &+& 7 \, x_{5} &=& 0 \\ & & & & x_{3} &+& 2 \, x_{4} &+& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 0 & 1 & 0 & -2 & 2 & 0 \\ -1 & -1 & 3 & 9 & 7 & 0 \\ 0 & 0 & 1 & 2 & 3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & -1 & 0 & 0 \\ 0 & 1 & 0 & -2 & 2 & 0 \\ 0 & 0 & 1 & 2 & 3 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} a \\ 2 \, a - 2 \, b \\ -2 \, a - 3 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 1 \\ 2 \\ -2 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 0 \\ -2 \\ -3 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 7 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &-& 2 \, x_{2} &-& 7 \, x_{3} &+& x_{4} &=& 0 \\-x_{1} &-& x_{2} &+& x_{3} &+& 5 \, x_{4} &=& 0 \\ & & 2 \, x_{2} &+& 4 \, x_{3} &-& 4 \, x_{4} &=& 0 \\2 \, x_{1} &+& 2 \, x_{2} &-& 2 \, x_{3} &-& 10 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & -2 & -7 & 1 & 0 \\ -1 & -1 & 1 & 5 & 0 \\ 0 & 2 & 4 & -4 & 0 \\ 2 & 2 & -2 & -10 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & -3 & -3 & 0 \\ 0 & 1 & 2 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 3 \, a + 3 \, b \\ -2 \, a + 2 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 3 \\ -2 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 3 \\ 2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 8 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &-& x_{2} &+& 6 \, x_{3} &+& 6 \, x_{4} &=& 0 \\-x_{1} &-& 2 \, x_{2} &+& 7 \, x_{3} &+& 4 \, x_{4} &=& 0 \\ & & 2 \, x_{2} &-& 9 \, x_{3} &-& 7 \, x_{4} &=& 0 \\-x_{1} &-& x_{2} &+& 3 \, x_{3} &+& x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & -1 & 6 & 6 & 0 \\ -1 & -2 & 7 & 4 & 0 \\ 0 & 2 & -9 & -7 & 0 \\ -1 & -1 & 3 & 1 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ -a \\ -a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ -1 \\ -1 \\ 1 \end{array}\right] \right\}$$.
Example 9 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} 3 \, x_{1} &-& 2 \, x_{2} &-& 3 \, x_{3} &+& 3 \, x_{4} &+& 8 \, x_{5} &=& 0 \\-2 \, x_{1} &-& 3 \, x_{2} &+& 2 \, x_{3} &+& 11 \, x_{4} &-& x_{5} &=& 0 \\-x_{1} &+& 2 \, x_{2} &+& x_{3} &-& 5 \, x_{4} &-& 4 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 3 & -2 & -3 & 3 & 8 & 0 \\ -2 & -3 & 2 & 11 & -1 & 0 \\ -1 & 2 & 1 & -5 & -4 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & -1 & -1 & 2 & 0 \\ 0 & 1 & 0 & -3 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} a + b - 2 \, c \\ 3 \, b + c \\ a \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 1 \\ 0 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 3 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -2 \\ 1 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 10 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 2 \, x_{1} &+& 3 \, x_{2} &-& 6 \, x_{3} &=& 0 \\-x_{1} &-& 3 \, x_{2} &+& 6 \, x_{3} &=& 0 \\-2 \, x_{1} &-& 6 \, x_{2} &+& 12 \, x_{3} &=& 0 \\-x_{1} &+& x_{2} &-& 2 \, x_{3} &=& 0 \\-x_{1} &-& x_{2} &+& 2 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 2 & 3 & -6 & 0 \\ -1 & -3 & 6 & 0 \\ -2 & -6 & 12 & 0 \\ -1 & 1 & -2 & 0 \\ -1 & -1 & 2 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 11 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &+& 4 \, x_{2} &-& 5 \, x_{3} &+& 5 \, x_{4} &-& 6 \, x_{5} &=& 0 \\ & & & & & & x_{4} &-& x_{5} &=& 0 \\x_{1} &+& 4 \, x_{2} &-& 5 \, x_{3} &-& x_{4} & & &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 4 & -5 & 5 & -6 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 \\ 1 & 4 & -5 & -1 & 0 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 4 & -5 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -4 \, a + 5 \, b + c \\ a \\ b \\ c \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -4 \\ 1 \\ 0 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 5 \\ 0 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 0 \\ 0 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 12 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} 7 \, x_{1} &+& 5 \, x_{2} &-& 5 \, x_{3} &-& 7 \, x_{4} &-& 3 \, x_{5} &=& 0 \\-3 \, x_{1} &-& 2 \, x_{2} &+& 2 \, x_{3} &+& 3 \, x_{4} &+& x_{5} &=& 0 \\-3 \, x_{1} &-& 5 \, x_{2} &+& 6 \, x_{3} & & &+& 10 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 7 & 5 & -5 & -7 & -3 & 0 \\ -3 & -2 & 2 & 3 & 1 & 0 \\ -3 & -5 & 6 & 0 & 10 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & -1 & 1 & 0 \\ 0 & 1 & 0 & -3 & 1 & 0 \\ 0 & 0 & 1 & -3 & 3 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} a - b \\ 3 \, a - b \\ 3 \, a - 3 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 1 \\ 3 \\ 3 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ -1 \\ -3 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 13 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} & & &-& 3 \, x_{3} &-& 8 \, x_{4} &+& 4 \, x_{5} &=& 0 \\-x_{1} &+& x_{2} &+& 3 \, x_{3} &+& 6 \, x_{4} &-& 3 \, x_{5} &=& 0 \\ &-& x_{2} &+& x_{3} &+& 4 \, x_{4} &-& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 0 & -3 & -8 & 4 & 0 \\ -1 & 1 & 3 & 6 & -3 & 0 \\ 0 & -1 & 1 & 4 & -3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & -2 & -2 & 0 \\ 0 & 1 & 0 & -2 & 1 & 0 \\ 0 & 0 & 1 & 2 & -2 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a + 2 \, b \\ 2 \, a - b \\ -2 \, a + 2 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ 2 \\ -2 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ -1 \\ 2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 14 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} -2 \, x_{1} &-& 5 \, x_{2} & & &=& 0 \\ & & x_{2} & & &=& 0 \\ & & 3 \, x_{2} & & &=& 0 \\-x_{1} &+& 8 \, x_{2} & & &=& 0 \\x_{1} & & & & &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} -2 & -5 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ -1 & 8 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 0 \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 15 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &+& 3 \, x_{2} &+& 4 \, x_{3} &=& 0 \\-2 \, x_{1} &-& 7 \, x_{2} &-& 9 \, x_{3} &=& 0 \\2 \, x_{1} &+& 7 \, x_{2} &+& 9 \, x_{3} &=& 0 \\ &-& x_{2} &-& x_{3} &=& 0 \\ & & x_{2} &+& x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & 3 & 4 & 0 \\ -2 & -7 & -9 & 0 \\ 2 & 7 & 9 & 0 \\ 0 & -1 & -1 & 0 \\ 0 & 1 & 1 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ -a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ -1 \\ 1 \end{array}\right] \right\}$$.
Example 16 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} -x_{1} &-& 5 \, x_{2} &-& 3 \, x_{3} &-& 10 \, x_{4} &+& 8 \, x_{5} &=& 0 \\x_{1} &+& 5 \, x_{2} &+& 2 \, x_{3} &+& 7 \, x_{4} &-& 6 \, x_{5} &=& 0 \\2 \, x_{1} &+& 10 \, x_{2} &-& 2 \, x_{3} &-& 4 \, x_{4} & & &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} -1 & -5 & -3 & -10 & 8 & 0 \\ 1 & 5 & 2 & 7 & -6 & 0 \\ 2 & 10 & -2 & -4 & 0 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 5 & 0 & 1 & -2 & 0 \\ 0 & 0 & 1 & 3 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -5 \, a - b + 2 \, c \\ a \\ -3 \, b + 2 \, c \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -5 \\ 1 \\ 0 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ 0 \\ -3 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ 0 \\ 2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 17 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} & & & & x_{3} &-& x_{4} &=& 0 \\-x_{1} &-& 2 \, x_{2} &+& 6 \, x_{3} &-& 3 \, x_{4} &=& 0 \\-3 \, x_{1} &-& 6 \, x_{2} &+& 10 \, x_{3} &-& x_{4} &=& 0 \\-2 \, x_{1} &-& 4 \, x_{2} &+& 12 \, x_{3} &-& 6 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 0 & 0 & 1 & -1 & 0 \\ -1 & -2 & 6 & -3 & 0 \\ -3 & -6 & 10 & -1 & 0 \\ -2 & -4 & 12 & -6 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 2 & 0 & -3 & 0 \\ 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -2 \, a + 3 \, b \\ a \\ b \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -2 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 3 \\ 0 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 18 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} -x_{1} &-& 4 \, x_{2} &-& 7 \, x_{3} &-& 6 \, x_{4} &=& 0 \\x_{1} &+& 4 \, x_{2} &+& 6 \, x_{3} &+& 5 \, x_{4} &=& 0 \\-2 \, x_{1} &-& 8 \, x_{2} &-& 12 \, x_{3} &-& 10 \, x_{4} &=& 0 \\3 \, x_{1} &+& 12 \, x_{2} &+& 10 \, x_{3} &+& 7 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} -1 & -4 & -7 & -6 & 0 \\ 1 & 4 & 6 & 5 & 0 \\ -2 & -8 & -12 & -10 & 0 \\ 3 & 12 & 10 & 7 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 4 & 0 & -1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -4 \, a + b \\ a \\ -b \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -4 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 0 \\ -1 \\ 1 \end{array}\right] \right\}$$.
Example 19 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} & & &+& 2 \, x_{3} &+& 2 \, x_{4} &=& 0 \\ & & x_{2} &+& 2 \, x_{3} &-& x_{4} &=& 0 \\ & & 5 \, x_{2} &+& 10 \, x_{3} &-& 5 \, x_{4} &=& 0 \\x_{1} &-& 7 \, x_{2} &-& 12 \, x_{3} &+& 9 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & 0 & 2 & 2 & 0 \\ 0 & 1 & 2 & -1 & 0 \\ 0 & 5 & 10 & -5 & 0 \\ 1 & -7 & -12 & 9 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 2 & 2 & 0 \\ 0 & 1 & 2 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -2 \, a - 2 \, b \\ -2 \, a + b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -2 \\ -2 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -2 \\ 1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 20 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &+& x_{2} &+& 2 \, x_{3} &+& x_{4} &-& x_{5} &=& 0 \\-x_{1} &-& 3 \, x_{2} &-& 4 \, x_{3} &-& 7 \, x_{4} &-& x_{5} &=& 0 \\ & & x_{2} &+& x_{3} &+& 3 \, x_{4} &+& x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 1 & 2 & 1 & -1 & 0 \\ -1 & -3 & -4 & -7 & -1 & 0 \\ 0 & 1 & 1 & 3 & 1 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 1 & -2 & -2 & 0 \\ 0 & 1 & 1 & 3 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a + 2 \, b + 2 \, c \\ -a - 3 \, b - c \\ a \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ -1 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ -3 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ -1 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 21 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &-& 3 \, x_{2} &-& 11 \, x_{3} &=& 0 \\x_{1} &-& 2 \, x_{2} &-& 8 \, x_{3} &=& 0 \\ &-& 4 \, x_{2} &-& 12 \, x_{3} &=& 0 \\ &-& 2 \, x_{2} &-& 6 \, x_{3} &=& 0 \\ &-& 3 \, x_{2} &-& 9 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & -3 & -11 & 0 \\ 1 & -2 & -8 & 0 \\ 0 & -4 & -12 & 0 \\ 0 & -2 & -6 & 0 \\ 0 & -3 & -9 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -2 & 0 \\ 0 & 1 & 3 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a \\ -3 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ -3 \\ 1 \end{array}\right] \right\}$$.
Example 22 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 2 \, x_{1} &+& 2 \, x_{2} & & &=& 0 \\-4 \, x_{1} &-& 11 \, x_{2} & & &=& 0 \\-4 \, x_{1} &-& 9 \, x_{2} & & &=& 0 \\ & & 4 \, x_{2} & & &=& 0 \\-x_{1} &+& x_{2} & & &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 2 & 2 & 0 & 0 \\ -4 & -11 & 0 & 0 \\ -4 & -9 & 0 & 0 \\ 0 & 4 & 0 & 0 \\ -1 & 1 & 0 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 0 \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 23 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &-& x_{2} &+& 2 \, x_{3} &=& 0 \\-2 \, x_{1} &+& 3 \, x_{2} &-& 5 \, x_{3} &=& 0 \\ &-& 2 \, x_{2} &+& 2 \, x_{3} &=& 0 \\5 \, x_{1} &-& 6 \, x_{2} &+& 11 \, x_{3} &=& 0 \\3 \, x_{1} &-& 7 \, x_{2} &+& 10 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & -1 & 2 & 0 \\ -2 & 3 & -5 & 0 \\ 0 & -2 & 2 & 0 \\ 5 & -6 & 11 & 0 \\ 3 & -7 & 10 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 24 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &-& 5 \, x_{2} &+& 10 \, x_{3} &=& 0 \\ & & x_{2} &-& 2 \, x_{3} &=& 0 \\ & & x_{2} &-& 2 \, x_{3} &=& 0 \\ & & x_{2} &-& 2 \, x_{3} &=& 0 \\x_{1} &-& 6 \, x_{2} &+& 12 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & -5 & 10 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 1 & -6 & 12 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 25 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &-& x_{2} &+& 5 \, x_{3} &-& 8 \, x_{4} &=& 0 \\2 \, x_{1} &-& x_{2} &+& 5 \, x_{3} &-& 8 \, x_{4} &=& 0 \\ &-& x_{2} &+& 6 \, x_{3} &-& 10 \, x_{4} &=& 0 \\ & & 2 \, x_{2} &-& 7 \, x_{3} &+& 10 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & -1 & 5 & -8 & 0 \\ 2 & -1 & 5 & -8 & 0 \\ 0 & -1 & 6 & -10 & 0 \\ 0 & 2 & -7 & 10 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & -2 & 0 \\ 0 & 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \, a \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 2 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 26 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 4 \, x_{1} &-& 7 \, x_{2} &+& 11 \, x_{3} &=& 0 \\x_{1} &-& 3 \, x_{2} &+& 4 \, x_{3} &=& 0 \\ & & 4 \, x_{2} &-& 4 \, x_{3} &=& 0 \\-x_{1} &-& x_{2} & & &=& 0 \\-x_{1} &+& x_{2} &-& 2 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 4 & -7 & 11 & 0 \\ 1 & -3 & 4 & 0 \\ 0 & 4 & -4 & 0 \\ -1 & -1 & 0 & 0 \\ -1 & 1 & -2 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 27 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} -2 \, x_{1} &+& 6 \, x_{2} &+& 7 \, x_{3} &=& 0 \\3 \, x_{1} &-& 9 \, x_{2} &-& 11 \, x_{3} &=& 0 \\-2 \, x_{1} &+& 6 \, x_{2} &+& 3 \, x_{3} &=& 0 \\-2 \, x_{1} &+& 6 \, x_{2} &+& 8 \, x_{3} &=& 0 \\-2 \, x_{1} &+& 6 \, x_{2} &+& 3 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} -2 & 6 & 7 & 0 \\ 3 & -9 & -11 & 0 \\ -2 & 6 & 3 & 0 \\ -2 & 6 & 8 & 0 \\ -2 & 6 & 3 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & -3 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 3 \, a \\ a \\ 0 \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 3 \\ 1 \\ 0 \end{array}\right] \right\}$$.
Example 28 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} -x_{1} &-& 3 \, x_{2} &+& 4 \, x_{3} &=& 0 \\ & & x_{2} &-& x_{3} &=& 0 \\x_{1} &-& x_{2} & & &=& 0 \\-x_{1} &+& 6 \, x_{2} &-& 5 \, x_{3} &=& 0 \\-2 \, x_{1} &+& 11 \, x_{2} &-& 9 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} -1 & -3 & 4 & 0 \\ 0 & 1 & -1 & 0 \\ 1 & -1 & 0 & 0 \\ -1 & 6 & -5 & 0 \\ -2 & 11 & -9 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -1 & 0 \\ 0 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} a \\ a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 1 \\ 1 \\ 1 \end{array}\right] \right\}$$.
Example 29 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &-& 8 \, x_{2} &+& 4 \, x_{3} &+& 4 \, x_{4} &+& 9 \, x_{5} &=& 0 \\ & & x_{2} & & &-& x_{4} &-& x_{5} &=& 0 \\ & & 3 \, x_{2} &+& x_{3} &-& 4 \, x_{4} &-& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & -8 & 4 & 4 & 9 & 0 \\ 0 & 1 & 0 & -1 & -1 & 0 \\ 0 & 3 & 1 & -4 & -3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & -1 & -1 & 0 \\ 0 & 0 & 1 & -1 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -b \\ a + b \\ a \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 1 \\ 1 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ 1 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 30 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &+& x_{2} &-& 3 \, x_{3} &+& 7 \, x_{4} &=& 0 \\ & & x_{2} &-& 4 \, x_{3} &+& 7 \, x_{4} &=& 0 \\2 \, x_{1} &+& x_{2} &-& x_{3} &+& 5 \, x_{4} &=& 0 \\ &-& x_{2} &-& x_{3} &+& 3 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & 1 & -3 & 7 & 0 \\ 0 & 1 & -4 & 7 & 0 \\ 2 & 1 & -1 & 5 & 0 \\ 0 & -1 & -1 & 3 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & 2 & 0 \\ 0 & 1 & 0 & -1 & 0 \\ 0 & 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -2 \, a \\ a \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -2 \\ 1 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 31 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} -x_{1} &+& 4 \, x_{2} &-& 10 \, x_{3} &-& 6 \, x_{4} &+& 8 \, x_{5} &=& 0 \\-2 \, x_{1} &+& x_{2} &+& x_{3} &+& 2 \, x_{4} &+& 2 \, x_{5} &=& 0 \\x_{1} &-& 2 \, x_{2} &+& 4 \, x_{3} &+& 2 \, x_{4} &-& 4 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} -1 & 4 & -10 & -6 & 8 & 0 \\ -2 & 1 & 1 & 2 & 2 & 0 \\ 1 & -2 & 4 & 2 & -4 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & -2 & -2 & 0 & 0 \\ 0 & 1 & -3 & -2 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a + 2 \, b \\ 3 \, a + 2 \, b - 2 \, c \\ a \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ 3 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 2 \\ 2 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 0 \\ -2 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 32 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &-& 8 \, x_{2} &+& x_{3} &+& 7 \, x_{4} &=& 0 \\5 \, x_{1} &-& 9 \, x_{2} &+& 5 \, x_{3} &+& 4 \, x_{4} &=& 0 \\ & & 2 \, x_{2} & & &-& 2 \, x_{4} &=& 0 \\3 \, x_{1} &-& x_{2} &+& 3 \, x_{3} &-& 2 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & -8 & 1 & 7 & 0 \\ 5 & -9 & 5 & 4 & 0 \\ 0 & 2 & 0 & -2 & 0 \\ 3 & -1 & 3 & -2 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 1 & -1 & 0 \\ 0 & 1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a + b \\ b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 33 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} & & &-& 3 \, x_{3} &-& 8 \, x_{4} &-& 2 \, x_{5} &=& 0 \\ & & x_{2} &+& x_{3} &+& 2 \, x_{4} &+& 4 \, x_{5} &=& 0 \\ &-& x_{2} & & & & &-& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 0 & -3 & -8 & -2 & 0 \\ 0 & 1 & 1 & 2 & 4 & 0 \\ 0 & -1 & 0 & 0 & -3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & -2 & 1 & 0 \\ 0 & 1 & 0 & 0 & 3 & 0 \\ 0 & 0 & 1 & 2 & 1 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a - b \\ -3 \, b \\ -2 \, a - b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ 0 \\ -2 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ -3 \\ -1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 34 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &+& 2 \, x_{2} &-& 3 \, x_{3} &=& 0 \\2 \, x_{1} &+& 11 \, x_{2} &-& 6 \, x_{3} &=& 0 \\x_{1} &+& 3 \, x_{2} &-& 3 \, x_{3} &=& 0 \\ & & 3 \, x_{2} & & &=& 0 \\3 \, x_{1} &+& 11 \, x_{2} &-& 9 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & 2 & -3 & 0 \\ 2 & 11 & -6 & 0 \\ 1 & 3 & -3 & 0 \\ 0 & 3 & 0 & 0 \\ 3 & 11 & -9 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -3 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 3 \, a \\ 0 \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 3 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 35 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &+& 2 \, x_{2} &+& 11 \, x_{3} &-& 11 \, x_{4} &-& 12 \, x_{5} &=& 0 \\-x_{1} &-& x_{2} &-& 8 \, x_{3} &+& 8 \, x_{4} &+& 8 \, x_{5} &=& 0 \\x_{1} &+& 2 \, x_{2} &+& 11 \, x_{3} &-& 10 \, x_{4} &-& 11 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 2 & 11 & -11 & -12 & 0 \\ -1 & -1 & -8 & 8 & 8 & 0 \\ 1 & 2 & 11 & -10 & -11 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 5 & 0 & 1 & 0 \\ 0 & 1 & 3 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -5 \, a - b \\ -3 \, a + b \\ a \\ -b \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -5 \\ -3 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ 1 \\ 0 \\ -1 \\ 1 \end{array}\right] \right\}$$.
Example 36 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} -2 \, x_{1} &-& 5 \, x_{2} &-& 8 \, x_{3} &=& 0 \\x_{1} &-& 4 \, x_{2} &-& 9 \, x_{3} &=& 0 \\x_{1} & & &-& x_{3} &=& 0 \\-x_{1} &+& 2 \, x_{2} &+& 5 \, x_{3} &=& 0 \\-x_{1} & & &+& x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} -2 & -5 & -8 & 0 \\ 1 & -4 & -9 & 0 \\ 1 & 0 & -1 & 0 \\ -1 & 2 & 5 & 0 \\ -1 & 0 & 1 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -1 & 0 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} a \\ -2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 1 \\ -2 \\ 1 \end{array}\right] \right\}$$.
Example 37 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} -3 \, x_{1} &+& 4 \, x_{2} &-& 2 \, x_{3} &-& 8 \, x_{4} &+& 3 \, x_{5} &=& 0 \\x_{1} & & &+& 3 \, x_{3} &-& x_{4} &+& 11 \, x_{5} &=& 0 \\4 \, x_{1} &-& 5 \, x_{2} &+& 3 \, x_{3} &+& 10 \, x_{4} &-& 2 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} -3 & 4 & -2 & -8 & 3 & 0 \\ 1 & 0 & 3 & -1 & 11 & 0 \\ 4 & -5 & 3 & 10 & -2 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & 2 & -1 & 0 \\ 0 & 1 & 0 & -1 & 2 & 0 \\ 0 & 0 & 1 & -1 & 4 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -2 \, a + b \\ a - 2 \, b \\ a - 4 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -2 \\ 1 \\ 1 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ -2 \\ -4 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 38 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} -x_{1} &-& 5 \, x_{2} &-& x_{3} &+& 7 \, x_{4} &=& 0 \\x_{1} &+& 5 \, x_{2} &-& 2 \, x_{3} &+& 5 \, x_{4} &=& 0 \\-x_{1} &-& 5 \, x_{2} &+& x_{3} &-& x_{4} &=& 0 \\ & & &-& 3 \, x_{3} &+& 12 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} -1 & -5 & -1 & 7 & 0 \\ 1 & 5 & -2 & 5 & 0 \\ -1 & -5 & 1 & -1 & 0 \\ 0 & 0 & -3 & 12 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 5 & 0 & -3 & 0 \\ 0 & 0 & 1 & -4 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -5 \, a + 3 \, b \\ a \\ 4 \, b \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -5 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 3 \\ 0 \\ 4 \\ 1 \end{array}\right] \right\}$$.
Example 39 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &-& 2 \, x_{2} &+& 5 \, x_{3} &+& x_{4} & & &=& 0 \\x_{1} &-& x_{2} &+& 3 \, x_{3} & & &+& x_{5} &=& 0 \\ & & 3 \, x_{2} &-& 6 \, x_{3} &-& 3 \, x_{4} &+& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & -2 & 5 & 1 & 0 & 0 \\ 1 & -1 & 3 & 0 & 1 & 0 \\ 0 & 3 & -6 & -3 & 3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 1 & -1 & 2 & 0 \\ 0 & 1 & -2 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a + b - 2 \, c \\ 2 \, a + b - c \\ a \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 2 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 1 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -2 \\ -1 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 40 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 3 \, x_{1} &+& 10 \, x_{2} &-& 6 \, x_{3} &=& 0 \\-x_{1} &-& 3 \, x_{2} &+& 2 \, x_{3} &=& 0 \\x_{1} &-& x_{2} &-& 2 \, x_{3} &=& 0 \\3 \, x_{1} &+& 10 \, x_{2} &-& 6 \, x_{3} &=& 0 \\ & & 5 \, x_{2} & & &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 3 & 10 & -6 & 0 \\ -1 & -3 & 2 & 0 \\ 1 & -1 & -2 & 0 \\ 3 & 10 & -6 & 0 \\ 0 & 5 & 0 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -2 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a \\ 0 \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 41 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} x_{1} &-& 4 \, x_{2} &-& 6 \, x_{3} &=& 0 \\x_{1} &-& 3 \, x_{2} &-& 5 \, x_{3} &=& 0 \\ & & & & 0 &=& 0 \\ &-& 5 \, x_{2} &-& 5 \, x_{3} &=& 0 \\x_{1} &-& x_{2} &-& 3 \, x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 1 & -4 & -6 & 0 \\ 1 & -3 & -5 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & -5 & -5 & 0 \\ 1 & -1 & -3 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & -2 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 2 \, a \\ -a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 2 \\ -1 \\ 1 \end{array}\right] \right\}$$.
Example 42 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} x_{1} &+& x_{2} &+& x_{3} &-& 2 \, x_{4} &=& 0 \\-x_{1} & & &-& 4 \, x_{3} &+& 4 \, x_{4} &=& 0 \\ & & x_{2} &-& 3 \, x_{3} &+& 3 \, x_{4} &=& 0 \\5 \, x_{1} &+& 3 \, x_{2} &+& 11 \, x_{3} &-& 12 \, x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} 1 & 1 & 1 & -2 & 0 \\ -1 & 0 & -4 & 4 & 0 \\ 0 & 1 & -3 & 3 & 0 \\ 5 & 3 & 11 & -12 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 4 & 0 & 0 \\ 0 & 1 & -3 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -4 \, a \\ 3 \, a \\ a \\ 0 \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -4 \\ 3 \\ 1 \\ 0 \end{array}\right] \right\}$$.
Example 43 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} & & &-& 5 \, x_{3} &+& 9 \, x_{4} &-& 9 \, x_{5} &=& 0 \\ & & x_{2} &-& 5 \, x_{3} &+& 3 \, x_{4} &-& 11 \, x_{5} &=& 0 \\-x_{1} & & &+& 6 \, x_{3} &-& 10 \, x_{4} &+& 11 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 0 & -5 & 9 & -9 & 0 \\ 0 & 1 & -5 & 3 & -11 & 0 \\ -1 & 0 & 6 & -10 & 11 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & 4 & 1 & 0 \\ 0 & 1 & 0 & -2 & -1 & 0 \\ 0 & 0 & 1 & -1 & 2 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -4 \, a - b \\ 2 \, a + b \\ a - 2 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -4 \\ 2 \\ 1 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ 1 \\ -2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 44 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &-& x_{2} &-& 6 \, x_{3} &+& 4 \, x_{4} & & &=& 0 \\ & & x_{2} &+& 2 \, x_{3} &-& 2 \, x_{4} &-& x_{5} &=& 0 \\-2 \, x_{1} &-& x_{2} &+& 6 \, x_{3} &-& 2 \, x_{4} &+& 3 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & -1 & -6 & 4 & 0 & 0 \\ 0 & 1 & 2 & -2 & -1 & 0 \\ -2 & -1 & 6 & -2 & 3 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & -4 & 2 & -1 & 0 \\ 0 & 1 & 2 & -2 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 4 \, a - 2 \, b + c \\ -2 \, a + 2 \, b + c \\ a \\ b \\ c \end{array}\right] \middle|\,a\text{\texttt{,}}b\text{\texttt{,}}c\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 4 \\ -2 \\ 1 \\ 0 \\ 0 \end{array}\right] , \left[\begin{array}{c} -2 \\ 2 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ 1 \\ 0 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 45 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} & & 5 \, x_{2} &-& 10 \, x_{3} &=& 0 \\x_{1} &+& 6 \, x_{2} &-& 11 \, x_{3} &=& 0 \\ &-& 4 \, x_{2} &+& 8 \, x_{3} &=& 0 \\x_{1} &+& x_{2} &-& x_{3} &=& 0 \\x_{1} & & &+& x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 0 & 5 & -10 & 0 \\ 1 & 6 & -11 & 0 \\ 0 & -4 & 8 & 0 \\ 1 & 1 & -1 & 0 \\ 1 & 0 & 1 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ 2 \, a \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 2 \\ 1 \end{array}\right] \right\}$$.
Example 46 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} & & x_{2} & & &+& 4 \, x_{4} &+& 3 \, x_{5} &=& 0 \\-x_{1} &-& x_{2} &-& 2 \, x_{3} &-& x_{4} &-& 8 \, x_{5} &=& 0 \\-2 \, x_{1} &-& x_{2} &-& 3 \, x_{3} &+& 2 \, x_{4} &-& 11 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 0 & 1 & 0 & 4 & 3 & 0 \\ -1 & -1 & -2 & -1 & -8 & 0 \\ -2 & -1 & -3 & 2 & -11 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & -3 & 1 & 0 \\ 0 & 1 & 0 & 4 & 3 & 0 \\ 0 & 0 & 1 & 0 & 2 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} 3 \, a - b \\ -4 \, a - 3 \, b \\ -2 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 3 \\ -4 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ -3 \\ -2 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 47 🔗
Consider the homogeneous system of equations \begin{alignat*}{5} -2 \, x_{1} & & & & &+& 2 \, x_{4} &=& 0 \\-x_{1} &-& x_{2} & & &-& 2 \, x_{4} &=& 0 \\3 \, x_{1} &+& 2 \, x_{2} & & &+& 3 \, x_{4} &=& 0 \\-x_{1} & & & & &+& x_{4} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{cccc|c} -2 & 0 & 0 & 2 & 0 \\ -1 & -1 & 0 & -2 & 0 \\ 3 & 2 & 0 & 3 & 0 \\ -1 & 0 & 0 & 1 & 0 \end{array}\right] = \left[\begin{array}{cccc|c} 1 & 0 & 0 & -1 & 0 \\ 0 & 1 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} b \\ -3 \, b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} 1 \\ -3 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 48 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} & & &+& 2 \, x_{3} &-& x_{4} &+& x_{5} &=& 0 \\ & & x_{2} &-& 3 \, x_{3} &+& 5 \, x_{4} & & &=& 0 \\-4 \, x_{1} &-& 2 \, x_{2} &-& x_{3} &-& 7 \, x_{4} &-& 5 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 0 & 2 & -1 & 1 & 0 \\ 0 & 1 & -3 & 5 & 0 & 0 \\ -4 & -2 & -1 & -7 & -5 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & 1 & 3 & 0 \\ 0 & 1 & 0 & 2 & -3 & 0 \\ 0 & 0 & 1 & -1 & -1 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a - 3 \, b \\ -2 \, a + 3 \, b \\ a + b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ -2 \\ 1 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -3 \\ 3 \\ 1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 49 🔗
Consider the homogeneous system of equations \begin{alignat*}{6} x_{1} &+& x_{2} &-& 9 \, x_{3} &+& 10 \, x_{4} &+& 9 \, x_{5} &=& 0 \\ & & x_{2} &-& 5 \, x_{3} &+& 6 \, x_{4} &+& 4 \, x_{5} &=& 0 \\x_{1} & & &-& 3 \, x_{3} &+& 3 \, x_{4} &+& 4 \, x_{5} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccccc|c} 1 & 1 & -9 & 10 & 9 & 0 \\ 0 & 1 & -5 & 6 & 4 & 0 \\ 1 & 0 & -3 & 3 & 4 & 0 \end{array}\right] = \left[\begin{array}{ccccc|c} 1 & 0 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & -1 & 0 \\ 0 & 0 & 1 & -1 & -1 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -b \\ -a + b \\ a + b \\ a \\ b \end{array}\right] \middle|\,a\text{\texttt{,}}b\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} 0 \\ -1 \\ 1 \\ 1 \\ 0 \end{array}\right] , \left[\begin{array}{c} -1 \\ 1 \\ 1 \\ 0 \\ 1 \end{array}\right] \right\}$$.
Example 50 🔗
Consider the homogeneous system of equations \begin{alignat*}{4} 4 \, x_{1} &-& 12 \, x_{2} &+& 4 \, x_{3} &=& 0 \\3 \, x_{1} &-& 5 \, x_{2} &+& 3 \, x_{3} &=& 0 \\x_{1} &-& 5 \, x_{2} &+& x_{3} &=& 0 \\3 \, x_{1} &-& 10 \, x_{2} &+& 3 \, x_{3} &=& 0 \\x_{1} &-& 2 \, x_{2} &+& x_{3} &=& 0 \\ \end{alignat*}
1. Find the solution space of this system.
2. Find a basis of the solution space.
$\operatorname{RREF} \left[\begin{array}{ccc|c} 4 & -12 & 4 & 0 \\ 3 & -5 & 3 & 0 \\ 1 & -5 & 1 & 0 \\ 3 & -10 & 3 & 0 \\ 1 & -2 & 1 & 0 \end{array}\right] = \left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
1. The solution space is $$\left\{ \left[\begin{array}{c} -a \\ 0 \\ a \end{array}\right] \middle|\,a\in\mathbb{R}\right\}$$
2. A basis of the solution space is $$\left\{ \left[\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right] \right\}$$. | {"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": 1.0000090599060059, "perplexity": 1711.8492544149226}, "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/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00726.warc.gz"} |
https://mirrors.sunsite.dk/pub/putty/putty-0.70/htmldoc/Chapter6.html | # Chapter 6: Using PSFTP to transfer files securely
PSFTP, the PuTTY SFTP client, is a tool for transferring files securely between computers using an SSH connection.
PSFTP differs from PSCP in the following ways:
• PSCP should work on virtually every SSH server. PSFTP uses the new SFTP protocol, which is a feature of SSH-2 only. (PSCP will also use this protocol if it can, but there is an SSH-1 equivalent it can fall back to if it cannot.)
• PSFTP allows you to run an interactive file transfer session, much like the Windows ftp program. You can list the contents of directories, browse around the file system, issue multiple get and put commands, and eventually log out. By contrast, PSCP is designed to do a single file transfer operation and immediately terminate.
## 6.1 Starting PSFTP
The usual way to start PSFTP is from a command prompt, much like PSCP. To do this, it will need either to be on your PATH or in your current directory. To add the directory containing PSFTP to your PATH environment variable, type into the console window:
set PATH=C:\path\to\putty\directory;%PATH%
Unlike PSCP, however, PSFTP has no complex command-line syntax; you just specify a host name and perhaps a user name:
psftp server.example.com
or perhaps
psftp [email protected]
Alternatively, if you just type psftp on its own (or double-click the PSFTP icon in the Windows GUI), you will see the PSFTP prompt, and a message telling you PSFTP has not connected to any server:
C:\>psftp
psftp: no hostname specified; use "open host.name" to connect
psftp>
At this point you can type open server.example.com or open [email protected] to start a session.
PSFTP accepts all the general command line options supported by the PuTTY tools, except the ones which make no sense in a file transfer utility. See section 3.8.3 for a description of these options. (The ones not supported by PSFTP are clearly marked.)
PSFTP also supports some of its own options. The following sections describe PSFTP's specific command-line options.
### 6.1.1 -b: specify a file containing batch commands
In normal operation, PSFTP is an interactive program which displays a command line and accepts commands from the keyboard.
If you need to do automated tasks with PSFTP, you would probably prefer to specify a set of commands in advance and have them executed automatically. The -b option allows you to do this. You use it with a file name containing batch commands. For example, you might create a file called myscript.scr containing lines like this:
cd /home/ftp/users/jeff
del jam-old.tar.gz
ren jam.tar.gz jam-old.tar.gz
put jam.tar.gz
chmod a+r jam.tar.gz
and then you could run the script by typing
psftp user@hostname -b myscript.scr
When you run a batch script in this way, PSFTP will abort the script if any command fails to complete successfully. To change this behaviour, you can add the -be option (section 6.1.3).
PSFTP will terminate after it finishes executing the batch script.
### 6.1.2 -bc: display batch commands as they are run
The -bc option alters what PSFTP displays while processing a batch script specified with -b. With the -bc option, PSFTP will display prompts and commands just as if the commands had been typed at the keyboard. So instead of seeing this:
C:\>psftp fred@hostname -b batchfile
Sent username "fred"
Remote working directory is /home/fred
Listing directory /home/fred/lib
drwxrwsr-x 4 fred fred 1024 Sep 6 10:42 .
drwxr-sr-x 25 fred fred 2048 Dec 14 09:36 ..
drwxrwsr-x 3 fred fred 1024 Apr 17 2000 jed
lrwxrwxrwx 1 fred fred 24 Apr 17 2000 timber
drwxrwsr-x 2 fred fred 1024 Mar 13 2000 trn
you might see this:
C:\>psftp fred@hostname -bc -b batchfile
Sent username "fred"
Remote working directory is /home/fred
psftp> dir lib
Listing directory /home/fred/lib
drwxrwsr-x 4 fred fred 1024 Sep 6 10:42 .
drwxr-sr-x 25 fred fred 2048 Dec 14 09:36 ..
drwxrwsr-x 3 fred fred 1024 Apr 17 2000 jed
lrwxrwxrwx 1 fred fred 24 Apr 17 2000 timber
drwxrwsr-x 2 fred fred 1024 Mar 13 2000 trn
psftp> quit
### 6.1.3 -be: continue batch processing on errors
When running a batch file, this additional option causes PSFTP to continue processing even if a command fails to complete successfully.
You might want this to happen if you wanted to delete a file and didn't care if it was already not present, for example.
### 6.1.4 -batch: avoid interactive prompts
If you use the -batch option, PSFTP will never give an interactive prompt while establishing the connection. If the server's host key is invalid, for example (see section 2.2), then the connection will simply be abandoned instead of asking you what to do next.
This may help PSFTP's behaviour when it is used in automated scripts: using -batch, if something goes wrong at connection time, the batch job will fail rather than hang.
## 6.2 Running PSFTP
Once you have started your PSFTP session, you will see a psftp> prompt. You can now type commands to perform file-transfer functions. This section lists all the available commands.
Any line starting with a # will be treated as a comment and ignored.
### 6.2.1 General quoting rules for PSFTP commands
Most PSFTP commands are considered by the PSFTP command interpreter as a sequence of words, separated by spaces. For example, the command ren oldfilename newfilename splits up into three words: ren (the command name), oldfilename (the name of the file to be renamed), and newfilename (the new name to give the file).
Sometimes you will need to specify file names that contain spaces. In order to do this, you can surround the file name with double quotes. This works equally well for local file names and remote file names:
psftp> get "spacey file name.txt" "save it under this name.txt"
The double quotes themselves will not appear as part of the file names; they are removed by PSFTP and their only effect is to stop the spaces inside them from acting as word separators.
If you need to use a double quote (on some types of remote system, such as Unix, you are allowed to use double quotes in file names), you can do this by doubling it. This works both inside and outside double quotes. For example, this command
psftp> ren ""this"" "a file with ""quotes"" in it"
will take a file whose current name is "this" (with a double quote character at the beginning and the end) and rename it to a file whose name is a file with "quotes" in it.
(The one exception to the PSFTP quoting rules is the ! command, which passes its command line straight to Windows without splitting it up into words at all. See section 6.2.19.)
### 6.2.2 Wildcards in PSFTP
Several commands in PSFTP support ‘wildcards’ to select multiple files.
For local file specifications (such as the first argument to put), wildcard rules for the local operating system are used. For instance, PSFTP running on Windows might require the use of *.* where PSFTP on Unix would need *.
For remote file specifications (such as the first argument to get), PSFTP uses a standard wildcard syntax (similar to POSIX wildcards):
• * matches any sequence of characters (including a zero-length sequence).
• ? matches exactly one character.
• [abc] matches exactly one character which can be a, b, or c.
[a-z] matches any character in the range a to z.
[^abc] matches a single character that is not a, b, or c.
Special cases: [-a] matches a literal hyphen (-) or a; [^-a] matches all other characters. [a^] matches a literal caret (^) or a.
• \ (backslash) before any of the above characters (or itself) removes that character's special meaning.
A leading period (.) on a filename is not treated specially, unlike in some Unix contexts; get * will fetch all files, whether or not they start with a leading period.
### 6.2.3 The open command: start a session
If you started PSFTP by double-clicking in the GUI, or just by typing psftp at the command line, you will need to open a connection to an SFTP server before you can issue any other commands (except help and quit).
To create a connection, type open host.name, or if you need to specify a user name as well you can type open [email protected]. You can optionally specify a port as well: open [email protected] 22.
Once you have issued this command, you will not be able to issue it again, even if the command fails (for example, if you mistype the host name or the connection times out). So if the connection is not opened successfully, PSFTP will terminate immediately.
### 6.2.4 The quit command: end your session
When you have finished your session, type the command quit to close the connection, terminate PSFTP and return to the command line (or just close the PSFTP console window if you started it from the GUI).
You can also use the bye and exit commands, which have exactly the same effect.
### 6.2.5 The close command: close your connection
If you just want to close the network connection but keep PSFTP running, you can use the close command. You can then use the open command to open a new connection.
### 6.2.6 The help command: get quick online help
If you type help, PSFTP will give a short list of the available commands.
If you type help with a command name - for example, help get - then PSFTP will give a short piece of help on that particular command.
### 6.2.7 The cd and pwd commands: changing the remote working directory
PSFTP maintains a notion of your ‘working directory’ on the server. This is the default directory that other commands will operate on. For example, if you type get filename.dat then PSFTP will look for filename.dat in your remote working directory on the server.
To change your remote working directory, use the cd command. If you don't provide an argument, cd will return you to your home directory on the server (more precisely, the remote directory you were in at the start of the connection).
To display your current remote working directory, type pwd.
### 6.2.8 The lcd and lpwd commands: changing the local working directory
As well as having a working directory on the remote server, PSFTP also has a working directory on your local machine (just like any other Windows process). This is the default local directory that other commands will operate on. For example, if you type get filename.dat then PSFTP will save the resulting file as filename.dat in your local working directory.
To change your local working directory, use the lcd command. To display your current local working directory, type lpwd.
### 6.2.9 The get command: fetch a file from the server
To download a file from the server and store it on your local PC, you use the get command.
In its simplest form, you just use this with a file name:
get myfile.dat
If you want to store the file locally under a different name, specify the local file name after the remote one:
get myfile.dat newname.dat
This will fetch the file on the server called myfile.dat, but will save it to your local machine under the name newname.dat.
To fetch an entire directory recursively, you can use the -r option:
get -r mydir
get -r mydir newname
(If you want to fetch a file whose name starts with a hyphen, you may have to use the -- special argument, which stops get from interpreting anything as a switch after it. For example, ‘get -- -silly-name-’.)
### 6.2.10 The put command: send a file to the server
To upload a file to the server from your local PC, you use the put command.
In its simplest form, you just use this with a file name:
put myfile.dat
If you want to store the file remotely under a different name, specify the remote file name after the local one:
put myfile.dat newname.dat
This will send the local file called myfile.dat, but will store it on the server under the name newname.dat.
To send an entire directory recursively, you can use the -r option:
put -r mydir
put -r mydir newname
(If you want to send a file whose name starts with a hyphen, you may have to use the -- special argument, which stops put from interpreting anything as a switch after it. For example, ‘put -- -silly-name-’.)
### 6.2.11 The mget and mput commands: fetch or send multiple files
mget works almost exactly like get, except that it allows you to specify more than one file to fetch at once. You can do this in two ways:
• by giving two or more explicit file names (‘mget file1.txt file2.txt’)
• by using a wildcard (‘mget *.txt’).
Every argument to mget is treated as the name of a file to fetch (unlike get, which will interpret at most one argument like that, and a second argument will be treated as an alternative name under which to store the retrieved file), or a wildcard expression matching more than one file.
The -r and -- options from get are also available with mget.
mput is similar to put, with the same differences.
### 6.2.12 The reget and reput commands: resuming file transfers
If a file transfer fails half way through, and you end up with half the file stored on your disk, you can resume the file transfer using the reget and reput commands. These work exactly like the get and put commands, but they check for the presence of the half-written destination file and start transferring from where the last attempt left off.
The syntax of reget and reput is exactly the same as the syntax of get and put:
reget myfile.dat
reget myfile.dat newname.dat
reget -r mydir
These commands are intended mainly for resuming interrupted transfers. They assume that the remote file or directory structure has not changed in any way; if there have been changes, you may end up with corrupted files. In particular, the -r option will not pick up changes to files or directories already transferred in full.
### 6.2.13 The dir command: list remote files
To list the files in your remote working directory, just type dir.
You can also list the contents of a different directory by typing dir followed by the directory name:
dir /home/fred
dir sources
And you can list a subset of the contents of a directory by providing a wildcard:
dir /home/fred/*.txt
dir sources/*.c
The ls command works exactly the same way as dir.
### 6.2.14 The chmod command: change permissions on remote files
PSFTP allows you to modify the file permissions on files and directories on the server. You do this using the chmod command, which works very much like the Unix chmod command.
The basic syntax is chmod modes file, where modes represents a modification to the file permissions, and file is the filename to modify. You can specify multiple files or wildcards. For example:
chmod go-rwx,u+w privatefile
chmod a+r public*
chmod 640 groupfile1 groupfile2
The modes parameter can be a set of octal digits in the Unix style. (If you don't know what this means, you probably don't want to be using it!) Alternatively, it can be a list of permission modifications, separated by commas. Each modification consists of:
• The people affected by the modification. This can be u (the owning user), g (members of the owning group), or o (everybody else - ‘others’), or some combination of those. It can also be a (‘all’) to affect everybody at once.
• A + or - sign, indicating whether permissions are to be added or removed.
• The actual permissions being added or removed. These can be r (permission to read the file), w (permission to write to the file), and x (permission to execute the file, or in the case of a directory, permission to access files within the directory).
So the above examples would do:
• The first example: go-rwx removes read, write and execute permissions for members of the owning group and everybody else (so the only permissions left are the ones for the file owner). u+w adds write permission for the file owner.
• The second example: a+r adds read permission for everybody to all files and directories starting with ‘public’.
In addition to all this, there are a few extra special cases for Unix systems. On non-Unix systems these are unlikely to be useful:
• You can specify u+s and u-s to add or remove the Unix set-user-ID bit. This is typically only useful for special purposes; refer to your Unix documentation if you're not sure about it.
• You can specify g+s and g-s to add or remove the Unix set-group-ID bit. On a file, this works similarly to the set-user-ID bit (see your Unix documentation again); on a directory it ensures that files created in the directory are accessible by members of the group that owns the directory.
• You can specify +t and -t to add or remove the Unix ‘sticky bit’. When applied to a directory, this means that the owner of a file in that directory can delete the file (whereas normally only the owner of the directory would be allowed to).
### 6.2.15 The del command: delete remote files
To delete a file on the server, type del and then the filename or filenames:
del oldfile.dat
del file1.txt file2.txt
del *.o
Files will be deleted without further prompting, even if multiple files are specified.
del will only delete files. You cannot use it to delete directories; use rmdir for that.
The rm command works exactly the same way as del.
### 6.2.16 The mkdir command: create remote directories
To create a directory on the server, type mkdir and then the directory name:
mkdir newstuff
You can specify multiple directories to create at once:
mkdir dir1 dir2 dir3
### 6.2.17 The rmdir command: remove remote directories
To remove a directory on the server, type rmdir and then the directory name or names:
rmdir oldstuff
rmdir *.old ancient
Directories will be deleted without further prompting, even if multiple directories are specified.
Most SFTP servers will probably refuse to remove a directory if the directory has anything in it, so you will need to delete the contents first.
### 6.2.18 The mv command: move and rename remote files
To rename a single file on the server, type mv, then the current file name, and then the new file name:
mv oldfile newname
You can also move the file into a different directory and change the name:
mv oldfile dir/newname
To move one or more files into an existing subdirectory, specify the files (using wildcards if desired), and then the destination directory:
mv file dir
mv file1 dir1/file2 dir2
mv *.c *.h ..
The rename and ren commands work exactly the same way as mv.
### 6.2.19 The ! command: run a local Windows command
You can run local Windows commands using the ! command. This is the only PSFTP command that is not subject to the command quoting rules given in section 6.2.1. If any command line begins with the ! character, then the rest of the line will be passed straight to Windows without further translation.
For example, if you want to move an existing copy of a file out of the way before downloading an updated version, you might type:
psftp> !ren myfile.dat myfile.bak
psftp> get myfile.dat
using the Windows ren command to rename files on your local PC.
## 6.3 Using public key authentication with PSFTP
Like PuTTY, PSFTP can authenticate using a public key instead of a password. There are three ways you can do this.
Firstly, PSFTP can use PuTTY saved sessions in place of hostnames. So you might do this:
• Run PuTTY, and create a PuTTY saved session (see section 4.1.2) which specifies your private key file (see section 4.22.8). You will probably also want to specify a username to log in as (see section 4.14.1).
• In PSFTP, you can now use the name of the session instead of a hostname: type psftp sessionname, where sessionname is replaced by the name of your saved session.
Secondly, you can supply the name of a private key file on the command line, with the -i option. See section 3.8.3.18 for more information.
Thirdly, PSFTP will attempt to authenticate using Pageant if Pageant is running (see chapter 9). So you would do this:
• Ensure Pageant is running, and has your private key stored in it.
• Specify a user and host name to PSFTP as normal. PSFTP will automatically detect Pageant and try to use the keys within it.
For more general information on public-key authentication, see chapter 8.
If you want to provide feedback on this manual or on the PuTTY tools themselves, see the Feedback page.
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https://leastaction.wordpress.com/category/physics/ | # Least Action
Nontrivializing triviality..and vice versa.
## Fun with Homology
There is a theorem (currently being attributed to Wikipedia, but I’m sure I can do better given more time) which states that
All closed surfaces can be produced by gluing the sides of some polygon and all even-sided polygons (2n-gons) can be glued to make different manifolds.
Conversely, a closed surface with $n$ non-zero classes can be cut into a 2n-gon.
Two interesting cases of this are:
1. Gluing opposite sides of a hexagon produces a torus $T^2$.
2. Gluing opposite sides of an octagon produces a surface with two holes, topologically equivalent to a torus with two holes.
I had trouble visualizing this on a piece of paper, so I found two videos which are fascinating and instructive, respectively.
The two-torus from a hexagon
The genus-2 Riemann surface from an octagon
I would like to figure out how one can make such animations, and generalizations of these, using Mathematica or Sagemath.
There are a bunch of other very cool examples on the Youtube channels of these users. Kudos to them for making such instructive videos!
PS – I see that $\LaTeX$ on WordPress has become (or is still?) very sloppy! 😦
Written by Vivek
October 20, 2016 at 21:57
## Divergence Theorem in Complex Coordinates
The divergence theorem in complex coordinates,
$\int_R d^2{z} (\partial_z v^z + \partial_{\bar{z}}v^{\bar{z}}) = i \oint_{\partial R}(v^z d\bar{z} - v^{\bar{z}}dz)$
(where the contour integral circles the region R counterclockwise) appears in the context of two dimensional conformal field theory, to derive Noether’s Theorem and the Ward Identity for a conformally invariant scalar field theory (for example), and is useful in general in 2D CFT/string theory. This is equation (2.1.9) of Polchinski’s volume 1, but a proof is not given in the book.
This is straightforward to prove by converting both sides separately to Cartesian coordinates $(\sigma^1, \sigma^2)$, through
$z = \sigma^1 + i \sigma^2$
$\bar{z} = \sigma^1 - i \sigma^2$
$\partial_z = \frac{1}{2}(\partial_1 - i \partial_2)$
$\partial_{\bar{z}} = \frac{1}{2}(\partial_1 + i \partial_2)$
$d^2 z = 2 d\sigma^1 d\sigma^2 = 2 d^2 \sigma$
and using the Green’s theorem in the plane
$\oint_{\partial R}(L dx + M dy) = \int \int_{R} \left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right) dx dy$
with the identifications
$x \rightarrow \sigma^1, y \rightarrow \sigma^2$
$L \rightarrow -v^2, M \rightarrow v^1$
There is perhaps a faster and more elegant way of doing this directly in the complex plane, but this particular line of reasoning makes contact with the underlying Green’s theorem in the plane, which is more familiar from real analysis.
Written by Vivek
October 12, 2014 at 20:47
## The Yang Mills Field Strength: a motivation for differential forms
Although their importance and applications are widely recognized in theoretical physics, differential forms are not part of the standard curriculum in physics courses, except for the rare mention in a general relativity course, e.g. if you have used the book by Sean Carroll. In this blog post, we describe the construction of the field strength tensor for Yang Mills Theory, using differential forms. The derivation (which is based on the one given by Tony Zee in his QFT book) is elegant, and mathematically less tedious than the more conventional derivation based on the matrix gauge field. It also illustrates the power of the differential forms approach.
To begin with, let me define a normalized matrix gauge field $A_\mu$ which is $-i$ times the usual matrix gauge field. So in the equations that appear below, the covariant derivative has no lurking factors of $-i$. This greatly simplifies the algebra for us, as we don’t have to keep track of conjugations and sign changes associated with $i$. The covariant derivative is thus $D_\mu = \partial_\mu + A_\mu$ in terms of this new gauge field. The matrix 1-form $A$ is
$A = A_\mu dx^\mu$
So, $A^2 = A_\mu A_\nu dx^\mu dx^\nu$. But since $dx^\mu dx^\nu = -dx^\nu dx^\mu$, only the antisymmetric part of the product survives and hence we can write
$A^2 = \frac{1}{2}[A_\mu, A_\nu] dx^\mu dx^\nu$
We want to construct an appropriate 2-form $F = \frac{1}{2}F_{\mu\nu}dx^\mu dx^\nu$ from this 1-form A. Now, if d denotes the exterior derivative, then dA is a 2-form, as is A^2. These are the only two forms we can construct from A. So, $F$ must be a linear combination of these two forms. This is a very simple, and neat argument!
Now, the transformation law for the gauge potential is
$A \rightarrow U A U^\dagger + U dU^\dagger$
where $U$ is a 0 form (so $dU^\dagger = \partial_\mu U^\dagger dx^\mu$). Applying d to the transformation law, we get
$dA \rightarrow U dA U^\dagger + dU A U^\dagger - U A dU^\dagger + dU dU^\dagger$
where the negative sign in the third term comes from moving the 1-form d past the 1-form A. Squaring the transformation law yields
$A^2 \rightarrow UA^2 U^\dagger + U A dU ^\dagger + U dU^\dagger U A U^\dagger + U dU^\dagger U dU^\dagger$
Now, $UU^\dagger = 1$, so applying d again to both sides we get $U dU^\dagger = -dU U^\dagger$. So, we can write the square transformation law as
$A^2 \rightarrow U A^2 U^\dagger + U A dU^\dagger - dU A U^\dagger - dU dU^\dagger$
whereas if we recall the expression for the transformation of $dA$, it was just
$dA \rightarrow U dA U^\dagger + dU A U^\dagger - U A dU^\dagger + dU dU^\dagger$
Clearly if we merely add $A^2$ and $dA$, the last 3 terms on the RHS of each cancel out, and we get
$A^2 + dA \rightarrow U(A^2 + dA)U^\dagger$
which is the expected transformation law for a field strength of the form $F = A^2 + dA$:
$F \rightarrow U F U^{\dagger}$
The differential form approach uses compact notation that suppresses the Lorentz index $\mu$ as well as the group index $a$, and gives us a fleeting glimpse into the connection between gauge theory and fibre bundles.
For a gentle yet semi-rigorous introduction to differential forms, the reader is referred to the book on General Relativity by Sean Carroll.
Written by Vivek
June 11, 2014 at 10:53
## From engineering to physics graduate school
This blog post is about switching to physics graduate school, when you do not have a physics undergrad per se, but something like an engineering degree. I have been meaning to write this post for years, as I never found one myself when I was trying to figure things out for myself. In some sense, this is a personal chronicle of my experiences, opinions and beliefs which have been shaped over the past 8 years or so. Before I proceed though, I should warn readers that I am by no means an authority on either physics graduate school, or this particular career path. I cannot also say with any degree of finality that things have worked out optimally for me. This is also not a philosophical career advice post, and at this point, I have no intention to adapt it to different kinds of individuals who may have different tastes, inclinations or backgrounds. Ultimately, and I cannot emphasize this enough, no advice is good advice.
Physics is a challenging and tricky subject that requires a lot of dedication and focus. I dislike the use of the term “genius” because while there are luminaries and experts in physics, use of this term suggests that it is possible for some people to do nothing and yet do extremely well in physics. This is deceptive. I believe everyone you see who is really very good has worked hard in his or her own way by solving lots of problems, understanding things properly and patiently, and persisting. Some people require less time, but it is incorrect to say that they do not have to work hard to achieve the same amount as someone else because they are geniuses.
But having said that, physics isn’t for the weak-hearted (nor is engineering actually, but there’s a greater commercial value associated with it, so it manages to attract more weak-hearted and feeble souls than the pure sciences do). Switching to physics is going to be a rocky road and if you are putting off physics for practicality so that you can do engineering (or something else) now and “always switch to physics later”, this is a bad idea. There are exceptions, which this post is about, so we’ll get to them later.
Why do I say this? Well, that’s because physics has several foundational pillars which you really can’t do without, and a patchy education means you will spend many years gathering confidence and learning things which you ought to have learnt systematically through courses and books. So the bottom line is if you are into physics because of the popular science books on dark mater and string theory, then you are either in for a rude shock or you’re being misled. So start reading real physics books!
Also, be advised that you will probably not have a lot of time for “hobbies” and for doing things like playing guitar and skydiving and fixing radios and watching all your favorite movies and TV shows all at the same time. You could have done all of that as an undergrad (perhaps even a physics undergrad at a less demanding college) and yet managed to scrape through by studying at the last minute. But progress in the long term will demand some major task scheduling. And yet, I should add that a lot of very enthusiastic, excellent and bright people I know do manage to do all these things and also pace their physics work. So yes, its more of how you manage yourself.
Reading books by yourself is a good idea, but there is a reason why courses are more effective in getting you started: they expose you to the 40% or so of the things you can find in a book, but with discipline. You attend classes, work out problems in homeworks, take exams (okay, not the best thing in the world), and more importantly, discuss with peers and your professors.
3. Take core courses seriously
There is a lot of physics in engineering courses, more than you may realize. If you are a mechanical engineer, you have excellent opportunities to learn about stress tensors, Lagrangians and Hamiltonians, thermodynamics and some statistical mechanics, etc. If you are an electrical engineer, semiconductor device physics is a playground for statistical mechanics, solid state physics and even some quantum mechanics (these days, with people in engineering research playing with things like NEGF and simulations, “some” is an understatement). There’s a lot of physics and classical mechanics in particular, in things like linear systems analysis, control system theory, and of course, RF and electromagnetism. From a practical standpoint, doing badly in engineering courses, and better in physics courses only shows lack of commitment and not physicsy brilliance.
4. Take courses on Classical Mechanics, Quantum Mechanics, Electromagnetic Theory and Statistical Mechanics
You may be able to impress people with fancy courses like quantum field theory and particle physics as an undergrad, but everyone who does any serious physics knows the importance of the four pillar courses. A good foundation in Classical Mechanics at the level of Goldstein, is more vital to a good understanding of QM, SM, EMT and even more advanced courses. I don’t have a “below Goldstein” suggestion if you didn’t do calculus in high school (in India calculus is taught in the 11th year of school, and every science student knows a good deal of calculus irrespective of whether he/she does science or engineering). But Giancoli’s books are good to finish off by the end of your freshman year if you haven’t done so before (I personally read them in 11th and 12th grade, but that’s because of the Indian system). There’s also a very tried and tested book on Mechanics by Kleppener and Kolenkow from MIT, which is worth checking out. For a first course in Quantum Mechanics, I strongly suggest being able to do almost every problem of Griffiths’s book, but for a text there is no dearth of choices. I recommend having a good library of all the ‘standard’ books (these days you can get ebooks, but its probably a good idea to have hard copies nonetheless) like Shankar, Griffiths, Sakurai, Cohen-Tannoudji, Powell and Crasemann, Townsend, Merzbacher, Gottfried to name a few. For Statistical Mechanics, I believe Reif’s two books (the non-Berkeley series one as well as the Berkeley series one), Thermal Physics by Schroeder, and of course Pathria are good choices, though over time other books such as the one by Kubo have emerged as options too.
For EM, I suggest reading Griffiths cover to cover definitely, and working out as many problems as you can (ideally, all). This will form a great foundation for starting that Bible of EM called Jackson. Something I’ve realized in graduate school is that almost everyone (including wannabe serious physicists) hate electromagnetism. This came as a surprise to me as an electrical engineering undergraduate, because EM for me was one of the most important courses, and it was taught in a way that I couldn’t dislike it. So, for me doing Jackson problems — albeit in a very limited way given the time constraints of first semester in grad school — was fun. I could not understand why electromagnetic theory, which gives you quick returns in the form of visualizable, sensible, physical predictions, and is a good way to flex your muscle with special functions, mathematical methods, computer programming, etc. is loathed so much. I can find two reasons: (a) lack of time, (b) an enormous negative reputation built up by generations of practicing physicists, graduate students. Of course, Jackson problems are hard, and you will probably benefit a lot from discussing them (instead of just looking up solutions off the web). But this is somewhere you can make yourself different from the herd. That of course doesn’t mean you should keep Jackson’s book under your pillow and have sleepless nights filled with Bessel function integrals in your head. You could choose the former, or the latter.
There is also a very nicely written graduate textbook on EM Theory by Andrew Zangwill, which is also definitely worth checking out. Having used it alongside Jackson, I will say that it complements Jackson very well, though having never taught the course or developed enough conviction about it to say such things, I cannot opine on whether it can be an adequate replacement for Jackson, which remains a source of challenging problems and insights.
5. Improve your programming skills, get familiar with Mathematica, Python, C, Matlab, etc.
6. Take difficult courses after doing the foundational courses
It helps to develop more experience by challenging yourself by taking tougher courses in theoretical physics, even if you want to end up doing experiments later. For one, it teaches you the importance of the core courses, and provides you room to apply the skills you learnt in those courses. But it also exposes you to a wider range of physics, and sometimes even some research.
7. Do research
If you end up in your sophomore or junior year as an engineering student who can’t wiggle out and do some physics, do not restrict yourself to reading books and spending time watching popular science expositions of string theory as a theory of everything which will solve global hunger and malnutrition. Instead, do research, take on projects even if they are in engineering topics. To a mature mind, there is no fundamental distinction between physics and engineering. Graduate schools and professors prefer students who have had some research exposure and possibly not even stellar grades over students who have perfect grades but have not proven themselves in an environment outside their comfort zone.
8. Form discussion groups with likeminded students, have blackboard talks, be involved, ask lots of questions! No question is a stupid question, and we all started somewhere. Hopefully people are not born knowing what supersymmetry is! I have learnt more by talking to friends doing different kinds of physics and engineering, than I have by merely reading books and following the internet.
There are of course, other administrative things like taking GREs, recommendations, etc. but I feel those are important yet clerical enough for you to be able to find adequate (and more expert) comments and treatments across the web, and hence I don’t think they merit an inclusion here.
Written by Vivek
May 24, 2014 at 11:00
Tagged with
## Gnuplot with C/C++
Sometimes, it is convenient to call gnuplot from within your own C/C++ code rather than having the code create a data file, and manually execute gnuplot every time to re-plot using the contents of the file. This is easy if you use Linux: just use a pipe. For instance:
#include <iostream> #include <stdio.h> #include <cstdlib>
using namespace std; int main(){ // Code for gnuplot pipe FILE *pipe = popen("gnuplot -persist", "w"); fprintf(pipe, "\n"); // Your code goes here
// Don't forget to close the pipe fclose(pipe); return 0; }
Note that we have had to use C routines to call gnuplot. But there’s a problem with this code: gnuplot will generate the plot only when the pipe is closed. So if you have multiple plot statements, or if you want to refresh the same plot (as for instance, in an animation scenario) you will find that the above approach will result in the plots getting asynchronously updated right at the end.
So how does one ensure that after every plot command, a plot is actually generated (or an existing one refreshed) Immediately? The key is to flush the buffer using fflush. Simply insert
fflush(pipe);
below every plot call to gnuplot. If you have an animation, then in order to make the transitions smoother, you might want to include a delay subroutine. A simple one can be built using the clock routines in time.h. For an example, click here.
Thanks to Vidushi Sharma for bringing these issues to my attention.
Written by Vivek
June 22, 2012 at 14:13
## Why V(x) = -1/x^2 has no bound state
Here we present a scaling-based argument to show that the attractive potential
$V(x) = -\frac{\lambda}{x^2}$
($\lambda > 0$), has no bound states (i.e. states with energy E < 0). Consider the Time Independent Schrodinger equation for this potential, which is the eigenvalue equation for the corresponding Hamiltonian,
$-\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} - \frac{\lambda}{x^2}V(x)\psi = E\psi$
This can be rearranged as
$\frac{d^2\psi}{dx^2} + \frac{2m\lambda}{\hbar^2}\frac{1}{x^2}\psi = -\frac{2mE}{\hbar^2}\psi$
Now, it is easy to see that the quantity
$\frac{2m\lambda}{\hbar^2}$
is dimensionless. So, this problem has no independent scale, even though naively one might think that $\lambda$ specifies a scale for this problem. We claim that for such a system, there can be no bound state. This is proved below.
Suppose we perform the scale transformation $x \rightarrow \alpha x$ where $\alpha$ is some nonzero real number, we see from the equation above that if $E$ is an eigenvalue, then so is $\alpha^2 E$.
Suppose now that a bound ground state exists, with energy $E_{G}$. By definition $E_{G} < 0$. Then scale invariance implies that $\alpha^2 E_{G}$ must also be the energy of some bound state. But
$\alpha^2 E_{G} < E_{G}$
as multiplying the negative ground state energy by a positive number only makes it more negative. This contradicts the fact that the ground state has energy $E_{G}$. In fact, we can make a stronger statement, viz. the ground state energy can be made as small as we want. Therefore, there is no finite energy ground state for this system, and consequently there can be no bound states.
Note that there is no such problem with scattering states, i.e. states with positive energy. One can take an arbitrarily small positive energy scattering state and from it obtain valid energies of the continuum of higher energy scattering states by performing a scale transformation.
Incidentally, this is why potentials like $-\lambda[\delta(x)]^2$ and $-\lambda\delta(x)/x$ also have no bound states.
Written by Vivek
February 8, 2012 at 08:48
## Evaluation of Complex Error Functions erf(z) using GSL/C
For a small QFT calculation, I needed to numerically evaluate the imaginary error function erfi(x) = erf(i x). But it turns out that GSL (and most other numerical recipe code I could find) can only deal with erf(x), where x is real. Here’s a poor man’s implementation of erf(z) through a standard Taylor expansion,
$erf(z) = \frac{2}{\sqrt{\pi}}\sum_{n = 0}^{\infty}\frac{(-1)^n z^{2n+1}}{n!(2n+1)}$
The catch here is to deal with propagation of errors in the complex Taylor series, and to also somehow benchmark the results. Well, I haven’t been able to think about this yet, but I was able to confirm that for real arguments, my Taylor series code is about as good as the GSL error function gsl_sf_erf(x).
I am working on a CUDA implementation of this now, because in my project, I need to perform a numerical integration over the error function, which is quite intensive even for Mathematica. For now, I’m just sharing the serial implementation. (Hint: if you can write wrapper for each of the gsl functions inside my Taylor series calculating method, you can embed them within a __global__ kernel call through a struct. Alternatively — and less fun — you can just parallelize the for loop.)
/* Function to compute erf(z) using a Taylor series expansion
/* Author: Vivek Saxena
/* Last updated: January 28, 2011 21:11 hrs */
#include <gsl/gsl_complex_math.h>
#include <gsl/gsl_sf_erf.h>
#include <gsl/gsl_sf_pow_int.h>
#include <gsl/gsl_sf_gamma.h>
#include <stdio.h>
#define PI 3.1415926543
double cz = 2/sqrt(PI);
const int TERMS = 10; // no of terms to use in the Taylor series
gsl_complex erfTaylor( gsl_complex z, int trunc ){
gsl_complex res = gsl_complex_rect(0,0),
num = gsl_complex_rect(0,0),
den = gsl_complex_rect(1,0),
snum = gsl_complex_rect(1,0),
temp = gsl_complex_rect(0,0);
for(int i = 0; i < trunc; i++){
snum = gsl_complex_rect( cz * gsl_sf_pow_int(-1, i), 0 );
num = gsl_complex_mul(snum, gsl_complex_pow_real(z, 2*i+1));
den = gsl_complex_rect((2*i + 1)*gsl_sf_fact(i),0);
temp = gsl_complex_div(num, den);
}
return res;
}
int main ( void ){
printf( "Real error function\n\n");
for ( float i = 0; i <= 1; i += 0.01 ){
float gslerror = gsl_sf_erf(i);
float taylor = GSL_REAL( erfTaylor( gsl_complex_rect(i, 0), 10 ) );
printf("erf(%f): gsl = %f, taylor = %f, mag error = %f\n", i, gslerror, taylor, abs(gslerror-taylor));
}
gsl_complex t, arg;
printf( "\n\nImaginary error function\n\n");
for (float i = 0; i <= 1; i += 0.01 ){
/* this would be your generic argument z in erf(z).
* so if z = x + iy, then
* arg = gsl_complex_rect(x, y);
*/
arg = gsl_complex_rect(0, i);
t = erfTaylor( arg, TERMS );
printf("erf(%f + i %f) = %f + i %f\n", GSL_REAL(arg), GSL_IMAG(arg), GSL_REAL(t), GSL_IMAG(t));
}
return 0;
}
Written by Vivek
January 28, 2011 at 21:12 | {"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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 58, "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": 0.5706217288970947, "perplexity": 806.5582979781584}, "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-2018-09/segments/1518891816841.86/warc/CC-MAIN-20180225170106-20180225190106-00343.warc.gz"} |
https://www.omnimaga.org/ti-z80-calculator-projects/calcshield-2010-(blast-antivirus-version-5-0)-beta-testers-needed/ | ### Author Topic: CalcShield 2010 (Blast AntiVirus Version 5.0) - Beta Testers Needed (Read 8503 times)
0 Members and 1 Guest are viewing this topic.
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### CalcShield 2010 (Blast AntiVirus Version 5.0) - Beta Testers Needed
« on: March 24, 2010, 06:20:46 pm »
Version 5 of my antivirus software for the TI-83+ or compatible is underway. Features will include this:
1. A single installer program uses Celtic3 to create the actual antivirus software. No more keeping track of multiple program files or groups (except Celtic3). Upon installation, the installer script will be automatically archived in the event of a crash.
2. Virus definitions stored as a program, not a string, stored in archive, and accessed through Celtic3, line by line.
3. Addition of new program names to the virus definitions manually will be supported.
4. Option to delete will be given, as opposed to Version 4, where a matching program is deleted without you being told.
5. Firewall (asm subroutine) that intercepts incoming silent-linked programs and stores their names to some variable. Then, it will compare the name to the contents of the virus definitions file and give you the reject option if a matching entry is found.
« Last Edit: March 24, 2010, 06:21:16 pm by ACagliano »
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #1 on: March 24, 2010, 08:03:14 pm »
For anyone who is interested, by the way, my previous version of the Antivirus (Version 4.0) is provided below. When I made it, I was amazed by its ability, but now, it seems horrible, thus my intent to release Version 5.0
Version 4.0: http://www.mediafire.com/?kohymtqdwew
You can email any comments or suggestions to me. (or put them here).
#### DJ Omnimaga
• Former TI programmer
• CoT Emeritus
• LV15 Omnimagician (Next: --)
• Posts: 55838
• Rating: +3151/-232
• CodeWalrus founder & retired Omnimaga founder
##### Re: Blast Antivirus Version 5.0
« Reply #2 on: March 24, 2010, 11:20:06 pm »
One thing I wonder, will the program actually check for the virus code to detect them or just the program name? I am asking since if someone was to send you a virus or if you downloaded a fake program somewhere, your program could potentially miss it if the author changed the name. With Celtic you can copy parts of code to a string and then in your program you could check if parts of that code matches antivirus code.
Also the user should be allowed to setup antivirus sensitivity so for example it checks for program names and/or parts of their code. If the antivirus reports a bad program, then the user can decide what to do with it (in case it might be false positive)
Personally I don't think I would use it much, though, since there aren't a lot of viruses for calc (ticalc.org deletes them if reported, anyway) and I never send anything to my calc when programming except maybe Mirage, Axe, Celtic III, etc, but maybe some people who have trouble at school with people sending viruses could like this.
In case you are wondering where I went, I left Omni back in 2015 to form CodeWalrus due to various reasons explained back then, but I stopped calc dev in 2016 and am now mostly active on the CW Discord server at https://discord.gg/cuZcfcF
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #3 on: March 25, 2010, 02:08:24 am »
I would like to write that in, but I would also like it to be able to decompile asm programs and check the hex for malcodes. Of course, I would need to be annoying and bug you assembly people for a subroutine, then. Maybe Basic interpretation atm.
#### Eeems
• Mr. Dictator
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• little oof
##### Re: Blast Antivirus Version 5.0
« Reply #4 on: March 25, 2010, 11:40:45 am »
Well if you knew the hex codes you could use some of Celtic III's bin->hex to figure it out.
/e
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #5 on: March 25, 2010, 12:23:11 pm »
Yep. So I humbly ask any asm programmers who are familiar with destructive hex routines to please post them here or to email them to me at [email protected]
#### SirCmpwn
• Guest
##### Re: Blast Antivirus Version 5.0
« Reply #6 on: March 25, 2010, 12:24:18 pm »
Code: [Select]
pop hlret
#### mapar007
• LV7 Elite (Next: 700)
• Posts: 550
• Rating: +28/-5
• The Great Mata Mata
##### Re: Blast Antivirus Version 5.0
« Reply #7 on: March 25, 2010, 12:28:50 pm »
Code: [Select]
ld a,1ld (appInfo+2),abcall(50CBh)ld a,\$7Ebcall(_eraseFlash)
Or something similar... (it should erase the certificate, but I'm not sure if this will work without extra Weird Stuff)
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #8 on: March 25, 2010, 12:29:38 pm »
hex?
#### SirCmpwn
• Guest
##### Re: Blast Antivirus Version 5.0
« Reply #9 on: March 25, 2010, 12:46:43 pm »
pop bc ; A1
ret ; C9
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #10 on: March 25, 2010, 12:50:17 pm »
Ok. I'll add these to the definitions file as they come in.
#### mapar007
• LV7 Elite (Next: 700)
• Posts: 550
• Rating: +28/-5
• The Great Mata Mata
##### Re: Blast Antivirus Version 5.0
« Reply #11 on: March 25, 2010, 02:52:32 pm »
This will give LOADS of false alarms. The scanner will say a program is evil every time it pop's BC before a RET, while this sometimes is required. The code will only crash your calculator when the stack level at RET is different from the stack level at the routine's entry point.
#### SirCmpwn
• Guest
##### Re: Blast Antivirus Version 5.0
« Reply #12 on: March 25, 2010, 02:54:54 pm »
BB6DA1C9 wouldn't.
#### ACagliano
• Posts: 908
• Rating: +32/-2
##### Re: Blast Antivirus Version 5.0
« Reply #13 on: March 25, 2010, 06:49:51 pm »
This will give LOADS of false alarms. The scanner will say a program is evil every time it pop's BC before a RET, while this sometimes is required. The code will only crash your calculator when the stack level at RET is different from the stack level at the routine's entry point.
Don't worry. I will configure response to that as maximum security. Under lower security, it won't respond to it. Anything else?
#### Iambian
• Coder Of Tomorrow | {"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": 0.2957046627998352, "perplexity": 11836.598019005083}, "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/1593657145436.64/warc/CC-MAIN-20200713131310-20200713161310-00159.warc.gz"} |
http://blog.felixbreuer.net/2011/11/20/mckelvey.html | # Geometry, the Majority Vote and the Power of Agenda Control
These are notes for a talk I gave both in my course at SF State and at the teach-in against police violence at UC Berkeley. The talk at the teach-in found its way on IndyMedia and YouTube (Pt 1 2).
In a democracy, people are fighting all the time over control of the political agenda. Media campaigns, protests and lobbying are all examples of people trying to shape the political discourse. They seek to get “the public” to discuss a topic they care about, they seek to shift the focus of the current political discussion towards the points they think are important or they may even want to throw up a smokescreen to divert the public from a topic they consider dangerous for them. This process is vital for a democracy to work. In fact, I want to present a mathematical argument that supports the following bold claim: This process is more important for a democracy than voting! And perhaps the most amazing thing about this observation is that this is a direct consequence of the geometry of voting.
## Policies as points in space
Political choices can often be represented by points in space. By this I mean that often, all the different policies that can be adopted with regard to a given political issue can be represented by different points in space.
As an example, let us consider budget decisions. A state’s budget can be represented by three numbers:
• the state’s revenue (e.g. taxes)
• the state’s expenditures (e.g. public spending)
• the state’s deficit
In this way, we can view every possible budget decision as a point in three-dimensional space. However, these three values are not independent of each other. Instead they are related by
deficit = spending - taxes.
This equation defines a plane in three dimensional space. All possible budgets lie in this hyperplane. To visualize how this looks consider the following three dimensional coordinate system. The axes represent spending, taxes and deficit. The budget hyperplane lies slanted in space. Its intersections with the three coordinate hyperplanes are shown as dashed lines. For example, the horizontal dashed line is the set of budgets with spending = 0. It is a diagonal in the plane spanned by the deficit and taxes axes. Similarly, the other two dashed lines are diagonals in the deficit/spending and spending/taxes coordinate hyperplanes.
As we have seen, the set of all budgets with spending = 0 forms a line in the plane of all possible budgets. Increasing or decreasing spending by, say, 1 dollar corresponds to translating this line in the plane. Taking all translates by $k$ dollars, we obatin a family of parallel lines. And if we repeat this for the lines given by taxes = 0 and deficit = 0, we obtain a triangulation of the budget plane as shown below.
This picture shows a part of this triangular lattice. It allows us to visualize what happens if we change a given budget $b$. Say $b$ is given by a spending of 3 trillion dollars, tax revenues of 2 trillion dollars and a deficit of 1 trillion dollars and suppose we increase tax revenues by 1 dollar. This corresponds to moving from $b$ to the line given by 1 trillion and one dollar of tax revenues. However, we have to make a choice here. Do we use that one extra dollar to lower the deficit or increase spending? If we go “left” in the picture, we stay on a line where the deficit remains constant but we move from one “spending line” to the next thus increasing spending. On the other hand, if we go “right” we keep spending constant and decrease the deficit.
Now that we have a means to visualize how different budget decisions relate to each other, we can use that to visualize the current positions of various political actors in the US with regard to the federal budget.
We place the 2011 federal budget in the center of our picture at the point labeled $b$. Next we draw the three lines through $b$ along which spending, taxes and deficit are constant, respectively. Both, the democrats and the republicans want to decrease the deficit. So if you asked a democrat or republican where their ideal 2012 budget would be, then they would tell you that it lies below the deficit line through $b$. Ideally, however, a democrat would like to decrease the deficit by increasing taxes, without decreasing spending. So, qualitatively, a democrat’s ideal policy would lie in the blue region. A republican, on the other hand, would want to reduce spending to finance the decrease in deficit without raising taxes. So a republican’s ideal policy would lie in the red region. There are other people, though, e.g., Keynesian economists, who think that lowering the deficit is not a priority at the moment. They think that it is much more important to stimulate the economy by lowering taxes and increasing spending, even if that means that the deficit has to increase even further. People in this comparatively small group might have an ideal budget somewhere in the green region.
We have now seen how to think geometrically about politics. Now we are going to apply this point of view to analyze the dynamics of the majority vote.
## Spatial Voting and the Power of Agenda Control
So far, we have only visualized policies as points in space. Now we come to McKelvey’s theorem, the main result I want to tell you about. To be able to state this theorem, we need to formulate a model of voting, called spatial voting.
As we discussed, every policy corresponds to a point in space. Now, spatial voting simply means the following.
• Voters are asked to decide between two alternatives, the status quo which we call $x$ and a proposed new policy $z$. Voters can vote for either of these two alternatives.
• The alternative with the most votes wins, i.e., we are having a majority vote.
• Every voter has an ideal policy in mind. So the voters can be represented by a set of points in space.
• Finally, we make a very important assumption: Every voter will vote for the alternative closest to his or her ideal policy!
Consider as an example the following picture. The black points represent the ideal policies of all voters. The blue point labeled $x$ marks the status quo, while the red point labeled $z$ marks the proposed new policy. In this example, most voters are going to vote for $z$ as $z$ is closer to their ideal than $x$. As we are running a majority vote, this means that $z$ is going to be approved and will become the new policy.
Now we can state McKelvey’s theorem.
Theorem. (McKelvey 1976) For every status quo $x$ and every other policy $z$ there exist policies $y_1,y_2,\ldots,y_k$ such that
$x$ loses against $y_1$ which loses against $y_2$ which loses against $y_3$ … which loses against $y_{k-1}$ which loses against $y_k$ which loses against $z$
in the majority vote.
What does this mean? Suppose there were someone with complete control of the agenda. This agenda controller would have absolute control over which new policies are proposed. Whenever the agenda controllers proposes a new policy, the voters would get to vote and the agenda controller would be bound by their decision according to the majority rule. This means that an agenda controller cannot decide anything. All he can control is between which alternatives the voters get to choose.
So, suppose there is an aganda controller and the current status quo is $x$. Suppose further that the agenda controller wants voters to pass a new policy $z$ that he favors (but that everybody else may hate). McKelvey’s theorem now states that there are cleverly devised policies $y_1,\ldots,y_k$ such that the agenda controller can proceed as follows. First, he proposes $y_1$. The voters get to choose between $x$ and $y_1$ and they approve $y_1$ as the new policy because the majority of voters prefers $y_1$ to $x$. Now $y_1$ is the new status quo. Next, the agenda controller proposes $y_2$ and again, the voters prefer $y_2$ over $y_1$ so they are going to adopt $y_2$ as the new status quo of their own free will. The agenda controller continues in this fashion until the voters pass $y_k$ as their new policy. Then he makes his final move and proposes $z$, the policy that he likes but that everybody else hates. However, through his previous moves, he has managed to put the public in a position where the majority actually prefers $z$ to the current status quo $y_k$. And so they are going to approve of $z$ of their own free will.
In this way, someone in control of the political agenda is in complete power, even if he is bound by the majority vote of the population. This explains why, for example, freedom of speech and the right to protest are so important parts of democracy. Protest is a way of getting a certain item on the political agenda, trying to influence the direction that current policy should take. (See here for a recent example.) Conversely, if there is a small elite who dictates the political topic of the day, then this elite will get its way, no matter if vote or not. So the morale of the story is this:
Voting alone does not give the people any power! Just by voting, you can’t control anything. You also have to have a public discussion about political topics and this is what protest is about.
At this point, it is important to stress the difference between the provocative morale that I drew from the story and the statement of the original theorem. The theorem is provably true, but applies only to a very specific abstract model of a society. In reality, no one is in absolute control of the political agenda! And the theorem tells us that this is a very good thing!
So, while the theorem does not apply to western democracies such as the USA, it can still tell us something about the real world, by way of analogy, in just the same way that a good novel can reveal a truth about the world we live in. (See the Q&A section for more about this.)
Now that we have both a formal as well as an intuitive feeling of what McKelvey’s theorem is saying, let us try to get an idea why the theorem should be true.
## The Idea behind McKelvey’s Theorem
In this section, I want to give an idea how the sequence of policies $y_1,\ldots,y_k$ are constructed. If you want, this is a proof by example, but of course it is not a complete proof of the theorem. For a thorough proof I refer the interested reader to the literature cited at the end of the Q&A section.
We work with an example in 2 dimensions. There are three voters $v_1,v_2,v_3$ whose ideal policies are given by the three black points $p_1,p_2,p_3$ in the picture. We draw the lines through any pair of these three points. The status quo is given by the blue mark in the center of this triangle formed by the voters’ ideals. So, intuitively, the current status quo $x$ seems like a pretty good compromise between the voters’ preferences.
Which policies defeat the status quo $x$ in a majority vote? Remember that the three voters will vote for the alternative closest to their ideal policy. So, for each voter, we draw a circle around that voter’s ideal policy and we choose the radius of that circle such that the cirlcle passes through the status quo $x$. Let $C_1$ be the circle around voter $v_1$’s ideal policy $p_1$. $v_1$ will prefer any policy $y$ to $x$ that lies strictly inside the circle $C_1$!
Consequently, the policies that will defeat $x$ lie in the intersection of any two of the circles shown in the picture. The area corresponding to the set of policies that defeat $x$ are shaded green in the picture. As you notice, the shaded area extends outside of the triangle spanned by the three ideal policies $p_1,p_2,p_3$. Let $L_1$ denote the line through $p_1$ and $p_2$. If we reflect $x$ at $L_1$, then we will obtain a point $x’$ at exactly the same distance to $p_1$ and $p_2$ as $x$. If we now move $x’$ inwards for a little bit, the resulting point $x”$ will lie strictly in the interior of both $C_1$ and $C_2$. Thus $x”$ will defeat $x$ in a majority vote, because both voters $v_1$ and $v_2$ will like $x”$ slightly bettern than $x$. Note, however, that for $v_3$ the new policy $x”$ is much worse than the status quo $x$. Since we are working with a majority vote, however, this is not taken into account.
As it turns out, this construction always works! We summarize this observation as follows.
For any policy $x$ and any line $L$ through two of the voters’ ideal policies, the policy $x”$ obtained by first reflecting $x$ at $L$ and then moving the reflected point back towards $L$ a tiny bit, will always defeat $x$ in a majority vote. Typically, $x”$ will be “slightly better” than $x$ for two of the voters and much worse for the third voter.
This observation is the staples of the agenda controller’s strategy for manipulating the voters. Phrased provocatively, the agenda controller’s strategy is this:
Play off different groups of voters against each other! Offer a majority of voters marginal incentives to hurt a minority really bad!
So how can an agenda controller use this strategy to get voters to vote for his favorite policy? The following figure tells it all.
We start with a status quo $x$. This we reflect $x$ along the line $L_1$ through $p_1$ and $p_2$ by playing off voters $v_1$ and $v_2$ against voter $v_3$ to get to a new policy $y_1$. Next, we reflect $y_1$ along $L_3$ by playing off $p_1$ and $p_3$ against $p_2$ to get to $y_2$. Then, we reflect $y_2$ along $L_2$, by playing off $p_2$ and $p_3$ against $p_1$. We can keep going in this fashion as long as we like. Note that in each step we give two of our voters a tiny improvement (we move towards their ideal points by a tiny bit) while at the same time making the situation much worse for the third one (we move much further away from his ideal policy). In total, we make the situation worse in every step! So if we continue this process long enough, everybody will be so unhappy with the current policy ($y_k$ will be so far away from all voters’ ideal policies) that everybody will be happy to agree to the policy $z$ that the agenda controller had in mind all along.
I find this proof striking for a number of reasons. First of all, even from this small example, you get a clear idea how the proof will proceed in the general case (even though you need a couple of technical tools like median hyperplanes). Second, for three voters, the proof requires only an elementary geometric construction that (I hope) does not scare off people who do not feel that comfortable around mathematics. Finally, and this is most remarkable, this proof gives clear instructions how someone who wants to manipulate public decision making should go about it: Play off different groups of voters against each other! The fact that many political decisions are two or higher dimensional provides the necessary room to maneuver.
(In fact, I find it striking how similar the manipulative stragtegy suggested by the geometry of voting is to how many agents on the political stage actually behave. To manipulate public opinion, they try to reduce the public discussion on an issue to a one-dimensional problem. To a choice between two alternatives. They try to hide the fact that real world problems are higher-dimensional.)
## Conclusion
I hope to have convinced you that there is merit in looking at politics from a geometric point of view. A natural consequence of this point of view is McKelvey’s theorem, which states that an agenda controller can get voters to agree to anything the agenda controller wants of their own free will. Fortunately, there are no perfect agenda controllers in real world democracies! But McKelvey’s theorem reminds us that we had better exercise the freedom we have to shape the political agenda. Because without active political debate, the right to vote alone does not give the public any power at all.
## Q&A
There are a great many things more to say about all this. Here are a few of them.
### Budgets are more complicated than this!
Of course a state’s budget is much more complex than the model I suggested above. There are many more parameters to take into account! The advantage of this model is that it captures the gist of the problem while still being low-dimensional enough so that we can draw something!
### There are some assumptions missing from McKelvey’s theorem!
That is true. First of all, McKelvey’s theorem only works in dimensions two and up. If different policies all lie on a line, then McKelvey’s theorem fails. The same thing can happen in higher dimensions if the voters’ individual preferences have a particular pattern. For example, if all voters have the exact same ideal, then agenda control won’t work. The technical assumption I omitted in the above statement, is that the median hyperplanes (whatever that is) of the the voters’ ideal policies do not all intersect in a single point. However, this assumption is not critical for the following reason: By slightly perturbing the voters ideal policies we can always guarantee that this assumption is satisfied. Also, the theorem assumes that the set of policies is all of $\mathbb{R}^n$. This is not true in the budget example, as negative values for taxes or spending do not make sense (a negative deficit is fine, though). But generalizations of McKelvey’s theorem take care of this issue (see below). Finally, the theorem assumes an odd number of voters. McKelvey argues, however, that this makes no difference, as the agenda controller can decide to participate in the vote if and only if his vote is required to make the total number of votes odd.
It should also be mentioned that McKelvey’s theorem assumes that all voters use the Euclidean distance to measure which policies they prefer. However, this assumption is not essential as McKelvey showed in a subsequent paper. (See below.)
### What generalizations of McKelvey’s theorem are there?
McKelvey generalized his theorem considerably in subsequent work. For example, he showed that if the set of policies is an arbitrary connected subset $X$ of $\mathbb{R}^n$ and each voter measures with his or her own, private notion of distance (which has to be continuous) then, still, the top cycle of the majority rule is going to be all of $X$ (i.e., agenda control works). He concludes, in his own words:
“Regardless of other voters’ preferences, any one voter with complete information of the other voters’ preferences, control of the agenda, and the ability to cast his own vote as he chooses can always construct majority paths to get anywhere in space.”
### Is protest really more important than voting?
The provocative catchphrase that “protest is more important than voting” is meant in the following sense: A political system in which people do not shape the political agenda at all but only go to vote is not democratic. In this sense, active participation in the public political discourse is at least as important as going to vote. This is not to be construed as an excuse not to go voting, however!
### Is there a mathematical proof that influencing the political agenda is more important than voting?
No. Mathematics makes statements about abstract models. McKelvey’s theorem makes a statement about a particular abstract model of a society in which the people do not influence the political agenda at all and behave in a predictable way. This statement is provably true. But “mathematics” makes no claim whatsoever about what this statement about an abstract model has to do with reality.
### How realistic is the model of society assumed in McKelvey’s theorem?
First of all: I am not a political scientist, and I do not know of any empirical research on this subject. My personal opinion, however, is the following: Western democracies such as the USA do not fit the model of McKelvey’s theorem at all. In particular there are a number of important differences:
1. In practice, all actors on the political stage constantly strive to control the agenda! So McKelvey’s theorem does not apply to practical politics, but it offers an unconventional explanation why control of the agenda is so strongly contested.
2. The theorem assumes that the agenda controller has complete information about the preferences off all voters. This is not true in practice. However, never before was so much data about personal opinions readily available to anyone with an internet connection. So one could argue that western societies are converging on the condition required for McKelvey’s theorem to apply.
3. Voters oppinions change over time. The theorem assumes that opinions are constant. I would guess, though, that the theorem could be extended to account for changing opinions.
4. There are few voting processes where voters only decide to aprove or reject a single proposition. Presidential election in the US fit this description but are too closely tied to personality to admit a reasonable parameterization by points in space. In most other public elections, the voters have to decide between many alternatives, so spatial voting does not fit either. In process of passing a bill in congress fits the model accurately, however there voters are constantly trying to control the agenda. Ballot propositions also fit the model, but again, voters have direct influence on the available propositions through the initiative system.
5. As mentioned above, the theorem makes a couple of additional technical assumptions. However, I do not think that these are essential, especially with regard to McKelvey generalizations of his theorem.
6. There is one technical assumption that deserves special mention: continuity. I do not think that it is that much of a constraint to assume that voters preferences are continuous. Rather, I think it is a significant departure from reality to assume that the space of all policies is a continuum in the first place. For a budget, this is simply false: Two budgets cannot differ infinitessimally - they can only differ by cents.
So, while McKelvey’s theorem does not prove anything about real world democracies, I think it still provides insight on how democracies work.
### There is no policy that cannot be defeated by any other policy in a majority vote, right?
Exactly! But instead of looking for a policy that cannot be defeated, we can go for the policy that is least likely to be defeated! This is the policy for which the shaded green area in circle picture above is smallest. As it turns out this so-called “strong point” of the majority game lies roughly in the center of all voters’ ideal points. More precisely, it is given by a convex combination of the voters’ preferences, where the weights of the convex combination are given by spatial power indices of the voters. This means that centrist voters have more influence on the strong point than extremist voters. (Owen and Shapley 1989)
### Where can I read more on this?
I recommend the excellent article by P.D. Straffin Jr. in the Handbook of Game Theory and Richard McKelvey’s original articles on the subject.
1. Straffin, P. D. J. (1994). Power and stability in politics. Handbook of Game Theory with Economic Applications Volume 2 (Vol. 2, pp. 1127-1151). Elsevier.
2. McKelvey, R. D. (1979). General Conditions for Global Intransitivities in Formal Voting Models. Econometrica, 47(5), 1085-1112.
3. McKelvey, R. D. (1976). Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory, 12, 472-482. | {"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": 0.4353039264678955, "perplexity": 564.549623331227}, "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-2018-30/segments/1531676591455.76/warc/CC-MAIN-20180720002543-20180720022543-00010.warc.gz"} |
https://scholarworks.iu.edu/dspace/browse?value=Friedman%2C+Daniel++P&type=author | mirage
# Browsing by Author "Friedman, Daniel P"
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• ([Bloomington, Ind.] : Indiana University, 2010-06-16)
The promise of logic programming is that programs can be written <italic>relationally</italic>, without distinguishing between input and output arguments. Relational programs are remarkably ... | {"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": 0.963342547416687, "perplexity": 19096.415994744868}, "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-2015-11/segments/1424936463104.7/warc/CC-MAIN-20150226074103-00061-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://moderndata.plot.ly/r-markdown-and-knitr-tutorial-part-2/ | # R-Markdown and Knitr Tutorial (Part 2)
In our last post we quickly went over how to create a new R-Markdown document and embed a Plotly graph in it. In this post we’ll get into more details around how to control code output using chunk options.
As shown in our previous post, for the embedded R code to be evaluated, it’ll need to be written inside a code-chunk as shown below.
### Chunk options
Knitr provides a lot of ways to control the output that shows up in the final document. We’ll highlight a few common ones.
#### Echo
echo allows control over visibility of the actual R code in a chunk. Set it to FALSE to hide the R code from showing up. Note that the code chunk will still be evaluated and any outputs mirrored in the final document. Use eval = FALSE if you do not need a code chunk to be evaluated at all.
### Message
Notice how if you use include() in a code chunk, messages from the R console are mirrored in the final document as well? By default, when knitr evaluates a code chunk, it mirrors any messages that show up in the console as well. We can turn that off using message = FALSE.
With message = TRUE
With message = FALSE
### Results
Controls the mirroring of output when a code chunk is evaluated. This includes text output as well as charts / graphs. Four values can be assigned: (see http://yihui.name/knitr/options/ for more details)
• markup – markup output using output hook
• asis – raw output
• hold – shows output after all code is evaluated
• hide – no output is shown
With results = ‘markup’
With results = ‘asis’
‘data.frame’: 32 obs. of 11 variables: $mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 …$ cyl : num 6 6 4 6 8 6 8 4 4 6 … $disp: num 160 160 108 258 360 …$ hp : num 110 110 93 110 175 105 245 62 95 123 … $drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 …$ wt : num 2.62 2.88 2.32 3.21 3.44 … $qsec: num 16.5 17 18.6 19.4 17 …$ vs : num 0 0 1 1 0 1 0 1 1 1 … $am : num 1 1 1 0 0 0 0 0 0 0 …$ gear: num 4 4 4 3 3 3 3 4 4 4 … \$ carb: num 4 4 1 1 2 1 4 2 2 4 …
With results = ‘hide’ | {"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": 0.15696139633655548, "perplexity": 1436.4081886332524}, "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-2016-30/segments/1469257824230.71/warc/CC-MAIN-20160723071024-00050-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://www.ncbi.nlm.nih.gov/pubmed/3709967?dopt=Abstract | Format
Choose Destination
Dev Biol. 1986 Jun;115(2):340-52.
Acquisition of developmental autonomy in the equatorial region of the Xenopus embryo.
Abstract
This paper describes a continuing effort to define the location and mode of action of morphogenetic determinants which direct the development of dorsal body axis structures in embryos of the frog Xenopus laevis. Earlier results demonstrated that presumptive endodermal cells in one vegetal quadrant of the 64-cell embryo can, under certain experimental conditions, induce partial or complete body axis formation by progeny of adjacent equatorial cells. (R.L. Gimlich and J.C. Gerhart, 1984, Dev. Biol. 104, 117-130). I have now assessed the importance of other blastomeres for embryonic axis formation in a series of transplantation experiments using cells from the equatorial level of the 32-cell embryo. The transplant recipients were embryos which had been irradiated with ultraviolet light before first cleavage. Without transplantation, embryos failed to develop the dorsal structures of the embryonic body axis. However, cells of these recipients were competent to respond to inductive signals from transplanted tissue and to participate in normal embryogenesis. Dorsal equatorial cells, but not their lateral or ventral counterparts, often caused partial or complete body axis development in irradiated recipients, and themselves formed much of the notochord and some prechordal and somitic mesoderm. These are the same structures that they would have formed in the normal donor. Thus, the dorsal equatorial blastomeres were often at least partially autonomous in developing according to their prospective fates. In addition, they induced progeny of neighboring host cells to contribute to the axial mesoderm and to form most of the central nervous system. The frequency with which such transplants caused complete axis formation in irradiated hosts increased when they were made at later and later cleavage stages. In contrast, the inductive activity of vegetal cells remained the same or declined during the cleavage period. These and other results suggest that the egg cytoplasmic region containing "axial determinants" is distributed to both endodermal and mesodermal precursors in the dorsal-most quadrant of the early blastula.
PMID:
3709967
DOI:
10.1016/0012-1606(86)90254-x
[Indexed for MEDLINE] | {"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": 0.8019992709159851, "perplexity": 6837.939789800066}, "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-2019-43/segments/1570986657949.34/warc/CC-MAIN-20191015082202-20191015105702-00026.warc.gz"} |
https://www.sharesong.org/xxxtentacion-voice-memo-6-changes-lyrics.htm | ## Song “XXXTENTACION: voice memo 6: changes Lyrics” from XXXTENTACION Lyrics album:
Ayy, so, yeah, I said I’m doing some crazy shit
So, alright, we write it together
What I’m gonna do is, we gon’ come up with, um
We gon come up with like 3 or 4 tracks
And then me and you gon’ decide which ones we want, Okay
If there is a track that you want, that I want
We’ll do rock paper scissors, aight man haha
So that way we don’t have to, you know what I’m saying?
Yeah, yeah
Um, we’ll do that and then we’ll write the songs together, um (Mhm-mhm)
And then whatever one, um, whatever one we come up with
Let me see, one sec
Baby, I don’t understand this
[?] can’t take this damage
Don’t worry, it’s gon’ be more, I’m gon’ put more on it
But it’s gon’ have to be like
Oh, you know how to play keys?
I know how to do what you know do to do
Aight there we go, go ahead
Also I know what you tryna do
You tryna do this, look
Ooh, this gon’ be at the end tho
[?], I can’t stand it
My heart can’t take this damage
And the way I feel, can’t manage, ooh
Yeah I don’t understand it
[?] so look, so it’s not
It’s just these four
Aight so tryna remember that
Oh what we’ll do is, we’ll just record this part
And then we’ll come back to it (Mhm-mhm)
So baby, I don’t understand it
So baby, I don’t understand it
[?], this damage
This way I feel, can’t manage
Baby, I don’t understand it
Okay so, alright so the intro
So we can’t start like that, right?
So we have to start
No, no, this part, look so
‘Cause we can’t just come in realistically
We can’t just come in, “Baby I don’t understand it”
Why not?
Do you think we can?
Why not?
Do you have a metronome on?
Baby, I don’t- baby, I don’t understand this
You’re changing, I can’t stand it
This [?], take this damage
And the way I feel, can’t manage
Ooh, baby, I don’t understand this
You’re changing, I can’t stand it
My heart can’t take this damage
And the way I feel, can’t manage
Ooh, baby, I don’t understand this
[?] how it feels
Turn away, [?]
Findin’ out ways out [?]
Girl you know I can’t really have it
Okay, so, alright, so
You like that? And then I, and then we could come back
I could leave it open, so, alright
Robby you can hear me right?
Yeah? Good! Alright, so look, this is what I’m gonna do
I’m gonna record the keys
And then I want you to record this song
It’s recording now right?
## XXXTENTACION: voice memo 6: changes Lyrics from XXXTENTACION Lyrics
XXXTENTACION: voice memo 6: changes Lyrics Lyrics are property and copyright of their owners. XXXTENTACION: voice memo 6: changes Lyrics from XXXTENTACION Lyrics only provided to serve for educational purposes and personal use.
Share Song XXXTENTACION: voice memo 6: changes Lyrics and get comment bellow: | {"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": 0.8320273756980896, "perplexity": 12614.250978007023}, "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-2020-40/segments/1600401604940.65/warc/CC-MAIN-20200928171446-20200928201446-00406.warc.gz"} |
http://latex.org/forum/viewtopic.php?f=19&t=23257 | ## LaTeX forum ⇒ LyX ⇒ 3 Parallel text
Information and discussion about LyX, a WYSIWYM editor, available for Linux, Windows and Mac OS X systems.
tavariz91
Posts: 3
Joined: Fri May 17, 2013 3:38 pm
### 3 Parallel text
Hi everybody!
I turn to you whil I cannot find what I want anywhere...
My girlfriend is currently translating Latin textes. The package "parallel" exactly makes what she wants: Latin on a side and french on the other side.
But...
She now wants to put three texts in parallel, which correspond to three versions of a same text (6 pages per text...).
What I tried:
Use parallel IN parallel: not working at all (output = white).
Make a three-column board: Not working (Works for one page only, even with the "long board" thicked.).
So... What would you do?
I don't want to tell her to come back to Ms Word ...
Regards,
tavariz91
Tags:
kaiserkarl13
Posts: 582
Joined: Tue Mar 25, 2008 5:02 pm
Location: Columbia, Missouri, USA
I would try the parcolumns package and its parcolumns environment.
Incidentally, I did not know about this package until today---one of the reasons I post to this forum is that I often learn new things!
tavariz91
Posts: 3
Joined: Fri May 17, 2013 3:38 pm
Hi!
I tried, but... It actually doesn't work.
What I get is:
File ended while scanning use of \colchunk@.<*> parcolumns.tex *** (job aborted, no legal \end found)
(This happens with and without the \end{parcolumns}); I tried to remove the column numbers in \colchunk; the pdf is generated but Lyx says "error while viewing format: (< insert your favorite export format here >)
I joined my concept file. If someone can help...
Edit: Please Note: I have just trie with the paracol package, it works perfectly for short trying texts but there are many, many, many errors with the latin texts I want to put in, I suppose it's because of the footnotes...
Attachments
parcolumns.lyx
kaiserkarl13
Posts: 582
Joined: Tue Mar 25, 2008 5:02 pm
Location: Columbia, Missouri, USA
When I removed the space between the brackets and the braces, it worked---I suspect LaTeX was interpreting that space as the argument, instead of the stuff in braces.
One of the instances in which whitespace matters!
tavariz91
Posts: 3
Joined: Fri May 17, 2013 3:38 pm
Works perfectly; thank you so much for your help!
I hope my girlfirend doesn't want to put footnotes in the text.
(They already are somewhere else in her work)
kaiserkarl13
Posts: 582
Joined: Tue Mar 25, 2008 5:02 pm
Location: Columbia, Missouri, USA
Were your footnotes \protected? If so, then you might try separating them out using \footnotemark and \footnotetext (assuming there isn't a note about footnotes in the parcolumns package documentation, which I haven't checked before writing this reply). | {"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": 0.7123245596885681, "perplexity": 5858.160018438137}, "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-2017-17/segments/1492917120338.97/warc/CC-MAIN-20170423031200-00547-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://slideplayer.com/slide/3940071/ | # 1 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.
## Presentation on theme: "1 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY."— Presentation transcript:
1 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 2-5 Measures of Variation
2 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Waiting Times of Bank Customers at Different Banks in minutes Jefferson Valley Bank Bank of Providence 6.5 4.2 6.6 5.4 6.7 5.8 6.8 6.2 7.1 6.7 7.3 7.7 7.4 7.7 8.5 7.7 9.3 7.7 10.0
3 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Jefferson Valley Bank Bank of Providence 6.5 4.2 6.6 5.4 6.7 5.8 6.8 6.2 7.1 6.7 7.3 7.7 7.4 7.7 8.5 7.7 9.3 7.7 10.0 Jefferson Valley Bank 7.15 7.20 7.7 7.10 Bank of Providence 7.15 7.20 7.7 7.10 Mean Median Mode Midrange Waiting Times of Bank Customers at Different Banks in minutes
4 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Figure 2-14 Dotplots of Waiting Times
5 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Measures of Variation Range value highest lowest value
6 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman a measure of variation of the scores about the mean (average deviation from the mean) Measures of Variation Standard Deviation
7 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Sample Standard Deviation Formula Formula 2-4 ( x - x ) 2 n - 1 S =S =
8 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Population Standard Deviation calculators can compute the population standard deviation of data 2 ( x - µ ) N =
9 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Symbols for Standard Deviation Sample Population x x n s S x x n-1 Book Some graphics calculators Some non-graphics calculators Textbook Some graphics calculators Some non-graphics calculators Articles in professional journals and reports often use SD for standard deviation and VAR for variance.
10 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Measures of Variation Variance standard deviation squared s 2 2 } Notation Sample Variance Population Variance
11 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Sample Variance Population Variance Variance Formulas ( x - x ) 2 n - 1 s 2 = (x - µ)2 (x - µ)2 N 2 =
12 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Round-off Rule for measures of variation Carry one more decimal place than is present in the original set of values. Round only the final answer, never in the middle of a calculation.
13 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value)
14 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s
15 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s = highest value - lowest value 4
16 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman minimum ‘usual’ value (mean) - 2 (standard deviation) minimum x - 2(s) maximum ‘usual’ value (mean) + 2 (standard deviation) maximum x + 2(s) Usual Sample Values
17 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman x The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
18 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman x - s x x + sx + s 68% within 1 standard deviation 34% The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
19 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman x - 2s x - s x x + 2s x + sx + s 68% within 1 standard deviation 34% 95% within 2 standard deviations The Empirical Rule (applies to bell-shaped distributions ) 13.5% FIGURE 2-15
20 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman x - 3s x - 2s x - s x x + 2s x + 3s x + sx + s 68% within 1 standard deviation 34% 95% within 2 standard deviations 99.7% of data are within 3 standard deviations of the mean The Empirical Rule (applies to bell-shaped distributions ) 0.1% 2.4% 13.5% FIGURE 2-15
21 Chapter 2. Section 2-5. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Measures of Variation Summary For typical data sets, it is unusual for a score to differ from the mean by more than 2 or 3 standard deviations.
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https://tex.stackexchange.com/questions/301237/guitar-tablatures-typesetting-with-tabs-over-9-and-double-hitting-notes | # Guitar tablatures typesetting with tabs over #9 and double hitting notes?
Many previous posts give clue on how to strike a chord, with each of the finger placements on a guitar. Also, other posts even state how to do a note by note progression like clemens shows for stairway to heaven.
All this is not enough for me. I want to make a tablature of John Frusciante's Murderers. The double problem is:
• how to show notes that are above the 9th tab?
• how to show chords that strike in more than one note in a tablature?
• maybe this can be solved with lilypond? RTFM! – nilon May 7 '16 at 4:33
• no upvotes on question, perhpas I should remove? – nilon May 22 '16 at 21:53
This answer has already been answered to some extent by clemens with his additional last comments on that other post on guitar tablature typesetting. This is just a way of tackling the issue and to solve the problem with more detail and later on it may be proper to close or erase this post, due to lack of attention or perhaps usefulness.
Summing up, it's possible to do tablatures.
The two answers are, again by clemens:
• \Str{2}{11} means eleventh fret of the second string
• \Notes\str{6}{7}\Str{3}{6}\en is a two-note chord
Still, it'd be neat to get a cue on the underlying logic to other additional elements in this code. How can the spacing between notes be controlled? We need to combine the \hsk / \sk elements together with \STr \Str \str. How would one combine them so that the notes appear the closest together?
This mwe tries to show an approximation but still fails. Because the first two combinations of notes are close to the following but not so with the next ones...
\documentclass{article}
\usepackage{musixtex,graphicx}
% custom clef
\newcommand\TAB[1]{%
\setclefsymbol{#1}{\,\rotatebox{90}{TAB}}%
\setclef{#1}9}
% internal string choosing command
% #1: string (a number from 1--6)
% #2: finger
\makeatletter
\newcommand\@str[2]{%
\ifcase#1\relax\@strerror
\or\def\@strnr{-1}%
\or\def\@strnr{1}%
\or\def\@strnr{3}%
\or\def\@strnr{5}%
\or\def\@strnr{7}%
\or\def\@strnr{9}%
\else\@strerror
\fi
\zchar\@strnr{\footnotesize#2}}
% \@strerror could be defined to issue some warning/error
% User level commands
\newcommand\STr[2]{\@str{#1}{#2}\sk} % with a full note skip
\newcommand\Str[2]{\@str{#1}{#2}\hsk} % with a half note skip
\newcommand\str[2]{\@str{#1}{#2}} % with no skip
\makeatother
\begin{document}
(0:35)
\setlength\parindent{0pt}
\begin{music}
\instrumentnumber{1}
\nobarnumbers
\TAB1
\setlines1{6}
\startpiece
\Notes\hsk\str{1}{7}\Str{5}{9}\en
\Notes\str{1}{9}\Str{5}{10}\en
\Notes\str{1}{7}\Str{5}{9}\en
\Notes\str{1}{9}\Str{5}{9}\en
\endpiece
\end{music}
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https://eprints.soton.ac.uk/424998/ | The University of Southampton
University of Southampton Institutional Repository
# A note on a system theoretic approach to a conjecture by Peller-Khrushchev: The general case
Ober, Raimund (1990) A note on a system theoretic approach to a conjecture by Peller-Khrushchev: The general case. IMA Journal of Mathematical Control and Information, 7 (1), 35-45.
Record type: Article
## Abstract
Based on the construction of infinite-dimensional balanced realizations, an alternative solution to the following inverse spectral problem is presented. Given a decreasing sequence of positive numbers (σn)n>1 (i.e. σ1≥σ2≥σ3≥... ≥0), does there exist a Hankel operator whose sequance of singular values is (σn)n>1? This paper is an extension of a previously published paper in which the same approach was taken in the case of a monotonically decreasing sequence(σn)n>1.
Full text not available from this repository.
Published date: 1 March 1990
## Identifiers
Local EPrints ID: 424998
URI: http://eprints.soton.ac.uk/id/eprint/424998
ISSN: 0265-0754
PURE UUID: 99c27f68-68ab-4df8-ac38-701e633d05e0
ORCID for Raimund Ober: orcid.org/0000-0002-1290-7430
## Catalogue record
Date deposited: 09 Oct 2018 16:30
## Contributors
Author: Raimund Ober | {"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": 0.9510824084281921, "perplexity": 3857.5658474247607}, "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-2021-39/segments/1631780057202.68/warc/CC-MAIN-20210921101319-20210921131319-00518.warc.gz"} |
https://arxiv.org/abs/1905.05094v1 | math.RA
# Title:Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective
Abstract: We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new proof of some of the results of Robeva and Boralevi et al. Orthogonal decompositions over the field of complex numbers had not been studied previously; we give an explicit description of the set of decomposable tensors using polynomial equalities and inequalities, and we begin a study of their closures. The main open problem that arises from this work is to obtain a complete description of the closures. This question is akin to that of characterizing border rank of tensors in algebraic complexity. We give partial results using in particular a connection with approximate simultaneous diagonalization (the so-called "ASD property").
Subjects: Rings and Algebras (math.RA); Computational Complexity (cs.CC); Algebraic Geometry (math.AG) Cite as: arXiv:1905.05094 [math.RA] (or arXiv:1905.05094v1 [math.RA] for this version)
## Submission history
From: Pascal Koiran [view email]
[v1] Mon, 13 May 2019 15:38:09 UTC (33 KB)
[v2] Mon, 10 Jun 2019 19:51:01 UTC (33 KB) | {"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": 0.8005496859550476, "perplexity": 806.9556276549915}, "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-2019-26/segments/1560627999800.5/warc/CC-MAIN-20190625051950-20190625073950-00146.warc.gz"} |
http://www.helpteaching.com/questions/702108/sophie-has-34-quart-of-peanut-butter-if-she-divides-the-pean | ##### Question Info
This question is public and is used in 30 tests or worksheets.
Type: Multiple-Choice
Category: Fractions and Ratios
Standards: 6.NS.A.1
Author: springfieldkb
View all questions by springfieldkb.
# Fractions and Ratios Question
View this question.
Add this question to a group or test by clicking the appropriate button below.
## Grade 6 Fractions and Ratios CCSS: 6.NS.A.1
Sophie has $3/4$ quart of peanut butter. If she divides the peanut butter into containers that hold $1/16$ quart, how many containers can she fill?
1. $3/32$
2. 3
3. 12
4. 48
You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges. | {"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": 0.15505248308181763, "perplexity": 8746.037410922158}, "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-2017-26/segments/1498128320215.92/warc/CC-MAIN-20170624031945-20170624051945-00264.warc.gz"} |
http://mathhelpforum.com/algebra/136869-1-quater-squared.html | # Math Help - 1 quater squared
1. ## 1 quater squared
If you multiply 0.5 by itself then you get a quater..... so a half squared is 1/4 .......so 1/4 square rooted is a +/- a half?
yet trying to do the inverse.....and square rooting a half = (1/2)^-1/2 is +/- 1/sqrt2
Can someone kill my silly thought process please as I am sleepy and not thinking right!
2. Originally Posted by 200001
If you multiply 0.5 by itself then you get a quater..... so a half squared is 1/4 .......so 1/4 square rooted is a +/- a half?
yet trying to do the inverse.....and square rooting a half = (1/2)^-1/2 is +/- 1/sqrt2
Can someone kill my silly thought process please as I am sleepy and not thinking right!
Hi 200001,
It's hard to find a question is all that.
Look at this progression forwards and backwards.
$\left(\frac{1}{2}\right)^2=\frac{1}{4}$
$\sqrt{\frac{1}{4}}=\frac{1}{2}$
$\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$
$\left(\frac{1}{\sqrt{2}}\right)^2=\frac{1}{2}$
As far as killing your silly thought process...well
How's this ?
3. Cool!!
I shall digest that and get my head back on straight! | {"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": 4, "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": 0.911923348903656, "perplexity": 6547.372952146079}, "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-2015-22/segments/1433195036742.18/warc/CC-MAIN-20150601214356-00101-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://billy-inn.github.io/ | Notes on Convex Optimization (5): Newton's Method
For $x\in\mathbf{dom}\ f$, the vector
is called the Newton step (for $f$, at $x$).
Minimizer of second-order approximation
The second-order Taylor approximation $\hat f$ of $f$ at $x$ is
$$\hat f(x+v) = f(x) + \nabla f(x)^T v + \frac12 v^T \nabla^2 f(x) v. \tag{1} \label{eq:1}$$
which is a convex quadratic function of $v$, and is minimized when $v=\Delta x_{nt}$. Thus, the Newton step $\Delta x_{nt}$ is what should be added to the point $x$ to minimize the second-order approximation of $f$ at $x$.
Notes on Convex Optimization (4): Gradient Descent Method
Descent methods
• $f(x^{(k+1)}) < f(x^{(k)})$
• $\Delta x$ is the step or search direction; $t$ is the step size or step length
• from convexity, $\nabla f(x)^T \Delta x <0$
General descent method.
given a starting point $x \in \mathbf{dom} \enspace f$.
repeat
- Determine a descent direction $\Delta x$.
- Line search. Choose a step size $t > 0$.
- Update. $x := x+ t\Delta x$.
until stopping criterion is satisfied
Notes on Convex Optimization (3): Unconstrained Minimization Problems
Unconstrained optimization problems are defined as follows:
$$\text{minimize}\quad f(x) \tag{1} \label{eq:1}$$
where $f: \mathbf{R}^n \rightarrow \mathbf{R}$ is convex and twice continously differentiable (which implies that $\mathbf{dom}\enspace f$ is open). We denote the optimal value $\inf_xf(x)=f(x^\ast)$, as $p^\ast$. Since $f$ is differentiable and convex, a necessary and sufficient condition for a point $x^\ast$ to be optimal is
$$\nabla f(x^\ast)=0. \tag{2} \label{eq:2}$$
Thus, solving the unconstrained minimization problem \eqref{eq:1} is the same as finding a solution of \eqref{eq:2}, which is a set of $n$ equations in the $n$ variables $x_1, \dots, x_n$. Usually, the problem must be solved by an iterative algorithm. By this we mean an algorithm that computes a sequence of points $x^{(0)}, x^{(1)}, \dots \in \mathbf{dom}\enspace f$ with $f(x^{(k)})\rightarrow p^\ast$ as $k\rightarrow\infty$. The algorithm is terminated when $f(x^{k}) - p^\ast \le \epsilon$, where $\epsilon>0$ is some specified tolerance.
[Notes on Mathematics for ESL] Chapter 10: Boosting and Additive Trees
10.5 Why Exponential Loss?
Derivation of Equation (10.16)
Since $Y\in{-1,1}$, we can expand the expectation as follows:
In order to minimize the expectation, we equal derivatives w.r.t. $f(x)$ as zero:
which gives:
[Notes on Mathematics for ESL] Chapter 6: Kernel Smoothing Methods
6.1 One-Dimensional Kernel Smoothers
Notes on Local Linear Regression
Locally weighted regression solves a separate weighted least squares problem at each target point $x_0$:
The estimate is $\hat f(x_0)=\hat\alpha(x_0)+\hat\beta(x_0)x_0$. Define the vector-value function $b(x)^T=(1,x)$. Let $\mathbf{B}$ be the $N \times 2$ regression matrix with $i$th row row $b(x_i)^T$, $\mathbf{W}(x_0)$ the $N\times N$ diagonal matrix with $i$th diagonal element $K_\lambda (x_0, x_i)$, and $\theta=(\alpha(x_0), \beta(x_0))^T$.
Then the above optimization problem can be rewritten as
Equal the derivative w.r.t $\theta$ as zero, we get
[Notes on Mathematics for ESL] Chapter 5: Basis Expansions and Regularization
5.4 Smoothing Splines
Derivation of Equation (5.12)
Equal the derivative of Equation (5.11) as zero, we get
Put the terms related to $\theta$ on one side and the others on the other side, we get
Multiply the inverse of $N^TN+\lambda\Omega_N$ on both sides completes the derivation of Equation (5.12)
Notes on Convex Optimization (2): Convex Functions
1. Basic Properties and Examples
1.1 Definition
$f:\mathbb{R}^n \rightarrow \mathbb R$ is convex if $\mathbf{dom}\ f$ is a convex set and
for all $x,y\in \mathbf{dom}\ f, 0\le\theta\le1$
• $f$ is concave if $-f$ is convex
• $f$ is strictly convex if $\mathbf{dom}\ f$ is convex and $% $ for $x,y\in\mathbf{dom}\ f,x\ne y, 0<\theta<1$
$f:\mathbb{R}^n \rightarrow \mathbb R$ is convex if and only if the function $g: \mathbb{R} \rightarrow \mathbb{R}$,
is convex (in $t$) for any $x \in \mathbf{dom}\ f, v\in\mathbb R^n$
Notes on Convex Optimization (1): Convex Sets
1. Affine and Convex Sets
Suppose $x_1\ne x_2$ are two points in $\mathbb{R}^n$.
1.1 Affine sets
line through $x_1$, $x_2$: all points
affine set: contains the line through any two distinct points in the set
[Notes on Mathematics for ESL] Chapter 4: Linear Methods for Classification
4.3 Linear Discriminant Analysis
Derivation of Equation (4.9)
For that each class’s density follows multivariate Gaussian
Take the logarithm of $f_k(x)$, we get
where $c = -\log [(2\pi)^{p/2}\lvert\Sigma\rvert^{1/2}]$ and $\mu_k^T\Sigma^{-1}x=x^T\Sigma^{-1}\mu_k$. Following the above formula, we can derive Equation (4.9) easily
[Notes on Mathematics for ESL] Chapter 3: Linear Regression Models and Least Squares
3.2 Linear Regression Models and Least Squares
Derivation of Equation (3.8)
The least squares estimate of $\beta$ is given by the book’s Equation (3.6)
From the previous post, we know that $\mathrm{E}(\mathbf{y})=X\beta$. As a result, we obtain
Then, we get
The variance of $\hat \beta$ is computed as
If we assume that the entries of $\mathbf{y}$ are uncorrelated and all have the same variance of $\sigma^2$, then $\mathrm{Var}(\varepsilon)=\sigma^2I_N$ and the above equation becomes
This completes the derivation of Equation (3.8). | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.9906136393547058, "perplexity": 531.6185338954191}, "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-2021-49/segments/1637964358233.7/warc/CC-MAIN-20211127193525-20211127223525-00526.warc.gz"} |
https://www.gradesaver.com/textbooks/math/calculus/thomas-calculus-13th-edition/chapter-14-partial-derivatives-section-14-7-extreme-values-and-saddle-points-exercises-14-7-page-843/16 | ## Thomas' Calculus 13th Edition
Two Saddle points at $(0,0) , (-2,2)$; Local minimum at $(0,2)=-12$ and Local maximum at $(-2,0)=-4$
Given: $f_x(x,y)=3x^2+6x=0, f_y(x,y)=3y^2-6y=0$ Simplify the given two equations. Critical points: $(0,0),(0,2),(-2,0), (-2,2)$ In order to solve this problem we will have to apply Second derivative test that suggests the following conditions to calculate the local minimum, local maximum and saddle points of $f(x,y)$ or $f(x,y,z)$. 1. If $D(a,b)=f_{xx}(a,b)f_{yy}(a,b)-[f_{xy}(a,b)]^2 \gt 0$ and $f_{xx}(a,b)\gt 0$ , then $f(a,b)$ is a local minimum. 2. If $D(a,b)=f_{xx}(a,b)f_{yy}(a,b)-[f_{xy}(a,b)]^2 \gt 0$ and $f_{xx}(a,b)\lt 0$ , then $f(a,b)$ is a local maximum. 3. If $D(a,b)=f_{xx}(a,b)f_{yy}(a,b)-[f_{xy}(a,b)]^2 \lt 0$ , then $f(a,b)$ is a not a local minimum or local maximum but a saddle point. $D(0,0)=f_{xx}f_{yy}-f^2_{xy}=-36$ and $D=-36 \lt 0$ Thus, Saddle point at $(0,2)$ $D(0,2)=f_{xx}f_{yy}-f^2_{xy}=36 \gt 0$ and $f_{xx} \gt 0$ So, Local minimum point at $f(0,2)=-12$ $D(-2,0)=f_{xx}f_{yy}-f^2_{xy}=36$ and $D=36 \gt 0$ and $f_{xx} \lt 0$ Thus, Local maximum point at $f(-2,0)=-4$ $D(-2,2)=f_{xx}f_{yy}-f^2_{xy}=-36$ and $D=-36 \lt 0$ Hence, Two Saddle points at $(0,0) , (-2,2)$; Local minimum at $(0,2)=-12$ and Local maximum at $(-2,0)=-4$ | {"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": 0.8956664204597473, "perplexity": 96.02098684267055}, "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-2020-16/segments/1585370505731.37/warc/CC-MAIN-20200401130837-20200401160837-00441.warc.gz"} |
https://www.e-csd.org/journal/view.php?number=382 | Home | Register | Login | Inquiries | Alerts | Sitemap |
ORIGINAL ARTICLE Commun Sci Disord. 2009;14(1): 46-57.
Reliability and Validity Analyses of the Korean version of Frenchay Aphasia Screening Test in Brain-Damaged Patients Ji-Wan Ha , Sung-Bom Pyun , Ho Young Lee , Yu-mi Hwang , and Kichun Nam` Copyright ©2009 The Korean Academy of Speech-Language Pathology and Audiology 하지완(Ji-Wan Ha)| 편성범(Sung-Bom Pyun)| 이호영(Ho Young Lee)| 황유미(Yu-mi Hwang)| 남기춘(Kichun Nam) Share : ABSTRACT Background & Objectives Early identification, diagnosis, and treatment of aphasia are important steps in maximizing rehabilitation gains. A routine screening test is an invaluable tool in the identification and appropriate referral of patients with potential communication problems. Nevertheless, there is nostandardized aphasia screening test available in Korea. The purpose of this study was to test the reliability and validity of the Korean version of the Frenchay Aphasia Screening Test (K-FAST). Methods We used test data from 50 aphasic patients and 42 non-aphasic, brain-damaged patients. An internal consistency and intra-/inter-rater reliabilities of the K-FAST were analyzed by the Cronbach’s ? value and Kendall's coefficient of concordance, respectively. A constructive validity through correlations between the total and subtest scores and a concurrent validity through correlations between the scores of the K-FAST and K-WAB were measured. The diagnostic accuracy of the K-FAST in brain-damaged patients was measured by the area under the ROC curve, while the sensitivity and specificity were evaluated using the cut-off value of the normal data. Results Results obtained in the present study were as follows: indices of the internal consistency and intra-/inter-rater reliabilities of the K-FAST showed good reliabilities. There were significantly strong correlations between the total and subtest scores of the K-FAST, and between the scores of K-WAB and K-FAST. For detecting aphasia among brain-damaged patients, the sensitivity was high while the specificity was low. Discussion & Conclusion Our results show that K-FAST could be a reliable and valid tool for screening Korean Aphasics. However, the specificity of the K-FAST appeared to be adversely affected by the characteristics of the brain-damaged patients. Keywords: 실어증 | 선별검사 | K-FAST | 신뢰도 | 타당도 aphasia | screening test | K-FAST
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http://scratchpad.wikia.com/wiki/Zachary_and_Casey%27s_True_Love | # Zachary and Casey's True Love
224,236pages on
this wiki
Zachary and Casey's True Love is a The Suite Life of Shining Time Station (Pokemon Puzzle League version) episode.
## Plot
• While Zachary and Casey are away at the party, Ash, Kevin, Falkner, Mitchie, Latoya, Kimiko, Lisa, Timon, Pumbaa, The Steamettes, Samurai, Mordecai, Rigby, Bucky, Fox, Falco and The Conductors have to take care of Marty. But Zachary's little sister causes a mess at the station. Note: Kimiko is wearing her Master Monk Guan outfit also the music that Zachary and Casey are dancing to is Amigas Cheetahs from The Cheetah Girls 2.
## Characters
• Mr. Conductor 1
• Mr. Conductor 2
• Mr. Conductor 3
• Ash Ketchum
• Kevin Whitney
• Falkner
• Mitchie Ohara
• Latoya Parker
• Kimiko Tohomiko
• Lisa Tohomiko
• Timon
• Pumbaa
• Aya
• Satsuki
• Charmaine
• Samurai
• Mordecai
• Rigby
• Bucky
• Fox
• Falco
• Zachary Evans
• Casey
• Marty Evans
## Transcript
### Part 1
• (We see Ash and the others with Zachary and Casey)
• Zachary: Just take care of Marty while we were away.
• Casey: My Shirley Fenette outfit and my nude tights give me sexiness. I'm wearing sandals by the way.
• Ash: Bye Zachary.
• Zachary: See you later, Ash.
• Marty: Now what shall i do.
• Lisa: Behave yourself Marty.
• Kimiko: You know the rules.
• Marty: Okay.
• (The Conductors appear)
• Mr. Conductor 1: You're going to babysit Marty?
• Fox: Yes. Marty is Zachary's little sister.
• Mitchie: She was born when Mr. Evans died.
• Kimiko: And Steven was his new father.
• Mr. Conductor 2: That's good.
• Mr. Conductor 3: But of course.
• Ash: We have to babysit her.
• Mr. Conductor 1: That reminds me of Thomas when he left the conductor behind.
• Kimiko: Thomas left the conductor behind?
• Mr. Conductor 1: You'll see.
• (Mr. Conductor 1 blows his whistle and Thomas and The Conductor starts)
• Mr. Conductor 1: Thomas the Tank Engine is very proud of his branch line. He thinks it's the most important part of the whole railway. His two coaches Annie and Clarabel agree with him. Annie could only take passengers but Clarabel can take passengers, luggage and the conductor. They were both old and need new paint but Thomas loves them very much. As they run backwards and forwards along the line, they sing songs to each other. When Thomas starts from the station he sings...
• Thomas: Oh, come along, we're rather late. Oh, come along, we're rather late.
• Mr. Conductor 1: And the coaches sang...
• Annie and Clarabel: We're coming along. We're coming along.
• Mr. Conductor 1: They don't mind that Thomas says to them because he know he was trying to please Sir Topham Hatt, and to know to that if Thomas is cross, he's not cross with them. One day, they have to wait for Henry's train which made Thomas very cross.
• Thomas: How could I run my line properly if Henry is always late? He doesn't realize that Sir Topham Hatt depends on me.
• Mr. Conductor 1: Thomas whistled impatiently. He wanted to leave, but he have to wait for Henry's passengers. At last Henry came.
• Thomas: Where have you been, lazybones?
• Henry: Oh dear, my system is out of order. No one understands my case. You don't know what I suffer.
• Thomas: Rubbish!
• Mr. Conductor 1: Said Thomas.
• Thomas: You're too slow. You need exercise.
• Mr. Conductor 1: The conductor blew his whistle and Thomas started so quickly that he left him behind. The conductor waved his red flag to stop Thomas, but Thomas was on his way steaming out of the station.
• Thomas: Come along, come along.
• Mr. Conductor 1: Puffed Thomas, but Clarabel didn't want to come.
• Clarabel: I've lost my nice conductor, I've lose my nice conductor.
• Mr. Conductor 1: She sobbed. Annie tried to tell Thomas what had happened.
• Annie: We haven't a conductor, we haven't a conductor!
• Mr. Conductor 1: But he was hurrying and wouldn't listen. Annie and Clarabel tried to put on their brakes, but they couldn't without their conductor.
• Annie and Clarabel: Where's our conductor? Where's our conductor?
• Mr. Conductor 1: They cried, but Thomas didn't stop till they came to a signal.
• Thomas: Bother that signal.
• Mr. Conductor 1: Said Thomas.
• Thomas: What's the matter?
• Driver: I don't know.
• Mr. Conductor 1: Said his driver.
• Driver: The conductor will tell us in a minute.
• Mr. Conductor 1: They waited and waited but the conductor didn't come.
• Thomas: Peep peep peep, where's the conductor?
• Mr. Conductor 1: Whistled Thomas.
• Annie and Clarabel: We've left him behind!
• Mr. Conductor 1: Sobbed Annie and Clarabel together. Everyone looked, and there he was running as fast as he could along the line, with his flag on one hand and his whistle in the other. He was very hot, so he had a drink, and told them that Thomas had left him behind.
• Thomas: I'm very sorry.
• Mr. Conductor 1: Said Thomas.
• Conductor: We all made mistakes.
• Mr. Conductor 1: Replied the conductor.
• Conductor 1: Look, the signal's down. We can go. Let's make up for lost time.
• Mr. Conductor 1: Annie and Clarabel were so pleased to have their conductor again, but they sang...
• Annie and Clarabel: As fast as you like, as fast as you like!
• Mr. Conductor 1: ...to Thomas all the way. They reached the end of the line quicker than ever before.
• (Thomas and The Conductor ends)
• Ash: Thomas didn't know how he left the conductor behind.
• Mr. Conductor 1: That's because he made a mishap that's all.
• (The Conductors disappear)
• Kimiko: You adorable little sister, i love you bunches.
• (Kimiko hugs Lisa)
• Lisa: Aww i love you too.
• Ash: Now there's the problem.
• (End of Part 1)
### Part 2
• (We see Zachary asking Casey to dance at the party)
• Zachary: With your idea working, Casey, may i be your dance partner for the night.
• Casey: Sure, Zachary.
• (Zachary and Casey start dancing)
• (We cut to Ash and the others with Marty)
• Ash: Now Marty. You have to be very brave indeed.
• Marty: All right.
• Kimiko: See. It's always fun to behave.
• Fox: You're right.
• Marty: Must stay calm.
• (The Conductors reappear)
• Mr. Conductor 1: Good work.
• Kimiko: Marty isn't making a mess.
• Falco: All because of you, Kimiko.
• Mr. Conductor 2: That's great.
• Mr. Conductor 3: You're really awesome.
• Mr. Conductor 1: Reminds me of Thomas' fishy experience back on the Island of Sodor.
• Mr. Conductor 1: Yes, Samurai. I'll tell you the rest of his adventures.
• (Mr. Conductor 1 blows his whistle and Thomas Goes Fishing starts)
• Mr. Conductor 1: When Thomas puffed along his branch line, he always look forward to something special. The sight of the river. As they rumble over the bridge, he would see people fishing. Thomas often wanted to stay and watch, but his driver said...
• Driver: No! What would Sir Topham Hatt say if we were late?
• Mr. Conductor 1: Every time he met another engine he say...
• Thomas: I want to fish.
• James: Engines don't go fishing.
• Thomas: Silly stick in the muds.
• Mr. Conductor 1: Thought Thomas. One day, he stopped as usual to take him water at the station by the river. Out of order.
• Thomas: Bother!
• Mr. Conductor 1: Said Thomas.
• Thomas: I'm thirsty.
• Driver: Never mind.
• Mr. Conductor 1: Said his driver.
• Driver: We'll get some water from the river.
• Mr. Conductor 1: They found a bucket and some rope and went to the bridge. Then the driver left the bucket down to the water. The bucket was old and have five holes, so they had to fill it, pull it up, and empty it into Thomas' tank as quickly as they could several times over. They finished at last.
• Thomas: That's good, that's good.
• Mr. Conductor 1: Puffed Thomas and Annie and Clarabel ran happily behind. Suddenly, Thomas began to feel a pain in his boiler. Steam began to hiss with his safety valve in an alarming way.
• Driver: There's too much steam!
• Mr. Conductor 1: Said his driver.
• Thomas: Oh dear!
• Mr. Conductor 1: Groaned Thomas.
• Thomas: I'm going to burst! I'm going to burst!
• Mr. Conductor 1: They damped down his fire and struggled on.
• Thomas: I've got such a pain, I've got such a pain!
• Mr. Conductor 1: Thomas hissed. They stopped just outside the last station, uncoupled Annie and Clarabel and ran Thomas, who was still hissing fit to burst, on a siding right out of the way. Then, while the conductor telephoned for an engine inspector, the driver found notice in large letters, which he hung on Thomas in front and behind. Danger: Keep Away. Soon, the inspector and Sir Topham Hatt arrived.
• Inspector: Cheer up, Thomas.
• Mr. Conductor 1: They said.
• Inspector: We'll soon put you right.
• Mr. Conductor 1: The driver told them what had happened.
• Inspector: So the feed pipe is blocked.
• Mr. Conductor 1: Said the inspector.
• Inspector: I'll just look in the tanks.
• Mr. Conductor 1: He climbed up and peered in, then he came down.
• Inspector: Excuse me, sir, please look in the tank and tell me what you see.
• Sir Topham Hatt: Certainly, inspector.
• Mr. Conductor 1: Replied Sir Topham Hatt. He clambered up, looked in and nearly fell off in surprise.
• Sir Topham Hatt: Inspector.
• Mr. Conductor 1: He whispered.
• Sir Topham Hatt: Can you see fish? Gracious goodness me! How did the fish get there, driver?
• Driver: We must have fished them from the river with our bucket.
• Mr. Conductor 1: Replied Thomas' driver.
• Sir Topham Hatt: Well, Thomas, so you and your driver had been fishing. But fish don't suit you. We must get them out.
• Mr. Conductor 1: They all took turns and fishing into Thomas' tank while Sir Topham Hatt looked down and told them how to do it. When they had caught all the fish, they had a lovely picnic supper of fish and chips.
• Sir Topham Hatt: Mmm. That was good.
• Mr. Conductor 1: Said Sir Topham Hatt.
• Sir Topham Hatt: But fish don't suit you, Thomas, so you mustn't do it again.
• Thomas: No, sir, I won't.
• Mr. Conductor 1: Said Thomas sadly.
• Thomas: Engines don't go fishing. It's too uncomfortable.
• (Thomas Goes Fishing ends)
• Ash: That's how Thomas got into a fishy experience.
• Mr. Conductor 1: Yes, Ash. Engines can't go fishing.
• (The Conductors disappear)
• Marty: (sleeping)
• Kimiko: It looks like Marty has fallen asleep.
• Ash: Looks today that we finished our mission.
• Others: Yeah.
• (End of Part 2)
### Part 3
• (We see Zachary and Casey still dancing to music at the party)
• Zachary: Casey, my father Steven told me about the situations.
• Casey: That's all right, Zachary. I'm not going to marry you.
• Zachary: We already have a little sister.
• (We cut to Ash, the others and Marty sleeping while the Conductors reappear)
• Mr. Conductor 1: Take a nap, everyone.
• Mr. Conductor 2: It's nighttime.
• Mr. Conductor 3: Nighty night.
• (The Conductors high 5 each other as the episode ends)
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https://quantiki.org/wiki/bqp | # BQP
BQP, in computational complexity theory, stands for "Bounded error, Quantum, Polynomial time". It denotes the class of problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/4 for all instances.
In other words, there is an algorithm for a quantum computer that is guaranteed to run in polynomial time. On any given run of the algorithm, it has a probability of at most 1/4 that it will give the wrong answer. That is true, whether the answer is YES or NO.
The choice of 1/4 in the definition is arbitrary. Changing the constant to any real number k such that 0 < k < 1/2 does not change the set BQP. The idea is that there is a small probability of error, but running the algorithm many times produces an exponentially-small chance that the majority of the runs are wrong.
The number of qubits in the computer is allowed to be a function of the instance size. For example, algorithms are known for factoring an n-bit integer using just over 2n qubits.
Quantum computers have gained widespread interest because some problems of practical interest are known to be in BQP, but suspected to be outside P. Currently, only three such problems are known:
This class is defined for a quantum computer. The corresponding class for an ordinary Turing machine plus a source of randomness is BPP.
BQP contains P and BPP and is contained in PP and PSPACE. In fact, BQP is low for PP, meaning that a PP machine achieves no benefit from being able to solve BQP problems instantly, an indication of the vast difference in power between these similar classes. | {"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": 0.8696542978286743, "perplexity": 333.45081456894945}, "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-2018-13/segments/1521257648404.94/warc/CC-MAIN-20180323161421-20180323181421-00551.warc.gz"} |
http://www.intmath.com/blog/general/bilingualism-in-politics-735 | # Bilingualism in politics
By Murray Bourne, 18 Aug 2007
We should take bilingualism in politics more seriously. On this issue, Singapore may have some lessons for the US.
After September 11, the Americans realised there was a chronic shortage of Arabic speakers in the CIA, FBI and in most arms of government. In a 2003 abc.com article, quoted in campus-watch.org: Lack of Arabic Translators Hurting U.S., it says:
Despite an aggressive effort to recruit Arabic speakers in the two years since the Sept. 11 attacks, the U.S. government still suffers from a shortage that is hampering military, diplomatic and intelligence operations in the Middle East.
The story continues:
The State Department has fewer than 60 employees fluent in Arabic, out of a total of 279 Arabic speakers. Only five have the skills to go toe-to-toe with commentators on Middle Eastern television programs, according to an advisory commission Djerejian headed.
Robert Bryce (author of the book "Cronies") in The Arabic Speaker Deficit: The Language Barrier, says:
... the U.S. embassy in Baghdad, which, by the way, is the largest U.S. embassy on the planet, has some 1,000 State Department personnel. (That number does not include all of the service workers and security providers.)
But of that 1,000 people, just 33 speak Arabic and only six are fluent in Arabic.
## The Singapore Bilingual Situation
Cut now to Singapore. There are 4 official languages in Singapore:
• English
• Mandarin
• Malay
• Tamil
Ever since Lee Kuan Yew found himself in the position of prime minister of a newly independent state some 42 years ago, Singapore has been staunchly meritocratic. Whoever is best for the job, no matter what the person's race or religion, should get that job. (Well, it's not that simple of course, but Singapore's situation is better than that of neighboring Malaysia, where there is positive discrimination towards Malays, such that it is difficult for the minority Chinese and Indians to get very far.)
So the Singapore government is an interesting racial mix. While predominantly Chinese (no problem with that, since the country itself is predominantly Chinese), there is a fair smattering of Malay and Indians in the dominant political party, the Peoples Action Party. It is difficult to ascertain whether the proportion of races in the PAP reflects that of the wider community, but at least it is not a one-race party.
There appears to be a good working relationship between the government and MUIS (Majlis Ugama Islam Singapura), the Islamic Religious Council, a statutory body set up in 1968. This relationship was tested after September 11, especially when terrorists were arrested while plotting bomb attacks in the Republic.
## Bilingualism in Singapore
Early on, Lee Kuan Yew realised that Singapore would need to be an English-speaking country to survive. However, to ensure that each ethnic group did not get swamped, the PAP introduced a "mother tongue" policy in schools. So students would get most of their education in English, but would also attend lessons delivered in their mother tongue (Chinese, Malay or Tamil) as appropriate.
The result is that most of the population is comfortable (not necessarily competent) in at least 2 languages.
Now to the bilingualism in politics part.
The politicians in Singapore conduct parliament in English. However, when they are in "the heartlands", talking with their constituents, they will most likely need to use their mother tongue and possibly will need to be able to understand one or two other languages.
## The Lee Family and Bilingualism
Lee Kuan Yew was embarrassed as a young man when he arrived in England to complete his law degree, because of his lack of Chinese language ability.
He decided when he became prime minister of Singapore to push for bilingualism in school, bilingualism in society and bilingualism in politics. He put his language where his mouth was, and proceeded to study Chinese and Malay.
Lee made sure that his own son, Lee Hsien Loong (the current prime minister) learned Chinese and Malay, as well as English. Many of the PM's speeches are in all 3 languages.
## The Lessons
I can't help feeling that the US would be in a lot less hot water if it had made much better use of the Arabic speakers in its midst, long before September 11. Cultural sensitivity is bound to improve with knowledge of others' languages and culture. I hope it's not too late.
### 6 Comments on “Bilingualism in politics”
1. Entrepreneur says:
There are a lot of Arabic speakers in the US believe me. The problem is no one wants to work for the State Department- OR- their background would not be able to stand the scrutiny.
It's completely different from what Singapore is facing in terms of growing a nation of bilingual speakers. There are millions of Arab-Americans, they are just not trusted by the US government.
The issue here is far deeper than that of language. It is a lack of, and in fact, a refusal, to understand a culture other than one's own.
2. Peter says:
How will the Arabic speakers vote in this year's US election?
Will it be a majority going for the Democrats? I can't imagine too many of them supporting the Replublicans.
They, like me, probably can't wait for Bush's term to end.
3. Tim says:
You could not wait for Bush's term to end. Now that Obama has been in office for a while are you happy with what we have now? Go ahead I will wait............. Bush did a fine job the last year he was in office the economy started declining well what goes up must come down it was just timing. ?He kept us safe not only did he keep our country safe he kept others safe and no he did not finish what his dad started he did what he had to do and I support him. Obama has lied several times in speeches about not adding to our deficit and he has added a trillion in a year and if his health care bill goes through it is projected to add 3-5 trillion in the next 20 years. Honestlymost politicians are crooks the problem is finding out who is lieing the least.
4. Li says:
Actually Tim, though I'm not the biggest fan of Obama, or anybody except Ron Paul for that matter, Bush didn't have a good enough grasp on certain aspects of the country and how it should be taken of just as much as Obama lacks the same, just different aspects. And he has not added a trillion in a year, our debt has REACHED a trillion, and his health plan will not cost 3-5 trillion, they said something like roughly 34. some odd million over the next 10 years, and I got this from what I'm sure is your "beloved" fox news.
5. charley says:
Say there Timmy, how many planes hit buildings while any other president was in office??
That is not what I would call safe.
Obama is an idiot as well, but we haven't been attacked so far. I can not remember when there were so many wars that did not amount to anything. Bush senior spent 12 years in the White House, and junior spent 8. Count the wars and divide by 20!!!
6. Joat says:
Charley...........seriously, you should learn facts before answering....first, you cannot blame Bush Jr for Sept 11 as he had only 9 months in office. It takes about a 1 1/2 to 2 years for a president to fully grasp the true state of the country and enact real policies. Second, don't give Obama any credit for not being attacked as we are far more aware of dangers then prior to Sept 11 which may be reducing such attacks. Just watch the news and hear about all the attempts that have been made or were in planning stages. Second, since when did Bush Sr spend 12 years in office? He had one term from '88 to '92. That seems like only four years to me. Maybe my math is off.
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http://mathhelpforum.com/algebra/170993-adding-subtracting-radicals.html | # Math Help - Adding and Subtracting Radicals
How would you simplify and do these problems?
(square root of) 2/5 + (square root of) 1/2
8 - (square root of) 5/7
I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
2. Originally Posted by chandler
How would you simplify and do these problems?
(square root of) 2/5 + (square root of) 1/2
8 - (square root of) 5/7
I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
Are there two separate questions there?
Is the first one $\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}~?$
3. ## Yes, two seperate
Yes, these are two different equations.
Also... How do you make the square root symbol?
4. Originally Posted by chandler
How would you simplify and do these problems?
(square root of) 2/5 + (square root of) 1/2
8 - (square root of) 5/7
I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
$\displaystyle \sqrt{\frac{2}{5}} + \sqrt{\frac{1}{2}} = \sqrt{\frac{4}{10}} + \sqrt{\frac{5}{10}}$
$\displaystyle = \frac{\sqrt{4}}{\sqrt{10}} + \frac{\sqrt{5}}{\sqrt{10}}$
$\displaystyle = \frac{\sqrt{4} + \sqrt{5}}{\sqrt{10}}$
$\displaystyle = \frac{2 + \sqrt{5}}{\sqrt{10}}$
$\displaystyle = \frac{\sqrt{10}(2 + \sqrt{5})}{10}$
$\displaystyle = \frac{2\sqrt{10} + \sqrt{50}}{10}$
$\displaystyle = \frac{2\sqrt{10} + \sqrt{25}\sqrt{2}}{10}$
$\displaystyle = \frac{2\sqrt{10} + 5\sqrt{2}}{10}$.
5. Originally Posted by chandler
How do you make the square root symbol?
$$\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}$$ gives $\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}$
6. ## Thanks guys!
One more thing...
Please do this one too: $\sqrt {\dfrac{1}{2}} + \sqrt {\dfrac{1}{2}}$ =
7. Originally Posted by chandler
One more thing...
Please do this one too: $\sqrt {\dfrac{1}{2}} + \sqrt {\dfrac{1}{2}}$ =
$\sqrt {\dfrac{1}{2}}={\dfrac{\sqrt2}{2}}$ | {"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": 13, "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": 0.8904813528060913, "perplexity": 2460.859750403805}, "config": {"markdown_headings": true, "markdown_code": false, "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-2015-27/segments/1435375094690.4/warc/CC-MAIN-20150627031814-00255-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/solubility-of-chlorophyll-and-carotenoids.412083/ | # Homework Help: Solubility of chlorophyll and carotenoids
1. Jun 24, 2010
### Puchinita5
1. The problem statement, all variables and given/known data
okay. so i did a chromotography experiment with spinach leaves. A line of pigments separated from the spinach leaves was put on the chromatography paper. Then the paper was put in petroleum ether.
It showed carotene at the top, followed by xanthophylls, then chlorophyll A, then chlorophyll B. Therefore, I concluded that the carotenoids are less polar than the chlorophylls and is more soluble than chlorophylls.
THEN, and this is what makes no sense to me, we mixed a solution of ethanol and pigment with petroleum ether, shook it, and two layers formed. A dark dark layer and a yellowish layer. The p.ether was said to be at top cuz it was less dense.
WHY does chlorophyll separate into the p.ether while the carotenoids separate into the ethanol , whereas in the first experiment it was the other way around?! I would expect that the chlorphyll would dissolve more easily in ethanol and the carotenoids would separate into the petroleum ether.
2. Relevant equations
3. The attempt at a solution
2. Jun 24, 2010
### Puchinita5
i guess i could also ask the question, why would a non-polar pigment such as carotene dissolve more readily in a more polar substance (ethanol) rather than in a more non-polar substance (petroleum ether).
3. Jun 25, 2010
### chemisttree
Carotene is known to http://pubs.acs.org/doi/abs/10.1021/ja01326a056" [Broken] in plant tissues.
Remember that these essential oils and oily pigments are present in plant tissues which is an aqueous environment. Is it likely that water-insoluble compounds like carotene exist in pure form or as microemulsions associated with natural surfactants in plant tissues? How about in your extraction?
Compare the structure of chlorophyll with that of a typical surfactant. Do you see a non polar tail and a polar head?
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https://www.physicsforums.com/threads/proved-the-equilibrium-formula.22905/ | # Proved the equilibrium formula
1. Apr 27, 2004
### Haftred
In my general chemistry class, my professor proved the equilibrium formula:
Keq = ([C]c[D]d)/([A]ab)
However, I lost my notes ; hopefully someone can help derive it for me. Thanks.
2. Apr 27, 2004
### Mitch
3. Apr 28, 2004
### Haftred
it's not proved in my book
4. Apr 28, 2004
### himanshu121
Write Law of mass action for forward and backward rxn
At equilibrium rate of forward rxn= rate of backward rxn
And $$K_{eq} = \frac{k_f}{k_b}$$
Where kf & kb represent the rate constant for fwd & bkw rxn | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9899007081985474, "perplexity": 11882.841016139062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589404.50/warc/CC-MAIN-20180716154548-20180716174548-00003.warc.gz"} |
https://mathoverflow.net/questions/193469/schreiers-formula-and-supersolvable-groups | # Schreier's formula and supersolvable groups
A finitely generated profinite group $G$ is said to satisfy Schreier's formula if for every open subgroup $L \leq_o G$ we have $d(L) = (d(G)-1)[G:L] + 1$. Here $d$ stands for the smallest cardinality of a (topological) generating set of a group.
A group $G$ is called supersolvable if if there exists a normal series: $$\{1\} = H_0 \lhd H_1 \lhd \dots \lhd H_{n-1} \lhd H_{n} = G$$ such that each $H_{i+1}/H_i$ is cyclic and $H_i \lhd G$.
A group is called prosupersolvable if it is an inverse limit of finite supersolvable groups.
Let $p$ be a prime number. As $p$-groups are supersolvable, finitely generated free pro-$p$ groups satisfy Schreier's formula. Is this essentially the only example?
• Is every finitely generated prosupersolvable group $G$ satisfying Schreier's formula is virtually a free pro-$p$ group for some prime $p$?
• I studied this 10 years ago with Auinger. I believed we proved it has an open normal free pro-p subgroup such that the quotient is a finite abelian group of exponent dividing p-1 but I will double check – Benjamin Steinberg Jan 8 '15 at 18:17
• @BenjaminSteinberg I think that your arguments work only for varieties of groups. – Pablo Jan 8 '15 at 18:33
• The paper only gives the proof for relatively free groups because we were interested in that. My memory seems to be we had a more general proof that we left out because we had a slicker proof for the relatively free case. The problem is I don't recall it yet from 10 years ago! – Benjamin Steinberg Jan 8 '15 at 18:46
• At the moment I only remember the proof if there are only finitely many prime divisors of the order of the group. – Benjamin Steinberg Jan 8 '15 at 18:59
My vague memory is that we proved with Auinger 10 years ago that a freely indexed pro-supersolvable group is virtually pro-p. We were only interested in the case of relatively free groups, which appears in http://link.springer.com/article/10.1007%2Fs00208-006-0767-2
This case admits a number of simplifications and the published version is very different from the first proof we had, which I believe worked for what you want. I can't remember the details so let me outline a special case.
Suppose first that $G$ is finitely generated (and not pro-cyclic), freely indexed and pro-supersolvable with order divisible by only finitely many primes. Then by an old result of Oltikar and Ribes http://projecteuclid.org/euclid.pjm/1102806646 the Frattini subgroup of $G$ is open. The Frattini subgroup is also pro-nilpotent. An open normal subgroup of a freely indexed group is again freely indexed. A theorem of Lubotzky says that a pro-nilpotent freely indexed (and not procyclic) group is free pro-p for some prime p. Thus a freely indexed pro-supersolvable group with order divisible by only finitely many primes has Frattini subgroup open and free pro-p for some prime p.
So one wants to show in the general case that a freely indexed pro-supersolvable groups has only finitely many prime divisors of its order.
We gave a geometric consequence for the Cayley graph of a freely indexed profinite group. Namely, any closed connected (in the sense of Ribes and Guldenhuys) subgraph of the Cayley graph contains each edge between two of its vertices. Using this, we essentially showed that such a profinite group is not a subdirect product of two profinite groups. This is how we showed a relatively free pro-supersolvable group which is freely indexed has only finitely many prime divisors. I am not sure if one can use this in general. I'd have to reread the paper more carefully or dig up some ancient versions of the paper on long lost computers to see if we really did do the general case at one point.
• Thank you very much for the detailed explaination, I was aware of the reduction to the case of infinitely many primes dividing the order. There do exist freely indexed prosolvable groups with infinitely many prime divisors, constructed by Lubotzky and v.d. Dries. But their example is not prosupersolvable... – Pablo Jan 8 '15 at 19:06
• Supersolvable is crucial here. Every finite supersolvable group is a subdirect product of groups with a normal p-subgroups corresponding quotient an abelian group of order dividing p-1. This is what we used for the relatively free case. – Benjamin Steinberg Jan 8 '15 at 19:21
• What is a relatively free profinite group? – Pablo Jan 8 '15 at 19:24
• It means it is the pro-C completion of a free group with respect to a variety of finite groups in the sense of the book of Ribes and Zalesski. Or it is the free object in the class of profinite groups satisfying some profinite identity. – Benjamin Steinberg Jan 8 '15 at 20:03
• So in this case I suspect that every occurrence of prosolvable in your answer should be prosupersolvable. – Pablo Jan 8 '15 at 20:18 | {"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": 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": 0.8898830413818359, "perplexity": 380.25765907288326}, "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-2020-45/segments/1603107912807.78/warc/CC-MAIN-20201031032847-20201031062847-00227.warc.gz"} |
http://neutronstars.utk.edu/class/p616_s21/lect23.html | # Physics 616
• Prof. Andrew W. Steiner
(or Andrew or "Dr. Steiner")
• Office hour: 103 South College, Thursday 11am
• Email: [email protected]
• Homework: Electronically as .pdf
• You may work with each other on the homework, but you must write the solution in your own words
Use down and up arrows to proceed to the next or previous slide.
## Outline
• Cosmology by Weinberg
• Cyburt et al. (2016) for BBN
## Distance Indicators
• Distance measurements are key in determining the Hubble parameter and its dependence on redshift
• Is the Hubble parameter larger or smaller at earlier times? How would you determine this?
• For nearby objects
• Trigonometric parallax
• Photometric parallax
• Red clump stars
• RR Lyrae stars
• Eclipsing binaries
• Cepheid variables
• Confusion between "peculiar motion" and Hubble expansion
## Distance Indicators I - Tully-Fisher
Phenomenological correlation between angular velocity of stars in a galaxy around center and the luminosity of that galaxy Standard correlation includes only stars Slightly different correlations in different bands Found tighter correlation when luminosity includes stars and gas Mass $\propto v^{3-4}$ Originally applied to spiral galaxies, applied to ellipticals in "Faber-Jackson" relation Also evidence for dark matter Tully and Fisher (1977), this figure from Karachentsev et al. (2002)
## Distance Indicators II - Type Ia supernova
White dwarf always has a mass near the Chandrasekhar limit Luminosity correlated with rise and decline time of the emitted light Emitted light is from the decay of Nickel-56 "Phillips relationship" In detail, $$M_{\mathrm{max}}(B) = -21.7 + 2.7 \Delta m_{15}(B)$$ Calibrate correlation with other distance measurements "Standardizable candle" From Phillips
## More General Cosmological Models
• The Friedmann equations give $$\rho = \frac{3 H_0^2}{8 \pi G} \left[ \Omega_{\Lambda} + \Omega_M \left( \frac{a_0}{a}\right)^3 + \Omega_R \left(\frac{a_0}{a}\right)^4\right]$$ with $$\rho_{V0} = \frac{3 H_0^2 \Omega_{\Lambda}}{8 \pi G}, \quad \rho_{M0} = \frac{3 H_0^2 \Omega_{M}}{8 \pi G}, \quad \rho_{R0} = \frac{3 H_0^2 \Omega_{R}}{8 \pi G},$$ and $$\Omega_{\Lambda} + \Omega_M + \Omega_R = 1-\Omega_K$$ and $$\Omega_K = -\frac{K}{a_0^2 H_0^2}$$
• Using the Friedmann equation $$\dot{a}^2 + K = \frac{8 \pi G \rho a^2}{3}$$
## More General Cosmological Models II
• ...and defining $x \equiv a/a_0$, we get $$dt = \frac{dx}{H_0 x \sqrt{\Omega_{\Lambda} + \Omega_K x^{-2} + \Omega_M x^{-3}+ \Omega_R x^{-4}}}$$
• Define $t=0$ to be at $z=\infty$ and we have $a/a_0 = 1/(1+z)$ so $$dt = \frac{-dz}{H_0 (1+z) \sqrt{\Omega_{\Lambda} + \Omega_K (1+z)^{2} + \Omega_M (1+z)^{3}+ \Omega_R (1+z)^{4}}}$$ thus the age of the universe is $$t = \frac{1}{H_0} \int_0^{1} \frac{dx}{x \sqrt{\Omega_{\Lambda} + \Omega_K x^{-2} + \Omega_M x^{-3}+ \Omega_R x^{-4}}}$$
• This can be integrated in the approximation that $$\Omega_R \approx \Omega_K = 0$$
## Cosmic Microwave Background
• Energy density in radiation is $$U = \frac{8 \pi^5 k_B^4 T^4}{15 h^3 c^3}$$ which gives $$\Omega_{\gamma} \equiv \frac{\rho_{\gamma 0}}{\rho_{0,\mathrm{crit}}} = 2.47 \times 10^{-5} h^{-2}$$ where $$H = 100~h~\mathrm{km}/\mathrm{Mpc}/\mathrm{s}$$ which naturally implies that $\Omega_{\gamma}$ is too small enough to be ignored in the current epoch.
## Cosmic Microwave Background
• Neutrinos increase this energy density by about a factor of two
• The present number density of photons is $$n_{\gamma} = \frac{30 \zeta(3) a_B T^3}{\pi^4 k_B} = \frac{410~\mathrm{photons}}{\mathrm{cm}^3}$$
• Compare to baryons, $$n_B = \frac{3 \Omega_B H_0^2}{8 \pi G m_N} = 1.1 \times 10^{-5} \Omega_B h^2 ~\mathrm{nucleons}/\mathrm{cm}^3$$
• Current values of baryon-to-photon ratio actually a few $\times 10^{-10}$
## Recombination
• Matter and radiation decoupled when electrons and protons combine at $z=1100$ and $T=4000~\mathrm{K}$ and $t=360,000~\mathrm{yr}$.
• Rough estimate from Saha equation for $$p + e \leftrightarrow H + \gamma$$ is $$\frac{n_p n_e}{n_{\mathrm{H}}} = \left( \frac{m_e k_B T}{2 \pi \hbar^2} \right) \exp \left( - \frac{E_I}{k_B T}\right)$$ where $E_I$ is the ionization energy $13.6~\mathrm{eV}$ of hydrogen.
• In reality, excited states (2p, 2s) make a contribution
• Deviations from equilibrium impact these results at the 10% level
## Dipole Anisotropy
• CMB provides a frame of reference, solar system moves relative to this
• Number of photons is Lorentz invariant, so boost momenta $$| \mathbf{p} | = \left(\frac{1+\beta \cos \theta}{\sqrt{1-\beta^2}}\right) | \mathbf{p}^{\prime} | =$$ and this results in $$T^{\prime} = T \left(\frac{1+\beta \cos \theta}{\sqrt{1-\beta^2}}\right)$$
• Solar system "barycenter" has velocity of 370 km/s (0.1% of $c$) relative to CMB
• Local group of galaxies moves at 630 km/s relative to the CMB
## Sunayev-Zel'dovich effect
• Are CMB photons completely unimpeded by the time they reach the observer?
• No, galaxies contain high-temperature (but low-density) electrons
• Inverse Compton scattering increases the photon energy
• Change in temperature (for $\omega/k_B T_{\gamma} \ll 1$) $$\frac{\Delta T_{\gamma}}{T_{\gamma}} = \frac{\Delta N_{\gamma}}{N_{\gamma}} = - \frac{2 \sigma_T}{m_e c^2} \int~d\ell~n_e(\ell)~k_B T_e(\ell)$$
• Measure $n_e$ from X-ray observations, then use S-Z effect to determine $H_0$
## Big Bang Nucleosynthesis
• Neutron-to-proton ratio nearly equal until 1 second
• Protons slightly favored over neutrons from Saha equation
• Saha equation is relationship between chemical potentials in thermal equilibrium, in this case, $$\mu_n + m_n = \mu_p + m_p + \mu_e$$
• Freeze out (interactions slower than expansion) at $T\sim 0.8~\mathrm{MeV}$
• Competition between fusion and neutron decay leads to 25% deuterium by mass, 75% protons and trace amounts of helium-3, deuterium, lithium-7, etc.
• Uncertainty in neutron lifetime caused difficulties for early models
• These abundances strongly determined by baryon-to-photon ratio
## Big Bang Nucleosynthesis II
More helium-4 in the universe than can be explained by stellar evolution Deuterium is difficult to create (low binding energy) Observational determinations generally agree with model predictions based on CMB determinations of $\eta$ Except lithium 7, "no solution that is either not tuned or requires substantial departures from standard model physics" Cyburt et al. (2016) Stellar depletion of lithium-7 to explain why observed value is smaller than BBN prediction From NASA
## Big Bang Nucleosynthesis III
• 7 protons for each neutron
• Begin with $$n + p \rightarrow d + \gamma$$ but deuteron binding energy is small so photon breakup is significant until the deuterium bottleneck is resolved
• All neutrons end up in helium-4 $$Y_{\mathrm{helium}-4} = \frac{2(n/p)}{1+(n/p)} \approx 0.25$$
• An accurate fit is $$\eta_{10} = 273.3036 \Omega_B h^2 \left(1 + 7.16958\times10^{-3} Y_p \right) \left(\frac{2.7255~\mathrm{K}}{T_{\gamma}^0}\right)^3$$ where $T_{\gamma}^0$ is the current photon temperature
## Cold Dark Matter
• Cold if (i) non-relativistic, and (at the time of radiation-matter equality) (ii) dissipationless and (iii) collisionless
• Cold dark matter leads to bottom-up structure formation
• Bottom-up: small objects clump first, then merge to form larger object
• What is the opposite of "bottom-up"?
• WIMPs and axions
## WIMP Miracle
• Weak interaction magically provides good dark matter candidates
• Weak scale, $m_W \sim 100~\mathrm{GeV}$
• Weak coupling, $G_F~\sim 10^{-5}~\mathrm{GeV}^{-2}$
• Density of dark matter particles $$\frac{d (na^3)}{dt} = -n^2 a^3 \left<\sigma v\right>$$ or $$n a^3 = \frac{n(t_1) a^3(t_1)}{1+ n(t_1) a^3(t_1) \int_{t_1}^{\infty} \left<\sigma v\right> a^{-3}(t) dt^{\prime}}$$
• Turns out that $$\left<\sigma v\right> \sim G_F^2 m_W^2$$ gives almost exactly the right result
## Group Work
• shuffle list Group 1: Spokesperson: Erich Bermel Tuhin Das Ibrahim Mirza Group 2: Spokesperson: Jason Forson Satyajit Roy Group 3: Spokesperson: Leonard Mostella Andrew Tarrence
• In BBN, at freezeout, the neutron to proton ratio is determined by the Saha equation. Presume that the electron contribution is negligable, thus $\mu_n + m_n = \mu_p + m_p$ and that $n \propto \exp (\mu_i/T)$. What is the neutron to proton ratio at freezeout ($T=0.8~\mathrm{MeV}$) ?
• BBN is delayed until fusion can overcome the "deuterium bottleneck". Cyburt et al. states that this temperature is approximately when $$\eta^{-1} \exp(-E_B/T) = 1$$ where $E_B$ is the binding energy of the deuteron and $\eta$ is the baryon-to-photon ratio. What is $T$? | {"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": 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": 0.9528747797012329, "perplexity": 3349.8800301877077}, "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-2021-21/segments/1620243992440.69/warc/CC-MAIN-20210517180757-20210517210757-00550.warc.gz"} |
https://www.ojdo.de/wp/2014/08/how-to-use-custom-colours-in-latex/ | # How to use custom colours in LaTeX
I will post short minimum working examples (MWEs) of minimal LaTeX documents, showing a certain feature in action. Though the well-maintained LaTeX Wikibook is a much more extensive resource than a collection of such examples could ever be, they show directly compilable examples compared to isolated snippets.
I start simple: custom text colours, using different colour models. Shown here are RGB (0-255) and HTML (00-FF) style definitions. The text shows two different ways to access them. Bonus: these colours can be used in TikZ as well.
\documentclass{article}
\usepackage{xcolor}
\definecolor{cool}{RGB}{0, 110, 220}
\definecolor{heat}{RGB}{240, 120, 40}
\definecolor{pink}{HTML}{FF00FF}
\begin{document}
I am some \textcolor{heat}{really hot},
though \textcolor{cool}{also cold} text.
{\color{pink}Bright colors} are discouraged.
\end{document} | {"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": 0.4245748519897461, "perplexity": 12461.444483476062}, "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/1552912201329.40/warc/CC-MAIN-20190318132220-20190318153617-00012.warc.gz"} |
http://docs.gl/gl3/glPixelStore | # glPixelStore
## Name
glPixelStore — set pixel storage modes
## C Specification
void glPixelStoref( GLenum pname, GLfloat param);
void glPixelStorei( GLenum pname, GLint param);
## Parameters
pname
Specifies the symbolic name of the parameter to be set. Six values affect the packing of pixel data into memory: GL_PACK_SWAP_BYTES, GL_PACK_LSB_FIRST, GL_PACK_ROW_LENGTH, GL_PACK_IMAGE_HEIGHT, GL_PACK_SKIP_PIXELS, GL_PACK_SKIP_ROWS, GL_PACK_SKIP_IMAGES, and GL_PACK_ALIGNMENT. Six more affect the unpacking of pixel data from memory: GL_UNPACK_SWAP_BYTES, GL_UNPACK_LSB_FIRST, GL_UNPACK_ROW_LENGTH, GL_UNPACK_IMAGE_HEIGHT, GL_UNPACK_SKIP_PIXELS, GL_UNPACK_SKIP_ROWS, GL_UNPACK_SKIP_IMAGES, and GL_UNPACK_ALIGNMENT.
param
Specifies the value that pname is set to.
## Description
glPixelStore sets pixel storage modes that affect the operation of subsequent glReadPixels as well as the unpacking of texture patterns (see glTexImage1D, glTexImage2D, glTexImage3D, glTexSubImage1D, glTexSubImage2D, glTexSubImage3D).
pname is a symbolic constant indicating the parameter to be set, and param is the new value. Six of the twelve storage parameters affect how pixel data is returned to client memory. They are as follows:
GL_PACK_SWAP_BYTES
If true, byte ordering for multibyte color components, depth components, or stencil indices is reversed. That is, if a four-byte component consists of bytes $b 0$, $b 1$, $b 2$, $b 3$, it is stored in memory as $b 3$, $b 2$, $b 1$, $b 0$ if GL_PACK_SWAP_BYTES is true. GL_PACK_SWAP_BYTES has no effect on the memory order of components within a pixel, only on the order of bytes within components or indices. For example, the three components of a GL_RGB format pixel are always stored with red first, green second, and blue third, regardless of the value of GL_PACK_SWAP_BYTES.
GL_PACK_LSB_FIRST
If true, bits are ordered within a byte from least significant to most significant; otherwise, the first bit in each byte is the most significant one.
GL_PACK_ROW_LENGTH
If greater than 0, GL_PACK_ROW_LENGTH defines the number of pixels in a row. If the first pixel of a row is placed at location $p$ in memory, then the location of the first pixel of the next row is obtained by skipping
components or indices, where $n$ is the number of components or indices in a pixel, $l$ is the number of pixels in a row (GL_PACK_ROW_LENGTH if it is greater than 0, the $width$ argument to the pixel routine otherwise), $a$ is the value of GL_PACK_ALIGNMENT, and $s$ is the size, in bytes, of a single component (if $a < s$, then it is as if $a = s$). In the case of 1-bit values, the location of the next row is obtained by skipping
components or indices.
The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format GL_RGB, for example, has three components per pixel: first red, then green, and finally blue.
GL_PACK_IMAGE_HEIGHT
If greater than 0, GL_PACK_IMAGE_HEIGHT defines the number of pixels in an image three-dimensional texture volume, where image'' is defined by all pixels sharing the same third dimension index. If the first pixel of a row is placed at location $p$ in memory, then the location of the first pixel of the next row is obtained by skipping
components or indices, where $n$ is the number of components or indices in a pixel, $l$ is the number of pixels in a row (GL_PACK_ROW_LENGTH if it is greater than 0, the $width$ argument to glTexImage3D otherwise), $h$ is the number of rows in a pixel image (GL_PACK_IMAGE_HEIGHT if it is greater than 0, the $height$ argument to the glTexImage3D routine otherwise), $a$ is the value of GL_PACK_ALIGNMENT, and $s$ is the size, in bytes, of a single component (if $a < s$, then it is as if $a = s$).
The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format GL_RGB, for example, has three components per pixel: first red, then green, and finally blue.
GL_PACK_SKIP_PIXELS, GL_PACK_SKIP_ROWS, and GL_PACK_SKIP_IMAGES
These values are provided as a convenience to the programmer; they provide no functionality that cannot be duplicated simply by incrementing the pointer passed to glReadPixels. Setting GL_PACK_SKIP_PIXELS to $i$ is equivalent to incrementing the pointer by $i n$ components or indices, where $n$ is the number of components or indices in each pixel. Setting GL_PACK_SKIP_ROWS to $j$ is equivalent to incrementing the pointer by $j m$ components or indices, where $m$ is the number of components or indices per row, as just computed in the GL_PACK_ROW_LENGTH section. Setting GL_PACK_SKIP_IMAGES to $k$ is equivalent to incrementing the pointer by $k p$, where $p$ is the number of components or indices per image, as computed in the GL_PACK_IMAGE_HEIGHT section.
GL_PACK_ALIGNMENT
Specifies the alignment requirements for the start of each pixel row in memory. The allowable values are 1 (byte-alignment), 2 (rows aligned to even-numbered bytes), 4 (word-alignment), and 8 (rows start on double-word boundaries).
The other six of the twelve storage parameters affect how pixel data is read from client memory. These values are significant for glTexImage1D, glTexImage2D, glTexImage3D, glTexSubImage1D, glTexSubImage2D, and glTexSubImage3D
They are as follows:
GL_UNPACK_SWAP_BYTES
If true, byte ordering for multibyte color components, depth components, or stencil indices is reversed. That is, if a four-byte component consists of bytes $b 0$, $b 1$, $b 2$, $b 3$, it is taken from memory as $b 3$, $b 2$, $b 1$, $b 0$ if GL_UNPACK_SWAP_BYTES is true. GL_UNPACK_SWAP_BYTES has no effect on the memory order of components within a pixel, only on the order of bytes within components or indices. For example, the three components of a GL_RGB format pixel are always stored with red first, green second, and blue third, regardless of the value of GL_UNPACK_SWAP_BYTES.
GL_UNPACK_LSB_FIRST
If true, bits are ordered within a byte from least significant to most significant; otherwise, the first bit in each byte is the most significant one.
GL_UNPACK_ROW_LENGTH
If greater than 0, GL_UNPACK_ROW_LENGTH defines the number of pixels in a row. If the first pixel of a row is placed at location $p$ in memory, then the location of the first pixel of the next row is obtained by skipping
components or indices, where $n$ is the number of components or indices in a pixel, $l$ is the number of pixels in a row (GL_UNPACK_ROW_LENGTH if it is greater than 0, the $width$ argument to the pixel routine otherwise), $a$ is the value of GL_UNPACK_ALIGNMENT, and $s$ is the size, in bytes, of a single component (if $a < s$, then it is as if $a = s$). In the case of 1-bit values, the location of the next row is obtained by skipping
components or indices.
The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format GL_RGB, for example, has three components per pixel: first red, then green, and finally blue.
GL_UNPACK_IMAGE_HEIGHT
If greater than 0, GL_UNPACK_IMAGE_HEIGHT defines the number of pixels in an image of a three-dimensional texture volume. Where image'' is defined by all pixel sharing the same third dimension index. If the first pixel of a row is placed at location $p$ in memory, then the location of the first pixel of the next row is obtained by skipping
components or indices, where $n$ is the number of components or indices in a pixel, $l$ is the number of pixels in a row (GL_UNPACK_ROW_LENGTH if it is greater than 0, the $width$ argument to glTexImage3D otherwise), $h$ is the number of rows in an image (GL_UNPACK_IMAGE_HEIGHT if it is greater than 0, the $height$ argument to glTexImage3D otherwise), $a$ is the value of GL_UNPACK_ALIGNMENT, and $s$ is the size, in bytes, of a single component (if $a < s$, then it is as if $a = s$).
The word component in this description refers to the nonindex values red, green, blue, alpha, and depth. Storage format GL_RGB, for example, has three components per pixel: first red, then green, and finally blue.
GL_UNPACK_SKIP_PIXELS and GL_UNPACK_SKIP_ROWS
These values are provided as a convenience to the programmer; they provide no functionality that cannot be duplicated by incrementing the pointer passed to glTexImage1D, glTexImage2D, glTexSubImage1D or glTexSubImage2D. Setting GL_UNPACK_SKIP_PIXELS to $i$ is equivalent to incrementing the pointer by $i n$ components or indices, where $n$ is the number of components or indices in each pixel. Setting GL_UNPACK_SKIP_ROWS to $j$ is equivalent to incrementing the pointer by $j k$ components or indices, where $k$ is the number of components or indices per row, as just computed in the GL_UNPACK_ROW_LENGTH section.
GL_UNPACK_ALIGNMENT
Specifies the alignment requirements for the start of each pixel row in memory. The allowable values are 1 (byte-alignment), 2 (rows aligned to even-numbered bytes), 4 (word-alignment), and 8 (rows start on double-word boundaries).
The following table gives the type, initial value, and range of valid values for each storage parameter that can be set with glPixelStore.
pname Type Initial Value Valid Range
GL_PACK_SWAP_BYTES boolean false true or false
GL_PACK_LSB_FIRST boolean false true or false
GL_PACK_ROW_LENGTH integer 0 $0 ∞$
GL_PACK_IMAGE_HEIGHT integer 0 $0 ∞$
GL_PACK_SKIP_ROWS integer 0 $0 ∞$
GL_PACK_SKIP_PIXELS integer 0 $0 ∞$
GL_PACK_SKIP_IMAGES integer 0 $0 ∞$
GL_PACK_ALIGNMENT integer 4 1, 2, 4, or 8
GL_UNPACK_SWAP_BYTES boolean false true or false
GL_UNPACK_LSB_FIRST boolean false true or false
GL_UNPACK_ROW_LENGTH integer 0 $0 ∞$
GL_UNPACK_IMAGE_HEIGHT integer 0 $0 ∞$
GL_UNPACK_SKIP_ROWS integer 0 $0 ∞$
GL_UNPACK_SKIP_PIXELS integer 0 $0 ∞$
GL_UNPACK_SKIP_IMAGES integer 0 $0 ∞$
GL_UNPACK_ALIGNMENT integer 4 1, 2, 4, or 8
glPixelStoref can be used to set any pixel store parameter. If the parameter type is boolean, then if param is 0, the parameter is false; otherwise it is set to true. If pname is a integer type parameter, param is rounded to the nearest integer.
Likewise, glPixelStorei can also be used to set any of the pixel store parameters. Boolean parameters are set to false if param is 0 and true otherwise.
## Errors
GL_INVALID_ENUM is generated if pname is not an accepted value.
GL_INVALID_VALUE is generated if a negative row length, pixel skip, or row skip value is specified, or if alignment is specified as other than 1, 2, 4, or 8.
## Associated Gets
glGet with argument GL_PACK_SWAP_BYTES
glGet with argument GL_PACK_LSB_FIRST
glGet with argument GL_PACK_ROW_LENGTH
glGet with argument GL_PACK_IMAGE_HEIGHT
glGet with argument GL_PACK_SKIP_ROWS
glGet with argument GL_PACK_SKIP_PIXELS
glGet with argument GL_PACK_SKIP_IMAGES
glGet with argument GL_PACK_ALIGNMENT
glGet with argument GL_UNPACK_SWAP_BYTES
glGet with argument GL_UNPACK_LSB_FIRST
glGet with argument GL_UNPACK_ROW_LENGTH
glGet with argument GL_UNPACK_IMAGE_HEIGHT
glGet with argument GL_UNPACK_SKIP_ROWS
glGet with argument GL_UNPACK_SKIP_PIXELS
glGet with argument GL_UNPACK_SKIP_IMAGES
glGet with argument GL_UNPACK_ALIGNMENT | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 77, "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": 0.4596828520298004, "perplexity": 1744.6592489603543}, "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-2017-13/segments/1490218187717.19/warc/CC-MAIN-20170322212947-00001-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://imps.mcmaster.ca/manual/node19.html | Next: 15. The Iota Constructor Up: 2. User's Guide Previous: 13. Simplification
Subsections
# 14. Macetes
In addition to its simplifier, IMPS also provides a separate mechanism for manipulating formal expressions by applying theorems. Unlike simplification, it is under the control of the user. The basic idea is that some expression manipulation procedures--for instance, conditional rewrite rules--are in fact direct applications of theorems. Other expression manipulation procedures can be formed from existing ones using a simple combination language. These expression manipulation procedures are called macetes.14.1 Formally, a macete is a function M which takes as arguments a context and an expression e (called the source expression) and returns another expression (called the replacement expression). In general, the replacement expression does not have to be equal to the source expression.
Macetes serve two somewhat different purposes:
• They are a straightforward way to apply a theorem or a collection of theorems to a sequent in a deduction graph.
• They are also a mechanism for computing with theorems.
# 14.1 Classification
A macete can be atomic or compound. Compound macetes are obtained by applying a macete constructor to a list of one or more macetes.
Atomic macetes are classified as:
• Schematic macetes. A schematic macete is one in which the replacement expression is obtained from the source expression by matching and substitution. Schematic macetes can be thought of as conditional rewrite rules.
• Procedural macetes. These are macetes which compute the replacement expression by a more complicated procedure. There are only a few such procedures:
• simplify
• beta-reduce
• beta-reduce-insistently
Having these procedures as macetes allows you to build more powerful and useful compound macetes.
Macetes can be also classified according to the relation between the source and replacement expressions.
• Bidirectional. Whatever the context and source expression, the replacement expression is quasi-equal to the source expression, that is, given any legitimate model in which the context assumptions are true, either both source expression and replacement expression have no value or their value is identical.
• Backward-directional. Whatever the context and source expression, the replacement expression is quasi-equal to or implies the source expression. Notice that implication only makes sense for formulas of sort
• Nondirectional. There are contexts and source expressions in which the target expression is neither quasi-equal to nor implies the source expression.
# 14.2 Atomic Macetes
## 14.2.1 Schematic Macetes
A schematic macete can be associated to any formula in two ways depending on the kind of matching procedure used. IMPS has two general forms of matching called expression matching and translation matching.
Let us consider first the case of expression matching. To any IMPS formula we can associate:
• A source pattern. This is an expression s.
• A replacement pattern. This is an expression r.
• A list of condition patterns. This is a list of expressions
• A direction specifier: this specifier can be either bidirectional or backward-directional.
Suppose the formula is where itself is not a universal formula. The patterns are extracted from depending on the form of as described by the following table:
Form Source Replacement Conditions Spec. t1 t2 Bid. t1 t2 Bid. Bid. None Back. t1 t2 None Bid. t1 t2 None Bid. None Bid. None Bid. None Bid.
Notes
• If the replacement pattern according to the above table is of sort and contains free variables not occurring freely in the source pattern then consider instead the replacement pattern
• Nested implications are treated as single implications when applying the above table.
• In those cases marked with if t2 contains free variables which do not occur freely in t1, then consider instead the source pattern t1 = t2 or and replacement pattern or
We now describe how a schematic macete M is obtained from the source, replacement, condition patterns, and direction specifier of a formula. Given a context and an expression t, the result of applying M to and t is determined as follows: Let be the set of paths to subexpressions elof t which satisfy all of the following conditions:
• If the directional specifier is backward-directional, the parity of lmust be +1; otherwise, no condition is imposed on the path.
• The source pattern s matches el. Thus there is a substitution such that applied to s gives el.
• The validity of all the convergence requirements of the substitution and all the formulas in the context localized at the path l are called the minor premises generated by the macete application. These formulas may or may not generate applicability conditions:
• If the macete is being applied with the accumulation of minor premises, then these formulas are posted as new sequents and must be proven separately. No new applicability conditions are generated in this case.
• Otherwise, the minor premises must be recognized as valid by the simplifier.
• No smaller path satisfies the preceding conditions.
The replacement formula is obtained by replacing each subexpression el by Macetes obtained in this way are called elementary macetes.
Whenever you enter a theorem into a theory, the associated schematic macete is automatically installed, so that you can use it in deductions by hitting the key m.
The case of translation matching is similar, but instead of considering only convergence requirements, we need to insure that the translation component of the translation match is a theory interpretation. Macetes obtained in this way are called transportable macetes. The use of a theorem as a transportable macete must be entered into its usage list when the theorem is entered.
## 14.2.2 Nondirectional Macetes
Frequently it is useful to construct a schematic macete from an arbitrary formula by using a matching and substitution procedure which does not obey the variable capturing protections and other restrictions of normal matching. We refer to this as nullary matching and substitution. For instance, to apply a theorem which involves quantification over functions, one often has to build a lambda-abstraction of a sub-expression. We shall see later on how this can be done.
# 14.3 Compound Macetes
Compound macetes are built from atomic macetes and other compound macetes using macete constructors. The constructors are:
• Series: This constructor takes a list of macetes as arguments and yields a macete which applies every macete in the list once, from left to right. Thus given a context and an expression e,
• Sequential: This constructor takes any number of macetes as arguments. It works like the series constructor, except that when a macete fails to change an expression, subsequent macetes on the list are not applied.
• Parallel: This constructor takes a list of macetes as arguments and yields a macete which applies macetes in the list from left to right until a macete changes the expression. Thus given a context and an expression e,
provided and for all
• Repeat: Takes any number of macetes as arguments and yields a macete in the following way: The series composition M of is applied repeatedly to the expression e until no more change occurs. It may possibly compute forever. Thus the macete terminates if
stabilizes to some expression t. This expression is the value of
• Sound: This constructor takes a list M1,M2,M3 of three macetes and yields a macete characterized as follows: Given a context and an expression e, is
• if is alpha-equivalent to
• e otherwise.
• Without-minor-premises: This constructor takes a single argument macete M. It returns a new macete which applies M without minor premises. That is, macete substitution is only done when the macete requirements are satisfied.
Now whether the resulting macete is bidirectional or backward-directional, can be determined by considering the bidirectionality or backward-directionality each of the components.
• Series, sequential, parallel, repeat, and without-minor-premises macete constructors: If all the Mi are bidirectional macetes then the compound macete
is bidirectional. Similarly, if all the arguments Mi are backward-directional macetes then the compound macete is also backward-directional.
• Sound macete constructor: If M2,M3 are bidirectional, then the compound macete
is always bidirectional, regardless of M1. If M2 is backward-directional and M3 is bidirectional, then the compound macete is backward-directional. In all other cases, the compound macete is nondirectional.
# 14.4 Building Macetes
Schematic macetes are for the most part installed by the system when theorems installed.
1.
Elementary macetes are automatically installed when a theorem is added to a theory. The name of the installed macete is the same as the name of the theorem which generates it.
2.
Transportable macetes are installed when the transportable-macete modifier is present in the usage list of a theorem or axiom. Moreover, in this case, the name of the installed macete is the name of theorem which generates it with the prefix tr%.
Macetes are also automatically built when atomic sort and constant definitions are made by the user.
1.
For directly defined constants, the macete corresponding to the constant defining equation is installed. This macete is named
constant-name-equation_theory-name.
If the usage list of the definition includes the rewrite modifier and the defined constant is a function, the constant defining equation in applied form is also include as a macete named
constant-name-applied-equation_theory-name.
2.
For recursively defined constants, a number of macetes are installed:
(a)
The equation axioms named
constant-name-equation_theory-name
(b)
The minimality axiom named
definition-name-strong-minimality_theory-name
(c)
The minimality theorem named
definition-name-minimality_theory-name
3.
For defined atomic sorts a number of macetes are installed:
(a)
The sort defining axiom named
sort-name-defining-axiom_theory-name.
(b)
Some auxiliary theorems named
sort-name-in-quasi-sort_theory-name
and
sort-name-in-quasi-sort-domain_theory-name
Nondirectional schematic macetes usually are not associated to theorems. The form def-schematic-macete can be used for building schematic macetes of all kinds. You can build compound macetes using the form def-compound-macete.
# 14.5 Applicable Macetes
A macete is applicable'' to a formula if applying the macete modifies the formula in some way. The only sure-fire way of determining whether a macete is applicable, is to actually apply the macete and see the result. However, there are simple heuristic conditions which can be used to quickly determine that some macetes are not applicable. For example, for an elementary bidirectional macete, if the left hand side of the macete does not match any subexpression of the formula, then clearly the macete it is not applicable. For transportable macetes other similar inapplicability conditions are used. Macetes are tabulated in such a way that it is possible to quickly throw out inapplicable ones using these heuristic conditions. IMPS exploits this to provide users with a dynamic help facility for selecting macetes. The use of this facility is explained more extensively in Chapter 4.
# 14.6 Hints and Cautions
1.
Conceptually the macete mechanism is extremely simple. Users however, should not underestimate its power, usefulness, and flexibility. The utility of macetes hinges on three facts:
• The way a theorem is converted into a macete depends on the syntactic form of the the theorem as explained earlier in this section. In particular, it is important that theorems which are implications can be used as macetes along with those that are conditional equalities. Moreover, the conversion algorithm'' is based on a number of heuristics that in our experience work very well.
• Macetes can be combined using macete constructors. It has been our experience that carefully building a collection of compound macetes is an important part of developing a theory.
• Macetes are tabulated in such a way that the macetes which are applicable to a given formula can be retrieved very effectively and displayed to the user in a menu. In situations where over 500 macetes are installed, the menu usually contains less than twenty entries and takes less than ten seconds to compute.
2.
Though there are various modes of applying macetes, the default mode, with minor premises, is the one you want to use in most cases. The without-minor-premises macete constructor is often useful for building compound macetes to be used in this mode.
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http://math.stackexchange.com/questions/28352/ky-fan-norm-question | # Ky Fan Norm Question
How can one simply see that Ky Fan $k$-norm satisfies the triangle inequality? (The Ky Fan $k$-norm of a matrix is the sum of the $k$ largest singular values of the matrix)
Thanks.
-
Could you please define the Ky Fan $k$-norm and let us know what you already tried? Also, is this homework? – Glen Wheeler Mar 21 '11 at 19:17
The Ky Fan $k$-norm of a matrix is the sum of the $k$ largest singular values of the matrix – user4727 Mar 21 '11 at 19:28
@user4727 Thanks for the edit. Are you aware of the original papers by Ky Fan (~1950)? The reason why it is called the "Ky Fan norm" is because he proved it is a norm first. This might be a good opportunity for some "research"! :) – Glen Wheeler Mar 21 '11 at 19:47
For any $k$-plane $U$ in $\mathbb{C}^n$, let $i_U$ be the inclusion of $U$ into $\mathbb{C}^n$ and let $p_U$ be the orthogonal projection of $\mathbb{C}^n$ onto $U$.
Lemma: Let the singular values of $A$ be $\sigma_1 \geq \sigma_2 \geq \cdots \geq \sigma_n$. Then $\max_{U, V} \ \mathrm{Tr} \left( p_V \circ A \circ i_U \right)= \sigma_1+ \cdots +\sigma_k$, where the max is over all pairs of $k$-planes in $\mathbb{C}^n$.
Then $\max_{U, V} \ \mathrm{Tr} \left(p_V \circ (A+B) \circ i_U\right) \leq \max_{U, V} \ \mathrm{Tr} \left( p_V \circ A \circ i_U \right) + \max_{U, V} \ \mathrm{Tr} \left( p_V \circ B \circ i_U \right)$. | {"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": 0.955800473690033, "perplexity": 179.5767482445307}, "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-2015-27/segments/1435375098849.37/warc/CC-MAIN-20150627031818-00283-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://jmservera.com/solve-for-a-a1-82-2-56-5-242/ | # Solve for A A=((1/8)^2*(-2/5)^6*(-5/2)^4)^2
A=((18)2⋅(-25)6⋅(-52)4)2
Apply the product rule to 18.
A=(1282⋅(-25)6⋅(-52)4)2
One to any power is one.
A=(182⋅(-25)6⋅(-52)4)2
Raise 8 to the power of 2.
A=(164⋅(-25)6⋅(-52)4)2
Move the negative in front of the fraction.
A=(164⋅(-25)6⋅(-52)4)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to -25.
A=(164⋅((-1)6(25)6)⋅(-52)4)2
Apply the product rule to 25.
A=(164⋅((-1)62656)⋅(-52)4)2
A=(164⋅((-1)62656)⋅(-52)4)2
Simplify the expression.
Raise -1 to the power of 6.
A=(164⋅(12656)⋅(-52)4)2
Multiply 2656 by 1.
A=(164⋅2656⋅(-52)4)2
Raise 2 to the power of 6.
A=(164⋅6456⋅(-52)4)2
Raise 5 to the power of 6.
A=(164⋅6415625⋅(-52)4)2
A=(164⋅6415625⋅(-52)4)2
Cancel the common factor of 64.
Cancel the common factor.
A=(164⋅6415625⋅(-52)4)2
Rewrite the expression.
A=(115625⋅(-52)4)2
A=(115625⋅(-52)4)2
Use the power rule (ab)n=anbn to distribute the exponent.
Apply the product rule to -52.
A=(115625⋅((-1)4(52)4))2
Apply the product rule to 52.
A=(115625⋅((-1)45424))2
A=(115625⋅((-1)45424))2
Simplify the expression.
Raise -1 to the power of 4.
A=(115625⋅(15424))2
Multiply 5424 by 1.
A=(115625⋅5424)2
Raise 5 to the power of 4.
A=(115625⋅62524)2
Raise 2 to the power of 4.
A=(115625⋅62516)2
A=(115625⋅62516)2
Cancel the common factor of 625.
Factor 625 out of 15625.
A=(1625(25)⋅62516)2
Cancel the common factor.
A=(1625⋅25⋅62516)2
Rewrite the expression.
A=(125⋅116)2
A=(125⋅116)2
Multiply 125 and 116.
A=(125⋅16)2
Simplify the expression.
Multiply 25 by 16.
A=(1400)2
Apply the product rule to 1400.
A=124002
One to any power is one.
A=14002
Raise 400 to the power of 2.
A=1160000
A=1160000
The result can be shown in multiple forms.
Exact Form:
A=1160000
Decimal Form:
A=6.25⋅10-6
Solve for A A=((1/8)^2*(-2/5)^6*(-5/2)^4)^2
## Our Professionals
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https://library.kiwix.org/wikipedia_en_top_maxi/A/Trace_(linear_algebra) | # Trace (linear algebra)
In linear algebra, the trace of a square matrix A, denoted tr(A),[1][2] is defined to be the sum of elements on the main diagonal (from the upper left to the lower right) of A.
The trace of a matrix is the sum of its (complex) eigenvalues (counted with multiplicities), and it is invariant with respect to a change of basis. This characterization can be used to define the trace of a linear operator in general. The trace is only defined for a square matrix (n × n).
The trace is related to the derivative of the determinant (see Jacobi's formula).
## Definition
The trace of an n × n square matrix A is defined as[2][3][4]:34
${\displaystyle \operatorname {tr} (\mathbf {A} )=\sum _{i=1}^{n}a_{ii}=a_{11}+a_{22}+\dots +a_{nn}}$
where aii denotes the entry on the ith row and ith column of A.
## Example
Let A be a matrix, with
${\displaystyle \mathbf {A} ={\begin{pmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{pmatrix}}={\begin{pmatrix}1&0&3\\11&5&2\\6&12&-5\end{pmatrix}}}$
Then
${\displaystyle \operatorname {tr} (\mathbf {A} )=\sum _{i=1}^{3}a_{ii}=a_{11}+a_{22}+a_{33}=1+5+(-5)=1}$
## Properties
### Basic properties
The trace is a linear mapping. That is,[2][3]
{\displaystyle {\begin{aligned}\operatorname {tr} (\mathbf {A} +\mathbf {B} )&=\operatorname {tr} (\mathbf {A} )+\operatorname {tr} (\mathbf {B} )\\\operatorname {tr} (c\mathbf {A} )&=c\operatorname {tr} (\mathbf {A} )\end{aligned}}}
for all square matrices A and B, and all scalars c.[4]:34
A matrix and its transpose have the same trace:[2][3][4]:34
${\displaystyle \operatorname {tr} (\mathbf {A} )=\operatorname {tr} \left(\mathbf {A} ^{\mathsf {T}}\right).}$
This follows immediately from the fact that transposing a square matrix does not affect elements along the main diagonal.
### Trace of a product
The trace of a square matrix which is the product of two matrices can be rewritten as the sum of entry-wise products of their elements. More precisely, if A and B are two m × n matrices, then:
${\displaystyle \operatorname {tr} \left(\mathbf {A} ^{\mathsf {T}}\mathbf {B} \right)=\operatorname {tr} \left(\mathbf {A} \mathbf {B} ^{\mathsf {T}}\right)=\operatorname {tr} \left(\mathbf {B} ^{\mathsf {T}}\mathbf {A} \right)=\operatorname {tr} \left(\mathbf {B} \mathbf {A} ^{\mathsf {T}}\right)=\sum _{i,j}a_{ij}b_{ij}.}$
This means that the trace of a product of equal-sized matrices functions in a similar way to a dot product of vectors (imagine A and B as long vectors with columns stacked on each other). For this reason, generalizations of vector operations to matrices (e.g. in matrix calculus and statistics) often involve a trace of matrix products.
For real matrices A and B, the trace of a product can also be written in the following forms:
${\displaystyle \operatorname {tr} \left(\mathbf {A} ^{\mathsf {T}}\mathbf {B} \right)=\sum _{i,j}(\mathbf {A} \circ \mathbf {B} )_{ij}}$ (using the Hadamard product, also known as the entrywise product). ${\displaystyle \operatorname {tr} \left(\mathbf {A} ^{\mathsf {T}}\mathbf {B} \right)=\operatorname {vec} (\mathbf {B} )^{\mathsf {T}}\operatorname {vec} (\mathbf {A} )=\operatorname {vec} (\mathbf {A} )^{\mathsf {T}}\operatorname {vec} (\mathbf {B} )}$ (using the vectorization operator).
The matrices in a trace of a product can be switched without changing the result: If A is an m × n matrix and B is an n × m matrix, then[2][3][4]:34[note 1]
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )=\operatorname {tr} (\mathbf {B} \mathbf {A} )}$
Additionally, for real column matrices ${\displaystyle \mathbf {a} \in \mathbb {R} ^{n}}$ and ${\displaystyle \mathbf {b} \in \mathbb {R} ^{n}}$, the trace of the outer product is equivalent to the inner product:
${\displaystyle \operatorname {tr} \left(\mathbf {b} \mathbf {a} ^{\textsf {T}}\right)=\mathbf {a} ^{\textsf {T}}\mathbf {b} }$
### Cyclic property
More generally, the trace is invariant under cyclic permutations, that is,
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} \mathbf {C} \mathbf {D} )=\operatorname {tr} (\mathbf {B} \mathbf {C} \mathbf {D} \mathbf {A} )=\operatorname {tr} (\mathbf {C} \mathbf {D} \mathbf {A} \mathbf {B} )=\operatorname {tr} (\mathbf {D} \mathbf {A} \mathbf {B} \mathbf {C} ).}$
This is known as the cyclic property.
Arbitrary permutations are not allowed: in general,
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} \mathbf {C} )\neq \operatorname {tr} (\mathbf {A} \mathbf {C} \mathbf {B} ).}$
However, if products of three symmetric matrices are considered, any permutation is allowed, since:
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} \mathbf {C} )=\operatorname {tr} \left(\left(\mathbf {A} \mathbf {B} \mathbf {C} \right)^{\mathsf {T}}\right)=\operatorname {tr} (\mathbf {C} \mathbf {B} \mathbf {A} )=\operatorname {tr} (\mathbf {A} \mathbf {C} \mathbf {B} ),}$
where the first equality is because the traces of a matrix and its transpose are equal. Note that this is not true in general for more than three factors.
### Trace of a matrix product
Unlike the determinant, the trace of the product is not the product of traces, that is there exist matrices A and B such that
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )\neq \operatorname {tr} (\mathbf {A} )\operatorname {tr} (\mathbf {B} )}$
For example, if
${\displaystyle \mathbf {A} ={\begin{pmatrix}0&1\\0&0\end{pmatrix}},\ \ \mathbf {B} ={\begin{pmatrix}0&0\\1&0\end{pmatrix}},}$
then the product is
${\displaystyle \mathbf {AB} ={\begin{pmatrix}1&0\\0&0\end{pmatrix}},}$
and the traces are ${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )=1\neq 0\cdot 0=\operatorname {tr} (\mathbf {A} )\operatorname {tr} (\mathbf {B} ).}$
### Trace of a Kronecker product
The trace of the Kronecker product of two matrices is the product of their traces:
${\displaystyle \operatorname {tr} (\mathbf {A} \otimes \mathbf {B} )=\operatorname {tr} (\mathbf {A} )\operatorname {tr} (\mathbf {B} ).}$
### Full characterization of the trace
The following three properties:
{\displaystyle {\begin{aligned}\operatorname {tr} (\mathbf {A} +\mathbf {B} )&=\operatorname {tr} (\mathbf {A} )+\operatorname {tr} (\mathbf {B} ),\\\operatorname {tr} (c\mathbf {A} )&=c\operatorname {tr} (\mathbf {A} ),\\\operatorname {tr} (\mathbf {A} \mathbf {B} )&=\operatorname {tr} (\mathbf {B} \mathbf {A} ),\end{aligned}}}
characterize the trace completely in the sense that follows. Let f be a linear functional on the space of square matrices satisfying f(xy) = f(yx). Then f and tr are proportional.[note 2]
### Similarity invariance
The trace is similarity-invariant, which means that for any square matrix A and any invertible matrix P of the same dimensions, the matrices A and P−1AP have the same trace. This is because
${\displaystyle \operatorname {tr} \left(\mathbf {P} ^{-1}\mathbf {A} \mathbf {P} \right)=\operatorname {tr} \left(\mathbf {P} ^{-1}(\mathbf {A} \mathbf {P} )\right)=\operatorname {tr} \left((\mathbf {A} \mathbf {P} )\mathbf {P} ^{-1}\right)=\operatorname {tr} \left(\mathbf {A} \left(\mathbf {P} \mathbf {P} ^{-1}\right)\right)=\operatorname {tr} (\mathbf {A} ).}$
### Trace of product of symmetric and skew-symmetric matrix
If A is symmetric and B is skew-symmetric, then
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )=0}$.
#### Trace of the identity matrix
The trace of the n × n identity matrix is the dimension of the space, namely n.[1]
${\displaystyle \operatorname {tr} \left(\mathbf {I} _{n}\right)=n}$
This leads to generalizations of dimension using trace.
#### Trace of an idempotent matrix
The trace of an idempotent matrix A (a matrix for which A2 = A) is equal to the rank of A.
#### Trace of a nilpotent matrix
The trace of a nilpotent matrix is zero.
When the characteristic of the base field is zero, the converse also holds: if tr(Ak) = 0 for all k, then A is nilpotent.
When the characteristic n > 0 is positive, the identity in n dimensions is a counterexample, as ${\displaystyle \operatorname {tr} \left(\mathbf {I} _{n}^{k}\right)=\operatorname {tr} \left(\mathbf {I} _{n}\right)=n\equiv 0}$, but the identity is not nilpotent.
#### Trace equals sum of eigenvalues
More generally, if
${\displaystyle f(x)=\prod _{i=1}^{k}\left(x-\lambda _{i}\right)^{d_{i}}}$
is the characteristic polynomial of a matrix A, then
${\displaystyle \operatorname {tr} (\mathbf {A} )=\sum _{i=1}^{k}d_{i}\lambda _{i}}$
that is, the trace of a square matrix equals the sum of the eigenvalues counted with multiplicities.
### Trace of commutator
When both A and B are n × n matrices, the trace of the (ring-theoretic) commutator of A and B vanishes: tr([A,B]) = 0, because tr(AB) = tr(BA) and tr is linear. One can state this as "the trace is a map of Lie algebras glnk from operators to scalars", as the commutator of scalars is trivial (it is an Abelian Lie algebra). In particular, using similarity invariance, it follows that the identity matrix is never similar to the commutator of any pair of matrices.
Conversely, any square matrix with zero trace is a linear combinations of the commutators of pairs of matrices.[note 3] Moreover, any square matrix with zero trace is unitarily equivalent to a square matrix with diagonal consisting of all zeros.
### Trace of Hermitian matrix
The trace of a Hermitian matrix is real, because the elements on the diagonal are real.
### Trace of permutation matrix
The trace of a permutation matrix is the number of fixed points, because the diagonal term aii is 1 if the ith point is fixed and 0 otherwise.
### Trace of projection matrix
The trace of a projection matrix is the dimension of the target space.
{\displaystyle {\begin{aligned}\mathbf {P} _{\mathbf {X} }&=\mathbf {X} \left(\mathbf {X} ^{\mathsf {T}}\mathbf {X} \right)^{-1}\mathbf {X} ^{\mathsf {T}}\\[3pt]\Longrightarrow \operatorname {tr} \left(\mathbf {P} _{\mathbf {X} }\right)&=\operatorname {rank} (\mathbf {X} ).\end{aligned}}}
The matrix PX is idempotent, and more generally, the trace of any idempotent matrix equals its own rank.
## Exponential trace
Expressions like tr(exp(A)), where A is a square matrix, occur so often in some fields (e.g. multivariate statistical theory), that a shorthand notation has become common:
${\displaystyle \operatorname {tre} (A):=\operatorname {tr} (\exp(A)).}$
tre is sometimes referred to as the exponential trace function; it is used in the Golden–Thompson inequality.
## Trace of a linear operator
In general, given some linear map f : VV (where V is a finite-dimensional vector space), we can define the trace of this map by considering the trace of a matrix representation of f, that is, choosing a basis for V and describing f as a matrix relative to this basis, and taking the trace of this square matrix. The result will not depend on the basis chosen, since different bases will give rise to similar matrices, allowing for the possibility of a basis-independent definition for the trace of a linear map.
Such a definition can be given using the canonical isomorphism between the space End(V) of linear maps on V and VV*, where V* is the dual space of V. Let v be in V and let f be in V*. Then the trace of the indecomposable element vf is defined to be f(v); the trace of a general element is defined by linearity. Using an explicit basis for V and the corresponding dual basis for V*, one can show that this gives the same definition of the trace as given above.
### Eigenvalue relationships
If A is a linear operator represented by a square matrix with real or complex entries and if λ1, …, λn are the eigenvalues of A (listed according to their algebraic multiplicities), then
${\displaystyle \operatorname {tr} (\mathbf {A} )=\sum _{i}\lambda _{i}}$
This follows from the fact that A is always similar to its Jordan form, an upper triangular matrix having λ1, …, λn on the main diagonal. In contrast, the determinant of A is the product of its eigenvalues; that is,
${\displaystyle \det(\mathbf {A} )=\prod _{i}\lambda _{i}.}$
More generally,
${\displaystyle \operatorname {tr} \left(\mathbf {A} ^{k}\right)=\sum _{i}\lambda _{i}^{k}.}$
### Derivatives
The trace corresponds to the derivative of the determinant: it is the Lie algebra analog of the (Lie group) map of the determinant. This is made precise in Jacobi's formula for the derivative of the determinant.
As a particular case, at the identity, the derivative of the determinant actually amounts to the trace: tr = det′I. From this (or from the connection between the trace and the eigenvalues), one can derive a connection between the trace function, the exponential map between a Lie algebra and its Lie group (or concretely, the matrix exponential function), and the determinant:
${\displaystyle \det(\exp(\mathbf {A} ))=\exp(\operatorname {tr} (\mathbf {A} )).}$
For example, consider the one-parameter family of linear transformations given by rotation through angle θ,
${\displaystyle \mathbf {R} _{\theta }={\begin{pmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{pmatrix}}.}$
These transformations all have determinant 1, so they preserve area. The derivative of this family at θ = 0, the identity rotation, is the antisymmetric matrix
${\displaystyle A={\begin{pmatrix}0&-1\\1&0\end{pmatrix}}}$
which clearly has trace zero, indicating that this matrix represents an infinitesimal transformation which preserves area.
A related characterization of the trace applies to linear vector fields. Given a matrix A, define a vector field F on Rn by F(x) = Ax. The components of this vector field are linear functions (given by the rows of A). Its divergence div F is a constant function, whose value is equal to tr(A).
By the divergence theorem, one can interpret this in terms of flows: if F(x) represents the velocity of a fluid at location x and U is a region in Rn, the net flow of the fluid out of U is given by tr(A) · vol(U), where vol(U) is the volume of U.
The trace is a linear operator, hence it commutes with the derivative:
${\displaystyle \operatorname {d} \operatorname {tr} (\mathbf {X} )=\operatorname {tr} (\operatorname {d} \mathbf {X} ).}$
## Applications
The trace of a 2 × 2 complex matrix is used to classify Möbius transformations. First, the matrix is normalized to make its determinant equal to one. Then, if the square of the trace is 4, the corresponding transformation is parabolic. If the square is in the interval [0,4), it is elliptic. Finally, if the square is greater than 4, the transformation is loxodromic. See classification of Möbius transformations.
The trace is used to define characters of group representations. Two representations A, B : GGL(V) of a group G are equivalent (up to change of basis on V) if tr(A(g)) = tr(B(g)) for all gG.
The trace also plays a central role in the distribution of quadratic forms.
## Lie algebra
The trace is a map of Lie algebras ${\displaystyle \operatorname {tr}$ :{\mathfrak {gl}}_{n}\to K} from the Lie algebra ${\displaystyle {\mathfrak {gl}}_{n}}$ of linear operators on an n-dimensional space (n × n matrices with entries in ${\displaystyle K}$) to the Lie algebra K of scalars; as K is Abelian (the Lie bracket vanishes), the fact that this is a map of Lie algebras is exactly the statement that the trace of a bracket vanishes:
${\displaystyle \operatorname {tr} ([\mathbf {A} ,\mathbf {B} ])=0{\text{ for each }}\mathbf {A} ,\mathbf {B} \in {\mathfrak {gl}}_{n}.}$
The kernel of this map, a matrix whose trace is zero, is often said to be traceless or trace free, and these matrices form the simple Lie algebra ${\displaystyle {\mathfrak {sl}}_{n}}$, which is the Lie algebra of the special linear group of matrices with determinant 1. The special linear group consists of the matrices which do not change volume, while the special linear Lie algebra is the matrices which do not alter volume of infinitesimal sets.
In fact, there is an internal direct sum decomposition ${\displaystyle {\mathfrak {gl}}_{n}={\mathfrak {sl}}_{n}\oplus K}$ of operators/matrices into traceless operators/matrices and scalars operators/matrices. The projection map onto scalar operators can be expressed in terms of the trace, concretely as:
${\displaystyle \mathbf {A} \mapsto {\frac {1}{n}}\operatorname {tr} (\mathbf {A} )\mathbf {I} .}$
Formally, one can compose the trace (the counit map) with the unit map ${\displaystyle K\to {\mathfrak {gl}}_{n}}$ of "inclusion of scalars" to obtain a map ${\displaystyle {\mathfrak {gl}}_{n}\to {\mathfrak {gl}}_{n}}$ mapping onto scalars, and multiplying by n. Dividing by n makes this a projection, yielding the formula above.
In terms of short exact sequences, one has
${\displaystyle 0\to {\mathfrak {sl}}_{n}\to {\mathfrak {gl}}_{n}{\overset {\operatorname {tr} }{\to }}K\to 0}$
which is analogous to
${\displaystyle 1\to \operatorname {SL} _{n}\to \operatorname {GL} _{n}{\overset {\det }{\to }}K^{*}\to 1}$
(where ${\displaystyle K^{*}=K\setminus \{0\}}$) for Lie groups. However, the trace splits naturally (via ${\displaystyle 1/n}$ times scalars) so ${\displaystyle {\mathfrak {gl}}_{n}={\mathfrak {sl}}_{n}\oplus K}$, but the splitting of the determinant would be as the nth root times scalars, and this does not in general define a function, so the determinant does not split and the general linear group does not decompose:
${\displaystyle \operatorname {GL} _{n}\neq \operatorname {SL} _{n}\times K^{*}.}$
### Bilinear forms
The bilinear form (where X, Y are square matrices)
${\displaystyle B(\mathbf {X} ,\mathbf {Y} )=\operatorname {tr} (\operatorname {ad} (\mathbf {X} )\operatorname {ad} (\mathbf {Y} ))\quad {\text{where }}\operatorname {ad} (\mathbf {X} )\mathbf {Y} =[\mathbf {X} ,\mathbf {Y} ]=\mathbf {X} \mathbf {Y} -\mathbf {Y} \mathbf {X} }$
is called the Killing form, which is used for the classification of Lie algebras.
The trace defines a bilinear form:
${\displaystyle (\mathbf {X} ,\mathbf {Y} )\mapsto \operatorname {tr} (\mathbf {X} \mathbf {Y} ).}$
The form is symmetric, non-degenerate[note 4] and associative in the sense that:
${\displaystyle \operatorname {tr} (\mathbf {X} [\mathbf {Y} ,\mathbf {Z} ])=\operatorname {tr} ([\mathbf {X} ,\mathbf {Y} ]\mathbf {Z} ).}$
For a complex simple Lie algebra (such as ${\displaystyle {\mathfrak {sl}}}$n), every such bilinear form is proportional to each other; in particular, to the Killing form.
Two matrices X and Y are said to be trace orthogonal if
${\displaystyle \operatorname {tr} (\mathbf {X} \mathbf {Y} )=0}$.
## Inner product
For an m × n matrix A with complex (or real) entries and H being the conjugate transpose, we have
${\displaystyle \operatorname {tr} \left(\mathbf {A} ^{\mathsf {H}}\mathbf {A} \right)\geq 0}$
with equality if and only if A = 0.[5]:7
The assignment
${\displaystyle \langle \mathbf {A} ,\mathbf {B} \rangle =\operatorname {tr} \left(\mathbf {A} ^{\mathsf {H}}\mathbf {B} \right)}$
yields an inner product on the space of all complex (or real) m × n matrices.
The norm derived from the above inner product is called the Frobenius norm, which satisfies submultiplicative property as matrix norm. Indeed, it is simply the Euclidean norm if the matrix is considered as a vector of length mn.
It follows that if A and B are real positive semi-definite matrices of the same size then
${\displaystyle 0\leq \left[\operatorname {tr} (\mathbf {A} \mathbf {B} )\right]^{2}\leq \operatorname {tr} \left(\mathbf {A} ^{2}\right)\operatorname {tr} \left(\mathbf {B} ^{2}\right)\leq \left[\operatorname {tr} (\mathbf {A} )\right]^{2}\left[\operatorname {tr} (\mathbf {B} )\right]^{2}.}$[note 5]
## Generalizations
The concept of trace of a matrix is generalized to the trace class of compact operators on Hilbert spaces, and the analog of the Frobenius norm is called the Hilbert–Schmidt norm.
If K is trace-class, then for any orthonormal basis ${\displaystyle (\varphi _{n})_{n}}$, the trace is given by
${\displaystyle \operatorname {tr} (K)=\sum _{n}\left\langle \varphi _{n},K\varphi _{n}\right\rangle ,}$
and is finite and independent of the orthonormal basis.[6]
The partial trace is another generalization of the trace that is operator-valued. The trace of a linear operator Z which lives on a product space AB is equal to the partial traces over A and B:
${\displaystyle \operatorname {tr} (Z)=\operatorname {tr} _{A}\left(\operatorname {tr} _{B}(Z)\right)=\operatorname {tr} _{B}\left(\operatorname {tr} _{A}(Z)\right).}$
For more properties and a generalization of the partial trace, see traced monoidal categories.
If A is a general associative algebra over a field k, then a trace on A is often defined to be any map tr : Ak which vanishes on commutators: tr([a,b]) for all a, bA. Such a trace is not uniquely defined; it can always at least be modified by multiplication by a nonzero scalar.
A supertrace is the generalization of a trace to the setting of superalgebras.
The operation of tensor contraction generalizes the trace to arbitrary tensors.
## Coordinate-free definition
The trace can also be approached in a coordinate-free manner, i.e., without referring to a choice of basis, as follows: the space of linear operators on a finite-dimensional vector space V (defined over the field F) is isomorphic to the space VV via the linear map
${\displaystyle V\otimes V^{*}\to \operatorname {Hom} (V,V),v\otimes h\mapsto (w\mapsto h(w)v).}$
There is also a canonical bilinear function t : V × VF that consists of applying an element w of V to an element v of V to get an element of F:
${\displaystyle t\left(v,w^{*}\right):=w^{*}(v)\in F.}$
This induces a linear function on the tensor product (by its universal property) t : VV → F, which, as it turns out, when that tensor product is viewed as the space of operators, is equal to the trace.
In particular, given a rank one operator A (equivalently, a simple tensor ${\displaystyle v\otimes w^{*}}$), the square is ${\displaystyle A^{2}=\lambda A,}$ because on its one-dimensional image, A is just scalar multiplication. In terms of the tensor expression, ${\displaystyle \lambda =w^{*}(v),}$ and it is the trace (and only non-zero eigenvalue) of A; this gives a coordinate-free interpretation of the diagonal entry. Every operator on an n-dimensional space can be expressed as a sum of n rank one operators; this gives a coordinate-free version of the sum of diagonal entries.
This also clarifies why tr(AB) = tr(BA) and why tr(AB) ≠ tr(A)tr(B), as composition of operators (multiplication of matrices) and trace can be interpreted as the same pairing. Viewing
${\displaystyle \operatorname {End} (V)\cong V\otimes V^{*},}$
one may interpret the composition map
${\displaystyle \operatorname {End} (V)\times \operatorname {End} (V)\to \operatorname {End} (V)}$
as
${\displaystyle (V\otimes V^{*})\times (V\otimes V^{*})\to (V\otimes V^{*})}$
coming from the pairing V × VF on the middle terms. Taking the trace of the product then comes from pairing on the outer terms, while taking the product in the opposite order and then taking the trace just switches which pairing is applied first. On the other hand, taking the trace of A and the trace of B corresponds to applying the pairing on the left terms and on the right terms (rather than on inner and outer), and is thus different.
In coordinates, this corresponds to indexes: multiplication is given by
${\displaystyle (\mathbf {A} \mathbf {B} )_{ik}=\sum _{j}a_{ij}b_{jk},}$
so
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )=\sum _{ij}a_{ij}b_{ji}\quad {\text{and}}\quad \operatorname {tr} (\mathbf {B} \mathbf {A} )=\sum _{ij}b_{ij}a_{ji}}$
which is the same, while
${\displaystyle \operatorname {tr} (\mathbf {A} )\cdot \operatorname {tr} (\mathbf {B} )=\sum _{i}a_{ii}\cdot \sum _{j}b_{jj},}$
which is different.
For finite-dimensional V, with basis {ei} and dual basis {ei}, then eiej is the ij-entry of the matrix of the operator with respect to that basis. Any operator A is therefore a sum of the form
${\displaystyle \mathbf {A} =a_{ij}e_{i}\otimes e^{j}.}$
With t defined as above,
${\displaystyle \operatorname {tr} (\mathbf {A} )=a_{ij}\operatorname {tr} \left(e_{i}\otimes e^{j}\right).}$
The latter, however, is just the Kronecker delta, being 1 if i = j and 0 otherwise. This shows that tr(A) is simply the sum of the coefficients along the diagonal. This method, however, makes coordinate invariance an immediate consequence of the definition.
### Dual
Further, one may dualize this map, obtaining a map
${\displaystyle F^{*}=F\to V\otimes V^{*}\cong \operatorname {End} (V).}$
This map is precisely the inclusion of scalars, sending 1 ∈ F to the identity matrix: "trace is dual to scalars". In the language of bialgebras, scalars are the unit, while trace is the counit.
One can then compose these,
${\displaystyle F~{\overset {I}{\to }}~\operatorname {End} (V)~{\overset {\operatorname {tr} }{\to }}~F,}$
which yields multiplication by n, as the trace of the identity is the dimension of the vector space.
### Generalizations
Using the notion of dualizable objects and categorical traces, this approach to traces can be fruitfully axiomatized and applied to other mathematical areas.
• Trace of a tensor with respect to a metric tensor
• Characteristic function
• Field trace
• Golden–Thompson inequality
• Singular trace
• Specht's theorem
• Trace class
• Trace identity
• Trace inequalities
• von Neumann's trace inequality
## Notes
1. This is immediate from the definition of the matrix product:
${\displaystyle \operatorname {tr} (\mathbf {A} \mathbf {B} )=\sum _{i=1}^{m}\left(\mathbf {A} \mathbf {B} \right)_{ii}=\sum _{i=1}^{m}\sum _{j=1}^{n}a_{ij}b_{ji}=\sum _{j=1}^{n}\sum _{i=1}^{m}b_{ji}a_{ij}=\sum _{j=1}^{n}\left(\mathbf {B} \mathbf {A} \right)_{jj}=\operatorname {tr} (\mathbf {B} \mathbf {A} )}$.
2. Proof: f(eij) = 0 if and only if ij and f(ejj) = f(e11) (with the standard basis eij), and thus
${\displaystyle f(\mathbf {A} )=\sum _{i,j}[\mathbf {A} ]_{ij}f\left(e_{ij}\right)=\sum _{i}[\mathbf {A} ]_{ii}f\left(e_{11}\right)=f\left(e_{11}\right)\operatorname {tr} (\mathbf {A} ).}$
More abstractly, this corresponds to the decomposition
${\displaystyle {\mathit {gl}}_{n}={\mathit {sl}}_{n}\oplus k,}$
as tr(AB) = tr(BA) (equivalently, tr([A,B]) = 0) defines the trace on sln, which has complement the scalar matrices, and leaves one degree of freedom: any such map is determined by its value on scalars, which is one scalar parameter and hence all are multiple of the trace, a nonzero such map.
3. Proof: ${\displaystyle {\mathfrak {sl}}}$n is a semisimple Lie algebra and thus every element in it is a linear combination of commutators of some pairs of elements, otherwise the derived algebra would be a proper ideal.
4. This follows from the fact that tr(A*A) = 0 if and only if A = 0.
5. This can be proven with the Cauchy–Schwarz inequality.
## References
1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-09-09.
2. "Rank, trace, determinant, transpose, and inverse of matrices". fourier.eng.hmc.edu. Retrieved 2020-09-09.
3. Weisstein, Eric W. "Matrix Trace". mathworld.wolfram.com. Retrieved 2020-09-09.
4. Lipschutz, Seymour; Lipson, Marc (September 2005). Schaum's Outline of Theory and Problems of Linear Algebra. McGraw-Hill. ISBN 9780070605022.
5. Horn, Roger A.; Johnson, Charles R. (2013). Matrix Analysis (2nd ed.). Cambridge University Press. ISBN 9780521839402.
6. Teschl, G. (30 October 2014). Mathematical Methods in Quantum Mechanics. Graduate Studies in Mathematics. 157 (2nd ed.). American Mathematical Society. ISBN 978-1470417048. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 81, "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": 0.9801403284072876, "perplexity": 468.5655649083587}, "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-2021-43/segments/1634323587963.12/warc/CC-MAIN-20211026231833-20211027021833-00673.warc.gz"} |
https://bmjopen.bmj.com/content/5/9/e009497 | Article Text
Eliciting preferences for waterpipe tobacco smoking using a discrete choice experiment: implications for product regulation
1. Ramzi G Salloum1,
2. Wasim Maziak2,3,
3. David Hammond4,
4. Rima Nakkash5,
5. Farahnaz Islam6,
6. Xi Cheng6,
7. James F Thrasher6
1. 1Department of Health Outcomes and Policy, Institute for Child Health Policy, University of Florida College of Medicine, Gainesville, Florida, USA
2. 2Department of Epidemiology, Stempel College of Public Health and Social Work, Florida International University, Miami, Florida, USA
3. 3Syrian Center for Tobacco Studies, Aleppo, Syria
4. 4School of Public Health and Health Systems, University of Waterloo, Waterloo, Ontario, Canada
5. 5Department of Health Promotion and Community Health, Faculty of Health Sciences, American University of Beirut, Beirut, Lebanon
6. 6Arnold School of Public Health, University of South Carolina, Columbia, South Carolina, USA
1. Correspondence to Dr Ramzi G Salloum; rsalloum{at}ufl.edu
## Abstract
Objectives Waterpipe smoking is highly prevalent among university students, and has been increasing in popularity despite mounting evidence showing it is harmful to health. The aim of this study was to measure preferences for waterpipe smoking and determine which product characteristics are most important to smokers.
Setting A large university in the Southeastern USA.
Participants Adult waterpipe smokers attending the university (N=367).
Design Participants completed an Internet-based discrete choice experiment to reveal their preferences for, and trade-offs between, the attributes of hypothetical waterpipe smoking sessions. Participants were presented with waterpipe lounge menus, each with three fruit-flavoured options and one tobacco flavoured option, in addition to an opt out option. Nicotine content and price were provided for each choice. Participants were randomised to either receive menus with a text-only health-warning message or no message.
Outcome measures Multinomial and nested logit models were used to estimate the impact on consumer choice of attributes and between-subject assignment of health warnings respectively.
Results On average, participants preferred fruit-flavoured varieties to tobacco flavour. They were averse to options labelled with higher nicotine content. Females and non-smokers of cigarettes were more likely than their counterparts to prefer flavoured and nicotine-free varieties. Participants exposed to a health warning were more likely to opt out.
Conclusions Fruit-flavoured tobacco and lower nicotine content labels, two strategies widely used by the industry, increase the demand for waterpipe smoking among young adults. Waterpipe-specific regulation should limit the availability of flavoured waterpipe tobacco and require accurate labelling of constituents. Waterpipe-specific tobacco control regulation, along with research to inform policy, is required to curb this emerging public health threat.
• HEALTH ECONOMICS
• PREVENTIVE MEDICINE
This is an Open Access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
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## Statistics from Altmetric.com
### Strengths and limitations of this study
• This study is the first to elicit preferences for waterpipe smoking using the discrete choice experiment method.
• Fruit-flavoured tobacco and lower nicotine content labels both increase the demand for waterpipe smoking among young adults.
• Participants who were randomised to see waterpipe-specific health warnings on their menus were significantly more likely to opt out of choosing a waterpipe product.
• The study was limited to a convenience sample from a large US-based university and findings may not be generalisable.
## Introduction
Waterpipe smoking is a form of tobacco consumption that originated in the Middle East some five centuries ago and has recently experienced a worldwide resurgence.1 Even in Western societies that have achieved significant progress in curbing the prevalence of cigarette smoking, waterpipe smoking has been steadily gaining in popularity.2 In the USA, as in several Western countries, the highest prevalence of waterpipe smoking is among young adults, including university-aged students, of whom approximately one-third have ever smoked waterpipe tobacco.3 ,4
Despite the mounting evidence concerning the health risks and nicotine dependence associated with waterpipe smoking,5 it remains largely unregulated worldwide.6 There are several major challenges to waterpipe regulation. Whereas the cigarette market is dominated by a small number of multinationals, the waterpipe industry is characterised by a large number of producers, importers and manufacturers of tobacco and accessories. Waterpipe smoking products exhibit unique features when compared to cigarettes, including the use of charcoal to burn the tobacco, a smoking apparatus that varies in shape and size, and a wide array of tobacco flavours and packaging.
Current tobacco control policies are not clear about health warning requirements for the waterpipe. This is particularly important considering that those who smoke at waterpipe serving establishments do not routinely view waterpipe tobacco packages. For example, in 2011, Gulf Cooperation Council countries adopted standards for labelling of tobacco products, including pictorial health warnings specific to waterpipe tobacco, covering 50% of the front and back of the package.7 Even so, health warning labels on existing waterpipe tobacco are not evidence based, and waterpipe tobacco packets display a variety of deliberately misleading features, including incorrect labelling of constituents.8
The WHO has recently emphasised the need for research that examines ‘the extent to which flavoured tobacco, waterpipe cafés, and other marketing tools, economic factors and the absence of waterpipe-specific tobacco regulation influence the global spread of waterpipe tobacco smoking’.9 While flavour availability has been identified as a potential factor in attracting new smokers, especially youth and women,10 no empirical evidence exists that examines the influence of flavours on the demand for waterpipe tobacco smoking. The inaccurate labelling of waterpipe tobacco products,8 including waterpipe café menus, has been documented but the extent that this mislabelling influences waterpipe smoking has not been examined. Further, health warning labels have been shown to be effective in educating smokers about the harmful effects of cigarettes11 but have not been tested among waterpipe smokers.12
One approach that is well suited for measuring the influence of product characteristics on consumer choices is the discrete choice experiment (DCE).13 ,14 The basic premise of a DCE is that demand for a product, such as a waterpipe, can be explained using a set of product attributes and DCEs are commonly used in marketing research to test the influence of individual product attributes simultaneously. Respondents are given various sets of hypothetical situations in which they must choose between several alternatives. This methodology has recently been used by tobacco control researchers to assess patient preferences for competing smoking cessation strategies.15 ,16
In this study, a DCE was used to examine the influence of four waterpipe smoking product characteristics that are typically addressed by tobacco control regulations globally (flavour, nicotine content, price and health warnings) among previous waterpipe users. The study was conducted among university students who have some of the highest prevalence rates of waterpipe smoking in the USA.3
## Methods
### Theoretical framework
The DCE methodology is derived from the theory of value17 and assumes that individual choice for a product is determined by its characteristics or attributes.18 Random Utility Theory is used to analyse DCEs. The utility function is modelled using a systematic component—since consumers are assumed to know the nature of their utility functions—and a random or unexplained component.19 ,20 The systematic component in this study was estimated to reveal the relative importance of attributes involved in choosing a waterpipe smoking session. The random component of the utility function measures how changes in attributes affect choices through probabilistic analysis.20 In this study, we estimate the probability of choosing different hypothetical waterpipe product configurations for a smoking session using a waterpipe lounge menu. A price proxy was included in our choice sets in order to estimate willingness to pay, a monetary measure of value typically used in determining the relative ranking of attributes and the trade-offs across attributes.
Figure 1
Discrete choice experiment: Sample choice set*. *Attributes and levels: Flavour (Double Apple, Blue Mist, Pirate's Cave, Non-flavoured); Nicotine content (0.0%, 0.05%, 0.5%); Price ($5,$10, $20). ### Statistical analysis Percentages were calculated for categorical variables, and means and SDs for continuous variables. For the DCE, we took each choice between five-way options (four waterpipe products and an opt out option to not select any product) as a specific observation. Hence each respondent provided a maximum of 45 observations. We used multinomial logit regression to analyse the effect of product attributes on consumer choice. Parameter estimates for attribute levels were effect coded in relation to the grand mean, as opposed to a coded reference level. As such, positive values indicate greater preference for a given attribute level and negative values indicate less preference for a given attribute level. In each model, the choice among alternatives depended on the three attributes: flavour, price and nicotine content. We calculated the willingness to pay for marginal changes in nicotine level and for each waterpipe flavour relative to tobacco flavour (non-flavoured). These estimates were calculated as the ratio of the coefficient of interest to the negative of the coefficient on price. We used a nested logit model to analyse both the influence of the product's characteristics on choice and the impact of exposure to a health warning on the propensity to choose a waterpipe smoking session. To assess the influence of each attribute as a whole on consumer choice, a utility range for each attribute was calculated as the difference between the smallest and largest parameter estimates. The relative importance of each attribute was then calculated with respect to the sum of utility ranges. To estimate scaled preferences for waterpipe smoking attributes by respondent characteristics, we estimated additional multinomial logit models with interactions by gender (ie, female vs male) and cigarette smoking status (ie, smoker vs non-smoker). Data analyses were performed in April 2015 using SAS software (V.9.4; SAS Institute Inc). ## Results ### Sample characteristics Characteristics of study participants (N=367) are shown in table 1. The mean age of students in the study was 21.9 years (SD, 4 years). One half of the participants (50%) were female, 80% were undergraduates and nearly two-thirds (68%) were non-Hispanic white. Nearly 23% of the sample included concurrent cigarette smokers. Table 1 Sample characteristics ### Results of the DCE Participants were significantly more likely to choose Double Apple and Blue Mist flavours and significantly less likely to choose tobacco flavoured (non-flavoured) waterpipe products (table 2). They were significantly more likely to choose nicotine-free (0.0%) varieties over waterpipe products with higher nicotine content (0.05% and 0.5%), and significantly more likely to choose waterpipe smoking sessions priced at$5 or $10 versus$20. Results of the multinomial logit model with interaction terms indicated differences in consumer preferences across subpopulations, with females showing greater interest in flavoured and nicotine free varieties than that shown by males. Participants who did not currently smoke cigarettes were less interested in tobacco-flavoured and nicotine containing varieties. The nested logit model showed that all three flavoured varieties were preferred to the tobacco flavoured (non-flavoured) choices, and that respondent preferences were significantly associated with lower nicotine and price levels. Assignment to menus with the health warning message, older age of waterpipe smoking initiation and being a non-smoker of cigarettes were all significantly associated with a greater likelihood of choosing the opt out option.
Table 2
Multinomial and nested logit models of waterpipe smoking preference, and willingness to pay estimates (in USD)
### Relative importance of attributes
The relative importance of product attributes in predicting choice of a waterpipe smoking session reflects the relative weight that consumers placed on independent product characteristics when forming their choices. Attributes that have a stronger positive or negative impact on utility carry a greater relative weight. Overall, flavour accounted for almost two-thirds (65%) of the waterpipe smoking decision, followed by price (22%) and nicotine content (13%).
### Variation across subgroups
To explore whether the heterogeneity observed in table 2 is explained by differences in gender and cigarette smoking status, we estimated additional multinomial logit models that included interactions between attribute levels and gender (figure 2A), and cigarette smoking status (figure 2B). Compared with males, females were more likely to prefer Blue Mist and Pirate's Cave flavours and less likely to prefer tobacco flavour (non-flavoured). Females were also more likely than males to prefer nicotine-free (0.0%) waterpipe products and less likely to prefer products with the highest nicotine level (ie, 0.5%). When examining preferences by cigarette smoking status, non-smokers were more likely to prefer all flavoured varieties and less likely to prefer tobacco flavoured (non-flavoured) waterpipe products compared with smokers. Non-smokers were also more likely to prefer nicotine-free (0.0%) and less likely to prefer products with higher nicotine levels than were cigarette smokers.
Figure 2
Scaled estimates of waterpipe smoking preferences by gender and cigarette smoking status*. (Panel A): Gender Difference. (Panel B): Cigarette Smoker versus Non-smoker. *Estimates of the effect of each attribute level on waterpipe smoking preferences, stratified by gender (Panel A) and cigarette smoking status (Panel B). Models included correlated random main effects and fixed interactions between attribute levels and gender/cigarette smoking status. p Values indicate statistically significant differences between the respective groups, as measured by the interaction terms. Coefficients were scaled to range from 0 to 10.
## Discussion
To our knowledge, this study is the first to elicit preferences for waterpipe smoking using the DCE method. While prior research may have provided limited evidence on the determinants of waterpipe smoking when examined independently, the DCE tests the relative influence on choice of multiple attributes. This method is useful because it provides insight into forecasting the relative effect of different policy options. The results show that fruit-flavoured tobacco and lower nicotine content labels, two strategies widely used by the industry, may increase the demand for waterpipe smoking among young adults who have tried waterpipe, while waterpipe-specific health warnings may be effective at deterring smoking behaviour. The study findings also reveal heterogeneity in preferences for waterpipe smoking by gender and cigarette smoking status. These estimates can provide the first tangible targets for intervention and regulatory strategies to curb waterpipe smoking.
Among the three attributes and across the levels evaluated, the flavour attribute had the strongest influence on preferences, with fruit flavoured waterpipe products, on average, preferred to tobacco flavoured (non-flavoured) products. This effect was stronger among females (vs males) and non-smokers of cigarettes (vs cigarette smokers). This finding supports the proposition that flavours can lure women and non-smokers into waterpipe initiation.23 As such, targeting flavoured waterpipe tobacco can be an effective first step for regulatory effort to curb its use.
Price was the second most important attribute for influencing product preferences. Inclusion of price as a DCE attribute creates a more realistic market scenario for the participant and allows for the calculation of willingness-to-pay estimates for other attributes. Overall, consumers were more likely to choose less expensive waterpipe products. This is consistent with the behaviour of cigarette smokers, for whom demand is significantly reduced with higher prices.24 Price-based policies and taxation therefore represent viable options for an effective waterpipe regulatory framework.
The third attribute strongly associated with preferences is nicotine level. On average, participants preferred waterpipe products labelled as nicotine-free versus nicotine containing options. However, preferences for nicotine differed by gender and cigarette smoking status, with females and non-smokers of cigarettes more likely to choose nicotine-free products, compared with males and cigarette smokers, respectively. This may help explain why waterpipe tobacco manufacturers mislabel their products as containing low levels of nicotine,8 and calls for stricter regulations on labelling practices for waterpipe tobacco products. This issue is also relevant to current discussions about reducing nicotine levels in cigarettes, which may increase the appeal of tobacco to non-smokers.25 ,26
Participants who were randomised to see waterpipe-specific health warnings on their menus were significantly more likely to opt out of choosing a waterpipe product. This is consistent with the effectiveness of health warning labels in decreasing the demand for cigarettes and suggests that health warnings containing information about the harmful effects of waterpipe smoking may help discourage this behaviour.
Waterpipe smokers who participated in this study indicated their willingness to make certain trade-offs when choosing a waterpipe smoking session. The study design was based on a convenience sample, and no systematic attempts were made to regulate sampling factors such as time of day, day of the week and location. As such, findings may not be generalisable to a broader population, including those who have never tried waterpipe smoking. The study design did not include random ordering of flavour options within each choice set, which may have influenced the choice of a flavoured option over the non-flavoured option. The selected trade-offs were based on hypothetical scenarios and should be treated with caution because smokers may have indicated different preferences if actual waterpipe lounge menus had been presented to them, where the choices they made involved monetary exchange for and use of the product. Given that DCEs depend on responses to hypothetical scenarios, it is important to test the external validity of results using revealed preferences from subsequent evaluation of policies and interventions.13 Nonetheless, DCE is an established marketing methodology that enables the measurement of effects on consumer choice from multiple attributes simultaneously. The DCE in this study was selected based on a statistically efficient design with orthogonal and balanced choice sets. Further, presentation of waterpipe smoking session options within menus sought to emulate the experience of product selection for someone who visited a waterpipe lounge, where many users smoke waterpipe products.
The study results provide the first guidance for a regulatory framework to curb waterpipe smoking. Promising components of such a framework can include banning the use of flavoured tobacco, price increases on waterpipe products, accurate labelling of constituents and mandating health warning labels on waterpipe packets and café menus. Further research is needed to study these domains in greater depth, to assess potential trial among non-smokers and to gauge the effects of waterpipe-specific health warning labels, including different types of content and placement on waterpipe devices and products. In this study, we present policy guidance that is relevant to tobacco control efforts and the first of its kind to use a novel experimental approach to understand waterpipe smoking choices among young adults.
View Abstract
## Footnotes
• Contributors RGS and JFT were responsible for conception. All the authors contributed to the design of the study. RGS, FI and XC were responsible for the data analysis reported in this paper. All the authors contributed to the interpretation of the findings, contributed to successive drafts and approved the final manuscript.
• Funding RGS was supported by the Office of the Vice President for Research at the University of South Carolina (ASPIRE Programme) grant 35849. WM is funded by the National Institute on Drug Abuse (NIDA) grant R01 DA035160. The funding sources had no involvement in study design, collection, analysis and interpretation of the data, in writing the manuscript and decision to submit for publication.
• Competing interests None declared.
• Ethics approval This study was cleared for ethics by the University of South Carolina Institutional Review Board.
• Provenance and peer review Not commissioned; externally peer reviewed.
• Data sharing statement Additional data are available by emailing [email protected].
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https://mirror.las.iastate.edu/CRAN/web/packages/signnet/vignettes/complex_matrices.html | # Complex Matrices
This vignette describes the use of complex matrices for signed networks with ambivalent ties.
library(igraph)
library(signnet)
## Representing networks with ambivalent ties
The vignette on signed two-mode network introduces a third type of tie for signed networks, the ambivalent tie.
# construct network
el <- matrix(c(1,"a",1,"b",1,"c",2,"a",2,"b"),ncol = 2,byrow = TRUE)
g <- graph_from_edgelist(el,directed = FALSE)
E(g)$sign <- c(1,1,-1,1,-1) V(g)$type <- c(FALSE,TRUE,TRUE,TRUE,FALSE)
# vertex duplication
gu <- as_unsigned_2mode(g,primary = TRUE)
# project and binarize
pu <- bipartite_projection(gu,which = "true")
pu <- delete_edge_attr(pu,"weight")
# vertex contraction
ps <- as_signed_proj(pu)
igraph::as_data_frame(ps,"edges")
#> from to type
#> 1 a b A
#> 2 a c N
#> 3 b c N
Ambivalent ties add a new level of complexity for analytic tasks (especially involving matrices) since it is not clear which value to assign to them. Intuitively they should be “somewhere” between a positive and a negative tie but zero is already taken for the null tie.
We can construct a kind of adjacency matrix with the character values, but we can’t really work with characters analytically.
as_adj(ps,type = "both", attr = "type", sparse = FALSE)
#> a b c
#> a "" "A" "N"
#> b "A" "" "N"
#> c "N" "N" ""
This is where complex matrices come in. Instead of thinking about edge values being only in one dimension, we can add a second one for negative ties. That is, a positive tie would be coded as $$(1,0)$$ and a negative one as $$(0,1)$$. It is much easier in this case to include ambivalent ties by assigning $$(0.5,0.5)$$ to them.
Tuples like these can also be written as a complex number, i.e. $$(1,0)$$ turns into $$1+0i$$, $$(0,1)$$ into $$0+1i$$, and $$(0.5,0.5)$$ into $$0.5+0.5i$$. Complex numbers may be scary to some, but they have a kind of intuitive interpretation here. The real part is the positive value of an edge and the imaginary part is the negative part. So we could actually also have something like $$0.3+0.7i$$ which is an edge that is 30% positive and 70% negative. For now, though, the three values from above suffice.
The function as_adj_complex() can be used to return the complex adjacency matrix of a signed network with ambivalent ties.
as_adj_complex(ps,attr = "type")
#> a b c
#> a 0.0+0.0i 0.5+0.5i 0+1i
#> b 0.5-0.5i 0.0+0.0i 0+1i
#> c 0.0-1.0i 0.0-1.0i 0+0i
When there is a complex adjacency matrix, then there is also a complex Laplacian matrix. This matrix can be obtained with laplacian_matrix_complex().
laplacian_matrix_complex(ps, attr = "type")
#> a b c
#> a 1.707107+0.0i -0.500000-0.5i 0-1i
#> b -0.500000+0.5i 1.707107+0.0i 0-1i
#> c 0.000000+1.0i 0.000000+1.0i 2+0i
## Functions supporting ambivalent ties
So far, only the triangle routines support networks with ambivalent ties.
g <- graph.full(5)
E(g)\$type <- c(rep("P",3),rep("N",3),rep("A",4))
count_complex_triangles(g,attr = "type")
#> PPP PPN PNN NNN PPA PNA NNA PAA NAA AAA
#> 0 2 0 0 1 3 1 0 2 1 | {"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": 0.7452290058135986, "perplexity": 3115.6626582426848}, "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-2022-27/segments/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00058.warc.gz"} |
https://thoughtstreams.io/jtauber/thoughts/4111/ | # Thoughts
21 later thoughts
1
The new bridge near where I'm staying at the moment is closed today for its "opening". It's been open for weeks but it "opens" today which apparently involves it being closed.
11 earlier thoughts | {"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": 0.927847146987915, "perplexity": 10067.214970977142}, "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/1558232256381.7/warc/CC-MAIN-20190521122503-20190521144503-00400.warc.gz"} |
https://www.opuscula.agh.edu.pl/om-vol37iss4art3 | Opuscula Math. 37, no. 4 (2017), 501-508
http://dx.doi.org/10.7494/OpMath.2017.37.4.501
Opuscula Mathematica
# Spanning trees with a bounded number of leaves
Junqing Cai
Evelyne Flandrin
Hao Li
Qiang Sun
Abstract. In 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph $$G$$ with $$n\geq 3$$ vertices, if $$d(u)+d(v)\geq n-k+1$$ for all non-adjacent vertices $$u$$ and $$v$$ of $$G$$ ($$k\geq 1$$), then $$G$$ has a spanning tree with at most $$k$$ leaves. In this paper, we generalize this result by using implicit degree sum condition of $$t$$ ($$2\leq t\leq k$$) independent vertices and we prove what follows: Let $$G$$ be a connected graph on $$n\geq 3$$ vertices and $$k\geq 2$$ be an integer. If the implicit degree sum of any $$t$$ independent vertices is at least $$\frac{t(n-k)}{2}+1$$ for ($$k\geq t\geq 2$$), then $$G$$ has a spanning tree with at most $$k$$ leaves.
Keywords: spanning tree, implicit degree, leaves.
Mathematics Subject Classification: 05C07.
Full text (pdf)
1. A. Ainouche, An improvement of Fraisse's sufficient condition for hamiltonian graphs, J. Graph Theory 16 (1992), 529-543.
2. J.A. Bondy, U.S.R. Murty, Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, New York, 2008.
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7. E. Flandrin, T. Kaiser, R. Kužel, H. Li, Z. Ryjáčeck, Neighborhood unions and extremal spanning trees, Discrete Math. 308 (2008), 2343-2350.
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9. H. Li, Generalizations of Dirac's theorem in Hamiltonian graph theory - a survey, Discrete Math. 313 (2013), 2034-2053.
10. H. Li, Y. Zhu, Cyclable sets of vertices in 3-connected graphs, J. Comb. 7 (2016), 495-508.
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• Junqing Cai
• Qufu Normal University, School of Management, Rizhao, 276826, P.R. China
• LRI, UMR 6823 CNRS and Université Paris-Saclay, B.650, 91405 Orsay Cedex, France
• Evelyne Flandrin
• LRI, UMR 6823 CNRS and Université Paris-Saclay, B.650, 91405 Orsay Cedex, France
• Hao Li
• LRI, UMR 6823 CNRS and Université Paris-Saclay, B.650, 91405 Orsay Cedex, France
• Jianghan University, Institute for Interdisciplinary Research, 430056 Wuhan, P. R. China
• Qiang Sun
• LRI, UMR 6823 CNRS and Université Paris-Saclay, B.650, 91405 Orsay Cedex, France
• Communicated by Gyula O.H. Katona.
• Revised: 2016-12-13.
• Accepted: 2017-01-03.
• Published online: 2017-04-28. | {"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": 0.5664350390434265, "perplexity": 2776.9856296064513}, "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-2018-39/segments/1537267163704.93/warc/CC-MAIN-20180926061824-20180926082224-00433.warc.gz"} |
https://math.stackexchange.com/questions/850887/derivation-of-null-quantification-in-logic/850901#850901 | # Derivation of Null Quantification in Logic?
I was reading page 10-8 of this: https://faculty.washington.edu/smcohen/120/Chapter10.pdf and I was wondering if the distributive qualities could be derived, e.g. $\forall x (P \lor Q(x)) \Leftrightarrow P \lor \forall x Q(x)$, and the equivalent one for $\exists , \land$.
• In the Lecture Notes of the website there are (in the chapters following the one tou are referencing) the rules for quantifiers : $\forall$-intro, $\forall$-elim,... They must be used to prove the theroem above. Jun 29, 2014 at 8:00
The following proof uses the rules of Chapter 12: Methods of Proof for Quantifiers.
I'll consider only the case : $∀x(P∨Q(x)) \Rightarrow P∨∀xQ(x)$; the other one is similar.
(1) $∀x(P∨Q(x))$ --- assumed
(2) $P∨Q(a)$ --- from (1) by universal instantiation, or $\forall$-elim
Now we need some "propositional" transformation : we use the equivalence between $A \lor B$ and $\lnot A \Rightarrow B$
(3) $\lnot P \Rightarrow Q(a)$ --- from (2) by tautological equivalence
(4) $\lnot P$ --- assumed
(5) $Q(a)$ --- by $\Rightarrow$-elim (or modus ponens)
(6) $\forall xQ(x)$ --- by universal introduction (or $\forall$-intro) : the constant $a$ is not free in the assumptions
(7) $\lnot P \Rightarrow \forall xQ(x)$ --- from (4) and (6) by $\Rightarrow$-intro
(8) $P \lor \forall xQ(x)$ --- from (7) by tautological equivalence
(9) $∀x(P∨Q(x)) \Rightarrow P \lor \forall xQ(x)$ --- from (1) by $\Rightarrow$-intro.
Note
If we don't want to use the tautological equivalence in steps (3) and (8), we can use a "proof by cases".
From step :
(2) $P \lor Q(a)$
(3) $P$ --- assumed for $\lor$-elim
(4) $P \lor \forall x Q(x)$ --- from (3) by $\lor$-intro
(5) $Q(a)$ --- assumed for $\lor$-elim
(6) $\forall xQ(x)$ --- by universal introduction (or $\forall$-intro) : the constant $a$ is not free in the assumptions
(7) $P \lor \forall x Q(x)$ --- from (6) by $\lor$-intro
(8) $P \lor \forall x Q(x)$ --- from (2), (4) and (7) by $\lor$-elim, "discharging" the temporary assumptions (3) and (5).
Theorem follows as above, by $\Rightarrow$-intro.
The other "direction" is easier.
From the assumption : $P \lor \forall x Q(x)$, we derive from both $P$ and $\forall xQ(x)$ separately : $P \lor Q(a)$ [in one case by $\lor$-intro; in the other case by $\forall$-elim followed by $\lor$-intro].
Then we apply again proof by cases ($\lor$-elim) to conclude from : $P \lor \forall x Q(x)$ to : $P \lor Q(a)$.
Finally we apply $\forall$-intro to derive : $\forall x(P \lor Q(x))$ followed by a final $\Rightarrow$-intro.
Comment
Please note that, in general : $\forall xP(x) \lor \forall xQ(x) \vdash \forall x(P(x) \lor Q(x))$, but not vice versa, i.e. :
$\forall x(P(x) \lor Q(x)) \nvdash \forall xP(x) \lor \forall xQ(x)$.
In other words, the above proof does not works if $x$ is free in $P$.
Why so ?
Because (consider the first proof above) in step (6) we have to apply $\forall$-intro to $Q(a)$ to get $\forall xQ(x)$.
If $x$ is free in $P$ [and this is so if we try to apply the proof to the assumption $\forall x(P(x) \lor Q(x))$, because in step (2) we have instantiated it to $P(a) \lor Q(a)$], if we try to apply $\forall$-intro we have to violate the proviso that the constant $a$ must not be free in the assumptions, and at that step of the proof we still have an "undischarged" assumption containing $a$ : exactly $P(a)$.
• Why can you assume $\neg P$ in step 4?
– user82004
Jun 29, 2014 at 9:26
• @Anthony - We can assume whatever we need, provided that we "discharge" it before the end of the proof, if - as in this case - we are proving a logical theorem, i.e. a valid formula which does not depend on assumptions. Jun 29, 2014 at 10:06
• But don't you need to consider the situation where P is true as well? Or is it because the only thing you're really interested in with an implication is what happens when the antecedent is true?
– user82004
Jun 29, 2014 at 20:38
It doesn't seem like the notes you're reading define any deductive system for FOL at all, and you can't derive anything before you have a deductive system to do it in.
However, once you have a deductive system for FOL (of which there are several to choose among), you will be able to derive these laws in it. Otherwise the system you have is not FOL!
• Oof. I'm not sure what deductive system I normally use, I just was trying to figure out why Null Quantification makes sense.
– user82004
Jun 29, 2014 at 2:33
• @Anthony: If you're just trying to gain an intuitive understanding of why the rules hold, I think that's easier by thinking about the semantics rather than about derivations of them. To wit, in each possible world, $P$ is either true or false. So, depending on which of those is the case, the content of the rule is either $$\forall x({\sf True}\lor \cdots)\Leftrightarrow {\sf True}\lor \cdots$$ or $$\forall x(Q(x))\Leftrightarrow \forall x\,Q(x)$$ each of which is clearly always true. Jun 29, 2014 at 2:38
• I suppose I did want more than intuition though- derivations are always nice. There are a few other cases to consider, no?
– user82004
Jun 29, 2014 at 2:49
• @Anthony: The semantics of FOL can (and should) be formalized; it is not just intuitive handwaving. And I don't see which other cases there would be to consider. (The rules are only valid if $P$ does not contain $x$ free, and therefore in any given interpretation $P$ has the same truth value no matter which value $x$ is considered to have). Jun 29, 2014 at 2:56 | {"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": 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": 0.9043384790420532, "perplexity": 330.85284340749473}, "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-2022-27/segments/1656104249664.70/warc/CC-MAIN-20220703195118-20220703225118-00216.warc.gz"} |
https://lyusungwon.github.io/studies/2018/09/07/rrnn/ | # Relational Recurrent Neural Network
## WHY?
While conventional deep learning models have performed well on inference regarding individual entities, few models have been proposed focusing on inference regarding the relations among entities. Relational network aimed to capture relational information from images. In this paper, relational recurrent neural network tried to improve former memory augmented neural network models to capture relations among memories.
## WHAT?
Assume that we have memory matrix M. To capture interaction among these memories, Multi-Head Dot Product Attention(MHDPA) is used (also known as self-attention).
Linear projections are used to make queries(Q), keys(K) and values(V) for each memory. Dot product of queries and keys are normalized to gain attention weights. Weighted average of values are used as next memory.
Q = MW^q\\
K = MW^k\\
V = MW^v\\
A_{\theta}(M) = softmax(\frac{MW^q(MW^k)^T}{\sqrt{d_k}})MW^v = \tilde{M}
This composes one head of MHDPA. Assuming h is the number of head in MHDPA, F dimensional memories are projected to F/h dimension for each head, and heads are concatnated to represent next memory. New inputs for memory can be encoded easily without adding more parameters.
\tilde{M} = softmax(\frac{MW^q([M;x]W^k)^T}{\sqrt{d^k}})[M;x]W^v
Resulted memory can be used as memory cell in LSTM. row-wise MLP with layer normalization is used for g_{\psi}$g_{\psi}$.
s_{i,t} = (h_{i,t-1}, m_{i,t-1})\\
f_{i,t} = W^f x_t + U^f h_{i,t-1} + b^f\\
i_{i,t} = W^i x_t + U^i h_{i,t-1} + b^i\\
o_{i,t} = W^o x_t + U^o h_{i,t-1} + b^o\\
m_{i,t} = \sigma(f_{i,t} + \tilde{b}^f)\circ m_{i, t-1} + \sigma(i_{i,t})\circ g_{\psi}(\tilde{m}_{i,t})\\
h_{i,t} = \sigma(o_{i,t})\circ tanh(m_{i,t})\\
s_{i,t+1} = (m_{i,t}, h_{i,t})
## So?
RRN achieved good performance in Nth farthest vector calculation task, program evaluation, reinforcement learning task and language modeling.
## Critic
Beautiful, but not sure how this work. Need more experiments.
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https://physics.stackexchange.com/questions/166780/leapfrog-method-in-particle-in-cell | # Leapfrog method in Particle-in-cell
Recently, I wanted to write a 3D electromagnetic Particle-in-cell code with C++. I know that I should use leapfrog method, for example, when I calculate the position and velocity of particles，I should calculate according to the following order:
//firt move velocity back by 0.5dt
v = v - 0.5*q/m*E*dt;
//main loop
//update velocity and position
v = v + q/m*E*dt;
x = x + v*dt;
But when I want to write 3D PIC, I don't know the calculation order of $E,\,B,\,v,\,x$ (postion) and their formula. Can someone help me please?
• I'd be inclined to ask on the Computational Science SE – John Rennie Feb 24 '15 at 7:05
• I think the same method is valid - just calculate the 3 components of v instead of 1 when you get to the "calculate velocity" step; and the same for position. In other words - use vector quantities. – Floris Feb 24 '15 at 7:19
• Floris is correct, the three dimensions are treated independently. – lemon Feb 24 '15 at 9:36
• @Floris _ I am wondering if the question is more complicated - rather than just wanting position and velocity as vectors there is also the issue that $E$ and $B$ are determined from the positions of the charges and their velocities and, of course, determine the force on these particles. – tom Feb 24 '15 at 11:33
• I don't think this question is unclear. Nor does it fall afoul of the computational questions policy. – Kyle Kanos Feb 24 '15 at 13:57
For any PIC simulation, you are necessarily tying yourself to particles, particles that experience forces. Thus, we have the generic force law: \begin{align} m_i\frac{d\mathbf v_i}{dt}&=\mathbf F_i \tag{1a}\\ \frac{d\mathbf x_i}{dt}&=\mathbf v_i \tag{1b} \end{align} In the case of PIC, you are often considering the electromagnetic (Lorentz) force, so the force on particle $i$ is, $$\mathbf F_i=q_i\left(\mathbf E+\boldsymbol\beta_i\times\mathbf B\right)\tag{2}$$ with $\boldsymbol\beta=\mathbf v/c$. Since we've got particles, the electric and magnetic fields are defined as $$\mathbf E=\sum_{i\neq j}\frac{q_j}{r_{ij}^2}\hat{r}_j,\qquad\mathbf B=\sum_{j\neq i}\boldsymbol\beta_j\times\mathbf E$$
You've already mentioned the leapfrog method, which is one of the more common methods for PIC simulations (at least to my knowledge). Your question is how/when to compute $\mathbf E,\,\mathbf B$. The answer is quite simple: after you've computed $x$; after all, the electric and magnetic fields are functions of space.
Note, though, that the magnetic field term of the Lorentz force (eq (2)) contains a velocity component; this must also be leapfrogged: $$\mathbf v^{n+1/2}_i\sim\frac12\left(\mathbf v_i^{n-1/2}+\mathbf v_i^{n+1/2}\right)\times\mathbf B$$ which that $\mathbf v_i^{n+1/2}$ on the RHS makes it a little bit harder to solve (you'll likely need a linear algebra solver). There is an alternative, called the Boris method, that combines the velocity and electric field into a single term & you end up with a "rotation" without needing to involve the linear algebra solver needed; however, I am not well versed in this so I cannot say much beyond that.
Thus, the generic stepping algorithm would be something like,
while (t < tend)
computeEMFields(x, v, E, B);
newV = updateVelocity(v, E, B);
newX = moveParticles(v, newV, x);
computeDT();
t = t + dt;
x = newX
v = newV
end while
• Velocity (or position) Verlet methods are also useful here (also called Newmark methods in computational mechanics) -- these are related to the leapfrog method. Also, congrats on answering a question almost half-a-year after you left comments on it! – tpg2114 Jun 26 '15 at 1:45
• @tpg2114: Thank Community, it bumped it a bit ago & reminded me about it! – Kyle Kanos Jun 26 '15 at 1:46
The method you are using here is Euler-Cromer. It only really works for sytems with two variables (although I guess it could be modified for systems with any even number of variables - e.g. find $x, y, z$ then $vx, vy, vz$).
There is a more accurate method, which is more general, but more complicated to program. This is the 4th order Runge Kutta (RK) method. In your leapfrog method you change $x$, then $vx$, then $x$ again then $vx$ and so forth. In the RK method you first find the rates of change of $dx/dt, dy/t, dvx/dt,$ etc. and then find some new rates of change again having moved everything a half step forward in time using the old rates of change. In total four different rates of change for each independent variable are calculated and only then do we move a step forward in time and change $x$, $y$ etc. using a linear combination of all the different rates of change - more complicated to program, but more accurate and general for any number of independent variables.
• RK is "more accurate" only in a limited sense (it is not symplectic!), and thus it is likely that in the problem presented in the question RK would indeed lead to unphysical results (whereas velocity Verlet or leap-frog or even Euler-Cromer would probably work better). – alarge Jun 26 '15 at 1:14 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7506294846534729, "perplexity": 427.52513237100044}, "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/1566027318894.83/warc/CC-MAIN-20190823150804-20190823172804-00361.warc.gz"} |
https://brilliant.org/problems/circle-problem-3/ | # Circle problem
Geometry Level pending
Let AD be diameter of a circle of radius r, and let B,C be points on the circle such that AB=BC=r/2 and A is not equal to C. Find CD/r.
× | {"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": 0.9878260493278503, "perplexity": 1198.9221981274557}, "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-2017-51/segments/1512948512054.0/warc/CC-MAIN-20171211014442-20171211034442-00286.warc.gz"} |
https://tutoracademy.org/portfolio/opened-book | Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry’s standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged.
Insert math as
$${}$$ | {"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": 0.7255873680114746, "perplexity": 4603.106148800625}, "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/1618038921860.72/warc/CC-MAIN-20210419235235-20210420025235-00243.warc.gz"} |
https://arxiv.org/abs/1403.6185 | astro-ph.IM
(what is this?)
# Title:Physics of Fully Depleted CCDs
Abstract: In this work we present simple, physics-based models for two effects that have been noted in the fully depleted CCDs that are presently used in the Dark Energy Survey Camera. The first effect is the observation that the point-spread function increases slightly with the signal level. This is explained by considering the effect on charge-carrier diffusion due to the reduction in the magnitude of the channel potential as collected signal charge acts to partially neutralize the fixed charge in the depleted channel. The resulting reduced voltage drop across the carrier drift region decreases the vertical electric field and increases the carrier transit time. The second effect is the observation of low-level, concentric ring patterns seen in uniformly illuminated images. This effect is shown to be most likely due to lateral deflection of charge during the transit of the photogenerated carriers to the potential wells as a result of lateral electric fields. The lateral fields are a result of space charge in the fully depleted substrates arising from resistivity variations inherent to the growth of the high-resistivity silicon used to fabricate the CCDs.
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Instrumentation and Detectors (physics.ins-det) DOI: 10.1088/1748-0221/9/03/C03057 Cite as: arXiv:1403.6185 [astro-ph.IM] (or arXiv:1403.6185v1 [astro-ph.IM] for this version)
## Submission history
From: Chris Bebek [view email]
[v1] Mon, 24 Mar 2014 23:07:56 UTC (832 KB) | {"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": 0.8514081835746765, "perplexity": 2136.491449066155}, "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-2019-09/segments/1550247482347.44/warc/CC-MAIN-20190217172628-20190217194628-00206.warc.gz"} |
http://spmphysics.onlinetuition.com.my/2013/08/measuring-emf-and-internal-resistance_2681.html | Measuring e.m.f. and Internal Resistance - Simultaneous Equation
Example 1
When a 1Ω resistor is connected to the terminal of a cell, the current that flow through it is 8A. When the resistor is replaced by another resistor with resistance 4Ω, the current becomes 2⅔A. Find the
a. internal resistance of the cell
b. e.m.f. of the cell
Experiment 1
R1 = 1Ω
I1 = 8A
$E=IR+Ir E=(8)(1)+(8)r E−8r=8$
Experiment 2
R2 = 4Ω
I2 = 2⅔A
$E=IR+Ir E=(2 2 3 )(4)+(2 2 3 )r 3E−8r=32$
Solve the simultaneous equation
E = 12V, r = 0.5Ω
Example 2
The diagram on the left shows that the terminal potential difference of a batteries is 1.2V when a 4 Ω resistor is connected to it. The terminal potential become 1.45V when the resistor is replaced by another resistor of resistance 29Ω
Find the
a. internal resistance, r
b. e.m.f. of the batteries.
$I= V R I= 1.2 4 =0.3A$
$E=V+Ir E=1.2+0.3r E−0.3r=1.2$
$I= V R I= 1.45 29 =0.05A$
$E=V+Ir E=1.45+0.05r E−0.05r=1.45$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "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": 0.5790185332298279, "perplexity": 2245.630426835628}, "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-2019-22/segments/1558232258621.77/warc/CC-MAIN-20190526025014-20190526051014-00316.warc.gz"} |
https://zenodo.org/record/1250734/export/csl | Presentation Open Access
# Investigation of a method to identify socket-limb displacements of trans-radial amputees
Pobatschnig, Barbara; Unglaube, Fabian; Kranzl, Andreas
### Citation Style Language JSON Export
{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.1250734",
"language": "eng",
"title": "Investigation of a method to identify socket-limb displacements of trans-radial amputees",
"issued": {
"date-parts": [
[
2018,
5,
11
]
]
},
"abstract": "<p>Background:</p>\n\n<p>Providing secure fastening requires fundamental design and construction features for sockets. Due to the stiffness of the socket, motion between the socket and the residual limb (pistoning) can affect myoelectric control. Pattern recognition based myoelectric control provides more intuitively and naturally control. However, classification problems due to electrode shifts can limit prosthesis control. In literature, pistoning are less documented for upper limb prosthetics. The aim of this work is, therefore, a determination of an adequate method to measure socket-stump displacements in trans-radial amputees.</p>\n\n<p>Material and Methods:</p>\n\n<p>To quantify displacements three trans-radial amputees (S1, S2, S3) were measured synchronously with a 3D motion capture (14 infrared cameras) and an ultrasound system in four conditions (baseline, with weight, after first donning-D1 and after second donning-D2) and three arm positions (hanging arms, 90° elbow flexion, above head). All trials were repeated five times. Custom made test sockets with similar features like daily used sockets were constructed by an experienced orthopaedic technician. Gaps in the socket surface enable detecting of the proximal radius head via ultrasound. The probe was prepared with cluster markers to define the position and the orientation in the capture volume. The captured ultrasound points were subsequently transformed to 3D space. Two observers measured distances between the transformed points and a rigid marker attached to the socket in each condition and positions. To compare the conditions, the distances between the baseline and the other conditions, as well as the difference between observer 1 and observer 2 were estimated.</p>\n\n<p>Results:</p>\n\n<p>Differences between the observers are in the range of -0.09 to 1.16 mm for S1, -0.28 to 0.80 mm for S2 and -1.39 to 2.68 mm for S3. The mean distance differences overall subjects are 0.48 ±1.24 mm with weight, -0.91 ±1.19 mm in D1 and -1.46 ±1.24 mm in D2. In arm hanging position, all subjects show increased distances when weights affect the prostheses (with weight: 1.23 mm, 1.90 mm, 2.65 mm). The results of D1 and D2 vary within the subjects. In some cases subjects show reduced and in other cases, they show increased distances from baseline to D1 or D2.</p>\n\n<p>Conclusion</p>\n\n<p>In conclusion, pistoning is a key factor for clinical outcomes and studies in biomechanics and prosthetics. The results show homogenous values between observers. In arm hanging, distances of the socket and the anatomical landmark are increasing, because the sockets probably move against weight. D1 and D2 do not indicate such consistent results overall users because the distances increase and decrease within these positions. The maximum distance is about 6 mm overall users. In literature distances around 1 cm are likely in a clinical situation. Thus, a displacement about 6 mm could lead to limitations in myoelectric use.</p>",
"author": [
{
"family": "Pobatschnig, Barbara"
},
{
"family": "Unglaube, Fabian"
},
{
"family": "Kranzl, Andreas"
}
],
"type": "speech",
"id": "1250734"
}
33
4
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http://www.nag.com/numeric/fl/nagdoc_fl24/html/F06/f06wpf.html | F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
# NAG Library Routine DocumentF06WPF (ZTFSM)
Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
## 1 Purpose
F06WPF (ZTFSM) performs one of the matrix-matrix operations
$B←αA-1B , B←αA-HB , B←αBA-1 or B←αBA-H ,$
where $A$ is a complex triangular matrix stored in Rectangular Full Packed (RFP) format, $B$ is an $m$ by $n$ complex matrix, and $\alpha$ is a complex scalar. ${A}^{-\mathrm{H}}$ denotes ${\left({A}^{\mathrm{H}}\right)}^{-1}$ or equivalently ${\left({A}^{-1}\right)}^{\mathrm{H}}$. The RFP storage format is described in Section 3.3.3 in the F07 Chapter Introduction.
No test for singularity or near-singularity of $A$ is included in this routine. Such tests must be performed before calling this routine.
## 2 Specification
SUBROUTINE F06WPF ( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
INTEGER M, N, LDB COMPLEX (KIND=nag_wp) ALPHA, A(*), B(LDB,*) CHARACTER(1) TRANSR, SIDE, UPLO, TRANS, DIAG
The routine may be called by its LAPACK name ztfsm.
## 3 Description
F06WPF (ZTFSM) solves (for $X$) a triangular linear system of one of the forms
$AX=αB , AHX=αB , XA=αB or XAH=αB ,$
where $A$ is a complex triangular matrix stored in RFP format, $B$, $X$ are $m$ by $n$ complex matrices, and $\alpha$ is a complex scalar.
None.
## 5 Parameters
1: TRANSR – CHARACTER(1)Input
On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.
${\mathbf{TRANSR}}=\text{'N'}$
The matrix $A$ is stored in normal RFP format.
${\mathbf{TRANSR}}=\text{'C'}$
The conjugate transpose of the RFP representation of the matrix $A$ is stored.
Constraint: ${\mathbf{TRANSR}}=\text{'N'}$ or $\text{'C'}$.
2: SIDE – CHARACTER(1)Input
On entry: specifies whether $B$ is operated on from the left or the right, or similarly whether $A$ (or its transpose) appears to the left or right of the solution matrix in the linear system to be solved.
${\mathbf{SIDE}}=\text{'L'}$
$B$ is pre-multiplied from the left. The system to be solved has the form $AX=\alpha B$ or ${A}^{\mathrm{H}}X=\alpha B$.
${\mathbf{SIDE}}=\text{'R'}$
$B$ is post-multiplied from the right. The system to be solved has the form $XA=\alpha B$ or $X{A}^{\mathrm{H}}=\alpha B$.
Constraint: ${\mathbf{SIDE}}=\text{'L'}$ or $\text{'R'}$.
3: UPLO – CHARACTER(1)Input
On entry: specifies whether $A$ is upper or lower triangular.
${\mathbf{UPLO}}=\text{'U'}$
$A$ is upper triangular.
${\mathbf{UPLO}}=\text{'L'}$
$A$ is lower triangular.
Constraint: ${\mathbf{UPLO}}=\text{'U'}$ or $\text{'L'}$.
4: TRANS – CHARACTER(1)Input
On entry: specifies whether the operation involves ${A}^{-1}$ or ${A}^{-\mathrm{H}}$, i.e., whether or not $A$ is transpose conjugated in the linear system to be solved.
${\mathbf{TRANS}}=\text{'N'}$
The operation involves ${A}^{-1}$, i.e., $A$ is not transpose conjugated.
${\mathbf{TRANS}}=\text{'C'}$
The operation involves ${A}^{-\mathrm{H}}$, i.e., $A$ is transpose conjugated.
Constraint: ${\mathbf{TRANS}}=\text{'N'}$ or $\text{'C'}$.
5: DIAG – CHARACTER(1)Input
On entry: specifies whether $A$ has nonunit or unit diagonal elements.
${\mathbf{DIAG}}=\text{'N'}$
The diagonal elements of $A$ are stored explicitly.
${\mathbf{DIAG}}=\text{'U'}$
The diagonal elements of $A$ are assumed to be $1$, the corresponding elements of A are not referenced.
Constraint: ${\mathbf{DIAG}}=\text{'N'}$ or $\text{'U'}$.
6: M – INTEGERInput
On entry: $m$, the number of rows of the matrix $B$.
Constraint: ${\mathbf{M}}\ge 0$.
7: N – INTEGERInput
On entry: $n$, the number of columns of the matrix $B$.
Constraint: ${\mathbf{N}}\ge 0$.
8: ALPHA – COMPLEX (KIND=nag_wp)Input
On entry: the scalar $\alpha$.
9: A($*$) – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array A must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}×\left({\mathbf{M}}+1\right)/2\right)$ if ${\mathbf{SIDE}}=\text{'L'}$ and at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}×\left({\mathbf{N}}+1\right)/2\right)$ if ${\mathbf{SIDE}}=\text{'R'}$.
On entry: $A$, the $m$ by $m$ triangular matrix $A$ if ${\mathbf{SIDE}}=\text{'L'}$ or the $n$ by $n$ triangular matrix $A$ if ${\mathbf{SIDE}}=\text{'R'}$, stored in RFP format, as described in Section 3.3.3 in the F07 Chapter Introduction.
10: B(LDB,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array B must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
On entry: the $m$ by $n$ matrix $B$.
If ${\mathbf{ALPHA}}=0$, B need not be set.
On exit: the updated matrix $B$, or similarly the solution matrix $X$.
11: LDB – INTEGERInput
On entry: the first dimension of the array B as declared in the (sub)program from which F06WPF (ZTFSM) is called.
Constraint: ${\mathbf{LDB}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{M}}\right)$.
None.
Not applicable.
None.
## 9 Example
This example reads in the upper triangular part of a symmetric matrix $A$ which it converts to RFP format. It also reads in $\alpha$ and a $4$ by $3$ matrix $B$ and then performs the matrix-matrix operation $B←\alpha {A}^{-1}B$.
### 9.1 Program Text
Program Text (f06wpfe.f90)
### 9.2 Program Data
Program Data (f06wpfe.d)
### 9.3 Program Results
Program Results (f06wpfe.r) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 99, "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": 0.9993451237678528, "perplexity": 5233.496929511843}, "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-2014-41/segments/1410657137108.99/warc/CC-MAIN-20140914011217-00267-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/224041-ad-bc-proof-linear-independence.html | # Math Help - ad-bc proof of linear independence
1. ## ad-bc proof of linear independence
given 2 vectors x1=(a,b) and x2=(c,d), prove that they are linearly independent if and only if ad-bc doesn't equal zero.
I'm familiar with ad-bc as the determinant of a matrix and if it is equal to zero then the matrix is singular. ad-bc is the area of a parallelogram
2. ## Re: ad-bc proof of linear independence
Use the definition of "linearly dependent"! Two vectors, x1 and x2, are "linearly independent" if and only if there exist numbers, A and B, at least one non-zero, such that Ax1+ Bx2= 0. Here, that means A(a, b)+ B(c, d)= (Aa+ Bc, Ab+ Bd)= (0, 0) which is equivalent to Aa+ Bc= 0, Ab+ Bd= 0. Obviously, one solution is A= B= 0. What must be true so that is NOT the only solution? One way to answer that is to try to solve the equations! If we multiply the first equation by b, Aab+ Bbc= 0, multiply the second equation by a, Aab+ Bad= 0, and subtract it from the previous equation, we eliminate A: B(ad- bc)= 0.
IF ad- bc is not 0, we can divide both sides by it getting B= 0. Putting B= 0 into Aa+ Bc= 0, we have Aa= 0. If a is not 0, A=0. If a= 0, we can put B= 0 into the other equation Ab+ Bd= 0 to get Ab= 0. If b is not 0, A= 0 again. (If both A and B are 0, ad- bc= 0.) In any case, the vectors are independent.
If ad- bc is 0, then B(ad- bc)= 0 for any value of B- including non-zero values so the vectors are dependent.
In the case of just two vectors we can also say that if ad- bc= 0 and a is not 0, then d= bc/a so that <c, d>= <c, bc/a>= (c/a)<a, b> showing that <c, d> is just a multiple of <a, b>. If a= 0, ad- bc= 0 becomes bc= 0 so either b=0 or c= 0. If b= 0, <a, b>= <0, 0> which is linearly dependent with any other vector. If c= 0, then we have <0, b> and <0, d> so that <0, d>= (d/b)<0, b> and, again, one vector is a multiple of the other.
3. ## Re: ad-bc proof of linear independence
Thanks very much! I guess it's stronger to prove by algebra.
so you have to prove 2 things, 1. given linear independence, A=B=0, then ad-bc doesn't equal 0, is this because then B(ad-bc)=0 and ad-bc can be arbitrary and does not necessarily equal 0 (but then both B And ad-bc can equal 0 and the proof fails?) if A=B=0 then it doesn't follow necessarily from the Aa+Bc=0, Ab+Bd=0 that ad-bc doesn't equal 0...?
2.given ad-bc doesn't equal 0 then the vectors are linearly independent: B=0 leads to Aa=0, Ab=0, if A does not equal 0 then a=b=0 (0,0) is linearly dependent on (c,d)0. if a and b don't equal 0 then A=0 then you can prove linear independence but then a and b can equal 0 in the problem since the vectors are in all of V2?
the problem seems to allude to this proof: n vectors in Rn are linearly dependent if and only if the determinant of the matrix taking the vectors as its columns=0. or also Steinitz's theorem and linear independence is equivalent to the non-existence of non trivial solutions, proportionality to non trivial solutions (x,y) (-y,x)
from (a,c)=h(b,d) you can derive ad-bc=0 with h=1
I know we are all busy so can someone else please let me know if I've made any mistakes? is there another way to prove this using matrix theory?
4. ## Re: ad-bc proof of linear independence
Apparently there is a Leibniz formula in which the identity permutation is the only one that gives a nonzero contribution and from this or Laplace expansion you can deduce that
This n-linear function is an alternating form. This means that whenever two columns of a matrix are identical, or more generally some column can be expressed as a linear combination of the other columns (i.e. the columns of the matrix form a linearly dependent set), its determinant is 0.
so maybe you can prove in this way that the converse is true that then the columns of a matrix form a linearly independent set then it's determinant is nonzero. but how do you get the 2X2 matrix? ab+cd, V1+V2 gives you a parallelogram whose area is the determinant ad-bc and if Det=0 then the vectors are linearly dependent and the area of the parallelogram is 0. but if the vectors are linearly independent then they can be added to form a parallelogram whose area is non zero- kind of a geometric proof
5. ## Re: ad-bc proof of linear independence
I wonder why he gives this problem without the matrix theory (I started at chapter 12). can you intuitively prove this just from chapter 12 Apostol? it seems impossible to prove without some linear algebra
6. ## Re: ad-bc proof of linear independence
Originally Posted by mathnerd15
I wonder why he gives this problem without the matrix theory (I started at chapter 12). can you intuitively prove this just from chapter 12 Apostol?
You don't need matrix theory.
In $\mathcal{R}^2$ two vectors are linearly independent if and only if they are not parallel.
Two vectors are parallel if and only if they are scalar multiples of each other. | {"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": 1, "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": 0.9614332318305969, "perplexity": 759.4554486913477}, "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-2014-23/segments/1404776415016.1/warc/CC-MAIN-20140707234015-00019-ip-10-180-212-248.ec2.internal.warc.gz"} |
http://mail-archives.apache.org/mod_mbox/db-derby-dev/200608.mbox/%[email protected]%3E | # db-derby-dev mailing list archives
##### Site index · List index
Message view
Top
From Rick Hillegas <[email protected]>
Subject Re: installation issue: problems caused by spaces in path pointed to by DERBY_HOME or DERBY_INSTALL
Date Fri, 25 Aug 2006 15:55:17 GMT
Hey Andrew,
Here's a bit more information on this problem. Regards-Rick
It does not work correctly on Windows XP SP2. It adds extra characters
that are not the DOS 8.3 format and even changes the name of the db
directory in the PATH to db0. The error message we get is
Exception in thread "main" java.lang.NoClassDefFoundError:
org/apache/derby/tools/ij
The problem is the CLASSPATH set by setEmbeddedCP.bat. Once you set
DERBY_INSTALL, then run this batch file, the resulting CLASSPATH is:
CLASSPATH=C:\PROGRA~1\Java\JDK16~1.0\db0\db\lib\derby.jar;C:\PROGRA~1\Java\JDK16~1.0\db0\db\lib\derbytools.jar;.;
which you can clearly see has some strange problems in it. Somehow it
ads the directory db0 and really messes up the name of the jdk1.6.0
directory. However, if you remove that FOR statement, everything works
just fine.
Andrew McIntyre wrote:
> On 8/24/06, Rick Hillegas <[email protected]> wrote:
>
>> The following line in setEmbeddedCP.bat raises errors if there are
>> spaces in the path identified by DERBY_HOME or DERBY_INSTALL:
>>
>> @FOR %%X in ("%DERBY_HOME%") DO SET DERBY_HOME=%%~sX
>>
>> Is this a known problem? I'm not a DOS expert and I don't know
>> understand what "%%~sX" means.
>
>
> That should convert the value of DERBY_HOME to it's DOS 8.3 short form
> to avoid further problems with the path containing spaces. This is
> working for me on Windows 2000. What version of Windows are you using,
> and what is the error you are getting?
>
> andrew
Mime
View raw message | {"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": 0.8858025670051575, "perplexity": 9230.431720994751}, "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-2016-26/segments/1466783396027.60/warc/CC-MAIN-20160624154956-00037-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=113896 | # Series with Factorial
by dekoi
Tags: factorial, series
P: n/a I don't understand this conversion! $$\sum_{n=1}^\infty \frac{sin(n\pi /2)}{n!} = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}$$ I know that the numerator of the left side is 0 when n is an even number. When n is odd, the numerator is either +1 or -1. But how do i continue?
Math
Emeritus
Thanks
PF Gold
P: 38,706
Quote by dekoi I don't understand this conversion! $$\sum_{n=1}^\infty \frac{sin(n\pi /2)}{n!} = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}$$ I know that the numerator of the left side is 0 when n is an even number. When n is odd, the numerator is either +1 or -1. But how do i continue?
AS you say, if n is even then sin(n$\pi$)= 0. Let n= 2m+1 so that for every m= 1, 2, 3,... n is odd. Notice that $sin(\frac{\pi}{2})= 1$, $sin(\frac{3\pi}{2})= -1$, $sin(\frac{5\pi}{2})= 1$ etc. In other words, $sin(\frac{(2m+1)\pi}{2}$ is 1 if m even (0, 2, etc.) and -1 is m is odd.
$$sin(\frac{n\pi}{2})= sin(\frac{(2m+1)\pi}{2})= (-1)^m$$
so we have
$$\sum_{n=1}^\infty \frac{sin(\frac{n\pi}{2})}{n!}= \sum_{m=0}^\infty\frac{(-1)^m}{(2m+1)!}$$
Since m is a "dummy variable" (it just denotes a place in the series and doesn't appear in the final sum) just replace m by n to get the result you have- the two "n"s on either side of the equation have different meanings.
P: n/a How come the lower limit was replaced by 0 from 1? Thanks.
P: 347
## Series with Factorial
Because 2n+1 skips 1. So you could write 2n-1 instead.
HW Helper
P: 1,422
Quote by dekoi How come the lower limit was replaced by 0 from 1? Thanks.
Hmmm, look at the equality again:
$$\sum_{n = 1} ^ {\infty} \left( \frac{\sin \left( \frac{n \pi}{2} \right)}{n!} \right) = \sum_{n = 0} ^ {\infty} \left( \frac{(-1) ^ n}{(2n + 1)!} \right)$$
It's not only that n = 1 has been replaced by n = 0, but the n! in the denominator has also been replaced by (2n + 1)!. Do you notice this?
As HallsofIvy has already pointed out:
If n is even then
$$\frac{\sin \left( \frac{n \pi}{2} \right)}{n!} = 0$$, right? So you'll be left with the terms with odd n only, now let n = 2m + 1
This means n is odd right? And since n >= 1 (the series starts from n = 1, and 1 is an odd number), so 2m + 1 >= 1, so m >= 0, which means the new series will start from m = 0.
So change n to m, we have:
$$\sum_{n = 1} ^ {\infty} \left( \frac{\sin \left( \frac{n \pi}{2} \right)}{n!} \right) = \sum_{m = 0} ^ {\infty} \left( \frac{\sin \left( \frac{(2m + 1) \pi}{2} \right)}{(2m + 1)!} \right) = \sum_{m = 0} ^ {\infty} \left( \frac{(-1) ^ m}{(2m + 1)!} \right)$$
Can you get it now? :)
Related Discussions General Math 20 General Math 18 Calculus 5 Calculus & Beyond Homework 17 Calculus 7 | {"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": 0.9699826836585999, "perplexity": 555.883197982642}, "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-2014-10/segments/1393999675300/warc/CC-MAIN-20140305060755-00090-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/45927/exporting-definitions | # Exporting Definitions
Below is part of the code for my notes. I would like to "easily" create a new document displaying only the definitions, theorems, and lemmas. I can copy and paste this and just delete what I do not want, but if there is an easier way, that would be great.
\documentclass[12pt,letterpaper]{article}
\usepackage{amsmath} % just math
\usepackage{amssymb} % allow blackboard bold (aka N,R,Q sets)
\usepackage{amsthm} % allows thm environment
\usepackage{mathrsfs}
\usepackage{graphicx, framed} % allows graphics
\usepackage[none]{hyphenat} % allows graphics
\usepackage[usenames,dvipsnames]{color}
\usepackage{color}
\usepackage{wrapfig}
\definecolor{Def}{rgb}{0.85,0.65,0.13}
\definecolor{Ex}{rgb}{0,0.39,0}
\definecolor{Nt}{rgb}{1,0.08, 0.58}
\definecolor{Tm}{rgb}{0,0,0.80}
\definecolor{Pf}{rgb}{1,0.55,0}
\definecolor{white}{rgb}{1,1,1}
\textwidth 6.5truein % These 4 commands define more efficient margins
\textheight 9.4truein
\oddsidemargin 0.0in
\topmargin -0.6in
\parskip 5pt % Also, a bit of space between paragraphs
\newtheorem{theorem}{\color{Tm}{\textbf{\underline{Theorem}}}}
\newtheorem{cor}{\color{Tm}{\textbf{\underline{Corollary}}}}
\newtheorem{prop}{\color{Tm}{\textbf{\underline{Proposition}}}}
\newtheorem{claim}{\color{Tm}{\textbf{\underline{Claim}}}}
\theoremstyle{definition}\newtheorem{definition}{\color{Def}{\textbf{\underline{Definition}}}}
\newtheorem{lemma}{\color{Tm}{\textbf{\underline{Lemma}}}}
\newtheorem{exer}{\color{Plum}{\textbf{\underline{Exercise}}}}
\theoremstyle{definition}\newtheorem{note}{\color{Nt}{\textbf{\underline{Note}}}}
\theoremstyle{definition}\newtheorem{example}{\color{Ex}{\textbf{\underline{Example}}}}
\newtheorem{sidebar}{\color{Aquamarine}{\textbf{\underline{Sidebar}}}}
\newtheorem{pf}{\color{BurntOrange}{\textbf{\underline{Proof}}}}
\newcommand{\QEDend}{\linebreak \begin{flushright}\textbf{QED}\end{flushright}}
\newcommand{\QEDish}{\linebreak \begin{flushright}\textbf{$\approx$QED}\end{flushright}}
\newcommand{\bb}[1]{\mathbb{#1}}
\newcommand{\mcal}[1]{\mathcal{#1}}
\newcommand{\scr}[1]{\mathscr{#1}}
\newcommand{\R}[1]{$\mathbb{R}$}
\newcommand{\C}[1]{$\mathbb{C}$}
\newcommand{\N}[1]{$\mathbb{N}$}
\newcommand{\Q}[1]{$\mathbb{Q}$}
\newcommand{\lp}[1]{$\left({#1}\right)$}
\newcommand{\la}[1]{$\left|{#1}\right|$}
\newcommand{\as}[1]{\color{white}{*}\color{black}{}}
\newcommand{\ind}{\hspace*{30pt}}
\newcommand{\done}{\hfill \mbox{\raggedright \rule{0.1in}{0.1in}}}
\newcommand{\bigdotcup}{\ensuremath{\mathop{\makebox[-0.6pt]{\hspace{16pt}{$$\cdot$$}}\bigcup}}}
\newcommand{\dotcup}{\ensuremath{\mathop{\makebox[-0.6pt]{\hspace{13pt}{$$\cdot$$}}\bigcup}}}
\raggedright
\parindent 30pt
\newcommand{\ftheorem}[1]{\begin{framed}\begin{theorem}#1\end{theorem}\end{framed}}
\newcommand{\fdef}[1]{\begin{framed}\begin{definition}#1\end{definition}\end{framed}}
\newcommand{\fnote}[1]{\begin{framed}\begin{note}#1\end{note}\end{framed}}
\newcommand{\flemma}[1]{\begin{framed}\begin{lemma}#1\end{lemma}\end{framed}}
\newcommand{\fex}[1]{\begin{framed}\begin{example}#1\end{example}\end{framed}}
\newcommand{\fcor}[1]{\begin{framed}\begin{corollary}#1\end{corollary}\end{framed}}
\begin{document}
\section{Course Notes}
%January 23, 2012
\subsection{Metric Spaces}
\begin{definition}The metric space $M$ is a \underline{complete metric space} if every Cauchy sequence is convergent in $M$.
\end{definition}
\begin{example}
$\bb{R}$ is a complete metric space\done
\end{example}
\begin{example}
$C[0,1]$ is a complete metric space with $d(f,g) = \sup \mid f(t) - g(t) \mid$, $t \in [0,1]$.\done
\end{example}
\begin{theorem}
Any closed subset $A$ of a complete metric space $M$ is complete.
\end{theorem}
\begin{proof}
Let $A \subset M$ be closed and $<x_n>$ be any Cauchy sequence in $A$. Since $M$ is a complete metric space, $<x_n>$ is convergent in $M$, so $x_n \rightarrow x \in M$. Since $A$ is closed, $x \in A$. Thus, $A$ is complete.
\end{proof}
\end{document}
-
Please consider adding a minimum working example (MWE) of your code, with more information on what you're trying to achieve. The first and second sentences of your current posting, I'm afraid to say, sound a bit contradictory. Plus, are you using a package such as amsthm or ntheorem? – Mico Feb 27 '12 at 2:01
Mico, I have added some sample code showing the packages I am using and rephrased my question. Sorry about the confusion. – Tyler Clark Feb 28 '12 at 23:29
Well, there is still some missing info in your MWE, rendering it a MNWE;). But try this:
\documentclass{amsart}
\usepackage[active,
generate=short,
extract-cmd={section},
extract-env={definition,theorem}]{extract}
\begin{extract*}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\end{extract*}
as the preamble, compile your file and look into the file short.tex. See the documentation of the extract package for more info (this is important - this package messes with internals of LaTeX and will not work for any commands, for example!). Short info: the extract* environment puts its contents into the generated file (and processes them as usual as well); generate defines the name of the generated file, and extract-cmd and extract-env specify what to extract.
Also, consider avoiding \underline and using \emph` instead.
-
This works wonderfully. Thank you! – Tyler Clark Feb 29 '12 at 1:51 | {"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": 0.9829164147377014, "perplexity": 2088.670601485352}, "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/1386163828351/warc/CC-MAIN-20131204133028-00088-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://zbmath.org/?q=an:1045.33009 | # zbMATH — the first resource for mathematics
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Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials. (English) Zbl 1045.33009
There are now several ways to derive an asymptotic expansion for the Jacobi polynomials ${P}_{n}^{\left(\alpha ,\beta \right)}\left(cos\theta \right)$, as $n\to \infty$, which holds uniformly for $\theta \in \left[0,\frac{1}{2}\pi \right]$. One of these starts with a contour integral, involves a transformation which takes this integral into a canonical form, and makes repeated use of an integration-by-parts technique. There are two advantages to this approach: (i) it provides a recursive formula for calculating the coefficients in the expansion, and (ii) it leads to an explicit expression for the error term. In this paper, we point out that the estimate for the error term given previously is not sufficient for the expansion to be regarded as genuinely uniform for $\theta$ near the origin, when one takes into account the behavior of the coefficients near $\theta =0$. The aim is to use an alternative method to estimate the remainder. First it is shown that the coefficients in the expansion are bounded for $\theta \in \left[0,\frac{1}{2}\pi \right]$. Next, is given an estimate for the error term which is of the same order as the first neglected term.
##### MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type 41A30 Approximation by other special function classes | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "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": 0.8461006283760071, "perplexity": 2148.327002522008}, "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/1386163826391/warc/CC-MAIN-20131204133026-00021-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/20797/differentiating-propagator-greens-function-correlation-function-etc/20812 | # Differentiating Propagator, Greens function, Correlation function, etc
For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most foremost the associated abuse of language as well as difference and correlation (no pun intended):
Maybe including side notes regarding the distinction between Covariance, Covariance function and Cross-Covariance, the pair correlation function for different observables, relations to the autocorrelation function, the $n$-point function, the Schwinger function, the relation to transition amplitudes, retardation and related adjectives for Greens functions and/or propagators, the Heat-Kernel and its seemingly privileged position, the spectral density, spectra and the resolvent.
Edit: I'd still like to hear about the "Correlation fuction interpretation" of the quantum field theoretical framework. Can transition amplitudes be seen as a sort of auto-correlation? Like... such that the QFT dynamics at hand just determine the structure of the temporal and spatial overlaps?
-
The propagator, the two-point correlation function, and the two-point Green's function are all synonymous. They are used primarily in quantum mechanics, and quantum field theory. They represent the probability of preparing a one particle state at $\vec{x}$ and then finding the particle at $\vec{y}$. – kηives Feb 10 '12 at 14:08
The main distinction you want to make is between the Green function and the kernel. (I prefer the terminology "Green function" without the 's. Imagine a different name, say, Feynman. People would definitely say the Feynman function, not the Feynman's function. But I digress...)
Start with a differential operator, call it $L$. E.g., in the case of Laplace's equation, then $L$ is the Laplacian $L = \nabla^2$. Then, the Green function of $L$ is the solution of the inhomogenous differential equation $$L_x G(x, x^\prime) = \delta(x - x^\prime)\,.$$ We'll talk about its boundary conditions later on. The kernel is a solution of the homogeneous equation $$L_x K(x, x^\prime) = 0\,,$$ subject to a Dirichlet boundary condition $\lim_{x \rightarrow x^\prime}K(x,x^\prime) = \delta (x-x^\prime)$, or Neumann boundary condition $\lim_{x \rightarrow x^\prime} \partial K(x,x^\prime) = \delta(x-x^\prime)$.
So, how do we use them? The Green function solves linear differential equations with driving terms. $L_x u(x) = \rho(x)$ is solved by $$u(x) = \int G(x,x^\prime)\rho(x^\prime)dx^\prime\,.$$ Whichever boundary conditions we what to impose on the solution $u$ specify the boundary conditions we impose on $G$. For example, a retarded Green function propagates influence strictly forward in time, so that $G(x,x^\prime) = 0$ whenever $x^0 < x^{\prime\,0}$. (The 0 here denotes the time coordinate.) One would use this if the boundary condition on $u$ was that $u(x) = 0$ far in the past, before the source term $\rho$ "turns on."
The kernel solves boundary value problems. Say we're solving the equation $L_x u(x) = 0$ on a manifold $M$, and specify $u$ on the boundary $\partial M$ to be $v$. Then, $$u(x) = \int_{\partial M} K(x,x^\prime)v(x^\prime)dx^\prime\,.$$ In this case, we're using the kernel with Dirichlet boundary conditions.
For example, the heat kernel is the kernel of the heat equation, in which $$L = \frac{\partial}{\partial t} - \nabla_{R^d}^2\,.$$ We can see that $$K(x,t; x^\prime, t^\prime) = \frac{1}{[4\pi (t-t^\prime)]^{d/2}}\,e^{-|x-x^\prime|^2/4(t-t^\prime)},$$ solves $L_{x,t} K(x,t;x^\prime,t^\prime) = 0$ and moreover satisfies $$\lim_{t \rightarrow t^\prime} \, K(x,t;x^\prime,t^\prime) = \delta^{(d)}(x-x^\prime)\,.$$ (We must be careful to consider only $t > t^\prime$ and hence also take a directional limit.) Say you're given some shape $v(x)$ at time $0$ and want to "melt" is according to the heat equation. Then later on, this shape has become $$u(x,t) = \int_{R^d} K(x,t;x^\prime,0)v(x^\prime)d^dx^\prime\,.$$ So in this case, the boundary was the time-slice at $t^\prime = 0$.
Now for the rest of them. Propagator is sometimes used to mean Green function, sometimes used to mean kernel. The Klein-Gordon propagator is a Green function, because it satisfies $L_x D(x,x^\prime) = \delta(x-x^\prime)$ for $L_x = \partial_x^2 + m^2$. The boundary conditions specify the difference between the retarded, advanced and Feynman propagators. (See? Not Feynman's propagator) In the case of a Klein-Gordon field, the retarded propagator is defined as $$D_R(x,x^\prime) = \Theta(x^0 - x^{\prime\,0})\,\langle0| \varphi(x) \varphi(x^\prime) |0\rangle\,$$ where $\Theta(x) = 1$ for $x > 0$ and $= 0$ otherwise. The Wightman function is defined as $$W(x,x^\prime) = \langle0| \varphi(x) \varphi(x^\prime) |0\rangle\,,$$ i.e. without the time ordering constraint. But guess what? It solves $L_x W(x,x^\prime) = 0$. It's a kernel. The difference is that $\Theta$ out front, which becomes a Dirac $\delta$ upon taking one time derivative. If one uses the kernel with Neumann boundary conditions on a time-slice boundary, the relationship $$G_R(x,x^\prime) = \Theta(x^0 - x^{\prime\,0}) K(x,x^\prime)$$ is general.
In quantum mechanics, the evolution operator $$U(x,t; x^\prime, t^\prime) = \langle x | e^{-i (t-t^\prime) \hat{H}} | x^\prime \rangle$$ is a kernel. It solves the Schroedinger equation and equals $\delta(x - x^\prime)$ for $t = t^\prime$. People sometimes call it the propagator. It can also be written in path integral form.
Linear response and impulse response functions are Green functions.
These are all two-point correlation functions. "Two-point" because they're all functions of two points in space(time). In quantum field theory, statistical field theory, etc. one can also consider correlation functions with more field insertions/random variables. That's where the real work begins!
-
Very nice answer. I wonder why when you introduce the Kernel, the $lim$ is taken to be w.r.t. the same arguments $x$ and $x'$ as the delta function, but later, you only use times. Also, in statistical mechanics, is the correlation function (which depend on the correlation length and which specify how macroscopic the effect are) a Green(s) function? I don't see any differential equations there. That's generally the problem I think, that I read the name Greens function, where there are no Differential equations and deltas around. Lastly, what about the functions characterizing susceptibilities? – Nikolaj K. Feb 11 '12 at 23:46
In how many dimensions you take the limit (i.e. just time or time and space) is sort of a matter of terminology, due to the fact that the $\delta$ function is zero everywhere except one point. For the limit of the heat kernel, for example, all I'm getting at is that if the two time coordinates approach one another and the spatial points are not equal, the result vanishes. But if they are equal and then the time coordinates are made to approach, you get a quantity that behaves like a $d$-dimensional $\delta$ function. – josh Feb 12 '12 at 17:46
To see how quantities like $W(x,x^\prime)=\langle0|\varphi(x)\varphi(x^\prime)|0\rangle$ satisfy the right differential equations and boundary conditions, read about Schwinger-Dyson Equations in QFT. And don't forget that when you canonically quantize a Klein-Gordon field, the canonical momentum $\pi = \partial_t\varphi$ and so $[\varphi(x,t),\partial_t\varphi(x^\prime,t)] = i\hbar\delta(x-x^\prime)$. This will matter in getting the right boundary conditions on the time-slice boundary. – josh Feb 12 '12 at 17:50 | {"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": 0.905916690826416, "perplexity": 283.95315453015905}, "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-2014-10/segments/1394023864525/warc/CC-MAIN-20140305125104-00087-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://brilliant.org/discussions/thread/gasters-testing-room/ | # Gaster's Testing Room :)
To test $\LaTeX$ Code and delete the comment in around a week
Strictly only sensible code, no abysses of white death and voids and stuff...
Otherwise I'll summon staff LOL :)
Note by Frisk Dreemurr
8 months, 4 weeks ago
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Attempt at creating a button -
- 7 months, 2 weeks ago
bruh
- 7 months, 2 weeks ago
lol trollbait :)
- 7 months, 2 weeks ago
lol, i clicked it. i m a fool.
- 7 months, 2 weeks ago
lol xd lmao, can't believe people still fall for that lol
- 7 months, 2 weeks ago
btw, this can be partly copied. did u just use standard color codes {#FFFFFF}, {#3D99F6} or is there a list?
- 7 months, 2 weeks ago
no, I used blue and white, but it gets changed to hexadecimal when you copy\paste
- 7 months, 2 weeks ago
- 8 months, 3 weeks ago
@Percy Jackson, have a thee
And you too @Nathan Soliman :)
- 8 months, 3 weeks ago
Honestly, its not that cool. You probably just put the image code in the square brackets and added your profile link to it. @Frisk Dreemurr
- 8 months, 2 weeks ago
Yes LOL
But we can use this for other stuff as well :)
- 8 months, 2 weeks ago
can you give me the code for the button and show me where to put image links bc i want to use it for my problem i posted
- 8 months, 2 weeks ago
1 [{}](link)
1 [{: .left}](https://brilliant.org/profile/frisk-tyxukn/)
The code of my comment :)
- 8 months, 2 weeks ago
Does the button work @Nathan Soliman, @Percy Jackson?
- 8 months, 3 weeks ago
yes did u use latex to make it? cus it looks pretty good
- 8 months, 3 weeks ago
btw i am not planning to delete all my comments after a week, i am not bothered
- 8 months, 3 weeks ago
@Frisk Dreemurr, the buttons send to your homepage, not sure how it works.
- 8 months, 2 weeks ago
what is the latex for it
- 8 months, 2 weeks ago
same question.
- 8 months, 2 weeks ago
this is really cool. but buttons work. ty for this idea
- 7 months, 2 weeks ago
@Frisk Dreemurr, be cautious of online posting, in one of your posts someone revealed your real name, so just reminder to delete it maybe.
- 7 months, 4 weeks ago
it u mean hamza? that was her old username if thats what u r talking abouy
- 7 months, 4 weeks ago
ik, I saw that so i said it here, and you are revealing it again (cybersecurity alert!)
- 7 months, 4 weeks ago
lol I have no problem if you call me by my real name
- 7 months, 4 weeks ago
I don't worry much about cyber-security, so it is okay for me
- 7 months, 4 weeks ago
@NSCS 747, @Half pass3 - Today is my bff's birthday, so we are all going to be playing Among us from 4PM to 9 or 10PM lol
- 7 months, 2 weeks ago
ok ..... ..... ......
- 7 months, 2 weeks ago
First time playing Among Us...
- 7 months, 2 weeks ago
ok hope u win
- 7 months, 2 weeks ago
Tips?
- 7 months, 2 weeks ago
in admin if u see someone go in alone go down outside untill u can see the vent fromm the poutside if it opens then they vented
never go into electrical alone
make sure u have proof otherwise they will think u r sus
if u r imposter after killing find someone to be ur alibi
do a routine which others will think u will do so they wont suspect u
id someone does a task but the bar does not go up they r imposter
for skeld if they r doing weapons task go to the left wall and look for the firing animation
watch youtube vids for more tips
- 7 months, 2 weeks ago
thnx, now that I've got tips from a pro I will win lol xd
- 7 months, 2 weeks ago
can i join ur rep.it team thingy
- 7 months, 2 weeks ago
Did you sign in to repl.it? Only if you have a login you can join. I will delete this after you join, so that others can't join anonymously :)
- 7 months, 2 weeks ago
plz invite me too
- 7 months, 2 weeks ago
Choose a demigod name from these -
Piper McLean
Frank Zhang
Leo Valdez
Jason Grace
Hazel Levesque
Then keep it as your name in repl.it and i will click the above link that i sent to Nathan
- 7 months, 2 weeks ago
can i choose nemisis prime
- 7 months, 2 weeks ago
Demigod names only, as it is a Heroes of olympus group. Your username can be nemesis prime if you want
- 7 months, 2 weeks ago
I see ur profile, Australian train lines lol.
- 7 months, 2 weeks ago
Did you join Srijan's team too?
- 7 months, 2 weeks ago
yup, switching between 2 accounts
- 7 months, 2 weeks ago
ok...
- 7 months, 2 weeks ago
- 7 months, 2 weeks ago
how do I join
- 7 months, 2 weeks ago
Click the link in the above comment were I told nscs747 to join
- 7 months, 2 weeks ago
and then? how do I change my name lol
- 7 months, 2 weeks ago
I can see you guys, you have joined
- 7 months, 2 weeks ago
what happens next
- 7 months, 2 weeks ago
Open the team repl that I created, then in the bottom right corner, there is a chat button, click it, and then I'll telll you rest over there. And please change your names, or i will kick you out :)
- 7 months, 2 weeks ago
$text {Oh god, why did I even visit this page ts just blowing up with notifications :( }$
- 8 months, 2 weeks ago
LOL, you can unsubscribe, it is at the top of the note, after the text
- 8 months, 2 weeks ago
Thanks! I tried to unsubscribe on the daily problems page once, but my solution got erased, so I was scared something would happen here too that's why
- 8 months, 2 weeks ago
it doesnt do that with notes but i think u get notifications if u have commented here
- 8 months, 1 week ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "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": 0.7451708316802979, "perplexity": 8060.749593585476}, "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/1623487621450.29/warc/CC-MAIN-20210615145601-20210615175601-00294.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/127943-matrices-breaking-down-word-problem.html | # Thread: matrices, breaking down the word problem
1. ## matrices, breaking down the word problem
I have no problem working the matrix once i have set things up. I have worked four problems without a glitch and find myself stuck on how to form the equation to work using the Gauss Jordan elimination method
The problem: A private investment club has $200,000 earmarked for investment in stocks. to arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk, medium risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year, medium 10%/year and low 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment (assume that all the money available for the investment is invested)
I had set things up as
x=high
y=med
z=low
and started my matrix as
1+1+1=200,000
.15+.10+.06=20,000
1-1-1=0
I worked the problem correctly, only to find out that my answer did not fit into the problem, thus i have started with the wrong matix equation
2. Originally Posted by cline1687
I have no problem working the matrix once i have set things up. I have worked four problems without a glitch and find myself stuck on how to form the equation to work using the Gauss Jordan elimination method
The problem: A private investment club has $200,000 earmarked for investment in stocks. to arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk, medium risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year, medium 10%/year and low 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment (assume that all the money available for the investment is invested)
I had set things up as
x=high
y=med
z=low
and started my matrix as
1+1+1=200,000
.15+.10+.06=20,000
1-1-1=0
Here is your problem. This is x- y- z= 0 or x= y+ z. But x is the number of high risk stocks. You said "the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories". Your final equation should be z= x+y which is the same as x+ y- z= 0 and so your final row is 1+1-1= 0.
I worked the problem correctly, only to find out that my answer did not fit into the problem, thus i have started with the wrong matix equation | {"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": 0.638363242149353, "perplexity": 689.6534647140068}, "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-2016-44/segments/1476988720000.45/warc/CC-MAIN-20161020183840-00220-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.aanda.org/articles/aa/full_html/2010/09/aa13593-09/aa13593-09.html | Subscriber Authentication Point
Free Access
Issue A&A Volume 517, July 2010 A77 18 Extragalactic astronomy https://doi.org/10.1051/0004-6361/200913593 11 August 2010
A&A 517, A77 (2010)
## Relating dust, gas, and the rate of star formation in M 31
F. S. Tabatabaei - E. M. Berkhuijsen
Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
Received 3 November 2009 / Accepted 26 April 2010
Abstract
Aims. We investigate the relationships between dust and gas, and study Methods. We have derived distributions of dust temperature and dust opacity across M 31 at 45 resolution using the Spitzer data. With the opacity map and a standard dust model we de-reddened the H emission yielding the first H map of M 31 corrected for extinction. We compared the emissions from dust, H, HI, and H2 by means of radial distributions, pixel-to-pixel correlations, and wavelet cross-correlations. We calculated the star formation rate and star formation efficiency from the de-reddened H emission.
Results. The dust temperature steeply decreases from 30 K near the center to 15 K at large radii. The mean dust optical depth at the H wavelength along the line of sight is about 0.7. The radial decrease in the dust-to-gas ratio is similar to that of the oxygen abundance. Extinction is nearly linearly correlated with the total gas surface density within limited radial intervals. On scales <2 kpc, cold dust emission is best correlated with that of neutral gas, and warm dust emission with that of ionized gas. The H emission is slightly better correlated with emission at 70 m than at 24 m. The star formation rate in M 31 is low. In the area 6 kpc < R < 17 kpc, the total SFR is 0.3 . A linear relationship exists between surface densities of SFR and H2. The Kennicutt-Schmidt law between SFR and total gas has a power-law index of 1.30 0.05 in the radial range of R=7-11 kpc increasing by about 0.3 for R = 11-13 kpc.
Conclusions. The better 70 m-H than 24 m-H correlation plus an excess in the 24 m/70 m intensity ratio indicates that other sources than dust grains, e.g. those of stellar origin, contribute to the 24 m emission. The lack of H2 in the central region could be related to the lack of HI and the low opacity/high temperature of the dust. Since neither SFR nor SFE is well correlated with the surface density of H2 or total gas, other factors than gas density must play an important role in the formation of massive stars in M 31. The molecular depletion time scale of 1.1 Gyr indicates that M 31 is about three times less efficient in forming young massive stars than M 33.
Key words: galaxies: individual: M 31 - galaxies: ISM - dust, extinction - ISM: general - stars: formation
## 1 Introduction
Dust, neutral gas, and ionized gas are the major components of the interstellar medium (ISM) in galaxies. Observations of their properties and inter-relationships can give strong clues to the physics governing star formation. Relationships between components in the ISM are to be expected. Observations have shown that in the Galaxy dust and neutral gas are well mixed. In dense clouds of molecular gas mixed with cold dust most of the stars are formed. They subsequently heat the dust and gas in their surroundings and ionize the atomic gas. As the major coolants of the ISM are continuum emission and line emission at various frequencies, a close comparison of these emissions could shed light on spatial and physical connections between the emitting components. Present-day IR and radio telescopes have produced sensitive high-resolution maps of several nearby galaxies, which are ideal laboratories for studying the interplay between the ISM and star formation (e.g. Bigiel et al. 2008; Kennicutt et al. 2007; Verley et al. 2009).
The spiral galaxy nearest to us, the Andromeda Nebula (NGC 224), is a highly inclined Sb galaxy of low surface brightness. Table 1 lists the positional data on M 31. Its proximity and large extent on the sky (> ) enable detailed studies of the ISM over a wide radial range.
Surveys of M 31 at high angular resolution (< ) are available at many wavelengths. In the HI line the galaxy was mapped by Brinks & Shane (1984) at resolution, the northeastern half by Braun (1990) at 10 resolution, and most recently, the entire galaxy with high sensitivity by Braun et al. (2009) at a resolution of 15 . Nieten et al. (2006) made a survey in the 12CO(1-0) line at a resolution of 23 . Devereux et al. (1994) observed M 31 in the H line to obtain the distribution of the ionized gas. The dust emission from M 31 has recently been observed by the multiband imaging photometer Spitzer (MIPS, Rieke et al. 2004) with high sensitivity at 24 m, 70 m, and 160 m at resolutions .
Table 1: Positional data adopted for M 31.
Table 2: M 31 data used in this study.
The relationships between gas and dust, as well as between gas and star formation, in M 31 have been studied in the past at resolutions of several arcminutes. Walterbos & Schwering (1987) derived a nearly constant dust temperature across M 31 using the IRAS 100 m and 60 m maps. They also found a strong increase in the atomic gas-to-dust surface density ratio with increasing radius. This increase was confirmed by Walterbos & Kennicutt (1988) who used optical extinction as dust tracer, and by Nieten et al. (2006) using the ISO map at 175 m (Haas et al. 1998). Interestingly, the latter authors did not find a radial increase in the molecular gas-to-dust ratio.
The dependence of star formation on HI surface density in M 31 has been studied by a number of authors (Berkhuijsen 1977; Emerson 1974; Tenjes & Haud 1991; Nakai & Sofue 1984; Unwin 1980; Nakai & Sofue 1982) using the number density of HII regions or of OB stars as star formation tracers. They obtained power-law indices between 0.5 and 2, possibly depending on the region in M 31, the star formation tracer and the angular resolution. Braun et al. (2009) plotted the star formation density derived from the brightnesses at 8m, 24m, and UV against the surface densities of molecular gas, HI, and total gas, but did not fit power laws to their data.
The high-resolution data available for M 31 show the morphologies of the emission from dust and gas components in detail. We apply a 2-D wavelet analysis technique (Frick et al. 2001) to the MIPS IR data (Gordon et al. 2006) and the gas (HI, H2, and H) maps to study the scale distribution of emission power and to separate the diffuse emission components from compact sources. We then compare the wavelet-decomposed maps at various spatial scales. We also use pixel-to-pixel (Pearson) correlations to derive quantitative relations not only between different ISM components but also between them and the present-day star formation rate.
Following Walterbos & Schwering (1987) and Haas et al. (1998), we derive the dust temperature assuming a emissivity law for the MIPS bands at which the emission from the big grains and hence the LTE condition is relevant, and present a map of the dust color temperature. We also obtain the distribution of the optical depth and analyze the gas-to-dust surface-density ratio at a resolution of 45 (170 pc 660 pc along the major and minor axis, respectively, in the galaxy plane), 9 times higher than before (Walterbos & Schwering 1987). We use the optical depth map to de-redden the H emission observed by Devereux et al. (1994) yielding the distribution of the absorption-free emission from the ionized gas, and use this as an indicator of massive star formation. We compare it with the distributions of neutral gas to obtain the dependence of the star formation rate on gas surface density.
Figure 1: Dust temperature in M 31 obtained from the ratio / based on the Spitzer MIPS data. Only pixels with intensity above 3 noise level were used. The angular resolution of 45 is shown in the lower right-hand corner of the map. The cross indicates the location of the center. The bar at the top gives the dust temperature in Kelvin. Open with DEXTER
The paper is organized as follows: The relevant data sets are described in Sect. 2. In Sect. 3 we derive maps of the dust color temperature and optical depth, and correct the H emission for absorption by dust. Radial profiles of the dust and gas emission and of the various gas-to-dust ratios are obtained in Sect. 4. Section 5 is devoted to wavelet decompositions and wavelet spectra of the dust and gas distributions, and their cross correlations. Complementary, we discuss in Sect. 6 classical correlations between gas and dust. In Sect. 7 the dependence of the star formation rate on the gas surface density is presented. Finally, in Sect. 8 we summarize our results.
## 2 Data
Table 2 summarizes the data used in this work. M 31 was mapped in IR (at 24 m, 70 m, and 160 m) by MIPS in August 2004 covering a region of about 1 (Gordon et al. 2006). The basic data reduction and mosaicing was performed using the MIPS instrument team Data Analysis Tool versions 2.90 (Gordon et al. 2005).
M 31 was observed in the 12CO(1-0) line with the IRAM telescope by Nieten et al. (2006) at a resolution of 23 . They derived the distribution of the molecular gas using a constant conversion factor of X mol. K-1 km-1 s. The galaxy was observed in the 21-cm HI line with the Westerbork interferometer by Brinks & Shane (1984) at a resolution of 24 . The HI survey has been corrected for missing spacings. The H observations of Devereux et al. (1994) were carried out on the Case Western Burell-Schmidt telescope at the Kitt Peak National Observatory, providing a 2 field of view.
Although the resolution of 40 of the 160 m image is the lowest of the data listed in Table 2, we smoothed all maps to a Gaussian beam with a half-power width of 45 for a comparison with radio continuum data at 20 cm (Hoernes et al. 1998) in a forthcoming study (Tabatabaei et al. in prep.). As the point spread function (PSF) of the MIPS data is not Gaussian, we convolved the MIPS images using custom kernels created with Fast Fourier transforms to account for the detailed structure of the PSFs. Details of the kernel creation can be found in Gordon et al. (2007).
After convolution, the maps were transformed to the same grid of 15 width with the reference coordinates and position angle of the major axis given in Table 1. Finally, they were cut to a common extent of 110 , for which most data sets are complete. The field is not centred on the nucleus of M 31, but extends to 56 25 along the northern major axis (corresponding to a radius of R = 12.8 kpc) and to 53 75 along the southern major axis (R = 12.2 kpc). The H2 map of Nieten et al. (2006) extends to 48 5 along the southern major axis (R = 11.0 kpc). With an extent of 19 25 along the minor axis in both directions, the field covers radii of R <16.9 kpc in the plane of M 31. Hence, radial profiles derived by averageing the data in circular rings in the plane of the galaxy (equivalent to elliptical rings in the plane of the sky) are incomplete at R> 12 kpc because of missing data near the major axis.
## 3 Dust temperature and opacity
Walterbos & Schwering (1987) extensively studied the distributions of the dust temperature and opacity in M 31 using the IRAS data at 60 m and 100 m smoothed to a resolution of . Assuming a emissivity law, they found a remarkably constant dust temperature (21-22 K) across the disk between 2 kpc and 15 kpc radius. Using this temperature, they obtained the opacity distribution at 100 m. Below we apply a similar method to the 70 m and 160 m MIPS maps to derive the distributions of dust temperature and optical depth at the H wavelength at higher resolution and sensitivity.
### 3.1 Dust temperature
We derived the color temperature of the dust, , between 70 m and 160 m assuming a emissivity law that should be appropriate for interstellar grains emitting at these wavelengths (Draine & Lee 1984; Andriesse 1974). The resulting dust temperature map (Fig. 1) and a histogram of the temperatures (Fig. 2a) show that varies between 15.6 0.8 K and 30.8 0.3 K. The mean value of 18.7 1.4 K (standard deviation) is lower than that obtained by Walterbos & Schwering (1987) and close to the ISO measurements (16 2 K) of Haas et al. (1998). Figure 1 shows that dust of 18 K exists all over M 31. Warmer dust with K dominates in starforming regions and in an extended area around the center of the galaxy, while cooler dust dominates in interarm regions.
Figure 2b shows the dust temperature averaged in rings of 0.2 kpc width in the plane of M 31 against radius R. On both sides of the center the dust temperature falls very fast from about 30 K near the nucleus to 19 K at kpc. To the outer parts of the galaxy, it then stays within a narrow range of about 17 K-19 K in the north and 16 K-19 K in the south. This indicates different radiation characteristics between the inner 4 kpc and beyond. In the ring of bright emission, the so called 10 kpc ring'', the temperature is clearly enhanced, especially in the northern half. Thus, in contrast to the finding of Walterbos & Schwering (1987), is not constant in the range R = 2-15 kpc but varies between 22.5 0.5 K and 17.2 0.7 K.
It is interesting that the mean dust temperature obtained between 70 m and 160 m is about 3 K lower in M 31 than in M 33 (Tabatabaei et al. 2007b). The emission from cold dust in M 31 is stronger than in M 33, which can also be inferred from the total emission spectra based on IRAS and ISO observations (see Hippelein et al. 2003; Haas et al. 1998).
Figure 2: a) Histogram of the dust temperature shown in Fig. 1. b) Distribution of the dust temperature in rings of 0.2 kpc in the galactic plane in the northern and southern halves of M 31. Open with DEXTER
Figure 3: Distribution of the dust optical depth at H wavelength in M 31. The bar at the top shows . The angular resolution of 45 is shown in the lower right-hand corner of the map. The cross indicates the location of the center. Overlayed are contours of molecular gas column density N(H2) with levels of 250 and 800 mol. cm-2. Note that maxima in not always coincide with maxima in N(H2). Open with DEXTER
### 3.2 Dust opacity distribution
The total dust optical depth along the line of sight was obtained from the dust intensity at 160 m and the derived temperature. Following Tabatabaei et al. (2007b), was converted into the dust optical depth at the wavelength of the H line, , by multiplying it by the ratio of the dust extinction coefficient per unit mass at the corresponding wavelengths, (see e.g. Fig. 12.8 of Krügel 2003). Figure 3 shows the distribution of across the disk of M 31 at an angular resolution of 45 . Regions with considerable dust opacity ( ) follow the spiral arms, even the inner arms which are either weak or not detected in H emission. The high opacity clumps ( ), however, only occur in the arms at 5 kpc and in the 10 kpc ring''. On average, the optical depth is largest in the 10 kpc ring''. Hence, in this ring, dust has the highest density like the atomic gas (Brinks & Shane 1984). Figure 4a shows the histogram of , indicating a most probable value of 0.5 and a mean value of 0.7 0.4 across the galaxy. This agrees with the value of = 0.5 0.4 that follows from the mean total extinction obtained by Barmby et al. (2000) towards 314 globular clusters.
The variation of the mean dust optical depth with galactocentric radius is shown in Fig. 4b. In the north, peaks not only in the 10 kpc ring'' (with two maxima at R = 9.9 and 10.9 kpc) but also near 5 kpc (with two maxima at R = 4.3 and 5.9 kpc). Beyond 11 kpc drops with an exponential scale length of 2.48 0.07 kpc in the north and 5.06 0.22 kpc in the south (Sect. 4, Eq. (1)).
In Fig. 5 we compare the radial variation of for the total area with earlier determinations. The various estimates agree well given the large uncertainties. Xu & Helou (1996) derived from high-resolution IRAS data using a dust heating/cooling model and a sandwich configuration of dust and stars. Although they left out the discrete sources, their values may be too high because they did not include inter-arm regions in their study. Montalto et al. (2009) calculated the extinction from the total infrared TIR-to-FUV intensity ratio and a sandwich model for stars and dust. They note that at R < 8 kpc the geometry of M 31 may differ from the sandwich model due to the stars in the bulge, making the inner points less reliable. This would also affect the results of Xu & Helou (1996) at R <8 kpc. The TIR-to-FUV ratio is applicable if the dust is mainly heated by young stars, but in M 31 about 70% of the cold dust is heated by the ISRF (Xu & Helou 1996). Therefore, is overestimated, as was also found for M 33 (Verley et al. 2009). The curve of Tempel et al. (2010) closely agrees with our data. They derived from MIPS data and a star-dust model. Their smooth curve underestimates in the brightest regions by about 0.1 and may overestimate in regions of low brightness.
Figure 4: a) Histogram of the dust optical depth shown in Fig. 3, b) radial distribution of the mean optical depth at the H wavelength in rings of width of 0.2 kpc in the galactic plane in the north and south of M 31. The errors are smaller than the size of the symbols. Open with DEXTER
The opacity map in Fig. 3 can be used to correct the H emission for the extinction by dust. In general, extinction depends on the relative distribution of emitting regions and dust along the line of sight and changes with the geometry (e.g. well mixed diffuse medium or shell-like in HII regions Witt & Gordon 2000). In this study, individual HII regions are rarely resolved and the geometry is close to a mixed diffuse medium. Furthermore, there is no information about the relative position of emittors and absorbers along the line of sight. For the Milky Way, Dickinson et al. (2003) found indications of a non-uniform mixing by comparing the z-distribution of atomic gas and dust. They adopted one third of the total dust optical depth as the effective extinction as a first-order approach. This is also in agreement with Krügel (2009) taking scattering into account. Moreover, Magnier et al. (1997) found that on average the extinction comes from dust associated with only one-third of average N(HI) in their study of OB associations along the eastern spiral arm regions of M 31. Therefore, we use an effective optical depth in this paper. The attenuation factor for the H intensity then is e and we derive the intrinsic H intensity I0 from the observed H intensity . Integration of the H map out to a radius of 16 kpc yields a ratio of corrected-to-observed total H flux density of 1.29, thus about 30% of the total H emission is obscured by dust within M 31. The corrected H map is shown in Fig. 10a.
Figure 5: Radial variation of the (total) mean optical depth in H along the line of sight for the full area (north+south). Plusses: our data averaged in 0.2 kpc-wide rings in the plane of M 31 using i = 75; stars: same but with i = 77.5 for comparison with other work; triangles: Xu & Helou (1996), averages in 2 kpc-wide rings with i = 77 (scaled to D = 780 kpc); circles: Montalto et al. (2009), averages in 2 kpc-wide rings with i = 77.6; solid line: Tempel et al. (2010), semi-major axis cut through model with i = 77.5. The errors in our data and in the curve of Tempel et al. (2010) are about 10% of the mean values. Open with DEXTER
Near the center (R < 1 kpc), varies between 0.03 and 0.13, corresponding to an extinction of -0.14 mag. At larger radii, the mean extinction increases, particularly in dense clouds and starforming regions, reaching a maximum of 1.2 mag at the densest dust cloud in the south-east of the 10 kpc ring'' (RA = 00 41 05.10 and Dec = +40 38 17.73 ). The range of extinction values agrees with that derived from the optical study of dust lanes by Walterbos & Kennicutt (1988) and the photometric study of Williams (2003).
## 4 Radial distributions of dust and gas emission
In this section, we present the mean surface brightness along the line of sight of dust and gas components as a function of galactocentric radius R. The surface brightnesses are averaged in 200 pc-wide circular rings about the nucleus in the plane of M 31. This is equivalent to averaging in elliptical rings of 53 width in the plane of the sky.
For simplicity we used a constant inclination angle of 75 at all radii, appropriate for the emission at (6.8 kpc), although in H and HI the inner regions are seen more face-on (Chemin et al. 2009; Ciardullo et al. 1988; Braun 1991). However, using for instead of (the area-weighted mean of the inclinations for the interval R=1.9-6.8 kpc given by Chemin et al. 2009) does not change our results. The smaller inclination shifts the radial positions of the inner arms about 0.5 kpc inwards but the general shape of the profiles remains the same, and as all profiles change in a similar way their inter-comparison is not affected. Furthermore, the results of the classical correlations for presented in Sect. 6 are the same within the errors for and .
Figure 6 shows the mean IR intensities and the gas surface densities versus the galactocentric radius R for the northern and southern halves of M 31. The radial profiles of the IR emission at 24 m and 70 m are similar. The 160 m emission, representing the colder dust emission, however, shows a generally flatter radial distribution than the 24 m and 70 m emission. In particular, the fast decrease in the 24 m and 70 m profiles from the center to kpc does not occur at 160 m. This is in agreement with Haas et al. (1998) who concluded from their ISO 175 m map and IRAS data that the dust near the center is relatively warm. The fast central decrease in warmer dust emission may be attributed to a decrease in the UV radiation field outside the nucleus, as a similar trend is seen in the GALEX UV profiles presented by Thilker et al. (2005). At all three IR wavelengths the arms are visible, even the weak inner arms. The bright arms forming the 10 kpc ring'', are pronounced in the north and followed by an exponential decrease toward larger radii.
Figure 6: Top: radial profiles of the Spitzer IR emission from the northern ( left) and the southern ( right) halves of M 31. Bottom: radial profiles of the surface densities of the atomic, molecular and total neutral gas together with that of the ionized gas (de-reddened H) for the northern ( left) and southern ( right) halves of M 31. The units are 1018 atoms cm-2 for HI and HI+2H2, 1018 molecules cm-2 for H2, and 1010 erg s-1 cm-2 sr-1 for H profiles. The profiles show intensities along the line of sight averaged in circular rings of 0.2 kpc width in the plane of M 31 against the galactocentric radius. The errors are smaller than 5% for all profiles, only for H2 they increase from 10% to 25% at R>12.3 kpc and in the inner arms for R<4.5 kpc. Open with DEXTER
Although the general trend of the warm dust surface brightness (at 24 m and 70 m) resembles more that of H than those of the neutral gas profiles (Fig. 6, lower panels), small variations (e.g. in the inner 5 kpc and for R = 11-12 kpc in the south) follow those in the total gas distribution due to variations in the molecular gas. Beyond about 5 kpc, the radial profile of the cold dust (160 m) is similar to that of the molecular gas, but with smoother variations. The minimum between 5 kpc and 10 kpc radius at 24 m and 70 m is less deep at 160 m and is missing in the HI profile.
We obtained radial scale lengths between the maximum in the 10 kpc ring'' and R=14.9 kpc for the northern () and southern () halves of M 31 separately as well as for the total area (l). We fit an exponential function of the form
(1)
where I0 is the intensity at R = 10.9 kpc for the total area and in the north, and R = 8.9 kpc in the south. The resulting scale lengths are listed in Table 3.
In each half of M 31, the scale lengths of the warm dust emission are smaller than that of the cold dust. This confirms that the warm dust is mainly heated by the UV photons from the starforming regions in the 10 kpc ring'' and the cold dust mainly by the interstellar radiation field (ISRF) from old stars (Xu & Helou 1996).
Table 3: Exponential scale lengths of dust and gas emissions from M 31.
The scale lengths of the 24 m and 70 m emission are nearly the same and the 24 m-to-70 m intensity ratio (Fig. 7) hardly varies between kpc and kpc. This indicates a similar distribution of their origins. Assuming that the main source of the 24 m emission is very small dust grains and of the 70 m and 160 m emission is big grains, as argued by Walterbos & Schwering (1987), a constant intensity ratio of the 24 m-to-70 m and 24 m-to-160 m emission suggests that the very small and big grains are well mixed in the interstellar medium. Other possible origins of the 24 m emission are stars with dust shells like evolved AGB stars or Carbon stars. Using the IRAS data, (Soifer et al. 1986) attributed the 25 m emission from the bulge (central 8 ) of M 31 to circumstellar dust emission from late-type stars. In the disk of M 31, Walterbos & Schwering (1987) found no direct evidence of a contribution from stars with dust shells (contrary to that in the Milky Way, Cox et al. 1986).
The higher resolution and sensitivity of the MIPS IR intensity ratios (Fig. 7), however, provide more information. Although at R > 3 kpc the variations in the IR intensity ratios are not large, their radial behavior is not the same. For instance, the 24-to-70 m intensity ratio peaks between 5 kpc and 10 kpc radius, whereas the 70-to-160 m intensity ratio peaks in the 10 kpc ring''. The latter can be explained by the higher temperature of the dust heated by OB associations in the 10 kpc ring''. The fact that the 24-to-70 m intensity ratio is not enhanced in the 10 kpc ring'' (and in the central region) shows the invalidity of this ratio for temperature determination due to the important contribution from the very small grains. On the other hand, the enhancement of the 24-to-70 m in regions where there is no strong radiation field (between the arms) reveals possibly different origins of the 24 m and 70 m emission. The stellar origin, e.g. photosphere of cool stars or dust shell of the evolved stars, may provide the enhancement of the 24-to-70 m intensity ratio in the inter-arm region. In M 33, Verley et al. (2009) attributed a similar enhancement of the diffuse 24 m emission to dusty circumstellar shells of unresolved, evolved AGB stars. For M 31, this needs to be quantified through a more detailed study and modeling of the spectral energy distribution, which is beyond the scope of this paper.
Figure 7: Ratio of the MIPS IR intensities against galactocentric radius in M 31. Open with DEXTER
Figure 8: Radial profiles of the gas-to-dust ratios in M 31, the northern half and the southern half. Top: N(HI)/ , middle: N(2H2)/ , bottom: N(HI + 2H2)/ . In the middle panel, the northern profile is shifted by 300 units for clarity. The errors are smaller than 5% everywhere only for N(2H2)/ they increase from 10% to 25% at R>12.3 kpc and in the inner arms for R<4.5 kpc. Open with DEXTER
### 4.2 Gas-to-dust ratio
The gas-to-dust mass ratio and its variation across the galaxy can provide information about the metallicity distribution (e.g. Viallefond et al. 1982) and hence about the evolutionary history of the galaxy. The relative amount of dust and gas is expected to be correlated with the abundance of the heavy elements (Draine et al. 2007).
A number of authors has studied the gas-to-dust ratio in M 31 by comparing HI column densities and optical or UV extinction (Walterbos & Kennicutt 1988; Xu & Helou 1996; Savcheva & Tassev 2002; Bajaja & Gergely 1977; Nedialkov et al. 2000). All authors found an increase in the atomic gas-to-dust ratio with radius. Walterbos & Schwering (1987) derived the HI gas-to-dust ratio using dust optical depth from IRAS 60 m and 100 m data. They found a radial gradient that is 4-5 times larger than the abundance gradient of Blair et al. (1982). After adding the molecular and atomic gas column densities, Nieten et al. (2006) obtained a strong radial increase in the total gas-to-175 m intensity resulting from the increase in the atomic gas-to-175 m intensity. As the dust optical depth is a better measure for the dust column density than the temperature-dependent dust emission, we re-investigated the gas-to-dust ratio in M 31 taking advantage of the high resolution of the Spitzer MIPS data.
We calculated the radial profiles of the three gas-to-dust ratios from the mean column densities of N(HI), N(2H2), N(HI + 2H2) and in circular rings of 0.2 kpc width in the plane of the galaxy. Figure 8 (upper panel) shows that the atomic gas-to-dust ratio increases exponentially with radius by more than a factor of 10 from about at cm-2 at the center to about at cm-2 at R = 15 kpc. The increase is surprisingly smooth and, at least up to R = 13 kpc, nearly the same for the northern and southern half, indicating little variation between arm and inter-arm regions and within the arms. In contrast, the molecular gas-to-dust ratio (Fig. 8, middle panel) does not increase systematically with radius but shows clear enhancements of a factor 2-3 in the spiral arms and the 10 kpc ring''. The minima in the inter-arm regions are due to a stronger decrease in N(2H2) than in . Figure 3 shows that along the arms N(2H2)/ also varies significantly because maxima in H2 emission and are often not coincident. The variations in N(2H2)/ are visible in the profile of the total gas-to-dust ratio (Fig. 8, bottom panel) as weak enhancements at the positions of the arms near R = 6 kpc and R = 8-12 kpc. As the atomic gas is the dominant gas phase in M 31, dust mixed with HI gas largely determines the optical depth. Inspection of the distribution of the total gas-to-dust ratio across M 31 (not shown) reveals small-scale variations along the arms of typically a factor of 2.
Table 4: Exponential scale lengths L and radial gradients of dust-to-gas ratios and the abundance [O/H].
We conclude that the radial increase in the total gas-to-dust ratio of more than a factor 10 between the center and R=15 kpc is entirely due to that of the atomic gas-to-dust ratio, whereas the molecular gas-to-dust ratio is only increased in the arms. This confirms the conclusion of Nieten et al. (2006) based on the same gas data and the 175 m intensity.
At which radius in M 31 would the gas-to-dust ratio observed in the solar neighborhood occur? Bohlin et al. (1978) and Diplas & Savage (1994) derived N(HI)/ at cm-2 mag-1 and at cm-2 mag-1, respectively, using the extinction towards large samples of stars to determine the color excess E(B-V). Since E(B-V) = /, where the visual extinction = 1.234 mag (e.g. Krügel 2003) and the total/selective extinction = 2.8 0.3 in M 31 (Walterbos & Kennicutt 1988), we have E(B-V) = 0.44 mag-1. Hence, a value of N(HI)/ at cm-2 mag-1 corresponds to N(HI)/ = at cm-2, which occurs in M 31 near R=8.5 kpc (Fig. 8, top panel), just in the bright emission ring. The total gas-to-dust ratio near the sun of at cm-2 mag-1 (Bohlin et al. 1978) corresponding to N(gas)/ at cm-2 occurs at nearly the same radius (Fig. 8, bottom panel). Thus the gas-to-dust ratio near the sun is similar to that in the 10 kpc ring'' in M 31, in agreement with earlier studies (van Genderen 1973; Walterbos & Schwering 1987).
In contrast to Fig. 8, we present in Fig. 9 the radial profiles of the dust-to-gas ratios, here for the total area in M 31. The two lower curves closely follow exponentials with scale lengths of 6.1 0.2 kpc and 7.4 0.2 kpc for /N(HI) and /N(gas), respectively, between R = 5 kpc and R = 15 kpc (see Table 4). For nearly the same radial range (R = 3-15 kpc), Walterbos & Schwering (1987) derived a scale length of /N(HI) 4 kpc from data near the major axis. Walterbos & Kennicutt (1988) obtained a scale length of /N(HI) 9 kpc for the inner and outer dust lanes, and the /N(HI) ratio of Xu & Helou (1996) for diffuse spiral arm regions also indicates a scale length of about 4 kpc (all scale lengths were scaled to D = 780 kpc). Since our scale lengths are not restricted to specific areas, our results are more representative for the mean dust-to-gas ratios in the disk of M 31.
As dust consists of heavy elements and both dust and heavy elements are found in star formation regions, the radial variations in the dust-to-gas ratio and the metal abundance are expected to be similar (e.g. (Hirashita et al. 2002; Hirashita 1999). This has indeed been observed in several nearby galaxies (Issa et al. 1990). In M 31 the variation in the metallicity with radius is not well established. Measurements of the element abundance strongly depend on the empirical method and calibration applied (Trundle et al. 2002). Pagel et al. (1979) showed that the ([OII] + [OIII])/H ratio (the so called R23'') is a good probe of oxygen abundance and radial trends of this ratio have been studied in many nearby galaxies (e.g. Evans 1986; Pagel & Edmunds 1981; Henry & Howard 1995; Garnett et al. 1997). Blair et al. (1982) and Dennefeld & Kunth (1981) derived R23 for HII regions in M 31. We combined their results and derived a scale length of log [O/H] of 9.7 2.6 kpc corresponding to a gradient of 0.045 dex/kpc (Table 4). Comparing four different calibrations, Trundle et al. (2002) derived gradients of 0.027-0.013 dex/kpc using the 11 HII regions of Blair et al. (1982), with Pagel's calibration giving 0.017 0.001 dex/kpc. Since our value of the [O/H] gradient is based on 19 HII regions, we expect it to be more reliable than that of Trundle et al. (2002).
Table 4 shows that the radial gradient in /N(gas) best matches the metallicity gradient. In view of the large uncertainties, the gradients in the dust-to-gas surface-density ratio and the oxygen abundance in M 31 may indeed be comparable. A much larger sample of abundance measurements of HII regions is needed to verify this similarity. Our result agrees with the approximately linear trend between gradients in dust-to-gas ratios and [O/H] in nearby galaxies noted by Issa et al. (1990).
Figure 9: Dust-to-gas ratios as function of galactocentric radius for M 31, calculated from the radial profiles of , N(HI), N(2H2) and N(HI + 2H2) = N(gas). Open with DEXTER
## 5 Wavelet analysis of dust and gas emission
To investigate the physical properties of different phases of the interstellar medium as a function of the size of emitting regions, wavelet transformation is an ideal tool. We use the Pet Hat wavelet (see Frick et al. 2001; Tabatabaei et al. 2007a) to decompose the emissions of IR, HI, H2, HI + 2H2, and de-reddened H into 10 spatial scales starting at 0.4 kpc (about twice the resolution). The central 2 kpc was subtracted from all images before the wavelet transformation to prevent a strong influence of the nucleus on the results. As an example, we show the extinction-corrected H map and the H emission for 3 different scales in Fig. 10. On the scale of 0.4 kpc, the distribution of HII complexes and large HII regions is borne out. The scale of 1.6 kpc (the typical width of spiral arms) shows connected HII complexes along the arms, and on the scale of 4 kpc we see the extended emission from the 10 kpc ring''.
### 5.1 Wavelet spectra
The wavelet spectrum, M(a), represents the distribution of the emitting power as function of the scale a. The wavelet spectrum will smoothly increase towards larger scales if most of the emission is coming from diffuse structures forming the largest scales, here up to 25 kpc. On the other hand, the spectrum will decrease with increasing scale if compact structures are the dominant source of emission. The spectra of the IR and gas emission are shown in Fig. 11.
All IR and gas spectra are intermediate between the two cases described above. Only the spectra of the HI gas and the 160 m emission generally increase with scale indicating the importance of diffuse HI and cold dust emission. In addition, the HI spectrum exhibits a dominant scale at kpc corresponding to the width of the 10 kpc ring'', where strong diffuse emission occurs in interarm regions. The large width of the HI ring'' is also visible in the radial profiles in Fig. 6. The dominant scale of the emission from warm dust, molecular gas and H is near 1 kpc, where complexes of giant molecular clouds and starforming regions show up. The IR spectra at 24 m and 70 m on scales a< 6 kpc look most similar indicating that the starforming regions are the main heating sources at both wavelengths. On the other hand, the effect of the ISRF heating the cold dust is well indicated in the 160 m spectrum where a general increase towards larger scales is found. All spectra, apart from that of HI, show a minimum near a = 6 kpc corresponding to the large, weak interarm region inside the 10 kpc ring''. The spectrum of H is most similar to that of 70 m, which may explain why the H emission correlates better with 70 m emission than with that at 24 m (see Sect. 6.2 and Table 6).
The spectrum of the H emission is flat on small scales up to 1.6 kpc, the width of the spiral arms in the H map. This is understandable as the emission from very compact HII regions is unresolved at our resolution and not many large HII complexes exist especially in the south (see the decomposed map in Fig. 10b of a = 0.4 kpc).
### 5.2 Wavelet cross-correlations
We derive the cross-correlation coefficients, rw(a), for different scales following Tabatabaei et al. (2007a). The correlation coefficients are plotted in terms of scale in Fig. 12. They show that IR emission correlates with the emission from different gas phases on most scales. In all cases, emission from structures on scales larger than 10 kpc are best correlated. This corresponds to scales of the diameter of the 10 kpc ring'' and the over-all structure of the galaxy. On medium scales, the weakest correlation occurs between HI and dust emission on a= 6 kpc. This scale includes areas of significant diffuse HI emission where the dust emission is weak interior to the 10 kpc ring'' (compare also Fig. 11). On the smallest scale of 0.4 kpc, the cold dust emission is best correlated with that of the total neutral gas, while the warm dust emission at 70 m is best correlated with the ionized gas emission. Note that on this scale, the 24 m and 70 m (warm dust) emissions hardly correlate with HI ( rw(a)<0.5) because only a small fraction of the HI emission occurs on this scale (see Fig. 11). Furthermore, the coefficients of the 70 m-H correlation are higher than those of the 70 m-neutral gas correlation on scales a < 6.3 kpc.
Figure 10: Distribution of the de-reddened H emission a) and the wavelet decomposition for scales 0.4, 1.6, 4.0 kpc b) to d). The central 2 kpc was subtracted from the H map before the decomposition. The cross in the H map indicates the location of the center. Open with DEXTER
Figure 11: Wavelet spectra of MIPS IR ( left) and gas ( right) emission in M 31, shown in arbitrary units. The data points correspond to the scales 0.4, 0.6, 1.0, 1.6, 2.5, 4.0, 6.3, 10.0, 15.9, 25.1 kpc. Open with DEXTER
Figure 12: Wavelet cross correlations of atomic gas ( top-left), molecular gas ( top-right), and total neutral gas ( bottom-left) with IR emission in M 31. The IR correlation with the ionized gas ( bottom-right) is also shown. The data points correspond to the scales 0.4, 0.6, 1.0, 1.6, 2.5, 4.0, 6.3, 10.0, 15.9, and 25.1 kpc. Open with DEXTER
## 6 Classical correlations between dust and gas
The wavelet cross-correlations for different scales in Fig. 12 show on which scales the distributions of the various types of emission are significantly correlated. However, because the scale maps are normalized and information about absolute intensities is lost, they cannot be used to find quantitative relations between components of the ISM. Hence, to obtain numerical equations relating two distributions, we need classical correlations. Classical cross-correlations contain all scales that exist in a distribution. For example, the high-intensity points of the H-70m correlation in Fig. 14 represent high-emission peaks on small scales in the spiral arms (compare Fig. 10b), whereas low-intensity points represent weak emission around and between the arms on larger scales (compare Fig. 10d). The correlation coefficient of 79% is a mean of all scales, consistent with Fig. 12.
We made pixel-to-pixel correlations between the distributions of and H2, HI, total gas as well as between de-reddened H and 24 m, 70 m, and 160 m. We restricted the comparisons to radii where all data sets are complete, (or 11.4 kpc), and to intensities above 2 rms noise. To reduce the influence of the gradient in the gas-to-dust ratio (see Sect. 4.2), we calculated correlations for two radial ranges: and . We obtained sets of independent data points, i.e. a beam area overlap of <, by choosing pixels spaced by more than 1.67 the beamwidth. Since the correlated variables are not directly depending on each other, we fitted a power law to the bisector in each case (Isobe et al. 1990).
We also calculated the correlation coefficient, , to show how well two components are correlated, and the student-t test to indicate the statistical significance of the fit. For a number of independent points of n > 100, the fit is significant at the 3 level if t>3. Errors in intercept and slope b of the bisector are standard deviations (1).
We first discuss the correlations between the neutral gas and dust extinction, scaled from . Then we investigate the relationships between the emissions from dust and ionized gas. The results are given in Tables 5 and 6, and examples of correlation plots are shown in Figs. 13 to 15.
Figure 13: Classical cross-correlations between gas column densities and dust extinction A in the radial ranges and (or 6.8 kpc
### 6.1 Correlation between neutral gas and dust extinction
In search of a general relationship between neutral gas and dust extinction, a number of authors employed scatter plots between gas column densities and extinction, optical depth or FIR surface brightness (e.g. Savage et al. 1978; Walterbos & Kennicutt 1988; Nieten et al. 2006; Xu & Helou 1996; Boulanger et al. 1996; Neininger et al. 1998). They obtained nearly linear relationships between these quantities. As the studies on M 31 have various shortcomings (lower limits for extinction, H2 data not included and/or low angular resolution), we calculated classical correlations between the distribution of dust extinction and those of N(HI), N(2H2) and N(gas) at our resolution of 45 . As the correlations are restricted to gas column densities above 2 the rms noise, values of are not included (see upper panel of Fig. 13). The bisector fits given in Table 5 are plotted in the bottom panel of Fig. 13.
The relationships between and N(2H2) for the two radial ranges are the same within errors, so the two areas can be combined. With a correlation coefficient of 0.6, the correlation is not very good, indicating that only a small part of the extinction is caused by dust in molecular clouds. This is not surprising in view of the low molecular gas fraction in M 31 (see lower panels of Fig. 6) and the small area filling factor of the molecular gas compared to that of the atomic gas.
Table 5: Power-law relations and correlation coefficients between dust extinction and gas components.
The correlations between and N(HI) are indeed better ( ) than those between and N(2H2), but the relationships for the two radial intervals are not the same. Although both are nearly linear (power-law exponent ), their power laws are shifted (see Fig. 13) in the sense that the values of in are about a factor of 2 lower than those inside . This difference is caused by the radial decrease in /N(HI) discussed in Sect. 4.2. The variation of this ratio within each of the radial intervals contributes to the spread in the scatter plots and reduces the correlation coefficients.
The correlations between total gas N(gas) and A are best ( ), as represents dust mixed with both HI and H2. They are close to linear ( ) and differ by nearly a factor 2 in . The scatter plots for the two intervals are shown in the upper panel of Fig. 13. In linear plots both power-law fits are going through zero, suggesting that the dust causing the extinction and neutral gas are mixed down to very low densities.
Interestingly, extinction (or dust opacity) is proportional to the square root of N(2H2), while it is about linearly related to the atomic gas density. This is due to the quadratic dependence of N(2H2) on N(HI) in M 31 observed by (Nieten et al. 2006). This dependence is expected if in cool, dense, and dusty HI clouds the formation and destruction rates of H2 are balanced (Reach & Boulanger 1998).
### 6.2 Correlation between ionized gas and dust
Because the emission from ionized gas is a good tracer of the present-day star formation rate and massive stars both heat the dust and ionize the gas, a correlation between the emissions from warm dust and ionized gas is expected. Relationships between the emission at 24 m and Pa or H emission from HII regions in nearby galaxies as well as relationships between global luminosities of galaxies have been reported (see Kennicutt et al. 2009, and references therein).
For M 31, the correlation between the emission from dust and ionized gas was first tested by Hoernes et al. (1998), who found a good, nearly linear correlation between warm dust emission and free-free radio emission for the radial range , using HIRAS data and multi-wavelength radio data. Here we correlate the extinction-corrected H emission presented in Fig. 10a with dust emission in the MIPS maps.
The wavelet correlations in Fig. 12 (bottom-right) show that in M 31 H emission is best correlated with dust emission at 70 m. This suggests that of the MIPS bands, the 70 m emission could best be used as the tracer of present-day star formation, making a numerical relation between the emissions at 70 m and H of interest. Table 6 gives the bisector fits for the two radial ranges, which are very similar. Therefore, we present this correlation in Fig. 14 for the entire radial range of . The power-law fit for this radial interval is
where I70 is in MJy/sr and in 10-7 erg s-1 cm-2 sr-1. The correlation is quite good ( ) and nearly linear. In a linear plot the power-law fit goes through zero suggesting that the correlation is also valid for the lowest intensities. The good correlation indicates that the heating sources that power dust emission at 70 m and ionize the gas must indeed be largely the same.
Naturally, H emission is less correlated with the emission from cold dust at 160 m than with emission from warm dust seen at the shorter wavelengths. This is especially so at where the radial profiles differ most (see Fig. 6). Moreover, the relation between the emission from cold dust and H is non-linear (see the bisector slope b in Table 6).
Table 6 shows that the correlations with 24 m are slightly worse than those with 70 m. In contrast, in M 33 the 24 m-H correlation is better than the 70 m-H correlation (Tabatabaei et al. 2007a). This may suggest that in early-type galaxies like M 31 the contribution from evolved AGB stars to the 24 m emission is larger than in late-type galaxies like M 33. A significant stellar contribution to the 24 m emission from M 31 is also indicated by the enhancement of the 24 m-to-70 m intensity ratio in inter-arm regions where the radiation field is weak (Fig. 7).
Across M 31, the 24 m emission is linearly proportional to the extinction-corrected H emission ( ). A linear relationship was also found between the luminosities at 24 m and extinction-corrected Pa of HII regions in M 51 (Calzetti et al. 2005) and between the luminosities at 24 m and extinction-corrected Hof HII regions in M 81 (Pérez-González et al. 2006). Comparing the 24 m luminosities and corrected H luminosities of HII regions in 6 nearby galaxies (including M 51 and M 81), Relaño et al. (2007) obtained a somewhat steeper power law with index , in agreement with the index for global luminosities of galaxies (see also Calzetti et al. 2007). Thus, while the L24- relationship is linear within a single galaxy, the relationships for HII regions in a sample of galaxies and for global luminosities are non-linear. According to Kennicutt et al. (2009), the steepening is due to variations between galaxies in the contribution from evolved, non-ionizing stars to the heating of the dust that emits at 24 m.
Figure 14: Scatter plot between the surface brightnesses of ionized gas and dust emission at 70 m for the radial range 0 -50 . Only independent data points (separated by 1.67 beamwidth) with values above 2 rms noise are included. The line shows the power-law fit given in Table 6, which has an exponent close to 1. In a linear frame, this fit goes through the zero point of the plot. Open with DEXTER
Table 6: Power-law relations and correlation coefficients between the emission from dust and ionized gas.
## 7 Star formation rate and efficiency
Over the last 40 years many authors have studied the relationship between the rate of star formation and gas density in M 31 by comparing the number surface density of massive young stars or of HII regions with that of HI (Berkhuijsen 1977; Tenjes & Haud 1991; Nakai & Sofue 1984; Unwin 1980). They found power-law exponents near 2 as was also obtained for the solar neighborhood by Schmidt (1959), who first proposed this relationship with HI volume density. Kennicutt (1998a) showed that a similar relationship is expected between SFR and gas column densities. The early studies suffered from the effects of dust absorption and could not consider molecular gas (apart from Tenjes & Haud 1991). As the necessary data are now available, we again address this issue.
We compared the distribution of the H emission corrected for dust attenuation (see Fig. 10a) with those of HI, H2, and total gas. The corrected H emission is a good measure for the present-day star formation rate (SFR) that we first estimate for the total area observed using the relation of (Kennicutt 1998b):
(2)
where is the luminosity. In an area of (R<17 kpc), the luminosity of the de-reddened emission is erg s-1 or for the distance to M 31 of 780 kpc (see Table 1), giving SFR = 0.38 . However, this value is rather uncertain for two reasons. First, the contribution from the inner disk ( , nearly 6 kpc) is overestimated because in this area the number of ionizing stars is low and the gas must be mainly heated by other sources (see Sect. 7.1). Second, our H map is limited to about 55 (12.5 kpc) along the major axis, so some of the emission between R = 12.5 kpc and R=17 kpc is missing. Subtracting the luminosity from the area R <6 kpc gives a lower limit to the SFR of 0.27 yr-1 for the radial range 6 < R < 17 kpc. Earlier estimates of the recent SFR for a larger part of the disk indicated 0.35-1 yr-1 (Barmby et al. 2006; Williams 2003; Walterbos & Braun 1994). Recently, Kang et al. (2009) derived a SFR of 0.43 yr-1(for metallicity 2.5 Solar) from UV observations of young starforming regions (<10 Myr) within 120 from the center (R < 27 kpc). Their Fig. 13 suggests that about 20% of this SFR is coming from R > 17 kpc and a negligible amount from R < 6 kpc. So for the range 6 kpc < R < 17 kpc they find a SFR of about 0.34 yr-1, which is consistent with our lower limit of 0.27 yr-1.
Figure 15: Scatter plots between the surface density of the star formation rate and neutral gas surface densities for the radial interval (6.8 kpc
A SFR of 0.3 yr-1 yields a mean face-on surface density of Gyr-1 pc-2 between R =6 kpc and R=17 kpc. This is about 6 times lower than the value of = 2.3 Gyr-1 pc-2 that Verley et al. (2009) obtained for the disk of M 33 (R <7 kpc), also using de-reddened H data.
We can also calculate the star formation efficiency between R =6 kpc and R=17 kpc in M 31. The total molecular gas mass in the entire area of R<17 kpc in M 31 is M(H2) = 3.6 (Nieten et al. 2006) and that in the area 6 kpc < R <17 kpc is M(H2) = 2.9 . Hence the star formation efficiency SFE = SFR/M(H2) between 6 kpc and 17 kpc radius is SFE = 0.9 Gyr-1. It is equivalent to a molecular depletion time scale of 1.1 Gyr. Hence, the disk of M 31 is about three times less efficient in forming young massive stars than the northern part of the disk of M 33 (Gardan et al. 2007).
### 7.1 Star formation rate in the 10 kpc ring''
The radial distributions of H emission in the bottom panels of Fig. 6 show a steep decrease from the center to kpc, followed by a shallower decrease to a minimum near R =6 kpc. In the radial profile of , shown in the upper panel of Fig. 17 for the total area, the inner arms at R = 2.5 kpc and R = 5.5 kpc are only visible as little wiggles superimposed onto a high background. Clearly, the starforming regions in these arms hardly contribute to the ionization of the gas at R < 6 kpc. Devereux et al. (1994) noted that at these radii the H emission is filamentary and unlike that in starforming regions, and since not many young, massive, ionizing stars are found interior to the 10 kpc ring'' (Kang et al. 2009; Berkhuijsen & Humphreys 1989; Tenjes & Haud 1991) the gas must be ionized by other sources. Naturally, the same holds for the heating of the warm dust, the emission of which also strongly increases towards the center. In an extensive discussion, Devereux et al. (1994) concluded that a collision with another galaxy in the past may explain the ionization of the gas and the heating of the dust as well as several other peculiarities (e.g. the double nucleus) in the inner disk of M 31 (see also Block et al. 2006). We note that the UV emission may also be influenced by this event, because it shows a similarly steep increase towards the center as the H emission. Furthermore, all radial profiles that increase towards the center are anti- correlated with the radial profiles of HI and total gas (see Fig. 6, bottom panels). This leads to apparent deviations in the Kennicutt-Schmidt law in the inner disk if is calculated from the usual star formation tracers (see Yin et al. 2009; Boissier et al. 2007).
If massive stars are not responsible for the ionization of the gas and the heating of the dust, we can neither use the H emission nor the infrared emission as tracers of present-day star formation at R < 6 kpc in M 31, as was also pointed out by Devereux et al. (1994). Therefore, we investigated the relationship between SFR and neutral gas only for the interval (R= 6.8-11.4 kpc) containing the 10 kpc ring''.
Table 7: Kennicutt-Schmidt law in M 31 for .
The correlation plots in Fig. 15 and the results in Table 7 show that is not well correlated with the surface densities of either H2, HI or total gas ( -0.59). In spite of this, the fitted bisectors are statistically significant (t>3). Interestingly, we find a linear relationship between and (exponent ), which closely agrees with the average relationship for 7 nearby galaxies, much brighter than M 31 (see Fig. 15a), analyzed by Bigiel et al. (2008). While in these galaxies molecular hydrogen is the dominant gas phase, most of the neutral gas in M 31 is atomic (compare Fig. 15a,b). Hence, the surface density of SFR is linearly related to that of molecular gas, irrespective of the fraction of molecular gas or the absolute value of the total gas surface density in a galaxy. Bigiel et al. (2008) arrived at the same conclusion after comparing the galaxies in their sample.
The correlation between and total gas surface density is slightly better than that between and molecular gas surface density. The bisector fit in Table 7 yields the Kennicutt-Schmidt-law
(3)
where and are in pc-2 and Gyr-1 pc-2, respectively. The exponent of is well in the range of 1.1-2.7 derived by Bigiel et al. (2008). As a galaxy of low surface brightness, the SFRs in M 31 are correspondingly low. Our - relationship nicely fits on the low-brightness extension of the compilation of available galaxy data in Fig. 15 of Bigiel et al. (2008), formed by the outer parts of their 7 galaxies and the global values for 20 galaxies of low surface brightness.
Very recently, Braun et al. (2009) also studied the dependence of SFR on gas density in M 31 using the new Westerbork HI survey and the CO survey of Nieten et al. (2006). They estimated the SFR from the surface brightnesses at IRAC 8 m, MIPS 24 m and GALEX FUV following the procedure of Thilker et al. (2005). Our Fig. 15a is comparable to the radial range 8-16 kpc in their Fig. 20D that shows the same range in as we find. Note that the molecular gas densities of Braun et al. (2009) are a factor of 1.6 larger (+0.21 dex) and have a wider dynamic range than our values due to differences in scaling of the CO data, inclination, angular resolution and radial range. Scaling our relationship to the assumptions of Braun et al. (2009) gives , which is in good agreement with their Fig. 20D.
The dependencies of SFR surface density on total gas surface density in Fig. 15c and in Fig. 20E of Braun et al. (2009) have the same pear-like shape characterized by a broadening towards lower and a rather sharp cut-off near = 10 pc-2. The cut-off comes from the - relation (see Fig. 15b) and occurs at the same value as in the bright galaxies analyzed by Bigiel et al. (2008), who interpreted the lack of higher surface mass densities as a saturation effect. Braun et al. (2009) show that in M 31 this truncation indeed vanishes after correcting the HI data for opacity, which could lead to somewhat steeper slopes in Figs. 15b and c.
### 7.2 Radial variations in the Kennicutt-Schmidt law
In Fig. 16a, we plot the mean values in 0.5 kpc-wide rings in the plane of M 31 of against those of from R =6 kpc to R = 16 kpc. The points form a big loop with a horizontal branch for R =6-8.5 kpc and a maximum in the ring R = 10.5-11.0 kpc (see also Fig. 17). This behavior was already noted by Berkhuijsen (1977) and Tenjes & Haud (1991), who used the number density of HII regions as tracer of SFR and HI gas, and was recently confirmed by Boissier et al. (2007) from GALEX UV data and total gas. Both Berkhuijsen (1977) and Tenjes & Haud (1991) showed that the differences between the slopes inside and outside the maximum of the starforming ring is greatly reduced when the increase in the scale height of the gas with increasing radius is taken into account. We calculated the scale height, h, from the scale height of the HI gas given by Eq. (13) of Braun (1991), scaled to D = 780 kpc, assumed half this value for that of the H2 gas, and a constant scale height for the ionizing stars. Figure 16b shows as a function of gas volume density = N(HI)/2h + N(2H2)/h. The points have moved towards each other, but the horizontal branch remained and the behavior on the starforming ring has become more complicated.
The variations in slope in Fig. 16 are clear evidence of radial variations in the index of the Kennicutt-Schmidt law. Such variations are not specific to M 31 as they are also seen in some of the galaxies analyzed by Bigiel et al. (2008). In order to quantify the variations, we determined the bisectors in scatter plots for three circular rings: R = 7-9 kpc, R = 9-11 kpc and R = 11-13 kpc, covering the horizontal branch, the increasing part inside the maximum and the decreasing part outside the maximum, respectively. The results are given in Table 8. The index for the star fromation law for surface densities is unity for the 7-9 kpc ring and about 1.6 for the other two rings. Hence, the slope of b = 1.30 0.05 obtained for the 10 kpc ring'' (R =6.8-11.4 kpc) in Sect. 7.1 represents the mean value of the first two rings considered here. The scatter plots between and gas volume density yield bisector slopes that are about 0.2 smaller than those for surface density. The correlation coefficients are all close to for the 10 kpc ring'' (see Table 7), indicating that even in 2 kpc-wide rings the intrinsic scatter is considerable. This implies that on scales of a few hundred parsec significant variations in the index of the Kennicutt-Schmidt law and in the star formation efficiency occur.
Figure 16: Mean face-on values of , averaged in 0.5 kpc-wide circular rings in the plane of M 31, plotted against the corresponding mean values of a) gas surface density , and b) gas volume density . The upper left point is for the ring R =6.0-6.5 kpc, the maximum in is in ring 10.5-11.0 kpc and the minimum in ring R = 14.5-15.0 kpc. Typical errors are 0.01 Gyr-1 pc-2 in , 0.02 pc-2 in , and 3 10-5 pc-3 in . Points for R>12 kpc suffer from missing data points near the major axis, the number of which increases with radius. Open with DEXTER
Table 8: Kennicutt-Schmidt law in three radial intervals in M 31.
### 7.3 Radial variations in SFR and SFE
In Fig. 17 (upper panel) we present the radial profile of the SFR surface density between 6 kpc and 17 kpc, averaged in 0.5 kpc-wide circular rings in the plane of M 31. The face-on values vary between about 0.1 and 1 Gyr-1 pc-2. Boissier et al. (2007) and Braun et al. (2009) obtained similar values for in this radial range from GALEX UV data. They are about 10 times smaller than the surface densities of SFR between R = 1.5 kpc and R = 7 kpc in the northern part of M 33 observed by (Gardan et al. 2007).
In the lower panel of Fig. 17 we show the radial profiles of the surface density of the molecular gas and of the star formation efficiencies SFE = / and / . Although the maximum occurs on a relative maximum in the molecular gas density (in ring 10.5-11.0 kpc), is only about 70% of its maximum value where the molecular gas density is highest (in ring 9.0-9.5 kpc). Consequently, SFE varies significantly with radius. Between R=6 kpc and R=15 kpc SFE fluctuates around a value of 0.9 Gyr-1, with a minimum of 0.46 0.01 Gyr-1 near R = 9 kpc. Thus SFE is smallest where is highest! Up to R=12 kpc the efficiency / shows the same trend as SFE. The increase in SFE between 12 kpc and 15 kpc radius of a factor 1.5 results from the difference in radial scale lengths of (or H emission) and the molecular gas density (see Fig. 6 and Table 3). Interestingly, in M 33 (Gardan et al. 2007) found a radial increase in SFE of a factor 2 between 2 kpc and 6 kpc radius with similar fluctuations around the mean as we observe in M 31, but the mean value in M 31 is about three times lower than in M 33. Furthermore, Leroy et al. (2008) found significant variations in the efficiency on a linear scale of 800 pc in the sample of 12 spiral galaxies analyzed by them.
That large, small-scale variations in SFE exist in galaxies is also clear from the large spread in the scatter plots of - visible in Fig. 15a and in several figures of Bigiel et al. (2008). The same value of can occur in a range of spanning more than a factor of 10.
We may conclude that neither the present-day star formation rate nor the star formation efficiency SFE is well correlated with the molecular gas surface density. Hence, other factors than molecular gas density must play an important role in the star formation process. Bigiel et al. (2008) argue that local environmental circumstances largely determine the SFE in spiral galaxies. These factors are extensively discussed by e.g. Leroy et al. (2008).
Figure 17: Radial variation of the face-on surface density of the star formation rate and star formation efficiency SFE in M 31, averaged in 0.5 kpc-wide rings in the plane of the galaxy. Beyond R= 12 kpc the data are not complete, because the observed area is limited along the major axis (see Fig. 10a). Top: radial profile of . Bottom: full line - SFE = / ; long dashed line - / ; dots - radial profile of the molecular gas surface density seen face-on. Note that and do not peak at the same radius. Statistical errors in and are smaller than the symbols and those in SFE and / are smaller than the thickness of the lines. Only beyond R = 12 kpc the error in SFE slowly increases to at R = 15 kpc. Open with DEXTER
## 8 Summary
In this paper, we studied the emission from dust, neutral gas and ionized gas in the disk of M 31, and the relationships between these components on various linear scales. We compared the Spitzer MIPS maps at 24 m, 70 m and 160 m (Gordon et al. 2006) to the distributions of atomic gas seen in the HI line (Brinks & Shane 1984), molecular gas as traced by the 12CO(1-0) line (Nieten et al. 2006) and ionized gas observed in H (Devereux et al. 1994). All data were smoothed to an angular resolution of 45 corresponding to 170 pc 660 pc in the plane of the galaxy.
For each of the dust and gas maps, we calculated the mean intensity distribution as a function of radius (Fig. 6), separately for the northern and the southern half of M 31. Using wavelet analysis, we decomposed the dust and gas distributions in spatial scales and calculated cross-correlations as a function of scale. We also used classical correlations to derive quantitative relations between the various dust and gas components.
Using the MIPS 70 m and 160 m maps, we derived the distributions of the dust temperature and optical depth. The dust optical depth at the H wavelength was used to a) investigate the dust-to-gas ratio, b) derive scaling relations between extinction and neutral gas emission, and c) de-redden the H emission in order to estimate the recent star formation rate. We also presented the Kennicutt-Schmidt law indices obtained for the bright emission ring near R = 10 kpc in M 31. We summarize the main results and conclusions as follows.
1. Dust temperature and opacity:
The dust temperature steeply drops from about 30 K in the center to about 19 K near R= 4.5 kpc, and stays between about 17 K and 20 K beyond this radius (Fig. 2). The mean dust temperature in the area studied is about 18.5 K. This is 3 K less than the temperature obtained by Walterbos & Schwering (1987) between the IRAS maps at 60 m and 100 m that both trace warmer dust than the MIPS maps at 70 m and 160 m used here.
The dust optical depth at H along the line of sight varies in a range between about 0.2 near the center and about 1 in the 10 kpc ring'' (Fig. 4) with a mean value of 0.7 0.4 (the error is standard deviation) and a most probable value of 0.5, indicating that M 31 is mostly optically thin to the H emission. The total flux density of the H emission increases by 30% after correction for extinction.
The radial scale lengths between the maximum in the 10 kpc ring'' and R= 15 kpc of the warm dust are smaller than that of the cold dust, as is expected if the warm dust is mainly heated by UV photons from star forming regions and cold dust by the ISRF. With the largest scale length, atomic gas has the largest radial extent of the dust and gas components considered here.
The radial gradient of the total gas-to-dust ratio is consistent with that of the oxygen abundance in M 31. The gas-to-dust ratios observed in the solar neighborhood (Bohlin et al. 1978) occur near R= 8.5 kpc in the disk of M 31 where N(gas)/ at cm-2.
3. Properties as a function of scale:
Spatial scales larger than about 8 kpc contain most of the emitted power from the cold dust and the atomic gas, whereas the emissions from warm dust, molecular gas and ionized gas are dominated by scales near 1 kpc, typical for complexes of starforming regions and molecular clouds in spiral arms (Fig. 11).
Dust emission is correlated ( ) with both neutral and ionized gas on scales >1 kpc.
On scales <1 kpc, ionized gas is best correlated with warm dust and neutral gas (both HI and H2) with cold dust. On the smallest scale of 0.4 kpc, an HI-warm dust correlation hardly exists ( ) because not much HI occurs on the scale of starforming regions (see Fig. 11).
4. Relationships between gas and dust:
H emission is slightly better correlated with the emission at 70 m than at 24 m (Fig. 13, Table 6), especially on scales < 2 kpc (Fig. 12). As in M 33 the 24 m-H correlation is best, this suggests that in early-type galaxies like M 31 the contribution from evolved AGB stars to the 24 m emission is larger than in late-type galaxies like M 33.
Dust extinction is not well correlated with N(2H2) indicating that dust mixed with molecular clouds does not contribute much to the total extinction. Although the correlation with N(HI) is better, is best correlated with N(HI + 2H2).
Dust opacity is proportional to the square root of N(2H2) but about linearly related to N(HI), as was also found by Nieten et al. (2006) at 90 resolution. This is an indirect indication of a balance between the formation and destruction rates of H2 in cool, dusty HI clouds.
In the central 2 kpc both the dust opacity and the HI column density are very low and the dust temperature is high. This combination may explain the lack of H2 in this region.
5. SFR and SFE:
The SFR in M 31 is low. The total SFR in the observed field between R= 6 kpc and R= 17 kpc is and the star formation efficiency is 0.9 Gyr-1, yielding a molecular depletion time scale of 1.1 Gyr. This is about three times longer than observed in the northern part of M 33 (Gardan et al. 2007). The radial distribution of in 0.5 kpc-wide rings in the plane of the galaxy (Fig. 17) varies between about 0.1 and 1 Gyr-1 pc-2, values that are about 10 times smaller than in the northern part of M 33 (Gardan et al. 2007). Between R= 6 kpc and R= 15 kpc, SFE varies between about 0.5 Gyr-1 and 1.5 Gyr-1, whereas the efficiency with respect to the total gas surface density slowly decreases from about 0.18 Gyr-1 to about 0.03 Gyr-1.
SFR is not well correlated with neutral gas and worst of all with molecular gas in the radial range containing the 10 kpc ring'' (Fig. 15, Table 7). In spite of this, the power-law fits are statistically significant. We find a linear relationship between the surface densities of SFR and molecular gas (power-law exponent 0.96 0.03), and a power law with index 1.30 0.05 between the surface densities of SFR and total gas. These results agree with the average relationship for 7 nearby galaxies much brighter than M 31 (Bigiel et al. 2008). While in these galaxies molecular hydrogen is the dominant gas phase, most of the neutral gas in M 31 is atomic. Thus, the surface density of SFR depends linearly on that of molecular gas irrespective of the fraction of molecular gas or the absolute value of the total gas surface density in a galaxy.
Some important implications of this study are:
-
Precaution is required in using the total IR luminosity (TIR) as an indicator of recent SFR or to derive dust opacity for an early-type galaxy like M 31, because the cold dust is mainly heated by the ISRF and the warm dust emission at 24 m is partly due to evolved stars (especially in the bulge of the galaxy).
-
Neither the present-day SFR nor SFE is well correlated with the surface density of molecular gas or total gas. Therefore, other factors than gas density must play an important role in the process of star formation in M 31.
Acknowledgements
We are grateful to E. Krügel for valuable and stimulating comments. We thank K.M. Menten and R. Beck for comments and careful reading of the manuscript. The Spitzer MIPS data were kindly provided by Karl D. Gordon. E. Tempel kindly sent us a table of extinction values that we used for Fig. 5. We thank an anonymous referee for extensive comments leading to improvements in the manuscript. F.T. was supported through a stipend from the Max Planck Institute for Radio Astronomy (MPIfR).
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## Footnotes
... R
Because the spiral structure is different in the northern and southern half (northeast and southwest of the minor axis, i.e. left and right of the minor axis, respectively), we present all radial profiles for each half separately.
## All Tables
Table 1: Positional data adopted for M 31.
Table 2: M 31 data used in this study.
Table 3: Exponential scale lengths of dust and gas emissions from M 31.
Table 4: Exponential scale lengths L and radial gradients of dust-to-gas ratios and the abundance [O/H].
Table 5: Power-law relations and correlation coefficients between dust extinction and gas components.
Table 6: Power-law relations and correlation coefficients between the emission from dust and ionized gas.
Table 7: Kennicutt-Schmidt law in M 31 for .
Table 8: Kennicutt-Schmidt law in three radial intervals in M 31.
## All Figures
Figure 1: Dust temperature in M 31 obtained from the ratio / based on the Spitzer MIPS data. Only pixels with intensity above 3 noise level were used. The angular resolution of 45 is shown in the lower right-hand corner of the map. The cross indicates the location of the center. The bar at the top gives the dust temperature in Kelvin. Open with DEXTER In the text
Figure 2: a) Histogram of the dust temperature shown in Fig. 1. b) Distribution of the dust temperature in rings of 0.2 kpc in the galactic plane in the northern and southern halves of M 31. Open with DEXTER In the text
Figure 3: Distribution of the dust optical depth at H wavelength in M 31. The bar at the top shows . The angular resolution of 45 is shown in the lower right-hand corner of the map. The cross indicates the location of the center. Overlayed are contours of molecular gas column density N(H2) with levels of 250 and 800 mol. cm-2. Note that maxima in not always coincide with maxima in N(H2). Open with DEXTER In the text
Figure 4: a) Histogram of the dust optical depth shown in Fig. 3, b) radial distribution of the mean optical depth at the H wavelength in rings of width of 0.2 kpc in the galactic plane in the north and south of M 31. The errors are smaller than the size of the symbols. Open with DEXTER In the text
Figure 5: Radial variation of the (total) mean optical depth in H along the line of sight for the full area (north+south). Plusses: our data averaged in 0.2 kpc-wide rings in the plane of M 31 using i = 75; stars: same but with i = 77.5 for comparison with other work; triangles: Xu & Helou (1996), averages in 2 kpc-wide rings with i = 77 (scaled to D = 780 kpc); circles: Montalto et al. (2009), averages in 2 kpc-wide rings with i = 77.6; solid line: Tempel et al. (2010), semi-major axis cut through model with i = 77.5. The errors in our data and in the curve of Tempel et al. (2010) are about 10% of the mean values. Open with DEXTER In the text
Figure 6: Top: radial profiles of the Spitzer IR emission from the northern ( left) and the southern ( right) halves of M 31. Bottom: radial profiles of the surface densities of the atomic, molecular and total neutral gas together with that of the ionized gas (de-reddened H) for the northern ( left) and southern ( right) halves of M 31. The units are 1018 atoms cm-2 for HI and HI+2H2, 1018 molecules cm-2 for H2, and 1010 erg s-1 cm-2 sr-1 for H profiles. The profiles show intensities along the line of sight averaged in circular rings of 0.2 kpc width in the plane of M 31 against the galactocentric radius. The errors are smaller than 5% for all profiles, only for H2 they increase from 10% to 25% at R>12.3 kpc and in the inner arms for R<4.5 kpc. Open with DEXTER In the text
Figure 7: Ratio of the MIPS IR intensities against galactocentric radius in M 31. Open with DEXTER In the text
Figure 8: Radial profiles of the gas-to-dust ratios in M 31, the northern half and the southern half. Top: N(HI)/ , middle: N(2H2)/ , bottom: N(HI + 2H2)/ . In the middle panel, the northern profile is shifted by 300 units for clarity. The errors are smaller than 5% everywhere only for N(2H2)/ they increase from 10% to 25% at R>12.3 kpc and in the inner arms for R<4.5 kpc. Open with DEXTER In the text
Figure 9: Dust-to-gas ratios as function of galactocentric radius for M 31, calculated from the radial profiles of , N(HI), N(2H2) and N(HI + 2H2) = N(gas). Open with DEXTER In the text
Figure 10: Distribution of the de-reddened H emission a) and the wavelet decomposition for scales 0.4, 1.6, 4.0 kpc b) to d). The central 2 kpc was subtracted from the H map before the decomposition. The cross in the H map indicates the location of the center. Open with DEXTER In the text
Figure 11: Wavelet spectra of MIPS IR ( left) and gas ( right) emission in M 31, shown in arbitrary units. The data points correspond to the scales 0.4, 0.6, 1.0, 1.6, 2.5, 4.0, 6.3, 10.0, 15.9, 25.1 kpc. Open with DEXTER In the text
Figure 12: Wavelet cross correlations of atomic gas ( top-left), molecular gas ( top-right), and total neutral gas ( bottom-left) with IR emission in M 31. The IR correlation with the ionized gas ( bottom-right) is also shown. The data points correspond to the scales 0.4, 0.6, 1.0, 1.6, 2.5, 4.0, 6.3, 10.0, 15.9, and 25.1 kpc. Open with DEXTER In the text
Figure 13: Classical cross-correlations between gas column densities and dust extinction A in the radial ranges and (or 6.8 kpc
Figure 14: Scatter plot between the surface brightnesses of ionized gas and dust emission at 70 m for the radial range 0 -50 . Only independent data points (separated by 1.67 beamwidth) with values above 2 rms noise are included. The line shows the power-law fit given in Table 6, which has an exponent close to 1. In a linear frame, this fit goes through the zero point of the plot. Open with DEXTER In the text
Figure 15: Scatter plots between the surface density of the star formation rate and neutral gas surface densities for the radial interval (6.8 kpc
Figure 16: Mean face-on values of , averaged in 0.5 kpc-wide circular rings in the plane of M 31, plotted against the corresponding mean values of a) gas surface density , and b) gas volume density . The upper left point is for the ring R =6.0-6.5 kpc, the maximum in is in ring 10.5-11.0 kpc and the minimum in ring R = 14.5-15.0 kpc. Typical errors are 0.01 Gyr-1 pc-2 in , 0.02 pc-2 in , and 3 10-5 pc-3 in . Points for R>12 kpc suffer from missing data points near the major axis, the number of which increases with radius. Open with DEXTER In the text
Figure 17: Radial variation of the face-on surface density of the star formation rate and star formation efficiency SFE in M 31, averaged in 0.5 kpc-wide rings in the plane of the galaxy. Beyond R= 12 kpc the data are not complete, because the observed area is limited along the major axis (see Fig. 10a). Top: radial profile of . Bottom: full line - SFE = / ; long dashed line - / ; dots - radial profile of the molecular gas surface density seen face-on. Note that and do not peak at the same radius. Statistical errors in and are smaller than the symbols and those in SFE and / are smaller than the thickness of the lines. Only beyond R = 12 kpc the error in SFE slowly increases to at R = 15 kpc. Open with DEXTER In the text | {"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": 0.9049473404884338, "perplexity": 2411.5377500830673}, "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/1590347406785.66/warc/CC-MAIN-20200529214634-20200530004634-00540.warc.gz"} |
https://math.stackexchange.com/tags/asymptotics/hot | # Tag Info
6
(This is more like a comment with images) Here are some simulations of the values $c = c(p)$ using the grid of size $1000\times1000$ and $500$ steps together with some fitting curves. $\hspace{8em}$ The data clearly deviates from the polynomial $2p^2$, and although the above plot may seem to suggest that $c(p)$ assumes a nice closed form, I believe that ...
3
Seems fine but it is easier to note that $$n+1\leq 2n$$ for $n\geq 1$ whence $$(n+1)^3\leq (2n)^3=8n^3$$ for $n\geq 1$ as desired.
2
By the most recent bound on Linnik's Theorem, there is an absolute constant $c$ such that for every prime $q < cp_n^{1/5}$, there is a prime $p < p_n$ such that $p \equiv 1 \pmod{q}$. Your least common multiple is therefore divisible by all primes below $cp_n^{1/5}$. The prime number theorem implies that the product of all primes below $cp_n^{1/5}$ is ... 2 Your differential equation has closed-form solutions \eqalign{f \left( t \right) &=c_{{1}}{t}^{1/2-a/2}{{ J}_{-\sqrt {{a}^{2}-2\,a +4\,b+1}}\left(2\,{\frac {\sqrt {b\epsilon}}{\sqrt {t}}}\right)}\cr &+c_{{2 }}{t}^{1/2-a/2}{{ Y}_{-\sqrt {{a}^{2}-2\,a+4\,b+1}}\left(2\,{\frac {\sqrt {b\epsilon}}{\sqrt {t}}}\right)}} whereJ$and$Y$are Bessel ... 1 Here is a key lemma (which you can and should prove for yourself) that helps to resolve so many questions of this type. I'll phrase it in terms of functions of$x$where$x\to\infty$, although it holds for other domains as well. Lemma: Let$f,g\colon [1,\infty)\to[2,\infty)$be functions. If$\log f(x) = o(\log g(x))$as$x\to\infty$, then$f(x) = o(g(x))$... 1$\log((1/n) + n^2 )$If we just focus on the term inside of the logarithm.$ let x = 1/n + n^2$As n grows, we notice that the 1/n term effectively becomes zero and the overpowering term is$n^2$We can now state that$\log((1/n) + n^2 )$has growth$log(n^2)$when n gets large. We know from logarithms that$log(a^b) = b* log(a)$So$log(n^2)$can be ... 1 Yes it does. Let$t_N$denote the algorithm time. Let$f_N = \max\{t_M/M^2:M\le N\}$. Suppose$f_N$diverges. Then$t_N$fails to be$O(\sqrt{f_N} N^2)$. Therefore$f_N$does not diverge. Since$f_N$is a non-decreasing sequence, it must be bounded. Set$C= \sup f_N$. Then$t_N \le C N^2\$.
Only top voted, non community-wiki answers of a minimum length are eligible | {"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": 0.989678680896759, "perplexity": 925.0044005554669}, "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/1560627998298.91/warc/CC-MAIN-20190616202813-20190616224813-00505.warc.gz"} |
http://mathhelpforum.com/pre-calculus/56082-continuity-question.html | $g(x)=\left\{\begin{array}{cc}x^2+1,&\mbox{ if }x\leq 0\\x^2+bx\sin(\frac{1}{x})+c,&\mbox{ if }x>0\end{array}\right.$
$b\in$
$c\in$
2. The only possible point of discontinuity is at $x=0,$ hence, you must put $\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(x).$ | {"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": 5, "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": 0.9927082657814026, "perplexity": 256.0851825339668}, "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-2017-34/segments/1502886117519.92/warc/CC-MAIN-20170823035753-20170823055753-00496.warc.gz"} |
https://dbfin.com/logic/enderton/chapter-3/section-3-3-a-subtheory-of-number-theory/problem-6-solution/ | # Section 3.3: Problem 6 Solution
Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Is $3$ a sequence number? What is $\mbox{lh}3$ ? Find $(1\ast3)\ast6$ and $1\ast(3\ast6)$ .
$3=2^{0}\cdot3^{1}$ is not a sequence number, as $p_{1}=3$ divides $3$ but $p_{0}=2$ does not divide $3$ . However, formally, we can still calculate the formulas in the question.
First, formally, $\mbox{lh}b$ is defined as the least $n\in\mathbb{N}$ such that either $b=0$ or $\notin\mathcal{D}$ where $\mathcal{D}$ is the divisibility relation. In our case, $\notin\mathcal{D}$ , so that $\mbox{lh}3=0$ .
Second, formally, $(b)_{c}$ is defined as the least $n\in\mathbb{N}$ such that either $b=0$ or $\notin\mathcal{D}$ . In our case, $(3)_{c}=0$ for all $c\in\mathbb{N}$ (including $c=1$ for which $p_{1}=3$ ).
Finally, $a\ast b=a\cdot\prod_{i<\mbox{lh}b}p_{i+\mbox{lh}a}^{(b)_{i}+1}$ is defined for all natural numbers as well. In particular, since $\mbox{lh}1=0$ , $1\ast b=\prod_{i<\mbox{lh}b}p_{i}^{(b)_{i}+1}$ which is simply the maximum sequence number that divides $b$ . Therefore, $1\ast3=1$ and $(1\ast3)\ast6=6$ ($6=\langle0,0\rangle$ is a sequence number). Further, $3\ast6=3\cdot\prod_{i<2}p_{i}^{(6)_{i}+1}=3\cdot6=18=2^{1}\cdot3^{2}=<0,1>$ . Hence, $1\ast(3\ast6)=18$ .
Note. The exercise shows that the concatenation operation, as defined, is not associative on the set of all natural numbers, however, as mentioned in the text, it is associative on the set of sequence numbers. | {"extraction_info": {"found_math": true, "script_math_tex": 33, "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": 0.9901350736618042, "perplexity": 160.95423676393048}, "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-2021-25/segments/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00469.warc.gz"} |
http://www.science.gov/topicpages/a/ac+conductance+measurements.html | Sample records for ac conductance measurements
1. Accelerated life ac conductivity measurements of CRT oxide cathodes
Hashim, A. A.; Barratt, D. S.; Hassan, A. K.; Nabok, A.
2006-07-01
The ac conductivity measurements have been carried out for the activated Ba/SrO cathode with additional 5% Ni powder for every 100 h acceleration life time at the temperature around 1125 K. The ac conductivity was studied as a function of temperature in the range 300-1200 K after conversion and activation of the cathode at 1200 K for 1 h in two cathodes face to face closed configuration. The experimental results prove that the hopping conductivity dominate in the temperature range 625-770 K through the traps of the WO 3 associate with activation energy Ea = 0.87 eV, whereas from 500-625 K it is most likely to be through the traps of the Al 2O 3 with activation energy of Ea = 1.05 eV. The hopping conductivity at the low temperature range 300-500 K is based on Ni powder link with some Ba contaminants in the oxide layer stricture which indicates very low activation energy Ea = 0.06 eV.
2. AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media
Bru, J.-B.; de Siqueira Pedra, W.; Hertling, C.
2016-05-01
We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Green-Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems.
3. AC conductivity and dielectric measurements of metal-free phthalocyanine thin films dispersed in polycarbonate
Riad, A. S.; Korayem, M. T.; Abdel-Malik, T. G.
1999-10-01
The dielectric constant and the dielectric loss of thin films of metal-free phthalocyanine dispersed in polycarbonate using ohmic gold electrodes are investigated in the frequency range 20-10 5 Hz and within the temperature range 300-388 K. The frequency dependence of the impedance spectra plotted in the complex plane shows semicircles. The Cole-Cole diagrams have been used to determine the molecular relaxation time, τ, The temperature dependence of τ is expressed by thermally activated process. The AC conductivity σ AC (ω) is found to vary as ωs with the index s⩽1, indicating a dominant hopping process at low temperatures. From the temperature dependence of AC conductivity, free carrier conduction with mean activation energy of 0.33 eV is observed at higher temperatures. Capacitance and loss tangent are found to decrease with increasing frequency and increase with increasing temperature. Such characteristics are found to be in good qualitative agreement with existing equivalent circuit model assuming ohmic contacts.
4. Studies on the activation energy from the ac conductivity measurements of rubber ferrite composites containing manganese zinc ferrite
Hashim, Mohd.; Alimuddin; Kumar, Shalendra; Shirsath, Sagar E.; Mohammed, E. M.; Chung, Hanshik; Kumar, Ravi
2012-11-01
Manganese zinc ferrites (MZF) have resistivities between 0.01 and 10 Ω m. Making composite materials of ferrites with either natural rubber or plastics will modify the electrical properties of ferrites. The moldability and flexibility of these composites find wide use in industrial and other scientific applications. Mixed ferrites belonging to the series Mn(1-x)ZnxFe2O4 were synthesized for different ‘x’ values in steps of 0.2, and incorporated in natural rubber matrix (RFC). From the dielectric measurements of the ceramic manganese zinc ferrite and rubber ferrite composites, ac conductivity and activation energy were evaluated. A program was developed with the aid of the LabVIEW package to automate the measurements. The ac conductivity of RFC was then correlated with that of the magnetic filler and matrix by a mixture equation which helps to tailor properties of these composites.
5. AC resistance measuring instrument
DOEpatents
Hof, P.J.
1983-10-04
An auto-ranging AC resistance measuring instrument for remote measurement of the resistance of an electrical device or circuit connected to the instrument includes a signal generator which generates an AC excitation signal for application to a load, including the device and the transmission line, a monitoring circuit which provides a digitally encoded signal representing the voltage across the load, and a microprocessor which operates under program control to provide an auto-ranging function by which range resistance is connected in circuit with the load to limit the load voltage to an acceptable range for the instrument, and an auto-compensating function by which compensating capacitance is connected in shunt with the range resistance to compensate for the effects of line capacitance. After the auto-ranging and auto-compensation functions are complete, the microprocessor calculates the resistance of the load from the selected range resistance, the excitation signal, and the load voltage signal, and displays of the measured resistance on a digital display of the instrument. 8 figs.
6. AC Resistance measuring instrument
DOEpatents
Hof, Peter J.
1983-01-01
An auto-ranging AC resistance measuring instrument for remote measurement of the resistance of an electrical device or circuit connected to the instrument includes a signal generator which generates an AC excitation signal for application to a load, including the device and the transmission line, a monitoring circuit which provides a digitally encoded signal representing the voltage across the load, and a microprocessor which operates under program control to provide an auto-ranging function by which range resistance is connected in circuit with the load to limit the load voltage to an acceptable range for the instrument, and an auto-compensating function by which compensating capacitance is connected in shunt with the range resistance to compensate for the effects of line capacitance. After the auto-ranging and auto-compensation functions are complete, the microprocessor calculates the resistance of the load from the selected range resistance, the excitation signal, and the load voltage signal, and displays of the measured resistance on a digital display of the instrument.
7. Automated ac galvanomagnetic measurement system
NASA Technical Reports Server (NTRS)
Szofran, F. R.; Espy, P. N.
1985-01-01
An automated, ac galvanomagnetic measurement system is described. Hall or van der Pauw measurements in the temperature range 10-300 K can be made at a preselected magnetic field without operator attendance. Procedures to validate sample installation and correct operation of other system functions, such as magnetic field and thermometry, are included. Advantages of ac measurements are discussed.
8. Impedance, AC conductivity and dielectric behavior Adeninium Trichloromercurate (II)
Fersi, M. Amine; Chaabane, I.; Gargouri, M.
2016-09-01
In this work, we report the measurements impedance spectroscopy technique for the organic-inorganic hybrid compound (C5H6N5) HgCl3, 11/2H2O measured in the 209 Hz-5 MHz frequency range from 378 to 428 K. Besides, the Cole-Cole (Z″ versus Z‧) plots were well fitted to an equivalent circuit built up by a parallel combination of resistance (R), fractal capacitance (CPE) and capacitance (C). Furthermore, the AC conductivity was investigated as a function of temperature and frequency in the same range. The experiment results indicated that AC conductivityac) was proportional to σdc + A ωS . The obtained results are discussed in terms of the correlated barrier hopping (CBH) model. An agreement between the experimental and theoretical results suggests that the AC conductivity behavior of Adeninium Trichloromercurate (II) can be successfully explained by CBH model. The contribution of single polaron hopping to AC conductivity in a present alloy was also studied.
9. AC Conductivity and Dielectric Properties of Borotellurite Glass
Taha, T. A.; Azab, A. A.
2016-06-01
Borotellurite glasses with formula 60B2O3-10ZnO-(30 - x)NaF-xTeO2 (x = 0 mol.%, 5 mol.%, 10 mol.%, and 15 mol.%) have been synthesized by thermal melting. X-ray diffraction (XRD) analysis confirmed that the glasses were amorphous. The glass density (ρ) was determined by the Archimedes method at room temperature. The density (ρ) and molar volume (V m) were found to increase with increasing TeO2 content. The direct-current (DC) conductivity was measured in the temperature range from 473 K to 623 K, in which the electrical activation energy of ionic conduction increased from 0.27 eV to 0.48 eV with increasing TeO2 content from 0 mol.% to 15 mol.%. The dielectric parameters and alternating-current (AC) conductivityac) were investigated in the frequency range from 1 kHz to 1 MHz and temperature range from 300 K to 633 K. The AC conductivity and dielectric constant decreased with increasing TeO2 content from 0 mol.% to 15 mol.%.
10. ac-resistance-measuring instrument
SciTech Connect
Hof, P.J.
1981-04-22
An auto-ranging ac resistance measuring instrument for remote measurement of the resistance of an electrical device or circuit connected to the instrument includes a signal generator which generates an ac excitation signal for application to a load, including the device and the transmission line, a monitoring circuit which provides a digitally encoded signal representing the voltage across the load, and a microprocessor which operates under program control to provide an auto-ranging function by which range resistance is connected in circuit with the load to limit the load voltage to an acceptable range for the instrument, and an auto-compensating function by which compensating capacitance is connected in shunt with the range resistance to compensate for the effects of line capacitance.
11. Study of AC electrical conduction mechanisms in an epoxy polymer
Jilani, Wissal; Mzabi, Nissaf; Gallot-Lavallée, Olivier; Fourati, Najla; Zerrouki, Chouki; Zerrouki, Rachida; Guermazi, Hajer
2015-11-01
The AC conductivity of an epoxy resin was investigated in the frequency range 10^{-1} - 106 Hz at temperatures ranging from -100 to 120 °C. The frequency dependence of σ_{ac} was described by the law: σ_{ac}=ω \\varepsilon0\\varepsilon^''_{HN}+Aωs. The study of temperature variation of the exponent (s) reveals two conduction models: the AC conduction dependence upon temperature is governed by the small polaron tunneling mechanism (SPTM) at low temperature (-100 -60 °C) and the correlated barrier hopping (CHB) model at high temperature (80-120 °C).
12. Ac conduction in conducting poly pyrrole-poly vinyl methyl ether polymer composite materials
SciTech Connect
Saha, S.K.; Mandal, T.K.; Mandal, B.M.; Chakravorty, D.
1997-03-01
Composite materials containing conducting polypyrrole and insulating poly (vinyl methyl ether) (PVME) have been synthesized by oxidative polymerization of pyrrole in ethanol using FeCl{sub 3} oxidant in the presence of PVME. The ac conductivity measurements have been carried out in the frequency range of 100 Hz to 10 MHz and in the temperature range of 110 to 350 K. The frequency dependent conductivity has been explained on the basis of a small polaron tunnelling mechanism. {copyright} {ital 1997 American Institute of Physics.}
13. ac conductance of surface layer in lithium tetraborate single crystals
Kim, Chung-Sik; Park, Jong-Ho; Moon, Byung Kee; Seo, Hyo-Jin; Choi, Byung-Chun; Hwang, Yoon-Hwae; Kim, Hyung Kook; Kim, Jung Nam
2003-12-01
ac conductance for the electrode effect in Li2B4O7 single crystal was investigated by use of a coplanar electrode applied on the surface of a (001) plate. A coplanar electrode in this material more clearly shows conduction of the electrode effect than a conventional parallel planar electrode. The electrode effect in ac conductance is likely to be controlled by the surface layer, which is a poorly conductive depletion layer possibly filled with vacancies of lithium ions. We found that the surface layer is not locally distributed near the electrodes, but, rather, on the broad area of the surface (001) plane of the material. So we conclude that the electrode effect in ac conduction of Li2B4O7 single crystal is mainly due to the poor conductive surface layer distributed over the whole surface of the (001) plane and is not a secondary phase formed by reaction with the electrode material.
14. AC Conductivity Studies of Lithium Based Phospho Vanadate Glasses
Nagendra, K.; Babu, G. Satish; Reddy, C. Narayana; Gowda, Veeranna
2011-07-01
Glasses in the system xLi2SO4-20Li2O-(80-x) [80P2O5-20V2O5] (5⩾x⩾20 mol%) has been prepared by melt quenching method. Dc and ac conductivity has been studied over a wide range of frequency (10 Hz to 10 MHz) and temperature (298 K-523 K). The dc conductivity found to increase with increase of Li2SO4 concentration. The ac conductivities have been fitted to the Almond-West type single power law equation σ(ω) = σ(0)+Aωs where s' is the power law exponent. The ac conductivity found to increase with increase of Li2SO4 concentration. An attempt is made to elucidate the enhancement of lithium ion conduction in phosphor-vanadate glasses by considering the expansion of network structure.
15. dc piezoresistance and ac conductance of niobium dioxide
SciTech Connect
Guerra Vela, C.
1984-01-01
The resistance, R, of monocrystalline n-type NbO/sub 2/ in the semiconducting, distorted rutile-structured phase was measured at temperatures from 196 to 410 K and hydrostatic pressures, P, from one to 6000 atm. R/T increases exponentially with 1/T, and ..delta..R/R increases linearly with P/T at different rates along the a- and c-axes. Conduction is apparently due to adiabatic hopping of small polarons; values were obtained for phonon, electron transfer, and polaron binding energies, the pressure dependences of these energies, and of the small polaron activation energy. An electronic phase diagram is presented also. The complex ac conductivity was also measured using frequencies from 5 to 92 kHz between 1.5 and 300 K along the a- and c-axes of NbO/sub 2/. Above 200 K the real part of the conductivity sigma/sub a/ and sigma/sub c/ were independent of frequency, f, and strongly activated like the dc conductivity. Below 200 K, sigma/sub a/ decreased ever less rapidly until 120 K where a weakly activated regime began in which sigma/sub a/ varied about like f/sup 0.5/ implying transitions of polarons between centers with a characteristic energy difference.
16. Dynamic conductivity of ac-dc-driven graphene superlattice
Kukhar', E. I.; Kryuchkov, S. V.; Ionkina, E. S.
2016-06-01
The dynamic conductivity of graphene superlattice in the presence of ac electric field and dc electric field with longitudinal and transversal components with respect to superlattice axis was calculated. In the case of strong transversal component of dc field conductivity of graphene superlattice was shown to be such as if the electrons had got the effective mass. In the case of weak transversal component of dc field conductivity was shown to change its sign if the frequency of ac field was an integer multiple of half of Bloch frequency.
17. Tevatron optics measurements using an AC dipole
SciTech Connect
Miyamoto, R.; Kopp, S.E.; Jansson, A.; Syphers, M.J.; /Fermilab
2007-06-01
The AC dipole is a device to study beam optics of hadron synchrotrons. It can produce sustained large amplitude oscillations with virtually no emittance growth. A vertical AC dipole for the Tevatron is recently implemented and a maximum oscillation amplitude of 2{sigma} (4{sigma}) at 980 GeV (150 GeV) is achieved [1]. When such large oscillations are measured with the BPM system of the Tevatron (20 {micro}m resolution), not only linear but even nonlinear optics can be directly measured. This paper shows how to measure {beta} function using an AC dipole and the result is compared to the other measurement. The paper also shows a test to detect optics changes when small changes are made in the Tevatron. Since an AC dipole is nondestructive, it allows frequent measurements of the optics which is necessary for such an test.
18. Structural and AC conductivity study of CdTe nanomaterials
Das, Sayantani; Banerjee, Sourish; Sinha, T. P.
2016-04-01
Cadmium telluride (CdTe) nanomaterials have been synthesized by soft chemical route using mercapto ethanol as a capping agent. Crystallization temperature of the sample is investigated using differential scanning calorimeter. X-ray diffraction and transmission electron microscope measurements show that the prepared sample belongs to cubic structure with the average particle size of 20 nm. Impedance spectroscopy is applied to investigate the dielectric relaxation of the sample in a temperature range from 313 to 593 K and in a frequency range from 42 Hz to 1.1 MHz. The complex impedance plane plot has been analyzed by an equivalent circuit consisting of two serially connected R-CPE units, each containing a resistance (R) and a constant phase element (CPE). Dielectric relaxation peaks are observed in the imaginary parts of the spectra. The frequency dependence of real and imaginary parts of dielectric permittivity is analyzed using modified Cole-Cole equation. The temperature dependence relaxation time is found to obey the Arrhenius law having activation energy ~0.704 eV. The frequency dependent conductivity spectra are found to follow the power law. The frequency dependence ac conductivity is analyzed by power law.
19. AC Conductivity Studies of Lithium Based Phospho Vanadate Glasses
SciTech Connect
Nagendra, K.; Babu, G. Satish; Gowda, Veeranna; Reddy, C. Narayana
2011-07-15
Glasses in the system xLi{sub 2}SO{sub 4}-20Li{sub 2}O-(80-x) [80P{sub 2}O{sub 5}-20V{sub 2}O{sub 5}](5{>=}x{>=}20 mol%) has been prepared by melt quenching method. Dc and ac conductivity has been studied over a wide range of frequency (10 Hz to 10 MHz) and temperature (298 K-523 K). The dc conductivity found to increase with increase of Li{sub 2}SO{sub 4} concentration. The ac conductivities have been fitted to the Almond-West type single power law equation {sigma}({omega}) = {sigma}(0)+A{omega}{sup s} where 's' is the power law exponent. The ac conductivity found to increase with increase of Li{sub 2}SO{sub 4} concentration. An attempt is made to elucidate the enhancement of lithium ion conduction in phosphor-vanadate glasses by considering the expansion of network structure.
20. Broadband AC Conductivity of XUV Excited Warm Dense Gold
Chen, Z.; Tsui, Y.; Toleikis, S.; Hering, P.; Brown, S.; Curry, C.; Tanikawa, T.; Hoeppner, H.; Levy, M.; Goede, S.; Ziaja-Motyka, B.; Rethfeld, B.; Recoules, Vanina; Ng, A.; Glenzer, S.
2015-11-01
The properties of ultrafast laser excited warm dense gold have been extensively studied in the past decade. In those studies, a 400nm ultrashort laser pulse was used to excite the 5 d electrons in gold to 6s/p state. Here we will present our recent study of warm dense gold with 245eV, 70fs pulses to selectively excite 4 f electrons using the XUV-FEL at FLASH. The AC conductivity of the warm dense gold was measured at different wavelengths (485nm, 520nm, 585nm, 640nm and 720nm) to cover the range from 5 d-6 s / p interband transitions to 6 s/ p intraband transitions. Preliminary result suggests that the onset of 5 d-6 s / p band transition shifts from 2.3eV to ~ 2eV, which is in agreement with the study of 400nm laser pulse excited warm dense gold. More detailed analysis of our data will also be presented.
1. Structural, AC conductivity and dielectric properties of Sr-La hexaferrite
Singh, A.; Narang, S. B.; Singh, K.; Sharma, P.; Pandey, O. P.
2006-03-01
A series of M-type hexaferrite samples with composition Sr{1-x}La{x}Fe{12}O{19} (x = 0.00, 0.05, 0.15 and 0.25) were prepared by standard ceramic technique. AC electrical conductivity measurements were carried out at different frequencies (20 Hz 1 MHz) and at different temperatures. The dielectric constant and dielectric loss tangent were measured in the same range of frequencies. The experimental results indicate that AC electrical conductivity increases on increasing the frequency as well as the temperature, indicating magnetic semiconductor behavior of the samples. The increase in AC electrical conductivity with frequency and temperature has been explained on the basis of Koops Model whereas dielectric constant and dielectric loss tangent has been explained with the Maxwell Wagner type interfacial polarization in agreement with the Koops phenomenological theory.
2. Microwave ac Conductivity Spectrum of a Coulomb Glass
SciTech Connect
Lee, Mark; Stutzmann, M. L.
2001-07-30
We report the first observation of the transition between interacting and noninteracting behavior in the ac conductivity spectrum {sigma}({omega}) of a doped semiconductor in its Coulomb glass state near T=0 K . The transition manifests itself as a crossover from approximately linear frequency dependence below {approx}10 GHz , to quadratic dependence above {approx}15 GHz . The sharpness of the transition and the magnitude of the crossover frequency strongly suggest that the transition is driven by photon-induced excitations across the Coulomb gap, in contrast to existing theoretical descriptions.
3. ac conductivity and dielectric constant of conductor-insulator composites
Murtanto, Tan Benny; Natori, Satoshi; Nakamura, Jun; Natori, Akiko
2006-09-01
We study the complex admittance (ac conductivity and dielectric constant) of conductor-insulator composite material, based on a two-dimensional square network consisting of randomly placed conductors and capacitors. We derived some exact analytical relations between the complex admittances of high and low frequencies and of complementary conductor concentrations. We calculate the complex admittance by applying a transfer-matrix method to a square network and study the dependence on both the frequency and the conductor concentration. The numerical results are compared with an effective-medium theory, and the range of applicability and limitation of the effective-medium theory are clarified.
4. AC Loss Measurements on a 2G YBCO Coil
SciTech Connect
Rey, Christopher M; Duckworth, Robert C; Schwenterly, S W
2011-01-01
The Oak Ridge National Laboratory (ORNL) is collaborating with Waukesha Electric Systems (WES) to continue development of HTS power transformers. For compatibility with the existing power grid, a commercially viable HTS transformer will have to operate at high voltages in the range of 138 kV and above, and will have to withstand 550-kV impulse voltages as well. Second-generation (2G) YBCO coated conductors will be required for an economically-competitive design. In order to adequately size the refrigeration system for these transformers, the ac loss of these HTS coils must be characterized. Electrical AC loss measurements were conducted on a prototype high voltage (HV) coil with co-wound stainless steel at 60 Hz in a liquid nitrogen bath using a lock-in amplifier technique. The prototype HV coil consisted of 26 continuous (without splice) single pancake coils concentrically centered on a stainless steel former. For ac loss measurement purposes, voltage tap pairs were soldered across each set of two single pancake coils so that a total of 13 separate voltage measurements could be made across the entire length of the coil. AC loss measurements were taken as a function of ac excitation current. Results show that the loss is primarily concentrated at the ends of the coil where the operating fraction of critical current is the highest and show a distinct difference in current scaling of the losses between low current and high current regimes.
5. Calibration-free electrical conductivity measurements for highly conductive slags
SciTech Connect
MACDONALD,CHRISTOPHER J.; GAO,HUANG; PAL,UDAY B.; VAN DEN AVYLE,JAMES A.; MELGAARD,DAVID K.
2000-05-01
This research involves the measurement of the electrical conductivity (K) for the ESR (electroslag remelting) slag (60 wt.% CaF{sub 2} - 20 wt.% CaO - 20 wt.% Al{sub 2}O{sub 3}) used in the decontamination of radioactive stainless steel. The electrical conductivity is measured with an improved high-accuracy-height-differential technique that requires no calibration. This method consists of making continuous AC impedance measurements over several successive depth increments of the coaxial cylindrical electrodes in the ESR slag. The electrical conductivity is then calculated from the slope of the plot of inverse impedance versus the depth of the electrodes in the slag. The improvements on the existing technique include an increased electrochemical cell geometry and the capability of measuring high precision depth increments and the associated impedances. These improvements allow this technique to be used for measuring the electrical conductivity of highly conductive slags such as the ESR slag. The volatilization rate and the volatile species of the ESR slag measured through thermogravimetric (TG) and mass spectroscopy analysis, respectively, reveal that the ESR slag composition essentially remains the same throughout the electrical conductivity experiments.
6. AC Conductivity and Dielectric Relaxation Behavior of Sb2S3 Bulk Material
Abd El-Rahman, K. F.; Darwish, A. A. A.; Qashou, Saleem I.; Hanafy, T. A.
2016-04-01
The Sb2S3 bulk material was used for next-generation anode for lithium-ion batteries. Alternative current (AC) conductivity, dielectric properties and electric modulus of Sb2S3 have been investigated. The measurements were carried out in the frequency range from 40 Hz to 5 MHz and temperature range from 293 K to 453 K. The direct current (DC) conductivity, σ DC, shows an activated behavior and the calculated activation energy is 0.50 eV. The AC conductivity, σ AC, was found to increase with the increase of temperature and frequency. The conduction mechanism of σ AC was controlled by the correlated barrier hopping model. The behavior of the dielectric constant, ɛ', and dielectric loss index, ɛ'', reveal that the polarization process of Sb2S3 is dipolar in nature. The behavior of both ɛ' and ɛ'' reveals that bulk Sb2S3 has no ferroelectric or piezoelectric phase transition. The dielectric modulus, M, gives a simple method for evaluating the activation energy of the dielectric relaxation. The calculated activation energy from M is 0.045 eV.
7. AC Conductivity and Dielectric Relaxation Behavior of Sb2S3 Bulk Material
Abd El-Rahman, K. F.; Darwish, A. A. A.; Qashou, Saleem I.; Hanafy, T. A.
2016-07-01
The Sb2S3 bulk material was used for next-generation anode for lithium-ion batteries. Alternative current (AC) conductivity, dielectric properties and electric modulus of Sb2S3 have been investigated. The measurements were carried out in the frequency range from 40 Hz to 5 MHz and temperature range from 293 K to 453 K. The direct current (DC) conductivity, σ DC, shows an activated behavior and the calculated activation energy is 0.50 eV. The AC conductivity, σ AC, was found to increase with the increase of temperature and frequency. The conduction mechanism of σ AC was controlled by the correlated barrier hopping model. The behavior of the dielectric constant, ɛ', and dielectric loss index, ɛ'', reveal that the polarization process of Sb2S3 is dipolar in nature. The behavior of both ɛ' and ɛ'' reveals that bulk Sb2S3 has no ferroelectric or piezoelectric phase transition. The dielectric modulus, M, gives a simple method for evaluating the activation energy of the dielectric relaxation. The calculated activation energy from M is 0.045 eV.
8. ac and dc percolative conductivity of magnetite-cellulose acetate composites
SciTech Connect
Chiteme, C.; McLachlan, D. S.; Sauti, G.
2007-03-01
ac and dc conductivity results for a percolating system, which consists of a conducting powder (magnetite) combined with an 'insulating' powder (cellulose acetate), are presented. Impedance and modulus spectra are obtained in a percolation system. The temperature dependence of the resistivity of the cellulose acetate is such that at 170 deg. C, it is essentially a conductor at frequencies below 0.059{+-}0.002 Hz, and a dielectric above. The percolation parameters, from the dc conductivity measured at 25 and 170 deg. C, are determined and discussed in relation to the ac results. The experimental results scale as a function of composition, temperature, and frequency. An interesting result is the correlation observed between the scaling parameter (f{sub ce}), obtained from a scaling of the ac measurements, and the peak frequency (f{sub cp}) of the arcs, obtained from impedance spectra, above the critical volume fraction. Scaling at 170 deg. C is not as good as at 25 deg. C, probably indicating a breakdown in scaling at the higher temperature. The modulus plots show the presence of two materials: a conducting phase dominated by the cellulose acetate and the isolated conducting clusters below the critical volume fraction {phi}{sub c}, as well as the interconnected conducting clusters above {phi}{sub c}. These results are confirmed by computer simulations using the two exponent phenomenological percolation equation. These results emphasize the need to analyze ac conductivity results in terms of both impedance and modulus spectra in order to get more insight into the behavior of composite materials.
9. Measuring Salinity by Conductivity.
ERIC Educational Resources Information Center
Lapworth, C. J.
1981-01-01
Outlines procedures for constructing an instrument which uses an electrode and calibration methods to measure the salinity of waters in environments close to and affected by a saline estuary. (Author/DC)
10. RG flow of AC conductivity in soft wall model of QCD
Bhatnagar, Neha; Siwach, Sanjay
2016-03-01
We study the Renormalization Group (RG) flow of AC conductivity in soft wall model of holographic QCD. We consider the charged black hole metric and the explicit form of AC conductivity is obtained at the cutoff surface. We plot the numerical solution of conductivity flow as a function of radial coordinate. The equation of gauge field is also considered and the numerical solution is obtained for AC conductivity as a function of frequency. The results for AC conductivity are also obtained for different values of chemical potential and Gauss-Bonnet couplings.
11. Random free energy barrier hopping model for ac conduction in chalcogenide glasses
Murti, Ram; Tripathi, S. K.; Goyal, Navdeep; Prakash, Satya
2016-03-01
The random free energy barrier hopping model is proposed to explain the ac conductivityac) of chalcogenide glasses. The Coulomb correlation is consistently accounted for in the polarizability and defect distribution functions and the relaxation time is augmented to include the overlapping of hopping particle wave functions. It is observed that ac and dc conduction in chalcogenides are due to same mechanism and Meyer-Neldel (MN) rule is the consequence of temperature dependence of hopping barriers. The exponential parameter s is calculated and it is found that s is subjected to sample preparation and measurement conditions and its value can be less than or greater than one. The calculated results for a - Se, As2S3, As2Se3 and As2Te3 are found in close agreement with the experimental data. The bipolaron and single polaron hopping contributions dominates at lower and higher temperatures respectively and in addition to high energy optical phonons, low energy optical and high energy acoustic phonons also contribute to the hopping process. The variations of hopping distance with temperature is also studied. The estimated defect number density and static barrier heights are compared with other existing calculations.
12. Phonon-Induced Electron-Hole Excitation and ac Conductance in Molecular Junction
Ueda, Akiko; Utsumi, Yasuhiro; Imamura, Hiroshi; Tokura, Yasuhiro
2016-04-01
We investigate the linear ac conductance of molecular junctions under a fixed dc bias voltage in the presence of an interaction between a transporting electron and a single local phonon in a molecule with energy ω0. The electron-phonon interaction is treated by the perturbation expansion. The ac conductance as a function of the ac frequency ωac decreases or increases compared with the noninteracting case depending on the magnitude of the dc bias voltage. Furthermore, a dip emerges at ωac ˜ 2ω0. The dip originates from the modification of electron-hole excitation by the ac field, which cannot be obtained by treating the phonon in the linear regime of a classical forced oscillation.
13. Polaron conductivity mechanism in potassium acid phthalate crystal: AC-conductivity investigation
2016-08-01
The complex dielectric constant, \\varepsilon *(ν ,T), of potassium acid phthalate monocrystal (KAP) was investigated over the broad frequency and temperature range. While the imaginary part of dielectric constant ε‧‧(ν) increases rapidly with increasing temperature in the studied temperature range, the real part of dielectric constant ε‧(ν) increases only at high temperatures; there is almost no change of ε‧(ν) below 200 K. Both values of ε‧ and ε‧‧ are frequency dependent; the values increase with decreasing frequencies. At temperatures below 450 K the ac electrical conductivity and dielectric constant follow simultaneously the universal dielectric response (UDR). The analysis of the temperature dependence of the UDR parameter s in terms of the theoretical model for small polarons revealed that this mechanism governs the charge transport in KAP crystal in the studied temperature range.
14. AC conductivity and Dielectric Study of Chalcogenide Glasses of Se-Te-Ge System
Salman, Fathy
2004-01-01
The ac conductivity and dielectric properties of glassy system SexTe79 - xGe21, with x = 11, 14, 17 at.%, has been studied at temperatures 300 to 450 K and over a wide range of frequencies (50 Hz to 500 kHz). Experimental results indicate that the ac conductivity and the dielectric constants depend on temperature, frequency and Se content. The conductivity as a function of frequency exhibited two components: dc conductivity s dc, and ac conductivity s ac, where s ac ˜ w s. The mechanism of ac conductivity can be reasonably interpreted in terms of the correlated barrier hopping model (CBH). The activation energies are estimated and discussed. The dependence of ac conductivity and dielectric constants on the Se content x can be interpreted as the effect of Se fraction on the positional disorder. The impedance plot at each temperature appeared as a semicircle passes through the origin. Each semicircle is represented by an equivalent circuit of parallel resistance Rb and capacitance Cb.
15. Thermal conductivity Measurements of Kaolite
SciTech Connect
Wang, H
2003-02-21
Testing was performed to determine the thermal conductivity of Kaolite 1600, which primarily consists of Portland cement and vermiculite. The material was made by Thermal Ceramics for refractory applications. Its combination of light weight, low density, low cost, and noncombustibility made it an attractive alternative to the materials currently used in ES-2 container for radioactive materials. Mechanical properties and energy absorption tests of the Kaolite have been conducted at the Y-12 complex. Heat transfer is also an important factor for the application of the material. The Kaolite samples are porous and trap moisture after extended storage. Thermal conductivity changes as a function of moisture content below 100 C. Thermal conductivity of the Kaolite at high temperatures (up to 700 C) are not available in the literature. There are no standard thermal conductivity values for Kaolite because each sample is somewhat different. Therefore, it is necessary to measure thermal conductivity of each type of Kaolite. Thermal conductivity measurements will help the modeling and calculation of temperatures of the ES-2 containers. This report focuses on the thermal conductivity testing effort at ORNL.
16. Measurement of coupling resonance driving terms with the AC dipole
SciTech Connect
Miyamoto, R.
2010-10-01
Resonance driving terms for linear coupled betatron motion in a synchrotron ring can be determined from corresponding spectral lines of an excited coherent beam motion. An AC dipole is one of instruments to excite such a motion. When a coherent motion is excited with an AC dipole, measured Courant-Snyder parameters and betatron phase advance have apparent modulations, as if there is an additional quadrupole field at the location of the AC dipole. Hence, measurements of these parameters using the AC dipole require a proper interpretation of observed quantities. The situation is similar in measurements of resonance driving terms using the AC dipole. In this note, we derive an expression of coupled betatron motion excited with two AC dipoles in presence of skew quadrupole fields, discuss an impact of this quadrupole like effect of the AC dipole on a measurement of coupling resonance driving terms, and present an analytical method to determine the coupling resonance driving terms from quantities observed using the AC dipole.
17. Temperature correction in conductivity measurements
USGS Publications Warehouse
Smith, Stanford H.
1962-01-01
Electrical conductivity has been widely used in freshwater research but usual methods employed by limnologists for converting measurements to conductance at a given temperature have not given uniformly accurate results. The temperature coefficient used to adjust conductivity of natural waters to a given temperature varies depending on the kinds and concentrations of electrolytes, the temperature at the time of measurement, and the temperature to which measurements are being adjusted. The temperature coefficient was found to differ for various lake and stream waters, and showed seasonal changes. High precision can be obtained only by determining temperature coefficients for each water studied. Mean temperature coefficients are given for various temperature ranges that may be used where less precision is required.
18. AC motor controller with 180 degree conductive switches
NASA Technical Reports Server (NTRS)
Oximberg, Carol A. (Inventor)
1995-01-01
An ac motor controller is operated by a modified time-switching scheme where the switches of the inverter are on for electrical-phase-and-rotation intervals of 180.degree. as opposed to the conventional 120.degree.. The motor is provided with three-phase drive windings, a power inverter for power supplied from a dc power source consisting of six switches, and a motor controller which controls the current controlled switches in voltage-fed mode. During full power, each switch is gated continuously for three successive intervals of 60.degree. and modulated for only one of said intervals. Thus, during each 60.degree. interval, the two switches with like signs are on continuously and the switch with the opposite sign is modulated.
19. Structural, dielectric and AC conductivity properties of Co2+ doped mixed alkali zinc borate glasses
Madhu, B. J.; Banu, Syed Asma; Harshitha, G. A.; Shilpa, T. M.; Shruthi, B.
2013-02-01
The Co2+ doped 19.9ZnO+5Li2CO3+25Na2CO3+50B2O3 (ZLNB) mixed alkali zinc borate glasses have been prepared by a conventional melt quenching method. The structural (XRD & FT-IR), dielectric and a.c. conductivityac) properties have been investigated. Amorphous nature of these glasses has been confirmed from their XRD pattern. The dielectric properties and electrical conductivityac) of these glasses have been studied from 100Hz to 5MHz at the room temperature. Based on the observed trends in the a.c. conductivities, the present glass samples are found to exhibit a non-Debye behavior.
20. Critical field measurements in superconductors using ac inductive techniques
Campbell, S. A.; Ketterson, J. B.; Crabtree, G. W.
1983-09-01
The ac in-phase and out-of-phase response of type II superconductors is discussed in terms of dc magnetization curves. Hysteresis in the dc magnetization is shown to lead to a dependence of the ac response on the rate at which an external field is swept. This effect allows both Hc1 and Hc2 to be measured by ac techniques. A relatively simple mutual inductance bridge for making such measurements is described in the text, and factors affecting bridge sensitivity are discussed in the Appendix. Data for the magnetic superconductor ErRh4B4 obtained using this bridge are reported.
1. Calorimetric method of ac loss measurement in a rotating magnetic field.
PubMed
Ghoshal, P K; Coombs, T A; Campbell, A M
2010-07-01
A method is described for calorimetric ac-loss measurements of high-T(c) superconductors (HTS) at 80 K. It is based on a technique used at 4.2 K for conventional superconducting wires that allows an easy loss measurement in parallel or perpendicular external field orientation. This paper focuses on ac loss measurement setup and calibration in a rotating magnetic field. This experimental setup is to demonstrate measuring loss using a temperature rise method under the influence of a rotating magnetic field. The slight temperature increase of the sample in an ac-field is used as a measure of losses. The aim is to simulate the loss in rotating machines using HTS. This is a unique technique to measure total ac loss in HTS at power frequencies. The sample is mounted on to a cold finger extended from a liquid nitrogen heat exchanger (HEX). The thermal insulation between the HEX and sample is provided by a material of low thermal conductivity, and low eddy current heating sample holder in vacuum vessel. A temperature sensor and noninductive heater have been incorporated in the sample holder allowing a rapid sample change. The main part of the data is obtained in the calorimetric measurement is used for calibration. The focus is on the accuracy and calibrations required to predict the actual ac losses in HTS. This setup has the advantage of being able to measure the total ac loss under the influence of a continuous moving field as experienced by any rotating machines. PMID:20687748
2. Calorimetric method of ac loss measurement in a rotating magnetic field
Ghoshal, P. K.; Coombs, T. A.; Campbell, A. M.
2010-07-01
A method is described for calorimetric ac-loss measurements of high-Tc superconductors (HTS) at 80 K. It is based on a technique used at 4.2 K for conventional superconducting wires that allows an easy loss measurement in parallel or perpendicular external field orientation. This paper focuses on ac loss measurement setup and calibration in a rotating magnetic field. This experimental setup is to demonstrate measuring loss using a temperature rise method under the influence of a rotating magnetic field. The slight temperature increase of the sample in an ac-field is used as a measure of losses. The aim is to simulate the loss in rotating machines using HTS. This is a unique technique to measure total ac loss in HTS at power frequencies. The sample is mounted on to a cold finger extended from a liquid nitrogen heat exchanger (HEX). The thermal insulation between the HEX and sample is provided by a material of low thermal conductivity, and low eddy current heating sample holder in vacuum vessel. A temperature sensor and noninductive heater have been incorporated in the sample holder allowing a rapid sample change. The main part of the data is obtained in the calorimetric measurement is used for calibration. The focus is on the accuracy and calibrations required to predict the actual ac losses in HTS. This setup has the advantage of being able to measure the total ac loss under the influence of a continuous moving field as experienced by any rotating machines.
3. Calorimetric method of ac loss measurement in a rotating magnetic field
SciTech Connect
Ghoshal, P. K.; Coombs, T. A.; Campbell, A. M.
2010-07-15
A method is described for calorimetric ac-loss measurements of high-T{sub c} superconductors (HTS) at 80 K. It is based on a technique used at 4.2 K for conventional superconducting wires that allows an easy loss measurement in parallel or perpendicular external field orientation. This paper focuses on ac loss measurement setup and calibration in a rotating magnetic field. This experimental setup is to demonstrate measuring loss using a temperature rise method under the influence of a rotating magnetic field. The slight temperature increase of the sample in an ac-field is used as a measure of losses. The aim is to simulate the loss in rotating machines using HTS. This is a unique technique to measure total ac loss in HTS at power frequencies. The sample is mounted on to a cold finger extended from a liquid nitrogen heat exchanger (HEX). The thermal insulation between the HEX and sample is provided by a material of low thermal conductivity, and low eddy current heating sample holder in vacuum vessel. A temperature sensor and noninductive heater have been incorporated in the sample holder allowing a rapid sample change. The main part of the data is obtained in the calorimetric measurement is used for calibration. The focus is on the accuracy and calibrations required to predict the actual ac losses in HTS. This setup has the advantage of being able to measure the total ac loss under the influence of a continuous moving field as experienced by any rotating machines.
4. Ac-conductivity and dielectric response of new zinc-phosphate glass/metal composites
Maaroufi, A.; Oabi, O.; Lucas, B.
2016-07-01
The ac-conductivity and dielectric response of new composites based on zinc-phosphate glass with composition 45 mol%ZnO-55 mol%P2O5, filled with metallic powder of nickel (ZP/Ni) were investigated by impedance spectroscopy in the frequency range from 100 Hz to 1 MHz at room temperature. A high percolating jump of seven times has been observed in the conductivity behavior from low volume fraction of filler to the higher fractions, indicating an insulator - semiconductor phase transition. The measured conductivity at higher filler volume fraction is about 10-1 S/cm and is frequency independent, while, the obtained conductivity for low filler volume fraction is around 10-8 S/cm and is frequency dependent. Moreover, the elaborated composites are characterized by high dielectric constants in the range of 105 for conductive composites at low frequencies (100 Hz). In addition, the distribution of the relaxation processes was also evaluated. The Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami models in electric modulus formalism were used to model the observed relaxation phenomena in ZP/Ni composites. The observed relaxation phenomena are fairly simulated by Davidson-Cole model, and an account of the interpretation of results is given.
5. Low frequency ac conduction and dielectric relaxation in pristine poly(3-octylthiophene) films
Singh, Ramadhar; Kumar, Jitendra; Singh, Rajiv K.; Rastogi, Ramesh C.; Kumar, Vikram
2007-02-01
The ac conductivity σ(ω)m, dielectric constant ɛ'(ω) and loss ɛ''(ω) of pristine poly(3-octylthiophene) (P3OT) films (thickness ~ 20 μm) have been measured in wide temperature (77 350 K) and frequency (100 Hz 10 MHz) ranges. At low temperatures, σ(ω)m can be described by the relation σ(ω)m = Aωs, where s is ~ 0.61 at 77 K and decreases with increasing temperature. A clear Debye-type loss peak is observed by subtracting the contribution of σdc from σ(ω)m. The frequency dependence of conductivity indicates that there is a distribution of relaxation times. This is confirmed by measurement of the dielectric constant as a function of frequency and temperature. Reasonable estimates of various electrical parameters such as effective dielectric constant (ɛp), phonon frequency (νph), Debye temperature (θD), polaron radius (rp), small-polaron coupling constant (\\Upsilon ), effective polaron mass (mp), the density of states at the Fermi level N(EF), average hopping distance (R) and average hopping energy (W) from dc conductivity measurements suggest the applicability of Mott's variable range hopping model in this system.
6. AC conductivity and structural properties of Mg-doped ZnO ceramic
Othman, Zayani Jaafar; Hafef, Olfa; Matoussi, Adel; Rossi, Francesca; Salviati, Giancarlo
2015-11-01
Undoped ZnO and Zn1- x Mg x O ceramic pellets were synthesized by the standard sintering method at the temperature of 1200 °C. The influence of Mg doping on the morphological, structural and electrical properties was studied. The scanning electron microscopy images revealed rough surface textured by grain boundaries and compacted grains having different shapes and sizes. Indeed, the X-ray diffraction reveals the alloying of hexagonal ZnMgO phase and the segregation of cubic MgO phase. The crystallite size, strain and stress were studied using Williamson-Hall (W-H) method. The results of mean particle size of Zn1- x Mg x O composites showed an inter-correlation with W-H analysis and Sherrer method. The electrical conductivity of the films was measured from 173 to 373 K in the frequency range of 0.1 Hz-1 MHz to identify the dominant conductivity mechanism. The DC conductivity is thermally activated by electron traps having activation energy of about 0.09 to 0.8 eV. The mechanisms of AC conductivity are controlled by the correlated barrier hopping model for the ZnO sample and the small polaron tunneling (SPT) model for Zn0.64Mg0.36O and Zn0.60Mg0.40O composites.
7. Hydraulic Conductivity Measurements Barrow 2014
DOE Data Explorer
Katie McKnight; Tim Kneafsey; Craig Ulrich; Jil Geller
2015-02-22
Six individual ice cores were collected from Barrow Environmental Observatory in Barrow, Alaska, in May of 2013 as part of the Next Generation Ecosystem Experiment (NGEE). Each core was drilled from a different location at varying depths. A few days after drilling, the cores were stored in coolers packed with dry ice and flown to Lawrence Berkeley National Laboratory (LBNL) in Berkeley, CA. 3-dimensional images of the cores were constructed using a medical X-ray computed tomography (CT) scanner at 120kV. Hydraulic conductivity samples were extracted from these cores at LBNL Richmond Field Station in Richmond, CA, in February 2014 by cutting 5 to 8 inch segments using a chop saw. Samples were packed individually and stored at freezing temperatures to minimize any changes in structure or loss of ice content prior to analysis. Hydraulic conductivity was determined through falling head tests using a permeameter [ELE International, Model #: K-770B]. After approximately 12 hours of thaw, initial falling head tests were performed. Two to four measurements were collected on each sample and collection stopped when the applied head load exceeded 25% change from the original load. Analyses were performed between 2 to 3 times for each sample. The final hydraulic conductivity calculations were computed using methodology of Das et al., 1985.
8. Microfabricated Thin Film Impedance Sensor & AC Impedance Measurements
PubMed Central
Yu, Jinsong; Liu, Chung-Chiun
2010-01-01
Thin film microfabrication technique was employed to fabricate a platinum based parallel-electrode structured impedance sensor. Electrochemical impedance spectroscopy (EIS) and equivalent circuit analysis of the small amplitude (±5 mV) AC impedance measurements (frequency range: 1 MHz to 0.1 Hz) at ambient temperature were carried out. Testing media include 0.001 M, 0.01 M, 0.1 M NaCl and KCl solutions, and alumina (∼3 μm) and sand (∼300 μm) particulate layers saturated with NaCl solutions with the thicknesses ranging from 0.6 mm to 8 mm in a testing cell, and the results were used to assess the effect of the thickness of the particulate layer on the conductivity of the testing solution. The calculated resistances were approximately around 20 MΩ, 4 MΩ, and 0.5 MΩ for 0.001 M, 0.01 M, and 0.1 M NaCl solutions, respectively. The presence of the sand particulates increased the impedance dramatically (6 times and 3 times for 0.001 M and 0.1 M NaCl solutions, respectively). A cell constant methodology was also developed to assess the measurement of the bulk conductivity of the electrolyte solution. The cell constant ranged from 1.2 to 0.8 and it decreased with the increase of the solution thickness. PMID:22219690
9. Ac-electrical conductivity of poly(propylene) before and after X-ray irradiation
Gaafar, M.
2001-05-01
Study on the ac-electrical conductivity of poly(propylene), before and after X-ray irradiation within the temperature range 300-360 K are reported. The measurements have been performed in a wide range of frequencies (from 0 to 10 5 Hz) and under the effect of different X-ray irradiation doses (from 0 to 15 Gy). Cole-Cole diagrams have been used to show the frequency dependence of the complex impedance at different temperatures. The results exhibit semicircles which are consistent with existing equivalent circuit model. Analysis of the results reveal semiconducting features based mainly on a hopping mechanism. The study shows a pronounced effect of X-ray irradiation on the electrical conductivity at zero frequency σDC. At the early stage of irradiation, σDC increased as a result of free radical formation. As the irradiation progressed, it decreased as a result of crosslinking, then it increased again due to irradiation induced degradation, which motivates the generation of mobile free radicals. The study shows that this polymer is one among other polymers which its electrical conductivity is modified by irradiation.
10. Analytic formulation for the ac electrical conductivity in two- temperature, strongly coupled, overdense plasma: FORTRAN subroutine
SciTech Connect
Cauble, R.; Rozmus, W.
1993-10-21
A FORTRAN subroutine for the calculation of the ac electrical conductivity in two-temperature, strongly coupled, overdense plasma is presented. The routine is the result of a model calculation based on classical transport theory with application to plasmas created by the interaction of short pulse lasers and solids. The formulation is analytic and the routine is self-contained.
11. Charging in the ac Conductance of a Double Barrier Resonant Tunneling Structure
NASA Technical Reports Server (NTRS)
Anantram, M. P.; Saini, Subhash (Technical Monitor)
1998-01-01
There have been many studies of the linear response ac conductance of a double barrier resonant tunneling structure (DBRTS), both at zero and finite dc biases. While these studies are important, they fail to self consistently include the effect of the time dependent charge density in the well. In this paper, we calculate the ac conductance at both zero and finite do biases by including the effect of the time dependent charge density in the well in a self consistent manner. The charge density in the well contributes to both the flow of displacement currents in the contacts and the time dependent potential in the well. We find that including these effects can make a significant difference to the ac conductance and the total ac current is not equal to the simple average of the non-selfconsistently calculated conduction currents in the two contacts. This is illustrated by comparing the results obtained with and without the effect of the time dependent charge density included correctly. Some possible experimental scenarios to observe these effects are suggested.
12. How to Measure Thermal Conductivity
Ventura, Guglielmo; Perfetti, Mauro
The methods to measure the thermal conductivity at low temperature are described: the steady-state techniques, (Sect. 2.2 ); the 3ω technique (Sect. 2.3 ); and the thermal diffusivity measurement (Sect. 2.4 ). Each of these techniques has its own advantages as well as its inherent limitations, with some techniques more appropriate to specific sample geometry, such as the 3ω technique for thin films which is discussed in detail in Sect. 2.4.2 . The radial flux method is reported in Sect. 2.2.4 , the laser flash diffusivity method in Sect. 2.4.1 and the "pulsed power or Maldonado technique" in Sect. 2.3.2 .
13. AC Conductivity Studies in Lithium-Borate Glass Containing Gold Nanoparticles
Shivaprakash, Y.; Anavekar, R. V.
2011-07-01
Gold nanoparticles have been synthesized in a base glass with composition 30Li2O-70B2O3 using gold chloride (HAuCl4.3H2O) as a dopant. The samples are characterized using XRD, ESR, SEM and optical absorption in the visible range. AC conductivity studies have been performed at RT over a frequency range 100 to 10 MHz. The dc conductivity is calculated from the complex impedence plot. The dc conductivity is found to be increasing with the increase of dopant concentration. AC conductivity data is fitted with Almond-West law with power exponent s'. The values of `s' is found to lie in the range of 0.70-0.73.
14. Gas sensing properties of magnesium doped SnO{sub 2} thin films in relation to AC conduction
SciTech Connect
Deepa, S.; Skariah, Benoy Thomas, Boben; Joseph, Anisha
2014-01-28
Conducting magnesium doped (0 to 1.5 wt %) tin oxide thin films prepared by Spray Pyrolysis technique achieved detection of 1000 ppm of LPG. The films deposited at 304 °C exhibit an enhanced response at an operating temperature of 350 °C. The microstructural properties are studied by means of X-ray diffraction. AC conductivity measurements are carried out using precision LCR meter to analyze the parameters that affect the variation in sensing. The results are correlated with compositional parameters and the subsequent modification in the charge transport mechanism facilitating an enhanced LPG sensing action.
15. Measurement of the 225Ac half-life.
PubMed
Pommé, S; Marouli, M; Suliman, G; Dikmen, H; Van Ammel, R; Jobbágy, V; Dirican, A; Stroh, H; Paepen, J; Bruchertseifer, F; Apostolidis, C; Morgenstern, A
2012-11-01
The (225)Ac half-life was determined by measuring the activity of (225)Ac sources as a function of time, using various detection techniques: α-particle counting with a planar silicon detector at a defined small solid angle and in a nearly-2π geometry, 4πα+β counting with a windowless CsI sandwich spectrometer and with a pressurised proportional counter, gamma-ray spectrometry with a HPGe detector and with a NaI(Tl) well detector. Depending on the technique, the decay was followed for 59-141 d, which is about 6-14 times the (225)Ac half-life. The six measurement results were in good mutual agreement and their mean value is T(1/2)((225)Ac)=9.920 (3)d. This half-life value is more precise and better documented than the currently recommended value of 10.0 d, based on two old measurements lacking uncertainty evaluations. PMID:22940415
16. ac driving amplitude dependent systematic error in scanning Kelvin probe microscope measurements: Detection and correction
SciTech Connect
Wu Yan; Shannon, Mark A.
2006-04-15
The dependence of the contact potential difference (CPD) reading on the ac driving amplitude in scanning Kelvin probe microscope (SKPM) hinders researchers from quantifying true material properties. We show theoretically and demonstrate experimentally that an ac driving amplitude dependence in the SKPM measurement can come from a systematic error, and it is common for all tip sample systems as long as there is a nonzero tracking error in the feedback control loop of the instrument. We further propose a methodology to detect and to correct the ac driving amplitude dependent systematic error in SKPM measurements. The true contact potential difference can be found by applying a linear regression to the measured CPD versus one over ac driving amplitude data. Two scenarios are studied: (a) when the surface being scanned by SKPM is not semiconducting and there is an ac driving amplitude dependent systematic error; (b) when a semiconductor surface is probed and asymmetric band bending occurs when the systematic error is present. Experiments are conducted using a commercial SKPM and CPD measurement results of two systems: platinum-iridium/gap/gold and platinum-iridium/gap/thermal oxide/silicon are discussed.
17. Measurements of AC Losses and Current Distribution in Superconducting Cables
SciTech Connect
Nguyen, Doan A; Ashworth, Stephen P; Duckworth, Robert C; Carter, Bill; Fleshler, Steven
2011-01-01
This paper presents our new experimental facility and techniques to measure ac loss and current distribution between the layers for High Temperature Superconducting (HTS) cables. The facility is powered with a 45 kVA three-phase power supply which can provide three-phase currents up to 5 kA per phase via high current transformers. The system is suitable for measurements at any frequency between 20 and 500 Hz to better understand the ac loss mechanisms in HTS cables. In this paper, we will report techniques and results for ac loss measurements carried out on several HTS cables with and without an HTS shielding layer. For cables without a shielding layer, care must be taken to control the effect of the magnetic fields from return currents on loss measurements. The waveform of the axial magnetic field was also measured by a small pick-up coil placed inside a two-layer cable. The temporal current distribution between the layers can be calculated from the waveform of the axial field.
18. Temperature and frequency dependence of AC conductivity of new quaternary Se-Te-Bi-Pb chalcogenide glasses
2016-05-01
The aim of the present work is to study the temperature and frequency dependence of ac conductivity of new quaternary Se84-xTe15Bi1.0Pbx chalcogenide glasses. The Se84-xTe15Bi1.0Pbx (x = 2, 6) glassy alloys are prepared by using melt quenching technique. The temperature and frequency dependent behavior of ac conductivity σac(ω) has been carried out in the frequency range 42 Hz to 5 MHz and in the temperature range of 298-323 K below glass transition temperature. The behavior of ac conductivity is described in terms of the power law ωs. The obtained temperature dependence behavior of ac conductivity and frequency component (s) are explained by means of correlated barrier hopping model recommended by Elliot.
19. Microwave a.c. conductivity of domain walls in ferroelectric thin films
Tselev, Alexander; Yu, Pu; Cao, Ye; Dedon, Liv R.; Martin, Lane W.; Kalinin, Sergei V.; Maksymovych, Petro
2016-05-01
Ferroelectric domain walls are of great interest as elementary building blocks for future electronic devices due to their intrinsic few-nanometre width, multifunctional properties and field-controlled topology. To realize the electronic functions, domain walls are required to be electrically conducting and addressable non-destructively. However, these properties have been elusive because conducting walls have to be electrically charged, which makes them unstable and uncommon in ferroelectric materials. Here we reveal that spontaneous and recorded domain walls in thin films of lead zirconate and bismuth ferrite exhibit large conductance at microwave frequencies despite being insulating at d.c. We explain this effect by morphological roughening of the walls and local charges induced by disorder with the overall charge neutrality. a.c. conduction is immune to large contact resistance enabling completely non-destructive walls read-out. This demonstrates a technological potential for harnessing a.c. conduction for oxide electronics and other materials with poor d.c. conduction, particularly at the nanoscale.
20. Microwave a.c. conductivity of domain walls in ferroelectric thin films.
PubMed
Tselev, Alexander; Yu, Pu; Cao, Ye; Dedon, Liv R; Martin, Lane W; Kalinin, Sergei V; Maksymovych, Petro
2016-01-01
Ferroelectric domain walls are of great interest as elementary building blocks for future electronic devices due to their intrinsic few-nanometre width, multifunctional properties and field-controlled topology. To realize the electronic functions, domain walls are required to be electrically conducting and addressable non-destructively. However, these properties have been elusive because conducting walls have to be electrically charged, which makes them unstable and uncommon in ferroelectric materials. Here we reveal that spontaneous and recorded domain walls in thin films of lead zirconate and bismuth ferrite exhibit large conductance at microwave frequencies despite being insulating at d.c. We explain this effect by morphological roughening of the walls and local charges induced by disorder with the overall charge neutrality. a.c. conduction is immune to large contact resistance enabling completely non-destructive walls read-out. This demonstrates a technological potential for harnessing a.c. conduction for oxide electronics and other materials with poor d.c. conduction, particularly at the nanoscale. PMID:27240997
1. Microwave a.c. conductivity of domain walls in ferroelectric thin films
PubMed Central
Tselev, Alexander; Yu, Pu; Cao, Ye; Dedon, Liv R.; Martin, Lane W.; Kalinin, Sergei V.; Maksymovych, Petro
2016-01-01
Ferroelectric domain walls are of great interest as elementary building blocks for future electronic devices due to their intrinsic few-nanometre width, multifunctional properties and field-controlled topology. To realize the electronic functions, domain walls are required to be electrically conducting and addressable non-destructively. However, these properties have been elusive because conducting walls have to be electrically charged, which makes them unstable and uncommon in ferroelectric materials. Here we reveal that spontaneous and recorded domain walls in thin films of lead zirconate and bismuth ferrite exhibit large conductance at microwave frequencies despite being insulating at d.c. We explain this effect by morphological roughening of the walls and local charges induced by disorder with the overall charge neutrality. a.c. conduction is immune to large contact resistance enabling completely non-destructive walls read-out. This demonstrates a technological potential for harnessing a.c. conduction for oxide electronics and other materials with poor d.c. conduction, particularly at the nanoscale. PMID:27240997
2. Temperature dependence of conductivity measurement for conducting polymer
Gutierrez, Leandro; Duran, Jesus; Isah, Anne; Albers, Patrick; McDougall, Michael; Wang, Weining
2014-03-01
Conducting polymer-based solar cells are the newest generation solar cells. While research on this area has been progressing, the efficiency is still low because certain important parameters of the solar cell are still not well understood. It is of interest to study the temperature dependence of the solar cell parameters, such as conductivity of the polymer, open circuit voltage, and reverse saturation current to gain a better understanding on the solar cells. In this work, we report our temperature dependence of conductivity measurement using our in-house temperature-varying apparatus. In this project, we designed and built a temperature varying apparatus using a thermoelectric cooler module which gives enough temperature range as we need and costs much less than a cryostat. The set-up of the apparatus will be discussed. Temperature dependence of conductivity measurements for PEDOT:PSS films with different room-temperature conductivity will be compared and discussed. NJSGC-NASA Fellowship grant
3. Effect of nanosilica on optical, electric modulus and AC conductivity of polyvinyl alcohol/polyaniline films
El-Sayed, Somyia; Abel-Baset, Tarob; Elfadl, Azza Abou; Hassen, Arafa
2015-05-01
Nanosilica (NS) was synthesized by a sol-gel method and mixed with 0.98 polyvinyl alcohol (PVA)/0.02 polyaniline (PANI) in different amounts to produce nanocomposite films. High-resolution transmission electron microscopy (HR-TEM) revealed the average particle size of the NS to be ca. 15 nm. Scanning electron microscopy (SEM) showed that the NS was well-dispersed on the surface of the PVA/PNAI films. The Fourier transform infrared (FTIR) spectra of the samples showed a significant change in the intensity of the characteristic peak of the functional groups in the composite films with the amount of NS added. The absorbance and refractive index (n) of the composites were studied in the UV-vis range, and the optical energy band gap, Eg, and different optical parameters were calculated. The dielectric loss modulus, M″ and ac conductivity, σac, of the samples were studied within 300-425 K and 0.1 kHz-5 MHz, respectively. Two relaxation peaks were observed in the frequency dependence of the dielectric loss modulus, M″. The behavior of σac(f) for the composite films indicated that the conduction mechanism was correlated barrier hopping (CBH). The results of this work are discussed and compared with those of previous studies of similar composites.
4. Instabilities across the isotropic conductivity point in a nematic phenyl benzoate under AC driving.
PubMed
Kumar, Pramoda; Patil, Shivaram N; Hiremath, Uma S; Krishnamurthy, K S
2007-08-01
We characterize the sequence of bifurcations generated by ac fields in a nematic layer held between unidirectionally rubbed ITO electrodes. The material, which possesses a negative dielectric anisotropy epsilona and an inversion temperature for electrical conductivity anisotropy sigmaa, exhibits a monostable tilted alignment near TIN, the isotropic-nematic point. On cooling, an anchoring transition to the homeotropic configuration occurs close to the underlying smectic phase. The field experiments are performed for (i) negative sigmaa and homeotropic alignment, and (ii) weakly positive sigmaa and nearly homeotropic alignment. Under ac driving, the Freedericksz transition is followed by bifurcation into various patterned states. Among them are the striped states that seem to belong to the dielectric regime and localized hybrid instabilities. Very significantly, the patterned instabilities are not excited by dc fields, indicating their possible gradient flexoelectric origin. The Carr-Helfrich mechanism-based theories that take account of flexoelectric terms can explain the observed electroconvective effects only in part. PMID:17616118
5. Conductivity (ac and dc) in III-V amorphous semiconductors and chalcogenide glasses
Hauser, J. J.
1985-02-01
Variable-range hopping, as evidenced by a resistivity proportional to exp(T-1/4), has been induced in many III-V amorphous semiconductors (InSb, AlSb, and GaAs) and even in chalcogenide glasses (As2Te3, As2Te3-xSex, and GeTe) by depositing films at 77 K. It is therefore remarkable that the same procedure failed to generate variable-range hopping in GaSb, which is one of the less ionic III-V semiconductors. Besides differences in the dc conductivity, there are also different behaviors in the ac conductivity of amorphous semiconductors. The low-temperature ac conductivity of all amorphous semiconductors is proportional to ωsTn with s~=1 and n<1, which is consistent with a model of correlated barrier hopping of electron pairs between paired and random defects. However, in the case of a-SiO2 and a-GeSe2 one finds, in addition, that the capacitance obeys the scaling relation C=A ln(Tω-1), which would suggest a conduction mechanism by tunneling relaxation. Furthermore, this scaling relation cannot be fitted to the data for a-As2Te3, a-InSb, and a-GaSb although the functional dependence of C on T and ω are similar.
6. Iterative Precise Conductivity Measurement with IDEs
PubMed Central
Hubálek, Jaromír
2015-01-01
The paper presents a new approach in the field of precise electrolytic conductivity measurements with planar thin- and thick-film electrodes. This novel measuring method was developed for measurement with comb-like electrodes called interdigitated electrodes (IDEs). Correction characteristics over a wide range of specific conductivities were determined from an interface impedance characterization of the thick-film IDEs. The local maximum of the capacitive part of the interface impedance is used for corrections to get linear responses. The measuring frequency was determined at a wide range of measured conductivity. An iteration mode of measurements was suggested to precisely measure the conductivity at the right frequency in order to achieve a highly accurate response. The method takes precise conductivity measurements in concentration ranges from 10−6 to 1 M without electrode cell replacement. PMID:26007745
7. Study on AC-DC Electrical Conductivities in Warm Dense Matter Generated by Pulsed-power Discharge with Isochoric Vessel
Sasaki, Toru; Ohuchi, Takumi; Takahashi, Takuya; Kawaguchi, Yoshinari; Saito, Hirotaka; Miki, Yasutoshi; Takahashi, Kazumasa; Kikuchi, Takashi; Aso, Tsukasa; Harada, Nob.
2016-03-01
To observe AC and DC electrical conductivity in warm dense matter (WDM), we have demonstrated to apply the spectroscopic ellipsometry for a pulsed-power discharge with isochoric vessel. At 10 μs from the beginning of discharge, the generated parameters by using pulsed-power discharge with isochoric vessel are 0.1 ρ s (ρ s: solid density) of density and 4000 K of temperature, respectively. The DC electrical conductivity for above parameters is estimated to be 104 S/m. In order to measure the AC electrical conductivity, we have developed a four-detector spectroscopic ellipsometer with a multichannel spectrometer. The multichannel spectrometer, in which consists of a 16-channel photodiode array, a two-stages voltage adder, and a flat diffraction grating, has 10 MHz of the frequency response with covered visible spectrum. For applying the four-detector spectroscopic ellipsometer, we observe the each observation signal evolves the polarized behavior compared to the ratio as I 1/I 2.
8. Skin Conductance Measurement in Communication Research.
ERIC Educational Resources Information Center
Goodman, R. Irwin
1985-01-01
Describes skin conductance measurement as a physiological procedure to obtain information on onset, duration, intensity, and completion of private physiological responses to parts of films or media products. The mechanics of the technique, how measurements are recorded and analyzed, and types of skin conductance research literature are discussed.…
9. AC conductivity scaling behavior in grain and grain boundary response regime of fast lithium ionic conductors
Mariappan, C. R.
2014-05-01
AC conductivity spectra of Li-analogues NASICON-type Li1.5Al0.5Ge1.5P3O12 (LAGP), Li-Al-Ti-P-O (LATP) glass-ceramics and garnet-type Li7La2Ta2O13 (LLTO) ceramic are analyzed by universal power law and Summerfield scaling approaches. The activation energies and pre-exponential factors of total and grain conductivities are following the Meyer-Neldel (M-N) rule for NASICON-type materials. However, the garnet-type LLTO material deviates from the M-N rule line of NASICON-type materials. The frequency- and temperature-dependent conductivity spectra of LAGP and LLTO are superimposed by Summerfield scaling. The scaled conductivity curves of LATP are not superimposed at the grain boundary response region. The superimposed conductivity curves are observed at cross-over frequencies of grain boundary response region for LATP by incorporating the exp ( {{{ - (EAt - EAg )} {{{ - (EAt - EAg )} {kT}}} ) factor along with Summerfield scaling factors on the frequency axis, where EAt and EAg are the activation energies of total and grain conductivities, respectively.
10. AC and DC conductivity of ionic liquid containing polyvinylidene fluoride thin films
Frübing, Peter; Wang, Feipeng; Kühle, Till-Friedrich; Gerhard, Reimund
2016-01-01
Polarisation processes and charge transport in polyvinylidene fluoride (PVDF) with a small amount (0.01-10 wt%) of the ionic liquid (IL) 1-ethyl-3-methylimidazolium nitrate ({[EMIM]}^+[{NO}_3]^-) are investigated by means of dielectric spectroscopy. The response of PVDF that contains more than 0.01 wt% IL is dominated by a low-frequency relaxation which shows typical signatures of electrode polarisation. Furthermore, the α a relaxation, related to the glass transition, disappears for IL contents of more than 1 wt%, which indicates that the amorphous phase loses its glass-forming properties and undergoes structural changes. The DC conductivity is determined from the low-frequency limit of the AC conductivity and from the dielectric loss peak related to the electrode polarisation. DC conductivities of 10^{-10} to 10^{-2} {S}/{m} are obtained—increasing with IL content and temperature. The dependence of the DC conductivity on the IL content follows a power law with an exponent greater than one, indicating an increase in the ion mobility. The temperature dependence of the DC conductivity shows Vogel-Fulcher-Tammann behaviour, which implies that charge transport is coupled to polymer chain motion. Mobile ion densities and ion mobilities are calculated from the DC conductivity and the dielectric loss related to electrode polarisation, with the results that less than one per cent of the total ion concentration contributes to the conductivity and that the strong increase in conductivity with temperature is mainly caused by a strong increase in ion mobility. This leads to the conclusion that in particular the ion mobility must be reduced in order to decrease the DC conductivity.
11. Finding the asymmetric parasitic source and drain resistances from the a.c. conductances of a single MOS transistor
Raychaudhuri, A.; Deen, M. J.; King, M. I. H.; Kolk, J.
1996-06-01
Layout asymmetry, processing, or hot-carrier stressing can give rise to unequal source and drain parasitic resistances in a MOSFET. In these cases, it is necessary to extract these resistances separately without the aid of other transistors. In this paper, we present a simple method to extract the source and drain parasitic resistances separately. This method, unlike earlier ones that depend on the measurements of the d.c. resistances of several MOSFETs, is based on accurate formulations and measurements of the a.c. conductances with respect to the gate and drain terminals of a single transistor. This allows us to get reasonably accurate estimates of these resistances in a more straightforward manner. We also discuss the main error terms in detail.
12. AC conductivity and dielectric behavior of CoAl xFe 2- xO 4
Abo El Ata, A. M.; Attia, S. M.; Meaz, T. M.
2004-01-01
AC conductivity and dielectric properties have been studied for a series of polycrystalline spinel ferrite with composition CoAl xFe 2- xO 4, as a function of frequency and temperature. The results of AC conductivity were discussed in terms of the quantum mechanical tunneling and small polaron tunneling models. The dispersion of the dielectric constant was discussed in the light of Koops model and hopping conduction mechanism. The dielectric loss tangent tan δ curves exhibits a dielectric relaxation peaks which are attributed to the coincidence of the hopping frequency of the charge carriers with that of the external fields. The AC conductivity, dielectric constant, and dielectric loss tangent were found to increase with increasing the temperature due to the increase of the hopping frequency, while they decrease with increasing Al ion content due to the reduction of iron ions available for the conduction process at the octahedral sites.
13. Electric properties of carbon nano-onion/polyaniline composites: a combined electric modulus and ac conductivity study
Papathanassiou, Anthony N.; Mykhailiv, Olena; Echegoyen, Luis; Sakellis, Ilias; Plonska-Brzezinska, Marta E.
2016-07-01
The complex electric modulus and the ac conductivity of carbon nano-onion/polyaniline composites were studied from 1 mHz to 1 MHz at isothermal conditions ranging from 15 K to room temperature. The temperature dependence of the electric modulus and the dc conductivity analyses indicate a couple of hopping mechanisms. The distinction between thermally activated processes and the determination of cross-over temperature were achieved by exploring the temperature dependence of the fractional exponent of the dispersive ac conductivity and the bifurcation of the scaled ac conductivity isotherms. The results are analyzed by combining the granular metal model (inter-grain charge tunneling of extended electron states located within mesoscopic highly conducting polyaniline grains) and a 3D Mott variable range hopping model (phonon assisted tunneling within the carbon nano-onions and clusters).
14. Thunderstorm related variations in stratospheric conductivity measurements
NASA Technical Reports Server (NTRS)
Hu, Hua; Holzworth, Robert H.; Li, Ya QI
1989-01-01
The vector electric field and polar conductivities were measured by zero-pressure balloon-borne payloads launched from Wallops Island, Virgina during the summers of 1987 and 1988. Data were collected over thunderstorms (or electrified clouds) during 6-hour flights at altitudes near 30 km. The vector electric field measurements were made with the double Langmuir probe high-impedance method, and the direct conductivity measurements were obtained with the relaxation technique. Evidence is presented for conductivity variations over thunderstorms (or electrified clouds). It is found that both positive and negative polar conductivity data do show variations of up to a factor of 2 from ambient values associated with the disturbed periods. Some ideas for possible physical mechanisms which may be responsible for the conductivity variations over thunderstorms are also discussed in this paper.
15. AC conductivity and dielectric relaxation of tris(N,N-dimethylanilinium) hexabromidostannate(IV) bromide: (C8H12N)3SnBr6.Br
Chouaib, H.; Kamoun, S.
2015-10-01
The X-ray powder analysis, thermogravimetric analysis, differential scanning calorimetry analysis and complex impedance spectroscopic data have been carried out on (C8H12N)3SnBr6.Br compound. The results show that this compound exhibits a phase transition at (T=365±2 K) which has been characterized by differential scanning calorimetry (DSC), AC conductivity and dielectric measurements. The AC conductivity, the modulus analysis, the dielectric constants and the polarizability have been studied using impedance in the temperature range from 334 K to 383 K and in the frequency range between 20 Hz and 2 MHz. The temperature dependence of DC conductivity follows the Arrhenius law. Moreover, the frequency dependence of conductivity follows Jonscher's dynamical law with the relation: σ(ω , T) =σDC + B(T)ω s(T) . Relaxation peaks can be observed in the complex modulus analysis and after a transformation of the complex permittivity ε* to the complex polarizability α*.
16. An effective thermal conductivity measurement system
Madrid, F.; Jordà, X.; Vellvehi, M.; Guraya, C.; Coleto, J.; Rebollo, J.
2004-11-01
In the technical literature, there is a lack of reliable thermal parameters and, often, it is necessary to do in situ measurements for every particular material. An effective thermal conductivity measurement system has been designed and implemented to provide reliable and accurate values for that thermal parameter. The thermal conductivity of a given material is deduced from thermal resistance differential measurements of two samples. All parts of the implemented system as well as practical and theoretical solutions are described, including a power controller circuit exclusively conceived for this application. Experimental considerations to reduce the measurement error are exposed, as well as some results obtained for three different materials.
17. Transport ac losses of a second-generation HTS tape with a ferromagnetic substrate and conducting stabilizer
Li, Shuo; Chen, Du-Xing; Fang, Jin
2015-12-01
The current-voltage curve and transport ac loss of a second-generation HTS tape with a ferromagnetic NiW substrate and brass stabilizer are measured. It is found that the ac loss is up to two orders of magnitude larger than what is expected by the power-law E(J) determined by the current-voltage curve and increases with increasing frequency. Modeling results show that the overly large ac loss is contributed by the ac loss in the HTS strip enhanced by the NiW substrate and the magnetic hysteresis loss in the substrate, and the frequency-dependent loss occurs in the brass layer covering the substrate but not in the ferromagnetic substrate itself as assumed previously. The ac loss in the brass layer is associated with transport currents but not eddy currents, and it has some features similar to ordinary eddy-current loss with significant differences.
18. Thermal conductivity measurements of Summit polycrystalline silicon.
SciTech Connect
Clemens, Rebecca; Kuppers, Jaron D.; Phinney, Leslie Mary
2006-11-01
A capability for measuring the thermal conductivity of microelectromechanical systems (MEMS) materials using a steady state resistance technique was developed and used to measure the thermal conductivities of SUMMiT{trademark} V layers. Thermal conductivities were measured over two temperature ranges: 100K to 350K and 293K to 575K in order to generate two data sets. The steady state resistance technique uses surface micromachined bridge structures fabricated using the standard SUMMiT fabrication process. Electrical resistance and resistivity data are reported for poly1-poly2 laminate, poly2, poly3, and poly4 polysilicon structural layers in the SUMMiT process from 83K to 575K. Thermal conductivity measurements for these polysilicon layers demonstrate for the first time that the thermal conductivity is a function of the particular SUMMiT layer. Also, the poly2 layer has a different variation in thermal conductivity as the temperature is decreased than the poly1-poly2 laminate, poly3, and poly4 layers. As the temperature increases above room temperature, the difference in thermal conductivity between the layers decreases.
19. Conductance measurement circuit with wide dynamic range
NASA Technical Reports Server (NTRS)
Mount, Bruce E. (Inventor); Von Esch, Myron (Inventor)
1994-01-01
A conductance measurement circuit to measure conductance of a solution under test with an output voltage proportional to conductance over a 5-decade range, i.e., 0.01 uS to 1000 uS or from 0.1 uS to 10,000 uS. An increase in conductance indicates growth, or multiplication, of the bacteria in the test solution. Two circuits are used each for an alternate half-cycle time periods of an alternate squarewave in order to cause alternate and opposite currents to be applied to the test solution. The output of one of the two circuits may be scaled for a different range optimum switching frequency dependent upon the solution conductance and to enable uninterrupted measurement over the complete 5-decade range. This circuitry provides two overlapping ranges of conductance which can be read simultaneously without discontinuity thereby eliminating range switching within the basic circuitry. A VCO is used to automatically change the operating frequency according to the particular value of the conductance being measured, and comparators indicate which range is valid and also facilitate computer-controlled data acquisition. A multiplexer may be used to monitor any number of solutions under test continuously.
20. Absorption and Attenuation Coefficients Using the WET Labs ac-s in the Mid-Atlantic Bight: Field Measurements and Data Analysis
NASA Technical Reports Server (NTRS)
Ohi, Nobuaki; Makinen, Carla P.; Mitchell, Richard; Moisan, Tiffany A.
2008-01-01
Ocean color algorithms are based on the parameterization of apparent optical properties as a function of inherent optical properties. WET Labs underwater absorption and attenuation meters (ac-9 and ac-s) measure both the spectral beam attenuation [c (lambda)] and absorption coefficient [a (lambda)]. The ac-s reports in a continuous range of 390-750 nm with a band pass of 4 nm, totaling approximately 83 distinct wavelengths, while the ac-9 reports at 9 wavelengths. We performed the ac-s field measurements at nine stations in the Mid-Atlantic Bight from water calibrations to data analysis. Onboard the ship, the ac-s was calibrated daily using Milli Q-water. Corrections for the in situ temperature and salinity effects on optical properties of water were applied. Corrections for incomplete recovery of the scattered light in the ac-s absorption tube were performed. The fine scale of spectral and vertical distributions of c (lambda) and a (lambda) were described from the ac-s. The significant relationships between a (674) and that of spectrophotometric analysis and chlorophyll a concentration of discrete water samples were observed.
1. Local measurement of thermal conductivity and diffusivity
SciTech Connect
Hurley, David H.; Schley, Robert S.; Khafizov, Marat; Wendt, Brycen L.
2015-12-01
Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness for extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representative of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agree closely with literature values. Lastly, a distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility.
2. Local measurement of thermal conductivity and diffusivity.
PubMed
Hurley, David H; Schley, Robert S; Khafizov, Marat; Wendt, Brycen L
2015-12-01
Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness for extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representatives of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agreed closely with the literature values. A distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility. PMID:26724041
3. Local measurement of thermal conductivity and diffusivity
Hurley, David H.; Schley, Robert S.; Khafizov, Marat; Wendt, Brycen L.
2015-12-01
Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness for extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representatives of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agreed closely with the literature values. A distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility.
4. Local measurement of thermal conductivity and diffusivity
SciTech Connect
Hurley, David H.; Schley, Robert S.; Khafizov, Marat; Wendt, Brycen L.
2015-12-15
Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness for extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representatives of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agreed closely with the literature values. A distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility.
5. Local measurement of thermal conductivity and diffusivity
DOE PAGESBeta
Hurley, David H.; Schley, Robert S.; Khafizov, Marat; Wendt, Brycen L.
2015-12-01
Simultaneous measurement of local thermal diffusivity and conductivity is demonstrated on a range of ceramic samples. This was accomplished by measuring the temperature field spatial profile of samples excited by an amplitude modulated continuous wave laser beam. A thin gold film is applied to the samples to ensure strong optical absorption and to establish a second boundary condition that introduces an expression containing the substrate thermal conductivity. The diffusivity and conductivity are obtained by comparing the measured phase profile of the temperature field to a continuum based model. A sensitivity analysis is used to identify the optimal film thickness formore » extracting the both substrate conductivity and diffusivity. Proof of principle studies were conducted on a range of samples having thermal properties that are representative of current and advanced accident tolerant nuclear fuels. It is shown that by including the Kapitza resistance as an additional fitting parameter, the measured conductivity and diffusivity of all the samples considered agree closely with literature values. Lastly, a distinguishing feature of this technique is that it does not require a priori knowledge of the optical spot size which greatly increases measurement reliability and reproducibility.« less
6. Ac-loss measurement of a DyBCO-Roebel assembled coated conductor cable (RACC)
Schuller, S.; Goldacker, W.; Kling, A.; Krempasky, L.; Schmidt, C.
2007-10-01
Low ac-loss HTS cables for transport currents well above 1 kA are required for application in transformers and generators and are taken into consideration for future generations of fusion reactor coils. Coated conductors (CC) are suitable candidates for high field application at an operation temperature around 50-77 K, which is a crucial precondition for economical cooling costs. We prepared a short length of a Roebel bar cable made of industrial DyBCO coated conductor (Theva Company, Germany). Meander shaped tapes of 4 mm width with a twist pitch of 122 mm were cut from 10 mm wide CC tapes using a specially designed tool. Eleven of these strands were assembled to a cable. The electrical and mechanical connection of the tapes was achieved using a silver powder filled conductive epoxy resin. Ac-losses of a short sample in an external ac field were measured as a function of frequency and field amplitude in transverse and parallel field orientations. In addition, the coupling current time constant of the sample was directly measured.
7. AC Circuit Measurements with a Differential Hall Element Magnetometer
Calkins, Matthew W.; Nicks, B. Scott; Quintero, Pedro A.; Meisel, Mark W.
2013-03-01
As the biomedical field grows, there is an increasing need to quickly and efficiently characterize more samples at room temperature. An automated magnetometer was commissioned to do these room temperature magnetic characterizations. This magnetometer, which is inspired by a Differential Hall Element Magnetometer,[2] uses two commercially available Hall elements wired in series. One Hall element measures the external magnetic field of a 9 T superconducting magnet and the other measures the same external field plus the field due to the magnetization of the sample that sits on top of the Hall element. The difference between these two Hall elements is taken while a linear stepper motor sweeps through the external magnetic field. The linear motor and data acquisition are controlled by a LabVIEW program. Recently, the system was outfitted for AC circuit measurements and these data will be compared to DC circuit data. In addition, the lowest signal to noise ratio will be found in order to deduce the smallest amount of sample needed to register an accurate coercive field. Supported by the NSF via NHMFL REU (DMR-0654118), a single investigator grant (DMR-1202033 to MWM) and by the UF Undergraduate Scholars Program.
8. Measurement of AC Induced Flow using Mico PIV
Wang, Dazhi; Meinhart, Carl; Sigurdson, Marin
2002-11-01
The fluid motion in a wedge-shaped device subject to an AC electric field is measured using Micron-Resolution Particle Image Velocimetry (micro-PIV). The fluorescent polystyrene spherical particles are used as flow tracers. In the non-uniform electric field, the particles in the suspension experience dielectrophoretic forces, which cause difference of velocities between the particles and the fluid. In order to eliminate the velocity difference, two different size particles are used for the micro-PIV measurements to determine the fluid velocity field. A two-color PIV technique is used to determine uniquely the fluid velocity field. The wedge-shaped channel is 100-micron wide at the apex, and fabricated from a 550-micron thick silicon wafer. A voltage of 15Vrms at 100 kHz is applied to the electrodes. The particle volume fraction is set below 0.1% so that the effect of the particles on the fluid can be negligible. Fifty successive images are taken to record particle images and analyzed to estimate the particle velocity fields. The velocity fields of the two different size particles are then used to uniquely determine the underlying fluid velocity. The measured fluid flow is a saddle-point flow, which could be used for precision mixing and transport in microscale devices.
9. Origin of DC and AC conductivity anisotropy in iron-based superconductors: Scattering rate versus spectral weight effects
Schütt, Michael; Schmalian, Jörg; Fernandes, Rafael M.
2016-08-01
To shed light on the transport properties of electronic nematic phases, we investigate the anisotropic properties of the AC and DC conductivities. Based on the analytical properties of the former, we show that the anisotropy of the effective scattering rate behaves differently than the actual scattering rate anisotropy and even changes sign as a function of temperature. Similarly, the effective spectral weight acquires an anisotropy even when the plasma frequency is isotropic. These results are illustrated by an explicit calculation of the AC conductivity due to the interaction between electrons and spin fluctuations in the nematic phase of the iron-based superconductors and shown to be in agreement with recent experiments.
10. Inductive Measurement of Plasma Jet Electrical Conductivity
NASA Technical Reports Server (NTRS)
Turner, Matthew W.; Hawk, Clark W.; Litchford, Ron J.
2005-01-01
An inductive probing scheme, originally developed for shock tube studies, has been adapted to measure explosive plasma jet conductivities. In this method, the perturbation of an applied magnetic field by a plasma jet induces a voltage in a search coil, which, in turn, can be used to infer electrical conductivity through the inversion of a Fredholm integral equation of the first kind. A 1-inch diameter probe was designed and constructed, and calibration was accomplished by firing an aluminum slug through the probe using a light-gas gun. Exploratory laboratory experiments were carried out using plasma jets expelled from 15-gram high explosive shaped charges. Measured conductivities were in the range of 3 kS/m for unseeded octol charges and 20 kS/m for seeded octol charges containing 2% potassium carbonate by mass.
11. Flow rate measurement in aggressive conductive fluids
Dubovikova, Nataliia; Kolesnikov, Yuri; Karcher, Christian
2014-03-01
Two non-contact experimental methods of flow rate measurements for aggressive conductive liquids are described. The techniques are based on electromagnetic forces and Faraday's law: Lorentz force is induced inside moving conductive liquid under influence of variable magnetic field of permanent magnets. They are mounted along a liquid metal channel or (in case of the second method) inserted into rotated metal wheels. The force acts in the opposite of fluids' velocity direction and hence it is possible to measure reaction force of it that takes place according to Newton's law on magnetic field source - permanent magnets. And by knowing the force, which linearly depends on velocity, one can calculate mean flow rate of liquid. In addition experimental "dry" calibration and its results are described for one of the measurements' techniques.
12. Analytic formulation for the ac electrical conductivity in two-temperature, strongly coupled, overdense plasma: FORTRAN subroutine
Cauble, R.; Rozmus, W.
1993-10-01
A FORTRAN subroutine for the calculation of the ac electrical conductivity in two-temperature, strongly coupled, overdense plasma is presented. The routine is the result of a model calculation based on classical transport theory with application to plasmas created by the interaction of short pulse lasers and solids. The formulation is analytic and the routine is self-contained.
13. Martian Surface after Phoenix's Conductivity Measurements
NASA Technical Reports Server (NTRS)
2008-01-01
NASA's Phoenix Mars Lander's Robotic Arm Camera took this image on Sol 71 (August 6, 2008), the 71st Martian day after landing. The shadow shows the outline of Phoenix's Thermal and Electrical Conductivity Probe, or TECP. The holes seen in the Martian surface were made by this instrument to measure the soil's conductivity. A fork-like probe inserted into the soil checks how well heat and electricity move through the soil from one prong to another.
The measurements completed Wednesday ran from the afternoon of Phoenix's 70th Martian day, or sol, to the morning of Sol 71.
The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
14. Measuring Contact Thermal Conductances at Low Temperatures
NASA Technical Reports Server (NTRS)
Salerno, Louis J.; Kittel, Peter; Brooks, Walter; Spivak, Alan L.; Marks, William G., Jr.
1987-01-01
Instrument measures thermal conductance of pressed contacts in liquid helium. Makes measurements automatically as function of force on pairs of brass samples having various surface finishes. Developed as part of effort to determine heat-transfer characteristics of bolted joints on cryogenically cooled focal planes in infrared equipment. Cylindrical chamber hangs from cover plate in bath of liquid helium. Inside chamber rocker arm applies controlled force to samples. Upper sample made slightly wider than lower one so two samples remain in complete contact even under slight lateral misalignment.
15. AC hot wire measurement of thermophysical properties of nanofluids with 3ω method
Turgut, A.; Sauter, C.; Chirtoc, M.; Henry, J. F.; Tavman, S.; Tavman, I.; Pelzl, J.
2008-01-01
We present a new application of a hot wire sensor for simultaneous and independent measurement of thermal conductivity k and diffusivity α of (nano)fluids, based on a hot wire thermal probe with ac excitation and 3 ω lock-in detection. The theoretical modeling of imaginary part of the signal yields the k value while the phase yields the α value. Due to modulated heat flow in cylindrical geometry with a radius comparable to the thermal diffusion length, the necessary sample quantity is kept very low, typically 25 μl. In the case of relative measurements, the resolution is 0.1% in k and 0.3% in α. Measurements of water-based Aerosil 200V nanofluids indicate that ultrasound treatment is more efficient than high pressure dispersion method in enhancing their thermal parameters.
16. System for absolute measurement of electrolytic conductivity in aqueous solutions based on van der Pauw's theory
Zhang, Bing; Lin, Zhen; Zhang, Xiao; Yu, Xiang; Wei, Jiali; Wang, Xiaoping
2014-05-01
Based on an innovative application of van der Pauw's theory, a system was developed for the absolute measurement of electrolytic conductivity in aqueous solutions. An electrolytic conductivity meter was designed that uses a four-electrode system with an axial-radial two-dimensional adjustment structure coupled to an ac voltage excitation source and signal collecting circuit. The measurement accuracy, resolution and repeatability of the measurement system were examined through a series of experiments. Moreover, the measurement system and a high-precision electrolytic conductivity meter were compared using some actual water samples.
17. Measurement of heat conduction through stacked screens
NASA Technical Reports Server (NTRS)
Lewis, M. A.; Kuriyama, T.; Kuriyama, F.; Radebaugh, R.
1998-01-01
This paper describes the experimental apparatus for the measurement of heat conduction through stacked screens as well as some experimental results taken with the apparatus. Screens are stacked in a fiberglass-epoxy cylinder, which is 24.4 mm in diameter and 55 mm in length. The cold end of the stacked screens is cooled by a Gifford-McMahon (GM) cryocooler at cryogenic temperature, and the hot end is maintained at room temperature. Heat conduction through the screens is determined from the temperature gradient in a calibrated heat flow sensor mounted between the cold end of the stacked screens and the GM cryocooler. The samples used for these experiments consisted of 400-mesh stainless steel screens, 400-mesh phosphor bronze screens, and two different porosities of 325-mesh stainless steel screens. The wire diameter of the 400-mesh stainless steel and phosphor bronze screens was 25.4 micrometers and the 325-mesh stainless steel screen wire diameters were 22.9 micrometers and 27.9 micrometers. Standard porosity values were used for the experimental data with additional porosity values used on selected experiments. The experimental results showed that the helium gas between each screen enhanced the heat conduction through the stacked screens by several orders of magnitude compared to that in vacuum. The conduction degradation factor is the ratio of actual heat conduction to the heat conduction where the regenerator material is assumed to be a solid rod of the same cross sectional area as the metal fraction of the screen. This factor was about 0.1 for the stainless steel and 0.022 for the phosphor bronze, and almost constant for the temperature range of 40 to 80 K at the cold end.
18. Harmonic analysis of AC magnetostriction measurements under non-sinusoidal excitation
SciTech Connect
Mogi, Hisashi; Yabumoto, Masao; Mizokami, Masato; Okazaki Yasuo
1996-09-01
A new system for analyzing ac magnetostriction of electrical steel sheets has been developed. This system has the following advantages: (a) AC magnetostriction waveforms can be precisely measured up to 4 kHz, and analyzed to harmonic components; (b) non-sinusoidal flux density can be excited to simulate the distorted waveform in an actual transformer core.
19. Thermal Conductivity Measurements on consolidated Soil Analogs
Seiferlin, K.; Heimberg, M.; Thomas, N.
2007-08-01
Heat transport in porous media such as soils and regolith is significantly reduced compared to the properties of compact samples of the same material. The bottle neck for solid state heat transport is the contact area between adjacent grains. For "dry" and unconsolidated materials the contact areas and thus the thermal conductivity are extremely small. Sintering and cementation are two processes that can increase the cross section of interstitial bonds signifcantly. On Mars, cementation can be caused by condensation of water or carbon dioxide ice from the vapor phase, or from salts and minerals that fall out from aqueous solutions. We produced several artificially cemented samples, using small glass beads of uniform size as soil analog. The cementation is achieved by initially molten wax that is mixed with the glass beads while liqiud. The wax freezes preferably at the contact points between grains, thus minimizing surface energy, and consolidates the samples. The thermal conductivity of these samples is then measured in vacuum. We present the results of these measurements and compare them with theoretical models. The observed range of thermal conductivity values can explain some, but not all of the variations in thermal intertia that can be seen in TES remote sensing data.
20. Transport properties of random and nonrandom substitutionally disordered alloys. I. Exact numerical calculation of the ac conductivity
Hwang, M.; Gonis, A.; Freeman, A. J.
1987-06-01
Results of exact computer simulations for the zero-temperature ac conductivity of one-dimensional substitutionally disordered alloys are reported. These results are obtained by (i) solving for the eigenvalues and eigenvectors of a Hamiltonian associated with a specific configuration of 500 atoms on a linear chain, (ii) evaluating the ac conductivity of this configuration by using the Kubo-Greenwood formula, and (iii) averaging the resulting conductivities over 20 to 50 different configurations (the number of configurations depends on the type of disorder). In all cases convergence (i.e., a stable result) was obtained and confirmed by another independent approach (the recursive method). For not too weak disorder (defined precisely in the text), these results exhibit a great deal of fine structure that includes high peaks and gaps where the conductivity vanishes. These features are reminiscent of, and are correlated with, the similar kind of behavior of the densities of states of one-dimensional substitutionally disordered alloys. Thus we find that the fine structure in the ac-conductivity spectra of one-dimensional systems provides a rigorous testing ground for judging the validity of analytic theories for calculating the transport properties of substitutionally disordered systems.
1. Quantitative Thermal Microscopy Measurement with Thermal Probe Driven by dc+ac Current
Bodzenta, Jerzy; Juszczyk, Justyna; Kaźmierczak-Bałata, Anna; Firek, Piotr; Fleming, Austin; Chirtoc, Mihai
2016-07-01
Quantitative thermal measurements with spatial resolution allowing the examination of objects of submicron dimensions are still a challenging task. The quantity of methods providing spatial resolution better than 100 nm is very limited. One of them is scanning thermal microscopy (SThM). This method is a variant of atomic force microscopy which uses a probe equipped with a temperature sensor near the apex. Depending on the sensor current, either the temperature or the thermal conductivity distribution at the sample surface can be measured. However, like all microscopy methods, the SThM gives only qualitative information. Quantitative measuring methods using SThM equipment are still under development. In this paper, a method based on simultaneous registration of the static and the dynamic electrical resistances of the probe driven by the sum of dc and ac currents, and examples of its applications are described. Special attention is paid to the investigation of thin films deposited on thick substrates. The influence of substrate thermal properties on the measured signal and its dependence on thin film thermal conductivity and film thickness are analyzed. It is shown that in the case where layer thicknesses are comparable or smaller than the probe-sample contact diameter, a correction procedure is required to obtain actual thermal conductivity of the layer. Experimental results obtained for thin SiO2 and BaTiO_{3 }layers with thicknesses in the range from 11 nm to 100 nm are correctly confirmed with this approach.
2. Signature of Topological Insulators in Conductance Measurements
Hong, Seokmin; Diep, Vinh; Datta, Supriyo
2012-02-01
Following the discovery of spin-polarized states at the surface of three-dimensional topological insulators (TI) like Bi2Te3 and Bi2Se3, there are intense interests in possible electrical measurements demonstrating unique signatures of these unusual states. A recent interesting proposal suggests that a signature of TI material should be a change in the conductance measured between a normal contact and a magnetic contact when the magnetization of the latter is reversed. However, the generalized Onsager relation suggests that no such change is expected in two-terminal setups and a multi-terminal set up is needed to observe the proposed effect. We present numerical results using a Non-Equilibrium Green Function (NEGF) based model capable of covering both ballistic and diffusive transport regimes seamlessly. Simple expressions based on a semi-classical picture describe some of the results quite well. Finally, we estimate the magnitude of signal expected in realistic samples that have recently been studied experimentally and have shown evidence of surface conduction.
3. Reflectometer distance measurement between parallel conductive plates
NASA Technical Reports Server (NTRS)
Hearn, Chase P.; Neece, Robert T.
1995-01-01
This report presents an analytic and experimental investigation of the measurement problem in which a reflectometer is used to determine the distance to a target that is a highly conductive surface parallel to the reflectometer antenna ground plane. These parallel surfaces constitute a waveguide (WG) which can contribute parasitic perturbations that seriously degrade the accuracy of the measurements. Two distinct parallel-plate-waveguide (PPWG) phenomena are described, and their effects on both frequency and time-domain reflectometers are considered. The time-domain processing approach was found to be superior to a representative frequency-domain phase-measurement approach because of less susceptibility to perturbations produced by edge reflections and immunity to phase capture. Experimental results are presented which show that a simple radiating system modification can suppress parallel-plate (PP) propagation. The addition of a thin layer of lossy mu-metal 'magnetic absorber' to the antenna ground plane allowed a measurement accuracy of 0.025 cm (0.01 in.) when a vector network analyzer (VNA) is used as a time-domain reflectometer.
4. The change in dielectric constant, AC conductivity and optical band gaps of polymer electrolyte film: Gamma irradiation
SciTech Connect
Raghu, S. Subramanya, K. Sharanappa, C. Mini, V. Archana, K. Sanjeev, Ganesh Devendrappa, H.
2014-04-24
The effects of gamma (γ) irradiation on dielectric and optical properties of polymer electrolyte film were investigated. The dielectric constant and ac conductivity increases with γ dose. Also optical band gap decreased from 4.23 to 3.78ev after irradiation. A large dependence of the polymer properties on the irradiation dose was noticed. This suggests that there is a possibility of improving polymer electrolyte properties on gamma irradiation.
5. Measuring Thermal Conductivity at LH2 Temperatures
NASA Technical Reports Server (NTRS)
Selvidge, Shawn; Watwood, Michael C.
2004-01-01
For many years, the National Institute of Standards and Technology (NIST) produced reference materials for materials testing. One such reference material was intended for use with a guarded hot plate apparatus designed to meet the requirements of ASTM C177-97, "Standard Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus." This apparatus can be used to test materials in various gaseous environments from atmospheric pressure to a vacuum. It allows the thermal transmission properties of insulating materials to be measured from just above ambient temperature down to temperatures below liquid hydrogen. However, NIST did not generate data below 77 K temperature for the reference material in question. This paper describes a test method used at NASA's Marshall Space Flight Center (MSFC) to optimize thermal conductivity measurements during the development of thermal protection systems. The test method extends the usability range of this reference material by generating data at temperatures lower than 77 K. Information provided by this test is discussed, as are the capabilities of the MSFC Hydrogen Test Facility, where advanced methods for materials testing are routinely developed and optimized in support of aerospace applications.
6. Assessing Conduct Disorder: A New Measurement Approach
PubMed Central
Reavy, Racheal; Stein, L. A. R.; Quina, Kathryn; Paiva, Andrea L.
2015-01-01
The Delinquent Activities Scale (DAS) was used to develop indicators of conduct disorder (CD) in terms of symptom severity and age of onset. Incarcerated adolescents (N = 190) aged 14 to 19 were asked about their delinquent behaviors, including age the behavior was first performed, as well as substance use and parental and peer influences. Assessments were performed for the 12 months prior to incarceration and at 3-month postrelease follow-up. Evidence supports the utility of the DAS as a measure of CD diagnosis, including concurrent incremental validity. Furthermore, CD severity (symptom count) was significantly associated with two peer factors: friend substance use and friend prior arrests, with medium to large effect sizes (ESs). Earlier age of CD onset was associated with earlier marijuana use. This study finds that the DAS is a useful instrument in that it is easy to apply and has adequate psychometrics. PMID:24241820
7. AC conductivity and electrochemical studies of PVA/PEG based polymer blend electrolyte films
Polu, Anji Reddy; Kumar, Ranveer; Dehariya, Harsha
2012-06-01
Polymer blend electrolyte films based on Polyvinyl alcohol(PVA)/Poly(ethylene glycol)(PEG) and magnesium nitrate (Mg(NO3)2) were prepared by solution casting technique. Conductivity in the temperature range 303-373 K and transference number measurements have been employed to investigate the charge transport in this polymer blend electrolyte system. The highest conductivity is found to be 9.63 × 10-5 S/cm at 30°C for sample with 30 weight percent of Mg(NO3)2 in PVA/PEG blend matrix. Transport number data shows that the charge transport in this polymer electrolyte system is predominantly due to ions. Using this electrolyte, an electrochemical cell with configuration Mg/(PVA+PEG+Mg(NO3)2)/(I2+C+electrolyte) was fabricated and its discharge characteristics profile has been studied.
8. AC loss measurements in HTS coil assemblies with hybrid coil structures
Jiang, Zhenan; Long, Nicholas J.; Staines, Mike; Badcock, Rodney A.; Bumby, Chris W.; Buckley, Robert G.; Amemiya, Naoyuki
2016-09-01
Both AC loss and wire cost in coil windings are critical factors for high temperature superconductor (HTS) AC machinery applications. We present AC loss measurement results in three HTS coil assemblies at 77 K and 65 K which have a hybrid coil structure comprising one central winding (CW) and two end windings (EWs) wound with ReBCO and BSCCO wires with different self-field I c values at 77 K. All AC loss results in the coil assemblies are hysteretic and the normalized AC losses in the coil assemblies at different temperatures can be scaled with the I c value of the coil assemblies. The normalised results show that AC loss in a coil assembly with BSCCO CW can be reduced by using EWs wound with high I c ReBCO wires, whilst further AC loss reduction can be achieved by replacing the BSCCO CW with ReBCO CW. The results imply that a flexible hybrid coil structure is possible which considers both AC loss and wire cost in coil assemblies.
9. Sensitive bridge circuit measures conductance of low-conductivity electrolyte solutions
NASA Technical Reports Server (NTRS)
Schmidt, K.
1967-01-01
Compact bridge circuit measures sensitive and accurate conductance of low-conductivity electrolyte solutions. The bridge utilizes a phase sensitive detector to obtain a linear deflection of the null indicator relative to the measured conductance.
10. Measurements and calculations of transport AC loss in second generation high temperature superconducting pancake coils
Yuan, Weijia; Coombs, T. A.; Kim, Jae-Ho; Han Kim, Chul; Kvitkovic, Jozef; Pamidi, Sastry
2011-12-01
Theoretical and experimental AC loss data on a superconducting pancake coil wound using second generation (2 G) conductors are presented. An anisotropic critical state model is used to calculate critical current and the AC losses of a superconducting pancake coil. In the coil there are two regions, the critical state region and the subcritical region. The model assumes that in the subcritical region the flux lines are parallel to the tape wide face. AC losses of the superconducting pancake coil are calculated using this model. Both calorimetric and electrical techniques were used to measure AC losses in the coil. The calorimetric method is based on measuring the boil-off rate of liquid nitrogen. The electric method used a compensation circuit to eliminate the inductive component to measure the loss voltage of the coil. The experimental results are consistent with the theoretical calculations thus validating the anisotropic critical state model for loss estimations in the superconducting pancake coil.
11. Construction of Tunnel Diode Oscillator for AC Impedance Measurement
Shin, J. H.; Kim, E.
2014-03-01
We construct a tunnel diode oscillator (TDO) to study electromagnetic response of a superconducting thin film. Highly sensitive tunnel diode oscillators allow us to detect extremely small changes in electromagnetic properties such as dielectric constant, ac magnetic susceptibility and magnetoresistance. A tunnel diode oscillator is a self-resonant oscillator of which resonance frequency is primarily determined by capacitance and inductance of a resonator. Amplitude of the signal depends on the quality factor of the resonator. The change in the impedance of the sample electromagnetic coupled to one of inductors in the resonator alters impedance of the inductor, and leads to the shift in the resonance frequency and the change of the amplitude.
12. Measuring thermal diffusivity of mechanical and optical grades of polycrystalline diamond using an AC laser calorimetry method
SciTech Connect
Rule, Toby D.; Cai, Wei; Wang, Hsin
2013-01-01
Because of its extremely high thermal conductivity, measuring the thermal conductivity or diffusivity of optical-grade diamond can be challenging. Various methods have been used to measure the thermal conductivity of thick diamond films. For the purposes of commercial quality control, the AC laser calorimetry method is appealing because it enables fairly rapid and convenient sample preparation and measurement. In this paper, the method is used to measure the thermal diffusivity of optical diamond. It is found that sample dimensions and measurement parameters are critical, and data analysis must be performed with great care. The results suggest that the method as it is applied to optical-grade diamond could be enhanced by a more powerful laser, higher frequency beam modulation, and post-processing based on 2D thermal simulation.
13. Dielectric behavior and ac conductivity study of NiO /Al2O3 nanocomposites in humid atmosphere
2006-11-01
Humidity sensing characteristics of NiO /Al2O3 nanocomposites, prepared by sol-gel method, are studied by impedance spectroscopy. Modeling of the obtained impedance spectra with an appropriate equivalent circuit enables us to separate the electrical responses of the tightly bound chemisorbed water molecules on the grain surfaces and the loosely associated physisorbed water layers. Dependence of the dielectric properties and ac conductivity of the nanocomposites on relative humidity (RH) were studied as a function of the frequency of the applied ac signal in the frequency range of 0.1-105Hz. The electrical relaxation behavior of the investigated materials is presented in the conductivity formalism, where the conductivity spectra at different RHs are analyzed by the Almond-West formalism [D. P. Almond et al., Solid State Ionics 8, 159 (1983)]. The dc conductivity and the hopping rate of charge carriers, determined from this analysis, show similar dependences on RH, indicating that the concentration of mobile ions is independent of RH and is primarily determined by the chemisorption process of water molecules. Finally, the results are discussed in view of a percolation-type conduction mechanism, where mobile ions are provided by the chemisorbed water molecules and the percolation network is formed by the physisorbed water layers.
14. Calculation of the ac to dc resistance ratio of conductive nonmagnetic straight conductors by applying FEM simulations
Riba, Jordi-Roger
2015-09-01
This paper analyzes the skin and proximity effects in different conductive nonmagnetic straight conductor configurations subjected to applied alternating currents and voltages. These effects have important consequences, including a rise of the ac resistance, which in turn increases power loss, thus limiting the rating for the conductor. Alternating current (ac) resistance is important in power conductors and bus bars for line frequency applications, as well as in smaller conductors for high frequency applications. Despite the importance of this topic, it is not usually analyzed in detail in undergraduate and even in graduate studies. To address this, this paper compares the results provided by available exact formulas for simple geometries with those obtained by means of two-dimensional finite element method (FEM) simulations and experimental results. The paper also shows that FEM results are very accurate and more general than those provided by the formulas, since FEM models can be applied in a wide range of electrical frequencies and configurations.
15. 21 CFR 882.1550 - Nerve conduction velocity measurement device.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Nerve conduction velocity measurement device. 882... conduction velocity measurement device. (a) Identification. A nerve conduction velocity measurement device is a device which measures nerve conduction time by applying a stimulus, usually to a...
16. 21 CFR 882.1550 - Nerve conduction velocity measurement device.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Nerve conduction velocity measurement device. 882... conduction velocity measurement device. (a) Identification. A nerve conduction velocity measurement device is a device which measures nerve conduction time by applying a stimulus, usually to a...
17. 21 CFR 882.1550 - Nerve conduction velocity measurement device.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Nerve conduction velocity measurement device. 882... conduction velocity measurement device. (a) Identification. A nerve conduction velocity measurement device is a device which measures nerve conduction time by applying a stimulus, usually to a...
18. 21 CFR 882.1550 - Nerve conduction velocity measurement device.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Nerve conduction velocity measurement device. 882... conduction velocity measurement device. (a) Identification. A nerve conduction velocity measurement device is a device which measures nerve conduction time by applying a stimulus, usually to a...
19. 21 CFR 882.1550 - Nerve conduction velocity measurement device.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Nerve conduction velocity measurement device. 882... conduction velocity measurement device. (a) Identification. A nerve conduction velocity measurement device is a device which measures nerve conduction time by applying a stimulus, usually to a...
20. Development of the Exams Data Analysis Spreadsheet as a Tool to Help Instructors Conduct Customizable Analyses of Student ACS Exam Data
ERIC Educational Resources Information Center
Brandriet, Alexandra; Holme, Thomas
2015-01-01
The American Chemical Society Examinations Institute (ACS-EI) has recently developed the Exams Data Analysis Spread (EDAS) as a tool to help instructors conduct customizable analyses of their student data from ACS exams. The EDAS calculations allow instructors to analyze their students' performances both at the total score and individual item…
1. AC loss measurement of superconducting dipole magnets by the calorimetric method
SciTech Connect
Morita, Y.; Hara, K.; Higashi, N.; Kabe, A.
1996-12-31
AC losses of superconducting dipole magnets were measured by the calorimetric method. The magnets were model dipole magnets designed for the SSC. These were fabricated at KEK with 50-mm aperture and 1.3-m overall length. The magnet was set in a helium cryostat and cooled down to 1.8 K with 130 L of pressurized superfluid helium. Heat dissipated by the magnet during ramp cycles was measured by temperature rise of the superfluid helium. Heat leakage into the helium cryostat was 1.6 W and was subtracted from the measured heat to obtain AC loss of the magnet. An electrical measurement was carried out for calibration. Results of the two methods agreed within the experimental accuracy. The authors present the helium cryostat and measurement system in detail, and discuss the results of AC loss measurement.
2. Second VAMAS a.c. loss measurement intercomparison: a.c. magnetization measurement of hysteresis and coupling losses in NbTi multifilamentary strands
Schmidt, C.; Itoh, K.; Wada, H.
The article summarizes results of part of the second VAMAS a.c. loss measurement intercomparison. This program was carried out at 17 participating laboratories on two sets of multifilamentary NbTi strands (Set No. 1: copper matrix, fil. diam. between 0.5 and 12 μm; Set No. 2: cupronickel matrix, fil. diam. between 0.4 and 1.2 μm). The results reported here were measured by means of a.c. magnetization methods and separated into hysteresis and coupling losses. One laboratory used a calorimetric method. The data scatter in measured hysteresis losses among the participating laboratories was reasonably small for different measuring methods adopted and experimental arrangements used. On the other hand, the data scatter in coupling losses was large, mainly because in most laboratories a.c. losses were measured only at low frequencies (below 1 Hz), where the separation of coupling losses from total losses tends to be inaccurate. The comparison of measured hysteresis losses with the critical state model showed a large disagreement, which is assumed to be due to proximity effect coupling between filaments. 1997 Elsevier Science Limited
3. The Wechsler ACS Social Perception Subtest: A Preliminary Comparison with Other Measures of Social Cognition
ERIC Educational Resources Information Center
Kandalaft, Michelle R.; Didehbani, Nyaz; Cullum, C. Munro; Krawczyk, Daniel C.; Allen, Tandra T.; Tamminga, Carol A.; Chapman, Sandra B.
2012-01-01
Relative to other cognitive areas, there are few clinical measures currently available to assess social perception. A new standardized measure, the Wechsler Advanced Clinical Solutions (ACS) Social Perception subtest, addresses some limitations of existing measures; however, little is known about this new test. The first goal of this investigation…
4. Dielectric properties and study of AC electrical conduction mechanisms by non-overlapping small polaron tunneling model in Bis(4-acetylanilinium) tetrachlorocuprate(II) compound
Abkari, A.; Chaabane, I.; Guidara, K.
2016-09-01
In the present work, the synthesis and characterization of the Bis(4-acetylanilinium) tetrachlorocuprate(II) compound are presented. The structure of this compound is analyzed by X-ray diffraction which confirms the formation of single phase and is in good agreement the literature. Indeed, the Thermo gravimetric Analysis (TGA) shows that the decomposition of the compound is observed in the range of 420-520 K. However, the differential thermal analysis (DTA) indicates the presence of a phase transition at T=363 k. Furthermore, the dielectric properties and AC conductivity were studied over a temperature range (338-413 K) and frequency range (200 Hz-5 MHz) using complex impedance spectroscopy. Dielectric measurements confirmed such thermal analyses by exhibiting the presence of an anomaly in the temperature range of 358-373 K. The complex impedance plots are analyzed by an electrical equivalent circuit consisting of resistance, constant phase element (CPE) and capacitance. The activation energy values of two distinct regions are obtained from log σT vs 1000/T plot and are found to be E=1.27 eV (T<363 K) and E=1.09 eV (363 Kac conductivity, σac, has been analyzed by Jonscher's universal power law σ(ω)=σdc+Aωs. The value of s is to be temperature-dependent, which has a tendency to increase with temperature and the non-overlapping small polaron tunneling (NSPT) model is the most applicable conduction mechanism in the title compound. Complex impedance spectra of [C8H10NO]2CuCl4 at different temperatures.
5. Crystal structure, NMR study, dielectric relaxation and AC conductivity of a new compound [Cd3(SCN)2Br6(C2H9N2)2]n
Saidi, K.; Kamoun, S.; Ayedi, H. Ferid; Arous, M.
2013-11-01
The crystal structure, the 13C NMR spectroscopy and the complex impedance have been carried out on [Cd3(SCN)2Br6(C2H9N2)2]n. Crystal structure shows a 2D polymeric network built up of two crystallographically independent cadmium atoms with two different octahedral coordinations. This compound exhibits a phase transition at (T=355±2 K) which has been characterized by differential scanning calorimetry (DSC), X-rays powder diffraction, AC conductivity and dielectric measurements. Examination of 13C CP/MAS line shapes shows indirect spin-spin coupling (14N and 13C) with a dipolar coupling constant of 1339 Hz. The AC conductivity of this compound has been carried out in the temperature range 325-376 K and the frequency range from 10-2 Hz to 10 MHz. The impedance data were well fitted to two equivalent electrical circuits. The results of the modulus study reveal the presence of two distinct relaxation processes. One, at low frequency side, is thermally activated due to the ionic conduction of the crystal and the other, at higher frequency side, gradually disappears when temperature reaches 355 K which is attributed to the localized dipoles in the crystal. Moreover, the temperature dependence of DC-conductivity in both phases follows the Arrhenius law and the frequency dependence of σ(ω,T) follows Jonscher's universal law. The near values of activation energies obtained from the conductivity data and impedance confirm that the transport is through the ion hopping mechanism.
6. Development of Low-Frequency AC Voltage Measurement System Using Single-Junction Thermal Converter
Amagai, Yasutaka; Nakamura, Yasuhiro
Accurate measurement of low-frequency AC voltage using a digital multimeter at frequencies of 4-200Hz is a challenge in the mechanical engineering industry. At the National Metrology Institute of Japan, we developed a low-frequency AC voltage measurement system for calibrating digital multimeters operating at frequencies down to 1 Hz. The system uses a single-junction thermal converter and employs a theoretical model and a three-parameter sine wave fitting algorithm based on the least-square (LS) method. We calibrated the AC voltage down to 1Hz using our measurement system and reduced the measurement time compared with that using thin-film thermal converters. Our measurement results are verified by comparison with those of a digital sampling method using a high-resolution analog-to-digital converter; our data are in agreement to within a few parts in 105. Our proposed method enables us to measure AC voltage with an uncertainty of 25 μV/V (k = 1) at frequencies down to 4 Hz and a voltage of 10 V.
7. Measurements of the Seebeck coefficient of thermoelectric materials by an ac method
SciTech Connect
Goto, T.; Li, J.H.; Hirai, T.; Maeda, Y.; Kato, R.; Maesono, A.
1997-03-01
An ac method for measurement of the Seebeck coefficient was developed. Specimens were heated periodically at frequencies in the range 0.2--10 Hz using a semiconductor laser. The small temperature increase and the resultant thermoelectric power were measured with a Pt-Pt 13% Rh thermocouple (25 {micro}m in diameter) through a lock-in amplifier. The Seebeck coefficient of a Pt{sub 90}Rh{sub 10} foil measured by the ac method was in agreement with that obtained from the standard table. The optimum frequency and specimen thickness for the ac method were 0.2 Hz and 0.1--0.2 mm, respectively. The Seebeck coefficients of silicon single crystal and several thermoelectric semiconductors (Si{sub 80}Ge{sub 20}, PbTc, FeSi{sub 2}, SiB{sub 14}) measured by the ac method agreed with those measured by a conventional dc method in the temperature range between room temperature and 1200 K. The time needed for each measurement was less than a few tens of minutes, significantly shorter than that for a conventional dc method.
8. AC impedance analysis of ionic and electronic conductivities in electrode mixture layers for an all-solid-state lithium-ion battery
Siroma, Zyun; Sato, Tomohiro; Takeuchi, Tomonari; Nagai, Ryo; Ota, Akira; Ioroi, Tsutomu
2016-06-01
The ionic and electronic effective conductivities of an electrode mixture layers for all-solid-state lithium-ion batteries containing Li2Ssbnd P2S5 as a solid electrolyte were investigated by AC impedance measurements and analysis using a transmission-line model (TLM). Samples containing graphite (graphite electrodes) or LiNi0.5Co0.2Mn0.3O2 (NCM electrodes) as the active material were measured under a "substrate | sample | bulk electrolyte | sample | substrate" configuration (ion-electron connection) and a "substrate | sample | substrate" configuration (electron-electron connection). Theoretically, if the electronic resistance is negligibly small, which is the case with our graphite electrodes, measurement with the ion-electron connection should be effective for evaluating ionic conductivity. However, if the electronic resistance is comparable to the ionic resistance, which is the case with our NCM electrodes, the results with the ion-electron connection may contain some inherent inaccuracy. In this report, we theoretically and practically demonstrate the advantage of analyzing the results with the electron-electron connection, which gives both the ionic and electronic conductivities. The similarity of the behavior of ionic conductivity with the graphite and NCM electrodes confirms the reliability of this analysis.
9. AC Conduction and Time-Temperature Superposition Scaling in a Reduced Graphene Oxide-Zinc Sulfide Nanocomposite.
PubMed
Chakraborty, Koushik; Das, Poulomi; Chakrabarty, Sankalpita; Pal, Tanusri; Ghosh, Surajit
2016-05-18
We report, herein, the results of an in depth study and concomitant analysis of the AC conduction [σ'(ω): f=20 Hz to 2 MHz] mechanism in a reduced graphene oxide-zinc sulfide (RGO-ZnS) composite. The magnitude of the real part of the complex impedance decreases with increase in both frequency and temperature, whereas the imaginary part shows an asymptotic maximum that shifts to higher frequencies with increasing temperature. On the other hand, the conductivity isotherm reveals a frequency-independent conductivity at lower frequencies subsequent to a dispersive conductivity at higher frequencies, which follows a power law [σ'(ω)∝ω(s) ] within a temperature range of 297 to 393 K. Temperature-independent frequency exponent 's' indicates the occurrence of phonon-assisted simple quantum tunnelling of electrons between the defects present in RGO. Finally, this sample follows the "time-temperature superposition principle", as confirmed from the universal scaling of conductivity isotherms. These outcomes not only pave the way for increasing our elemental understanding of the transport mechanism in the RGO system, but will also motivate the investigation of the transport mechanism in other order-disorder systems. PMID:26864678
10. Note: Development of a microfabricated sensor to measure thermal conductivity of picoliter scale liquid samples
Park, Byoung Kyoo; Yi, Namwoo; Park, Jaesung; Kim, Dongsik
2012-10-01
This paper presents a thermal analysis device, which can measure thermal conductivity of picoliter scale liquid sample. We employ the three omega method with a microfabricated AC thermal sensor with nanometer width heater. The liquid sample is confined by a micro-well structure fabricated on the sensor surface. The performance of the instrument was verified by measuring the thermal conductivity of 27-picoliter samples of de-ionized (DI) water, ethanol, methanol, and DI water-ethanol mixtures with accuracies better than 3%. Furthermore, another analytical scheme allows real-time thermal conductivity measurement with 5% accuracy. To the best of our knowledge, this technique requires the smallest volume of sample to measure thermal property ever.
11. Fiber - Optic Devices as Temperature Sensors for Temperature Measurements in AC Magnetic Fields
Rablau, Corneliu; Lafrance, Joseph; Sala, Anca
2007-10-01
We report on the investigation of several fiber-optic devices as potential sensors for temperature measurements in AC magnetic fields. Common temperature sensors, such as thermocouples, thermistors or diodes, will create random and/or systematic errors when placed in a magnetic field. A DC magnetic field is susceptible to create a systematic offset to the measurement, while in an AC magnetic field of variable frequency random errors which cannot be corrected for can also be introduced. Fiber-Bragg-gratings and thin film filters have an inherent temperature dependence. Detrimental for their primary applications, the same dependence allows one to use such devices as temperature sensors. In an AC magnetic field, they present the advantage of being immune to electromagnetic interference. Moreover, for fiber-Bragg-gratings, the shape factor and small mass of the bare-fiber device make it convenient for temperature measurements on small samples. We studied several thin-film filters and fiber-Bragg-gratings and compared their temperature measurement capabilities in AC magnetic fields of 0 to 150 Gauss, 0 to 20 KHz to the results provided by off-the-shelf thermocouples and thermistor-based temperature measurement systems.
12. Second VAMAS a.c. loss measurement intercomparison: magnetization measurement of low-frequency (hysteretic) a.c. loss in NbTi multifilamentary strands
Collings, E. W.; Sumption, M. D.; Itoh, K.; Wada, H.; Tachikawa, K.
The results of the 2 nd VAMAS measurement intercomparison program on low-frequency (hysteretic) a.c. loss are presented and discussed. Two sets of multifilamentary NbTi strands (Set No. 1: copper matrix, fil. diams 0.5, 1, 3, and 12 μm; Set No. 2: cupronickel matrix, fil. diams 0.4, 0.5, and 1 μm) were subjected to interlaboratory testing. In an initial series of tests, samples in various forms (e.g. wire bundles, coils) were measured mostly by vibrating-sample- and SQUID magnetometry. Considerable scatter was noted especially in the small-filament-diameter a.c.-loss data. In a study of measurement accuracy, a supplementary series of tests compared the results of VSM measurement of a given pair of copper-matrix samples. In the light of all the results, factors contributing to a.c. loss error are discussed and recommendations are made concerning the specification of future a.c.-loss measurement intercomparisons.
13. Modelling and measurement of ac loss in BSCCO/Ag-tape windings
Oomen, M. P.; Nanke, R.; Leghissa, M.
2003-03-01
High-temperature superconducting (HTS) transformers promise decreased weight and volume and higher efficiency. A 1 MVA HTS railway transformer was built and tested at Siemens AG. This paper deals with the prediction of ac loss in the BSCCO/Ag-tape windings. In a railway transformer the tape carries ac current in alternating field, the temperature differs from 77 K, tapes are stacked or cabled and overcurrents and higher harmonics occur. In ac-loss literature these issues are treated separately, if at all. We have developed a model that predicts the ac loss in sets of BSCCO/Ag-tape coils, and deals with the above-mentioned issues. The effect of higher harmonics on the loss in HTS tapes is considered for the first time. The paper gives a complete overview of the model equations and required input parameters. The model is validated over a wide range of the input parameters, using the measured critical current and ac loss of single tapes, single coils and sets of coils in the 1 MVA transformer. An accuracy of around 25% is achieved in all relevant cases. Presently the model is developed further, in order to describe other HTS materials and other types of applications.
14. New ac microammeter for leakage current measurement of biomedical equipment
Branca, F. P.; Del Prete, Z.; Marinozzi, F.
1993-11-01
A new inexpensive current probe for on-line leakage current measurement of biomedical devices in hospital environment is described. The prototype is designed to detect and measure leakage currents on the ground wire of the device's power cord so that its integrity can be monitored in real time. Realized with a sensing coil specially matched to a low-noise op amp, this probe adds only negligible impedance on the monitored ground lines. From this preliminary study about the device's metrological performances, a sensitivity of 10 nArms for a current range 1-500 μArms has emerged, together with a mean linearity error of 0.03% and a frequency response flat within 1% of gain from 50 to 2000 Hz.
15. Monitoring colloidal stability of polymer-coated magnetic nanoparticles using AC susceptibility measurements.
PubMed
Herrera, Adriana P; Barrera, Carola; Zayas, Yashira; Rinaldi, Carlos
2010-02-15
The application of the response of magnetic nanoparticles to oscillating magnetic fields to probe transitions in colloidal state and structure of polymer-coated nanoparticles is demonstrated. Cobalt ferrite nanoparticles with narrow size distribution were prepared and shown to respond to oscillating magnetic fields through a Brownian relaxation mechanism, which is dependent on the mechanical coupling between the particle dipoles and the surrounding matrix. These nanoparticles were coated with covalently-attached poly(N-isopropylacrylamide) (pNIPAM) or poly(N-isopropylmethacrylamide) (pNIPMAM) through free radical polymerization. The temperature induced transitions of colloidal suspensions of these nanoparticles were studied through a combination of differential scanning calorimetry (DSC), dynamic light scattering (DLS), and AC susceptibility measurements. In the pNIPAM coated nanoparticles excellent agreement was found for a transition temperature of approximately 30 degrees C by all three methods, although the AC susceptibility measurements indicated aggregation which was not evident from the DLS results. Small-angle neutron scattering (SANS) results obtained for pNIPAM coated nanoparticles confirmed that aggregation indeed occurs above the lower critical transition temperature of pNIPAM. For the pNIPMAM coated nanoparticles DLS and AC susceptibility measurements indicated aggregation at a temperature of approximately 33-35 degrees C, much lower than the transition temperature peak at 40 degrees C observed by DSC. However, the transition observed by DSC is very broad, hence it is possible that aggregation begins to occur at temperatures lower than the peak, as indicated by the AC susceptibility and DLS results. These experiments and observations demonstrate the possibility of using AC susceptibility measurements to probe transitions in colloidal suspensions induced by external stimuli. Because magnetic measurements do not require optical transparency, these
16. Calorimetric AC loss measurement of MgB2 superconducting tape in an alternating transport current and direct magnetic field
See, K. W.; Xu, X.; Horvat, J.; Cook, C. D.; Dou, S. X.
2012-11-01
Applications of MgB2 superconductors in electrical engineering have been widely reported, and various studies have been made to define their alternating current (AC) losses. However, studies on the transport losses with an applied transverse DC magnetic field have not been conducted, even though this is one of the favored conditions in applications of practical MgB2 tapes. Methods and techniques used to characterize and measure these losses have so far been grouped into ‘electrical’ and ‘calorimetric’ approaches with external conditions set to resemble the application conditions. In this paper, we present a new approach to mounting the sample and employ the calorimetric method to accurately determine the losses in the concurrent application of AC transport current and DC magnetic fields that are likely to be experienced in practical devices such as generators and motors. This technique provides great simplification compared to the pickup coil and lock-in amplifier methods and is applied to a long length (˜10 cm) superconducting tape. The AC loss data at 20 and 30 K will be presented in an applied transport current of 50 Hz under external DC magnetic fields. The results are found to be higher than the theoretical predictions because of the metallic fraction of the tape that contributes quite significantly to the total losses. The data, however, will allow minimization of losses in practical MgB2 coils and will be used in the verification of numerical coil models.
17. Non-Contact Electrical Conductivity Measurement Technique for Molten Metals
NASA Technical Reports Server (NTRS)
Rhim, W. K.; Ishikawa, T.
1998-01-01
A non-contact technique of measuring the electrical conductivity (or resistivity) of conducting liquids while they are levitated by the high temperature electrostatic levitator in a high vacuum is reported.
18. Determination of the Si-conducting polymer interfacial properties using A-C impedance techniques
NASA Technical Reports Server (NTRS)
Nagasubramanian, G.; Di Stefano, Salvador; Moacanin, Jovan
1985-01-01
A study was made of the interfacial properties of poly(pyrrole) (PP) deposited electrochemically onto single crystal p-Si surfaces. The interfacial properties are dependent upon the counterions. The formation of 'quasi-ohmic' and 'nonohmic' contacts, respectively, of PP(ClO4) and PP films doped with other counterions (BF4 and para-toluene sulfonate) with p-Si, are explained in terms of the conductivity of these films and the flat band potential, V(fb), of PP relative to that of p-Si. The PP film seems to passivate or block intrinsic surface states present on the p-Si surface. The differences in the impedance behavior of para-toluene sulfonate doped and ClO4 doped PP are compared.
19. Thermal-Conductivity Measurement of Thermoelectric Materials Using 3{{\\upomega }} Method
Hahtela, O.; Ruoho, M.; Mykkänen, E.; Ojasalo, K.; Nissilä, J.; Manninen, A.; Heinonen, M.
2015-12-01
In this work, a measurement system for high-temperature thermal-conductivity measurements has been designed, constructed, and characterized. The system is based on the 3{\\upomega } method which is an ac technique suitable for both bulk and thin-film samples. The thermal-conductivity measurements were performed in a horizontal three-zone tube furnace whose sample space can be evacuated to vacuum or alternatively a protective argon gas environment can be applied to prevent undesired oxidation and contamination of the sample material. The system was tested with several dielectric, semiconductor, and metal bulk samples from room temperature up to 725 K. The test materials were chosen so that the thermal-conductivity values covered a wide range from 0.37 W\\cdot m^{-1}\\cdot K^{-1} to 150 {} \\cdot m^{-1}\\cdot K^{-1}. An uncertainty analysis for the thermal-conductivity measurements was carried out. The measurement accuracy is mainly limited by the determination of the third harmonic of the voltage over the resistive metal heater strip that is used for heating the sample. A typical relative measurement uncertainty in the thermal-conductivity measurements was between 5 % and 8 % (k=2). An extension of the 3{\\upomega } method was also implemented in which the metal heater strip is first deposited on a transferable Kapton foil. Utilizing such a prefabricated sensor allows for faster measurements of the samples as there is no need to deposit a heater strip on each new sample.
20. Studies of structural, optical, dielectric relaxation and ac conductivity of different alkylbenzenesulfonic acids doped polypyrrole nanofibers
Hazarika, J.; Kumar, A.
2016-01-01
Polypyrrole (PPy) nanofibers doped with alkylbenzenesulfonic acids (ABSA) have been synthesized using interfacial polymerization method. HRTEM studies confirm the formation of PPy nanofibers with average diameter ranging from 13 nm to 25 nm. Broad X-ray diffraction peak in 2 θ range 20-23.46° reveals amorphous structure of PPy nanofibers. The ordering or crystallinity of polymer chains increases, while their interplanar spacing (d) and interchain separation (R) decreases for short alkyl chain ABSA doped PPy nanofibers. FTIR studies reveal that short alkyl chain ABSA doped PPy nanofibers show higher value of "effective conjugation length". PPy nanofibers doped with short alkyl chain ABSA dopant exhibit smaller optical band gap. TGA studies show enhanced thermal stability of short alkyl chain ABSA doped PPy nanofibers. Decrease in dielectric permittivity ε ‧ (ω) with increasing frequency suggests presence of electrode polarization effects. Linear decrease in dielectric loss ε ″ (ω) with increasing frequency suggests dominant effect of dc conductivity process. Low value of non-exponential exponent β (<1) reveals non-Debye relaxation of charge carriers. Scaling of imaginary modulus (M ″) reveals that the charge carriers follow the same relaxation mechanism. Moreover, the charge carriers in PPy nanofibers follow the correlated barrier hopping (CBH) transport mechanism.
1. Measurement of solar cell ac parameters using the time domain technique
Deshmukh, M. P.; Kumar, R. Anil; Nagaraju, J.
2004-08-01
The instrumentation to measure solar cell ac parameters [cell capacitance (CP) and cell resistance (RP)] using the time domain technique is developed. The cell capacitance (CP) and series resistance (r) are calculated using open circuit voltage decay (OCVD) technique. It is calibrated with the help of an electrical network with passive components similar to ac equivalent circuit of a solar cell consisting of precision resistors and capacitors. The maximum error observed in the measurement of resistor and capacitor value is ±3.5%. The cell resistance (RP) is calculated from I-V characteristics of solar cell. The data obtained in time domain technique is compared with the impedance spectroscopy technique data measured on same solar cell and it is found that the deviation in cell capacitance and resistance are within ±8%.
2. Effective method to measure back emfs and their harmonics of permanent magnet ac motors
Jiang, Q.; Bi, C.; Lin, S.
2006-04-01
As the HDD spindle motors become smaller and smaller, the back electromotive forces (emfs) measurement faces the new challenges due to their low inertias and small sizes. This article proposes a novel method to measure the back emfs and their harmonic components of PM ac motors only through a freewheeling procedure. To eliminate the influence of the freewheeling deceleration, the phase flux linkages are employed to obtain the back emf amplitudes and phases of the fundamental and harmonic components by using finite Fourier series analysis. The proposed method makes the freewheeling measurement of the back emfs and their harmonics accurate and fast. It is especially useful for the low inertia PM ac motors, such as spindle motors for small form factor HDDs.
3. Measurement of the thermal contact conductance and thermal conductivity of anodized aluminum coatings
SciTech Connect
Peterson, G.P.; Fletcher, L.S. )
1990-08-01
An experimental investigation was conducted to determine the thermal contact conductance and effective thermal conductivity of anodized coatings. One chemically polished Aluminum 6061-T6 test specimen and seven specimens with anodized coatings varying in thickness from 60.9 {mu}m to 163.8 {mu}m were tested while in contact with a single unanodized aluminum surface. Measurements of the overall joint conductance, composed of the thermal contact conductance between the anodized coating and the bare aluminum surface and the bulk conductance of the coating material, indicated that the overall joint conductance decreased with increasing thickness of the anodized coating and increased with increasing interfacial load. Using the experimental data, a dimensionless expression was developed that related the overall joint conductance to the coating thickness, the surface roughness, the interfacial pressure, and the properties of the aluminum substrate. By subtracting the thermal contact conductance from the measured overall joint conductance, estimations of the effective thermal conductivity of the anodized coating as a function of pressure were obtained for each of the seven anodized specimens. At an extrapolated pressure of zero, the effective thermal conductivity was found to be approximately 0.02 W/m-K. In addition to this extrapolated value, a single expression for predicting the effective thermal conductivity as a function of both the interface pressure and the anodized coating thickness was developed and shown to be within {plus minus}5 percent of the experimental data over a pressure range of 0 to 14 MPa.
4. AC magnetic measurements of the ALS Booster Dipole Engineering Model Magnet
SciTech Connect
Green, M.I.; Keller, R.; Nelson, D.H.; Hoyer, E.
1989-03-01
10 Hz sine wave and 2 Hz sawtooth AC magnetic measurements of he curved ALS Booster Dipole Engineering Model Magnet have been accomplished. Long curved coils were utilized to measure the integral transfer function and uniformity. Point coils and a Hall Probe were used to measure magnetic induction and its uniformity. The data were logged and processed by a Tektronix 11401 digital oscilloscope. The dependence of the effective length on the field was determined from the ratio of the integral coil signals to the point coil signals. Quadrupole and sextupole harmonics were derived from the point and integral uniformity measurements. 5 refs., 4 figs., 2 tabs.
5. Direct Measurement of Ab and Ac at the Z0 Pole Using a Lepton Tag
Abe, Kenji; Abe, Koya; Abe, T.; Adam, I.; Akagi, T.; Allen, N. J.; Arodzero, A.; Ash, W. W.; Aston, D.; Baird, K. G.; Baltay, C.; Band, H. R.; Barakat, M. B.; Bardon, O.; Barklow, T. L.; Bashindzhagyan, G. L.; Bauer, J. M.; Bellodi, G.; Ben-David, R.; Benvenuti, A. C.; Bilei, G. M.; Bisello, D.; Blaylock, G.; Bogart, J. R.; Bolen, B.; Bower, G. R.; Brau, J. E.; Breidenbach, M.; Bugg, W. M.; Burke, D.; Burnett, T. H.; Burrows, P. N.; Byrne, R. M.; Calcaterra, A.; Calloway, D.; Camanzi, B.; Carpinelli, M.; Cassell, R.; Castaldi, R.; Castro, A.; Cavalli-Sforza, M.; Chou, A.; Church, E.; Cohn, H. O.; Coller, J. A.; Convery, M. R.; Cook, V.; Cotton, R.; Cowan, R. F.; Coyne, D. G.; Crawford, G.; Damerell, C. J.; Danielson, M. N.; Daoudi, M.; de Groot, N.; dell'Orso, R.; Dervan, P. J.; de Sangro, R.; Dima, M.; D'Oliveira, A.; Dong, D. N.; Doser, M.; Dubois, R.; Eisenstein, B. I.; Eschenburg, V.; Etzion, E.; Fahey, S.; Falciai, D.; Fan, C.; Fernandez, J. P.; Fero, M. J.; Flood, K.; Frey, R.; Gillman, T.; Gladding, G.; Gonzalez, S.; Goodman, E. R.; Hart, E. L.; Harton, J. L.; Hasan, A.; Hasuko, K.; Hedges, S. J.; Hertzbach, S. S.; Hildreth, M. D.; Huber, J.; Huffer, M. E.; Hughes, E. W.; Huynh, X.; Hwang, H.; Iwasaki, M.; Jackson, D. J.; Jacques, P.; Jaros, J. A.; Jiang, Z. Y.; Johnson, A. S.; Johnson, J. R.; Johnson, R. A.; Junk, T.; Kajikawa, R.; Kalelkar, M.; Kamyshkov, Y.; Kang, H. J.; Karliner, I.; Kawahara, H.; Kim, Y. D.; King, R.; King, M. E.; Kofler, R. R.; Krishna, N. M.; Kroeger, R. S.; Langston, M.; Lath, A.; Leith, D. W.; Lia, V.; Lin, C.-J. S.; Liu, X.; Liu, M. X.; Loreti, M.; Lu, A.; Lynch, H. L.; Ma, J.; Mahjouri, M.; Mancinelli, G.; Manly, S.; Mantovani, G.; Markiewicz, T. W.; Maruyama, T.; Masuda, H.; Mazzucato, E.; McKemey, A. K.; Meadows, B. T.; Menegatti, G.; Messner, R.; Mockett, P. M.; Moffeit, K. C.; Moore, T. B.; Morii, M.; Muller, D.; Murzin, V.; Nagamine, T.; Narita, S.; Nauenberg, U.; Neal, H.; Nussbaum, M.; Oishi, N.; Onoprienko, D.; Osborne, L. S.; Panvini, R. S.; Park, H.; Park, C. H.; Pavel, T. J.; Peruzzi, I.; Piccolo, M.; Piemontese, L.; Pieroni, E.; Pitts, K. T.; Plano, R. J.; Prepost, R.; Prescott, C. Y.; Punkar, G. D.; Quigley, J.; Ratcliff, B. N.; Reeves, T. W.; Reidy, J.; Reinertsen, P. L.; Rensing, P. E.; Rochester, L. S.; Rowson, P. C.; Russell, J. J.; Saxton, O. H.; Schalk, T.; Schindler, R. H.; Schumm, B. A.; Schwiening, J.; Sen, S.; Serbo, V. V.; Shaevitz, M. H.; Shank, J. T.; Shapiro, G.; Sherden, D. J.; Shmakov, K. D.; Simopoulos, C.; Sinev, N. B.; Smith, S. R.; Smy, M. B.; Snyder, J. A.; Staengle, H.; Stahl, A.; Stamer, P.; Steiner, R.; Steiner, H.; Strauss, M. G.; Su, D.; Suekane, F.; Sugiyama, A.; Suzuki, S.; Swartz, M.; Szumilo, A.; Takahashi, T.; Taylor, F. E.; Thom, J.; Torrence, E.; Toumbas, N. K.; Usher, T.; Vannini, C.; Va'Vra, J.; Vella, E.; Venuti, J. P.; Verdier, R.; Verdini, P. G.; Wagner, S. R.; Wagner, D. L.; Waite, A. P.; Walston, S.; Wang, J.; Ward, C.; Watts, S. J.; Weidemann, A. W.; Weiss, E. R.; Whitaker, J. S.; White, S. L.; Wickens, F. J.; Williams, B.; Williams, D. C.; Williams, S. H.; Willocq, S.; Wilson, R. J.; Wisniewski, W. J.; Wittlin, J. L.; Woods, M.; Word, G. B.; Wright, T. R.; Wyss, J.; Yamamoto, R. K.; Yamartino, J. M.; Yang, X.; Yashima, J.; Yellin, S. J.; Young, C. C.; Yuta, H.; Zapalac, G.; Zdarko, R. W.; Zhou, J.
1999-10-01
The parity violation parameters Ab and Ac of the Zbb¯ and Zcc¯ couplings have been measured directly, using the polar angle dependence of the Z0-pole polarized cross sections. Bottom and charmed hadrons were tagged via semileptonic decays. Both the muon and electron identification algorithms take advantage of new multivariate techniques, incorporating for the first time information from the SLD Cˇerenkov Ring Imaging Detector. Based on the 1993-1995 SLD sample of 150 000 Z0 decays produced with highly polarized electron beams, we measure Ab = 0.910+/-0.068\$$stat\$$+/-0.037\$$syst\$$, Ac = 0.642+/-0.110\$$stat\$$+/-0.063\$$syst\$$.
6. Ac hysteresis loop measurement of stator-tooth in induction motor
SciTech Connect
Son, D.
1999-09-01
The properties of ac hysteresis loop of a stator tooth in a 5 hp induction motor was measured and analyzed. The load increase on the motor decreased magnetic induction, however increase the minor hysteresis loops in the high induction region. This effect caused increase in the core loss. Depending on condition of the motor, the core loss of the stator tooth can be 50% greater than the core loss under sinusoidal magnetic induction waveform.
7. Crystal structure and AC conductivity mechanism of [N(C3H7)4]2CoCl4 compound
Moutia, N.; Oueslati, A.; Ben Gzaiel, M.; Khirouni, K.
2016-09-01
We found that the new organic-inorganic compound [N(C3H7)4]2 CoCl4, crystallizes at room temperature in the centrosymmetric monoclinic system with P21/c space group. The atomic arrangement can be described by an alternation of organic and organic-inorganic layers parallel to the (001) plan. Indeed, the differential scanning calorimetry (DSC) studies indicate a presence of three order-disorder phase transitions located at 332, 376 and 441 K. Furthermore, the conductivity was measured in the frequency range from 200 MHz to 5 MHz and temperatures between 318 K and 428 K using impedance spectroscopy. Analysis of the AC conductivity experimental data obtained, and the frequency exponent s with theoretical models reveals that the correlated barrier hopping (CBH) model is the appropriate mechanism for conduction in the title compound. The analysis of the dielectric constants ε ‧ and ε ″ versus temperature, at several frequencies, shows a distribution of relaxation times. This relaxation is probably due to the reorientational dynamics of [N(C3H7)4]+ cations.
8. Measuring the local electrical conductivity of human brain tissue
Akhtari, M.; Emin, D.; Ellingson, B. M.; Woodworth, D.; Frew, A.; Mathern, G. W.
2016-02-01
The electrical conductivities of freshly excised brain tissues from 24 patients were measured. The diffusion-MRI of the hydrogen nuclei of water molecules from regions that were subsequently excised was also measured. Analysis of these measurements indicates that differences between samples' conductivities are primarily due to differences of their densities of solvated sodium cations. Concomitantly, the sample-to-sample variations of their diffusion constants are relatively small. This finding suggests that non-invasive in-vivo measurements of brain tissues' local sodium-cation density can be utilized to estimate its local electrical conductivity.
9. Comparison of Measured and Estimated Unsaturated Hydraulic Conductivity
Parkes, M. E.; Waters, P. A.
1980-08-01
Most studies of empirical estimates of unsaturated hydraulic conductivity functions do not account for water which may be relatively immobile under the conditions in which field measurements of conductivity are made. To investigate this, unsaturated hydraulic conductivity data were obtained for three monolith lysimeters, 80 cm in diameter by 135 cm deep, using the instantaneous profile technique. The lysimeters contained well-structured, freely draining loam soil and moisture measurements were made using a neutron probe. Conductivity estimates were also obtained from laboratory measurements of soil moisture characteristics using the modified Millington and Quirk computational method. Ratios of the calculated to measured conductivities at a matching point near saturation were so large as to suggest that only a minor proportion of the soil pore space was contributing to flow through the whole profile.
10. Direct measurements of Ab and Ac using vertex and kaon charge tags at the SLAC detector.
PubMed
Abe, Koya; Abe, Kenji; Abe, T; Adam, I; Akimoto, H; Aston, D; Baird, K G; Baltay, C; Band, H R; Barklow, T L; Bauer, J M; Bellodi, G; Berger, R; Blaylock, G; Bogart, J R; Bower, G R; Brau, J E; Breidenbach, M; Bugg, W M; Burke, D; Burnett, T H; Burrows, P N; Calcaterra, A; Cassell, R; Chou, A; Cohn, H O; Coller, J A; Convery, M R; Cook, V; Cowan, R F; Crawford, G; Damerell, C J S; Daoudi, M; Dasu, S; de Groot, N; de Sangro, R; Dong, D N; Doser, M; Dubois, R; Erofeeva, I; Eschenburg, V; Etzion, E; Fahey, S; Falciai, D; Fernandez, J P; Flood, K; Frey, R; Hart, E L; Hasuko, K; Hertzbach, S S; Huffer, M E; Huynh, X; Iwasaki, M; Jackson, D J; Jacques, P; Jaros, J A; Jiang, Z Y; Johnson, A S; Johnson, J R; Kajikawa, R; Kalelkar, M; Kang, H J; Kofler, R R; Kroeger, R S; Langston, M; Leith, D W G; Lia, V; Lin, C; Mancinelli, G; Manly, S; Mantovani, G; Markiewicz, T W; Maruyama, T; McKemey, A K; Messner, R; Moffeit, K C; Moore, T B; Morii, M; Muller, D; Murzin, V; Narita, S; Nauenberg, U; Neal, H; Nesom, G; Oishi, N; Onoprienko, D; Osborne, L S; Panvini, R S; Park, C H; Peruzzi, I; Piccolo, M; Piemontese, L; Plano, R J; Prepost, R; Prescott, C Y; Ratcliff, B N; Reidy, J; Reinertsen, P L; Rochester, L S; Rowson, P C; Russell, J J; Saxton, O H; Schalk, T; Schumm, B A; Schwiening, J; Serbo, V V; Shapiro, G; Sinev, N B; Snyder, J A; Staengle, H; Stahl, A; Stamer, P; Steiner, H; Su, D; Suekane, F; Sugiyama, A; Suzuki, A; Swartz, M; Taylor, F E; Thom, J; Torrence, E; Usher, T; Va'vra, J; Verdier, R; Wagner, D L; Waite, A P; Walston, S; Weidemann, A W; Weiss, E R; Whitaker, J S; Williams, S H; Willocq, S; Wilson, R J; Wisniewski, W J; Wittlin, J L; Woods, M; Wright, T R; Yamamoto, R K; Yashima, J; Yellin, S J; Young, C C; Yuta, H
2005-03-11
Exploiting the manipulation of the SLAC Linear Collider electron-beam polarization, we present precise direct measurements of the parity-violation parameters A(c) and A(b) in the Z-boson-c-quark and Z-boson-b-quark coupling. Quark-antiquark discrimination is accomplished via a unique algorithm that takes advantage of the precise SLAC Large Detector charge coupled device vertex detector, employing the net charge of displaced vertices as well as the charge of kaons that emanate from those vertices. From the 1996-1998 sample of 400 000 Z decays, produced with an average beam polarization of 73.4%, we find A(c)=0.673+/-0.029(stat)+/-0.023(syst) and A(b)=0.919+/-0.018(stat)+/-0.017(syst). PMID:15783953
11. Direct Detection of Pure ac Spin Current by X-Ray Pump-Probe Measurements.
PubMed
Li, J; Shelford, L R; Shafer, P; Tan, A; Deng, J X; Keatley, P S; Hwang, C; Arenholz, E; van der Laan, G; Hicken, R J; Qiu, Z Q
2016-08-12
Despite recent progress in spin-current research, the detection of spin current has mostly remained indirect. By synchronizing a microwave waveform with synchrotron x-ray pulses, we use the ferromagnetic resonance of the Py (Ni_{81}Fe_{19}) layer in a Py/Cu/Cu_{75}Mn_{25}/Cu/Co multilayer to pump a pure ac spin current into the Cu_{75}Mn_{25} and Co layers, and then directly probe the spin current within the Cu_{75}Mn_{25} layer and the spin dynamics of the Co layer by x-ray magnetic circular dichroism. This element-resolved pump-probe measurement unambiguously identifies the ac spin current in the Cu_{75}Mn_{25} layer. PMID:27563981
12. Direct Detection of Pure ac Spin Current by X-Ray Pump-Probe Measurements
Li, J.; Shelford, L. R.; Shafer, P.; Tan, A.; Deng, J. X.; Keatley, P. S.; Hwang, C.; Arenholz, E.; van der Laan, G.; Hicken, R. J.; Qiu, Z. Q.
2016-08-01
Despite recent progress in spin-current research, the detection of spin current has mostly remained indirect. By synchronizing a microwave waveform with synchrotron x-ray pulses, we use the ferromagnetic resonance of the Py (Ni81Fe19 ) layer in a Py /Cu /Cu75Mn25/Cu /Co multilayer to pump a pure ac spin current into the Cu75Mn25 and Co layers, and then directly probe the spin current within the Cu75Mn25 layer and the spin dynamics of the Co layer by x-ray magnetic circular dichroism. This element-resolved pump-probe measurement unambiguously identifies the ac spin current in the Cu75Mn25 layer.
13. Recent Advances in AC-DC Transfer Measurements Using Thin-Film Thermal Converters
SciTech Connect
WUNSCH,THOMAS F.; KINARD,JOSEPH R.; MANGINELL,RONALD P.; LIPE,THOMAS E.; SOLOMON JR.,OTIS M.; JUNGLING,KENNETH C.
2000-12-08
New standards for ac current and voltage measurements, thin-film multifunction thermal converters (MJTCS), have been fabricated using thin-film and micro-electro-mechanical systems (MEMS) technology. Improved sensitivity and accuracy over single-junction thermoelements and targeted performance will allow new measurement approaches in traditionally troublesome areas such as the low frequency and high current regimes. A review is presented of new microfabrication techniques and packaging methods that have resulted from a collaborative effort at Sandia National Laboratories and the National Institute of Standards and Technology (MHZ).
14. A wide-frequency range AC magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia
Garaio, E.; Collantes, J. M.; Garcia, J. A.; Plazaola, F.; Mornet, S.; Couillaud, F.; Sandre, O.
2014-11-01
Measurement of specific absorption rate (SAR) of magnetic nanoparticles is crucial to assert their potential for magnetic hyperthermia. To perform this task, calorimetric methods are widely used. However, those methods are not very accurate and are difficult to standardize. In this paper, we present AC magnetometry results performed with a lab-made magnetometer that is able to obtain dynamic hysteresis-loops in the AC magnetic field frequency range from 50 kHz to 1 MHz and intensities up to 24 kA m-1. In this work, SAR values of maghemite nanoparticles dispersed in water are measured by AC magnetometry. The so-obtained values are compared with the SAR measured by calorimetric methods. Both measurements, by calorimetry and magnetometry, are in good agreement. Therefore, the presented AC magnetometer is a suitable way to obtain SAR values of magnetic nanoparticles.
15. Theory of the ac spin valve effect: a new method to measure spin relaxation time
Kochan, Denis; Gmitra, Martin; Fabian, Jaroslav
2012-02-01
Parallel (P) and antiparallel (AP) configurations of FNF junctions have, in a dc regime, different resistivities (RAP>RP), giving rise to the giant magnetoresistance (GMR) effect, which can be explained within the spin injection drift-diffusion model. We extend the model to include ac phenomena and predict new spin dynamical phenomenon; the resonant amplification and depletion of spin accumulation in the P and AP configurations, respectively. As the major new effect, the spin valve magnetoimpedance of the FNF junction oscillates with the driving ac frequency, which leads to negative GMR effect (|ZAP|<|ZP|). We show that from the spin-valve oscillation periods, measured all electrically in the GHz regime, the spin relaxation times could be extracted without any magnetic field and sample size changes (contrary to other techniques). For thin tunnel junctions the ac signal becomes pure Lorentzian, also enabling one to obtain the spin relaxation time of the N region from the signal width. This work, was published in Physical Review Letters,10, 176604 (2011).
16. In situ measurement of conductivity during nanocomposite film deposition
Blattmann, Christoph O.; Pratsinis, Sotiris E.
2016-05-01
Flexible and electrically conductive nanocomposite films are essential for small, portable and even implantable electronic devices. Typically, such film synthesis and conductivity measurement are carried out sequentially. As a result, optimization of filler loading and size/morphology characteristics with respect to film conductivity is rather tedious and costly. Here, freshly-made Ag nanoparticles (nanosilver) are made by scalable flame aerosol technology and directly deposited onto polymeric (polystyrene and poly(methyl methacrylate)) films during which the resistance of the resulting nanocomposite is measured in situ. The formation and gas-phase growth of such flame-made nanosilver, just before incorporation onto the polymer film, is measured by thermophoretic sampling and microscopy. Monitoring the nanocomposite resistance in situ reveals the onset of conductive network formation by the deposited nanosilver growth and sinternecking. The in situ measurement is much faster and more accurate than conventional ex situ four-point resistance measurements since an electrically percolating network is detected upon its formation by the in situ technique. Nevertheless, general resistance trends with respect to filler loading and host polymer composition are consistent for both in situ and ex situ measurements. The time lag for the onset of a conductive network (i.e., percolation) depends linearly on the glass transition temperature (Tg) of the host polymer. This is attributed to the increased nanoparticle-polymer interaction with decreasing Tg. Proper selection of the host polymer in combination with in situ resistance monitoring therefore enable the optimal preparation of conductive nanocomposite films.
17. Mutation Glu82Lys in lamin A/C gene is associated with cardiomyopathy and conduction defect
SciTech Connect
Wang Hu; Wang Jizheng; Zheng Weiyue; Wang Xiaojian; Wang Shuxia; Song Lei; Zou Yubao; Yao Yan; Hui Rutai . E-mail: [email protected]
2006-05-26
Dilated cardiomyopathy is a form of heart muscle disease characterized by impaired systolic function and ventricular dilation. The mutations in lamin A/C gene have been linked to dilated cardiomyopathy. We screened genetic mutations in a large Chinese family of 50 members including members with dilated cardiomyopathy and found a Glu82Lys substitution mutation in the rod domain of the lamin A/C protein in eight family members, three of them have been diagnosed as dilated cardiomyopathy, one presented with heart dilation. The pathogenic mechanism of lamin A/C gene defect is poorly understood. Glu82Lys mutated lamin A/C and wild type protein was transfected into HEK293 cells. The mutated protein was not properly localized at the inner nuclear membrane and the emerin protein, which interacts with lamin A/C, was also aberrantly distributed. The nuclear membrane structure was disrupted and heterochromatin was aggregated aberrantly in the nucleus of the HEK293 cells stably transfected with mutated lamin A/C gene as determined by transmission electron microscopy.
18. Measurement of volume resistivity/conductivity of metallic alloy in inhibited seawater by optical interferometry techniques
SciTech Connect
Habib, K.
2011-03-15
Optical interferometry techniques were used for the first time to measure the volume resistivity/conductivity of carbon steel samples in seawater with different concentrations of a corrosion inhibitor. In this investigation, the real-time holographic interferometry was carried out to measure the thickness of anodic dissolved layer or the total thickness, U{sub total}, of formed oxide layer of carbon steel samples during the alternating current (ac) impedance of the samples in blank seawater and in 5-20 ppm TROS C-70 inhibited seawater, respectively. In addition, a mathematical model was derived in order to correlate between the ac impedance (resistance) and the surface (orthogonal) displacement of the surface of the samples in solutions. In other words, a proportionality constant [resistivity ({rho}) or conductivity ({sigma})= 1/{rho}] between the determined ac impedance [by electrochemical impedance spectroscopy (EIS) technique] and the orthogonal displacement (by the optical interferometry techniques) was obtained. The value of the resistivity of the carbon steel sample in the blank seawater was found similar to the value of the resistivity of the carbon steel sample air, around 1 x 10{sup -5}{Omega} cm. On the contrary, the measured values of the resistivity of the carbon steel samples were 1.85 x 10{sup 7}, 3.35 x 10{sup 7}, and 1.7 x 10{sup 7}{Omega} cm in 5, 10, and 20 ppm TROS C-70 inhibited seawater solutions, respectively. Furthermore, the determined value range of {rho} of the formed oxide layers, from 1.7 x 10{sup 7} to 3.35 x 10{sup 7}{Omega} cm, is found in a reasonable agreement with the one found in literature for the Fe oxide-hydroxides, i.e., goethite ({alpha}-FeOOH) and for the lepidocrocite ({gamma}-FeOOH), 1 x 10{sup 9}{Omega} cm. The {rho} value of the Fe oxide-hydroxides, 1 x 10{sup 9}{Omega} cm, was found slightly higher than the {rho} value range of the formed oxide layer of the present study. This is because the former value was determined
19. Measurement of thermal conductivity in proton irradiated silicon
SciTech Connect
Marat Khafizov; Clarissa Yablinsky; Todd Allen; David Hurley
2014-04-01
We investigate the influence of proton irradiation on thermal conductivity in single crystal silicon. We apply laser based modulated thermoreflectance technique to extract the change in conductivity of the thin layer damaged by proton irradiation. Unlike time domain thermoreflectance techniques that require application of a metal film, we perform our measurement on uncoated samples. This provides greater sensitivity to the change in conductivity of the thin damaged layer. Using sample temperature as a parameter provides a means to deduce the primary defect structures that limit thermal transport. We find that under high temperature irradiation the degradation of thermal conductivity is caused primarily by extended defects.
20. Thermal conductivity of halide solid solutions: measurement and prediction.
PubMed
Gheribi, Aïmen E; Poncsák, Sándor; St-Pierre, Rémi; Kiss, László I; Chartrand, Patrice
2014-09-14
The composition dependence of the lattice thermal conductivity in NaCl-KCl solid solutions has been measured as a function of composition and temperature. Samples with systematically varied compositions were prepared and the laser flash technique was used to determine the thermal diffusivity from 373 K to 823 K. A theoretical model, based on the Debye approximation of phonon density of state (which contains no adjustable parameters) was used to predict the thermal conductivity of both stoichiometric compounds and fully disordered solid solutions. The predictions obtained with the model agree very well with our measurement. A general method for predicting the thermal conductivity of different halide systems is discussed. PMID:25217938
1. Measurements of prompt radiation induced conductivity of Kapton.
SciTech Connect
Preston, Eric F.; Zarick, Thomas Andrew; Sheridan, Timothy J.; Hartman, E. Frederick; Stringer, Thomas Arthur
2010-10-01
We performed measurements of the prompt radiation induced conductivity in thin samples of Kapton (polyimide) at the Little Mountain Medusa LINAC facility in Ogden, UT. Three mil samples were irradiated with a 0.5 {mu}s pulse of 20 MeV electrons, yielding dose rates of 1E9 to 1E10 rad/s. We applied variable potentials up to 2 kV across the samples and measured the prompt conduction current. Analysis rendered prompt conductivity coefficients between 6E-17 and 2E-16 mhos/m per rad/s, depending on the dose rate and the pulse width.
2. Indirect measurement of thermal conductivity in silicon nanowires
SciTech Connect
Pennelli, Giovanni Nannini, Andrea; Macucci, Massimo
2014-02-28
We report indirect measurements of thermal conductivity in silicon nanostructures. We have exploited a measurement technique based on the Joule self-heating of silicon nanowires. A standard model for the electron mobility has been used to determine the temperature through the accurate measurement of the nanowire resistance. We have applied this technique to devices fabricated with a top-down process that yields nanowires together with large silicon areas used both as electrical and as thermal contacts. As there is crystalline continuity between the nanowires and the large contact areas, our thermal conductivity measurements are not affected by any temperature drop due to the contact thermal resistance. Our results confirm the observed reduction of thermal conductivity in nanostructures and are comparable with those previously reported in the literature, achieved with more complex measurement techniques.
3. Non-Contact Conductivity Measurement for Automated Sample Processing Systems
NASA Technical Reports Server (NTRS)
Beegle, Luther W.; Kirby, James P.
2012-01-01
A new method has been developed for monitoring and control of automated sample processing and preparation especially focusing on desalting of samples before analytical analysis (described in more detail in Automated Desalting Apparatus, (NPO-45428), NASA Tech Briefs, Vol. 34, No. 8 (August 2010), page 44). The use of non-contact conductivity probes, one at the inlet and one at the outlet of the solid phase sample preparation media, allows monitoring of the process, and acts as a trigger for the start of the next step in the sequence (see figure). At each step of the muti-step process, the system is flushed with low-conductivity water, which sets the system back to an overall low-conductivity state. This measurement then triggers the next stage of sample processing protocols, and greatly minimizes use of consumables. In the case of amino acid sample preparation for desalting, the conductivity measurement will define three key conditions for the sample preparation process. First, when the system is neutralized (low conductivity, by washing with excess de-ionized water); second, when the system is acidified, by washing with a strong acid (high conductivity); and third, when the system is at a basic condition of high pH (high conductivity). Taken together, this non-contact conductivity measurement for monitoring sample preparation will not only facilitate automation of the sample preparation and processing, but will also act as a way to optimize the operational time and use of consumables
4. Estimation of Ionospheric Conductivity Based on the Measurements by Superdarn
Lee, Eun-Ah; An, Byung-Ho; Yi, Yu
2002-06-01
The ionosphere plays an important role in the electrodynamics of space environment. In particular, the information on the ionospheric conductivity distribution is indispensable in understanding the electrodynamics of the magnetosphere and ionosphere coupling study. To meet such a requirement, several attempts have been made to estimate the conductivity distribution over the polar ionosphere. As one of such attempts we compare the ionospheric plasma convection patterns obtained from the Super Dual Auroral Radar Network (SuperDARN), from which the electric field distribution is estimated, and the simultaneously measured ground magnetic disturbance. Specifically, the electric field measured from the Goose Bay and Stokkseyri radars and magnetic disturbance data obtained from the west coast chain of Greenland are compared. In order to estimate ionospheric conductivity distribution with these information, the overhead infinite sheet current approximation is employed. As expected, the Hall conductance, height-integrated conductivity, shows a wide enhancement along the center of the auroral electrojet. However, Pedersen conductance shows negative values over a wide portion of the auroral oval region, a physically unacceptable situation. To alleviate this problem, the effect of the field-aligned current is taken into account. As a result, the region with negative Pedersen conductance disappears significantly, suggesting that the effect of the field-aligned current should be taken into account, when one wants to estimate ionospheric conductance based on ground magnetic disturbance and electric field measurements by radars.
5. In vivo electrical conductivity measurements during and after tumor electroporation: conductivity changes reflect the treatment outcome
Ivorra, Antoni; Al-Sakere, Bassim; Rubinsky, Boris; Mir, Lluis M.
2009-10-01
Electroporation is the phenomenon in which cell membrane permeability is increased by exposing the cell to short high-electric-field pulses. Reversible electroporation treatments are used in vivo for gene therapy and drug therapy while irreversible electroporation is used for tissue ablation. Tissue conductivity changes induced by electroporation could provide real-time feedback of the treatment outcome. Here we describe the results from a study in which fibrosarcomas (n = 39) inoculated in mice were treated according to different electroporation protocols, some of them known to cause irreversible damage. Conductivity was measured before, within the pulses, in between the pulses and for up to 30 min after treatment. Conductivity increased pulse after pulse. Depending on the applied electroporation protocol, the conductivity increase after treatment ranged from 10% to 180%. The most significant conclusion from this study is the fact that post-treatment conductivity seems to be correlated with treatment outcome in terms of reversibility.
6. A noncontact thermal microprobe for local thermal conductivity measurement.
PubMed
Zhang, Yanliang; Castillo, Eduardo E; Mehta, Rutvik J; Ramanath, Ganpati; Borca-Tasciuc, Theodorian
2011-02-01
We demonstrate a noncontact thermal microprobe technique for measuring the thermal conductivity κ with ∼3 μm lateral spatial resolution by exploiting quasiballistic air conduction across a 10-100 nm air gap between a joule-heated microprobe and the sample. The thermal conductivity is extracted from the measured effective thermal resistance of the microprobe and the tip-sample thermal contact conductance and radius in the quasiballistic regime determined by calibration on reference samples using a heat transfer model. Our κ values are within 5%-10% of that measured by standard steady-state methods and theoretical predictions for nanostructured bulk and thin film assemblies of pnictogen chalcogenides. Noncontact thermal microprobing demonstrated here mitigates the strong dependence of tip-sample heat transfer on sample surface chemistry and topography inherent in contact methods, and allows the thermal characterization of a wide range of nanomaterials. PMID:21361625
7. A noncontact thermal microprobe for local thermal conductivity measurement
Zhang, Yanliang; Castillo, Eduardo E.; Mehta, Rutvik J.; Ramanath, Ganpati; Borca-Tasciuc, Theodorian
2011-02-01
We demonstrate a noncontact thermal microprobe technique for measuring the thermal conductivity κ with ˜3 μm lateral spatial resolution by exploiting quasiballistic air conduction across a 10-100 nm air gap between a joule-heated microprobe and the sample. The thermal conductivity is extracted from the measured effective thermal resistance of the microprobe and the tip-sample thermal contact conductance and radius in the quasiballistic regime determined by calibration on reference samples using a heat transfer model. Our κ values are within 5%-10% of that measured by standard steady-state methods and theoretical predictions for nanostructured bulk and thin film assemblies of pnictogen chalcogenides. Noncontact thermal microprobing demonstrated here mitigates the strong dependence of tip-sample heat transfer on sample surface chemistry and topography inherent in contact methods, and allows the thermal characterization of a wide range of nanomaterials.
8. Measuring the conductivity dependence of the Casimir force
Xu, Jun; Schafer, Robert; Banishev, Alexandr; Mohideen, Umar
2015-03-01
The strength and distance dependence of the Casimir force can be controlled through the conductivity of the material bodies, with lower conductivity in general leading to lower Casimir forces. However low conductivity, large bandgap materials which are insulating, have drawbacks as any surface electrostatic charges cannot be easily compensated. This restricts experiments to metallic or highly doped semiconductor materials. We will report on measurements of the Casimir force gradient using the frequency shift technique. Improvements in the measurement technique will be discussed. Measurements of the Casimir force gradient using low and high conductivity silicon surfaces will be reported. The authors thank G.L. Klimchitskaya and V.M. Mostepanenko for help with the theory and the US National Science Foundation for funding the research.
9. Optical sensor for heat conduction measurement in biological tissue
Gutierrez-Arroyo, A.; Sanchez-Perez, C.; Aleman-Garcia, N.
2013-06-01
This paper presents the design of a heat flux sensor using an optical fiber system to measure heat conduction in biological tissues. This optoelectronic device is based on the photothermal beam deflection of a laser beam travelling in an acrylic slab this deflection is measured with a fiber optic angle sensor. We measure heat conduction in biological samples with high repeatability and sensitivity enough to detect differences in tissues from three chicken organs. This technique could provide important information of vital organ function as well as the detect modifications due to degenerative diseases or physical damage caused by medications or therapies.
10. pH measurement of low-conductivity waters
USGS Publications Warehouse
1987-01-01
pH is an important and commonly measured parameter of precipitation and other natural waters. The various sources of errors in pH measurement were analyzed and procedures for improving the accuracy and precision of pH measurements in natural waters with conductivities of < 100 uS/cm at 25 C are suggested. Detailed procedures are given for the preparation of dilute sulfuric acid standards to evaluate the performance of pH electrodes in low conductivity waters. A daily check of the pH of dilute sulfuric acid standards and deionized water saturated with a gas mixture of low carbon dioxide at partial pressure (air) prior to the measurement of the pH of low conductivity waters is suggested. (Author 's abstract)
11. Estimation of charge-carrier concentration and ac conductivity scaling properties near the V-I phase transition of polycrystalline Na2 S O4
2005-11-01
The conductivity spectra of polycrystalline Na2SO4 have been investigated in the frequency range 42Hz-1MHz at different temperatures below and above the V-I phase transition temperature. The conductivity data have been analyzed using Almond-West formalism. The dc conductivity, the hopping frequency of the charge carriers, and their respective activation energies have been obtained from the analysis of the ac conductivity data, and the concentration of charge carriers was calculated at different temperatures. The power-law exponent n of the conductivity spectra has average values of 0.43 and 0.61 in phases V and I , respectively, which indicates different conduction properties in the two phases. Moreover, scaling of the conductivity spectra at the low- and high-temperature phases was performed in accord with Ghosh’s scaling approach. It is found that the scaling properties depend on the structure of the investigated material.
12. Noninvasive measurement of conductivity anisotropy at larmor frequency using MRI.
PubMed
Lee, Joonsung; Song, Yizhuang; Choi, Narae; Cho, Sungmin; Seo, Jin Keun; Kim, Dong-Hyun
2013-01-01
Anisotropic electrical properties can be found in biological tissues such as muscles and nerves. Conductivity tensor is a simplified model to express the effective electrical anisotropic information and depends on the imaging resolution. The determination of the conductivity tensor should be based on Ohm's law. In other words, the measurement of partial information of current density and the electric fields should be made. Since the direct measurements of the electric field and the current density are difficult, we use MRI to measure their partial information such as B1 map; it measures circulating current density and circulating electric field. In this work, the ratio of the two circulating fields, termed circulating admittivity, is proposed as measures of the conductivity anisotropy at Larmor frequency. Given eigenvectors of the conductivity tensor, quantitative measurement of the eigenvalues can be achieved from circulating admittivity for special tissue models. Without eigenvectors, qualitative information of anisotropy still can be acquired from circulating admittivity. The limitation of the circulating admittivity is that at least two components of the magnetic fields should be measured to capture anisotropic information. PMID:23554838
13. Analytical estimation of skeleton thermal conductivity of a geopolymer foam from thermal conductivity measurements
Henon, J.; Alzina, A.; Absi, J.; Smith, D. S.; Rossignol, S.
2015-07-01
The geopolymers are alumino-silicate binders. The addition of a high pores volume fraction, gives them a thermal insulation character desired in the building industry. In this work, potassium geopolymer foams were prepared at room temperature (< 70 ∘C) by a process of in situ gas release. The porosity distribution shows a multiscale character. However, the thermal conductivity measurements gave values from 0.35 to 0.12 Wm-1.K-1 for a pore volume fraction values between 65 and 85%. In the aim to predict the thermal properties of these foams and focus on the relationship "thermal-conductivity/microstructure", knowledge of the thermal conductivity of their solid skeleton (λ s ) is paramount. However, there is rare work on the determination of this value depending on the initial composition. By the formulation used, the foaming agent contributes to the final network, and it is not possible to obtain a dense material designate to make a direct measurement of λ s . The objective of this work is to use inverse analytical methods to identify the value of λ s . Measurements of thermal conductivity by the fluxmetre technique were performed. The obtained value of the solid skeleton thermal conductivity by the inverse numerical technique is situated in a framework between 0.95 and 1.35 Wm-1.K-1 and is in agreement with one issue from the literature.
14. Thermal and Electrical Conductivity Measurements of CDA 510 Phosphor Bronze
NASA Technical Reports Server (NTRS)
Tuttle, James E.; Canavan, Edgar; DiPirro, Michael
2009-01-01
Many cryogenic systems use electrical cables containing phosphor bronze wire. While phosphor bronze's electrical and thermal conductivity values have been published, there is significant variation among different phosphor bronze formulations. The James Webb Space Telescope (JWST) will use several phosphor bronze wire harnesses containing a specific formulation (CDA 510, annealed temper). The heat conducted into the JWST instrument stage is dominated by these harnesses, and approximately half of the harness conductance is due to the phosphor bronze wires. Since the JWST radiators are expected to just keep the instruments at their operating temperature with limited cooling margin, it is important to know the thermal conductivity of the actual alloy being used. We describe an experiment which measured the electrical and thermal conductivity of this material between 4 and 295 Kelvin.
15. AC photovoltaic module magnetic fields
SciTech Connect
Jennings, C.; Chang, G.J.; Reyes, A.B.; Whitaker, C.M.
1997-12-31
Implementation of alternating current (AC) photovoltaic (PV) modules, particularly for distributed applications such as PV rooftops and facades, may be slowed by public concern about electric and magnetic fields (EMF). This paper documents magnetic field measurements on an AC PV module, complementing EMF research on direct-current PV modules conducted by PG and E in 1993. Although not comprehensive, the PV EMF data indicate that 60 Hz magnetic fields (the EMF type of greatest public concern) from PV modules are comparable to, or significantly less than, those from household appliances. Given the present EMF research knowledge, AC PV module EMF may not merit considerable concern.
16. An AC constant-response method for electrophysiological measurements of spectral sensitivity functions.
PubMed
de Souza, J M; DeVoe, R D; Schoeps, C; Ventura, D F
1996-10-01
A number of methods have been used in the past to measure spectral sensitivity (S(lambda)) functions of electric responses in the visual system. We present here a microcomputer based, AC, constant-response method for automatic on-line measurement of S(lambda) in cells with or without a sustained tonic response. It is based on feedback adjustment of light intensity to obtain constant peak-to-peak amplitudes of response to a flickering stimulus as the spectrum is scanned between 300 and 700 nm in 4 nm steps. It combines the advantages of: (1) on-line presentation of S(lambda) curves; (2) constant light adaptation; (3) sampling of many points; and (4) fast data collection time. The system can be applied to sensitivity or threshold (e.g., S(lambda), dark adaptation, receptive field) measurements of any electrically recorded visual response. PMID:8912193
17. Method for Measuring Thermal Conductivity of Small Samples Having Very Low Thermal Conductivity
NASA Technical Reports Server (NTRS)
Miller, Robert A.; Kuczmarski, Maria a.
2009-01-01
This paper describes the development of a hot plate method capable of using air as a standard reference material for the steady-state measurement of the thermal conductivity of very small test samples having thermal conductivity on the order of air. As with other approaches, care is taken to ensure that the heat flow through the test sample is essentially one-dimensional. However, unlike other approaches, no attempt is made to use heated guards to block the flow of heat from the hot plate to the surroundings. It is argued that since large correction factors must be applied to account for guard imperfections when sample dimensions are small, it may be preferable to simply measure and correct for the heat that flows from the heater disc to directions other than into the sample. Experimental measurements taken in a prototype apparatus, combined with extensive computational modeling of the heat transfer in the apparatus, show that sufficiently accurate measurements can be obtained to allow determination of the thermal conductivity of low thermal conductivity materials. Suggestions are made for further improvements in the method based on results from regression analyses of the generated data.
18. In-Pile Thermal Conductivity Measurement Method for Nuclear Fuels
SciTech Connect
Joy L. Rempe; Brandon Fox; Heng Ban; Joshua E. Daw; Darrell L. Knudson; Keith G. Condie
2009-08-01
Thermophysical properties of advanced nuclear fuels and materials during irradiation must be known prior to their use in existing, advanced, or next generation reactors. Thermal conductivity is one of the most important properties for predicting fuel and material performance. A joint Utah State University (USU) / Idaho National Laboratory (INL) project, which is being conducted with assistance from the Institute for Energy Technology at the Norway Halden Reactor Project, is investigating in-pile fuel thermal conductivity measurement methods. This paper focuses on one of these methods – a multiple thermocouple method. This two-thermocouple method uses a surrogate fuel rod with Joule heating to simulate volumetric heat generation to gain insights about in-pile detection of thermal conductivity. Preliminary results indicated that this method can measure thermal conductivity over a specific temperature range. This paper reports the thermal conductivity values obtained by this technique and compares these values with thermal property data obtained from standard thermal property measurement techniques available at INL’s High Test Temperature Laboratory. Experimental results and material properties data are also compared to finite element analysis results.
19. In situ measurement of ceramic vacuum chamber conductive coating quality
SciTech Connect
Doose, C.; Harkay, K.; Kim, S.; Milton, S.
1997-08-01
A method for measuring the relative surface resistivity and quality of conductive coatings on ceramic vacuum chambers was developed. This method is unique in that it allows one to test the coating even after the ceramic chamber is installed in the accelerator and under vacuum; furthermore, the measurement provides a localized surface reading of the coating conductance. The method uses a magnetic probe is calibrated using the measured DC end-to-end resistance of the tube under test and by comparison to a high quality test surface. The measurement method has also been verified by comparison to high frequency impedance measurements. A detailed description, results, and sensitivity of the technique are given here.
20. Nerve conduction velocity measurements: improved accuracy using superimposed response waves.
PubMed
Halar, E M; Venkatesh, B
1976-10-01
A new procedure of serial motor nerve conduction velocity (NCV) measurements with the use of "superimposed response waves" technique (or double stimulus technique) was performed on 29 normal subjects. Six peripheral nerves were tested once a week for four to six weeks. A total of 760 NCV measurements were thus obtained to try to assess the magnitude of error in serial NCV testings. With the double stimulus technique employed, a significant reduction in variations of serial NCV measurements was found. The overall standard deviation of four to six consecutive NCV measurements in the 34 subjects was 1.3 meters per second with a coefficient of variation of 2.4%. These findings obtained with the double stimulus technique have proven to be approximately three times more accurate than results obtained by investigators who studied nerve conduction velocity measurement variation with single stimulus standard NCV testing techniques. PMID:184754
1. Measurement of thermal contact conductance of SPring-8 beamline components
Mochizuki, Tetsuro; Ohashi, Haruhiko; Sano, Mutsumi; Takahashi, Sunao; Goto, Shunji
2007-09-01
Direct cooling is adopted for most high heat load components in SPring-8 beamlines. On the other hand, contact cooling is employed for some components such as a graphite filter, aluminum filter, mirror, and cryogenic monochromator silicon crystal. For the thermal design of the contact cooling components, it is important to obtain reliable thermal contact conductance value. The conductance depends on many parameters such as the surface materials, surface roughness, flatness of the surface, interstitial materials, temperature of the contact surface, and contact pressure. An experimental setup is fablicated to measure the conductance at liquid nitrogen temperature and room temperature. The thermal contact conductance of a Si-Cu interface and that of a Si-In-Cu interface are measured at cryogenic temperature at contact pressures ranging from 0.1-1.1 MPa. The conductance of an Al-Cu interface and that of a graphite-Cu interface are measured using gold and silver foils as interstitial materials. The measurements are performed at room temperature and at pressures ranging from 0.5-4 MPa. The experimental setup and the results obtained are presented.
2. Measurements of prompt radiation induced conductivity in Teflon (PTFE).
SciTech Connect
Hartman, E. Frederick; Zarick, Thomas Andrew; Sheridan, Timothy J.; Preston, E.
2013-05-01
We performed measurements of the prompt radiation induced conductivity (RIC) in thin samples of Teflon (PTFE) at the Little Mountain Medusa LINAC facility in Ogden, UT. Three mil (76.2 microns) samples were irradiated with a 0.5 %CE%BCs pulse of 20 MeV electrons, yielding dose rates of 1E9 to 1E11 rad/s. We applied variable potentials up to 2 kV across the samples and measured the prompt conduction current. Details of the experimental apparatus and analysis are reported in this report on prompt RIC in Teflon.
3. VALIDATION OF A THERMAL CONDUCTIVITY MEASUREMENT SYSTEM FOR FUEL COMPACTS
SciTech Connect
Jeff Phillips; Colby Jensen; Changhu Xing; Heng Ban
2011-03-01
A high temperature guarded-comparative-longitudinal heat flow measurement system has been built to measure the thermal conductivity of a composite nuclear fuel compact. It is a steady-state measurement device designed to operate over a temperature range of 300 K to 1200 K. No existing apparatus is currently available for obtaining the thermal conductivity of the composite fuel in a non-destructive manner due to the compact’s unique geometry and composite nature. The current system design has been adapted from ASTM E 1225. As a way to simplify the design and operation of the system, it uses a unique radiative heat sink to conduct heat away from the sample column. A finite element analysis was performed on the measurement system to analyze the associated error for various operating conditions. Optimal operational conditions have been discovered through this analysis and results are presented. Several materials have been measured by the system and results are presented for stainless steel 304, inconel 625, and 99.95% pure iron covering a range of thermal conductivities of 10 W/m*K to 70 W/m*K. A comparison of the results has been made to data from existing literature.
4. Thermal Conductivity Measurements in Metals at High Pressures and Temperatures.
Konopkova, Z.; McWilliams, R. S.; Goncharov, A.
2014-12-01
The transport properties of iron and iron alloys at high pressures and temperatures are crucial parameters in planetary evolution models, yet are difficult to determine both theoretically and experimentally. Estimates of thermal conductivity in the Earth's core range from 30 to 150 W/mK, a substantial range leaving many open questions regarding the age of the inner core, the thermal structure of the outer core, and the conditions for a working geodynamo. Most experiments have measured electrical resistivity rather than directly measuring thermal conductivity, and have used models to extrapolate from low-temperature data to the high temperature conditions of the core. Here we present direct, in-situ high-pressure and high-temperature measurements of the thermal conductivity of metals in the diamond-anvil cell. Double-sided continuous laser heating is combined with one-side flash heating of a metallic foil, while the time-resolved temperature is measured from both sides with spectral radiometry in an optical streak camera. Emission and temperature perturbations measured on opposite sides of the foil were modeled using finite element calculations in order to extract thermal diffusivity and conductivity of foils. Results on platinum and iron at high pressures and temperatures will be presented.
5. Simultaneous specific heat and thermal conductivity measurement of individual nanostructures
Zheng, Jianlin; Wingert, Matthew C.; Moon, Jaeyun; Chen, Renkun
2016-08-01
Fundamental phonon transport properties in semiconductor nanostructures are important for their applications in energy conversion and storage, such as thermoelectrics and photovoltaics. Thermal conductivity measurements of semiconductor nanostructures have been extensively pursued and have enhanced our understanding of phonon transport physics. Specific heat of individual nanostructures, despite being an important thermophysical parameter that reflects the thermodynamics of solids, has remained difficult to characterize. Prior measurements were limited to ensembles of nanostructures in which coupling and sample inhomogeneity could play a role. Herein we report the first simultaneous specific heat and thermal conductivity measurements of individual rod-like nanostructures such as nanowires and nanofibers. This technique is demonstrated by measuring the specific heat and thermal conductivity of single ∼600–700 nm diameter Nylon-11 nanofibers (NFs). The results show that the thermal conductivity of the NF is increased by 50% over the bulk value, while the specific heat of the NFs exhibits bulk-like behavior. We find that the thermal diffusivity obtained from the measurement, which is related to the phonon mean free path (MFP), decreases with temperature, indicating that the intrinsic phonon Umklapp scattering plays a role in the NFs. This platform can also be applied to one- and two- dimensional semiconductor nanostructures to probe size effects on the phonon spectra and other transport physics.
6. Complex AC impedance, transference number and vibrational spectroscopy studies of proton conducting PVAc-NH 4SCN polymer electrolytes
Selvasekarapandian, S.; Baskaran, R.; Hema, M.
2005-03-01
The polymer electrolytes composed of poly (vinyl acetate) (PVAc) with various stoichiometric ratios of ammonium thiocyanate (NH 4SCN) salt have been prepared by solution casting method. The polymer-salt complex formation and the polymer-proton interactions have been analysed by FT-IR spectroscopy. The conductivity and dielectric measurements are carried out on these films as a function of frequency at various temperatures. The complex impedance spectroscopy results reveal that the high-frequency semicircle is due to the bulk effect of the material. The conductivity is found to increase in the order of 10 -8-10 -4 S cm -1 at 303 K with the increase in salt concentration. The ionic transference number of mobile ions has been estimated by Wagner's polarization method and the results reveal that the conducting species are predominantly due to ions. The transient ionic current (TIC) measurement technique has been used to detect the type of mobile species and to evaluate their mobilities. The dielectric spectra show the low-frequency dispersion, which is due to the space charge effects arising from the electrodes.
7. Comparison of DC and AC Transport in 1.5-7.5 nm Oligophenylene Imine Molecular Wires across Two Junction Platforms: Eutectic Ga-In versus Conducting Probe Atomic Force Microscope Junctions.
PubMed
Sangeeth, C S Suchand; Demissie, Abel T; Yuan, Li; Wang, Tao; Frisbie, C Daniel; Nijhuis, Christian A
2016-06-15
We have utilized DC and AC transport measurements to measure the resistance and capacitance of thin films of conjugated oligophenyleneimine (OPI) molecules ranging from 1.5 to 7.5 nm in length. These films were synthesized on Au surfaces utilizing the imine condensation chemistry between terephthalaldehyde and 1,4-benzenediamine. Near edge X-ray absorption fine structure (NEXAFS) spectroscopy yielded molecular tilt angles of 33-43°. To probe DC and AC transport, we employed Au-S-OPI//GaOx/EGaIn junctions having contact areas of 9.6 × 10(2) μm(2) (10(9) nm(2)) and compared to previously reported DC results on the same OPI system obtained using Au-S-OPI//Au conducting probe atomic force microscopy (CP-AFM) junctions with 50 nm(2) areas. We found that intensive observables agreed very well across the two junction platforms. Specifically, the EGaIn-based junctions showed: (i) a crossover from tunneling to hopping transport at molecular lengths near 4 nm; (ii) activated transport for wires >4 nm in length with an activation energy of 0.245 ± 0.008 eV for OPI-7; (iii) exponential dependence of conductance with molecular length with a decay constant β = 2.84 ± 0.18 nm(-1) (DC) and 2.92 ± 0.13 nm(-1) (AC) in the tunneling regime, and an apparent β = 1.01 ± 0.08 nm(-1) (DC) and 0.99 ± 0.11 nm(-1) (AC) in the hopping regime; (iv) previously unreported dielectric constant of 4.3 ± 0.2 along the OPI wires. However, the absolute resistances of Au-S-OPI//GaOx/EGaIn junctions were approximately 100 times higher than the corresponding CP-AFM junctions due to differences in metal-molecule contact resistances between the two platforms. PMID:27172452
8. Measurement of the anisotropic thermal conductivity of the porcine cornea.
PubMed
Barton, Michael D; Trembly, B Stuart
2013-10-01
Accurate thermal models for the cornea of the eye support the development of thermal techniques for reshaping the cornea and other scientific purposes. Heat transfer in the cornea must be quantified accurately so that a thermal treatment does not destroy the endothelial layer, which cannot regenerate, and yet is responsible for maintaining corneal transparency. We developed a custom apparatus to measure the thermal conductivity of ex vivo porcine corneas perpendicular to the surface and applied a commercial apparatus to measure thermal conductivity parallel to the surface. We found that corneal thermal conductivity is 14% anisotropic at the normal state of corneal hydration. Small numbers of ex vivo feline and human corneas had a thermal conductivity perpendicular to the surface that was indistinguishable from the porcine corneas. Aqueous humor from ex vivo porcine, feline, and human eyes had a thermal conductivity nearly equal to that of water. Including the anisotropy of corneal thermal conductivity will improve the predictive power of thermal models of the eye. PMID:23933570
9. Aqueous solubilities of phenol derivatives by conductivity measurements
SciTech Connect
Achard, C.; Jaoui, M.; Schwing, M.; Rogalski, M.
1996-05-01
The aqueous solubilities of five chlorophenols and three nitrophenols were measured by conductimetry at temperatures between 15 and 48C. The solubilities of 2-chlorophenol, 4-chlorophenol, 2,4-dichlorophenol, 2,4,6-trichlorophenol, pentachlorophenol, 2-nitrophenol, 4-nitrophenol, and 2,4-dinitrophenol were studied. Automatic conductivity measurements allow the determination of the solute concentration and, hence, the determination of the solubility. Emulsion formation can also be followed. Results obtained are in good agreement with literature values.
10. Measurement of soil hydraulic conductivity in relation with vegetation
Chen, Xi; Cheng, Qinbo
2010-05-01
Hydraulic conductivity is a key parameter which influences hydrological processes of infiltration, surface and subsurface runoff. Vegetation alters surface characteristics (e.g., surface roughness, litter absorption) or subsurface characteristics (e.g. hydraulic conductivity). Field infiltration experiment of a single ring permeameter is widely used for measuring soil hydraulic conductivity. Measurement equipment is a simple single-ring falling head permeameter which consists of a hollow cylinder that is simply inserted into the top soil. An optimization method on the basis of objective of minimum error between the measured and simulated water depths in the single-ring is developed for determination of the soil hydraulic parameters. Using the single ring permeameter, we measured saturated hydraulic conductivities (Ks) of the red loam soil with and without vegetation covers on five hillslopes at Taoyuan Agro-Ecology Experimental Station, Hunan Province of China. For the measurement plots without vegetation roots, Ks value of the soil at 25cm depth is much smaller than that of surface soil (1.52×10-4 vs. 1.10×10-5 m/s). For the measurement plots with vegetation cover, plant roots significantly increase Ks of the lower layer soil but this increase is not significant for the shallow soil. Moreover, influences of vegetation root on Ks depend on vegetation species and ages. Ks value of the Camellia is about three times larger than that of seeding of Camphor (2.62×10-4 vs. 9.82×10-5 m/s). Ks value of the matured Camellia is 2.72×10-4 m/s while Ks value of the young Camellia is only 2.17×10-4 m/s. Key words: single ring permeameter; soil hydraulic conductivity; vegetation
11. Time-resolved Measurements of Spontaneous Magnetic Deflagration of Mn12 tBuAc
Chen, Yizhang; Kent, A. D.; Zhang, Qing; Sarachik, M. P.; Baker, M. L.; Garanin, D. A.; Mhesn, Najah; Lampropoulos, Christos
Magnetic deflagration in molecular magnets has been triggered by heat pulses and acoustic waves. In this work we report spontaneous magnetic deflagration (i.e. deflagration that occurs without an external trigger) in the axially symmetric single molecule magnet Mn12 tBuAc . Magnetic hysteresis measurements show steps due to resonant quantum tunneling (RQT) below 1K, confirming the spin-Hamiltonian parameters for this material and previous results. Deflagration speeds measured with a newly constructed higher bandwidth (2MHz) setup will be presented as a function of transverse and longitudinal fields Hx ⊗Hz both on and off resonance. A large increase in front velocity near RQT steps is observed in experiments with swept transverse fields and will be discussed in light of models of deflagration. Work supported by NSF-DMR-1309202 (NYU); ARO W911NF-13-1-0125 (CCNY); DMR-1161571(Lehman); Cottrell College Science Award (UNF).
12. Test Results of the AC Field Measurements of Fermilab Booster Corrector Magnets
SciTech Connect
DiMarco, E.Joseph; Harding, D.J.; Kashikhin, V.S.; Kotelnikov, S.K.; Lamm, M.J.; Makulski, A.; Nehring, R.; Orris, D.F.; Schlabach, P.; Sylvester, C.; Tartaglia, Michael Albert; /Fermilab
2008-06-25
Multi-element corrector magnets are being produced at Fermilab that enable correction of orbits and tunes through the entire cycle of the Booster, not just at injection. The corrector package includes six different corrector elements--normal and skew orientations of dipole, quadrupole, and sextupole--each independently powered. The magnets have been tested during typical AC ramping cycles at 15Hz using a fixed coil system to measure the dynamic field strength and field quality. The fixed coil is comprised of an array of inductive pick-up coils around the perimeter of a cylinder which are sampled simultaneously at 100 kHz with 24-bit ADC's. The performance of the measurement system and a summary of the field results are presented and discussed.
13. Measurement of electrical conductivity for a biomass fire.
PubMed
Mphale, Kgakgamatso; Heron, Mal
2008-08-01
A controlled fire burner was constructed where various natural vegetation species could be used as fuel. The burner was equipped with thermocouples to measure fuel surface temperature and used as a cavity for microwaves with a laboratory quality 2-port vector network analyzer to determine electrical conductivity from S-parameters. Electrical conductivity for vegetation material flames is important for numerical prediction of flashover in high voltage power transmission faults research. Vegetation fires that burn under high voltage transmission lines reduce flashover voltage by increasing air electrical conductivity and temperature. Analyzer determined electrical conductivity ranged from 0.0058 - 0.0079 mho/m for a fire with a maximum temperature of 1240 K. PMID:19325812
14. Experiment of electrical conductivity at low temperature (preliminary measurement)
SciTech Connect
Zhao, Y.; Wang, H.
1998-07-01
A muon collider needs very large amount of RF power, how to reduce the RF power consumption is of major concern. Thus the application of liquid nitrogen cooling has been proposed. However, it is known that the electrical conductivity depends on many factors and the data from different sources vary in a wide range, especially the data of conductivity of beryllium has no demonstration in a real application. Therefore it is important to know the conductivity of materials, which are commercially available, and at a specified frequency. Here, the results of the preliminary measurement on the electrical conductivity of copper at liquid nitrogen temperature are summarized. Addressed also are the data fitting method and the linear expansion of copper.
15. Measurement of Electrical Conductivity for a Biomass Fire
PubMed Central
Mphale, Kgakgamatso; Heron, Mal
2008-01-01
A controlled fire burner was constructed where various natural vegetation species could be used as fuel. The burner was equipped with thermocouples to measure fuel surface temperature and used as a cavity for microwaves with a laboratory quality 2-port vector network analyzer to determine electrical conductivity from S-parameters. Electrical conductivity for vegetation material flames is important for numerical prediction of flashover in high voltage power transmission faults research. Vegetation fires that burn under high voltage transmission lines reduce flashover voltage by increasing air electrical conductivity and temperature. Analyzer determined electrical conductivity ranged from 0.0058 - 0.0079 mho/m for a fire with a maximum temperature of 1240 K. PMID:19325812
16. Measurements of prompt radiation induced conductivity of alumina and sapphire.
SciTech Connect
Hartman, E. Frederick; Zarick, Thomas Andrew; Sheridan, Timothy J.; Preston, Eric F.
2011-04-01
We performed measurements of the prompt radiation induced conductivity in thin samples of Alumina and Sapphire at the Little Mountain Medusa LINAC facility in Ogden, UT. Five mil thick samples were irradiated with pulses of 20 MeV electrons, yielding dose rates of 1E7 to 1E9 rad/s. We applied variable potentials up to 1 kV across the samples and measured the prompt conduction current. Analysis rendered prompt conductivity coefficients between 1E10 and 1E9 mho/m/(rad/s), depending on the dose rate and the pulse width for Alumina and 1E7 to 6E7 mho/m/(rad/s) for Sapphire.
17. Determining aerodynamic conductance of spar chambers from energy balance measurements
Technology Transfer Automated Retrieval System (TEKTRAN)
The aerodynamic conductance (gA) of SPAR chambers was determined from measurements of energy balance and canopy temperature over a peanut canopy. gA was calculated from the slope of sensible heat flux (H) versus canopy-to-air temperature difference. H and the canopy-to-air temperature were varied by...
18. Measuring Impulsivity in Adolescents with Serious Substance and Conduct Problems
ERIC Educational Resources Information Center
Thompson, Laetitia L.; Whitmore, Elizabeth A.; Raymond, Kristen M.; Crowley, Thomas J.
2006-01-01
Adolescents with substance use and conduct disorders have high rates of aggression and attention deficit hyperactivity disorder (ADHD), all of which have been characterized in part by impulsivity. Developing measures that capture impulsivity behaviorally and correlate with self-reported impulsivity has been difficult. One promising behavioral…
19. Apparatus measures thermal conductivity of honeycomb-core panels
NASA Technical Reports Server (NTRS)
1966-01-01
Overall thermal conductivity of honeycomb-core panels at elevated temperatures is measured by an apparatus with a heater assembly and a calibrated heat-rate transducer. The apparatus has space between the heater and transducer for insertion of a test panel and insulation.
20. Spectral Measurements from the Optical Emission of the A.C. Plasma Anemometer
Matlis, Eric; Marshall, Curtis; Corke, Thomas; Gogineni, Sivaram
2015-11-01
The optical emission properties of a new class of AC-driven flow sensors based on a glow discharge (plasma) is presented. These results extend the utility of the plasma sensor that has recently been developed for measurements in high-enthalpy flows. The plasma sensor utilizes a high frequency (1MHz) AC discharge between two electrodes as the main sensing element. The voltage drop across the discharge correlates to changes in the external flow which can be calibrated for mass-flux (ρU) or pressure depending on the design of the electrodes and orientation relative to the free-stream flow direction. Recent experiments examine the potential for spectral analysis of the optical emission of the discharge to provide additional insight to the flow field. These experiments compare the optical emission of the plasma to emission from breakdown due to an ND:YAG laser. The oxygen 777.3 nm band in particular is a focus of interest as a marker for the determination of gas density.
1. Measuring the hydraulic conductivity of shallow submerged sediments.
PubMed
Kelly, Susan E; Murdoch, Lawrence C
2003-01-01
The hydraulic conductivity of submerged sediments influences the interaction between ground water and surface water, but few techniques for measuring K have been described with the conditions of the submerged setting in mind. Two simple, physical methods for measuring the hydraulic conductivity of submerged sediments have been developed, and one of them uses a well and piezometers similar to well tests performed in terrestrial aquifers. This test is based on a theoretical analysis that uses a constant-head boundary condition for the upper surface of the aquifer to represent the effects of the overlying water body. Existing analyses of tests used to measure the hydraulic conductivity of submerged sediments may contain errors from using the same upper boundary conditions applied to simulate terrestrial aquifers. Field implementation of the technique requires detecting minute drawdowns in the vicinity of the pumping well. Low-density oil was used in an inverted U-tube manometer to amplify the head differential so that it could be resolved in the field. Another technique was developed to measure the vertical hydraulic conductivity of sediments at the interface with overlying surface water. This technique uses the pan from a seepage meter with a piezometer fixed along its axis (a piezo-seep meter). Water is pumped from the pan and the head gradient is measured using the axial piezometer. Results from a sandy streambed indicate that both methods provide consistent and reasonable estimates of K. The pumping test allows skin effects to be considered, and the field data show that omitting the skin effect (e.g., by using a single well test) can produce results that underestimate the hydraulic conductivity of streambeds. PMID:12873006
2. Comparison of different methods for measuring thermal conductivities
SciTech Connect
Hartung, D.; Gather, F.; Klar, P. J.
2012-06-26
Two different methods for the measurement of the thermal conductivity have been applied to a glass (borosilicate) bulk sample. The first method was in the steady-state using an arrangement of gold wires on the sample to create a thermal gradient and to measure the temperatures locally. This allows one to calculate the in-plane thermal conductivity of the sample. The same wire arrangement was also used for a 3{omega}-measurement of the direction-independent bulk thermal conductivity. The 3{omega}-approach is based on periodical heating and a frequency dependent analysis of the temperature response. The results of both methods are in good agreement with each other for this isotropic material, if thermal and radiative losses are accounted for. Our results demonstrate that especially in the case of thin-film measurements, finite element analysis has to be applied to correct for heat losses due to geometry and radiation. In this fashion, the wire positions can be optimized in order to minimize measurement errors.
3. Thermal conductance measurement of windows: An innovative radiative method
SciTech Connect
Arpino, F.; Buonanno, G.; Giovinco, G.
2008-09-15
Heat transfer through window surfaces is one of the most important contributions to energy losses in buildings. Therefore, great efforts are made to design new window frames and glass assemblies with low thermal conductance. At the same time, it is also necessary to develop accurate measurement techniques in thermal characterisation of the above-mentioned building components. In this paper the authors show an innovative measurement method mainly based on radiative heat transfer (instead of the traditional convective one) which allows window thermal conductance measurements with corresponding uncertainty budget evaluation. The authors used the 3D finite volume software FLUENT {sup registered} to design the experimental apparatus. The numerical results have been employed for the system optimisation and metrological characterisation. (author)
4. Thermal Conductivity Measurement of Liquid-Quenched Higher Manganese Silicides
Nishino, Shunsuke; Miyata, Masanobu; Ohdaira, Keisuke; Koyano, Mikio; Takeuchi, Tsunehiro
2016-03-01
Higher manganese silicides (HMSs, MnSi γ , γ ˜ 1.75) show promise for use as low-cost and environmentally friendly thermoelectric materials. To reduce their thermal conductivity, we partially substituted the Mn site with heavy elements using liquid quenching. Fabricated samples possess a curly ribbon-shape with about a 10- μm thickness and 1-mm width, with high surface roughness. In this study, we determined the thermal conductivity of the curly-ribbon-shaped samples using two independent methods: the 3 ω method with two heat flow models, and the steady-state method using a physical property measurement system (PPMS; Quantum Design). We succeeded in estimating the thermal conductivity at the temperature range of 100-200 K using the PPMS. The estimated thermal conductivity of non-doped HMSs shows a constant value without temperature dependence of 2.2 ± 0.8 W K-1m-1 at 100-200 K. The difference of thermal conductivities of W-doped and non-doped HMSs was not recognized within the measurement error.
5. Device and method for measuring thermal conductivity of thin films
NASA Technical Reports Server (NTRS)
Amer, Tahani R. (Inventor); Subramanian, Chelakara (Inventor); Upchurch, Billy T. (Inventor); Alderfer, David W. (Inventor); Sealey, Bradley S. (Inventor); Burkett, Jr., Cecil G. (Inventor)
2001-01-01
A device and method are provided for measuring the thermal conductivity of rigid or flexible, homogeneous or heterogeneous, thin films between 50 .mu.m and 150 .mu.m thick with relative standard deviations of less than five percent. The specimen is sandwiched between like material, highly conductive upper and lower slabs. Each slab is instrumented with six thermocouples embedded within the slab and flush with their corresponding surfaces. A heat source heats the lower slab and a heat sink cools the upper slab. The heat sink also provides sufficient contact pressure onto the specimen. Testing is performed within a vacuum environment (bell-jar) between 10.sup.-3 to 10.sup.-6 Torr. An anti-radiant shield on the interior surface of the bell-jar is used to avoid radiation heat losses. Insulation is placed adjacent to the heat source and adjacent to the heat sink to prevent conduction losses. A temperature controlled water circulator circulates water from a constant temperature bath through the heat sink. Fourier's one-dimensional law of heat conduction is the governing equation. Data, including temperatures, are measured with a multi-channel data acquisition system. On-line computer processing is used for thermal conductivity calculations.
6. Error and uncertainty in Raman thermal conductivity measurements
SciTech Connect
Thomas Edwin Beechem; Yates, Luke; Graham, Samuel
2015-04-22
We investigated error and uncertainty in Raman thermal conductivity measurements via finite element based numerical simulation of two geometries often employed -- Joule-heating of a wire and laser-heating of a suspended wafer. Using this methodology, the accuracy and precision of the Raman-derived thermal conductivity are shown to depend on (1) assumptions within the analytical model used in the deduction of thermal conductivity, (2) uncertainty in the quantification of heat flux and temperature, and (3) the evolution of thermomechanical stress during testing. Apart from the influence of stress, errors of 5% coupled with uncertainties of ±15% are achievable for most materials under conditions typical of Raman thermometry experiments. Error can increase to >20%, however, for materials having highly temperature dependent thermal conductivities or, in some materials, when thermomechanical stress develops concurrent with the heating. A dimensionless parameter -- termed the Raman stress factor -- is derived to identify when stress effects will induce large levels of error. Together, the results compare the utility of Raman based conductivity measurements relative to more established techniques while at the same time identifying situations where its use is most efficacious.
7. Error and uncertainty in Raman thermal conductivity measurements
DOE PAGESBeta
Thomas Edwin Beechem; Yates, Luke; Graham, Samuel
2015-04-22
We investigated error and uncertainty in Raman thermal conductivity measurements via finite element based numerical simulation of two geometries often employed -- Joule-heating of a wire and laser-heating of a suspended wafer. Using this methodology, the accuracy and precision of the Raman-derived thermal conductivity are shown to depend on (1) assumptions within the analytical model used in the deduction of thermal conductivity, (2) uncertainty in the quantification of heat flux and temperature, and (3) the evolution of thermomechanical stress during testing. Apart from the influence of stress, errors of 5% coupled with uncertainties of ±15% are achievable for most materialsmore » under conditions typical of Raman thermometry experiments. Error can increase to >20%, however, for materials having highly temperature dependent thermal conductivities or, in some materials, when thermomechanical stress develops concurrent with the heating. A dimensionless parameter -- termed the Raman stress factor -- is derived to identify when stress effects will induce large levels of error. Together, the results compare the utility of Raman based conductivity measurements relative to more established techniques while at the same time identifying situations where its use is most efficacious.« less
8. Frequency and voltage dependent profile of dielectric properties, electric modulus and ac electrical conductivity in the PrBaCoO nanofiber capacitors
Demirezen, S.; Kaya, A.; Yerişkin, S. A.; Balbaşı, M.; Uslu, İ.
In this study, praseodymium barium cobalt oxide nanofiber interfacial layer was sandwiched between Au and n-Si. Frequency and voltage dependence of ε‧, ε‧, tanδ, electric modulus (M‧ and M″) and σac of PrBaCoO nanofiber capacitor have been investigated by using impedance spectroscopy method. The obtained experimental results show that the values of ε‧, ε‧, tanδ, M‧, M″ and σac of the PrBaCoO nanofiber capacitor are strongly dependent on frequency of applied bias voltage. The values of ε‧, ε″ and tanδ show a steep decrease with increasing frequency for each forward bias voltage, whereas the values of σac and the electric modulus increase with increasing frequency. The high dispersion in ε‧ and ε″ values at low frequencies may be attributed to the Maxwell-Wagner and space charge polarization. The high values of ε‧ may be due to the interfacial effects within the material, PrBaCoO nanofibers interfacial layer and electron effect. The values of M‧ and M″ reach a maximum constant value corresponding to M∞ ≈ 1/ε∞ due to the relaxation process at high frequencies, but both the values of M‧ and M″ approach almost to zero at low frequencies. The changes in the dielectric and electrical properties with frequency can be also attributed to the existence of Nss and Rs of the capacitors. As a result, the change in the ε‧, ε″, tanδ, M‧, M″ and ac electric conductivityac) is a result of restructuring and reordering of charges at the PrBaCoO/n-Si interface under an external electric field or voltage and interface polarization.
9. Simple uniaxial pressure device for ac-susceptibility measurements suitable for closed cycle refrigerator system.
PubMed
Arumugam, S; Manivannan, N; Murugeswari, A
2007-06-01
A simple design of the uniaxial pressure device for the measurement of ac-susceptibility at low temperatures using closed cycle refrigerator system is presented for the first time. This device consists of disc micrometer, spring holder attachment, uniaxial pressure cell, and the ac-susceptibility coil wound on stycast bobbin. It can work under pressure till 0.5 GPa and at the temperature range of 30-300 K. The performance of the system at ambient pressure is tested and calibrated with standard paramagnetic salts [Gd(2)O(3), Er(2)O(3), and Fe(NH(4)SO(4))(2)6H(2)O], Fe(3)O(4), Gd metal, Dy metal, superconductor (YBa(2)Cu(3)O(7)), manganite (La(1.85)Ba(0.15)MnO(3)), and spin glass material (Pr(0.8)Sr(0.2)MnO(3)). The performance of the uniaxial pressure device is demonstrated by investigating the uniaxial pressure dependence of La(1.85)Ba(0.15)MnO(3) single crystal with P||c axis. The Curie temperature (T(c)) decreases as a function of pressure with P||c axis (dT(c)dP(||c axis)=-11.65 KGPa) up to 46 MPa. The design is simple, is user friendly, and does not require pressure calibration. Measurement can even be made on thin and small size oriented crystals. The failure of the coil is remote under uniaxial pressure. The present setup can be used as a multipurpose uniaxial pressure device for the measurement of Hall effect and thermoelectric power with a small modification in the pressure cell. PMID:17614625
10. Measurement of Fracture Geometry for Accurate Computation of Hydraulic Conductivity
Chae, B.; Ichikawa, Y.; Kim, Y.
2003-12-01
Fluid flow in rock mass is controlled by geometry of fractures which is mainly characterized by roughness, aperture and orientation. Fracture roughness and aperture was observed by a new confocal laser scanning microscope (CLSM; Olympus OLS1100). The wavelength of laser is 488nm, and the laser scanning is managed by a light polarization method using two galvano-meter scanner mirrors. The system improves resolution in the light axis (namely z) direction because of the confocal optics. The sampling is managed in a spacing 2.5 μ m along x and y directions. The highest measurement resolution of z direction is 0.05 μ m, which is the more accurate than other methods. For the roughness measurements, core specimens of coarse and fine grained granites were provided. Measurements were performed along three scan lines on each fracture surface. The measured data were represented as 2-D and 3-D digital images showing detailed features of roughness. Spectral analyses by the fast Fourier transform (FFT) were performed to characterize on the roughness data quantitatively and to identify influential frequency of roughness. The FFT results showed that components of low frequencies were dominant in the fracture roughness. This study also verifies that spectral analysis is a good approach to understand complicate characteristics of fracture roughness. For the aperture measurements, digital images of the aperture were acquired under applying five stages of uniaxial normal stresses. This method can characterize the response of aperture directly using the same specimen. Results of measurements show that reduction values of aperture are different at each part due to rough geometry of fracture walls. Laboratory permeability tests were also conducted to evaluate changes of hydraulic conductivities related to aperture variation due to different stress levels. The results showed non-uniform reduction of hydraulic conductivity under increase of the normal stress and different values of
11. Method of simultaneous measurement of radiative and lattice thermal conductivity.
NASA Technical Reports Server (NTRS)
Schatz, J. F.; Simmons, G.
1972-01-01
A new technique of high-temperature thermal-conductivity measurement is described. A CO2 gas laser is used to generate a low-frequency temperature wave at one face of a small disk-shaped sample, and an infrared detector views the opposite face to detect the phase of the emerging radiation. A mathematical expression is derived which enables phase data at several frequencies to be used for the simultaneous determination of thermal diffusivity and mean extinction coefficient. Lattice and radiative thermal conductivities are then calculated. Test results for sintered aluminum oxide at temperatures from 530 to 1924 K are within the range of error of previously existing data.
12. Assembly for electrical conductivity measurements in the piston cylinder device
DOEpatents
Watson, Heather Christine; Roberts, Jeffrey James
2012-06-05
An assembly apparatus for measurement of electrical conductivity or other properties of a sample in a piston cylinder device wherein pressure and heat are applied to the sample by the piston cylinder device. The assembly apparatus includes a body, a first electrode in the body, the first electrode operatively connected to the sample, a first electrical conductor connected to the first electrode, a washer constructed of a hard conducting material, the washer surrounding the first electrical conductor in the body, a second electrode in the body, the second electrode operatively connected to the sample, and a second electrical conductor connected to the second electrode.
13. Electrical conductivity measurements on silicate melts using the loop technique
NASA Technical Reports Server (NTRS)
Waff, H. S.
1976-01-01
A new method is described for measurement of the electrical conductivity of silicate melts under controlled oxygen partial pressure at temperatures to 1550 C. The melt samples are suspended as droplets on platinum-rhodium loops, minimizing iron loss from the melt due to alloying with platinum, and providing maximum surface exposure of the melt to the oxygen-buffering gas atmosphere. The latter provides extremely rapid equilibration of the melt with the imposed oxygen partial pressure. The loop technique involves a minimum of setup time and cost, provides reproducible results to within + or - 5% and is well suited to electrical conductivity studies on silicate melts containing redox cations.
14. System to Measure Thermal Conductivity and Seebeck Coefficient for Thermoelectrics
NASA Technical Reports Server (NTRS)
Kim, Hyun-Jung; Skuza, Jonathan R.; Park, Yeonjoon; King, Glen C.; Choi, Sang H.; Nagavalli, Anita
2012-01-01
The Seebeck coefficient, when combined with thermal and electrical conductivity, is an essential property measurement for evaluating the potential performance of novel thermoelectric materials. However, there is some question as to which measurement technique(s) provides the most accurate determination of the Seebeck coefficient at elevated temperatures. This has led to the implementation of nonstandardized practices that have further complicated the confirmation of reported high ZT materials. The major objective of the procedure described is for the simultaneous measurement of the Seebeck coefficient and thermal diffusivity within a given temperature range. These thermoelectric measurements must be precise, accurate, and reproducible to ensure meaningful interlaboratory comparison of data. The custom-built thermal characterization system described in this NASA-TM is specifically designed to measure the inplane thermal diffusivity, and the Seebeck coefficient for materials in the ranging from 73 K through 373 K.
15. Measurement of the ac Stark shift with a guided matter-wave interferometer
Deissler, B.; Hughes, K. J.; Burke, J. H. T.; Sackett, C. A.
2008-03-01
The dynamic polarizability of Rb87 atoms was measured using a guided-wave Bose-Einstein condensate interferometer. Taking advantage of the large arm separations obtainable in our device, a well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. The technique requires relatively low laser intensity and works for arbitrary optical frequencies. For off-resonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states.
16. Application of inverse heat conduction problem on temperature measurement
Zhang, X.; Zhou, G.; Dong, B.; Li, Q.; Liu, L. Q.
2013-09-01
For regenerative cooling devices, such as G-M refrigerator, pulse tube cooler or thermoacoustic cooler, the gas oscillating bring about temperature fluctuations inevitably, which is harmful in many applications requiring high stable temperatures. To find out the oscillating mechanism of the cooling temperature and improve the temperature stability of cooler, the inner temperature of the cold head has to be measured. However, it is difficult to measure the inner oscillating temperature of the cold head directly because the invasive temperature detectors may disturb the oscillating flow. Fortunately, the outer surface temperature of the cold head can be measured accurately by invasive temperature measurement techniques. In this paper, a mathematical model of inverse heat conduction problem is presented to identify the inner surface oscillating temperature of cold head according to the measured temperature of the outer surface in a GM cryocooler. Inverse heat conduction problem will be solved using control volume approach. Outer surface oscillating temperature could be used as input conditions of inverse problem and the inner surface oscillating temperature of cold head can be inversely obtained. A simple uncertainty analysis of the oscillating temperature measurement also will be provided.
17. An AC phase measuring interferometer for measuring dn/dT of fused silica and calcium fluoride at 193 nm
SciTech Connect
Shagam, R.N.
1998-09-01
A novel method for the measurement of the change in index of refraction vs. temperature (dn/dT) of fused silica and calcium fluoride at the 193 nm wavelength has been developed in support of thermal modeling efforts for the development of 193 nm-based photolithographic exposure tools. The method, based upon grating lateral shear interferometry, uses a transmissive linear grating to divide a 193 nm laser beam into several beam paths by diffraction which propagate through separate identical material samples. One diffracted order passing through one sample overlaps the undiffracted beam from a second sample and forms interference fringes dependent upon the optical path difference between the two samples. Optical phase delay due to an index change from heating one of the samples causes the interference fringes to change sinusoidally with phase. The interferometer also makes use of AC phase measurement techniques through lateral translation of the grating. Results for several samples of fused silica and calcium fluoride are demonstrated.
18. Thermal conductivity measurements of particulate materials under Martian conditions
NASA Technical Reports Server (NTRS)
Presley, M. A.; Christensen, P. R.
1993-01-01
The mean particle diameter of surficial units on Mars has been approximated by applying thermal inertia determinations from the Mariner 9 Infrared Radiometer and the Viking Infrared Thermal Mapper data together with thermal conductivity measurement. Several studies have used this approximation to characterize surficial units and infer their nature and possible origin. Such interpretations are possible because previous measurements of the thermal conductivity of particulate materials have shown that particle size significantly affects thermal conductivity under martian atmospheric pressures. The transfer of thermal energy due to collisions of gas molecules is the predominant mechanism of thermal conductivity in porous systems for gas pressures above about 0.01 torr. At martian atmospheric pressures the mean free path of the gas molecules becomes greater than the effective distance over which conduction takes place between the particles. Gas particles are then more likely to collide with the solid particles than they are with each other. The average heat transfer distance between particles, which is related to particle size, shape and packing, thus determines how fast heat will flow through a particulate material.The derived one-to-one correspondence of thermal inertia to mean particle diameter implies a certain homogeneity in the materials analyzed. Yet the samples used were often characterized by fairly wide ranges of particle sizes with little information about the possible distribution of sizes within those ranges. Interpretation of thermal inertia data is further limited by the lack of data on other effects on the interparticle spacing relative to particle size, such as particle shape, bimodal or polymodal mixtures of grain sizes and formation of salt cements between grains. To address these limitations and to provide a more comprehensive set of thermal conductivities vs. particle size a linear heat source apparatus, similar to that of Cremers, was assembled to
19. Thermal conductivity measurements of proton-heated warm dense matter
McKelvey, A.; Fernandez-Panella, A.; Hua, R.; Kim, J.; King, J.; Sio, H.; McGuffey, C.; Kemp, G. E.; Freeman, R. R.; Beg, F. N.; Shepherd, R.; Ping, Y.
2015-06-01
Accurate knowledge of conductivity characteristics in the strongly coupled plasma regime is extremely important for ICF processes such as the onset of hydrodynamic instabilities, thermonuclear burn propagation waves, shell mixing, and efficient x-ray conversion of indirect drive schemes. Recently, an experiment was performed on the Titan laser platform at the Jupiter Laser Facility to measure the thermal conductivity of proton-heated warm dense matter. In the experiment, proton beams generated via target normal sheath acceleration were used to heat bi-layer targets with high-Z front layers and lower-Z back layers. The stopping power of a material is approximately proportional to Z2 so a sharp temperature gradient is established between the two materials. The subsequent thermal conduction from the higher-Z material to the lower-Z was measured with time resolved streaked optical pyrometry (SOP) and Fourier domain interferometry (FDI) of the rear surface. Results will be used to compare predictions from the thermal conduction equation and the Wiedemann-Franz Law in the warm dense matter regime. Data from the time resolved diagnostics for Au/Al and Au/C Targets of 20-200 nm thickness will be presented.
20. Thermal Conductivity Based on Modified Laser Flash Measurement
NASA Technical Reports Server (NTRS)
Lin, Bochuan; Ban, Heng; Li, Chao; Scripa, Rosalia N.; Su, Ching-Hua; Lehoczky, Sandor L.
2005-01-01
The laser flash method is a standard method for thermal diffusivity measurement. It employs single-pulse heating of one side of a thin specimen and measures the temperature response of the other side. The thermal diffusivity of the specimen can be obtained based on a one-dimensional transient heat transfer analysis. This paper reports the development of a theory that includes a transparent reference layer with known thermal property attached to the back of sample. With the inclusion of heat conduction from the sample to the reference layer in the theoretical analysis, the thermal conductivity and thermal diffusivity of sample can be extracted from the temperature response data. Furthermore, a procedure is established to select two points from the data to calculate these properties. The uncertainty analysis indicates that this method can be used with acceptable levels of uncertainty.
1. Heating rate controller for thermally stimulated conductivity and thermoluminescence measurements.
NASA Technical Reports Server (NTRS)
Manning, E. G.; Littlejohn, M. A.; Oakley, E. M.; Hutchby , J. A.
1972-01-01
A temperature controller is described which enables the temperature of a sample mounted on a cold finger to be varied linearly with time. Heating rates between 0.5 and 10 K/min can be achieved for temperatures between 90 and 300 K. Provision for terminating the sample heating at any temperature between these extremes is available. The temperature can be held at the terminating temperature or be reduced to the starting temperature in a matter of minutes. The controller has been used for thermally stimulated conductivity measurements and should be useful for thermoluminescence measurements as well.
2. The role of probe oxide in local surface conductivity measurements
SciTech Connect
Barnett, C. J.; Kryvchenkova, O.; Wilson, L. S. J.; Maffeis, T. G. G.; Cobley, R. J.; Kalna, K.
2015-05-07
Local probe methods can be used to measure nanoscale surface conductivity, but some techniques including nanoscale four point probe rely on at least two of the probes forming the same low resistivity non-rectifying contact to the sample. Here, the role of probe shank oxide has been examined by carrying out contact and non-contact I V measurements on GaAs when the probe oxide has been controllably reduced, both experimentally and in simulation. In contact, the barrier height is pinned but the barrier shape changes with probe shank oxide dimensions. In non-contact measurements, the oxide modifies the electrostatic interaction inducing a quantum dot that alters the tunneling behavior. For both, the contact resistance change is dependent on polarity, which violates the assumption required for four point probe to remove probe contact resistance from the measured conductivity. This has implications for all nanoscale surface probe measurements and macroscopic four point probe, both in air and vacuum, where the role of probe oxide contamination is not well understood.
3. TRISO fuel compact thermal conductivity measurement instrument development
Jensen, Colby
Thermal conductivity is an important thermophysical property needed for effectively predicting fuel performance. As part of the Next Generation Nuclear Plant (NGNP) program, the thermal conductivity of tri-isotropic (TRISO) fuel needs to be measured over a temperature range characteristic of its usage. The composite nature of TRISO fuel requires that measurement be performed over the entire length of the compact in a non-destructive manner. No existing measurement system is capable of performing such a measurement. A measurement system has been designed based on the steady-state, guarded-comparative-longitudinal heat flow technique. The system as currently designed is capable of measuring cylindrical samples with diameters ˜12.3-mm (˜0.5″) with lengths ˜25-mm (˜1″). The system is currently operable in a temperature range of 400 K to 1100 K for materials with thermal conductivities on the order of 10 W/m/K to 70 W/m/K. The system has been designed, built, and tested. An uncertainty analysis for the determinate errors of the system has been performed finding a result of 5.5%. Finite element modeling of the system measurement method has also been accomplished demonstrating optimal design, operating conditions, and associated bias error. Measurements have been performed on three calibration/validation materials: SS304, 99.95% pure iron, and inconel 625. In addition, NGNP graphite with ZrO2 particles and NGNP AGR-2 graphite matrix only, both in compact form, have been measured. Results from the SS304 sample show agreement of better than 3% for a 300--600°C temperature range. For iron between 100--600°C, the difference with published values is <8% for all temperatures. The maximum difference from published data for inconel 625 is 5.8%, near 600°C. Both NGNP samples were measured from 100--800°C. All results are presented and discussed. Finally, a discussion of ongoing work is included as well as a brief discussion of implementation under other operating
4. Silicate bonding properties: Investigation through thermal conductivity measurements
Lorenzini, M.; Cesarini, E.; Cagnoli, G.; Campagna, E.; Haughian, K.; Hough, J.; Losurdo, G.; Martelli, F.; Martin, I.; Piergiovanni, F.; Reid, S.; Rowan, S.; van Veggel, A. A.; Vetrano, F.
2010-05-01
A direct approach to reduce the thermal noise contribution to the sensitivity limit of a GW interferometric detector is the cryogenic cooling of the mirrors and mirrors suspensions. Future generations of detectors are foreseen to implement this solution. Silicon has been proposed as a candidate material, thanks to its very low intrinsic loss angle at low temperatures and due to its very high thermal conductivity, allowing the heat deposited in the mirrors by high power lasers to be efficiently extracted. To accomplish such a scheme, both mirror masses and suspension elements must be made of silicon, then bonded together forming a quasi-monolithic stage. Elements can be assembled using hydroxide-catalysis silicate bonding, as for silica monolithic joints. The effect of Si to Si bonding on suspension thermal conductance has therefore to be experimentally studied. A measurement of the effect of silicate bonding on thermal conductance carried out on 1 inch thick silicon bonded samples, from room temperature down to 77 K, is reported. In the explored temperature range, the silicate bonding does not seem to affect in a relevant way the sample conductance.
5. Evaluation of DC electric field distribution of PPLP specimen based on the measurement of electrical conductivity in LN2
Hwang, Jae-Sang; Seong, Jae-Kyu; Shin, Woo-Ju; Lee, Jong-Geon; Cho, Jeon-Wook; Ryoo, Hee-Suk; Lee, Bang-Wook
2013-11-01
High temperature superconducting (HTS) cable has been paid much attention due to its high efficiency and high current transportation capability, and it is also regarded as eco-friendly power cable for the next generation. Especially for DC HTS cable, it has more sustainable and stable properties compared to AC HTS cable due to the absence of AC loss in DC HTS cable. Recently, DC HTS cable has been investigated competitively all over the world, and one of the key components of DC HTS cable to be developed is a cable joint box considering HVDC environment. In order to achieve the optimum insulation design of the joint box, analysis of DC electric field distribution of the joint box is a fundamental process to develop DC HTS cable. Generally, AC electric field distribution depends on relative permittivity of dielectric materials but in case of DC, electrical conductivity of dielectric material is a dominant factor which determines electric field distribution. In this study, in order to evaluate DC electric field characteristics of the joint box for DC HTS cable, polypropylene laminated paper (PPLP) specimen has been prepared and its DC electric field distribution was analyzed based on the measurement of electrical conductivity of PPLP in liquid nitrogen (LN2). Electrical conductivity of PPLP in LN2 has not been reported yet but it should be measured for DC electric field analysis. The experimental works for measuring electrical conductivity of PPLP in LN2 were presented in this paper. Based on the experimental works, DC electric field distribution of PPLP specimen was fully analyzed considering the steady state and the transient state of DC. Consequently, it was possible to determine the electric field distribution characteristics considering different DC applying stages including DC switching on, DC switching off and polarity reversal conditions.
6. Analysis of measurements of the thermal conductivity of liquid urania
SciTech Connect
Fink, J.K.; Leibowitz, L.
1984-09-17
An analysis was performed of the three existing measurements of the thermal conductivity and thermal diffusivity of molten uranium dioxide. A transient heat transfer code (THTB) was used for this analysis. A much smaller range of values for thermal conductivity than originally reported was found: the original values ranged from 2.4 to 11 W . m/sup -1/ . K/sup -1/, with a mean of 7.3 W . m/sup -1/ . K/sup -1/, whereas the recalculated values ranged from 4.5 to 6.75 W . m/sup -1/ . K/sup -1/, with a mean of 5.6 W . m/sup -1/ . K/sup -1/.
7. Thermal conductivity measurements in a 2D Yukawa system
Nosenko, V.; Ivlev, A.; Zhdanov, S.; Morfill, G.; Goree, J.; Piel, A.
2007-03-01
Thermal conductivity was measured for a 2D Yukawa system. First, we formed a monolayer suspension of microspheres in a plasma, i.e., a dusty plasma, which is like a colloidal suspension, but with an extremely low volume fraction and a partially-ionized rarefied gas instead of solvent. In the absence of manipulation, the suspension forms a 2D triangular lattice. To melt this lattice and form a liquid, we used a laser-heating method. Two focused laser beams were moved rapidly around in the monolayer. The kinetic temperature of the particles increased with the laser power applied, and above a threshold a melting transition occurred. We used digital video microscopy for direct imaging and particle tracking. The spatial profiles of the particle kinetic temperature were calculated. Using the heat transport equation with an additional term to account for the energy dissipation due to the gas drag, we analyzed the temperature distribution to derive the thermal conductivity.
8. Thermal conductivity measurements of CH and Be by refraction-enhanced x-ray radiography
Ping, Yuan; King, Jim; Landen, Otto; Whitley, Heather; London, Rich; Hamel, Sebastien; Sterne, Phil; Panella, Amalia; Freeman, Rick; Collins, Gilbert
2015-06-01
Transport properties of warm dense matter are important for modeling the growth of hydrodynamic instabilities near the fuel-ablator interface in an ICF capsule, which determines the mix level in the fuel and thus is critical for successful ignition. A novel technique, time-resolved refraction-enhanced x-ray radiography, has been developed to study thermal conductivity at an interface. Experiments using OMEGA laser have been carried out for CH/Be targets isochorically heated by x-rays to measure the evolution of the density gradient at the interface due to thermal conduction. The sensitivity of this radiographic technique to discontinuities enabled observation of shock/rarefraction waves propagating away from the interface. The radiographs provide enough constraints on the temperatures, densities and scale lengths in CH and Be, respectively. Preliminary data analysis suggests that the thermal conductivities of CH and Be at near solid density and a few eV temperature are higher than predictions by the commonly used Lee-More model. Detailed analysis and comparison with various models will be presented. The work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
9. Thermal conductivity and emissivity measurements of uranium carbides
Corradetti, S.; Manzolaro, M.; Andrighetto, A.; Zanonato, P.; Tusseau-Nenez, S.
2015-10-01
Thermal conductivity and emissivity measurements on different types of uranium carbide are presented, in the context of the ActiLab Work Package in ENSAR, a project within the 7th Framework Program of the European Commission. Two specific techniques were used to carry out the measurements, both taking place in a laboratory dedicated to the research and development of materials for the SPES (Selective Production of Exotic Species) target. In the case of thermal conductivity, estimation of the dependence of this property on temperature was obtained using the inverse parameter estimation method, taking as a reference temperature and emissivity measurements. Emissivity at different temperatures was obtained for several types of uranium carbide using a dual frequency infrared pyrometer. Differences between the analyzed materials are discussed according to their compositional and microstructural properties. The obtainment of this type of information can help to carefully design materials to be capable of working under extreme conditions in next-generation ISOL (Isotope Separation On-Line) facilities for the generation of radioactive ion beams.
10. The unsaturated hydraulic conductivity: measurement and non-equilibrium effects
Weller, U.; Vogel, H.
2010-12-01
The unsaturated hydraulic conductivity of porous media is a central item in hydraulic modeling. It is hard to measure and therefore in most applications it is represented by some kind of model based on indirect measurements. The validity is hardly ever checked. We have developed a fairly easy and automatic measurement procedure that allows to determine directly the hydraulic conductivity of a sample at different water potentials. The sample is placed on a plate where the potential can be controlled. It is then irrigated from the top with a constant, predefined flow rate. Tensiometers control the water potential within the sample, the topmost one is used to steer the potential at the lower boundary. It can be seen that the sample equilibrates fairly quick to a constant potential throughout the sample, and thus the conductivity of the material at the measured potential is equal to the applied flux while gravity is the only driving force. The change in water content is monitored by a balance. We have measured several materials, soils and sand substrates, with a protocol where we first lower the flux stepwise and then rise it again. The samples reach quick an equilibrium, as can be seen by the control tensiometer. Coming from the wet side, with a high flux, and lowering this flux, we observe a fast drop in potential, and in water content. But then the water potential rises again, while the water content remains constant or drops even slightly. When rising the flux again, we observe the opposite effect, but less pronounced: after the initial rise in water potential while the system adapts to the new flow rate, the potential lowers slightly. This behavior occurs over a certain range of water potential, it is not present in the very wet or very dry range. Also, the range in which it occurs and the magnitude of the effect depends on the studied material: pure sands express the pattern very clearly, it is much less obvious in loamy soils. Also, the relation between water
11. Experimental measurements of the thermal conductivity of ash deposits: Part 1. Measurement technique
SciTech Connect
A. L. Robinson; S. G. Buckley; N. Yang; L. L. Baxter
2000-04-01
This paper describes a technique developed to make in situ, time-resolved measurements of the effective thermal conductivity of ash deposits formed under conditions that closely replicate those found in the convective pass of a commercial boiler. Since ash deposit thermal conductivity is thought to be strongly dependent on deposit microstructure, the technique is designed to minimize the disturbance of the natural deposit microstructure. Traditional techniques for measuring deposit thermal conductivity generally do not preserve the sample microstructure. Experiments are described that demonstrate the technique, quantify experimental uncertainty, and determine the thermal conductivity of highly porous, unsintered deposits. The average measured conductivity of loose, unsintered deposits is 0.14 {+-} 0.03 W/(m K), approximately midway between rational theoretical limits for deposit thermal conductivity.
12. Apparent thermal conductivity measurements by an unguarded technique
Graves, R. S.; Yarbrough, D. W.; McElroy, D. L.
An unguarded longitudinal heat flow apparatus for measuring the apparent thermal conductivity (lambda/sub a) of insulations was tested. Heat flow is provided by a horizontal electrically heated Nichrome screen sandwiched between test samples that are bounded by temperature controlled copper plates and 9 cm of mineral fiber insulation. A determinate error analysis shows lambda/sub a/ measurement uncertainty to be less than + or - 1.7% for insulating materials as thin as 3 cm. Three-dimensional thermal modeling indicates negligible error in lambda/sub a/ due to edge loss for insulations up to 7.62 cm thick when the temperature difference across the sample is measured at the screen center. System repeatability and reproducibility were determined to be + or - 0.2%. Differences of lambda/sub a/ results from the screen tester and results from the National Bureau of Standards were 0.1% for a 10-kg/m(3) Calibration Transfer Standard and 0.9% for 127-kg/m(3) fibrous glass board (SRM 1450b). Measurements on fiberglass and rock wool batt insulations showed the dependence of lambda/sub a/ on density, temperature, temperature difference, plate emittance, and heat flow direction. Results obtained for lambda/sub a/ as a function of density at 240C differed by less than 2% from values obtained with a guarded hot plate. It is demonstrated that this simple technique has the accuracy and sensitivity needed for useful lambda/sub a/ measurements on thermal insulating materials.
13. Measurement of klystron phase modulation due to ac-powered filaments
NASA Technical Reports Server (NTRS)
Finnegan, E. J.
1977-01-01
A technique for determining the intermodulation components in the RF spectrum of the S-band radar transmitter generated by having the klystron filaments heated by 400-Hz ac power is described. When the klystron is being operated with 400-Hz (ac) on the filament, the IPM is buried in the 400-Hz equipment interference noise. The modulation sidebands were separated and identified and found to be-67 db below the main carrier. This is well below the transmitter specifications, and operating the filaments on ac would not degrade the spectrum to where it would be detrimental to the radiated RF.
14. Quantitative measurements of root water uptake and root hydraulic conductivities
Zarebanadkouki, Mohsen; Javaux, Mathieu; Meunier, Felicien; Couvreur, Valentin; Carminati, Andrea
2016-04-01
How is root water uptake distributed along the root system and what root properties control this distribution? Here we present a method to: 1) measure root water uptake and 2) inversely estimate the root hydraulic conductivities. The experimental method consists in using neutron radiography to trace deuterated water (D2O) in soil and roots. The method was applied to lupines grown aluminium containers filled with a sandy soil. When the lupines were 4 weeks old, D2O was locally injected in a selected soil regions and its transport was monitored in soil and roots using time-series neutron radiography. By image processing, we quantified the concentration of D2O in soil and roots. We simulated the transport of D2O into roots using a diffusion-convection numerical model. The diffusivity of the roots tissue was inversely estimated by simulating the transport of D2O into the roots during night. The convective fluxes (i.e. root water uptake) were inversely estimating by fitting the experiments during day, when plants were transpiring, and assuming that root diffusivity did not change. The results showed that root water uptake was not uniform along the roots. Water uptake was higher at the proximal parts of the lateral roots and it decreased by a factor of 10 towards the distal parts. We used the data of water fluxes to inversely estimate the profile of hydraulic conductivities along the roots of transpiring plants growing in soil. The water fluxes in the lupine roots were simulated using the Hydraulic Tree Model by Doussan et al. (1998). The fitting parameters to be adjusted were the radial and axial hydraulic conductivities of the roots. The results showed that by using the root architectural model of Doussan et al. (1998) and detailed information of water fluxes into different root segments we could estimate the profile of hydraulic conductivities along the roots. We also found that: 1) in a tap-rooted plant like lupine water is mostly taken up by lateral roots; (2) water
15. Contactless electrical conductivity measurement of metallic submicron-grain material: Application to the study of aluminum with severe plastic deformation.
PubMed
Mito, M; Matsui, H; Yoshida, T; Anami, T; Tsuruta, K; Deguchi, H; Iwamoto, T; Terada, D; Miyajima, Y; Tsuji, N
2016-05-01
We measured the electrical conductivity σ of aluminum specimen consisting of submicron-grains by observing the AC magnetic susceptibility resulting from the eddy current. By using a commercial platform for magnetic measurement, contactless measurement of the relative electrical conductivity σn of a nonmagnetic metal is possible over a wide temperature (T) range. By referring to σ at room temperature, obtained by the four-terminal method, σn(T) was transformed into σ(T). This approach is useful for cylinder specimens, in which the estimation of the radius and/or volume is difficult. An experiment in which aluminum underwent accumulative roll bonding, which is a severe plastic deformation process, validated this method of evaluating σ as a function of the fraction of high-angle grain boundaries. PMID:27250440
16. High-Resolution ac Measurements of the Hall Effect in Organic Field-Effect Transistors
Chen, Y.; Yi, H. T.; Podzorov, V.
2016-03-01
We describe a high resolving power technique for Hall-effect measurements, efficient in determining Hall mobility and carrier density in organic field-effect transistors and other low-mobility systems. We utilize a small low-frequency ac magnetic field (Brms<0.25 T ) and a phase-sensitive (lock-in) detection of Hall voltage, with the necessary corrections for Faraday induction. This method significantly enhances the signal-to-noise ratio and eliminates the necessity of using high magnetic fields in Hall-effect studies. With the help of this method, we are able to obtain the Hall mobility and carrier density in organic transistors with a mobility as low as μ ˜0.3 cm2 V-1 s-1 by using a compact desktop apparatus and low magnetic fields. We find a good agreement between Hall-effect and electric-field-effect measurements, indicating that, contrary to the common belief, certain organic semiconductors with mobilities below 1 cm2 V-1 s-1 can still exhibit a fully developed, band-semiconductor-like Hall effect, with the Hall mobility and carrier density matching those obtained in longitudinal transistor measurements. This suggests that, even when μ <1 cm2 V-1 s-1 , charges in organic semiconductors can still behave as delocalized coherent carriers. This technique paves the way to ubiquitous Hall-effect studies in a wide range of low-mobility materials and devices, where it is typically very difficult to resolve the Hall effect even in very high dc magnetic fields.
17. Structural characterization, thermal, ac conductivity and dielectric properties of (C7H12N2)2[SnCl6]Cl2.1.5H2O
Hajji, Rachid; Oueslati, Abderrazek; Hajlaoui, Fadhel; Bulou, Alain; Hlel, Faouzi
2016-05-01
(C7H12N2)2[SnCl6]Cl2.1.5H2O is crystallized at room temperature in the monoclinic system (space group P21/n). The isolated molecules form organic and inorganic layers parallel to the (a, b) plane and alternate along the c-axis. The inorganic layer is built up by isolated SnCl6 octahedrons. Besides, the organic layer is formed by 2,4-diammonium toluene cations, between which the spaces are filled with free Cl- ions and water molecules. The crystal packing is governed by means of the ionic N-H...Cl and Ow-H...Cl hydrogen bonds, forming a three-dimensional network. The thermal study of this compound is reported, revealing two phase transitions around 360(±3) and 412(±3) K. The electrical and dielectric measurements were reported, confirming the transition temperatures detected in the differential scanning calorimetry (DSC). The frequency dependence of ac conductivity at different temperatures indicates that the correlated barrier hopping (CBH) model is the probable mechanism for the ac conduction behavior.
18. Use of an advanced composite material in construction of a high pressure cell for magnetic ac susceptibility measurements
Wang, X.; Misek, M.; Jacobsen, M. K.; Kamenev, K. V.
2014-10-01
The applicability of fibre-reinforced polymers for fabrication of high pressure cells was assessed using finite element analysis and experimental testing. Performance and failure modes for the key components of the cell working in tension and in compression were evaluated and the ways for optimising the designs were established. These models were used in construction of a miniature fully non-metallic diamond anvil cell for magnetic ac susceptibility measurements in a magnetic property measurement system. The cell is approximately 14 mm long, 8.5 mm in diameter and was demonstrated to reach a pressure of 5.6 GPa. AC susceptibility data collected on Dy2O3 demonstrate the performance of the cell in magnetic property measurements and confirm that there is no screening of the sample by the environment which typically accompanies the use of conventional metallic high pressure cells in oscillating magnetic fields.
19. Electrical conductivity measurements of bacterial nanowires from Pseudomonas aeruginosa
Maruthupandy, Muthusamy; Anand, Muthusamy; Maduraiveeran, Govindhan; Sait Hameedha Beevi, Akbar; Jeeva Priya, Radhakrishnan
2015-12-01
The extracellular appendages of bacteria (flagella) that transfer electrons to electrodes are called bacterial nanowires. This study focuses on the isolation and separation of nanowires that are attached via Pseudomonas aeruginosa bacterial culture. The size and roughness of separated nanowires were measured using transmission electron microscopy (TEM) and atomic force microscopy (AFM), respectively. The obtained bacterial nanowires indicated a clear image of bacterial nanowires measuring 16 nm in diameter. The formation of bacterial nanowires was confirmed by microscopic studies (AFM and TEM) and the conductivity nature of bacterial nanowire was investigated by electrochemical techniques. Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS), which are nondestructive voltammetry techniques, suggest that bacterial nanowires could be the source of electrons—which may be used in various applications, for example, microbial fuel cells, biosensors, organic solar cells, and bioelectronic devices. Routine analysis of electron transfer between bacterial nanowires and the electrode was performed, providing insight into the extracellular electron transfer (EET) to the electrode. CV revealed the catalytic electron transferability of bacterial nanowires and electrodes and showed excellent redox activities. CV and EIS studies showed that bacterial nanowires can charge the surface by producing and storing sufficient electrons, behave as a capacitor, and have features consistent with EET. Finally, electrochemical studies confirmed the development of bacterial nanowires with EET. This study suggests that bacterial nanowires can be used to fabricate biomolecular sensors and nanoelectronic devices.
20. Scanning Ion Conductance Microscopy for living cell membrane potential measurement
Panday, Namuna
Recently, the existence of multiple micro-domains of extracellular potential around individual cells have been revealed by voltage reporter dye using fluorescence microscopy. One hypothesis is that these long lasting potential patterns play a vital role in regulating important cell activities such as embryonic patterning, regenerative repair and reduction of cancerous disorganization. We used multifunctional Scanning Ion Conductance Microscopy (SICM) to study these extracellular potential patterns of single cell with higher spatial resolution. To validate this novel technique, we compared the extracellular potential distribution on the fixed HeLa cell surface and Polydimethylsiloxane (PDMS) surface and found significant difference. We then measured the extracellular potential distributions of living melanocytes and melanoma cells and found both the mean magnitude and spatial variation of extracellular potential of the melanoma cells are bigger than those of melanocytes. As compared to the voltage reporter dye based fluorescence microscope method, SICM can achieve quantitative potential measurements of non-labeled living cell membranes with higher spatial resolution.
1. Thermal contact conductance measurements on Doublet III armor tile graphite
SciTech Connect
Doll, D.W.; Reis, E.
1983-12-01
Several tests were performed on the Doublet III wall armor tiles to determine the cool-down rate and to evaluate improvements made by changing the conditions at the interface between the graphite tile and the stainless steel backing plate. Thermal diffusivity tests were performed in vacuum on both TiC coated and bare graphite tiles with and without 0.13 mm (.005'') thick silver foil at the interface. The results of the armor tile cool-down tests showed improvement when a 0.13 mm (0.005'') silver foil is used at the interface. At 2.1 x 10/sup 5/ Pa (30 psi) contact pressure, the e-folding cool-down times for a TiC coated tile, bare graphite and bare graphite with a 0.06 mm (0.0035'') silver shim were 10 min., 5.0 min., and 4.1 min., respectively. Tests using high contact pressures showed that the cool-down rates converged to approx. 4.0 min. At this limit, the conduction path along the backing plate to the two cooling tubes controls the heat flow, and no further improvement could be expected. Thermal diffusivity measurements confirmed the results of the cool-down test showing that by introducing a silver foil at the interface, the contact conductance between Poco AXF-5Q graphite and 316 stainless steel could be improved by a factor of three to eight. The tests showed an increasing improvement over a range of temperatures from 25/sup 0/C to 400/sup 0/C. The data provides a technical basis for further applications of graphite tiles to cooled backing plates.
2. Improved direct measurement of A(b) and A(c) at the Z(0) pole using a lepton tag.
PubMed
Abe, Kenji; Abe, Koya; Abe, T; Adam, I; Akimoto, H; Aston, D; Baird, K G; Baltay, C; Band, H R; Barklow, T L; Bauer, J M; Bellodi, G; Berger, R; Blaylock, G; Bogart, J R; Bower, G R; Brau, J E; Breidenbach, M; Bugg, W M; Burke, D; Burnett, T H; Burrows, P N; Calcaterra, A; Cassell, R; Chou, A; Cohn, H O; Coller, J A; Convery, M R; Cook, V; Cowan, R F; Crawford, G; Damerell, C J S; Daoudi, M; de Groot, N; de Sangro, R; Dong, D N; Doser, M; Dubois, R; Erofeeva, I; Eschenburg, V; Fahey, S; Falciai, D; Fernandez, J P; Flood, K; Frey, R; Hart, E L; Hasuko, K; Hertzbach, S S; Huffer, M E; Huynh, X; Iwasaki, M; Jackson, D J; Jacques, P; Jaros, J A; Jiang, Z Y; Johnson, A S; Johnson, J R; Kajikawa, R; Kalelkar, M; Kang, H J; Kofler, R R; Kroeger, R S; Langston, M; Leith, D W G; Lia, V; Lin, C; Mancinelli, G; Manly, S; Mantovani, G; Markiewicz, T W; Maruyama, T; McKemey, A K; Messner, R; Moffeit, K C; Moore, T B; Morii, M; Muller, D; Murzin, V; Narita, S; Nauenberg, U; Neal, H; Nesom, G; Oishi, N; Onoprienko, D; Osborne, L S; Panvini, R S; Park, C H; Peruzzi, I; Piccolo, M; Piemontese, L; Plano, R J; Prepost, R; Prescott, C Y; Ratcliff, B N; Reidy, J; Reinertsen, P L; Rochester, L S; Rowson, P C; Russell, J J; Saxton, O H; Schalk, T; Schumm, B A; Schwiening, J; Serbo, V V; Shapiro, G; Sinev, N B; Snyder, J A; Staengle, H; Stahl, A; Stamer, P; Steiner, H; Su, D; Suekane, F; Sugiyama, A; Suzuki, S; Swartz, M; Taylor, F E; Thom, J; Torrence, E; Usher, T; Va'vra, J; Verdier, R; Wagner, D L; Waite, A P; Walston, S; Weidemann, A W; Weiss, E R; Whitaker, J S; Williams, S H; Willocq, S; Wilson, R J; Wisniewski, W J; Wittlin, J L; Woods, M; Wright, T R; Yamamoto, R K; Yashima, J; Yellin, S J; Young, C C; Yuta, H
2002-04-15
The parity violation parameters A(b) and A(c) of the Zb(b) and Zc(c) couplings have been measured directly, using the polar angle dependence of the polarized cross sections at the Z(0) pole. Bottom and charmed hadrons were tagged via their semileptonic decays. Both the electron and muon analyses take advantage of new multivariate techniques to increase the analyzing power. Based on the 1993-1998 SLD sample of 550,000 Z(0) decays produced with highly polarized electron beams, we measure A(b) = 0.919+/-0.030(stat)+/-0.024(syst), and A(c) = 0.583+/-0.055(stat)+/-0.055(syst). PMID:11955189
3. AC conductivity and relaxation mechanism in (Nd1/2Li1/2)(Fe1/2V1/2)O3 ceramics
Nath, Susmita; Barik, Subrat Kumar; Choudhary, R. N. P.
2016-05-01
In the present study we have synthesized polycrystalline sample of (Nd1/2Li1/2)(Fe1/2V1/2)O3 ceramic by a standard high-temperature solid-state reaction technique. Studies of dielectric and electrical properties of the compound have been carried out in a wide range of temperature (RT - 400 °C) and frequency (1kHz - 1MHz) using complex impedance spectroscopic technique. The imaginary vs. real component of the complex impedance plot (Nyquist plot) of the prepared sample exhibits the existence of grain, grain boundary contributions in the complex electrical parameters and negative temperature coefficient of resistance (NTCR) type behavior like semiconductor. Details study of ac conductivity plot reveals that the material obeys universal Jonscher's power law.
4. Analyzing the Effects of Capacitances-to-Shield in Sample Probes on AC Quantized Hall Resistance Measurements
PubMed Central
Cage, M. E.; Jeffery, A.
1999-01-01
We analyze the effects of the large capacitances-to-shields existing in all sample probes on measurements of the ac quantized Hall resistance RH. The object of this analysis is to investigate how these capacitances affect the observed frequency dependence of RH. Our goal is to see if there is some way to eliminate or minimize this significant frequency dependence, and thereby realize an intrinsic ac quantized Hall resistance standard. Equivalent electrical circuits are used in this analysis, with circuit components consisting of: capacitances and leakage resistances to the sample probe shields; inductances and resistances of the sample probe leads; quantized Hall resistances, longitudinal resistances, and voltage generators within the quantum Hall effect device; and multiple connections to the device. We derive exact algebraic equations for the measured RH values expressed in terms of the circuit components. Only two circuits (with single-series “offset” and quadruple-series connections) appear to meet our desired goals of measuring both RH and the longitudinal resistance Rx in the same cool-down for both ac and dc currents with a one-standard-deviation uncertainty of 10−8 RH or less. These two circuits will be further considered in a future paper in which the effects of wire-to-wire capacitances are also included in the analysis.
5. Incorporating residential AC load control into ancillary service markets: Measurement and settlement
SciTech Connect
Bode, Josh L.; Sullivan, Michael J.; Berghman, Dries; Eto, Joseph H.
2013-05-01
Many pre-existing air conditioner load control programs can provide valuable operational flexibility but have not been incorporated into electricity ancillary service markets or grid operations. Multiple demonstrations have shown that residential air conditioner (AC) response can deliver resources quickly and can provide contingency reserves. A key policy hurdle to be overcome before AC load control can be fully incorporated into markets is how to balance the accuracy, cost, and complexity of methods available for the settlement of load curtailment. Overcoming this hurdle requires a means for assessing the accuracy of shorter-term AC load control demand reduction estimation approaches in an unbiased manner. This paper applies such a method to compare the accuracy of approaches varying in cost and complexity ? including regression analysis, load matching and control group approaches ? using feeder data, household data and AC end-use data. We recommend a practical approach for settlement, relying on an annually updated set of tables, with pre-calculated reduction estimates. These tables allow users to look up the demand reduction per device based on daily maximum temperature, geographic region and hour of day, simplifying settlement and providing a solution to the policy problem presented in this paper.
6. Steady heat conduction-based thermal conductivity measurement of single walled carbon nanotubes thin film using a micropipette thermal sensor
Shrestha, R.; Lee, K. M.; Chang, W. S.; Kim, D. S.; Rhee, G. H.; Choi, T. Y.
2013-03-01
In this paper, we describe the thermal conductivity measurement of single-walled carbon nanotubes thin film using a laser point source-based steady state heat conduction method. A high precision micropipette thermal sensor fabricated with a sensing tip size varying from 2 μm to 5 μm and capable of measuring thermal fluctuation with resolution of ±0.01 K was used to measure the temperature gradient across the suspended carbon nanotubes (CNT) film with a thickness of 100 nm. We used a steady heat conduction model to correlate the temperature gradient to the thermal conductivity of the film. We measured the average thermal conductivity of CNT film as 74.3 ± 7.9 W m-1 K-1 at room temperature.
7. Steady heat conduction-based thermal conductivity measurement of single walled carbon nanotubes thin film using a micropipette thermal sensor.
PubMed
Shrestha, R; Lee, K M; Chang, W S; Kim, D S; Rhee, G H; Choi, T Y
2013-03-01
In this paper, we describe the thermal conductivity measurement of single-walled carbon nanotubes thin film using a laser point source-based steady state heat conduction method. A high precision micropipette thermal sensor fabricated with a sensing tip size varying from 2 μm to 5 μm and capable of measuring thermal fluctuation with resolution of ±0.01 K was used to measure the temperature gradient across the suspended carbon nanotubes (CNT) film with a thickness of 100 nm. We used a steady heat conduction model to correlate the temperature gradient to the thermal conductivity of the film. We measured the average thermal conductivity of CNT film as 74.3 ± 7.9 W m(-1) K(-1) at room temperature. PMID:23556837
8. Synthesis and characterization of cancrinite-type zeolite, and its ionic conductivity study by AC impedance analysis
Kriaa, A.; Ben Saad, K.; Hamzaoui, A. H.
2012-12-01
The synthesis of cancrinite in the system NaOH-SiO2-Al2O3-NaHCO3-H2O was performed, according to methods described in the literature, in an autoclave under hydrothermal conditions at T = 473 K. The electrical properties of cancrinite-type zeolite pellets were investigated by complex impedance spectroscopy in the temperature range 465-800°C. The effect of temperature on impedance parameters was studied using an impedance analyzer in a wide frequency range (1 Hz to 13 MHz). The real and imaginary parts of complex impedance trace semicircles in the complex plane are plotted. The bulk resistance of the material decreases with rise in temperature. This exhibits a typical negative temperature coefficient of resistance (NTCR) behavior of the material. The results of bulk electrical conductivity and its activation energy are presented. The modulus analysis suggests that the electrical transport processes in the material are very likely to be of electronic nature. Relaxation frequencies follow an Arrhenius behavior with activation energy values not comparable to those found for the electrical conductivity.
9. SPHINX Measurements of Radiation Induced Conductivity of Foam
SciTech Connect
Ballard, W.P.; Beutler, D.E.; Burt, M.; Dudley, K.J.; Stringer, T.A.
1998-12-14
Experiments on the SPHINX accelerator studying radiation-induced conductivity (RIC) in foam indicate that a field-exclusion boundary layer model better describes foam than a Maxwell-Garnett model that treats the conducting gas bubbles in the foam as modifying the dielectric constant. In both cases, wall attachment effects could be important but were neglected.
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http://www.physicsforums.com/showthread.php?p=3782266 | # Obama's Candidacy
by Pythagorean
Tags: candidacy, obama
P: 1,123 It seems like the debate over high gas prices has picked up right where it left off in 2008. my bold http://www.usatoday.com/news/politic...inflated_N.htm "The Department of Energy estimates that keeping tires properly inflated can help improve gas mileage by about 3.3%. It's one step the agency recommends to reduce fuel costs, along with removing items from the trunk, replacing clogged air filters and getting regular tuneups. The Obama campaign could not provide figures to back up his claim that inflating tires and getting tuneups would save just as much oil as could be produced by offshore drilling. Offshore drilling is off limits under current law, but McCain wants to lift the ban to alleviate high gas prices. Obama said last week he would be willing to support limited additional offshore oil drilling as part of a comprehensive energy policy, a shift from his previous position. But McCain is wrong when he says inflating tires is the only thing Obama is proposing to address America's energy challenges. Besides the recommendation to keep tires properly inflated, Obama also suggested providing incentives for people to trade in gas guzzling vehicles for more fuel-efficient cars; investing in research and development to produce new fuel-saving technologies like long-running batteries; encouraging innovation in alternative energies; and retrofitting buildings to make them more energy efficient." I just realized "Cash for Clunkers" was part of the Obama energy policy.
P: 927
Quote by WhoWee Besides the recommendation to keep tires properly inflated, Obama also suggested providing incentives for people to trade in gas guzzling vehicles for more fuel-efficient cars; investing in research and development to produce new fuel-saving technologies like long-running batteries; encouraging innovation in alternative energies; and retrofitting buildings to make them more energy efficient."[/I]
While I understand the morivation behind the cash for clunkers and other similar programs, I have to wonder if people driving more fuel efficient cars isn't offset by the idea (in their heads) that now they can drive more.
P: 1,123
Quote by daveb While I understand the morivation behind the cash for clunkers and other similar programs, I have to wonder if people driving more fuel efficient cars isn't offset by the idea (in their heads) that now they can drive more.
I suppose a few people might drive more if there's gas remaining in their tank - my teenagers are classic examples.
P: 172 Why in the world would I trade in a truck that's paid for only to borrow money to buy a new truck with better gas mileage? That's like trading in my wife for one that's a better cook. I may get what I want, but it'll cost me a lot more ;-) - and No, my wife will never read this, lol Seriously, I remember the first gas lines during Carter's presidency. You had to buy a foreign car to get good gas mileage, and people did. I came back (as I suspect others did) to US made cars when they started getting the mileage, reliability, and style right. Cars and trucks will evolve and we'll move toward them. My 61' Willy only got 8mpg and it was a 6-cylinder! IMO, we don't need the government pushing us to borrow more money to buy a car just for more mpg, we have enough debt now. I'll run my truck until it won't run, then I'll look for my next truck and mpg will be a factor, so will 4x4, A/C, safety, etc. I tend to think oil speculation is a big factor. As one oil trader put it, http://www.thereformedbroker.com/201...ative-premium/ , perhaps to the tone of $40/barrel or more. From http://www.philstockworld.com/2012/0...geye-rebuttal/ 'According to a recent paper by the Federal Reserve Bank of St. Louis titled, “Speculation in the Oil Market” (Juvenal and Petrella), it has been “estimated that assets allocated to commodity index trading strategies rose from$13 billion in 2004 to $260 billion as of March 2008”. This paper concludes: “Our results confirm that Kilian’s (2009) conclusion that global demand shocks as the main drivers of oil fluctuations remains robust. In addition, we show that speculative shocks are the second most important driver of oil prices.”' IMO, the rolling of futures contracts until the price is "right" is a problem. In the links you'll see the speculation is often by investment groups that don't do anything with oil except trade it up for a better price. I'd like to see the government require oil contracts to require the buyer prove they can take delivery in 30 days or loose their "investment". One thing I don't think Americans can continue to do is tell the rest of the world to drill every gallon you can so we don't have to. Until technology replaces oil, we need to be working as hard to get oil from here as they are from there. We're "farming" gas from dumps, natural gas, etc., I just don't see us that far away. T.B. Picken's push to move commercial trucking to CNG seems like a good start. I remember when 18 wheelers were about all that used diesel, now diesel is everywhere. Perhaps the same thing could happen with CNG. Obama's not wrong about making your car run better, but we're not going to "save" our way out of a gas/oil future. Emeritus Sci Advisor PF Gold P: 11,154 Quote by WhoWee We really don't know which taxes he's referring to or their specific income level or filing classification - do we? They might be small business owners facing cost increases - we don't know. The payroll tax cut (the one that reduces your contribution to social security at a time when social security is facing insolvency) might not be enough to offset a lost deduction of some type? The payroll tax cut is only a part of all the middle-class tax cuts that Obama has signed over the past 3 years. But even so, I'm not aware of any lost deductions that come close to offsetting the payroll cuts. Are you? As for medical, we really don't know the medical history or reasons for increases - do we? For instance, are you certain that healthcare mandates (PPACA/Obamacre) aren't causing insurance premiums to rise? Also, are you certain that changes to the Medicare reimbursement rates haven't somehow impacted the specific health care costs of these particular people? We'll if we don't really know these things, one could hardly make definitive assertions about the blame lying solely with Obama! But that's exactly what Pengwuino does. If Pengwuino decides to share more details - then perhaps a definitive response can be given - until then - we just don't know enough about their particular situation to render a conclusion - IMO of course. While we may not be able to arrive at a conclusive analysis of the Pengwuino family tax history, we certainly can say something about the tax rates affecting the average middle class family (which is, in fact, who Pengwuino specifically mentions before giving the example of his own family), and the reality, last time I checked, is that the vast majority of these families have gotten net decreases in taxes over the past three years adding to somewhere near three thousand dollars per family (just from "Making Work Pay" in 2009 + payroll tax cuts for 2010 and 2011) fpr the average family. As for small businesses, Obama signed over a dozen different tax cuts for them, including things like: eliminating all capitals gains taxes on key investments, doubling the investment limit that businesses can write off, a new deduction for health insurance for the self-employed, deductions for start up investments, etc. http://www.ctj.org/obamastaxcuts.php http://www.washingtonpost.com/busine...AUR_story.html http://www.bloomberg.com/news/2012-0...ax-breaks.html 2010 Tax Year Summary [pdf] --> http://tax.cchgroup.com/downloads/fi...ax-yearend.pdf 2011 Tax Year Summary [pdf] --> http://tax.cchgroup.com/downloads/fi...011yearend.pdf PF Gold P: 3,021 Recall that the President also raised tobacco taxes, about$1.5B/year, back in 2008. Also in effect now is the "Snooki" tanning bed tax. Signed into law by the President but not yet in effect include: o Uninsured penalty/tax/whatever, $695 up to$2085, 2014 to 2016 o Medicare tax hike of 0.9%, medicare investment income tax at 3.8% for incomes>$200K/year, 2013 http://www.politifact.com/truth-o-me...t-raise-taxes/ PF Gold P: 183 Quote by russ_watters The link to the citation is dead. I've been hearing 2037 for a while now - has that number been updated to account for the recession and cuts in the payroll tax rate? Yes, both of those things are considered. Here is another link: http://cbo.gov/publication/42212 P: 1,123 Quote by SixNein Yes, both of those things are considered. Here is another link: http://cbo.gov/publication/42212 Given the date of the report - is it likely the shrinking of the workforce (as reported in recent unemployment stats) was factored in for future years? Fewer workers will probably mean lower revenues. Also, the new extension of the social security reduction wouldn't be included - would it? Emeritus Sci Advisor PF Gold P: 11,154 Quote by mheslep Recall that the President also raised tobacco taxes, about$1.5B/year, back in 2008. Also in effect now is the "Snooki" tanning bed tax.
I'm aware of those, but hardly think they come anywhere close to offsetting the tax cuts for most people.
Quote by Gokul43201 So I'd be surprised if any significant fraction of the population has seen an increase yet (though that may change in the next few years). I think you'd have to be a chain smoking (see: tobacco tax increase) paper mill to have seen more tax raises than cuts.
PF Gold
P: 183
Quote by WhoWee Given the date of the report - is it likely the shrinking of the workforce (as reported in recent unemployment stats) was factored in for future years? Fewer workers will probably mean lower revenues. Also, the new extension of the social security reduction wouldn't be included - would it?
PF Gold
P: 3,021
Quote by SixNein Yes, both of those things are considered. Here is another link: http://cbo.gov/publication/42212
As the chart in that CBO report shows, SS revenues have been falling short of outlays for a couple years now and the gap is about to expand rapidly. The parlor games with the SS trust fund/lock box continue here with the payroll tax cut, which will decrease revenues \$100B. If one still believes in the lock box concept, SS loses no revenue here because it simply takes more money from the general revenue, i.e. the left hand of the govt. pays the right, and the left hand borrows more.
P: 1,414
Quote by Obama I have to explain why abortion violates some principle that is accessible to people of all faiths, including those with no faith at all.
Quote by russ watters I don't think they are all that useful - even a little disingenuous - since the "principle" at issue is clearly accessible to people of all/no faith.
The question is: what principle, that's accessible to both theistic religious people and atheists, does abortion violate?
Apparently, what Obama's saying is that he can't pinpoint such a principle. Therefore, he can't advocate outlawing abortion in his capacity as chief executive, even though he might personally and religiously be against abortion.
I think this makes sense. Whether it's disingenuous or not is another question.
But to say that Obama doesn't acknowledge what the issue is would be wrong, imo. The point being that the endowment of 'personhood' on a developing fetus at some point in its development is arbitrary.
Does personhood begin at the instant of conception? Sometime in the first trimester? The second trimester?
What exists is a situation in which Obama, or anyone else, can't explain why "abortion violates some principle that is accessible to people of all faiths, including those who have no faith at all."
P: 1,414
Quote by turbo If we start taxing the wealthy on just a bit more of of their income, SS can be solvent forever.
This seems to be the case. If that increased revenue is actually used for SS. But the bottom line is that if taxes on the wealthy aren't increased, then there's no hope of saving SS. Which is quite ok if one happens to be relatively well off. But of course not ok for the majority of Americans.
P: 1,123
Quote by SixNein I posted a link.
Yes you did. However, the projections show Social Security contributions increasing - even though the size of the workforce is shrinking and the contribution reductions were extended.
P: 194 I'm not an American, but... For both your sake and the sake of the rest of the world, I hope Obama wins the election. The USA has not been incredibly popular with the rest of the world for years now. However, when Obama won the election in 2008, I know that many people I know were quite happy and thought he would make an able president. Many people around me still think the same thing (although they are a bit disappointed he didn't make it life paradise in a few years). Romney and Santorum, on the other hand, pretty much everyone I know utterly dislikes. Romney is an American exceptionalist who feels the need to tell anyone how much more important the USA is than any other country, which makes him well-hated by anyone I know. While I try very hard to ignore this, even I sometimes get the idea that people from the USA are annoyingly 'proud' of their country. When a president feels the need to excessively show this, I start worrying. Santorum is simply an idiot for believing such strange things as the Dutch performing euthanasia on all the elderly who don't wear an "I don't want to be killed"-bracelet, for actively saying being gay is bad, and openly saying he would bomb Iranian facilities if they don't show everything they're doing to America (because, of course, all Iranians are bad peopleTM and should do as the Americans say[1]). In other words: diplomatically speaking, Obama is a million times more capable than the Republican candidates I've seen so far. I should add that, given that the above is based on interaction with people in my country and things I've heard people say in public, my view might be inaccurate or only be accurate for many people in my country (the Netherlands). As far as the economy goes, I don't think I can change anyone's view on this one: I think Obama's been much better than most people give him credit for. However, I suspect that the people who wouldn't like to see him re-elected gladly say he hasn't done enough for the economy. Then there's the matter of political positions on ethical and social issues. I've already hinted a bit at this in my rant about Santorum, but I also think Obama is much more capable in that regard. To give a few examples, Romney is in favor of abstinence-only education, he opposes same-sex marriage, doesn't favor legalizing medical cannabis (even though cannabis is less harmful than tobacco, but meh), and would ban federal funding of stem-cell research. The other Republican candidates speak of similar things. Of course, I don't agree with everything the presidential candidates of the Republican party have said so far, but, like I said, I believe (and hope) Obama is the way to go for 2012-2016. [1] I don't want to say too much about this now, seeing as this is a thread about Obama's candidacy, not about my views on Iran, but I feel it might be necessary. I'm not particularly thrilled about the possibility of Iran building nuclear weapons, that's true. And if they do, I think there has to be something we can do about it. However, I also try to see it from their point of view. And from their point of view, 1. Israel is their sworn enemy, and the USA is 'with them', 2. the USA have nukes, 3. they pretty much get told that they will be completely destroyed if they will build nukes (several important people in the USA have by now called for a strike on Iran), 4. if they *don't* have nukes, they're doomed if/when Israel decides to attack them. What choice do they have but to build nukes in secret, and pretend they're only building these facilities for nuclear energy? (There is, of course, the possibility that they're speaking the truth, in which case it would still be prudent not to let an enemy see their facilities out of fear for espionage. But, for the moment, I'll assume people's worst-case scenarios are correct.)
P: 1,123
Quote by Hobin I'm not an American, but... For both your sake and the sake of the rest of the world, I hope Obama wins the election. The USA is not incredibly popular with the rest of the world for years now. However, when Obama won the election in 2008, I know that many people in my direct vicinity were quite happy and thought he would make an able president. Many people around me still think the same thing. Romney and Santorum, on the other hand, pretty much everyone I know utterly dislikes. Romney is an American exceptionalist who feels the need to tell anyone how much more important the USA is than any other country, which makes him well-hated by anyone I know. Santorum is simply an idiot for believing such strange things as the Dutch performing euthanasia on all the elderly who don't wear an "I don't want to be killed"-bracelet, for actively saying gays are stupid, and openly saying he would bomb Iranian facilities if they don't show everything they're doing to American (because, of course, all Iranians are bad peopleTM). In other words: diplomatically speaking, Obama is a million times more capable than the Republican candidates I've seen so far. I should add that, given that the above is based on interaction with people in my country and things I've heard people say in public, my view might be inaccurate or only be accurate for many people in my country (the Netherlands). As far as the economy goes, I don't think I can change anyone's view on this one: I think Obama's been much better than most people give him credit for. However, I suspect that the people who wouldn't like to see him re-elected gladly say he hasn't done enough for the economy. Then there's the matter of political positions on ethical and social issues. I've already hinted a bit at this in my rant about Santorum, but I also think Obama is much more capable in that regard. To give a few examples, Romney is in favor of abstinence-only education, he opposes same-sex marriage, doesn't favor legalizing medical cannabis (even though cannabis is less harmful than tobacco, but meh), and would ban federal funding of stem-cell research. The other Republican candidates speak of similar things. Of course, I don't agree with everything the presidential candidates of the Republican party have said so far, but, like I said, I believe (and hope) Obama is the way to go for 2012-2016.
We have threads for bashing Santorum and Romney - you might want to post these opinions in those threads?
P: 194
Quote by WhoWee We have threads for bashing Santorum and Romney - you might want to post these opinions in those threads?
I'm aware. This was not to show my personal opinion so much as what most of the people around me think - and why it would (diplomatically speaking) be best if Obama gets elected.
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http://math.stackexchange.com/questions/490343/nine-digit-sequences-with-exactly-one-zero-two-ones-three-twos | # Nine digit sequences with exactly one zero, two ones, three twos
I'm working on a problem where I am to find the number of nine digit sequences when there are exactly one zero, two ones and three twos. I worked up a solution, but is it correct? Here's my line of thinking:
There are six fixed numbers, which leaves three free. These free can be 3, 4, ..., 9. They can be chosen in $7^3$ different ways. As order matters, 9 objects may be permuted in $9!$ ways. However, there are two ones and three twos, which forces us to divide by $2!3!$. All in all, this gives us
$$\frac{7^3 9!}{2!3!}$$
This is under the assumption that a zero can come first. The question doesn't address this, but if it cannot then we have the same situation as above only that the zero must not come first. So from $\frac{7^3 9!}{2!3!}$ we need to subtract the disallowed situations. Fixing the first number to zero leaves us 8 numbers to permute giving a final count of:
$$\frac{7^3 9!}{2!3!}-\frac{7^3 8!}{2!3!}=\frac{7^3}{12}\left(9!-8!\right)$$
Is this correct? Am I missing something? As I wrote it down here I realized I should probably divide by something more -- don't I, for example, need to account for the cases when the free digits are not unique?
-
The positions for the symbols in $\{0,1,2\}$ can be chosen in $\binom{9}{6}=84$. Once chosen, the symbols $0,1,1,2,2,2$ can be arranged in those cells in $\binom{6}{1,2,3}=60$ ways, using the multinomial coefficient.
The remaining $3$ cells must be assigned symbols from $\{3,4,\ldots,9\}$, which can be achieved in $7^3$ ways.
So, in total we have $$\binom{9}{6}\binom{6}{1,2,3}7^3=1728720$$ such sequences.
-
Iam i correct we seem to differ – Willemien Sep 11 '13 at 17:42
@Willemien no you have the same answers. ${n \choose 6}{6 \choose 1, 2, 3}7^3=\frac{9!}{6!3!}\frac{6!}{1!2!3!}7^3=\frac{9!7^3}{2!3!3!}$ which you also got. Thanks both of you! – hejseb Sep 13 '13 at 8:35
sorry you are missing something
see it as 4 groups
• one 0
• two 1
• three 2
• tree others
for the 3 others there are $7^3$ possibilities
and for the groups
$$\frac{ 9!}{2!3!3!}$$
so in total $$\frac{7^3 9!}{2!3!3!}$$
(you are a factor 6 off)
if the first number cannot be 0 , multiply it by 8 divide by 9.
Good luck
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https://aimsciences.org/article/doi/10.3934/dcds.2013.33.4123 | # American Institute of Mathematical Sciences
September 2013, 33(9): 4123-4155. doi: 10.3934/dcds.2013.33.4123
## The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula
1 School of Mathematical Sciences, Peking University, Beijing 100871, China 2 BICMR and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
Received October 2010 Revised December 2012 Published March 2013
Consider a random cocycle $\Phi$ on a separable infinite-dimensional Hilbert space preserving a probability measure $\mu$, which is supported on a random compact set $K$. We show that if $\Phi$ is $C^2$ (over $K$) and satisfies some mild integrable conditions of the differentials, then Pesin's entropy formula holds if $\mu$ has absolutely continuous conditional measures on the unstable manifolds. The converse is also true under an additional condition on $K$ when the system has no zero Lyapunov exponent.
Citation: Zhiming Li, Lin Shu. The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4123-4155. doi: 10.3934/dcds.2013.33.4123
##### References:
[1] L. Arnold, "Random Dynamical Systems,", Springer Monographs in Mathematics, (1998). [2] J. Bahnmüller and P.-D. Liu, Characterization of measures satisfying the Pesin entropy formula for random dynamical systems,, J. Dynam. Differential Equations, 10 (1998), 425. doi: 10.1023/A:1022653229891. [3] T. Bogenschütz, Entropy, pressure, and a variational principle for random dynamical systems,, Random Comput. Dynam., 1 (): 99. [4] H. Crauel and F. Flandoli, Attractors for random dynamical systems,, Probab. Theory Related Fields, 100 (1994), 365. doi: 10.1007/BF01193705. [5] H. Crauel, "Random Probability Measures on Polish Spaces,", Stochastics Monographs, 11 (2002). [6] J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors,, Rev. Modern Phys., 57 (1985), 617. doi: 10.1103/RevModPhys.57.617. [7] G. Froyland, S. Lloyd and A. Quas, Coherent structures and isolated spectrum for Perron-Frobenius cocycles,, Ergodic Theory Dynam. Systems, 30 (2010), 729. doi: 10.1017/S0143385709000339. [8] A. Katok and J.-M. Strelcyn, "Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities,", with the collab. of F. Ledrappier and F. Przytycki, 1222 (1986). [9] F. Ledrappier, Propriétés ergodiques des mesures de Sinaï, (French) [Ergodic properties of Sinaï measures],, Inst. Hautes Études Sci. Publ. Math., (1984), 163. [10] F. Ledrappier and J.-M. Strelcyn, A proof of the estimation from below in Pesin's entropy formula,, Ergodic Theory Dynam. Systems, 2 (1982), 203. doi: 10.1017/S0143385700001528. [11] F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math. (2), 122 (1985), 509. [12] F. Ledrappier and L.-S. Young, Entropy formula for random transformations,, Probab. Theory Related Fields, 80 (1988), 217. doi: 10.1007/BF00356103. [13] Z.-M. Li and L. Shu, The metric entropy of random dynamical systems in a Banach space: Ruelle inequality,, to appear in Ergodic Theory Dynam. Systems., (). [14] Z. Lian and K.-N. Lu, "Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space,", Memoirs of AMS, (2009). [15] P.-D. Liu and M. Qian, "Smooth Ergodic Theory of Random Dynamical Systems,", Lecture Notes in Mathematics, 1606 (1995). [16] P.-D. Liu, Pesin's entropy formula for endomorphisms,, Nagoya Math. J., 150 (1998), 197. [17] R. Mañé, A proof of Pesin's formula,, Ergodic Theory Dynam. Systems, 1 (1981), 95. [18] R. Mañé, Lyapounov exponents and stable manifolds for compact transformations,, in, 1007 (1983), 522. doi: 10.1007/BFb0061433. [19] V.-I. Oseledeč, A multiplicative ergodic theorem. Characteristic Lyapunov numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 197. [20] R.-R. Phelps, "Lectures on Choquet's Theorem,", D. Van Nostrand Co., (1966). [21] M. Qian and Z. S. Zhang, Ergodic theory for Axiom A endomorphisms,, Ergodic Theory Dynam. Systems, 15 (1995), 161. doi: 10.1017/S0143385700008294. [22] M. Qian and S. Zhu, SRB measures and Pesin's entropy formula for endomorphisms,, Trans. Amer. Math. Soc., 354 (2002), 1453. doi: 10.1090/S0002-9947-01-02792-1. [23] D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space,, Ann. of Math. (2), 115 (1982), 243. doi: 10.2307/1971392. [24] D. Ruelle, Characteristic exponents for a viscous fluid subjected to time dependent forces,, Comm. Math. Phys., 93 (1984), 285. [25] K.-U. Schaumlöffel, "Zufällige Evolutionsoperatoren Für Stochastische Partielle Differentialgleichungen,", Dissertation, (1990). [26] K.-U. Schaumlöffel and F. Flandoli, A multiplicative ergodic theorem with applications to a first order stochastic hyperbolic equation in a bounded domain,, Stochastics Stochastics Rep., 34 (1991), 241. [27] P. Thieullen, Fibrés dynamiques asymptotiquement compacts. Exposants de Lyapounov. Entropie. Dimension, (French) [Asymptotically compact dynamic bundles. Lyapunov exponents. Entropy. Dimension],, Ann. Inst. H. Poincaré Anal. Non Linéaire, 4 (1987), 49. [28] P. Thieullen, Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems,, J. Dynam. Differential Equations, 4 (1992), 127. doi: 10.1007/BF01048158. [29] P. Thieullen, Fibres dynamiques. Entropie et dimension, (French) [Dynamical bundles. Entropy and dimension],, Ann. Inst. H. Poincaré Anal. Non Linéaire, 9 (1992), 119. [30] P. Walters, "An Introduction to Ergodic Theory,", Graduate Texts in Mathematics, 79 (1982).
show all references
##### References:
[1] L. Arnold, "Random Dynamical Systems,", Springer Monographs in Mathematics, (1998). [2] J. Bahnmüller and P.-D. Liu, Characterization of measures satisfying the Pesin entropy formula for random dynamical systems,, J. Dynam. Differential Equations, 10 (1998), 425. doi: 10.1023/A:1022653229891. [3] T. Bogenschütz, Entropy, pressure, and a variational principle for random dynamical systems,, Random Comput. Dynam., 1 (): 99. [4] H. Crauel and F. Flandoli, Attractors for random dynamical systems,, Probab. Theory Related Fields, 100 (1994), 365. doi: 10.1007/BF01193705. [5] H. Crauel, "Random Probability Measures on Polish Spaces,", Stochastics Monographs, 11 (2002). [6] J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors,, Rev. Modern Phys., 57 (1985), 617. doi: 10.1103/RevModPhys.57.617. [7] G. Froyland, S. Lloyd and A. Quas, Coherent structures and isolated spectrum for Perron-Frobenius cocycles,, Ergodic Theory Dynam. Systems, 30 (2010), 729. doi: 10.1017/S0143385709000339. [8] A. Katok and J.-M. Strelcyn, "Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities,", with the collab. of F. Ledrappier and F. Przytycki, 1222 (1986). [9] F. Ledrappier, Propriétés ergodiques des mesures de Sinaï, (French) [Ergodic properties of Sinaï measures],, Inst. Hautes Études Sci. Publ. Math., (1984), 163. [10] F. Ledrappier and J.-M. Strelcyn, A proof of the estimation from below in Pesin's entropy formula,, Ergodic Theory Dynam. Systems, 2 (1982), 203. doi: 10.1017/S0143385700001528. [11] F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math. (2), 122 (1985), 509. [12] F. Ledrappier and L.-S. Young, Entropy formula for random transformations,, Probab. Theory Related Fields, 80 (1988), 217. doi: 10.1007/BF00356103. [13] Z.-M. Li and L. Shu, The metric entropy of random dynamical systems in a Banach space: Ruelle inequality,, to appear in Ergodic Theory Dynam. Systems., (). [14] Z. Lian and K.-N. Lu, "Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space,", Memoirs of AMS, (2009). [15] P.-D. Liu and M. Qian, "Smooth Ergodic Theory of Random Dynamical Systems,", Lecture Notes in Mathematics, 1606 (1995). [16] P.-D. Liu, Pesin's entropy formula for endomorphisms,, Nagoya Math. J., 150 (1998), 197. [17] R. Mañé, A proof of Pesin's formula,, Ergodic Theory Dynam. Systems, 1 (1981), 95. [18] R. Mañé, Lyapounov exponents and stable manifolds for compact transformations,, in, 1007 (1983), 522. doi: 10.1007/BFb0061433. [19] V.-I. Oseledeč, A multiplicative ergodic theorem. Characteristic Lyapunov numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 197. [20] R.-R. Phelps, "Lectures on Choquet's Theorem,", D. Van Nostrand Co., (1966). [21] M. Qian and Z. S. Zhang, Ergodic theory for Axiom A endomorphisms,, Ergodic Theory Dynam. Systems, 15 (1995), 161. doi: 10.1017/S0143385700008294. [22] M. Qian and S. Zhu, SRB measures and Pesin's entropy formula for endomorphisms,, Trans. Amer. Math. Soc., 354 (2002), 1453. doi: 10.1090/S0002-9947-01-02792-1. [23] D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space,, Ann. of Math. (2), 115 (1982), 243. doi: 10.2307/1971392. [24] D. Ruelle, Characteristic exponents for a viscous fluid subjected to time dependent forces,, Comm. Math. Phys., 93 (1984), 285. [25] K.-U. Schaumlöffel, "Zufällige Evolutionsoperatoren Für Stochastische Partielle Differentialgleichungen,", Dissertation, (1990). [26] K.-U. Schaumlöffel and F. Flandoli, A multiplicative ergodic theorem with applications to a first order stochastic hyperbolic equation in a bounded domain,, Stochastics Stochastics Rep., 34 (1991), 241. [27] P. Thieullen, Fibrés dynamiques asymptotiquement compacts. Exposants de Lyapounov. Entropie. Dimension, (French) [Asymptotically compact dynamic bundles. Lyapunov exponents. Entropy. Dimension],, Ann. Inst. H. Poincaré Anal. Non Linéaire, 4 (1987), 49. [28] P. Thieullen, Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems,, J. Dynam. Differential Equations, 4 (1992), 127. doi: 10.1007/BF01048158. [29] P. Thieullen, Fibres dynamiques. Entropie et dimension, (French) [Dynamical bundles. Entropy and dimension],, Ann. Inst. H. Poincaré Anal. Non Linéaire, 9 (1992), 119. [30] P. Walters, "An Introduction to Ergodic Theory,", Graduate Texts in Mathematics, 79 (1982).
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2017 Impact Factor: 1.179 | {"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": 0.8077210187911987, "perplexity": 6541.224378546686}, "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/1560627998605.33/warc/CC-MAIN-20190618023245-20190618045245-00294.warc.gz"} |
http://www.severnsolutions.co.uk/twblog/category/osx_1/ | 1
1 - 4 [4]
## Automating X11 Rootless Mode
Also relates to OSX
Many of the applications I use on a daily basis come from the KDE toolkit or other X11 software most notably Konqueror, eSVN, Kompare, Karm, XEmacs and (of course) Amarok. If I am working extensively with KDE apps I will load up the K Desktop Environment as my window manager in full screen mode. However, sometimes I find I want to share X11 and native OS X applications. It is a little frustrating having to keep changing the initialisation file for X11 and switch to rootless mode in the Preferences pane. So I decided to concote a script to do this automatically.
By default my .xinitrc file will start up KDE with:
startkde >/tmp/kde.log 2>&1
Then I also have a start up file for the quartz window manager (.xinitrc.quartz) with:
exec quartz-wm
Then the startup script for X11 applications (based on the Xdroplets scripts) looks to see if X11 is already running by searching for display lock files in the tmp dir. If it is not another script is called which switches X11 to rootless mode and boots it with the Quartz window manager initialisation file. This allows me to start up X11 using its application link if I want to use KDE or to just open an X11 application if I want it to run in rootless mode seamlessly with native OSX applications.
The main challenge with achieveing this is switching the preference since this is stored in a binary plist file (~/Library/Preferences/com.apple.x11.plist). Fortunately the property list utility (plutil command) makes this task relatively simple:
if [ ! -z $1 ] && [$1 == 'false' ] ; then
pattern='s/true/false/'
else
pattern='s/false/true/'
fi
plutil -convert xml1 -o /tmp/com.apple.x11.plist ~/Library/Preferences/com.apple.x11.plist
sed "/rootless/{ n; $pattern; }" /tmp/com.apple.x11.plist > /tmp/com.apple.x11-new.plist plutil -convert binary1 -o ~/Library/Preferences/com.apple.x11.plist /tmp/com.apple.x11-new.plist \rm /tmp/com.apple.x11{,-new}.plist The property list utility converts the binary file to XML so that sed can then replace the state of the rootless property. So now I can open an X11 app or two without having to either boot a KDE session or reconfigure my .xinitrc or X11 preferences. ## Plastic Fantastic KDE Also relates to Browsers Last week I finally installed Tiger and at the same time set up a dedicated partition for Fink to simplify future upgrades in the absence of extensive backup media. The disadvantage of this decision was that I could no longer use the default /sw directory for Fink package management - well by mounting the directory onto the partition I probably could (a course of action I choose for the OS X Users directory on a third partition) but I also wanted to store other open source material in the partition so the /sw directory would not be at the root level. This did not present any major problems other than the fact I would be restricted to only building source from the Fink tree. Just calls for a little patience - and the occassional piece of detective work! Unfortunately progress was slow when I initially choose to build QCad being half way through a scale drawing of my soon to materialise new home - probably one of the few programs acknowledged to be incompatible with Tiger's GCC version 4. Still following a trip to a colleague's broadband fitted office I had the source for bundle-gnome and bundle-kde waiting to go. The plan was to leave them alone for a while and try and settle on a comfortable working environment in Tiger, but finally having the mammoth tetex source files that would allow me to build the monopd server was just too tempting. Of course I didn't consider at the time this would also mean building the entire KDE-games package which in turn would mean building the KDE-base package. So around about 6 hours later (not bad for my lowly iBook!) I had the core KDE 3.4 ready to go as a full-screen replacement for Apple's rootless quartz window manager. At first I disregarded this as I had not found the binary KDE 3.1 build that inspiring on Panther, and had generally stuck with Gnome or WindowMaker if I wanted to use a full screen window manager for X11. But the Plastik theme and the countless number of improvements over 3.1 are simply delectable! Performance is excellent on Tiger and other than the erratic sound behaviour and current absence of several office applications I can see this becoming a regular set up. Most noticeable, and pleasing, is the vast improvement in the CSS and script support of the Konqueror browser which now, among other odds and ends, handles my CSS negative margins experiment from last year perfectly. Ok, its not quite pure Linux (yet) but this laptop never ceases to amaze me! Posted on Jul 19, 2005 at 02:26:12. ## PHP Function Lookup from XEmacs Also relates to PHP and Apache, IDEs Ok, I have gone all XEmacs, and am really impressed. For the best part of two years now I have been using UltraEdit for must web scripting with a little bit of Eclipse on the side for command line testing with PHP5 development. With a large amount of the development work now migrated to my IBook, it was time to seek out a new editor. Currently I am undecided between Eclipse, BBEdit, Vim, Quanta, Kate and XEmacs, although I am very drawn to the latter. Despite the learning curve, with a bit of Lisp knowledge in hand, the power of XEmacs quickly becomes apparent. Of course an essential feature for any scripting language is syntax highlighting and efficient function lookup. The first is easy enough - add the prog-modes package (which includes an Emacs lisp file for PHP major mode) and all other dependant packages from the package manager. I also enabled syntax highlighting by default in ~/.xemcas/init.el with: (require 'font-lock) While perusing the settings for PHP mode from the Options menu (and directly from the package file prog-modes/php-mode.el) I discovered that the key command sequence Ctrl C Ctrl F performs a search for the function currently selected at php.net. This was a problem since the machine is not going to be on a permanant connection. So, I decided to store the PHP Documentation on my local server. Nothing out of the ordinary, except it give me the opportunity to use the RewriteMap directive in the Apache configuration. 1. Grab the multi-file PHP documentation from php.net. And extract all files to a suitable location on disc (note there are over two thousand separate HTML files and they will all be extracted to same directory, so make sure it is the right place!) 2. Create a name-based virtual server to access the documentation locally by first adding a new machine name (eg phpdocumentation) to the Netinfo Database in OSX. 3. Add a virtual server entry to the httpd configuration file. I currently have the system configured to reboot Apache with a different principle conf file for each PHP version - as with my Window 98 box - so I put virtual server directives in one of the user conf files (from /etc/httpd/users) instead. <VirtualHost 127.0.0.1> ServerName phpdocumentation # Rewrite Directives will go here… DocumentRoot "/path/to/php/documentation/dir" <Directory "/path/to/php/documentation/dir"> AllowOverride All Options +FollowSymLinks </Directory> </VirtualHost> 4. Now, instead of hacking the Lisp code in php-mode.el, which could readily be destroyed by a future update of prog-modes, I decided to throw in a rewrite rule to fix the request URI. From XEmacs the request would be for http://phpdocumentation/function_name, so the following might work: RewriteEngine On RewriteRule ^([-_a-z0-9])$ /function.$1.html Sadly not! All function help files take the form function.[the-function-name].html. And that is where I hit the stumbling block! Underscores are replaced by hyphens in the HTML file names for functions. I was reluctant to resort to Lisp hacking, so decided to try one of the rewrite directives I have had little use for previously - RewriteMap. 1. Create an executable script that can be called in the rewriting process to replace the underscores. I choose Perl and, due the simplicity of the rewrite, only needed one more line of code than the actual Apache manual: #!/usr/bin/perl # php-func-map.pl # avoid buffered I/O$| = 1;
while (<STDIN>) {
# globally change the underscore to a hyphen
s/_/-/g;
print $_; } 2. Then set up the rewriting directives - for RewriteMap these have to go under the VirtualHost directive in the conf rather than in .htaccess file. RewriteEngine On RewriteMap php-func-map prg:/path/to/php-func-map.pl RewriteRule /([-_a-z0-9]+)$ /function.${php-func-map:$1}.html
And that is that. The magic is in ${php-func-map:$1} which will pass the pattern match \$1 to the file defined by php-func-map and get back a PHP manual friendly file name. Of course this could be extended further to perform searches beyond just the manual's function set but servers my purpose well for the time being. So, now when I forget if the needle or the haystack goes first, a quick key combination and the manual entry is available.
## AWOL Explained
Also relates to OSX
This is just a quick summary really, and if I can find time to drag myself away from the captivating transit of Io in my RXVT shell - courtesy of Xplanet - I will post some extended blogs on my first experiences and the tools that assisted me in getting my Ibook development ready.
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http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_multinormal_distri.htm | Multivariate normal distribution
We suggest that you first report to the entry about the bivariate normal distribution.
-----
The multivariate normal distribution (or "multinormal distribution") is the most important multidimensional distribution. It is common for real world data to be at least approximately multinormally distributed, and some techniques like Discriminant Analysis explicitely make this assumption.
# Definition of the multivariate normal distribution
Our goal is to generalize the ordinary (univariate) normal distribution to random vectors. This can be done in several different ways.
## The wrong way
We first insist on what the multivariate normal distribution is not.
A natural idea would be to "define" the multivariate normal distribution as a distribution whose marginals are all normal. But we know that there exist bivariate distributions whose marginals are normal, and yet that are not binormal.
We therefore have to forego this erroneous approach.
## The bivariate normal distribution
We defined the bivariate normal distribution by introducing an adjustable correlation coefficient between its two normal marginals.
Generalizing this approach to more than two variates is cumbersome, and will not be pursued.
## Linear combinations of the marginals
It is possible to define the multivariate normal distribution as a distribution such that any linear combination of its marginals is (univariate) normal.
We will not use this definition, but we'll show that this result is indeed a characteristic property of the multivariate normal distribution.
## Transformation of the standard spherical multinormal distribution
The standard spherical multivariate normal distribution is defined as the joint distribution of p independent univariate standard normal variables.
The (general) multivariate normal distribution may be defined as the transform of this standard spherical distribution under any regular linear transformation.
## Formal generalization of the univariate normal distribution
In this Glossary, we define the multivariate normal distribution by the analytical form of its probability density, that we'll choose to be a formal generalization of the univariate case.
Recall that the normal distribution is :
f(x) = k.exp[-1/2.a(x - b)²]
where k and a are appropriate coefficients (see here).
This expression is generalized to the multidimensional case as follows :
* The variable x is replaced by the vector x = {x1, x2, ..., xp} with p components.
* The normalization coefficient k is replaced by the coefficient K whose role is also to make the integral of the density equal to 1.
* The term a(x - b)² is replaced by a quadratic form in (x - b) :
(x - b)A(x - b)'
where b is a vector.
In the univariate case, we have a = 1/², which is always positive. By analogy, we impose to the matrix A to be symmetric positive definite, a property that generalizes the notion of "positiveness" to matrices.
-----
So, by definition, the distribution of the random vector X = {X1, X2, ..., Xp} is said to be a multivariate normal distribution if its probability density is :
f(x) = K.exp[-1/2.(x - b)A(x - b)']
with A a symmetric positive definite matrix.
# Basic properties of the multivariate normal distribution
In the Tutorial below, we'll establish the following results :
## Normalization coefficient
Recall that the normalisation coefficient of the (univariate) normal distribution is :
We'll show that the normalisation coefficient of the multivariate normal distribution is :
where "det" stands for "determinant".
## Mean
Recall that the mean µ of the (univariate) normal distribution is equal to b.
We'll establish that the mean vector of the multivariate normal distribution is equal to the vector b.
E[X] = b
Therefore, we'll later on replace b by µ.
## Covariance matrix
In the univariate case, we have :
a = 1/²
and we'll show that in the multivariate case, we have :
A = -1
where is the covariance matrix of X.
## Final form
Bringing these these results together, we'll obtain the following final result :
The density of a multivariate normal vector is : f(x) = (2)- p / 2.[det(-1)]-1/2 .exp[-1/2.(x - µ)-1(x - µ)']
that will be denoted N(µ, ) by analogy with the notation N(µ, ²) used for the univariate normal distribution.
-----
So there's a perfect analogy with the univariate case, with the covariance matrix playing now the role that ² was playing for the univariate case.
Of course, this expression reduces to the ordinary normal distribution when the "vector" X is reduced to a single component.
# Marginal distributions of the multivariate normal distribution
Let X = {X1, X2, ..., Xp} be a random vector.
A marginal distribution of X is the joint distribution of any subset of the variables (X1, X2, ..., Xp). So there are as many marginal distributions as there are such subsets, that is 2 p - 2 (ignoring the empty and the complete subsets of variables).
The following illustration shows the two marginal distributions of a bivariate normal distribution :
We'll show that the marginal distributions of the multivariate normal distribution are also multinormal, a fundamental result.
Let X = {X1, X2, ..., Xp} be a p-dimensional multinormal vector, and consider the vector X1 made up of the first k components of X :
X1 = {X1, X2, ..., Xk} k < p
The p components of X can always be indexed in such a way that any subset of k components is made to be the subset of the first k components.
Then :
* The distribution of X1 is a multivariate normal distribution. * The k components of the mean vector of this distribution are the means of the k variables Xi. * Its covariance matrix (of order k) is made up of the pairwise covariances of the k variables Xi.
This illustration represents the covariance matrix of X :
The covariance matrix X1 of X1 is just the upper left corner square submatrix of order k of X (lower image of the illustration).
This submatrix is traditionally denoted 11.
-----
When k = 1, this result shows that the individual components Xi of X = {X1, X2, ..., Xp} are (univariate) normal variables.
# Conditional distributions of the multivariate normal distribution
Let X = {X1, X2, ..., Xp} be a random vector.
A "conditional distribution" of X is the joint distribution of any subset of of the variables (X1, X2, ..., Xp) when the other variables are held fixed. In other words, it is the normalized profile of a "cut" through the distribution of X made by a hyperplane defined by the (fixed) values assigned to the other variables. So there are as many marginal distributions as there are such subsets, that is 2 p - 2 (ignoring the empty and the complete subsets of variables).
This illustration shows one of the two conditional distributions of a bivariate normal distribution.
Let X = {X1, X2, ..., Xp} be a multinormal vector, that we partition into two sub-vectors :
X = (X1, X2 )
We'll show that the distribution of X1 conditionally to X2 is multinormal, a fundamental property.
In addition, we'll show the two following important properties :
* The mean vector of this condtional distribution depends linearly on X2. * The covariance matrix of this conditional distribution does not depend on X2.
This last point means that if a cutting hyperplane is translated parallel to itself, all the cuts it generates have the same covariance matrix.
# Multivariate normal distribution and Regression
We now consider the multinormal distribution from the point of view of using X2 for predicting X1.
Identifying the conditional distributions of the multivariate normal distribution, and in particular the expectation of X1 conditionally to the value of X2 allows considering the multivariate normal distribution as a linear model of regression.
For example, this figure illustrates the prediction of the vector X1 = (u, v) by the unique quantity X2 = (w).
This illustration is reproduced and commented more thoroughly in the Tutorial below.
This model exhibits strong similarities with the standard model of Multiple Linear Regression (MLR) :
* The expectation of the response variable is a linear function of the predictors.
* The residuals are normal an uncorrelated,
but with also two important differences :
* In MLR, the predictors are considered as fixed, and therefore are not random variables, whereas X2 is here a random vector.
* MLR tries to predict the value of a unique response variable y, whereas the response variable is here a vector (a group of variables).
We'll show that the model based on the conditional distributions of the multivariate normal distribution is better than any other linear model X1 = f(X2 ) in two respects :
* It minimizes the Mean Square Error (MSE) between predictions and observations.
* It maximizes the correlation coefficient between each of the variables and any linear combination of the other variables used for predicting the value of this variable. This coefficient is called the Multiple Correlation Coefficient attached to the variable, and we'll calculate its value.
# Moment generating function of the multivariate normal distribution
Let X ~ N(µ, ).
We'll show that its m.g.f. MX(t) is :
MX(t) = exp{t'µ + 1/2.t't}
where t is a vector parameter.
We'll then use this result for demonstrating again and generalize some of the previous results, and also establish a useful characteristic property of the multivariate normal distribution.
# Quadratic forms in multivariate normal variables
Statistics is often facing quadratic forms is multivariate normal variables, in particular :
* In Analysis of Variance (ANOVA),
Under certain conditions that are detailed here, these quadratic forms follow (exactly) a Chi-square distribution.
-----
The squared Mahalanobis distance is a quadratic form which follows a Chi-square distribution when the variable is a multinormal vector.
# Simulation of a multinormal random vector
We explain here how the association of the Box-Muller transform and the Mahalanobis transformation can be used for simulating an arbitrary multivariate normal distribution.
___________________________________________________________________________
Tutorial 1
We first show that an appropriate linear transformation transforms the general multivariate normal distribution into the simplest possible multivariate normal distribution : the standard spherical normal distribution, which is defined as the joint distribution of p independent standard normal variables (lower image of this illustration).
This transformation is useful in many circumstances, as it allows to carry problems about the general multivariate normal distribution over to this particularly simple distribution.
-----
From this result, we'll derive :
* The value of the normalization coefficient K,
* And the mean µ,
of the multivariate normal distribution.
We'll then calculate the covariance matrix of the multivariate normal distribution, and show that it is equal to A-1, a fundamental result.
THE MULTIVARIATE NORMAL DISTRIBUTION
Spherization of the multivariate normal distribution Reduction of a positive definite matrix to the identity matrix Spherization The transformation The Jacobian The standard spherical normal distribution Normalization coefficient of the multivariate normal distribution Mean of the multivariate normal distribution Covariance matrix of the multivariate normal distribution Complete form of the multivariate normal distribution TUTORIAL
__________________________________________________________________
Tutorial 2
In this Tutorial, we show that the marginal distributions of the normal multivariate distribution are also multinormal, and we calculate their parameters.
There exist several ways to establish this important result, of which we give three.
1) We first use a very orthodox method, a bit lengthy but that stays close to intuition and delivers the additional important result that uncorrelated marginals are necessarily independent.
- We first show that a regular linear transformation changes a multinormal distribution into another multinormal distribution, whose parameters we'll calculate. This lemma is useful in just about any circumstance involving multivariate normal distributions.
- We then address the special case where every component Xi (i k) of X1 = {X1, X2, ..., Xk} is uncorrelated with any component Xj ( j > k) of
X2 = {Xk + 1, X k + 2, ..., Xp}. We then show that the distribution of the marginal X1 is multinormal (with of course a similar result for X2 ).
In passing, we'll also show that this lack of correlation between Xi and Xj is in fact genuine independence.
- We finally address the general problem where no assumption whatever is made about the correlation between the components of X. We'll show that it is still true that the marginals X1 and X2 are multinormally distributed by identifying an appropriate transformation that will transform the original distribution into a new distribution for which the two marginals are uncorrelated. We'll then be able to deduce the multinormality of the marginals of the original distribution.
2) We then give a second demonstration that uses the above mentioned lemma to short-circuit all algebraic developments. It delivers the result in just a few lines, and is an illustration of the power of Linear Algebra at the expense of intuition.
3) Finally, we'll use the the moment generating function of the multivariate normal distribution to again establish this result in a simple and elegant manner (see below).
MARGINALS ARE MULTINORMAL
UNCORRELATED MARGINALS ARE INDEPENDENT
Linear transform of a multinormal vector Transform of the quadratic form The Jacobian The distribution of the transform is multinormal Special case : the two groups of variables are uncorrelated Partitioning the covariance matrix Partitioning the quadratic form The marginals are multinormal Lack of correlation implies independence General case Transformation of the original distribution The marginals of the transformed distribution are multinormal The marginals of the original distribution are multinormal Second demonstration TUTORIAL
_______________________________________________________________
Tutorial 3
We now calculate the conditional distributions of the multivariate normal distribution.
The most straightforward method would be to call on the fundamental property of conditional distributions, which states that a conditional distribution is equal to :
* The joint distribution of the complete set of variables,
* Divided by the joint distribution of the conditioning variables.
In this particular case, this approach leads to fairly cumbersome calculations, and we'll find it more convenient to first transform the original distribution into a new distribution that can be conveniently factored. The inverse transformation will then allow us to write the original distribution is a form that will make calculating the conditional distributions very simple.
-----
We'll then remark that :
1) A conditional distribution of a multivariate normal distribution is multinormal.
2) Its mean vector depends linearly on the conditioning vector.
3) Its covariance matrix does not depend on the value assigned to the conditioning vector.
CONDITIONAL DISTRIBUTIONS
OF THE MULTIVARIATE NORMAL DISTRIBUTION
Factorization of the joint distribution Transformation of the joint distribution Definition of the transformation Mean vector Covariance matrix Factorization of the transformed distibution Factorization of the original distibution Conditional distributions of the multivariate normal distribution The conditional distributions are multinormal The mean vector depends linearly on the conditioning vector The covariance matrix does not depend on the conditioning vector TUTORIAL
_______________________________________________________________
Tutorial 4
In this Tutorial, we look at the multinormal vector X = (X1, X2 ) from the point of view of using X2 for predicting X1.
Identifying the conditional distributions of the multivariate normal distribution, and in particular the expectation of X1 conditionally to the value of X2 allows considering the multivariate normal distribution as a linear model of regression.
-----
We will show that this model is better than any other linear model in at least two respects :
* It minimizes the Mean Square Error (MSE) between predictions and observations.
* It maximizes the correlation coefficient between each of the variables and any linear combination of the other variables used for predicting the value of this variable. This coefficient is called the Multiple Correlation Coefficient attached to the variable, and we'll calculate its value.
MINIMIZATION OF THE PREDICTION MEAN SQUARED ERRORS
MAXIMIZATION OF THE MULTIPLE CORRELATION COEFFICIENT
Residuals Residual vector Predictor and residual are uncorrelated Minimization of the prediction Mean Squared Errors Multiple correlation coefficient Correlation between observations and predictions, multiple correlation The conditional expectation model maximizes the multiple correlation coefficient Value of the multiple correlation coefficient TUTORIAL
________________________________________________________________________
Tutorial 5
We now calculate the moment generating function M(t) of the multivariate normal distribution. Because this distribution is multivariate, the parameter t is a vector, but the function itself is scalar.
As is often the case, the m.g.f. turns out to be a very convenient and powerful tool for establishing all sorts of results about a distribution, sometimes in a concise and elegant manner. We'll go over some of results that we already obtained somewhat laboriously using Linear Algebra, and show how they can also be obtained by using the m.g.f.. In particular, we'll generalize the result about linear transforms of a multinormal vector to the case where :
* The matrix of the transformation is square, but singular.
* The matrix of the transformation is rectangular.
We'll also show that a characteristic property of the multinormal distribution is that any linear combination of its components is (univariate) normal. Recall that this property is sometimes used as the definition of the multivariate normal distribution.
MOMENT GENERATING FUNCTION
OF THE MULTIVARIATE NORMAL DISTRIBUTION
Moment generating function of the multivariate normal distribution Special case : the spherical standard multinormal distribution The general case Some immediate consequences of the Moment Generating Function General linear transform of a multinormal vector is multinormal Marginals are multinormal Uncorrelation implies independence A vector is multinormal iff all linear combinations of its components are normal TUTORIAL
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition/chapter-5-trigonometric-functions-5-1-angles-5-1-exercises-page-504/31 | ## Precalculus (6th Edition)
$(9x+6)^\circ=69^\circ$ $(3x)^\circ=21^\circ$
If two angles are complementary, the sum of the two angles is a right angle ($90^\circ$): $(9x+6)^\circ+(3x)^\circ=(12x+6)^\circ=90^\circ$ $12x+6=90$ $12x=84$ $x=7$ $(9x+6)^\circ=69^\circ$ $(3x)^\circ=21^\circ$ | {"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": 0.7809131741523743, "perplexity": 492.82927516612693}, "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-2018-30/segments/1531676596463.91/warc/CC-MAIN-20180723125929-20180723145929-00122.warc.gz"} |
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Minimizing broadband excitation under dissipative conditions
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10.1063/1.2136155
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Affiliations:
1 Department of Physical Chemistry and the Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91904, Israel
a) Electronic mail: [email protected]
J. Chem. Phys. 123, 234506 (2005)
/content/aip/journal/jcp/123/23/10.1063/1.2136155
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/23/10.1063/1.2136155
View: Figures
## Figures
FIG. 1.
The pulse intensity spectrum along with absorption (solid line) and fluorescence (dashed line) spectra of LDS750 molecule in acetonitrile. Adapted from Ref. 2.
FIG. 2.
Excited-state population as a function of the linear chirp for the isolated system . The population is shown at the end of the pulse for the high (solid line) and the low (dashed line) fluences. The duration of the corresponding transform-limited pulse is . Note the different scale for the excited population for two energy regimes.
FIG. 3.
(Top panel) Time evolution of the excited-state population of the isolated system for the high-energy excitation. The population is calculated for a negatively [, solid line] and a positively [, dashed line] chirped pulses. (Bottom panel) The imaginary part of the transition dipole moment multiplied by the field amplitude.
FIG. 4.
(Color online) (Top panel) Trajectories of the transition dipole moment renormalized by its maximal amplitude for excitation by the linear negatively chirped pulse . (Bottom panel) Excited-state population at the end of the pulse as a function of the linear chirp parameter . The calculations are performed for the system without dissipation (solid line) and for the system with vibrational relaxation with weak (, dashed line), medium (, dashed-dotted line), and strong (, dotted line) system-bath couplings.
FIG. 5.
(Color online) (Top panel) Trajectories of the transition dipole moment renormalized by its maximal amplitude for excitation by the linear negatively chirped pulse . (Bottom panel) Excited-state population at the end of the pulse as a function of the linear chirp parameter . The calculations are performed for the isolated system (solid line) and for the system with pure electronic dephasing: weak (, dashed line), medium (, dashed-dotted line) and strong (, dotted line) couplings.
FIG. 6.
Time evolution of the excited-state population of the isolated system for the high-energy excitation. The population is calculated for a linear negatively chirped pulse (solid line) and for the optimal pulse (dashed line) obtained by using a genetic algorithm with the random phases, generated at discrete points of the frequency spectrum. The inset figure shows the temporal profile of the optimized pulse.
FIG. 7.
(Color) Calculations for nondissipative system. Time-frequency Wigner distribution corresponding to the optimized linear (top panel) and nonlinear (bottom panel) chirped pulses. The right sides show the frequency spectra of the pulses, while their temporal profiles are shown in the upper panels. The phase is expanded in the Taylor series up to the second order (linear chirp) and in the basis of periodic functions (nonlinear chirp).
FIG. 8.
(Top panel) Evolution of the excited-state population of the isolated system for the high-energy excitation. The population is calculated for a linear negatively chirped pulse (solid line) and for the optimal pulse (dashed line) obtained by using a genetic algorithm with the phase expanded in the basis of periodic functions. (Bottom panel) Trajectories of the transition dipole moment renormalized by its maximal amplitude. Solid and dashed lines refer to the linear chirped pulse and its nonlinear analog, respectively.
FIG. 9.
(Top panel) Time evolution of the excited-state population of the dissipative system for the high-energy excitation. The population is calculated for a linear negatively chirped pulse (solid line) and for the optimal pulse obtained by using a genetic algorithm (dashed line). (Bottom panel) Trajectories of the transition dipole moment renormalized by its maximal amplitude. Calculations were performed for the system with weak vibrational relaxation and medium pure electronic dephasing .
FIG. 10.
(Color) Calculations for the dissipative system. Time-frequency Wigner distribution corresponding to the optimal linear (top panel) and nonlinear (bottom panel) chirped pulses. Calculations were performed for the system with medium vibrational relaxation and electronic dephasing .
FIG. 11.
(Color) (Top panel) Time evolution of the excited-state population of the dissipative system for the high-energy excitation. The population is calculated for a linear negatively chirped pulse (solid line) and for the optimal pulse obtained by using a genetic algorithm (dashed line). (Bottom panel) Time-frequency Wigner distribution corresponding to the optimized nonlinear chirped pulse. The calculations were performed for the primary system with the following parameters: the ground-state and the excited-state frequencies and the dimensionless displacement of . The right sides show the frequency spectra of the pulses, while their temporal profiles are shown in the upper panels. The phase is expanded in the basis of periodic functions.
FIG. 12.
Effect of the intensity for linearly chirped pulses. The value of the linear chirp is plotted as a function of the pulse fluence (the amplitude of the corresponding transform-limited pulse). Calculations were performed for the isolated system (squares) and as well as for a dissipative system (triangles) with f medium vibrational relaxation and medium pure electronic dephasing .
FIG. 13.
The excited-state population at the end of the pulse as function of the pulse fluence (the amplitude of the corresponding transform-limited pulse). Calculations were performed (top panel) for the system without dissipation and (bottom panel) for the system with medium vibrational relaxation ) and medium pure electronic dephasing . The arrow points to the maximal fluence used in the experiment by Nahmias et al. (Ref. 2)
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https://quant.stackexchange.com/questions/41795/a-question-about-stationarity-and-ergodicity | # A question about stationarity and ergodicity
Given daily returns of a stock index over 50+ years, a homework question asks:
Plot the annual sample mean and variances of the returns and their absolute values. Are these estimates in agreement with the assumption of an ergodic time series?
Having done so, I am unsure how to proceed. How do I judge whether my time series are ergodic based on the annual sample mean and variances of returns and their absolute values?
That seems like a strange question given the complicated definition of what it means to be ergodic. I know that a time series is ergodic if all "nice" functions of the time series satisfy the strong law of large numbers. How in the world would I be able to judge that by the plots I made?
• Look at the variance of return during recession years (1960,1970,1974-1975,1980,1990,2001,2008-2009). Are these the same as in the other years? What do you conclude about the hypothesis that variance is constant over time (stationary)? – noob2 Sep 18 '18 at 15:58
• I know how to judge stationarity, it's the ergodicity that has me confused. – Dasum Sep 18 '18 at 16:43
• @noob2 Different conditional variance during recession years doesn't violate stationarity. I can easily write a stationary, ergodic, Markov regime switching model with two states and different conditional volatility in each state. – Matthew Gunn Sep 18 '18 at 16:56
• Yes. We can reject a model where variance is constant, but we can accept a more complicated model where it varies. The parameters of this model might be stationary. – Alex C Sep 18 '18 at 17:01
If variances are not stationary, this raises the possibility that the process is non-ergodic. However all is not lost, as there are models in which variance can switch between a higher and a lower value according to a random Markov process; if the transition probabilities and $\sigma_H,\sigma_L$ are themselves ergodic (can be estimated from a historical sample) then the process is ergodic. | {"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": 0.7349634170532227, "perplexity": 462.8261089333565}, "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/1581875144979.91/warc/CC-MAIN-20200220131529-20200220161529-00251.warc.gz"} |
http://math.stackexchange.com/questions/296909/the-number-of-ways-of-selecting-n-cards-out-of-unlimited-number-of-cards-beari/296914 | The number of ways of selecting $n$ cards out of unlimited number of cards bearing the number $0,9,3$
If the number of ways of selecting $n$ cards out of unlimited number of cards bearing the number $0,9,3$ so that they can't be used to write the number $903$ is $93$ then $n$ is
-
If you select $n$ cards and you cannot make 903, then you know that those $n$ cards can only be one or two distinct numbers. The number of ways to select $n$ cards that can only be one or two distinct numbers (out of 0, 9, 3) is $$3 + 3(n-1)$$ because there are 3 ways to pick one distinct number ($n$ zeroes, $n$ nines, $n$ threes) and for each pair of numbers are there are $n-1$ ways to pick $n$ cards of those two distinct numbers (pick between 1 and $n-1$ cards of one number, and the rest for the other number).
So you want this quantity to be $93$, which makes $n$ be $31$. | {"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": 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": 0.6923060417175293, "perplexity": 48.69562581049749}, "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-2016-07/segments/1454701154682.35/warc/CC-MAIN-20160205193914-00302-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.aimsciences.org/journal/1551-0018/2015/12/4 | # American Institute of Mathematical Sciences
ISSN:
1551-0018
eISSN:
1547-1063
All Issues
## Mathematical Biosciences & Engineering
2015 , Volume 12 , Issue 4
Special issue dedicated to the 70th birthday of Glenn F. Webb
Select all articles
Export/Reference:
2015, 12(4): i-iv doi: 10.3934/mbe.2015.12.4i +[Abstract](2252) +[PDF](115.3KB)
Abstract:
This special issue is dedicated to the 70th birthday of Glenn F. Webb. The topics of the 12 articles appearing in this special issue include evolutionary dynamics of population growth, spatio-temporal dynamics in reaction-diffusion biological models, transmission dynamics of infectious diseases, modeling of antibiotic-resistant bacteria in hospitals, analysis of Prion models, age-structured models in ecology and epidemiology, modeling of immune response to infections, modeling of cancer growth, etc. These topics partially represent the broad areas of Glenn's research interest.
2015, 12(4): xvii-xxii doi: 10.3934/mbe.2015.12.4xvii +[Abstract](2219) +[PDF](336.7KB)
Abstract:
I began working with Glenn F. Webb in 1997. At that time, I was on the faculty of Vanderbilt University, in the School of Medicine, in the Department of Medicine, in its Division of Infectious Diseases. As with mathematics, modern medicine has its different disciplines (e.g. Surgery and Internal Medicine), and then further subdivisions (e.g. Cardiology and Infectious Diseases). Within Internal Medicine, most of the divisions are based on the treatment of conditions that relate to a single organ or group of organs -- the heart, the lungs, the kidneys, the digestive system. But the discipline of Infectious Diseases was based on a different concept: the war between humans and microbes.
2015, 12(4): v-xvi doi: 10.3934/mbe.2015.12.4v +[Abstract](3068) +[PDF](390.8KB)
Abstract:
It is my distinct pleasure to introduce this volume honoring the 70th birthday of Professor Glenn F. Webb. The existence of this compiled volume is in itself a testimony of Glenn's dedication to, his pursuit of, and his achievement of scientific excellence. As we honor Glenn, we honor what is excellent in our profession. Aristotle clearly articulated his concept of excellence. We are what we repeatedly do. Excellence, then, is not an act, but a habit." As we look over the course of his career we observe ample evidence of Glenn Webb's habitual practice of excellence. Beginning with Glenn's first paper [1], one observes a constant stream of productivity and high impact work. Glenn has authored or co-authored over 160 papers, written one research monograph, and co-edited six volumes. He has delivered plenary lectures, colloquia, and seminars across the globe, and he serves on the editorial boards of 11 archival journals. He is a Fellow of the American Mathematical Society. Glenn's scientific career chronicles an evolution of scientific work that began with his interest in nonlinear semigroup theory and leads up to his current activity in biomedical mathematics. At each stage we see seminal contributions in the areas of nonlinear semigroups, functional differential equations, infinite dimensional dynamical systems, mathematical population dynamics, mathematical biology and biomedical mathematics. Glenn's work is distinguished by a clarity and accessibility of exposition, a precise identification and description of the problem or model under consideration, and thorough referencing. He uses elementary methods whenever possible but couples this with an ability to employ power abstract methods when necessitated by the problem.
2015, 12(4): 643-660 doi: 10.3934/mbe.2015.12.643 +[Abstract](3294) +[PDF](464.5KB)
Abstract:
An evolutionary game theoretic model for a population subject to predation and a strong Allee threshold of extinction is analyzed using, among other methods, Poincaré-Bendixson theory. The model is a nonlinear, plane autonomous system whose state variables are population density and the mean of a phenotypic trait, which is subject to Darwinian evolution, that determines the population's inherent (low density) growth rate (fitness). A trade-off is assumed in that an increase in the inherent growth rate results in a proportional increase in the predator's attack rate. The main results are that orbits equilibrate (there are no cycles or cycle chains of saddles), that the extinction set (or Allee basin) shrinks when evolution occurs, and that the meant trait component of survival equilibria occur at maxima of the inherent growth rate (as a function of the trait).
2015, 12(4): 661-686 doi: 10.3934/mbe.2015.12.661 +[Abstract](3185) +[PDF](474.1KB)
Abstract:
A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
2015, 12(4): 687-697 doi: 10.3934/mbe.2015.12.687 +[Abstract](2193) +[PDF](421.0KB)
Abstract:
In the current study, probit and logistic models were employed to fit experimental mortality data of the Khapra beetle, Trogoderma granarium (Everts) (Coleoptera: Dermestidae), when fumigated with three plant oils of the gens Achillea. A generalized inverse matrix technique was used to estimate the mortality model parameters instead of the usual statistical iterative maximum likelihood estimation. As this technique needs to perturb the observed mortality proportions if the proportions include 0 or 1, the optimal perturbation in terms of minimum least squares ($L_2$) error was also determined. According to our results, it was better to log-transform concentration and time as explanatory variables in modeling mortality of the test insect. Estimated data using the probit model were more accurate in terms of $L_2$ errors, than the logistic one. Results of the predicted mortality revealed also that extending the fumigation period could be an effective control strategy, even, at lower concentrations. Results could help in using a relatively safe and effective strategy for the control of this serious pest using alternative control strategy to reduce the health and environmental drawbacks resulted from the excessive reliance on the broadly toxic chemical pesticides and in order to contribute safeguard world-wide grain supplies.
2015, 12(4): 699-715 doi: 10.3934/mbe.2015.12.699 +[Abstract](2801) +[PDF](2913.5KB)
Abstract:
In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions. Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopf bifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.
2015, 12(4): 717-737 doi: 10.3934/mbe.2015.12.717 +[Abstract](3069) +[PDF](551.1KB)
Abstract:
This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.
2015, 12(4): 739-760 doi: 10.3934/mbe.2015.12.739 +[Abstract](3128) +[PDF](773.3KB)
Abstract:
The fundamental problem of collecting data in the best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical $D$-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.
2015, 12(4): 761-787 doi: 10.3934/mbe.2015.12.761 +[Abstract](2113) +[PDF](2782.2KB)
Abstract:
A model of epidemic bacterial infections in hospitals is developed. The model incorporates the infection of patients and the contamination of healthcare workers due to environmental causes. The model is analyzed with respect to the asymptotic behavior of solutions. The model is interpreted to provide insight for controlling these nosocomial epidemics.
2015, 12(4): 789-801 doi: 10.3934/mbe.2015.12.789 +[Abstract](2578) +[PDF](377.6KB)
Abstract:
We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [11]. The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.
2015, 12(4): 803-840 doi: 10.3934/mbe.2015.12.803 +[Abstract](3497) +[PDF](1952.9KB)
Abstract:
Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation - the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.
2015, 12(4): 841-858 doi: 10.3934/mbe.2015.12.841 +[Abstract](3632) +[PDF](423.8KB)
Abstract:
The past century's description of oncolytic virotherapy as a cancer treatment involving specially-engineered viruses that exploit immune deficiencies to selectively lyse cancer cells is no longer adequate. Some of the most promising therapeutic candidates are now being engineered to produce immunostimulatory factors, such as cytokines and co-stimulatory molecules, which, in addition to viral oncolysis, initiate a cytotoxic immune attack against the tumor.
This study addresses the combined effects of viral oncolysis and T-cell-mediated oncolysis. We employ a mathematical model of virotherapy that induces release of cytokine IL-12 and co-stimulatory molecule 4-1BB ligand. We found that the model closely matches previously published data, and while viral oncolysis is fundamental in reducing tumor burden, increased stimulation of cytotoxic T cells leads to a short-term reduction in tumor size, but a faster relapse.
In addition, we found that combinations of specialist viruses that express either IL-12 or 4-1BBL might initially act more potently against tumors than a generalist virus that simultaneously expresses both, but the advantage is likely not large enough to replace treatment using the generalist virus. Finally, according to our model and its current assumptions, virotherapy appears to be optimizable through targeted design and treatment combinations to substantially improve therapeutic outcomes.
2015, 12(4): 859-877 doi: 10.3934/mbe.2015.12.859 +[Abstract](3558) +[PDF](474.9KB)
Abstract:
In this paper, we study an age-structured virus dynamics model with Beddington-DeAngelis infection function. An explicit formula for the basic reproductive number $\mathcal{R}_{0}$ of the model is obtained. We investigate the global behavior of the model in terms of $\mathcal{R}_{0}$: if $\mathcal{R}_{0}\leq1$, then the infection-free equilibrium is globally asymptotically stable, whereas if $\mathcal{R}_{0}>1$, then the infection equilibrium is globally asymptotically stable. Finally, some special cases, which reduce to some known HIV infection models studied by other researchers, are considered.
2015, 12(4): 879-905 doi: 10.3934/mbe.2015.12.879 +[Abstract](3248) +[PDF](6066.4KB)
Abstract:
Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.
2018 Impact Factor: 1.313 | {"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": 0.7587980628013611, "perplexity": 1398.2824152336996}, "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-2022-27/segments/1656103640328.37/warc/CC-MAIN-20220629150145-20220629180145-00756.warc.gz"} |
https://the-geophysicist.com/new-on-stackexchange-temporal-resolution-of-seismic-data | # New on StackExchange: Temporal Resolution of Seismic data
Radius of the Fresnel zone is given by
$Rf=(v/2)(t_0/f_\mathrm{dom})^{1/2}$
where v: velocity of layer
$t_0$: two way travel time
$f_\mathrm{dom}$ :dominant frequency in the spectrum
This shows that high frequencies give better resolution than lower frequencies and resolution deteriorates with depth and increasing velocities.
However I found some text in “Seismic Data Analysis- Yilmaz” which is contradictory.
“Just having low or high frequencies does not improve temporal resolution. Both low and high frequencies are needed to increase temporal resolution. This is demonstrated further in Figure 1.1-30.”
Could someone explain what the author is trying to say here or am I making a mistake in interpretation somewhere ?
This was a question on StackExchange, see the question here.
In seismic data analysis, we have to distinguish between vertical (temporal) and horizontal resolution.
The (First) Fresnel zone is linked to the vertical resolution and defines the area in which the collected energy will still stack constructively.
The temporal resolution, however, defines what the wave “sees”. The events can still be resolved if their thickness is within a fourth of the wavelength (lambda). However, in some cases it can go down to (lambda / 32). This is a matter of detectability of events.
Don’t forget that we’re dealing with superpositions of different frequencies so basically low frequencies will give use the necessary energy content of general trends while high frequencies enable us to make a distinction between geologic features.
This file from the university of Oslo gives a nice overview.
(The picture is from a blog post I’ve written on knowing your wavelength it’s CC-BY-SA Source1 Source2
from EarthScience Stackexchange
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#### JesperDramsch
... is a geophysicist by heart. I work in seismic interpolation. My interest extend to data security, software engineering, geology and science comm. After work I love to go rock climbing and lift some heavy weights. In the evening I endulge in board games with friends and my wonderful partner. The Way of the geophysicist. | {"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": 3, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7879840135574341, "perplexity": 1671.310627156653}, "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-2018-05/segments/1516084887746.35/warc/CC-MAIN-20180119045937-20180119065937-00236.warc.gz"} |
http://accesssurgery.mhmedical.com/content.aspx?bookid=386§ionid=39944121 | Chapter 74
Eyelid Surface
Eyelid skin is the thinnest in the body with relatively sparse subcutaneous fat. This allows free movement of the lid in closure and blinking. The upper eyelid skin is thinner than that of the lower lid. The skin itself has many fine hairs as well as sebaceous and sweat glands. Healing occurs quickly in this area and scarring is usually minute.
The lid crease of the upper eyelid is formed by the insertion of the levator aponeurosis fibers into the skin and the orbicularis oculi muscle. It is approximately 8–12 mm superior to the lash line and lies just at the level of the upper edge of the tarsal plate. Medially and laterally, the crease is closer to the lid margin and has an arc shape across the lid. The Asian eye usually lacks this crease due to the lower insertion of the levator aponeurosis on the tarsus.
The lid fold describes the tissue above the lid crease and may extend throughout the length of the upper lid or it may be more localized. Excess tissue may develop in the aging face and sag over the lid crease, sometimes obscuring vision. A combination of excess skin, hypertrophied orbicularis oculi muscle, and herniated fat can be responsible for this process.
Orbicularis Oculi Muscle
The orbicularis oculi muscle provides the main mimetic function to the eyelid. It receives its innervation from the temporal and zygomatic branches of the facial nerve. The muscle is elliptical and divided into three bands (the pretarsal, preseptal, and preorbital), which attach to the bony orbit at the medial and lateral canthal tendons. The muscle can become hypertrophied over time and result in a full appearance of the eyelids.
Orbital Fat
Orbital fat cushions the globe and its associated structures, and its anterior limit is the orbital septum. In the upper eyelid, the fat separates the levator aponeurosis posteriorly and the orbital septum anteriorly. Here it is divided into two fat compartments: central and medial. In the lower lid, there are three fat compartments: lateral, central, and medial (Figure 74–1).
Figure 74–1.
The orbital fat is divided into the upper medial and central compartments, and the lower medial, central, and lateral compartments.
The levator muscle acts to elevate the upper eyelid and has its origin in the periorbita posteriorly. The muscle runs above the superior rectus and fans out anteriorly to become the levator aponeurosis. Insertion occurs at the level of the tarsus, as previously described, forming the lid crease (Figure 74–2). Its innervation is by cranial nerve III (the oculomotor nerve).
Figure 74–2.
Coronal view of the orbit and ...
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Connect to the full suite of AccessSurgery content and resources including more than 160 instructional videos, 16,000+ high-quality images, interactive board review, 20+ textbooks, and more. | {"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": 0.20899109542369843, "perplexity": 5273.841232320978}, "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-2017-13/segments/1490218188914.50/warc/CC-MAIN-20170322212948-00002-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://motls.blogspot.com/2007/05/michael-mann-vs-alexander-cockburn.html | ## Sunday, May 06, 2007 ... //
### Michael Mann vs Alexander Cockburn
Michael Mann didn't like Alexander Cockburn's essay in which Cockburn correctly compares carbon permits and indulgences - well, your humble correspondent might have been the first person who called the permits "indulgences". At least, it was an independent invention :-) because I had to find the word "indulgence" in a Czech-English dictionary. What is the real reason why Michael Mann considers Cockburn's text illogical? Well, here it is:
• As if to drive the point home further, pundit Alexander Cockburn, known generally for his progressive views, has perplexingly disputed the existence of any link between CO2 emissions and rising CO2 concentrations...
Michael Mann tells us that it is completely unexpected from a progressive pundit to write something wrong about the global warming orthodoxy. It may be expected from conservative contrarians but if a progressive pundit writes something like that, that's a real sin! Well, such a comment reveals what are the primary ideas that drive Michael Mann's thinking and "science": it's pure politics. Everything else is adjusted to agree with his politics.
The infamous hockey stick graph, the only well-known result he has, is unfortunately another example.
Incidentally, global warming alarmism and leftism are correlated but they're not identical. I find it pretty reasonable if a progressive pundit is afraid of similar policies that existed under the Catholic Church - because progressive pundits are generally expected to dislike these religious policies, aren't they? There are many left-wing skeptics, for example Philip Stott. Many such people dislike the efforts to keep the third world poor. But good scientists must be able to separate science from politics.
In order to assure us that it wasn't just a typo, Mann makes this political analysis even more detailed. We learn that Cockburn is not allowed to write these things because they sound more skeptical even than the opinions of Patrick Michaels. Well, Patrick Michaels is probably considered to be the ultimate upper bound on the amount of skepticism that a human being can possibly have. ;-)
Well, I hope it is not a complete secret what I will tell you: I was sitting next to Patrick Michaels during a lunch in D.C. two months ago and he was the greenest person in the room. Even his shoes (combined with his suit) were green :-) and he has raised some arguably legitimate criticism of some of the scientific opinions about the climate held by the organizer of that lunch. ;-)
But let's get to the actual questions:
Cockburn claims that there is zero empirical evidence showing the CO2 impact on temperatures...
...and Mann doesn't like it, saying that even Patrick Michaels thinks that there is such a connection. But Patrick Michaels says something slightly different: he says that there is a convincing theory that shows that such an influence should exist. This influence is pretty close to the overall warming in the 20th century and the effect from every new CO2 molecule is smaller than the effect of the previous molecule which implies that even if the emissions of CO2 were accelerating, the temperature would only increase linearly or so.
Patrick Michaels, just like any sane person, realizes that CO2 is just one of many factors influencing the climate. In the Swindle documentary, it was him who explained that the people who think that CO2 drove most of the climate change in the 20th century haven't looked at the basic numbers.
I think that Cockburn is right when he says that there is no empirical observation that proves the relationship and the attribution. If such a paper existed, we would constantly hear its title - instead of vacuous and false comments about consensus. It would also mean that the value of the climate sensitivity would be known. It's not. How can we have empirical evidence for this effect if we don't know what its strength, after all feedbacks are included, is? It's like saying that we can observe a cat but we can't say whether it's bigger than an elephant or not.
Mann criticizes Cockburn for questioning whether the increase of CO2 is due to human activities. Well, I happen to think that if there were no industry but everything else were kept untouched, the CO2 increase wouldn't exist or it would be much smaller. But one can't say that the extra CO2 in the atmosphere is exactly the CO2 that was added by our civilization. There are many other sources of CO2 that are stronger, by orders of magnitude, than our production. But they're a part of the natural carbon cycle and this cycle would be close to equilibrium without our contributions.
But anyway, it's not correct to say that the extra CO2 "is" ours. You could equally well say that it came from some portion of dying vegetation.
Millions years ago, the concentrations could have been much higher. Note that the whole transportation produces less CO2 than farm animals, even today, and there could have been more animals around in the past. 450 million years ago the concentration of CO2 was probably around 3000 ppm, eight times higher than today - we can deduce it from the small number of stomata on the fossils of leaves.
Water vapor
The concentration of water vapor in the atmosphere is changing quickly and it arguably approaches some equilibrium value dictated by other quantities but it is a very rough approximation to say that water vapor is "a feedback not a forcing". In the real world, there is no strict separation to feedbacks and forcings. Every effect is influenced by others and it also affects others.
Water vapor in the atmosphere has a huge impact. Water is the #1 greenhouse gas and, more importantly, it is the material that creates clouds. Incidentally, in April, NASA has published a new finding that there exist "semi-clouds" (my term), a huge "twilight zone" (GRL) around clouds that covers about 60% of the sunny skies. In the existing climate models, these 60% of the sunny skies were described uniformly. The NASA finding makes it pretty clear that the existing climate models don't describe 60% of the clear skies quite adequately.
At any rate, the dynamics of water vapor is influenced by many quantities and water vapor also has a huge impact on many other things, and if you neglect one of the two groups of influences in this sentence, you are bound to end up with misleading results.
CO2 is a product, not a cause
Michael Mann also mentions the "tiny" problem that the Vostok ice core data show that the primary detectable influence was the influence of temperature on the concentration of many gases - CO2, CH4, and others. The 800-year lag is one of many ways to show the anti-Gore direction of the causal relationship. Everyone who still fails to understand that the ice core data don't contain any empirical evidence for the greenhouse effect reveals his or her inadequate thinking skills.
We have discussed this issue in detail, including some analysis of the hypothesis of a strong amplification of the initial temperature variations. Such an amplification is not only invisible in the data but it is very unlikely to be significant because it it were larger than the influence of temperature on the concentrations during the 800 years where a change of the trend could be seen, the climate would be a positive-feedback system that would have already exponentially grown out of the control in the past. The data make it much more likely that there are many negative, self-regulating feedbacks in the system.
In fact, I am sure that even most of the part of the public that has been exposed to arguments about this question from both sides has understood that the ice core data don't provide Al Gore with the argument he needed.
CNN viewers invited to make a Google search
Michael Mann also mentions that the viewers of Glenn Beck's special were encouraged to make a single, most important Google search. They were told to find about the
You can replace co.jp by com: I am just afraid that Google penalizes such links to their search queries and a smaller version of Google could be better.
Mann thanks CNN because the first hit is their blog. Well, my mouse can be defunct but when I click at his link (search for "Google that" at RealClimate.ORG), the first link shown on my screen is The Reference Frame. ;-) The pages of course depend on the details of the query but you can check that The Reference Frame is ahead of them in most similar queries you can write down, e.g. for the following queries:
• inconvenient truth ice core graph (#1)
• carbon dioxide correlation temperature (#1)
• al gore ice core correlation (#1)
• 800-year-lag (#1)
• ice core cause effect (#1)
• ice core co2 follows temperature (#1)
• warming or co2 first (#1)
• ice co2 concentration graphs (#1)
and many others. Mann's statement that RealClimate.ORG is the #1 in "that" query is just another example of his manifestly biased treatment of any data and his cherry-picking.
Entertaining update: When Michael Mann noticed that the Google hit #1 was The Reference Frame, he changed the search query from carbon dioxide to carbon monoxide. According to "experts" at RealClimate.ORG, the global warming was caused by CO not CO2. ;-) The readers probably didn't like CO much so they returned "carbon dioxide lags temperature ice core" without quotes and The Reference Frame returned to #1. Later, Michael Mann finally figured out the easy solution: "co2 lags temperature" without quotes gives them #1. However, when you replace "co2" by "carbon dioxide" or add "ice core" or virtually any other relevant words, The Reference Frame returns to the top. ;-)
Nature's new blog
Finally, Mann has to mention a new climate change blog of Nature. I guess that this entry drives him up the wall much more intensely than Alexander Cockburn and Glenn Beck because one of the first postings on that blog is about the decay of his "hockey stick". But he can't quite say it openly because that would damage the illusion of consensus - so he just says that "first reviews [of the new Nature blog] are decidedly mixed."
It can't be too easy for a person like Mann to be entangled into an ever more complex web of untrue assertions.
And that's the memo.
Other popular climate change articles on The Reference Frame | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42842453718185425, "perplexity": 1434.290005548063}, "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-2021-49/segments/1637964362992.98/warc/CC-MAIN-20211204124328-20211204154328-00511.warc.gz"} |
http://physics.stackexchange.com/questions/59469/why-frequency-doesnt-change-during-refraction/59488 | # Why frequency doesn't change during refraction?
When light goes through one medium to another it's velocity and wavelength changes. Why frequency doesn't change in this phenomenon?
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Closely related to many other questions. May have an answer from Chris here or here and also here – Waffle's Crazy Peanut Mar 30 '13 at 13:19
The electric and magnetic fields have to remain continuous at the refractive index boundary. If the frequency changed, the light at each side of the boundary would be continuously changing it's relative phase and there would be no way to match the fields.
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I think it's the simplest explanation... – Arafat Mar 30 '13 at 17:56
@Kazi Then you should probably accept this answer. – Douglas B. Staple Apr 10 '13 at 17:24
I'm not sure I quite buy this answer. The things that have to be continuous at the boundary are $D_\perp$, $E_\parallel$, $B_\perp$, and $H_\parallel$. On the other hand, there can be discontinuities in $D_\parallel$, $E_\perp$, $B_\parallel$, and $H_\perp$. So I think there is really more that needs to be filled in to make this a valid argument. – Ben Crowell Sep 15 '13 at 20:24
When we think of light, we can describe it as an electromagnetic wave or as a flux of particles - photons. The latter description is more fundamental: If you could have a light source with sensitive enough intensity knob, then after just turning it on (minimum intensity), you'd be sending out photons one by one. I believe that answers to your deep questions lie therein. Behold:
Energy of one light quantum (one photon) can be written $E = hf$, where $h$ is a universal (Planck's) constant, $E$ is energy and $f$ is frequency. We cannot divide photon in pieces, so its energy must stay constant and frequency goes the same way. Devices that appear to divide photons (or change photons' frequency) actually first swallow-destroy the incoming photons and then emit other photons at a different frequency. Frequency of light does not ever change, as long as you can be sure that the photons are the same as the photons at the beginning.
Wavelength $L$ is, on the other hand, tied with energy through its speed, $E = hf = hv/L$ . Atoms of materials, even gases like air, impede the flow of photons - photons bounce off of the atoms (elastic collisions) or are swallowed and re-emitted by the atoms (inelastic collisions). Like I wrote above, a photon swallowed and re-emitted is a different photon. So, it is not part of the original light stream. The Snell's laws speak only about the part of light (photons) that experienced only elastic collisions in a material.
So, in passing from one material to another, light changes wavelength proportionally to the change of speed, so that the ratio $v/L = f$ remains constant. But does that mean that it changes color? That depends, how you define color! As color is usually defined via wavelength (i.e. visible light wavelengths in the range 300-700 nm), then indeed, color changes on the interface of two optical materials with different indexes of refraction (like air-glass, air-water, etc).
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Is there any example where photon and atoms have inelastic collision? – Arafat Mar 30 '13 at 18:03
Think of it like this: At the boundary/interface of the medium, the number of waves you send is the number of waves you receive, at the other side, almost instantly. Frequency doesn't change because it depends on travelling of waves across the interface.
But speed and wavelength change as the material on the other side may be different, so now it might have a longer/shorter size of wave and so the number of waves per unit time changes.
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This is not really a specific fact about electromagnetic waves. It's a fact about all waves. The basic reason for it is cause and effect. Think of how people "do the wave" in a stadium. The way you know it's your turn to go is that the person next to you goes. When a wave travels from medium 1 to medium 2, the thing that's causing the vibration of the wave on the medium-2 side is the vibration of the wave on the medium-1 side.
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## protected by Qmechanic♦Nov 5 '13 at 19:19
Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site. | {"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": 0.8990455269813538, "perplexity": 566.4807541442722}, "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-2014-41/segments/1412037663754.0/warc/CC-MAIN-20140930004103-00482-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://www.leancrew.com/all-this/2011/05/new-circarolla-steno-notebook/ | # New Circa/Rolla steno notebook
A few years ago I made a steno-style notebook with Circa/Rolla disks. It’s worked out really well, but the cardboard covers are looking a little beat up from field use. So today I made a new one using plastic covers. It doesn’t have the rustic look of the old one, and I had to modify one of my planner insert designs, but it took no time at all to make.
My old steno notebook uses 5½ × 8½ paper—letter-sized paper cut in two—and is bound at the top with six disks.
The advantage of this for field use is that the binding doesn’t get in the way of your writing hand the way it does in a standard, side-bound notebook.
Levenger used to make a Circa steno notebook, but it seems to have disappeared from the web site. Probably not a big seller. So premade steno covers aren’t available anymore. I took a pair of Rolla letter-sized covers, turned them sideways, and cut them to a 6″ width.
Filled with paper, this makes a nice little notebook. The template I use for the paper is based on Cornell note paper, but doesn’t have the summary section at the bottom.
The plastic covers aren’t quite as stiff as the thicker cardboard ones, but they’re stiff enough to write on, especially when the top cover is flipped around to the back.
One problem is that the covers are only 8½″ long—the same length as a letter-sized sheet cut in half. To keep the paper clean, I needed to redesign my notebook paper grid to be ¼″ shorter.
This turned out to be pretty simple. The PDF I use for top-bound notebook paper is generated from a hand-written PostScript file1, so all I had to do was change four lines, one of which was a comment. The new page looks like this when printed
After printing on letter-sized paper, I cut the paper in half, then slice ¼″ off the bottom and punch the mushroom holes in the top.
The GitHub repository that holds all my notebook paper templates now has four designs:
1. Letter-sized paper (8½ × 11) with side binding margins. These are the files with names that start with notes-letter.
2. Junior-sized paper (5½ × 8¼) with side binding margins. These are the files with names that start with notes-junior.
3. Junior-sized paper (5½ × 8½) with top binding margins. These are the files with names that start with notes-topbinding.
4. Slightly shorter junior-sized paper (5½ × 8¼) with top binding margins (this is the new one). These are the files with names that start with notes-topbinding-short.
If you’re interested in these paper designs, the repository includes the generated PDFs, so you don’t have to know anything about PostScript programming to download and use them.
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https://read.dukeupress.edu/genre/search-results?q=late%20style | 1-20 of 216 Search Results for
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Journal Article
Genre (2014) 47 (1): 79–102.
Published: 01 April 2014
... and style: from narcissism, emotional exile, and thwarted confession to compassionate love and consolatory elegy, from what Edward W. Said called “late style” to its antithesis, “timeliness.” Closely reading each text's presentation of perspective and closure and elements of the film's style, including mise...
Journal Article
Genre (2016) 49 (3): 331–357.
Published: 01 December 2016
... by University of Oklahoma 2016 Adrienne Rich poetic commitment late style cruel optimism postmodern lyric Works Cited Aravamudan Srinivas . 2001 . “The Return of Anachronism.” Modern Language Quarterly 62 , no. 4 : 331 – 53 . Benjamin Walter . 2005 . Selected Writings...
Journal Article
Genre (2017) 50 (3): 371–395.
Published: 01 December 2017
... of “late style” and Gilles Deleuze’s meditations on modern cinema, each of which views the registration of formal incommensurability as immanent to artistic expression. Against Casanova, then, Bewes (2011, 80) insists that “Naipaul’s work is intimately formed by historical circumstance...
Journal Article
Genre (2016) 49 (1): 27–50.
Published: 01 April 2016
... that “Bowen’s work surely addresses problems of style, waning imperial power, and total war in ways that complement these arguments [by Miller, Esty, and Mackay] and, to be sure, offers other ways to think about late modernist form and history.” James (2009, 52) suggests that Bowen negotiates between...
Journal Article
Genre (2010) 43 (3-4): 239–277.
Published: 01 September 2010
...- 644), rep- resented by Yuan Hongdao ( 568- 6 0Yuan Zhongdao ( 575- 630), and 袁宗 道Yuan Zongdao ( 560- 600). It advocated against the imitation of the literary style of the ancients and for the free expression of the individual. Jingling, another literary school at the late Ming Dynasty...
Journal Article
Genre (2006) 39 (4): 1–21.
Published: 01 December 2006
... . Theodore Dreiser's An American Tragedy . Giles Paul . “ Dreiser's Style .” Ed. Cassuto Lawrence . The Cambridge Companion to Theodore Dreiser . Howard June . Form and History in American Literary Naturalism . Chapel Hill : University of North Carolina Press , 1985...
Journal Article
Genre (2006) 39 (1): 1–18.
Published: 01 March 2006
...Megan Early Alter COPYRIGHT © 2007 BY THE UNIVERSITY OF OKLAHOMA 2007 A PERILOUS PERFORMANCE: AESTHETICIZING FETISHISM IN TRILBY MEGAN EARLY ALTER, UNIVERSITY OF IOWA Late in George Du Maurier's 1894 novel Trilby, the lovelorn character Taffy sees the drawing of his...
Journal Article
Genre (2004) 37 (2): 245–259.
Published: 01 June 2004
... : Blue Ribbon Books , 1925 . Graves Joseph . The Emperor's New Clothes: Biological Theories of Race at the Millennium . New Brunswick, NJ : Rutgers UP , 2001 . Gridley Mark . Jazz Styles: History and Analysis . Upper Saddle River, NJ : Prentice Hall , 2000...
Journal Article
Genre (2006) 39 (4): 85–103.
Published: 01 December 2006
.... COPYRIGHT © 2007 BY THE UNIVERSITY OF OKLAHOMA 2007 WORKS CITED Bai Ronnie . “ Dances with Mei Lanfang: Brecht and the Alienation Effect .” Comparative Drama 32.3 ( Fall 1998 ): 389 - 433 . Clifford James . “ Diasporas ” in Routes: Travel and Translation in the Late...
Journal Article
Genre (2001) 34 (3-4): 243–264.
Published: 01 September 2001
.... Classic Music: Expression, Form, and Style . New York : Schirmer Books , 1980 . Roxon Lillian . Lillian Roxon's Rock Encyclopedia . New York : Grosset and Dunlap , 1969 . Schaefer John . New Sounds: A Listener's Guide to New Music . New York : Harper & Row , 1987...
Journal Article
Genre (2004) 37 (1): 1–46.
Published: 01 March 2004
..." style of the late 1950s for untrammeled interstellar regions to which he was sometimes impelled by shrieks, squeals and mantra-like repetitions. In trying capture this difficult music, however, many Coltrane poems end up illustrating jazz poetry's INTRODUCTION...
Journal Article
Genre (2015) 48 (3): 383–404.
Published: 01 December 2015
... the THE UNACCOUNTED IN TESS AND TRISHNA 385 late nineteenth to the early twentieth century (Flynn 2010, 87). Hardy’s Wessex novels evince a sense of loss of centuries-old traditions and customs to the inevi- table modernization of English society and an accompanying desire to record historical continuity...
Journal Article
Genre (2001) 34 (3-4): 291–305.
Published: 01 September 2001
.... I should, however, declare my own allegiances and potential sources of bias. For while my musical tastes are omnivorous and include many styles of rock and jazz, and while I have regularly taught the histories of both forms in a course on "youth cultures," I have published on rock only...
Journal Article
Genre (2009) 42 (3-4): 5–20.
Published: 01 September 2009
... Logic of Late Capitalism . Durham : Duke UP , 1991 . Print . Jones Daryl . The Dime Novel Western . Bowling Green : Bowling Green University Popular Press , 1978 . Print . Jones Susan . “ Into the Twentieth Century: Imperial Romance from Haggard to Buchan .” A Companion...
Journal Article
Genre (2004) 37 (2): 261–283.
Published: 01 June 2004
... Eric . Double V, Double-Time: Bebop's Politics of Style .'' The Jazz Cadence of American Culture . 1988 . Ed. O'Meally Robert G. . New York : Columbia UP , 1998 . 456 - 68 . Lyne William . The Signifying Modernist: Ralph Ellison and the Limits of the Double Consciousness...
Journal Article
Genre (2011) 44 (1): 93–104.
Published: 01 March 2011
..., consisting of ten lectures delivered in 2002–3, now put in the form of a four-hundred-page published book, has strengths and weak- nesses warranting critical assessment. Like much of his work, particularly the late works, it is loose in structure and style (Leitch 2008). From a scholarly point...
Journal Article
Genre (2002) 35 (3-4): 537–561.
Published: 01 September 2002
...Sylvia Kleinert © COPYRIGHT 2003 BY THE UNIVERSITY OF OKLAHOMA 2003 WORKS CITED Angel A. “Art of the Insider: Northern Territory ‘Gaol Art’ in the Late Nineteenth Century and Since,” Melbourne Historical Journal , Vol. 30 , 2002 , 26 - 41 . Bardon G. Aboriginal...
Journal Article
Genre (2020) 53 (3): 271–277.
Published: 01 December 2020
... thought of as ironic affiliation under the sign of disaffiliation (77). Indeed, Chandler con- structs his macho protagonist in opposition to the very dandy figures that Mar- lowe imitates and bests through pithy acts of verbal dexterity in a style derived in part from the sort of epigrammatic speech...
Journal Article
Genre (2012) 45 (1): 29–55.
Published: 01 March 2012
...Cristanne Miller Emily Dickinson's metrical structures were as fully influenced by the ballad as by the hymn, and other elements of her style may also have been shaped by the huge popularity of ballads in the early nineteenth century in the United States. Understanding that the ballad...
Journal Article
Genre (2004) 37 (2): 301–318.
Published: 01 June 2004
... to investigate the ways jazz functions within the conceptual framework of late modernity. In fact, Hodeir's texts in this volume raise similar issues to those evoked by Theodor Adorno's polemical articles about jazz. Hodeir, who dedicated much of his life to jazz, clearly did not share Adorno's... | {"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": 0.17916177213191986, "perplexity": 23464.13742456282}, "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/1652662543264.49/warc/CC-MAIN-20220522001016-20220522031016-00380.warc.gz"} |
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加拿大 學簽 四大被拒原因
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alternatively, on the other hand, not to mention (this), indeed, further, as well (as this), as a matter of fact, in all honesty, and, furthermore, in addition (to this), besides (this), to tell the truth, or, in fact, actually, to say nothing of, too, let alone, much less additionally, nor,
either (neither), not only (this) but also (that) as well, also, moreover, what is more, as a matter of fact, in all honesty, and, furthermore, in addition (to this), besides (this), to tell the truth, or, in fact, actually, to say nothing of, too, let alone, much less additionally, nor,
as a matter of fact, in all honesty, and, furthermore, in addition (to this), besides (this), to tell the truth, or, in fact, actually, to say nothing of, too, let alone, much less additionally, nor,
alternatively, on the other hand, not to mention (this), indeed, further, as well (as this), either (neither) not only (this) but also (that)as well, also, moreover, what is more, as a matter of fact | {"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": 0.9828517436981201, "perplexity": 10991.190028553077}, "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-2021-43/segments/1634323585246.50/warc/CC-MAIN-20211019074128-20211019104128-00574.warc.gz"} |
http://mathhelpforum.com/calculus/17992-functions-differenciate.html | Math Help - functions differenciate
1. functions differenciate
given 2 functions: f(x) = 2x, g(x) = -2x²+5x
im supposed to determine the following
g(f)
inverse of g
g (g inverse)
the difference quotient for f
the average rate of change for f
yeah... a lot of Q's. someone pls explain the process to me, cuz i fail to understand it...
2. Originally Posted by brokedude
given 2 functions: f(x) = 2x, g(x) = -2x²+5x
im supposed to determine the following
g(f)
inverse of g
g (g inverse)
First part:
$[g(f)](x)=g(f(x))=-2(f(x))^2+5f(x)=2(2x)^2+5(2x)=8x^2+10x
$
Second part:
There is no function $g^{-1}$, as for most $y$ there are two $x$s such that $g(x)=y$.
RonL
3. Originally Posted by brokedude
given 2 functions: f(x) = 2x, g(x) = -2x²+5x
im supposed to determine the following:
the difference quotient for f
the average rate of change for f
The difference quotient for $f$ is:
$
DQ(f,h)=\frac{f(x+h)-f(x)}{h}=\frac{2(x+h)-2x}{h}=\frac{2h}{h}=2
$
Thus we see that the average rate of change of $f$ over
any interval $(x, x+h)$ is $2$
RonL
4. Originally Posted by brokedude
g(x) = -2x²+5x
im supposed to determine the following
g(f)
inverse of g
g (g inverse)
the difference quotient for f
the average rate of change for f
Originally Posted by CaptainBlack
First part:
Second part:
There is no function $g^{-1}$, as for most $y$ there are two $x$s such that $g(x)=y$.
RonL
CaptainBlack is absolutely correct about the inverse of g. It has no inverse. However we may informally get an inverse (that is to say, the process is correct even if the application is not) by:
$g(x) = -2x^2 + 5x$
Let $y = -2x^2 + 5x$
Now switch the roles of x and y:
$x = -2y^2 + 5y$
Now solve for y:
$2y^2 - 5y + x = 0$
$y = \frac{5 \pm \sqrt{25 - 8x}}{4}$ <-- via the quadratic formula
Thus
$g^{-1}(x) = \frac{5 \pm \sqrt{25 - 8x}}{4}$
The problem, as CaptainBlack mentioned, is that for the graph y = g(x) there are two y values for every x (except at the vertex point), so we need to be very careful about defining a domain on which an inverse exists and just what that inverse is. (It will either be the "+" or the "-" of the inverse formula given above.)
-Dan
5. thanks for your help !!
6. Originally Posted by topsquark
CaptainBlack is absolutely correct about the inverse of g. It has no inverse. However we may informally get an inverse (that is to say, the process is correct even if the application is not) by:
$g(x) = -2x^2 + 5x$
Let $y = -2x^2 + 5x$
Now switch the roles of x and y:
$x = -2y^2 + 5y$
Now solve for y:
$2y^2 - 5y + x = 0$
$y = \frac{5 \pm \sqrt{25 - 8x}}{4}$ <-- via the quadratic formula
Thus
$g^{-1}(x) = \frac{5 \pm \sqrt{25 - 8x}}{4}$
The problem, as CaptainBlack mentioned, is that for the graph y = g(x) there are two y values for every x (except at the vertex point), so we need to be very careful about defining a domain on which an inverse exists and just what that inverse is. (It will either be the "+" or the "-" of the inverse formula given above.)
-Dan
There is a way around the problem which is to extend $g$ from $\bold{R}$ to $\mathcal{P}(\bold{R})$, when:
$g(g^{-1})=I$ the identity function $I(S)=S$ for all subsets of $\bold{R}$
but I doubt that this is what is wanted.
RonL | {"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": 32, "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": 0.9410299062728882, "perplexity": 922.1148924875991}, "config": {"markdown_headings": false, "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-2014-15/segments/1397609524644.38/warc/CC-MAIN-20140416005204-00451-ip-10-147-4-33.ec2.internal.warc.gz"} |
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