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https://googology.wikia.org/wiki/Quinhexar
|
11,052 Pages
Quinhexar is equal to $$Q_{1,4}(6)$$ in the Q-supersystem.[1] It's comparable to $$f_{\omega+4}(6)$$ in the fast-growing hierarchy. The term was coined by Boboris02.
## Approximations
Notation Approximation
Fast-growing hierarchy $$f_{\omega+4}(6)$$
Hardy hierarchy $$H_{\omega^{\omega+4}}(6)$$
Chained arrow notation $$6\rightarrow 6\rightarrow 6\rightarrow 5$$
BEAF $$\{6,6,4,2\}$$
Hyperfactorial array notation $$6![5]$$
Strong array notation s(6,6,5,2)
## Sources
Community content is available under CC-BY-SA unless otherwise noted.
| 2021-06-21T13:33:02 |
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|
https://conferences.lbl.gov/event/36/contributions/2085/
|
# TAUP 2013
8-13 September 2013
Asilomar, California
US/Pacific timezone
## Latest results and current status of the MEG and Mu2e charged lepton flavor violation experiments
11 Sep 2013, 17:00
20m
Asilomar, California
#### Asilomar, California
Asilomar Conference Grounds, 800 Asilomar Avenue, Pacific Grove, CA 93950-3704
Oral Neutrino Oscillations/ Neutrino Beam Physics
### Speaker
Dr Gordon Lim (University of California, Irvine)
### Description
Charged lepton flavor violation processes are ideal probes for new physics due to the suppression of Standard Model backgrounds. In particular, $\mu^+\rightarrow e^+\gamma$ decay and neutrinoless $\mu \rightarrow e$ conversion have been used extensively in the search for new physics by many experiments in the past. Currently, the MEG collaboration is searching for $\mu^+\rightarrow e^+\gamma$ with unprecedented precision at the Paul Scherrer Institute in Switzerland, while the Mu2e collaboration is planning an experiment at Fermilab to improve the current upper bound on neutrinoless $\mu \rightarrow e$ conversion by four orders of magnitude. The latest results of the MEG experiment and the status of the Mu2e experiment will be presented, and a future outlook for both experiments will be given.
### Primary author
Dr Gordon Lim (University of California, Irvine)
### Presentation Materials
There are no materials yet.
| 2022-01-26T17:53:59 |
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|
https://heasarc.gsfc.nasa.gov/lheasoft/ftools/headas/colfilter.html
|
# Column and Keyword Filtering Syntax
The column filtering specifier can be used to create or modify table columns and/or header keywords in the input HDU. The presence of a column filter causes CFITSIO to create a new virtual file (usually in memory) that contains the specified modifications. Any other HDUs in the input file are also copied to the virtual file. The actual physical input file is not modified.
The column filtering specifier must begin with the keyword 'col' and is enclosed in square brackets following the name of an input FITS file. The column filter can be used to perform the following types of operations. More than one operation may be specified by separating them with commas or semi-colons.
## Select a subset of columns from the input table
The list of columns to be included in the virtual table should be separated by commas or semi-colons. For example,
file.fits[events][col X, Y]
will create a virtual copy of the input events table that only contains the X and Y columns. The '*' and '\$' wildcard characters may be used to match the names of more than one column to be selected. It is sometimes more convenient to list the columns to be excluded from the virtual table, as in:
file.fits[events][col -DETX, -DETY]
or
file.fits[events][col !DETX; !DETY]
These examples will copy all but the DETX and DETY columns to the virtual table.
## Compute the values for a column
Append a new column to the table or recompute the values in an existing column. For example,
file.fits[events][col PI = PHA * 1.05, X, Y]
will modify the values in the PI column, (or will create a new PI column if it does not already exist) using the arithmetic expression 'PHA * 1.05' (where PHA is a column in the input table) to calculate the values for the column. The expression that is used to compute the columns or keyword values can be arbitrarily complex and may be a function of other header keyword values and other columns. The full syntax and available functions for the expression are described in the calc_express help file.
In the above example, the virtual file will contain only 3 columns: PI, X, and Y. The '*' wildcard character may be used when specifying the name of the columns to be copied to the virtual file, as in these examples:
file.fits[events][col PI = PHA * 1.05, X, Y, *DET]
file.fits[events][col PI = PHA * 1.05, *]
In the first example, the virtual table will contain the PI, X, and Y columns and any other columns whose name ends with the string 'DET'. In the second example, the virtual table will contain all the columns present in the input table, as well as the PI column.
When a new column is created, an appropriate data type will be chosen by default based on the form of the expression used to calculate the values. Alternatively, one may specify the desired column data type in parentheses, followed the column name, as in '[col PI(I) = PHA * 1.05]'. The datatype is specified using the same code letters that are allowed for the value of the FITS TFORMn keyword (e.g., 'I' for integer*2, 'J' for integer*4, 'E' for real*4, and 'D' for real*8, etc. for binary tables, and 'I8', F12.3', 'E20.12', etc. for ASCII tables). The full range of FITS data types is supported including character string, logical, bit, byte and complex data types. Vector columns are also supported in binary tables.
## Create or modify a header keyword
Create a new header keyword or modify the value of an existing keyword by prefixing the keyword name with a pound sign '#'. The expression must evaluate to a constant scalar (i.e., cannot have a column name in the expression). The comment string for the keyword may be specified in parentheses immediately following the keyword name (instead of supplying a datatype as in the case of creating a new column). For example:
file.fits[events][col #VEL(radial velocity) = 23.4]
will create the keyword
VEL = 23.4 / radial velocity
COMMENT and HISTORY keywords may also be created with the following syntax:
#COMMENT = 'This is a comment keyword'
#HISTORY = 'This is a history keyword'
Note that the equal sign and the quote characters will be removed, so that the resulting header keywords in these cases will look like this:
COMMENT This is a comment keyword
HISTORY This is a history keyword
These two special keywords are always appended to the end of the header and will not affect any previously existing COMMENT or HISTORY keywords.
It is possible to delete an existing keyword using a preceding '-'. Either of these examples will delete the keyword named VEL.
-VEL;
-#VEL;
## Wildcard Patterns to Delete Columns or Keywords
It is possible to use wildcard syntax to delete either keywords or columns that match a pattern. Recall that to delete either a keyword or a column, precede its name with a '-' character.
Wildcard patterns are: \verb+'*'+, which matches any string of characters; \verb+'?'+, which matches any single character; and \verb+'#'+ which matches any numerical string. For example these statements:
-VEL*; # remove single column (or keyword) beginning with VEL
-VEL_?; # remove single column (or keyword) VEL_? where ? is any character
-#DEC_*; # remove single keyword beginning with DEC_
-#TUNIT#; # remove single keyword TUNIT ending w. number
will remove the columns or keywords as noted. Be aware that if a '#' is not present, the CFITSIO engine will check for columns with the given name first, followed by keywords. The above expressions will only delete the first item which matches the pattern. If following columns or keywords in the same CHDU match the pattern, they will not be deleted. To delete zero or more keywords that match the pattern, add a trailing '+'.
-VEL*; # remove all columns (or keywords) beginning with VEL
-VEL_?; # remove all columns (or keyword) VEL_? where ? is any character
-#DEC_*+; # remove all keywords beginning with DEC_
-#TUNIT#+; # remove all keywords TUNIT ending w. number
\end{verbatim}
Note that, as a 0-or-more matching pattern, this form will succeed if
the requested column or keyword is not present. In that case, the
deletion expression will silently proceed as if no deletion was requested.
Rename a column
Rename an existing column or keyword with the syntax 'NewName
== OldName', as in:
file.fits[events][col NEWPHA == PHA]
Using a text file
For complex or commonly used operations, one can also place the
operations into a text file and import it into the column filter
using the syntax '[col @filename.txt]'. The operations can extend
over multiple lines of the file, but multiple operations must still
be separated by commas or semicolons. Any lines in the external text file that
begin with 2 slash characters ('//') will be ignored and may be used
Multiple column filtering expressions
When using column filtering to open a file "on the fly," it is permitted
to use multiple column filtering expressions. For example, the
syntax
filename.fits[col *][col -Y][col Z=X+1]
would be treated as equivalent to joining the expressions with semicolons,
or
filename.fits[col *; -Y;col Z=X+1]
Please note that if multiple column filtering expressions are used, it is
not permitted to also use the [col @filename.txt] syntax in any
of the individual expressions.
filenames,
imfilter,
rowfilter,
binfilter.
pixfilter.
calc_express.
| 2021-06-23T06:07:17 |
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|
https://cnls.lanl.gov/External/showtalksummary.php?selection=1430
|
Lab Home | Phone | Search
Current Affiliates Alumni Visitors Students
2007 2006 2005 2004 2003 2002 2001 2000 <1999
Colloquia Colloquia Archive Seminars Postdoc Seminars Archive Quantum Lunch CMS Colloquia Q-Mat Seminars Q-Mat Seminars Archive Archive
Description Past Visitors
Thursday, September 13, 2007
2:00 PM - 3:30 PM
CNLS Conference Room (TA-3, Bldg 1690)
Postdoc Seminar
Thermalization and Bottleneck in Turbulence
Jian-Zhou Zhu
T-7
It is conjectured that for many equations of hydrodynamical type (including the 3D Navier--Stokes equations, the Burgers equation and various models of turbulence) the use of hyperviscous dissipation with a high power $\alpha$ (dissipativity) of the Laplacian and suitable rescaling of the hyperviscosity becomes asymptotically equivalent to using a Galerkin truncation with zero dissipation and suppression of all Fourier modes whose wavenumber exceeds a cutoff $k_d$. From recent work of Cichowlas et al (\textit{Phys.\ Rev. Lett.} {\bf 95} (2005) 264502), it is known that when $k_d$ is large enough the solution of Galerkin-truncated equations develop a thermalized range at high wavenumbers (with a $k2$ spectrum in 3D). It is proposed to interpret the phenomenon of bottleneck, which becomes stronger when increasing $\alpha$, as an aborted thermalization. In this first talk, I will discuss the cases of eddy-damped-quasi-normal-Markovian (EDQNM) type models. Artifacts which can appear when using hyperviscosity are also discussed along with the numerical verifications.
| 2019-01-23T13:10:36 |
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|
https://par.nsf.gov/biblio/10280249-protocols-assessing-transformation-rates-nitrous-oxide-water-column
|
Protocols for Assessing Transformation Rates of Nitrous Oxide in the Water Column
Nitrous oxide (N 2 O) is a potent greenhouse gas and an ozone destroying substance. Yet, clear step-by-step protocols to measure N 2 O transformation rates in freshwater and marine environments are still lacking, challenging inter-comparability efforts. Here we present detailed protocols currently used by leading experts in the field to measure water-column N 2 O production and consumption rates in both marine and other aquatic environments. We present example 15 N-tracer incubation experiments in marine environments as well as templates to calculate both N 2 O production and consumption rates. We discuss important considerations and recommendations regarding (1) precautions to prevent oxygen (O 2 ) contamination during low-oxygen and anoxic incubations, (2) preferred bottles and stoppers, (3) procedures for 15 N-tracer addition, and (4) the choice of a fixative. We finally discuss data reporting and archiving. We expect these protocols will make 15 N-labeled N 2 O transformation rate measurements more accessible to the wider community and facilitate future inter-comparison between different laboratories.
Authors:
; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10280249
Journal Name:
Frontiers in Marine Science
Volume:
8
ISSN:
2296-7745
National Science Foundation
##### More Like this
1. Abstract The ocean is a net source of N 2 O, a potent greenhouse gas and ozone-depleting agent. However, the removal of N 2 O via microbial N 2 O consumption is poorly constrained and rate measurements have been restricted to anoxic waters. Here we expand N 2 O consumption measurements from anoxic zones to the sharp oxygen gradient above them, and experimentally determine kinetic parameters in both oxic and anoxic seawater for the first time. We find that the substrate affinity, O 2 tolerance, and community composition of N 2 O-consuming microbes in oxic waters differ from those in the underlying anoxic layers. Kinetic parameters determined here are used to model in situ N 2 O production and consumption rates. Estimated in situ rates differ from measured rates, confirming the necessity to consider kinetics when predicting N 2 O cycling. Microbes from the oxic layer consume N 2 O under anoxic conditions at a much faster rate than microbes from anoxic zones. These experimental results are in keeping with model results which indicate that N 2 O consumption likely takes place above the oxygen deficient zone (ODZ). Thus, the dynamic layer with steep O 2 and N 2 Omore »
2. The balance between sources and sinks of molecular oxygen in the oceans has greatly impacted the composition of Earth’s atmosphere since the evolution of oxygenic photosynthesis, thereby exerting key influence on Earth’s climate and the redox state of (sub)surface Earth. The canonical source and sink terms of the marine oxygen budget include photosynthesis, respiration, photorespiration, the Mehler reaction, and other smaller terms. However, recent advances in understanding cryptic oxygen cycling, namely the ubiquitous one-electron reduction of O 2 to superoxide by microorganisms outside the cell, remains unexplored as a potential player in global oxygen dynamics. Here we show that dark extracellular superoxide production by marine microbes represents a previously unconsidered global oxygen flux and sink comparable in magnitude to other key terms. We estimate that extracellular superoxide production represents a gross oxygen sink comprising about a third of marine gross oxygen production, and a net oxygen sink amounting to 15 to 50% of that. We further demonstrate that this total marine dark extracellular superoxide flux is consistent with concentrations of superoxide in marine environments. These findings underscore prolific marine sources of reactive oxygen species and a complex and dynamic oxygen cycle in which oxygen consumption and corresponding carbon oxidation aremore »
3. (Ed.)
ABSTRACT The cyanobacterium Trichodesmium is an important contributor of new nitrogen (N) to the surface ocean, but its strategies for protecting the nitrogenase enzyme from inhibition by oxygen (O 2 ) remain poorly understood. We present a dynamic physiological model to evaluate hypothesized conditions that would allow Trichodesmium to carry out its two conflicting metabolic processes of N 2 fixation and photosynthesis. First, the model indicates that managing cellular O 2 to permit N 2 fixation requires high rates of respiratory O 2 consumption. The energetic cost amounts to ∼80% of daily C fixation, comparable to the observed diminution of the growth rate of Trichodesmium relative to other phytoplankton. Second, by forming a trichome of connected cells, Trichodesmium can segregate N 2 fixation from photosynthesis. The transfer of stored C to N-fixing cells fuels the respiratory O 2 consumption that protects nitrogenase, while the reciprocal transfer of newly fixed N to C-fixing cells supports cellular growth. Third, despite Trichodesmium lacking the structural barrier found in heterocystous species, the model predicts low diffusivity of cell membranes, a function that may be explained by the presence of Gram-negative membrane, production of extracellular polysaccharide substances (EPS), and “buffer cells” that intervene between Nmore »
4. Climate-driven depletion of ocean oxygen strongly impacts the global cycles of carbon and nutrients as well as the survival of many animal species. One of the main uncertainties in predicting changes to marine oxygen levels is the regulation of the biological respiration demand associated with the biological pump. Derived from the Redfield ratio, the molar ratio of oxygen to organic carbon consumed during respiration (i.e., the respiration quotient,$r−O2:C$) is consistently assumed constant but rarely, if ever, measured. Using a prognostic Earth system model, we show that a 0.1 increase in the respiration quotient from 1.0 leads to a 2.3% decline in global oxygen, a large expansion of low-oxygen zones, additional water column denitrification of 38 Tg N/y, and the loss of fixed nitrogen and carbon production in the ocean. We then present direct chemical measurements of$r−O2:C$using a Pacific Ocean meridional transect crossing all major surface biome types. The observed$r−O2:C$has a positive correlation with temperature, and regional mean values differ significantly from Redfield proportions. Finally, an independent global inverse model analysis constrained with nutrients, oxygen, and carbon concentrations supports a positive temperature dependence of$r−O2:C$in exported organic matter. We provide evidence against the common assumption of a staticmore »
5. Stable isotope paleoaltimetry is one of the most commonly used approaches for quantifying the paleoelevation history of an orogen yet this methodology is often limited to arid to semi-arid climates, mountain systems with a clear orographic rainshadow and terrestrial basins. We present a new approach to reconstructing past topography and relief that uses the catchment-integrated signature of organic molecular biomarkers to quantify the hypsometry of fluvially-exported biomass. Because terrestrially-produced biomolecules are synthesized over the full range of global climate conditions and can be preserved in both terrestrial and marine sediments, the geochemistry of fluvially-transported sedimentary biomarkers can provide a means of interrogating the evolution of topography for a range of environments and depositional settings, including those not well suited for a traditional isotope paleoaltimetry approach. We show an example from Taiwan, a rapidly eroding tropical mountain system that is characterized by high rates of biomass production and short organic residence time and discuss key factors that can influence molecular isotope signal production, transport and integration. Data show that in high relief catchments of Taiwan, river sediments can record integration of biomass produced throughout the catchment. Sedimentary biomarker δ 2 H n C29 in low elevation river deposition sites is generallymore »
| 2022-12-03T03:18:59 |
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|
https://zbmath.org/authors/lorch.lee
|
## Lorch, Lee
Compute Distance To:
Author ID: lorch.lee Published as: Lorch, Lee; Lorch, L. External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND
Documents Indexed: 83 Publications since 1944 2 Further Contributions Biographic References: 2 Publications Co-Authors: 12 Co-Authors with 43 Joint Publications 294 Co-Co-Authors
all top 5
### Co-Authors
40 single-authored 20 Szego, Peter 9 Muldoon, Martin E. 6 Newman, Donald J. 3 Leviatan, Dany 3 Russell, Dennis C. 2 Elbert, Árpád 2 Livingston, Arthur Eugene 1 Askey, Richard Allen 1 Bretlau, Jytte 1 Christensen, Villy K. 1 1 Erdélyi, Arthur 1 Gasper, George Jun 1 Holst, Jens Jørgen 1 Ismail, Mourad El-Houssieny 1 Jørgensen, Margrethe 1 Jørgensen, Tove Lund 1 Laforgia, Andrea 1 Larsen, Karen Skov 1 Lew, John S. 1 Love, Eric Russell 1 Mikolás, Miklós 1 Moser, Leo 1 Osler, Thomas J. 1 Pedersen, Niels Wendell 1 Ross, Bertram 1 Sørensen, Leif Hautop 1 Steffensen, Per Amdal 1 Tzimbalario, Jean 1 Uberti, Riccardo 1 Vestergaard, Preben Dahl
all top 5
### Serials
8 Canadian Mathematical Bulletin 7 Proceedings of the American Mathematical Society 5 Canadian Journal of Mathematics 5 Duke Mathematical Journal 5 SIAM Journal on Mathematical Analysis 4 American Mathematical Monthly 4 Journal of Mathematical Analysis and Applications 4 Methods and Applications of Analysis 3 Acta Mathematica Academiae Scientiarum Hungaricae 3 Archivum Mathematicum 2 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Acta Mathematica 1 American Journal of Mathematics 1 Bulletin of the Calcutta Mathematical Society 1 Colloquium Mathematicum 1 Glasgow Mathematical Journal 1 Indian Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Studia Scientiarum Mathematicarum Hungarica 1 Rendiconti del Seminario Matematico 1 Analysis 1 Facta Universitatis. Series Mathematics and Informatics 1 Mathematica Balkanica. New Series 1 Numerical Algorithms 1 Analysis (München) 1 Analysis and Applications (Singapore) 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 1 Scripta Mathematica 1 Buletinul Institutului Politehnic din Iași, New Series
all top 5
### Fields
35 Special functions (33-XX) 10 Ordinary differential equations (34-XX) 6 Real functions (26-XX) 5 Sequences, series, summability (40-XX) 4 Number theory (11-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 2 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Approximations and expansions (41-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX)
### Citations contained in zbMATH Open
60 Publications have been cited 362 times in 275 Documents Cited by Year
Completely monotonic functions associated with the gamma function and its q-analogues. Zbl 0589.33001
Ismail, Mourad E. H.; Lorch, Lee; Muldoon, Martin E.
1986
Inequalities for ultraspherical polynomials and the gamma function. Zbl 0532.33007
Lorch, Lee
1984
Alternative proof of a sharpened form of Bernstein’s inequality for Legendre polynomials. Zbl 0505.33007
Lorch, Lee
1983
Monotonicity of the zeros of a cross product of Bessel functions. Zbl 0840.33002
Lorch, Lee
1994
Higher monotonicity properties of certain Sturm-Liouville functions. Zbl 0111.06502
Lorch, Lee; Szego, Peter
1963
On the composition of completely monotonic functions and completely monotonic sequences and related questions. Zbl 0547.26010
Lorch, Lee; Newman, Donald J.
1983
Higher monotonicity properties of certain Sturm-Liouville functions. III. Zbl 0212.40703
Lorch, L.; Muldoon, M. E.; Szego, P.
1970
Higher monotonicity properties of certain Sturm-Liouville functions. IV. Zbl 0242.34030
Lorch, Lee; Muldoon, Martin E.; Szego, Peter
1972
Some inequalities for the first positive zeros of Bessel functions. Zbl 0773.33003
Lorch, Lee
1993
Monotonic sequences related to zeros of Bessel functions. Zbl 1171.33304
Lorch, Lee; Muldoon, Martin E.
2008
The Lebesgue constants for regular Hausdorff methods. Zbl 0108.06104
Lorch, L.; Newman, D. J.
1961
A remark on completely monotonic sequences with an application to summability. Zbl 0122.30601
Lorch, Lee; Moser, Leo
1963
The Lebesgue constants for $$(E, 1)$$ summation of Fourier series. Zbl 0046.06701
Lorch, Lee
1952
“Best possible” upper bounds for the first positive zeros of Bessel functions – the finite part. Zbl 0866.65014
Lorch, Lee; Uberti, Riccardo
1996
Bounds and monotonicities for the zeros of derivatives of ultraspherical Bessel functions. Zbl 0805.33002
Lorch, Lee; Szego, Peter
1994
Closed expressions for some infinite series of Bessel and Struve functions. Zbl 0621.33010
Lorch, Lee; Szego, Peter
1987
On the zeros of derivatives of Bessel functions. Zbl 0666.33006
Lorch, Lee; Szego, Peter
1988
Inequalities for some Whittaker functions. Zbl 0205.36102
Lorch, L.
1967
The Lebesgue constants for Jacobi series. I. Zbl 0092.06501
Lorch, Lee
1959
Turanians and Wronskians for the zeros of Bessel functions. Zbl 0446.33011
Lorch, Lee
1980
Higher monotonicity properties of certain Sturm-Liouville functions. II. Zbl 0113.27704
Lorch, Lee; Szego, Peter
1963
A characterization of totally regular $$[J,f(x)]$$ transforms. Zbl 0184.08803
Leviatan, D.; Lorch, L.
1969
A singular integral whose kernel involves a Bessel function. Zbl 0066.05201
Lorch, Lee; Szego, Peter
1955
Some monotonicity properties of Bessel functions. Zbl 0227.33008
Lorch, Lee; Muldoon, M. E.; Szego, Peter
1973
Additional monotonicity properties of the zeros of Bessel functions. Zbl 0741.33003
Elbert, Árpád; Laforgia, Andrea; Lorch, Lee
1991
On approximation by Fejer means to periodic functions satisfying a Lipschitz condition. Zbl 0115.28102
Lorch, L.
1962
Monotonicity of the differences of zeros of Bessel functions as a function of order. Zbl 0126.08603
Lorch, Lee; Szego, Peter
1964
A supplement to the Sturm separation theorem, with applications. Zbl 0135.29702
Lorch, L.; Newman, D. J.
1965
The Gibbs phenomenon for Borel means. Zbl 0078.25501
Lorch, Lee
1957
The real zeros of the derivatives of cylinder functions of negative order. Zbl 0958.33002
Lorch, Lee; Muldoon, Martin E.
1999
The Lebesgue constants for Borel summability. Zbl 0063.03632
Lorch, Lee
1944
Elementary comparison techniques for certain classes of Sturm-Liouville equations. Zbl 0406.34027
Lorch, Lee
1977
Monotonicity in terms of order of the zeros of the derivatives of Bessel functions. Zbl 0693.33004
Lorch, Lee
1990
On the points of inflection of Bessel functions of positive order. I. Zbl 0716.33003
Lorch, Lee; Szego, Peter
1990
Inflection points of Bessel functions of negative order. Zbl 0762.33002
Lorch, Lee; Muldoon, Martin E.; Szego, Peter
1991
On Bessel functions of equal order and argument. Zbl 0796.33002
Lorch, L.
1992
The Lebesgue constants for $$(\gamma,r)$$ summation of Fourier series. Zbl 0116.04802
Lorch, Lee; Newman, Donald J.
1963
A Bessel function inequality connected with stability of least square smoothing. Zbl 0163.30803
Lorch, Lee; Szego, Peter
1966
The Gibbs phenomenon and Lebesgue constants for regular [J,f(x)] means. Zbl 0197.35101
Leviatan, D.; Lorch, L.
1970
Asymptotic expressions for some integrals which include certain Lebesgue and Fejér constants. Zbl 0050.05905
Lorch, Lee
1953
On a monotonicity property of some Hausdorff transforms of certain Fourier series. Zbl 0518.42012
Lorch, L.; Newman, D. J.
1983
Open questions for research. Zbl 0303.26005
1975
Continuous ranking of zeros of cylinder functions. Zbl 1144.33001
Lorch, Lee
2005
Monotonicity of the zeros of the third derivative of Bessel functions. Zbl 0833.33003
Lorch, Lee; Szego, Peter
1995
Alternative proof of a sharpened form of Berstein’s inequality for Legendre polynomials: Corrigendum. Zbl 0795.33006
Lorch, Lee
1993
A property of completely [absolutely] monotonic and other logarithmically convex [concave] functions. Zbl 1042.26005
Lorch, Lee
2003
A quasi-equivalence between Borel summability and convergence for Fourier-Laguerre series at the end-point. Zbl 0439.42009
Lorch, Lee; Tzimbalario, Jean
1979
A singular integral whose kernel involves a Bessel function. II. Zbl 0108.06701
Lorch, Lee; Szego, Peter
1962
The limits of indetermination for Riemann summation in terms of Bessel functions. Zbl 0143.07801
Lorch, L.
1966
On the $$[F,d_ n]$$ summation of Fourier series. Zbl 0144.06501
Lorch, L.; Newman, D. J.
1962
Translativity for strong Borel summability. Zbl 0145.28901
Lorch, L.
1966
A Bessel function inequality connected with stability of least square smoothing. II. Zbl 0185.29702
Lorch, Lee; Szego, Peter
1968
On the connectedness of the sets of limit points of certain transforms of bounded sequences. Zbl 0212.41202
Leviatan, D.; Lorch, L.
1971
The principal term in the asymptotic expansion of the Lebesgue constants. Zbl 0055.29504
Lorch, Lee
1954
On Fejer’s calculation of the Lebesgue constants. Zbl 0060.18206
Lorch, Lee
1945
The zeros of certain sine-like integrals. Zbl 0073.04604
Livingston, A. E.; Lorch, Lee
1956
Corrections and a remark to: A singular integral whose kernel involves a Bessel function. Zbl 0078.25801
Lorch, Lee; Szego, Peter
1957
Supplement to a theorem of Cesàro. Zbl 0084.05803
Lorch, Lee
1958
The Lebesgue constants for Euler (E,1) summation of Laplace series. Zbl 0538.40007
Lorch, L.
1983
The zeros of the third derivative of Bessel functions of order less than one. Zbl 0843.33001
Lorch, Lee
1995
Monotonic sequences related to zeros of Bessel functions. Zbl 1171.33304
Lorch, Lee; Muldoon, Martin E.
2008
Continuous ranking of zeros of cylinder functions. Zbl 1144.33001
Lorch, Lee
2005
A property of completely [absolutely] monotonic and other logarithmically convex [concave] functions. Zbl 1042.26005
Lorch, Lee
2003
The real zeros of the derivatives of cylinder functions of negative order. Zbl 0958.33002
Lorch, Lee; Muldoon, Martin E.
1999
“Best possible” upper bounds for the first positive zeros of Bessel functions – the finite part. Zbl 0866.65014
Lorch, Lee; Uberti, Riccardo
1996
Monotonicity of the zeros of the third derivative of Bessel functions. Zbl 0833.33003
Lorch, Lee; Szego, Peter
1995
The zeros of the third derivative of Bessel functions of order less than one. Zbl 0843.33001
Lorch, Lee
1995
Monotonicity of the zeros of a cross product of Bessel functions. Zbl 0840.33002
Lorch, Lee
1994
Bounds and monotonicities for the zeros of derivatives of ultraspherical Bessel functions. Zbl 0805.33002
Lorch, Lee; Szego, Peter
1994
Some inequalities for the first positive zeros of Bessel functions. Zbl 0773.33003
Lorch, Lee
1993
Alternative proof of a sharpened form of Berstein’s inequality for Legendre polynomials: Corrigendum. Zbl 0795.33006
Lorch, Lee
1993
On Bessel functions of equal order and argument. Zbl 0796.33002
Lorch, L.
1992
Additional monotonicity properties of the zeros of Bessel functions. Zbl 0741.33003
Elbert, Árpád; Laforgia, Andrea; Lorch, Lee
1991
Inflection points of Bessel functions of negative order. Zbl 0762.33002
Lorch, Lee; Muldoon, Martin E.; Szego, Peter
1991
Monotonicity in terms of order of the zeros of the derivatives of Bessel functions. Zbl 0693.33004
Lorch, Lee
1990
On the points of inflection of Bessel functions of positive order. I. Zbl 0716.33003
Lorch, Lee; Szego, Peter
1990
On the zeros of derivatives of Bessel functions. Zbl 0666.33006
Lorch, Lee; Szego, Peter
1988
Closed expressions for some infinite series of Bessel and Struve functions. Zbl 0621.33010
Lorch, Lee; Szego, Peter
1987
Completely monotonic functions associated with the gamma function and its q-analogues. Zbl 0589.33001
Ismail, Mourad E. H.; Lorch, Lee; Muldoon, Martin E.
1986
Inequalities for ultraspherical polynomials and the gamma function. Zbl 0532.33007
Lorch, Lee
1984
Alternative proof of a sharpened form of Bernstein’s inequality for Legendre polynomials. Zbl 0505.33007
Lorch, Lee
1983
On the composition of completely monotonic functions and completely monotonic sequences and related questions. Zbl 0547.26010
Lorch, Lee; Newman, Donald J.
1983
On a monotonicity property of some Hausdorff transforms of certain Fourier series. Zbl 0518.42012
Lorch, L.; Newman, D. J.
1983
The Lebesgue constants for Euler (E,1) summation of Laplace series. Zbl 0538.40007
Lorch, L.
1983
Turanians and Wronskians for the zeros of Bessel functions. Zbl 0446.33011
Lorch, Lee
1980
A quasi-equivalence between Borel summability and convergence for Fourier-Laguerre series at the end-point. Zbl 0439.42009
Lorch, Lee; Tzimbalario, Jean
1979
Elementary comparison techniques for certain classes of Sturm-Liouville equations. Zbl 0406.34027
Lorch, Lee
1977
Open questions for research. Zbl 0303.26005
1975
Some monotonicity properties of Bessel functions. Zbl 0227.33008
Lorch, Lee; Muldoon, M. E.; Szego, Peter
1973
Higher monotonicity properties of certain Sturm-Liouville functions. IV. Zbl 0242.34030
Lorch, Lee; Muldoon, Martin E.; Szego, Peter
1972
On the connectedness of the sets of limit points of certain transforms of bounded sequences. Zbl 0212.41202
Leviatan, D.; Lorch, L.
1971
Higher monotonicity properties of certain Sturm-Liouville functions. III. Zbl 0212.40703
Lorch, L.; Muldoon, M. E.; Szego, P.
1970
The Gibbs phenomenon and Lebesgue constants for regular [J,f(x)] means. Zbl 0197.35101
Leviatan, D.; Lorch, L.
1970
A characterization of totally regular $$[J,f(x)]$$ transforms. Zbl 0184.08803
Leviatan, D.; Lorch, L.
1969
A Bessel function inequality connected with stability of least square smoothing. II. Zbl 0185.29702
Lorch, Lee; Szego, Peter
1968
Inequalities for some Whittaker functions. Zbl 0205.36102
Lorch, L.
1967
A Bessel function inequality connected with stability of least square smoothing. Zbl 0163.30803
Lorch, Lee; Szego, Peter
1966
The limits of indetermination for Riemann summation in terms of Bessel functions. Zbl 0143.07801
Lorch, L.
1966
Translativity for strong Borel summability. Zbl 0145.28901
Lorch, L.
1966
A supplement to the Sturm separation theorem, with applications. Zbl 0135.29702
Lorch, L.; Newman, D. J.
1965
Monotonicity of the differences of zeros of Bessel functions as a function of order. Zbl 0126.08603
Lorch, Lee; Szego, Peter
1964
Higher monotonicity properties of certain Sturm-Liouville functions. Zbl 0111.06502
Lorch, Lee; Szego, Peter
1963
A remark on completely monotonic sequences with an application to summability. Zbl 0122.30601
Lorch, Lee; Moser, Leo
1963
Higher monotonicity properties of certain Sturm-Liouville functions. II. Zbl 0113.27704
Lorch, Lee; Szego, Peter
1963
The Lebesgue constants for $$(\gamma,r)$$ summation of Fourier series. Zbl 0116.04802
Lorch, Lee; Newman, Donald J.
1963
On approximation by Fejer means to periodic functions satisfying a Lipschitz condition. Zbl 0115.28102
Lorch, L.
1962
A singular integral whose kernel involves a Bessel function. II. Zbl 0108.06701
Lorch, Lee; Szego, Peter
1962
On the $$[F,d_ n]$$ summation of Fourier series. Zbl 0144.06501
Lorch, L.; Newman, D. J.
1962
The Lebesgue constants for regular Hausdorff methods. Zbl 0108.06104
Lorch, L.; Newman, D. J.
1961
The Lebesgue constants for Jacobi series. I. Zbl 0092.06501
Lorch, Lee
1959
Supplement to a theorem of Cesàro. Zbl 0084.05803
Lorch, Lee
1958
The Gibbs phenomenon for Borel means. Zbl 0078.25501
Lorch, Lee
1957
Corrections and a remark to: A singular integral whose kernel involves a Bessel function. Zbl 0078.25801
Lorch, Lee; Szego, Peter
1957
The zeros of certain sine-like integrals. Zbl 0073.04604
Livingston, A. E.; Lorch, Lee
1956
A singular integral whose kernel involves a Bessel function. Zbl 0066.05201
Lorch, Lee; Szego, Peter
1955
The principal term in the asymptotic expansion of the Lebesgue constants. Zbl 0055.29504
Lorch, Lee
1954
Asymptotic expressions for some integrals which include certain Lebesgue and Fejér constants. Zbl 0050.05905
Lorch, Lee
1953
The Lebesgue constants for $$(E, 1)$$ summation of Fourier series. Zbl 0046.06701
Lorch, Lee
1952
On Fejer’s calculation of the Lebesgue constants. Zbl 0060.18206
Lorch, Lee
1945
The Lebesgue constants for Borel summability. Zbl 0063.03632
Lorch, Lee
1944
all top 5
### Cited by 287 Authors
16 Lorch, Lee 12 Baricz, Árpád 11 Laforgia, Andrea 11 Yang, Zhenhang 9 Muldoon, Martin E. 8 Alzer, Horst 8 Elbert, Árpád 8 Qi, Feng 7 Ismail, Mourad El-Houssieny 6 Szego, Peter 6 Tian, Jingfeng 5 Ashbaugh, Mark S. 5 Ishiguro, Kazuo 5 Salem, Ahmed 5 Vancostenoble, Judith 4 Chasman, Laura Mercredi 4 Giordano, Carla 4 Jankov Maširević, Dragana 4 Martinez, Patrick 4 Ustina, Fred 4 Zheng, Shenzhou 3 Allal, Brahim 3 Askey, Richard Allen 3 Batir, Necdet 3 Benguria, Rafael D. 3 Cannarsa, Piermarco 3 Chu, Yuming 3 Collino, Francis 3 Guo, Bai-Ni 3 Guo, Senlin 3 Kerimov, Movlud Kerimovich 3 Koumandos, Stamatis 3 Leviatan, Dany 3 Mai, Jan-Frederik 3 Ponnusamy, Saminathan 3 Salhi, Jawad 3 Scherer, Matthias 3 Srivastava, Hari Mohan 3 Stanković, Miomir S. 3 Tričković, Slobodan B. 3 Vidanović, Mirjana V. 3 Wong, Roderick Sue-Chuen 2 Alzahrani, Faris Saeed 2 Biccari, Umberto 2 Carayol, Quentin 2 Freud, Géza 2 Gaunt, Robert Edward 2 Golubov, Boris Ivanovich 2 Grinshpan, Arcadii Z. 2 Grunau, Hans-Christoph 2 Hacik, Milos 2 Holland, Anthony S. B. 2 Ikeno, Kyuhei 2 Kokologiannaki, Chrysi G. 2 Koornwinder, Tom H. 2 Krasikov, Ilia 2 Laugesen, Richard Snyder 2 Liu, Yongping 2 Lohöfer, Georg 2 Luo, Qiuming 2 Markett, Clemens 2 Natalini, Pierpaolo 2 Neuman, František 2 Nowak, Adam 2 Pečarić, Josip 2 Pedersen, Henrik Laurberg 2 Pogány, Tibor K. 2 Sbai, Amine 2 Segura, Javier 2 Singh, Sanjeev 2 Stark, Eberhard L. 2 Steinig, John 2 Telyakovskiĭ, Sergeĭ Aleksandrovich 2 Trench, William F. 2 Troestler, Christophe 2 van den Berg, Michiel 2 Xue, Qingying 2 Yabuta, Kôzô 2 Yagmur, Nihat 2 Yin, Li 2 Zhang, Ruiming 2 Zhao, Tiehong 1 Adcock, Ben 1 Agarwal, Ravi P. 1 Aguech, Rafik 1 Ahn, Jaewook 1 Al-Jararha, Jehad M. 1 Al-Jararha, Mohammadkheer M. 1 Al-Salam, Waleed A. 1 Amiri, Leila 1 Anoop, Thazhe Veetil 1 Arenas, Alberto 1 Balabdaoui, Fadoua 1 Baskakov, Viktor Alekseevich 1 Beekmann, Wolfgang 1 Belton, Alexander C. R. 1 Benamou, Jean-David 1 Berg, Christian 1 Bernardi, Giulia 1 Bisht, Nitin ...and 187 more Authors
all top 5
### Cited in 117 Serials
20 Journal of Mathematical Analysis and Applications 20 Proceedings of the American Mathematical Society 18 Journal of Approximation Theory 11 Journal of Computational and Applied Mathematics 11 Journal of Inequalities and Applications 9 Transactions of the American Mathematical Society 7 Mathematische Zeitschrift 7 Integral Transforms and Special Functions 5 Computers & Mathematics with Applications 5 Aequationes Mathematicae 4 Acta Mathematica Academiae Scientiarum Hungaricae 4 Mathematics of Computation 4 The Ramanujan Journal 3 Applicable Analysis 3 Mathematical Methods in the Applied Sciences 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 3 Journal of Differential Equations 3 Journal of Multivariate Analysis 3 Results in Mathematics 3 Tôhoku Mathematical Journal. Second Series 3 Acta Mathematica Hungarica 3 Computational Mathematics and Mathematical Physics 3 SIAM Journal on Mathematical Analysis 3 Mathematical Inequalities & Applications 3 Analysis and Applications (Singapore) 3 Mathematical Control and Related Fields 2 Communications in Mathematical Physics 2 Mathematical Notes 2 Rocky Mountain Journal of Mathematics 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Advances in Mathematics 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Constructive Approximation 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Georgian Mathematical Journal 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Advances in Difference Equations 2 Proceedings of the Japan Academy 2 Electronic Journal of Statistics 2 Evolution Equations and Control Theory 1 Analysis Mathematica 1 Bulletin of the Australian Mathematical Society 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Lithuanian Mathematical Journal 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Arkiv för Matematik 1 Acta Mathematica 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 BIT 1 Calcolo 1 Computing 1 Duke Mathematical Journal 1 Glasgow Mathematical Journal 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Journal of Optimization Theory and Applications 1 Journal of Soviet Mathematics 1 Journal of Statistical Planning and Inference 1 Monatshefte für Mathematik 1 Numerische Mathematik 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 SIAM Journal on Numerical Analysis 1 Advances in Applied Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Complexity 1 Numerical Methods for Partial Differential Equations 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 The Journal of Geometric Analysis 1 Numerical Algorithms 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Statistical Computation and Simulation 1 Expositiones Mathematicae 1 Computational Statistics and Data Analysis 1 Indagationes Mathematicae. New Series 1 Potential Analysis 1 Filomat 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Computational Mathematics 1 Arab Journal of Mathematical Sciences 1 Journal of Applied Analysis 1 Journal of Vibration and Control 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Abstract and Applied Analysis 1 Positivity 1 Fractional Calculus & Applied Analysis 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics ...and 17 more Serials
all top 5
### Cited in 35 Fields
142 Special functions (33-XX) 57 Real functions (26-XX) 37 Partial differential equations (35-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 27 Approximations and expansions (41-XX) 24 Numerical analysis (65-XX) 22 Ordinary differential equations (34-XX) 15 Number theory (11-XX) 14 Sequences, series, summability (40-XX) 14 Integral transforms, operational calculus (44-XX) 12 Probability theory and stochastic processes (60-XX) 11 Functions of a complex variable (30-XX) 11 Systems theory; control (93-XX) 10 Statistics (62-XX) 8 Difference and functional equations (39-XX) 8 Operator theory (47-XX) 6 Mechanics of deformable solids (74-XX) 4 Quantum theory (81-XX) 3 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
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https://dlmf.nist.gov/5.9
|
# §5.9 Integral Representations
## §5.9(i) Gamma Function
5.9.1 $\frac{1}{\mu}\Gamma\left(\frac{\nu}{\mu}\right)\frac{1}{z^{\nu/\mu}}=\int_{0}^% {\infty}\exp\left(-zt^{\mu}\right)t^{\nu-1}\mathrm{d}t,$
$\Re\nu>0$, $\mu>0$, and $\Re z>0$. (The fractional powers have their principal values.)
### Hankel’s Loop Integral
5.9.2 $\frac{1}{\Gamma\left(z\right)}=\frac{1}{2\pi i}\int_{-\infty}^{(0+)}e^{t}t^{-z% }\mathrm{d}t,$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\int$: integral and $z$: complex variable A&S Ref: 6.1.4 (in a slightly different form.) Referenced by: §5.21, §5.9(i) Permalink: http://dlmf.nist.gov/5.9.E2 Encodings: TeX, pMML, png See also: Annotations for §5.9(i), §5.9(i), §5.9 and Ch.5
where the contour begins at $-\infty$, circles the origin once in the positive direction, and returns to $-\infty$. $t^{-z}$ has its principal value where $t$ crosses the positive real axis, and is continuous. See Figure 5.9.1.
5.9.3 $c^{-z}\Gamma\left(z\right)=\int_{-\infty}^{\infty}|t|^{2z-1}e^{-ct^{2}}\mathrm% {d}t,$ $c>0$, $\Re z>0$,
where the path is the real axis.
5.9.4 $\Gamma\left(z\right)=\int_{1}^{\infty}t^{z-1}e^{-t}\mathrm{d}t+\sum_{k=0}^{% \infty}\frac{(-1)^{k}}{(z+k)k!},$ $z\neq 0,-1,-2,\dots$.
5.9.5 $\Gamma\left(z\right)=\int_{0}^{\infty}t^{z-1}\left(e^{-t}-\sum_{k=0}^{n}\frac{% (-1)^{k}t^{k}}{k!}\right)\mathrm{d}t,$ $-n-1<\Re z<-n$.
5.9.6 $\displaystyle\Gamma\left(z\right)\cos\left(\tfrac{1}{2}\pi z\right)$ $\displaystyle=\int_{0}^{\infty}t^{z-1}\cos t\mathrm{d}t,$ $0<\Re z<1$, 5.9.7 $\displaystyle\Gamma\left(z\right)\sin\left(\tfrac{1}{2}\pi z\right)$ $\displaystyle=\int_{0}^{\infty}t^{z-1}\sin t\mathrm{d}t,$ $-1<\Re z<1$.
5.9.8 $\Gamma\left(1+\frac{1}{n}\right)\cos\left(\frac{\pi}{2n}\right)=\int_{0}^{% \infty}\cos\left(t^{n}\right)\mathrm{d}t,$ $n=2,3,4,\dots$,
5.9.9 $\Gamma\left(1+\frac{1}{n}\right)\sin\left(\frac{\pi}{2n}\right)=\int_{0}^{% \infty}\sin\left(t^{n}\right)\mathrm{d}t,$ $n=2,3,4,\dots$.
### Binet’s Formula
5.9.10 $\operatorname{Ln}\Gamma\left(z\right)=\left(z-\tfrac{1}{2}\right)\ln z-z+% \tfrac{1}{2}\ln\left(2\pi\right)+2\int_{0}^{\infty}\frac{\operatorname{arctan}% \left(t/z\right)}{e^{2\pi t}-1}\mathrm{d}t,$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\mathrm{e}$: base of natural logarithm, $\int$: integral, $\operatorname{arctan}\NVar{z}$: arctangent function, $\operatorname{Ln}\NVar{z}$: general logarithm function, $\ln\NVar{z}$: principal branch of logarithm function and $z$: complex variable A&S Ref: 6.1.50 Referenced by: §5.9(i), §5.9(ii), Erratum (V1.0.10) for Equations (5.9.10), (5.9.11), (5.10.1), (5.11.1), (5.11.8) Permalink: http://dlmf.nist.gov/5.9.E10 Encodings: TeX, pMML, png Addition (effective with 1.0.10): To increase the region of validity of this equation, the logarithm of the gamma function that appears on its left-hand side has been changed to $\operatorname{Ln}\Gamma\left(z\right)$, where $\operatorname{Ln}$ is the general logarithm. Originally $\ln\Gamma\left(z\right)$ was used, where $\ln$ is the principal branch of the logarithm. Suggested 2015-02-13 by Philippe Spindel See also: Annotations for §5.9(i), §5.9(i), §5.9 and Ch.5
where $|\operatorname{ph}z|<\pi/2$ and the inverse tangent has its principal value.
5.9.11 $\operatorname{Ln}\Gamma\left(z+1\right)=-\gamma z-\frac{1}{2\pi i}\int_{-c-% \infty i}^{-c+\infty i}\frac{\pi z^{-s}}{s\sin\left(\pi s\right)}\zeta\left(-s% \right)\mathrm{d}s,$ ⓘ Symbols: $\Gamma\left(\NVar{z}\right)$: gamma function, $\gamma$: Euler’s constant, $\zeta\left(\NVar{s}\right)$: Riemann zeta function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{d}\NVar{x}$: differential of $x$, $\mathrm{i}$: imaginary unit, $\int$: integral, $\operatorname{Ln}\NVar{z}$: general logarithm function, $\ln\NVar{z}$: principal branch of logarithm function, $\sin\NVar{z}$: sine function, $s$: real or complex variable and $z$: complex variable Referenced by: §5.9(i), §5.9(ii), Erratum (V1.0.10) for Equations (5.9.10), (5.9.11), (5.10.1), (5.11.1), (5.11.8) Permalink: http://dlmf.nist.gov/5.9.E11 Encodings: TeX, pMML, png Addition (effective with 1.0.10): To increase the region of validity of this equation, the logarithm of the gamma function that appears on its left-hand side has been changed to $\operatorname{Ln}\Gamma\left(z+1\right)$, where $\operatorname{Ln}$ is the general logarithm. Originally $\ln\Gamma\left(z+1\right)$ was used, where $\ln$ is the principal branch of the logarithm. Suggested 2015-02-13 by Philippe Spindel See also: Annotations for §5.9(i), §5.9(i), §5.9 and Ch.5
where $|\operatorname{ph}z|\leq\pi-\delta$ ($<\pi$), $1, and $\zeta\left(s\right)$ is as in Chapter 25.
For additional representations see Whittaker and Watson (1927, §§12.31–12.32).
## §5.9(ii) Psi Function, Euler’s Constant, and Derivatives
For $\Re z>0$,
5.9.12 $\psi\left(z\right)=\int_{0}^{\infty}\left(\frac{e^{-t}}{t}-\frac{e^{-zt}}{1-e^% {-t}}\right)\mathrm{d}t,$
5.9.13 $\psi\left(z\right)=\ln z+\int_{0}^{\infty}\left(\frac{1}{t}-\frac{1}{1-e^{-t}}% \right)e^{-tz}\mathrm{d}t,$
5.9.14 $\psi\left(z\right)=\int_{0}^{\infty}\left(e^{-t}-\frac{1}{(1+t)^{z}}\right)% \frac{\mathrm{d}t}{t},$
5.9.15 $\psi\left(z\right)=\ln z-\frac{1}{2z}-2\int_{0}^{\infty}\frac{t\mathrm{d}t}{(t% ^{2}+z^{2})(e^{2\pi t}-1)}.$
5.9.16 $\psi\left(z\right)+\gamma=\int_{0}^{\infty}\frac{e^{-t}-e^{-zt}}{1-e^{-t}}% \mathrm{d}t=\int_{0}^{1}\frac{1-t^{z-1}}{1-t}\mathrm{d}t.$
5.9.17 $\psi\left(z+1\right)=-\gamma+\frac{1}{2\pi i}\int_{-c-\infty i}^{-c+\infty i}% \frac{\pi z^{-s-1}}{\sin\left(\pi s\right)}\zeta\left(-s\right)\mathrm{d}s,$
where $|\operatorname{ph}z|\leq\pi-\delta(<\pi)$ and $1.
5.9.18 $\gamma=-\int_{0}^{\infty}e^{-t}\ln t\mathrm{d}t=\int_{0}^{\infty}\left(\frac{1% }{1+t}-e^{-t}\right)\frac{\mathrm{d}t}{t}=\int_{0}^{1}(1-e^{-t})\frac{\mathrm{% d}t}{t}-\int_{1}^{\infty}e^{-t}\frac{\mathrm{d}t}{t}=\int_{0}^{\infty}\left(% \frac{e^{-t}}{1-e^{-t}}-\frac{e^{-t}}{t}\right)\mathrm{d}t.$ ⓘ Symbols: $\gamma$: Euler’s constant, $\mathrm{d}\NVar{x}$: differential of $x$, $\mathrm{e}$: base of natural logarithm, $\int$: integral and $\ln\NVar{z}$: principal branch of logarithm function A&S Ref: 6.3.22 Referenced by: (9.12.31) Permalink: http://dlmf.nist.gov/5.9.E18 Encodings: TeX, pMML, png See also: Annotations for §5.9(ii), §5.9 and Ch.5
5.9.19 ${\Gamma}^{(n)}\left(z\right)=\int_{0}^{\infty}(\ln t)^{n}e^{-t}t^{z-1}\mathrm{% d}t,$ $n\geq 0$, $\Re z>0$.
| 2021-01-27T14:28:48 |
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https://pdglive.lbl.gov/DataBlock.action?node=S067S2
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# (C) Other neutrino mixing results
The LSND collaboration reported in AGUILAR 2001 a signal which is consistent with ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillations. In a three neutrino framework, this would be a measurement of $\theta _{12}$ and $\Delta \mathit m{}^{2}_{21}$. This does not appear to be consistent with most of the other neutrino data. The following listings include results from ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ , ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ appearance and ${{\mathit \nu}_{{\mu}}}$, ${{\overline{\mathit \nu}}_{{\mu}}}$, ${{\mathit \nu}_{{e}}}$, and ${{\overline{\mathit \nu}}_{{e}}}$ disappearance experiments, and searches for $\mathit CPT$ violation.
# sin$^2(2{}\theta )$ for Large'' $\Delta \boldsymbol m{}^{2}$ ( ${{\overline{\boldsymbol \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\boldsymbol \nu}}_{{e}}}$ ) INSPIRE search
VALUE ($10^{-3}$) CL% DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<6.4\times 10^{2}$ 90 1
2013 A
ICAR ${{\overline{\mathit \nu}}_{{e}}}$ appearance
$<150$ 90 2
2012
MBNE MiniBooNE/SciBooNE
$\text{0.4 - 9.0}$ 99 3
2010
MBNE E$_{{{\mathit \nu}}}>$ 475 MeV
$\text{0.4 - 9.0}$ 99 4
2010
MBNE E$_{{{\mathit \nu}}}>$ 200 MeV
$<3.3$ 90 5
2009 B
MBNE MiniBooNE
$<1.7$ 90 6
2002
KAR2 Liquid Sci. calor.
$<1.1$ 90
2002
NTEV NUTEV FNAL
$5.3$ $\pm1.3$ $\pm9.0$ 7
2001
LSND LAMPF
$6.2$ $\pm2.4$ $\pm1.0$ 8
1996
LSND LAMPF
$\text{3 - 12}$ 80 9
1995
$<6$ 90 10
1995
1 ANTONELLO 2013A obtained the limit by assuming ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillation from the $\sim{}2\%$ of ${{\overline{\mathit \nu}}_{{\mu}}}$ evnets contamination in the CNGS beam.
2 CHENG 2012 is a combined fit of MiniBooNE and SciBooNE antineutrino data.
3 This value is for a two neutrino oscillation analysis for excess antineutrino events with E$_{{{\mathit \nu}}}>$ 475 MeV. At 90$\%$ CL there is no solution at high $\Delta \mathit m{}^{2}$. The best fit is at maximal mixing. The allowed region is consistent with LSND reported by AGUILAR 2001 . Supercedes AGUILAR-AREVALO 2009B.
4 This value is for a two neutrino oscillation analysis for excess antineutrino events with E$_{{{\mathit \nu}}}>$ 200 MeV with subtraction of the expected 12 events low energy excess seen in the neutrino component of the beam. At 90$\%$ CL there is no solution at high $\Delta \mathit m{}^{2}$. The best fit value is 0.007 for $\Delta \mathit m{}^{2}$ = 4.4 eV${}^{2}$.
5 This result is inconclusive with respect to small amplitude mixing suggested by LSND.
6 ARMBRUSTER 2002 is the final analysis of the KARMEN$~$2 data. See footnote in the preceding table for further details, and the paper for the exclusion plot.
7 AGUILAR 2001 is the final analysis of the LSND full data set. The deduced oscillation probability is $0.264$ $\pm0.067$ $\pm0.045\%$; the value of sin$^22\theta$ for large $\Delta \mathit m{}^{2}$ is twice this probability (although these values are excluded by other constraints). See footnote in preceding table for further details, and the paper for a plot showing allowed regions. Supersedes ATHANASSOPOULOS 1995 , ATHANASSOPOULOS 1996 , and ATHANASSOPOULOS 1998 .
8 ATHANASSOPOULOS 1996 reports ($0.31$ $\pm0.12$ $\pm0.05)\%$ for the oscillation probability; the value of sin$^22\theta$ for large $\Delta \mathit m{}^{2}$ should be twice this probability. See footnote in preceding table for further details, and see the paper for a plot showing allowed regions.
9 ATHANASSOPOULOS 1995 error corresponds to the $1.6\sigma$ band in the plot. The expected background is $2.7$ $\pm0.4$ events. Corresponds to an oscillation probability of ($0.34$ ${}^{+0.20}_{-0.18}$ $\pm0.07)\%$. For a different interpretation, see HILL 1995 . Replaced by ATHANASSOPOULOS 1996 .
10 HILL 1995 is a report by one member of the LSND Collaboration, reporting a different conclusion from the analysis of the data of this experiment (see ATHANASSOPOULOS 1995 ). Contrary to the rest of the LSND Collaboration, Hill finds no evidence for the neutrino oscillation ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ and obtains only upper limits.
References:
ANTONELLO 2013A
EPJ C73 2599 Search for Anomalies in the ${{\mathit \nu}_{{e}}}$ Appearance from a ${{\mathit \nu}_{{\mu}}}$ Beam
CHENG 2012
PR D86 052009 Dual Baseline Search for Muon Antineutrino Disappearance at 0.1 eV${}^{2}$ $<$ $\Delta$m${}^{2}$ $<$ 100 eV${}^{2}$
AGUILAR-AREVALO 2010
PRL 105 181801 Event Excess in the MiniBooNE Search for ${{\overline{\mathit \nu}}_{{\mu}}}\leftrightarrow{{\overline{\mathit \nu}}_{{e}}}$ Oscillations
AGUILAR-AREVALO 2009B
PRL 103 111801 A Search for Electron Antineutrino Appearance at the $\Delta \mathit m{}^{2}$ $\sim{}$ 1$~$eV${}^{2}$ Scale
ARMBRUSTER 2002
PR D65 112001 Upper Limits for Neutrino Oscillations ${{\overline{\mathit \nu}}_{{\mu}}}-{{\overline{\mathit \nu}}_{{e}}}$ from Muon Decay at Rest
AVVAKUMOV 2002
PRL 89 011804 A Search for ${{\mathit \nu}_{{\mu}}}-{{\mathit \nu}_{{e}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}-{{\overline{\mathit \nu}}_{{e}}}$ Oscillations at NUTeV
AGUILAR 2001
PR D64 112007 Evidence for Neutrino Oscillations from the Observation of ${{\overline{\mathit \nu}}_{{e}}}$ Appearance in a ${{\overline{\mathit \nu}}_{{\mu}}}$ Beam
ATHANASSOPOULOS 1996
PR C54 2685 Evidence for Neutrino Oscillations from Muon Decay at Rest
ATHANASSOPOULOS 1995
PRL 75 2650 Candidate Events in a Search for ${{\overline{\mathit \nu}}_{{\mu}}}$ $\leftrightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ Oscillations
HILL 1995
PRL 75 2654 Alternative Analysis of the LSND Neutrino Oscillation Search Data on ${{\overline{\mathit \nu}}_{{\mu}}}$ $\leftrightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$
| 2020-09-21T10:44:43 |
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http://dlmf.nist.gov/28.1
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# §28.1 Special Notation
(For other notation see Notation for the Special Functions.)
$m,n$ integers. real variables. complex variable. order of the Mathieu function or modified Mathieu function. (When $\nu$ is an integer it is often replaced by $n$.) arbitrary small positive number. real or complex parameters of Mathieu’s equation with $q=h^{2}$. unless indicated otherwise, derivatives with respect to the argument
The main functions treated in this chapter are the Mathieu functions
$\mathop{\mathrm{ce}_{\nu}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{se}_{\nu}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{fe}_{n}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{ge}_{n}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{me}_{\nu}\/}\nolimits\!\left(z,q\right)$,
and the modified Mathieu functions
$\mathop{\mathrm{Ce}_{\nu}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{Se}_{\nu}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{Fe}_{n}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{Ge}_{n}\/}\nolimits\!\left(z,q\right)$, $\mathop{\mathrm{Me}_{\nu}\/}\nolimits\!\left(z,q\right)$, $\mathop{{\mathrm{M}^{(j)}_{\nu}}\/}\nolimits\!\left(z,h\right)$, $\mathop{{\mathrm{Mc}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$, $\mathop{{\mathrm{Ms}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$, $\mathop{\mathrm{Ie}_{n}\/}\nolimits\!\left(z,h\right)$, $\mathop{\mathrm{Io}_{n}\/}\nolimits\!\left(z,h\right)$, $\mathop{\mathrm{Ke}_{n}\/}\nolimits\!\left(z,h\right)$, $\mathop{\mathrm{Ko}_{n}\/}\nolimits\!\left(z,h\right)$.
The functions $\mathop{{\mathrm{Mc}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$ and $\mathop{{\mathrm{Ms}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$ are also known as the radial Mathieu functions.
The eigenvalues of Mathieu’s equation are denoted by
$\mathop{a_{n}\/}\nolimits\!\left(q\right),$ $\mathop{b_{n}\/}\nolimits\!\left(q\right),$ $\mathop{\lambda_{\nu}\/}\nolimits\!\left(q\right).$
The notation for the joining factors is
$g_{\mathit{e},n}(h),$ $g_{\mathit{o},n}(h),$ $f_{\mathit{e},n}(h),$ $f_{\mathit{o},n}(h).$
Alternative notations for the parameters $a$ and $q$ are shown in Table 28.1.1.
Alternative notations for the functions are as follows.
## Arscott (1964b) and McLachlan (1947)
$\displaystyle\mathrm{Fey}_{n}(z,q)$ $\displaystyle=\sqrt{\tfrac{1}{2}\pi}g_{\mathit{e},n}(h)\mathop{\mathrm{ce}_{n}% \/}\nolimits\!\left(0,q\right)\mathop{{\mathrm{Mc}^{(2)}_{n}}\/}\nolimits\!% \left(z,h\right),$ $\displaystyle\mathrm{Me}_{n}^{(1,2)}(z,q)$ $\displaystyle=\sqrt{\tfrac{1}{2}\pi}g_{\mathit{e},n}(h)\mathop{\mathrm{ce}_{n}% \/}\nolimits\!\left(0,q\right)\mathop{{\mathrm{Mc}^{(3,4)}_{n}}\/}\nolimits\!% \left(z,h\right),$ $\displaystyle\mathrm{Gey}_{n}(z,q)$ $\displaystyle=\sqrt{\tfrac{1}{2}\pi}g_{\mathit{o},n}(h)\mathop{\mathrm{se}_{n}% \/}\nolimits'\!\left(0,q\right)\mathop{{\mathrm{Ms}^{(2)}_{n}}\/}\nolimits\!% \left(z,h\right),$ $\displaystyle\mathrm{Ne}_{n}^{(1,2)}(z,q)$ $\displaystyle=\sqrt{\tfrac{1}{2}\pi}g_{\mathit{o},n}(h)\mathop{\mathrm{se}_{n}% \/}\nolimits'\!\left(0,q\right)\mathop{{\mathrm{Ms}^{(3,4)}_{n}}\/}\nolimits\!% \left(z,h\right).$
Arscott (1964b) also uses $-\mathrm{i}\mu$ for $\nu$.
## Campbell (1955)
$\displaystyle\mathrm{in}_{n}$ $\displaystyle=\mathop{\mathrm{fe}_{n}\/}\nolimits,$ $\displaystyle\mathrm{ceh}_{n}$ $\displaystyle=\mathop{\mathrm{Ce}_{n}\/}\nolimits,$ $\displaystyle\mathrm{inh}_{n}$ $\displaystyle=\mathop{\mathrm{Fe}_{n}\/}\nolimits,$ $\displaystyle\mathrm{jn}_{n}$ $\displaystyle=\mathop{\mathrm{ge}_{n}\/}\nolimits,$ $\displaystyle\mathrm{seh}_{n}$ $\displaystyle=\mathop{\mathrm{Se}_{n}\/}\nolimits,$ $\displaystyle\mathrm{jnh}_{n}$ $\displaystyle=\mathop{\mathrm{Ge}_{n}\/}\nolimits.$
## Abramowitz and Stegun (1964, Chapter 20)
$F_{\nu}(z)=\mathop{\mathrm{Me}_{\nu}\/}\nolimits\!\left(z,q\right).$
## National Bureau of Standards (1967)
With $s=4q$,
$\displaystyle\mathrm{Se}_{n}(s,z)$ $\displaystyle=\dfrac{\mathop{\mathrm{ce}_{n}\/}\nolimits\!\left(z,q\right)}{% \mathop{\mathrm{ce}_{n}\/}\nolimits\!\left(0,q\right)},$ $\displaystyle\mathrm{So}_{n}(s,z)$ $\displaystyle=\dfrac{\mathop{\mathrm{se}_{n}\/}\nolimits\!\left(z,q\right)}{% \mathop{\mathrm{se}_{n}\/}\nolimits'\!\left(0,q\right)}.$
## Stratton et al. (1941)
With $c=2\sqrt{q}$,
$\displaystyle\mathrm{Se}_{n}(c,z)$ $\displaystyle=\dfrac{\mathop{\mathrm{ce}_{n}\/}\nolimits\!\left(z,q\right)}{% \mathop{\mathrm{ce}_{n}\/}\nolimits\!\left(0,q\right)},$ $\displaystyle\mathrm{So}_{n}(c,z)$ $\displaystyle=\dfrac{\mathop{\mathrm{se}_{n}\/}\nolimits\!\left(z,q\right)}{% \mathop{\mathrm{se}_{n}\/}\nolimits'\!\left(0,q\right)}.$
## Zhang and Jin (1996)
The radial functions $\mathop{{\mathrm{Mc}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$ and $\mathop{{\mathrm{Ms}^{(j)}_{n}}\/}\nolimits\!\left(z,h\right)$ are denoted by $\mathop{{\mathrm{Mc}^{(j)}_{n}}\/}\nolimits\!\left(z,q\right)$ and $\mathop{{\mathrm{Ms}^{(j)}_{n}}\/}\nolimits\!\left(z,q\right)$, respectively.
| 2017-01-22T05:57:27 |
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https://par.nsf.gov/biblio/10106887-new-near-infrared-jhk-light-curve-templates-rr-lyrae-variables
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New near-infrared JHK s light-curve templates for RR Lyrae variables
We provide homogeneous optical ( U B V R I ) and near-infrared (NIR, J H K ) time series photometry for 254 cluster ( ω Cen, M 4) and field RR Lyrae (RRL) variables. We ended up with more than 551 000 measurements, of which only 9% are literature data. For 94 fundamental (RRab) and 51 first overtones (RRc) we provide a complete optical/NIR characterization (mean magnitudes, luminosity amplitudes, epoch of the anchor point). The NIR light curves of these variables were adopted to provide new light-curve templates for both RRc and RRab variables. The templates for the J and the H bands are newly introduced, together with the use of the pulsation period to discriminate among the different RRab templates. To overcome subtle uncertainties in the fit of secondary features of the light curves we provide two independent sets of analytical functions (Fourier and periodic Gaussian series). The new templates were validated by using 26 ω Cen and Bulge RRLs. We find that the difference between the measured mean magnitude along the light curve and the mean magnitude estimated by using the template on a single randomly extracted phase point is better than 0.01 mag ( σ = more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10106887
Journal Name:
Astronomy & Astrophysics
Volume:
625
Page Range or eLocation-ID:
A1
ISSN:
0004-6361
While conventional Type Ia supernova (SN Ia) cosmology analyses rely primarily on rest-frame optical light curves to determine distances, SNe Ia are excellent standard candles in near-infrared (NIR) light, which is significantly less sensitive to dust extinction. An SN Ia spectral energy distribution (SED) model capable of fitting rest-frame NIR observations is necessary to fully leverage current and future SN Ia data sets from ground- and space-based telescopes including HST, LSST, JWST, and RST. We construct a hierarchical Bayesian model for SN Ia SEDs, continuous over time and wavelength, from the optical to NIR (B through H, or $0.35{-}1.8\, \mu$m). We model the SED as a combination of physically distinct host galaxy dust and intrinsic spectral components. The distribution of intrinsic SEDs over time and wavelength is modelled with probabilistic functional principal components and the covariance of residual functions. We train the model on a nearby sample of 79 SNe Ia with joint optical and NIR light curves by sampling the global posterior distribution over dust and intrinsic latent variables, SED components and population hyperparameters. Photometric distances of SNe Ia with NIR data near maximum obtain a total RMS error of 0.10 mag with our BayeSN model, compared tomore »
| 2022-10-07T15:41:21 |
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http://webarchive.nationalarchives.gov.uk/20110809091832/http:/www.teachingandlearningresources.org.uk/node/4829
|
This snapshot, taken on
11/08/2011
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# Unit 2 learning overview
You can use this overview to inform your planning and help secure children's learning of the mathematics covered in the unit. It includes understanding the value of each digit in decimal numbers, multiplying and dividing decimals by 10, 100 or 1000, developing written methods to include multiplication and division, and deciding when to use mental, written or calculator methods to solve problems.
Children secure understanding of the value of each digit in decimal numbers with up to two places. For example, they use coins (£1, 10 p and 1 p) or base-10 apparatus (with a 'flat' representing one whole) to model the number 2.45, recognising that this number is made up of two wholes, four tenths and five hundredths.
They understand the relationship between hundredths, tenths and wholes and use this to answer questions such as:
• 'Which of these decimals is equal to $\frac{19}{100}$?'
• 1.9
• 10.19
• 0.19
• 19.1
• 'How many hundredths are the same as three tenths?'
Children use images such as bead strings or number lines to help them count in tenths and hundredths from various start numbers. They position decimals on number lines, explaining for example that 2.85 lies halfway between 2.8 and 2.9. They suggest numbers that lie between, say, 13.5 and 13.6.
Children create and continue sequences of decimals, for example counting up from zero in steps of 0.2 or backwards from 3 in steps of 0.3. They identify the rule for a given sequence and use this to find the next or missing terms, e.g. finding the missing numbers in the sequence: 1.4, ☐, 1.8, 2, 2.2, ☐. They use counting to answer questions such as $0.2×6 \text{or} 1.8÷0.3$, explaining how they worked out the answer.
Children partition decimals using both decimal and fraction notation, for example, recording 6.38 as $6+\frac{3}{10}+\frac{8}{100}$ and as $6+0.3+0.08$. They write a decimal given its parts: e.g. they record the number that is made from 4 wholes, 2 tenths and 7 hundredths as 4.27. They apply their understanding in activities such as:
• 'Find the missing number in $17.82-\square =17.22$'
• 'Play "Zap the digit": in pairs, choose a decimal to enter into a calculator, e.g. 47.25. Take turns to "zap" (remove) a particular digit using subtraction. For example, to "zap" the 2 in 47.25, subtract 0.2 to leave 47.05.'
Children extend their understanding of multiplying and dividing by 10, 100 or 1000 to decimals. They use digit cards and a place value grid to practise multiplying and dividing numbers by 10, 100 and 1000, e.g. moving each digit two columns to the right to work out that $132÷100=1.32$. They recognise that as each digit moves one column to the right, its value becomes 10 times smaller (and the reverse for multiplication). They apply this understanding in a range of activities such as:
• 'Find the missing number in $0.42×\square =42$'
• 'Play 'Stepping stones': work out what operation to enter into a calculator to turn the number in one stepping stone into the number in the next stepping stone.'
Children extend written methods for addition to include numbers with one and two decimal places. They use their understanding that ten tenths make one whole and ten hundredths make one tenth to explain each stage of their calculation, for example, to add 72.8 km and 54.6 km.
8 tenths add 6 tenths makes 14 tenths, or 1 whole and 4 tenths. The one whole is 'carried' into the units column and the four tenths is written in the tenths column.
With subtraction of three-digit numbers and decimals, some children may be ready to use more compact methods. The number of steps in the vertical recording of the 'counting up' method is reduced.
For $326-178$, they extend their understanding of 'difference' by counting up from 178 to 326, initially using an empty number line and then moving on to vertical recording.
$\begin{array}{ccc}& 326& \\ -& \underset{——}{178}& \\ & \phantom{22}2& \phantom{\rule{0.1em}{0ex}}\to 180\\ \phantom{-}& \phantom{2}20& \phantom{\rule{0.1em}{0ex}}\to 200\\ & 100& \phantom{\rule{0.1em}{0ex}}\to 300\\ & \underset{——}{\phantom{2}26}& \phantom{\rule{0.1em}{0ex}}\to 326\\ & 148& \end{array}$
$\begin{array}{ccc}& 326& \\ -& \underset{——}{178}& \\ & \phantom{2}22& \phantom{\rule{0.1em}{0ex}}\to 200\\ \phantom{-}& \underset{——}{126}& \phantom{\rule{0.1em}{0ex}}\to 326\\ & 148& \end{array}$
The examples below work towards the decomposition method. For example: $563-248$, adjustment from the tens to the ones, or 'borrowing ten'
$\begin{array}{cc}& 500+60+3\\ -& \underset{———————}{200+40+8}\end{array}$
$\begin{array}{ccc}\hfill \phantom{-}5& \hfill \stackrel{5}{\overline{)6}}& \hfill \stackrel{13}{\overline{)3}}\\ \hfill -\underline{2}& \hfill \underline{\phantom{\rule{0.5em}{0ex}}\stackrel{\phantom{5}}{4}}& \hfill \underline{\phantom{\rule{0.5em}{0ex}}\stackrel{\phantom{13}}{8}}\\ \hfill \phantom{-}3& \hfill \stackrel{\phantom{5}}{1}& \hfill \stackrel{\phantom{13}}{5}\end{array}$
Discuss how $60+3$ can be partitioned into $50+13$. The subtraction of the ones becomes 'thirteen minus eight', a known fact.
Example: $563-271$, adjustment from the hundreds to the tens, or 'borrowing one hundred'
$\begin{array}{cc}& 500+60+3\\ -& \underline{200+70+1}\end{array}$
$\begin{array}{c}\hfill \phantom{-}\stackrel{400}{\overline{)500}}+\stackrel{160}{\overline{)60}}+3\\ \hfill -\underline{\phantom{\rule{0.5em}{0ex}}\stackrel{\phantom{400}}{200}+\stackrel{\phantom{160}}{70}+1}\\ \hfill \phantom{-}\stackrel{\phantom{500}}{200}+\stackrel{\phantom{113}}{90}+2\end{array}$
$\begin{array}{ccc}\hfill \phantom{-}\stackrel{4}{\overline{)5}}& \hfill \stackrel{16}{\overline{)6}}& \hfill 3\\ \hfill -\underline{2}& \hfill \underline{\phantom{\rule{0.5em}{0ex}}\stackrel{\phantom{16}}{7}}& \hfill \underline{\phantom{\rule{0.5em}{0ex}}1}\\ \hfill \phantom{-}2& \hfill \stackrel{\phantom{16}}{9}& \hfill 2\end{array}$
Discuss how $500+60$ can be partitioned into $400+160$. The subtraction of the tens becomes '160 minus 70', an application of subtraction of multiples of ten.
Children continue to rehearse their recall of multiplication and division facts and use these facts and their knowledge of place value to multiply and divide multiples of 10 and 100. They use jottings to record, support or explain mental multiplication and division of TU by U, forging links to the written methods that they are developing and refining. For example: $38×7$, $38×7=\left(30×7\right)+\left(8×7\right)=210+56=266$.
× 7 30 210 8 56 266
The number with the most digits is placed in the left-hand column of the grid so that it is easier to add the partial products.
30 + 8 × 7 210 56 266
The next step is to move the number being multiplied (38) to an extra row at the top of the grid. Presenting the grid like this helps children to set out and add the partial products 210 and 56.
$\begin{array}{ccc}& 30+8& \\ ×& \underline{\phantom{30}\phantom{+}7}& \\ & \phantom{30}210& 30×7=210\\ & \underline{\phantom{\rule{0.5em}{0ex}}\phantom{30}56}& \phantom{3}8×7=\phantom{2}56\\ & \underline{\phantom{30}266}& \end{array}$
The next step is to represent the method of recording to a column format, but showing the working. Point out the links with the grid method.
$\begin{array}{cc}& \phantom{2}38\\ ×& \underline{\phantom{32}7}\\ & 210\\ & \underline{\phantom{3}56}\\ & \underline{266}\end{array}$
Children should describe what they do by referring to the actual values of the digits in the columns (e.g. the first step in $38×7$ is 'thirty multiplied by seven', not 'three times seven', although the relationship to $3×7$ should be stressed).
Children use the multiplication and division facts that they know to find factors of numbers, for example, determining that 35 has a factor pair of 7 and 5, so 350 has a factor pair of 70 and 5 or 7 and 50. They use their knowledge of factors for special cases of multiplication and division calculations. For example, to multiply 15 by 6, they work out $15×3×2=45×2=90$, and to divide 72 by 6 they halve it to get 36, then divide by 3. They find common multiples, investigating questions such as:
• 'What is the smallest whole number that is divisible by five and by three?'
• 'Tell me a number that is both a multiple of four and a multiple of six. Are there any other possibilities?'
Children solve a range of one-step and two-step word problems, choosing whether to use mental, written or calculator methods. They record their method in a clear and logical way, using jottings and diagrams where appropriate. They compare their methods with others, recognising where another method is more efficient than the one that they chose. They solve inverse operation problems such as $3.42+\square =10$, and word problems such as:
• 'Emma saves £3.50 each week. How much has she saved after 16 weeks?'
• 'I buy presents costing £9.63, £5.27 and £3.72. How much change do I have from £20?'
• '1 bag of sugar weighs 2.2 pounds. How much will ten bags of sugar weigh?'
• 'Zak saves half of his pocket money each month. In one year he saves £51. How much pocket money does he get each month?'
| 2013-06-18T22:28:17 |
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|
https://www.anl.gov/reference/the-advanced-photon-source-a-bright-light-for-drug-discovery
|
# Argonne National Laboratory .st0{fill:none;} .st1{fill:#007934;} .st2{fill:#0082CA;} .st3{fill:#101E8E;} .st4{fill:#FFFFFF;} .st5{fill:#A22A2E;} .st6{fill:#D9272E;} .st7{fill:#82BC00;} Argonne National Laboratory
Reference | Factsheet | Argonne National Laboratory
# The Advanced Photon Source: A Bright Light for Drug Discovery
Development of many critically important pharmaceuticals, existing and yet to come, grows out of macromolecular x-ray crystallography (MX)-based research carried out at sources of high-brightness x-rays such as the U.S. Department of Energy Office of Science’s Advanced Photon Source (APS) at Argonne National Laboratory, and at the proposed APS Upgrade that will open new vistas in drug discovery.
| 2019-10-22T04:16:51 |
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https://pdglive.lbl.gov/DataBlock.action?node=S126SHH
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# ${{\boldsymbol H}^{0}}{{\boldsymbol H}^{0}}$ Production INSPIRE search
The 95$\%$ CL limits are for the cross section (CS) and Higgs self coupling (${{\mathit \kappa}_{{\lambda}}}$) scaling factors both relative to the SM predictions.
CS ${{\mathit \kappa}_{{\lambda}}}$ CL% DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<6.9$ $-5.0$ to 12.0 95 1
2020 C
ATLS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit W}}{{\mathit W}^{*}}{{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit W}}{{\mathit W}^{*}}{{\mathit W}}{{\mathit W}^{*}}$
$<40$ 95 2
2020 E
ATLS 13 TeV, ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$
$<12.9$ 95 3
2019 A
ATLS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$
$<300$ 95 4
2019 O
ATLS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$
$<160$ 95 5
2019 T
ATLS 13 TeV, ${{\mathit W}}{{\mathit W}^{*}}{{\mathit W}}{{\mathit W}^{*}}$
$<24$ $-11$ to 17 95 6
2019
CMS 13 TeV, ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$
$<75$ 95 7
2019 AB
CMS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$
$<22.2$ $-11.8$ to 18.8 95 8
2019 BE
CMS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \gamma}}{{\mathit \gamma}}$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit Z}}{{\mathit Z}^{*}}$
$<179$ 95 9
2019 H
CMS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$
$<230$ 95 10
2018 BU
ATLS 13 TeV, ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}^{*}}$
$<12.7$ 95 11
2018 CQ
ATLS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$
$<22$ $-8.2$ to 13.2 95 12
2018 CW
ATLS 13 TeV, ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$
$<30$ 95 13
2018 A
CMS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$
$<79$ 95 14
2018 F
CMS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$
$<43$ 95 15
2017 CN
CMS 8 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$
$<108$ 95 16
2016 I
ATLS 13 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$
$<74$ 95 17
2016 BQ
CMS 8 TeV, ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$
$<70$ 95 18
2015 CE
ATLS 8 TeV, ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}}$
1 AAD 2020C combine results of up to 36.1 fb${}^{-1}$ data at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit W}}{{\mathit W}^{*}}{{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit W}}{{\mathit W}^{*}}{{\mathit W}}{{\mathit W}^{*}}$ (AABOUD 2018CW, AABOUD 2018CQ, AABOUD 2019A, AABOUD 2019O, AABOUD 2018BU, and AABOUD 2019T).
2 AAD 2020E search non-resonant for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ , where one of the Higgs bosons decays to ${{\mathit b}}{{\overline{\mathit b}}}$ and the other decays to either ${{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit Z}}{{\mathit Z}^{*}}$ , or ${{\mathit \tau}}{{\mathit \tau}}$ , with data of 139 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section at 95$\%$ CL is measured to be 1.2 pb, which corresponds to about 40 times the SM prediction.
3 AABOUD 2019A search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ with data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ production cross section at 95$\%$ is measured to be 147 fb, which corresponds to about 12.9 times the SM prediction.
4 AABOUD 2019O search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$ with data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section at 95$\%$ CL is calculated to be 10 pb from the observed upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit W}}{{\mathit W}^{*}}$ production cross section of 2.5 pb assuming the SM branching fractions. The former corresponds to about 300 times the SM prediction.
5 AABOUD 2019T search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}{{\mathit W}}{{\mathit W}^{*}}$ with data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section at 95$\%$ is measured to be 5.3 pb, which corresponds to about 160 times the SM prediction.
6 SIRUNYAN 2019 search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ with data of 35.9 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ production cross section at 95$\%$ CL is measured to be 2.0 fb, which corresponds to about 24 times the SM prediction. The effective Higgs boson self-coupling $\kappa _{\lambda }$ ( = $\lambda _{ {{\mathit H}} {{\mathit H}} {{\mathit H}} }$ $/$ $\lambda {}^{SM}_{ {{\mathit H}} {{\mathit H}} {{\mathit H}} }$) is constrainted to be $-11$ $<$ $\kappa _{\lambda }$ $<$ $17$ at 95$\%$ CL assuming all other Higgs boson couplings are at their SM value.
7 SIRUNYAN 2019AB search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , where 4 heavy flavor jets from two Higgs bosons are resolved, with data of 35.9 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ production cross section at 95$\%$ is measured to be 847 fb, which corresponds to about 75 times the SM prediction.
8 SIRUNYAN 2019BE combine results of 13 TeV 35.9 fb${}^{-1}$ data: SIRUNYAN 2019 , SIRUNYAN 2018A, SIRUNYAN 2019AB, SIRUNYAN 2019H, and SIRUNYAN 2018F.
9 SIRUNYAN 2019H search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , where one of ${{\mathit b}}{{\overline{\mathit b}}}$ pairs is highly boosted and the other one is resolved, with data of 35.9 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ production cross section at 95$\%$ is measured to be 1980 fb, which corresponds to about 179 times the SM prediction.
10 AABOUD 2018BU search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}^{*}}$ with the final state of ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit j}}{{\mathit j}}$ using data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section at 95$\%$ CL is measured to be 7.7 pb, which corresponds to about 230 times the SM prediction. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}^{*}}$ at 95$\%$ CL is measured to be 7.5 fb (see thier Table 6).
11 AABOUD 2018CQ search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ with data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ production cross section at 95$\%$ is measured to be 30.9 fb, which corresponds to about 12.7 times the SM prediction.
12 AABOUD 2018CW search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ with data of 36.1 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section at 95$\%$ is measured to be 0.73 pb, which corresponds to about 22 times the SM prediction. The effective Higgs boson self-coupling $\kappa _{\lambda }$ is constrained to be $-8.2$ $<$ $\kappa _{\lambda }$ $<$ $13.2$ at 95$\%$ CL assuming all other Higgs boson couplings are at their SM value.
13 SIRUNYAN 2018A search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ with data of 35.9 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit g}}$ ${{\mathit g}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ production cross section is measured to be 75.4 fb, which corresponds to about 30 times the SM prediction. Limits on Higgs-boson trilinear coupling ${{\mathit \lambda}_{{HHH}}}$ and top Yukawa coupling ${{\mathit y}_{{t}}}$ are also given (see their Fig. 6).
14 SIRUNYAN 2018F search non-resonant for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ , where ${{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ is either ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ or ${{\mathit Z}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \nu}}$ (${{\mathit \ell}}$ is ${{\mathit e}}$ , ${{\mathit \mu}}$ or a leptonically decaying ${{\mathit \tau}}$), with data of 35.9 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ production cross section at 95$\%$ CL is measured to be 72 fb, which corresponds to about 79 times the SM prediction.
15 SIRUNYAN 2017CN search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ with data of 18.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. Results are then combined with the published results of the ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , which use data of up to 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The upper limit on the ${{\mathit g}}$ ${{\mathit g}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section is measured to be 0.59 pb from ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , which corresponds to about 59 times the SM prediction (gluon fusion). The combined upper limit is 0.43 pb, which is about 43 times the SM prediction. The quoted values are given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV.
16 AABOUD 2016I search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ with data of 3.2 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. The upper limit on the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ production cross section is measured to be 1.22 pb. This result corresponds to about 108 times the SM prediction (gluon fusion), which is $11.3$ ${}^{+0.9}_{-1.0}$ fb (NNLO+NNLL) including top quark mass effects. The quoted values are given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125 GeV .
17 KHACHATRYAN 2016BQ search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ with data of 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The upper limit on the ${{\mathit g}}$ ${{\mathit g}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ production is measured to be 1.85 fb, which corresponds to about 74 times the SM prediction and is translated into 0.71 pb for ${{\mathit g}}$ ${{\mathit g}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section. Limits on Higgs-boson trilinear coupling $\lambda$ are also given.
18 AAD 2015CE search for ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production using ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ and ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}}$ with data of 20.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. These results are then combined with the published results of the ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit H}^{0}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , which use data of up to 20.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The upper limits on the ${{\mathit g}}$ ${{\mathit g}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit H}^{0}}$ production cross section are measured to be 1.6 pb, 11.4 pb, 2.2 pb and 0.62 pb from ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}}{{\mathit \tau}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ , respectively. The combined upper limit is 0.69 pb, which corresponds to about 70 times the SM prediction. The quoted results are given for ${\mathit m}_{{{\mathit H}^{0}}}$ = 125.4 GeV. See their Table 4.
References:
PL B800 135103 Combination of searches for Higgs boson pairs in $pp$ collisions at $\sqrt{s} =$13 TeV with the ATLAS detector
PL B801 135145 Search for non-resonant Higgs boson pair production in the $bb\ell\nu\ell\nu$ final state with the ATLAS detector in $pp$ collisions at $\sqrt{s} = 13$ TeV
AABOUD 2019T
JHEP 1905 124 Search for Higgs boson pair production in the $WW^{(*)}WW^{(*)}$ decay channel using ATLAS data recorded at $\sqrt{s}=13$ TeV
AABOUD 2019O
JHEP 1904 092 Search for Higgs boson pair production in the $b\bar{b}WW^{*}$ decay mode at $\sqrt{s}=13$ TeV with the ATLAS detector
AABOUD 2019A
JHEP 1901 030 Search for pair production of Higgs bosons in the $b\bar{b}b\bar{b}$ final state using proton-proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector
SIRUNYAN 2019H
JHEP 1901 040 Search for production of Higgs boson pairs in the four b quark final state using large-area jets in proton-proton collisions at $\sqrt{s}=$ 13 TeV
SIRUNYAN 2019
PL B788 7 Search for Higgs boson pair production in the $\gamma\gamma\mathrm{b\overline{b}}$ final state in pp collisions at $\sqrt{s}=$ 13 TeV
SIRUNYAN 2019AB
JHEP 1904 112 Search for nonresonant Higgs boson pair production in the $\mathrm{b\overline{b}b\overline{b}}$ final state at $\sqrt{s} =$ 13 TeV
SIRUNYAN 2019BE
PRL 122 121803 Combination of searches for Higgs boson pair production in proton-proton collisions at $\sqrt{s} =$ 13 TeV
AABOUD 2018CQ
PRL 121 191801 Search for resonant and non-resonant Higgs boson pair production in the ${b\bar{b}\tau^+\tau^-}$ decay channel in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
AABOUD 2018BU
EPJ C78 1007 Search for Higgs boson pair production in the $\gamma\gamma WW^{*}$ channel using $pp$ collision data recorded at $\sqrt{s} = 13$ TeV with the ATLAS detector
AABOUD 2018CW
JHEP 1811 040 Search for Higgs boson pair production in the $\gamma\gamma b\bar{b}$ final state with 13 TeV $pp$ collision data collected by the ATLAS experiment
SIRUNYAN 2018A
PL B778 101 Search for Higgs Boson Pair Production in Events with Two Bottom Quarks and Two Tau Leptons in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2018F
JHEP 1801 054 Search for Resonant and Nonresonant Higgs Boson Pair Production in the ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ Final State in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017CN
PR D96 072004 Search for Higgs Boson Pair Production in the ${\mathit {\mathit b}}{\mathit {\mathit b}}{{\mathit \tau}}{{\mathit \tau}}$ Final State in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
AABOUD 2016I
PR D94 052002 Search for Pair Production of Higgs Bosons in the ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ Final State using Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
KHACHATRYAN 2016BQ
PR D94 052012 Search for Two Higgs Bosons in Final States Containing Two Photons and Two Bottom Quarks in Proton-Proton Collisions at 8 TeV
PR D92 092004 Searches for Higgs Boson Pair Production in the ${{\mathit h}}$ ${{\mathit h}}$ $\rightarrow$ ${\mathit {\mathit b}}{\mathit {\mathit b}}{{\mathit \tau}}{{\mathit \tau}}$, ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}^{*}}$, ${{\mathit \gamma}}{{\mathit \gamma}}{\mathit {\mathit b}}{\mathit {\mathit b}}$, ${\mathit {\mathit b}}{\mathit {\mathit b}}{\mathit {\mathit b}}{\mathit {\mathit b}}$ Channels with the ATLAS Detector
| 2021-02-28T19:39:10 |
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|
http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lec2_6.html
|
##### Personal tools
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You are here: Home More on Random Variables
# More on Random Variables
##### Document Actions
Expectation :: Properties :: Pairs :: Independence :: Two R.V.S. :: Functions :: Inequalities :: Conditional :: General
## Characteristic functions
The characteristic function is essentially the Fourier transform of the p.d.f. or p.m.f. They are useful in practice not for the usual reasons engineers use Fourier transforms (e.g., frequency content), but because they can provide a means of computing moments (as we will see), and they are useful in finding distributions of sums of independent random variables.
Let us write some more explicit formulas. Suppose is a continuous random variable. Then (by the law of the unconcious statistician)
This may be recognized as the Fourier transform of , where is the ''frequency'' variable. (Comment on sign of exponent.) Note that given we can determine by an inverse Fourier transform:
If is a discrete r.v.,
which we recognize as the discrete-time Fourier transform, and as before is the ''frequency'' variable. (Comment on the sign of the exponent.) Given a , we can find by the inverse discrete-time Fourier transform.
Properties:
1. . (Why?)
2. . (Why?)
3. and form a unique Fourier transform pair.
Thus, provides yet another way of displaying the probability structure of .
4. . This is referred to as the Fourier-Stieltjes transform of .
5. is uniformly continuous.
We can write
Theorem 1 If then
That is, we can obtain moments by differentiating the characteristic function. For this reason, characteristic functions (or functions which are very similarly defined) are sometimes referred to as moment generating functions .
Then and are uniquely related (two-dimensional Fourier transforms).
Properties:
1. Moments:
2. and are independent if and only if for all .
## Sums of independent random variables
Let and be independent r.v.s, and let
Then
But also
So
If and are continuous r.v.s, then so is .
by the convolution theorem .
Thus, when continuous independent random variables are added, the p.d.f of the sum is the convolution of the p.d.f.s (and respectively p.m.f. for discrete independent r.v.s).
## An example: Jointly Gaussian
If , then
We make an observation here: the ''form'' of the Gaussian p.d.f. is the exponential of quadratics. The form of the Fourier transform of the eponential of quadratics is of the form exponential of quadratics. This little fact gives rise to much of the analytical and practical usefulness of Gaussian r.v.s.
## Characteristic functions marginals
We observe that
In our Gaussian example, we have
which is the ch.f. for a Gaussian,
We could, of course, have obtained a similar result via integration, but this is much easier.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 31). More on Random Variables. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lec2_6.html. This work is licensed under a Creative Commons License
| 2017-12-15T00:41:06 |
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https://www.usgs.gov/media/files/iron-ore-2017-tables-only-release
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# Iron Ore in 2017, tables-only release
Iron Ore in 2017, tables-only release
## Detailed Description
Advance data tables (XLSX format) for the iron ore chapter of the Minerals Yearbook 2017. A version with an embedded text document and also a PDF of text and tables will follow.
| 2020-04-01T02:00:13 |
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https://www.federalreserve.gov/econres/notes/ifdp-notes/emerging-market-nonfinancial-corporate-debt-how-concerned-should-we-be-20170601.htm
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June 01, 2017
### Emerging Market Nonfinancial Corporate Debt: How Concerned Should We Be?1
Daniel Beltran, Keshav Garud, and Aaron Rosenblum
1. Introduction
Nonfinancial corporate (NFC) debt in emerging market economies (EMEs) has tripled since the global financial crisis (GFC), reaching roughly \$25 trillion, or 112 percent of GDP, in mid-2016. Several factors have contributed to the surge: the low interest rate environment since the GFC, financial deepening and maturation of EMEs, on-going financial globalization, and policy-induced stimulus channeled through EME state-owned banks. The rapidity of the rise in EME corporate debt to now significant levels has raised concerns about the risk this debt poses for EME countries and the global economy (IMF, 2016; BIS, 2016). In particular, many fear that a rise in global interest rates could lead to higher debt-service costs, more depreciated currencies, capital outflows, and lower earnings. Such developments could put further pressure on EME corporates, especially those that have issued dollar-denominated debt, and potentially trigger broader financial stress (Shin, 2013; McCauley et al., 2015; Acharya et al., 2015).2
In this note, we assess these concerns. We begin by providing an overview of the run-up in EME corporate debt. We then focus on the vulnerability of EME corporate balance sheets to shocks, including increases in global interest rates and exchange rate depreciations. Note that in this paper we look at the vulnerabilities side only and not at how much resources different countries would have to address the problems, if some of the risks discussed were to materialize.3 We evaluate the extent to which corporate borrowers could experience financial distress using balance sheet and income statement data for roughly 8,500 firms and in 15 emerging market economies.4 Finally, we assess the degree to which moves in financial markets would exacerbate the vulnerabilities of EME corporates. To do so, we stress test EME corporate balance sheets by imposing shocks to firms' borrowing costs, earnings, and the exchange rate.
We find a moderate degree of vulnerability at present. Only a few EMEs exhibit significant levels of risky corporate debt as a share of total debt. The results become even more positive when we scale the share of risky debt by GDP to gauge systemic importance. By this metric, outside of China, risky debt for most EMEs is around a tenth of GDP, which is considerably lower than the share of 50 percent for the East Asian economies before the Asian Financial Crisis. That said, the amount of risky debt appears quite sensitive to earnings, interest rate, and exchange rate shocks. Under our stress exercise, risky debt rises to notable shares of GDP in a number of countries, importantly China but also Brazil, Turkey, India, and Korea. For EMEs overall, the earnings and interest rate shocks are the most material. EME corporates appear less vulnerable to currency devaluations, because the portion of EME corporate debt denominated in foreign currency has been steadily declining for over a decade.
Other studies on EME corporate vulnerabilities also stress test the shares of risky corporate debt (IMF, 2014; Chow, 2015; IMF, 2016), but provide little guidance on what constitutes an elevated share of risky debt, which makes it difficult to interpret their findings. Furthermore, these studies do not opine on which types of shocks may be most consequential. For example, in the event of a depreciation of EME currencies and higher global interest rates, which of these channels would be more detrimental for EME debt servicing capacity? We therefore make two contributions to the debate on the riskiness of EME corporate debt. First, we assess the health and resilience of the EME corporate sector by comparing two key metrics--leverage and the systemic importance of the risky debt-- to levels seen in the past, including for the East Asian economies on the eve of the Asian Financial Crisis. Alfaro et al. (2017) previously used the Asian Financial Crisis as a benchmark; they find that emerging markets post-GFC (2009-2014) have lower leverage ratios than the five Asian crisis countries in the run-up to the Asian Financial Crisis (1992-1997). Second, we try to assess which of the shocks we consider are most detrimental for the EME corporate sector.
2. A Bird's Eye View of EME Corporate Vulnerabilities
Since 2007, EME nonfinancial corporate debt (or NFC debt) has tripled in dollar value (Figure 1a) and roughly doubled as a share of EME GDP (Figure 1b). The majority of this increase is accounted for by China, where NFC debt is now 170 percent of GDP. NFC debt in several other EMEs (Figure 2) has also risen sharply. For some EMEs, the expansion in overall credit has exceeded that seen in emerging Asia and Mexico in the run-up to their crises.
More reassuringly, though rising in nominal amounts, the portion of EME corporate debt denominated in foreign currency has been declining (Figure 3) and is smaller today than before previous financial crises (BIS, 2016). These findings suggest that the risks associated with currency mismatches in the EMEs may have been somewhat overblown. Consistent with this view, we note that EMEs have not suffered widespread corporate defaults despite substantial currency depreciations in some of them since mid-2011.
##### Figure 3 - FX Share of NFC Debt
That said, sufficiently large depreciations would likely create problems for some firms, and the run-up in EME corporate debt is worrisome on other grounds as well. Firm-level data suggest that EME earnings have declined notably from their pre-crisis peaks (Figure 4), especially in China, which could have implications for the servicing of the corporate debt as discussed below.5
In this note, we assess corporate vulnerabilities by looking at two common metrics related to debt-servicing capacity: leverage (the ratio of debt to equity), and the interest coverage ratio (the ratio of earnings to interest expense). High leverage makes firms vulnerable to increases in borrowing costs and declines in earnings. But even a highly levered firm may be able to easily service its debt if it is highly profitable or if the interest rate on its debt is low. Conversely, a firm with moderate leverage may face difficulties in servicing its debt if it is not generating a profit from its operations, or if it pays a high interest rate on its debt. The interest coverage ratio (ICR) provides a more direct measure of the ability of firms to service their debt payments with earnings.
For EME firms, the reduction in earnings since 2010 has eroded the interest coverage ratio (Figure 5). In contrast, the ICR for the advanced foreign economies (AFEs) has remained fairly stable since 2010.6 An ICR of 2 or less is typically associated with an increased likelihood of distress. For example, just before the Asian financial crisis, firms in Korea, Thailand, and Indonesia had an average ICR of 2 (Pomerleano, 1998). In its April 2014 Global Financial Stability Report, the IMF used an ICR threshold of 2 to classify at risk borrowers, and we use the same threshold in our analysis.7
##### Figure 5 - Interest Coverage Ratio
To judge the debt-servicing capacity of the firms in our sample, Figure 6 compares the levels of aggregate leverage, as measured by the ratio of debt to equity, and interest coverage as of 2016:Q3. By these measures, firms in Brazil, Argentina, Chile, China, India, South Africa, and Turkey appear to be the most vulnerable. And this vulnerability has increased over the last 5 years, as shown in Figure 7, which compares the change in leverage and interest coverage since 2011. Some of the countries with the highest leverage--Argentina, Russia, South Africa and Brazil-- are also the ones that experienced the fastest increases in leverage and the steepest declines in interest coverage. Alfaro et al. (2017) also find that corporate liquidity and solvency indicators have deteriorated for most EMEs in the post-GFC period. However, they find that average levels of various vulnerability indicators in the post-GFC period are not as severe as they were for the East Asian economies in the run-up to the East Asian crisis. With regards to China, they do not find that post-GFC leverage in China is higher than the average for the East Asian economies on the eve of the East Asian crisis. We note, however, that China's current corporate debt to GDP ratio-- a broad measure of corporate leverage--is above the average of 100 percent for the East Asian economies before the Asian Financial Crisis.
In sum, the surge in EME corporate debt has been associated with a deterioration in debt servicing capacity. However, it is difficult to assess vulnerabilities based on aggregate measures alone: An aggregate interest-coverage ratio of 8 may mask significant risks if a few large firms have extremely low coverage ratios; conversely, a much lower interest-coverage ratio may still be consistent with solid financial conditions, if the preponderance of firms meet adequate standards. To better understand the systemic risks stemming from the EME corporate sector, in the next section we use firm-level data to quantify the amount of debt which is at risk, and provide a more granular assessment of vulnerabilities across countries and sectors.
##### Figure 7 - Changes in Leverage & ICR, 2011:Q1 to 2016:Q3
3. Debt at Risk and Leverage in the EME Nonfinancial Corporate Sector
We compute the overall riskiness of the EME corporate debt stock by country and sector using balance sheet and income statement data from Capital IQ for a sample of roughly 8,500 publicly listed firms in 15 emerging market economies. For a given region, country, or sector, we measure the share of risky debt as the debt of firms with ICRs less than 2, divided by the total debt of firms in our sample. The share of risky NFC debt for the countries in our sample has nearly doubled since 2011 to roughly a quarter of total EME NFC debt (Figure 8), surpassing the previous peak. Even so, the share of risky EME corporate debt is considerably lower today than it was for the East Asian countries preceding the Asian financial crisis. Excluding China, the share of risky debt has trended down very recently, as earnings have started to recover from their post-crisis lows, and is now below its pre-GFC level.
##### Figure 8 – Debt at Risk to Total Debt
Chart 1 presents a heat map of the share of the nonfinancial corporate debt (both domestic and external) that is considered at risk by sector and country, as of 2016:Q3.8 For the heat maps shown in this table and the tables to follow, the gradations for the colors are based on where the current value lies in the distribution of values over the past 10 years. In particular, the dark red shading for 'elevated' denotes countries or sectors where the current share of debt at risk falls in the 95th percentile or higher of the values seen over the past 10 years. As shown in the first column, the share of risky debt is notable (between the 75th and 94th percentile of the historical distribution) in China and Brazil, where nearly a third of the nonfinancial corporate debt is at risk. In the next tier, India, Argentina, and Turkey have a share of risky debt ranging between a fifth and a quarter of total debt.
##### Chart 1 – Debt at Risk to Total Debt (percent), as of 2016 Q3
Looking across sectors, most countries in our sample have at least one sector with notable or elevated shares of risky debt. For example, risky debt is elevated in the utilities sector for a third of the countries in our sample. For EMEs overall (bottom row), the industrial goods, materials, and consumer goods sectors have the highest share of debt at risk.
Chart 2 provides a similar heat map, but for the leverage ratio (total domestic and external debt relative to equity) across countries and sectors. As shown in the first column, corporates in Mexico and Argentina have elevated levels of leverage (at or above the 95th percentile of their historical distribution), followed by those in Brazil, India, Russia, and South Africa, where leverage is notably high (between the 75th and 94th percentile).9 Leverage is low or moderate in most other EMEs. Looking across sectors, most of the countries in our sample have at least two sectors with elevated or notable leverage ratios. And, in most countries, the industrial and utilities sectors appear to have high leverage. Thus, overall, corporate leverage seems moderate relative to historical levels.
##### Chart 2 – Leverage (Ratio of Debt to Equity), as of 2016 Q3
Previous studies examining EME corporate vulnerabilities have focused on the share of debt that is risky. But even if a high share of corporate debt is at risk in a particular country, it may pose limited systemic risk if corporate debt is itself a small share of GDP. Conversely, systemic risk may be greater if corporate debt outstanding is large relative to GDP, even with a smaller share of debt at risk. To provide an estimate of the systemic importance of the risky corporate debt, we scale risky debt for each country by GDP. This can help us gauge the potential costs to the government of bailing out these companies or their lenders if the debt were to turn bad.10
However, because our sample does not include all the firms in a country, we need to scale up our estimate of risky debt to approximate its likely total size. We use BIS data on credit to the nonfinancial private sector (total debt) as a share of GDP as the scale factor. Specifically, we compute the ratio of debt at risk to GDP as follows:
$$\frac{\text{Debt at Risk}}{\text{GDP}}=\frac{\text{Share of risky debt x Total debt}}{\text{GDP}}=\frac{\text{Debt at Risk}}{\underbrace{\text{Total Debt}}_{\text{Capital IQ}}}\times\frac{\text{Total Debt}}{\underbrace{\text{GDP}}_{\text{BIS}}}$$
Implicit in this scaling is the assumption that the share of risky debt of the firms in our sample is the same as that of the entire corporate sector in each country.11
As shown in Figure 9, when scaled by GDP, EME debt at risk has well surpassed its previous pre-GFC peak and is approaching one third of EME GDP. Most of this increase, however, is coming from China, where risky debt as a share of GDP has climbed steeply since 2011, exceeding the share for the East Asian economies before the Asian Financial Crisis. Excluding China, EME NFC debt at risk has been fairly stable at around 10 percent of GDP, which seems manageable.
Chart 3 shows the estimates of the ratio of debt at risk (DAR) to GDP for different countries. The first column shows our estimated share of risky corporate debt from Chart 1. The second column shows the ratio of corporate debt to GDP (from the BIS data). By multiplying these shares, we obtain the DAR/GDP estimates shown in the last column. Among these EMEs, China stands out as having both the largest share of risky corporate debt and the highest corporate debt-to-GDP ratio, which gives rise to its elevated share of risky debt to GDP in the last column. Risky debt ranges from 12-14 percent of GDP in Brazil, South Korea, Turkey, and India, which is still significantly lower than the average of 50 percent for the East Asian economies before the Asian Financial Crisis. For the other EMEs, the share of risky debt to GDP is low. For example, although nearly a quarter of the corporate debt stock in Argentina is at risk, this risky debt makes up only 3 percent of GDP, making it less of a concern.
##### Chart 3 – Derivation of Debt at Risk to GDP, as of 2016 Q3
4. Stress-testing the EME Corporate Sector
The analysis above has assessed the current state of the corporate sector. Next we examine its vulnerability to a range of plausible shocks. During bouts of financial stress, it is not unusual for EMEs to simultaneously experience higher borrowing costs, currency depreciations, and slower growth (Calvo and Talvi, 2005). Therefore, we now investigate how corporate vulnerabilities in emerging markets would change if EME firms are faced with adverse shocks arising from these sources.
4.1 Calibrating the shocks
Starting with the current amount of debt at risk, we cumulatively stress each firm's financials by: 1) reducing earnings 20 percent; 2) increasing the average interest rate paid by each firm on its debt 1 percentage point; and 3) imposing a 20 percent exchange rate devaluation on the amount of debt that is denominated in foreign currency. These shocks are large but, as discussed below, we regard them as plausible.
The earnings shock corresponds to roughly half of the decline in EME earnings experienced in the aftermath of the GFC. We note that even among the advanced economies, a 20 percent annual decline in earnings is not unusual. Since 2010, earnings have declined by this magnitude at least once in Canada, Italy, Spain, and the United Kingdom. We shy away from making the earnings shocks bigger than this as EME earnings are already depressed relative to their pre-crisis levels; in 2016:Q3 the average return on assets (EBITDA/Assets) of the EME firms in our sample was 7.5 percent per annum, compared to 15 percent in mid-2007.
The interest rate shock is an increase of 100 basis points in the average borrowing cost on both domestic and external debt.12 We estimate that the average borrowing cost of EMEs declined from about 7 percent in 2009 to 4-1/2 percent in 2016, partly reflecting the low interest rate global environment and strong demand for EME bonds. Our interest rate shock undoes less than half of this decline. Given that the average interest rate for the EME firms in our sample is 4-1/2 percent per annum, the 1 percentage point interest rate shock increases the interest expense (and lowers the ICR) by about 20 percent, similar to the earnings shock. Although a 1 percentage point increase does not seem extraordinary--global rates may rise much more than that over the next couple of years--this metric reflects the average interest rate of the entire debt stock, not just the increase on the newly issued debt.
We also consider an exchange rate depreciation shock of 20 percent, which would seem to be well within the range of possibilities. In 2015, for example, the Brazilian real, South African rand, and Malaysian ringgit depreciated against the dollar by more than this. Because firm-level data on the currency composition of assets and liabilities are scarce, we compute the effect of this shock on the level of debt at risk by using aggregate foreign currency shares of debt provided by Ayala et al. (2015). That is, we assume that each firm within a country holds the same share of foreign currency debt, equal to the aggregate share.13 Then, for the share of debt denominated in foreign currencies, we increase interest expense by 20 percent, which arises from the currency depreciation. Because we do not take into account any hedging of foreign currency exposures, whether natural or using derivatives, we are likely overstating the effect of the exchange rate shock on the level of debt at risk.
4.2 Results
Taken together, the shocks boost the share of risky debt for the EME aggregate from 24 percent to roughly 40 percent (Figure 10). Excluding China, the share of risky debt more than doubles from 15 percent to 35 percent. Thus, the EME corporate sector appears to be vulnerable to negative shocks, consistent with the results in Chow (2015) and IMF (2016). Currently, only two countries (China and Brazil) have a notable share of risky debt (between the 75th and 94th percentile of their historical distribution). After the shocks, the share of risky debt is notable or elevated for 9 of the 15 countries shown. As a share of GDP, the shocks applied simultaneously boost the level of aggregate EME risky debt from roughly 26 percent to 45 percent (Figure 11). The increase comes mainly from China, where risky debt jumps to 80 percent of GDP.
Even outside of China, the share of risky debt appears highly sensitive to the three shocks.14 In particular, after the shocks are applied, the share of risky debt more than doubles in Mexico, Russia, Indonesia, Chile, Malaysia, Poland, Thailand, and South Africa. For some countries, such as Mexico and Indonesia, this heightened sensitivity arises from the fact that a large portion of the corporate debt is concentrated in just a few large firms whose debt moves to the at risk category after the shocks. Although the shocks boost risky debt in Indonesia and Mexico to over half of total debt (Figure 10), this risky debt is still a much smaller share of GDP, around 15 percent (Figure 11). All told, even under our stress scenario, the only emerging market economy whose level of risky debt (as a share of GDP) exceeds that of the East Asian economies on the eve of the Asian financial crisis is China.
##### Figure 10 – Debt at Risk to Total Debt
4.2.1 Relative importance of shocks
Next, we explore which shocks are most relevant for each country, by applying the shocks individually. The results are summarized in Table 4. For EMEs overall, the earnings shock and interest rate shock each boost the share of risky debt from 25 percent of debt to 31 percent of debt. Excluding China, the earnings shock appears to be somewhat more detrimental than the interest rate shock. In contrast, the exchange rate shock boosts overall risky debt by only 1 percentage point (to 26 percent). Thus, although much attention has been paid to the risks associated with currency mismatch facing emerging market NFCs, in most cases (with the exception of Indonesia and Mexico, which have a fairly large portion of debt denominated in foreign currency) a 20 percent exchange rate depreciation shock against the dollar does not change the share of risky debt much. This result holds partly because a 20 percent devaluation would boost debt service on foreign-currency debt by about the same amount as the other two shocks being considered (20 percent fall in earnings, one percentage point rise in interest rates), but the share of debt denominated in foreign-currency is relatively low for most countries. For other countries (Hungary, Turkey, and Chile, for example), despite a relatively high share of foreign currency debt, a 20 percent currency depreciation still does not change the amount of risky debt much because firms in these countries have sufficiently high ICRs.15
##### Table 1 – Debt at Risk Sensitivity to Shocks
Level of DAR/Total Debt (%)
Country Current After only earnings shock After only interest rate shock After only currency deval. shock After all 3 shocks together Memo: FX share of debt (%)
All EMEs 25 31 31 26 41 16
EMEs ex. China 15 20 18 15 34 32
China 32 39 40 35 48 9
Brazil 30 37 34 30 45 28
India 23 29 28 23 35 16
Argentina 22 23 22 22 25 37
Turkey 20 21 20 20 26 48
Indonesia 15 20 20 20 62 56
South Korea 13 18 15 13 23 14
South Africa 10 10 10 10 30 26
Thailand 6 15 17 6 19 18
Russia 4 32 4 4 33 44
Chile 4 4 4 4 21 47
Malaysia 4 5 7 4 20 16
Mexico 2 3 3 3 53 63
Poland 2 4 3 2 7 49
Hungary 1 1 1 1 1 68
Source: Authors' estimates using Capital IQ data as of 2016: Q3, and Ayala et al. (2015) for foreign-currency share of debt. DAR = Debt at Risk. The EME aggregate includes the 15 countries shown individually.
References
Acharya, V., S. G. Cecchetti, J. D. Gregorio, S. Kalemli-Ozcan, P. R. Lane, and U. Panizza (2015): "Corporate Debt in Emerging Economies: A Threat to Financial Stability," Discussion paper, Brookings Institution, Committee on International Economic Policy and Reform.
Alfaro, L., G. Asis, A. Chari, and U. Panizza (2017): "Lessons Unlearned? Corporate Debt in Emerging Markets," Mimeo.
Ayala, D., M. Nedeljkovic, and C. Saborowski (2015): "What Slice of the Pie? The Corporate Bond Market Boom in Emerging Economies," IMF Working Paper 148, International Monetary Fund.
Bank for International Settlements (2016): "2016 Annual Report," June 26, 2016.
Bruno, V., and H. S. Shin (2015): "Global dollar credit and carry trades: a firm-level analysis," BIS Working Papers 510, Bank for International Settlements.
Caballero, J., U. Panizza, and A. Powell (2015): "The second wave of global liquidity: Why are firms acting like financial intermediaries?" IHEID Working Papers 21-2015, Economics Section, The Graduate Institute of International Studies.
Calvo, G., and E. Talvi (2005): "Sudden Stop, Financial Factors and Economic Collapse in Latin America: Learning from Argentina and Chile," NBER Working Paper 11153, National Bureau of Economic Research.
Chow, J. (2015): "Stress Testing Corporate Balance Sheets in Emerging Economies," IMF Working Paper 216, International Monetary Fund.
Claessens, S., S. Djankov, and G. Ferri (1999): "Corporate Distress in East Asia," Public Policy for the Private Sector Discussion Paper 172, The World Bank Group.
International Monetary Fund (2014): "Moving From Liquidity- to Growth-Driven Markets," Chapter 1, April 2014.
International Monetary Fund (2016): "Global Financial Stability Report: Financial Stability Challenges in a Low-Growth Era," October 2016.
Maliszewski, W., Arslanalp, S., Caparusso, J., Garrido, J., Guo, S., Kang, J.S., Lam, W. R., Law, T. D., Liao, W., Rendak, N., Wingender, P., Yu, J., Zhang, L. "Resolving China's Corporate Debt Problem," IMF Working Paper 203, International Monetary Fund.
McCauley, R., P. McGuire, and V. Sushko (2015): "Global dollar credit: links to US monetary policy and leverage," BIS Working Papers 483, Bank for International Settlements.
Pomerleano, M. (1998): "Corporate Finance Lessons from the East Asian Crisis," Discussion Paper 155, The World Bank Group.
Shin, H. S. (2013): "The Second Phase of Global Liquidity and Its Impact on Emerging Economies," Keynote address at the Federal Reserve Bank of San Francisco Asia Economic Policy Conference on November 7, 2013.
1. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. We thank Shaghil Ahmed, Stijn Claessens, Steven Kamin, and Beth Anne Wilson for helpful comments. We also thank Chris Collins for excellent research assistance. All errors are our own. Return to text
2. Bruno and Shin (2015) show that EME corporates tend to borrow in dollars to maintain higher levels of cash and liquid assets during periods when domestic interest rates exceed U.S. rates and thus the dollar carry trade is favorable, and Caballero et al. (2015) show that this especially true for countries that have tighter capital controls. Return to text
3. For example, even though China has greater vulnerabilities with respect to corporate debt, it is also generally believed that they have relatively more resources to address problems that may arise. Return to text
4. The 15 countries are those for which we have data on total corporate debt outstanding (Bank for International Settlements), foreign-currency shares of debt (Ayala et al., 2015), and firm-level balance sheets and income statements (Capital IQ), namely: Argentina, Brazil, Chile, China (includes Hong Kong), Hungary, India, Indonesia, Malaysia, Mexico, Poland, Russia, South Africa, South Korea, Thailand, and Turkey. We combine China and Hong Kong, as many firms domiciled in Hong Kong conduct significant business in China, and vice-versa. Return to text
5. Throughout, earnings refers to earnings before interest, taxes, depreciation, and amortization, or EBITDA. Return to text
6. The United States is not included in the AFEs. Return to text
7. To compute ICRs, we use the 4-quarter average of both earnings and interest expense. Return to text
8. For most countries in Chart 1, our estimates of the share of risky corporate debt (using an ICR cutoff of 2) are very close to those in the IMF (2016), with the exception of China, Turkey, and Mexico (where we estimate a higher share of risky debt). Return to text
9. The elevated aggregate leverage ratio for Mexico owes mostly to the large, negative equity reported by the state-controlled oil company Petroleos Mexicanos (Pemex). Leverage of the Mexican energy sector is elevated if we use an alternative definition of leverage, Debt/(Debt+Equity). Return to text
10. Chow (2015) and IMF (2016) assess the adequacy of EME banks' capital and loan loss reserves in absorbing an increase in corporate nonperforming loans (NPLs). As they point out, however, bank buffers are often overstated, and the level of nonperforming loans are often understated. Return to text
11. This assumption may be adequate for Latin America and the Asian EMEs excluding China, where our sample comprises roughly two-thirds of their total NFC debt. For China, however, the debt of the firms in our sample is just a quarter of total Chinese NFC debt. Even so, we believe our estimates may understate the true share of risky corporate debt in China because the larger state-owned enterprises (SOEs), which are over-represented in our sample, have fairly healthy ICRs. The healthy ICRs for Chinese SOEs partly reflects their easy access to cheap credit from state-owned banks (Maliszewski et al. 2016). Return to text
12. To apply this shock, we first calculate the average interest rate each firm pays on its debt by dividing its annualized interest expense by its debt stock. We then shock this interest rate by 100 basis points and use the new rate to determine the firm's interest expense. Return to text
13. We do not consider the possibility that, in some countries, debt may be concentrated in large firms with elevated shares of foreign-currency debt, which would heighten the sensitivity of DAR to the exchange rate depreciation shock. Return to text
14. Chow (2015) also finds that debt in Indonesia, Mexico, and China is quite sensitive to earnings, interest rate, and exchange rate shocks. For India, however, the (higher) estimate of debt at risk changes little in response to the shocks. Return to text
15. Using more recent data on Turkey's foreign-currency share of corporate debt, which is closer to two-thirds, we arrive at almost identical estimates of risky debt for Turkey. Return to text
| 2017-11-21T10:15:55 |
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https://www.usgs.gov/center-news/volcano-watch-measuring-ground-movements-koae-fault-system
|
# Volcano Watch - Measuring ground movements in the Koae fault system
Release Date:
Kilauea has one of the most active fault systems in the world. The Koae fault system is 2-3 km (1.2-1.8 miles) wide and extends about 17 km (10 miles) between the east and southwest rift zones, south of Kilauea's caldera.
Map showing Koae fault system (sinuous east-northeast-trending lines from unpublished map by Tina Neal and Jack Lockwood) and survey networks spanning it. Yellow dots, leveling benchmarks. Red triangles, EDM benchmarks; lines between EDM benchmarks are measured. Also shown are some cracks in southwest rift zone and around Kīlauea's caldera. Note that one leveling line and part of EDM network span southwest rift zone. All leveling lines are tied into summit leveling network (not shown).
(Public domain.)
The Koae fault system is an infrequently visited area, crossed only by the Hilina Pali Road between the Chain of Craters Road and Kulanaokuaiki Pali. The Mauna Iki Trail, heavily used only during the Kilauea marathon, takes an easy route across the Koae fault system between Kulanaokuaiki Pali and Cone Crater. Few if any eruptions take place within the fault system, and so there is little reason for the general public to hike across this remarkable country.
But remarkable it is. Creased by deep cracks and corrugated by vertical pali as high as 15 m (50 feet), measurements of open cracks show that the fault system has opened by at least 32 m (100 feet) since the latest lava flow covered the area 600-700 years ago. The most recent major faulting event, in December 1965, offset the Hilina Pali Road 2.4 m (8 feet) vertically where it crosses the fault that forms Kulanaokuaiki Pali.
The faults trend east-northeast, parallel to the east rift zone. In fact, the fault system can be viewed as a noneruptive continuation of the east rift zone. One interpretation is that the east rift zone, Koae fault system, and lower southwest rift zone form a "breakaway zone" separating the relatively stable part of Kilauea to the north from the mobile part of the volcano to the south.
The big earthquake swarm and faulting event in December 1965 piqued the interest of HVO scientists. Within several years, a detailed network of surveying stations (benchmarks) was established and measured. The surveys enable both vertical and horizontal changes to be detected. Small changes were measured as a result of an intrusion into the eastern part of the fault system in May 1973 and the Kalapana earthquake in November 1975.
Additional benchmarks were added during the early 1990s, bringing the total number of survey points to nearly 300. Three leveling lines, used to measure vertical changes, cross the Koae fault system at right angles, and two of the lines are connected by a line parallel to the faults. These lines, each consisting of benchmarks 90 m (300 feet) apart, are located between the Mauna Iki Trail and the boundary between the Keauhou and Kapapala ahupuaa.
Horizontal changes can be measured at 50 benchmarks forming a network that spans the fault system from Puu Koae eastward to the ahupuaa boundary. The network used to reach still farther east, but the incursion of the faya bush has made the forest into a jungle that inhibits surveying.
Later this month, scientists from the Smithsonian Institution and the Hawaiian Volcano Observatory will join forces to resurvey the complete network, which was last done in 1998. This enterprise, estimated to take 7-10 very full days, may be the last time that the originators of the networks in the late 1960s are able to take part in the rigorous surveys.
This will also be the time to change the instrument for making the horizontal surveys. The network has always been measured with an Electronic Distance Meter (EDM), which requires a clear line of sight between the end points of each line-something increasingly difficult to maintain as the forest grows taller. This year, the EDM will be used for the last time, and a nearly contemporaneous Global Positioning System (GPS) survey will be made at many of the same benchmarks. The GPS survey will take more time but does not require line-of-sight visibility.
The surveying puts money in the bank. The account may not be drawn upon for some time, but the interest accumulates in the form of new ideas that can be tested when a big event-such as an earthquake swarm in the Koae fault system-takes place. Then, the banked information can be compared with new surveying results to provide a better understanding of the process that caused the earthquakes and faulting.
### Volcano Activity Update
Eruptive activity at the Puu Oo vent of Kilauea Volcano continued unabated during the past week. Scattered surface breakouts from the western "Kohola" lobe of the Mother's Day flow are seen throughout the inflating flow. Streaks, patches, and spots of incandescence are visible from the coast to Paliuli. Two fingers of lava from the eastern side of the Kohola flow made it over the sea cliff onto the Wilipea delta but stagnated before reaching the ocean. A western finger burned more asphalt, then stopped after crossing the road. Several tongues of lava from breakouts of the main Mother's Day tube system are wending their way down Pulama pali and giving visitors a great view. The only lava entering the ocean is at the West Highcastle delta.
The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The steam clouds are highly acidic and laced with glass particles. The National Park Service has erected a rope barricade to delineate the edge of the restricted area. Do not venture beyond this rope boundary and onto the lava deltas and benches.
One earthquake was reported felt during the past week. Residents of Glenwood and Volcano felt an earthquake at 4:34 a.m. on April 1. The magnitude-2.8 event was located 10 km (6 mi) southeast of Kilauea Summit at a depth of 9 km (5.4 mi).
Mauna Loa is not erupting. The summit region continues to inflate, but seismic activity remains low, with only one earthquake located in the summit area during the last seven days.
| 2019-11-15T03:40:59 |
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https://www.usgs.gov/center-news/volcano-watch-new-staff-member-hvo
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# Volcano Watch - New staff member at HVO
Release Date:
Any institution, whether commercial, academic, or governmental, requires novel ideas to thrive. Fresh ideas come from training, sudden insights (the proverbial light bulb is turned on), hard work, and young talented staff members who bring in innovative concepts and abundant energy.
Introduction of new scientists to a research institution such as HVO is especially vital. They provide an up-to-date link to the latest concepts developed at universities and help to keep older staff members aware of current developments possibly otherwise overlooked.
This week, HVO is pleased to welcome such a new staff member. Dr. Marie Edmonds was awarded a prestigious Mendenhall Postdoctoral Fellowship by the U.S. Geological Survey to spend 2 years at HVO.
Marie hails from the U.K., and normally this would have disqualified her for the fellowship, which favors American citizens. Marie, however, does something that no American is currently doing, and her presence at HVO will introduce this cutting-edge technique into American volcanology. The fellowship award, despite her non-citizen status, indicates how highly her work is regarded.
Marie will be applying her expertise in Open-Path Fourier Transform Infrared Spectroscopy (OP-FTIR) to the development of novel ways to monitor gas emissions from Kīlauea. She will be working closely with Jeff Sutton and Tamar Elias, who form the gas team at HVO.
Volcanic gas is composed of many different species; water, carbon dioxide, and sulfur dioxide are the most common. OP-FTIR allows several different species to be detected and measured at the same time with a high degree of accuracy, so that a more nearly complete gas composition can be determined.
The methodology can be designed to operate continuously during daylight hours. Data can be radioed to HVO from a remote instrument site downwind of Puu Oo. This procedure will enable a rapid assessment of changing gas compositions. The technique stands an excellent chance of becoming a part of the routine real-time monitoring now done at Kīlauea.
The OP-FTIR equipment was purchased by the University of Hawaii-Hilo through a cooperative agreement with the USGS-HVO. Thus, the new methodologies could eventually be incorporated into the training program operated by the university's Center for the Study of Active Volcanoes.
Marie comes to HVO directly from the small Caribbean island of Montserrat, where she worked as a volcanologist with the British Geological Survey for 3 years at the Montserrat Volcano Observatory (MVO). MVO has responsibility for the monitoring of the Soufriere Hills Volcano, which is currently erupting an andesite lava dome.
During the past 3 years, the volcano has mostly erupted effusively at rates of 2-4 cubic meters (6.5-13 cubic feet) per second--about the same rate as lava is currently erupting from Puu Oo. Occasionally, however, the volcano entered periods of explosive activity, sending eruptive columns up to 15 km (9 miles) high, with pumice fallout and ash fall up to 15 cm (6 inches) thick in inhabited areas.
Hazard and risk assessment are especially critical on Montserrat, where people live within a few kilometers of a volcano whose activity is characterized by fast-moving pyroclastic flows traveling up to 60 m/s (200 feet/second).
MVO undertakes a monitoring regime similar to that of HVO. Visual observations, seismicity, ground deformation, gas emissions and environmental monitoring are the mainstays of the operation. Marie's role at MVO involved general volcanologic observations of lava dome growth, geologic mapping, sampling, hazard and risk assessment, and gas-emission monitoring.
This last task led Marie to develop state-of-the-art spectroscopic techniques to receive gas-emission rates every minute or so throughout the day. The gas data can now be obtained about as frequently as other modern geophysical data. This enables cross-correlations between gas emissions and, say, ground tilt or seismicity, at a time scale previously impossible. Marie's work at HVO will build on this experience.
### Volcano Activity Update
Eruptive activity at the Puu Oo vent of Kīlauea Volcano continued unabated during the past week. Most lava flows been at the lower end of the rootless shield complex along the Mother's Day lava tube, at the 2200-2300-foot elevation south of Puu Oo. Vents within the crater of Puu Oo remain incandescent. No active flows are on Pulama pali or the coastal flat below Paliuli. No lava is entering the ocean.
Four earthquakes were felt on the island during the busy week ending early February 5. A magnitude 3.8 earthquake took place at 5:39 p.m. on February 1, located 9 km (6 miles) north-northwest of Kaena Point at a depth of 9 km (6 miles). It was felt from Papa Bay to Wainaku. At 7:09 a.m. on February 3, another earthquake from the same area shook residents from Volcano to Wainaku; it had a magnitude of 3.1. The next day, a resident of Honaunau felt a magnitude 2.5 earthquake at 1:23 p.m., located 6 km (4 miles) east-southeast of Hookena at a depth of 14 km (8 miles). At 12:19 a.m. on February 5, another magnitude 3.8 earthquake awakened residents from Papa`aloa to Waipunalei; it took place 3 km (2 miles) northwest of Kalapana at a depth of 35 km (22 miles).
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains very low, with no earthquakes located in the summit area during the last 7 days.
| 2019-11-17T00:11:15 |
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http://jde27.uk/blog/equivalence-relation.html
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# Equivalence relations
[2017-09-17 Sun]
Equivalence relations are an important concept in mathematics, but sometimes they are not given the emphasis they deserve in an undergraduate course. Having a good grasp of equivalence relations is very important in the course MATHM205 (Topology and Groups) which I'm teaching this term, so I have written this blog post to remind you what you need to know about them. I will kick off with a few examples, then give a more formal definition.
## Examples
### Clock arithmetic
The simplest interesting example of an equivalence relation is equivalence of integers mod 2. You consider two integers to be equivalent if they have the same parity (both even or both odd), otherwise you consider them to be inequivalent. You end up with two equivalence classes of integers: the odd and the even integers. You can do arithmetic/algebra just as well with these equivalence classes as you could with the integers themselves: even + even = even, odd + even = odd, odd + odd = even etc.
More generally, given a number $$n$$ you can consider equivalence of integers modulo $$n$$: we write $$x\sim_n y$$ if and only if $$n$$ divides $$y-x$$. We now have $$n$$ equivalence classes according to the remainder you get when you divide by $$n$$.
### Cut-and-paste
Let's take a different example, this time from topology. One way to think about a particle living on the 2-dimensional torus is as follows. You let the particle move around on the unit square in the $$(x,y)$$-plane. Every time it falls off the right-hand side, you pick it up and put it onto the left-hand side at the same $$y$$-coordinate (and vice versa). Every time it falls off the top, you pick it up and put it onto the bottom at the same $$x$$-coordinate. In other words, we want to consider the points $$(x,0)$$ and $$(x,1)$$ to be the same point on the torus, and we want to consider the points $$(0,y)$$ and $$(1,y)$$ to be the same point on the torus. To formalise this, we introduce an equivalence relation on the set of points in the square for which $$(x,0)\sim (x,1)$$ and $$(0,y)\sim (1,y)$$ and we consider the torus to be the set of equivalence classes of points in the square modulo this equivalence relation. This proves to be a very useful way of constructing spaces (and we will see in the course how to equip the set of equivalence classes with a topology).
## Formalities
More formally, an equivalence relation on $$X$$ is a subset $$\sim\subset X\times X$$ with the following properties:
• $$(x,y)\in\sim$$ implies $$(x,y)\in\sim$$;
• $$(x,x)\in\sim$$ for all $$x\in X$$;
• $$(x,y)\in\sim$$ and $$(y,z)\in\sim$$ implies $$(x,z)\in\sim$$.
This becomes less mysterious if we write $$x\sim y$$ instead of $$(x,y)\in\sim$$. Then we see that an equivalence relation is a criterion for two points in $$X$$ to be identified as equivalent'', in such a way that this equivalence is symmetric in $$x$$ and $$y$$, reflexive (in the sense that $$x$$ is equivalent to itself) and transitive (so that if $$x$$ is equivalent to $$y$$ and $$y$$ is equivalent to $$z$$ then $$x$$ is also equivalent to $$z$$).
Given a point $$x\in X$$, the equivalence class of $$x$$ modulo $$\sim$$ is the subset $[x]=\{y\in X\ :\ x\sim y\}.$ The quotient $$X/\sim$$ is defined to be the set of equivalence classes modulo $$\sim$$.
## Examples revisited
Let us revisit the earlier examples, along with some new ones:
• Equality of integers is an equivalence relation on $$\mathbf{Z}$$: it is given by the diagonal'' subset $\{(x,x)\ :\ x\in \mathbf{Z}\}\subset \mathbf{Z}\times \mathbf{Z}.$
• Equality of integers mod $$p$$ is also an equivalence relation on $$\mathbf{Z}$$: it is given by the subset $\sim_p=\{(x,y)\in\mathbf{Z}\times\mathbf{Z}\ :\ p|(x-y)\} \subset\mathbf{Z}\times\mathbf{Z}.$
• Congruence is an equivalence relation on the collection of triangles in the plane with $$\sim$$ being the set of pairs $$(T_1,T_2)$$ of triangles such that $$T_1$$ is congruent to $$T_2$$.
• The equivalence relation which allows us to turn a square into a torus is: $\left\{((x,y),(x',y'))\in X\times X\ :\mbox{ one of }\begin{array}{1}x=x',y=y'\\ x=x',y=0,y'=1\\ x=x',y=1,y'=0\\ y=y',x=0,x'=1\\ y=y',x=1,x'=0. \end{array}\mbox{ holds.}\right\}$
• If $$G$$ is a group and $$H\subset G$$ is a subgroup then the set $$G/H$$ of cosets of $$H$$ in $$G$$ is the set of equivalence classes of $$G$$ modulo the equivalent relation $x\sim y\Leftrightarrow x=yh\mbox{ for some }h\in H.$
## Subtleties
We use this final example of quotienting a group by a subgroup to illustrate some of the subtleties with equivalence relations.
It's always easy to form the quotient $$X/\sim$$ as a set, but usually we have some structure (a group law, topology, or something) on $$X$$ and we want $$X/\sim$$ to inherit the same kind of structure.
When we quotient out by a subgroup, we usually don't have a canonical way to write down a group structure on the quotient. If we try the most naive thing and define the product on cosets by: \g_2\] then we run in to the following problem. Suppose we pick different representatives $$g_1$$ and $$g'_1$$ of the same equivalence class. Then $$g_1=g_1'h$$ for some $$h\in H$$. Now there is no guarantee that $$g_1g_2$$ and $$g'_1g_2=g_1hg_2$$ represent the same coset, which they would need to if the product we wrote down above were to be well-defined. Indeed, this only reliably works if $$H$$ is a /normal subgroup/, that is $$ghg^{-1}\in H$$ for all $$h\in H$$ and $$g\in G$$, because then $g_1hg_2=g_1g_2h'$ for some $$h'\in H$$, so $$g'_1g_2$$ and $$g_1g_2$$ define the same coset of $$H$$.
Comments, corrections and contributions are very welcome; please drop me an email at j.d.evans at lancaster.ac.uk if you have something to share.
CC-BY-SA 4.0 Jonny Evans.
| 2023-03-24T22:02:49 |
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|
http://dlmf.nist.gov/24.15
|
# §24.15 Related Sequences of Numbers
## §24.15(i) Genocchi Numbers
24.15.1 $\displaystyle\frac{2t}{e^{t}+1}$ $\displaystyle=\sum_{n=1}^{\infty}G_{n}\frac{t^{n}}{n!},$ 24.15.2 $\displaystyle G_{n}$ $\displaystyle=2(1-2^{n})B_{n}.$ Symbols: $B_{\NVar{n}}$: Bernoulli numbers, $n$: integer and $G_{n}$: Genocchi numbers Permalink: http://dlmf.nist.gov/24.15.E2 Encodings: TeX, pMML, png See also: Annotations for 24.15(i)
See Table 24.15.1.
## §24.15(ii) Tangent Numbers
24.15.3 $\mathop{\tan\/}\nolimits t=\sum_{n=0}^{\infty}T_{n}\frac{t^{n}}{n!},$
24.15.4 $T_{2n-1}=(-1)^{n-1}\frac{2^{2n}(2^{2n}-1)}{2n}B_{2n},$ $n=1,2,\dots$, Symbols: $B_{\NVar{n}}$: Bernoulli numbers, $n$: integer and $T_{n}$: tangent numbers Referenced by: §24.19(i) Permalink: http://dlmf.nist.gov/24.15.E4 Encodings: TeX, pMML, png See also: Annotations for 24.15(ii)
24.15.5 $T_{2n}=0,$ $n=0,1,\dots$. Symbols: $n$: integer and $T_{n}$: tangent numbers Permalink: http://dlmf.nist.gov/24.15.E5 Encodings: TeX, pMML, png See also: Annotations for 24.15(ii)
## §24.15(iii) Stirling Numbers
The Stirling numbers of the first kind $\mathop{s\/}\nolimits\!\left(n,m\right)$, and the second kind $\mathop{S\/}\nolimits\!\left(n,m\right)$, are as defined in §26.8(i).
24.15.6 $\displaystyle B_{n}$ $\displaystyle=\sum_{k=0}^{n}(-1)^{k}\frac{k!\mathop{S\/}\nolimits\!\left(n,k% \right)}{k+1},$ 24.15.7 $\displaystyle B_{n}$ $\displaystyle=\sum_{k=0}^{n}(-1)^{k}\genfrac{(}{)}{0.0pt}{}{n+1}{k+1}\mathop{S% \/}\nolimits\!\left(n+k,k\right)\bigg{/}\genfrac{(}{)}{0.0pt}{}{n+k}{k},$ 24.15.8 $\displaystyle\sum_{k=0}^{n}(-1)^{n+k}\mathop{s\/}\nolimits\!\left(n+1,k+1% \right)B_{k}$ $\displaystyle=\frac{n!}{n+1}.$
In (24.15.9) and (24.15.10) $p$ denotes a prime. See Horata (1991).
24.15.9 $p\frac{B_{n}}{n}\equiv\mathop{S\/}\nolimits\!\left(p-1+n,p-1\right)\pmod{p^{2}},$ $1\leq n\leq p-2$, Symbols: $B_{\NVar{n}}$: Bernoulli numbers, $\mathop{S\/}\nolimits\!\left(\NVar{n},\NVar{k}\right)$: Stirling number of the second kind, $n$: integer and $p$: prime Referenced by: §24.15(iii) Permalink: http://dlmf.nist.gov/24.15.E9 Encodings: TeX, pMML, png See also: Annotations for 24.15(iii)
24.15.10 $\frac{2n-1}{4n}p^{2}B_{2n}\equiv{\mathop{S\/}\nolimits\!\left(p+2n,p-1\right)% \pmod{p^{3}}},$ $2\leq 2n\leq p-3$. Symbols: $B_{\NVar{n}}$: Bernoulli numbers, $\mathop{S\/}\nolimits\!\left(\NVar{n},\NVar{k}\right)$: Stirling number of the second kind, $n$: integer and $p$: prime Referenced by: §24.15(iii) Permalink: http://dlmf.nist.gov/24.15.E10 Encodings: TeX, pMML, png See also: Annotations for 24.15(iii)
## §24.15(iv) Fibonacci and Lucas Numbers
The Fibonacci numbers are defined by $u_{0}=0$, $u_{1}=1$, and $u_{n+1}=u_{n}+u_{n-1}$, $n\geq 1$. The Lucas numbers are defined by $v_{0}=2$, $v_{1}=1$, and $v_{n+1}=v_{n}+v_{n-1}$, $n\geq 1$.
24.15.11 $\displaystyle\sum_{k=0}^{\left\lfloor\ifrac{n}{2}\right\rfloor}{n\choose 2k}% \left(\frac{5}{9}\right)^{k}B_{2k}u_{n-2k}$ $\displaystyle=\frac{n}{6}v_{n-1}+\frac{n}{3^{n}}v_{2n-2},$ 24.15.12 $\displaystyle\sum_{k=0}^{\left\lfloor\ifrac{n}{2}\right\rfloor}{n\choose 2k}% \left(\frac{5}{4}\right)^{k}E_{2k}v_{n-2k}$ $\displaystyle=\frac{1}{2^{n-1}}.$
For further information on the Fibonacci numbers see §26.11.
| 2017-01-23T10:37:59 |
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|
http://wsx.lanl.gov/RSX/RSX_experiment.htm
|
A brief description of the Reconnection Scaling eXperiment
Introduction
RSX Experimental apparatus
Introduction
Magnetic reconnection refers to the local breaking of magnetic field lines and subsequent change in the global topology of the magnetic field in the presence of plasmas or conducting fluids. During this process, magnetic field lines of opposite polarity are convected toward each other by fluid flow in the so-called diffusion region. This region is centered around a neutral magnetic line, across which the reconnecting component of the magnetic field changes sign. In the diffusion region, the "frozen-in" condition of ideal MagnetoHydroDynamics (MHD) equations is broken. The magnetic field can diffuse through the plasma allowing the annihilation of opposite directed magnetic field lines and conversion of magnetic field energy into Ohmic heating and particle acceleration.
During the last four decades, a large effort has been devoted to study magnetic reconnection in plasmas since it is considered to play a crucial role in a variety of different astrophysical and laboratory phenomena. Examples are in the evolution of solar flares, in the dynamics of the earth magnetosphere and in the redistribution of the energy in the universe. In magnetically confined laboratory plasmas for fusion research, a major role is played by magnetic reconnection in determining the dynamics of relaxation processes, such as sawtooth oscillations and major disruptions in tokamaks or dynamo effects in Reversed Field Pinches.
Early 3D laboratory experiments on magnetic reconnection provided detailed measurements of the relaxation to a force-free state produced by the coalescence of two current channels inthe LPD linear device. Interacting current channels were produced by coating a large cathode source nonuniformly and then biasing it with respect to an external anode. Although 3D features of magnetic reconnection were studied, the Lundquist number of the interacting current channels was limited by the plasma production scheme and ions were not magnetized (EMHD regime). Over the past few years, developments in plasma gun technology have made plasma guns a reliable laboratory source capable of producing plasmas with large Lundquist number. The Reconnection Scaling Experiment uses this innovative plasma gun technology to study the coalescence of parallel current channels in a 3D linear geometry. The emphasis will be on using many repetitive plasma discharges to acquire detailed spatial and temporal measurements as the two current channels merge along the axis of the linear device. One major advantage of the plasma gun technology is that it allows a high degree of flexibility in scaling independently the different parameters important in the reconnection process.
RSX Experimental apparatus
A view of the RSX device is shown in Fig. 1 (a),(b) together with a schematic view of the linear geometry of two interacting current channels, Fig.1 (c). For a picture of the actual status of RSX, click here. In this section, the main elements of the RSX device are described together with the plasma production technique. An overview is presented of the control and data acquisition system and main diagnostics.
Figure 1. Cross section of RSX device: (a) lateral view, (b) head on view; and (c) schematics of two interacting current channels along the axis of the device. RSX main elements are shown: (1) plasma guns, (2) head flange accomodating a large window, (3) magnet coils, (4) external anode, (5) stainless steel vacuum vessel, (6) schematics of the vacuum system, and (7) electro mechanical valve for gas puffing.
Vacuum vessel and vacuum system
The RSX vessel consists of a cylindrical vacuum chamber with approximately 4m length and 20 cm radius, Fig. 1 (a), which is formed by 3 sections 48 inch in length recycled from the Field Reversed Configuration experiment FRX-C. Each section is fabricated from stainless steel (SS304) tubing with a 40.6 cm nominal outside diameter, a 0.48 cm wall thickness and has 16 x 2.75 inch and 12 x 6 inch Conflat flanges facing radially, allowing for easy placement of diagnostics and flexibility in the plasma gun geometry arrangement. The use of standard Conflat hardware ensures ultrahigh vacuum capability at reasonable cost. The conductivity of the vessel and the numerous Conflat flanges adds a delay on the order of $600 \mu sec$ for magnetic field penetration from the external solenoid coils. End flanges accomodate large windows, probe access, and eventually mounts for plasma gun arrays. The vacuum system consists of a 5500 liter/sec roughing and backing mechanical pumps with a 110 liter/sec turbo pump which provides a 10^{-7} Torr base vacuum before plasma formation. The vacuum control system encompasses an automatic gauge controller and safety interlock which closes appropriate valves and shuts down the turbo pump in the case of an accidental pressure or power failure. During operation of the plasma guns, this system is disabled to prevent its intervention following the plasma formation and the subsequent pressure increase.
Plasma guns, pulser supply and discharge sequence
Presently, RSX is equipped with four plasma guns radially inserted through 2.75 inch flanges into the vacuum chamber and equally spaced in the poloidal direction as shown in Fig. 1(b). The plasma guns, originally designed for current profile modification in the Madison Symmetric Torus, allow the injection of parallel current channels along the axial direction of the RSX device as it is schematically shown in Fig. 1(c). The radial distance between plasma guns can be modified to provide flexibility in the geometry of the interacting current channels.
Each plasma gun, with a 2.5 cm external radius, contains a miniaturized plasma source with a circular 0.79 cm^2 nozzle aperture in which a cylindrical plasma is produced by an arc discharge between a molybdenum anode and a cathode. A stack of molybdenum and boron nitride washers 1.5 cm high defines the arc channel between the anode and the cathode. The gas, usually H or He, is supplied through the cathode by an electromagnetic valve, Fig. 1, which is pulsed 12 ms before the arc discharge. This time delay corresponds to the gas travelling time from the puff valve to the miniaturized discharge chamber. When the arc anode is negatively biased with respect to an external electrode, which in the following we will refer to as external anode, a fraction of the arc current is diverted towards the external anode as plasma current. In Fig. 1, the external anode is shown consisting of a 50 cm^2 SS304 plate bolted to copper rod which is electrically insulated from the vacuum vessel by a ceramic feedthrough. The external anode can be moved along the RSX vessel to modify the length of a single current channel. In Fig. 2, the schematic of the discharge pulser circuit is shown.
Figure 2. Schematic view of the exciter circuit for the plasma guns. When the arc anode is negatively biased with respect to the external anode (see Fig. 1), a fraction of the arc current I_arc is diverted towards the external anode as plasma current. Shown are the pulse forming network (PFN), the silicon controlled rectifier (SCR), the arc and bias power supply (PS) with switch relays (S1,S3).
The arc plasma is maintained by a Pulse Forming Network (PFN) which sets the internal gun arc voltage to V_arc~ 80-100 V and determines the discharge pulse length which is presently approximately 10 ms. The impedance of the PFN matches the arc impedance and is set to ~100 mOhms. The PFN capacitors are charged up to a maximum voltage V_cap~1 kV and the arc discharge is initiated by applying a gate pulse to a silicon controlled rectifier (SCR), SCR1 in Fig. 2. The arc current, I_arc can be varied from 0.3 to 1 kA. The bias pulser, shown on the left of Fig. 3 is designed to lower the potential of the arc anode below that of the grounded external anode so that by varying the external bias voltage, V_bias=0-300 V$, a desired fraction of the arc current can be extracted as external anode (i.e. plasma) current. The bias discharge is initiated by applying a gate pulse to SCR2 approximately 2 ms after the beginning of the arc discharge corresponding to the maximum of I_arc. The duration of the bias discharge can be manually varied between 0.5 to 8 ms by shorting the bias capacitor bank into a dump resistor through SCR3. Magnet coils and switching Figure 3 presents a schematic of the pulse exciter and basic control circuitry for the magnet coils. Figure3. Schematic view of the exciter circuit for the magnet coils together with the MOSFET driver for the SCR switch starting the discharge. Also shown are the capacitor bank, power supply (PS) and safety circuitry encompassing two high power switches (S1, S2) to dump the capacitor bank before and after each discharge. A set of 12 identical copper coils with 125 cm external diameter and 53 cm internal diameter per coil surrounds the RSX vessel (see Fig. 1) and provides the axial guide field B_z. Each coil has self-inductance of 820 microH and resistance of 80 mOhms. In the present arrangement, a limited set of 5 pairs of series coils are connected in parallel and energized by an 0.16 F, electrolytic capacitor bank with a quarter cycle time of 16 ms. The capacitor bank is charged by a 800 V, 10 Amps power supply and for the present bank and magnet configuration the maximum central magnetic field is B_z0=0.1 T at 1 kA current per coil. At this current level, magnet operation only requires straight forward SCR switched network for a 32 ms half cycle pulse length, with diode crowbar at the zero voltage crossing time. The SCR is controlled by a MOSFET switch which is gated by a +24 V, 35 ms pulse provided by the control system described in the last section}. The power supply control system encompasses an automatic safety circuitry (see high voltage switches S2, S3 in Fig. 3) that shorts the positive and negative side of the capacitor bank before and after each shot to prevent from accidental charging of the capacitor bank. Initial operation at pulse repetition of 60-120 s can be achieved with air cooling of the coils. Water cooling at 10 gpm using a closed loop deionized water system can be easily added to extend the operation of the device to much higher repetition rate. Diagnostics RSX is equipped with an initial set of diagnostics consisting of internal probes and noninvasive optical systems. Presently, internal probes are inserted into the vacuum vessel through flexible bellows and sliding seals allowing a two dimensional scanning of plasma parameters in the plane perpendicular to the axis of the device. Each probe can be moved along the axis of the device into a different porthole. The three component of the magnetic field are measured using a single probe consisting of electrostatically shielded, small (3.175 mm diameter), orthogonal magnetic loops with 30 turns each. A miniaturized Rogowski coil with 1 cm internal diameter allows measurements of the radial profile of current channels. A double Langmuir probe consisting of two electrically insulated tungsten wires provides measurements of electron density and temperature. A CCD single frame camera, fast framing camera \cite{phantom4 camera} and multiple photomultiplier tubes allow monitoring of visible light emission from the plasma through portholes. A feature of paramount importance in 3D magnetic reconnection experiments is the ability of measuring plasma parameters and magnetic field structures and fluctuations in three dimensions A new three axis moveable probe drive, which will be the subject of a future article, has been designed and is presently under construction. This system will allow a complete three dimensional scan of the plasma with an interchangeable probe head which accomodates different types of probes. Control and data acquisition system The RSX control, data acquisition and data storage system is based on a distributed architecture including a National Instruments FP-2000 Ethernet module and commercial personal computers (PCs). All the machines communicate through Ethernet links. The FP-2000 module runs embedded LabView Real Time and controls a National Instruments FP-DO-401 discrete output module. This module provides$+24\$ V pulses for the timing sequence with a time accuracy within few ms. Events which require higher accuracy (i.e. gun arc and bias start and stop) are provided by digital hardware delays.
The RSX data acquisition system consists of digital Tektronix oscilloscopes and multiple Le Croy transient recorders which are housed in CAMAC crates controlled via GPIB interfaces by a commercial PC running Windows 2000. The sequence of configuring and arming the digitizers followed by data retrieval is performed by Labview6 routines which are grouped in a single GUI. A high level programming language such as Labview6 allows use and integration of many different digitizers with modest software development.
The PC which controls the acquisition system is linked via Ethernet to the RSX data storage system. This consists of a commercial PC running Linux RedHat7.2 operating system in which a MDS+ server database is installed. The data are archived on a 60 GB disk drive in MDS+ compressed format and analyzed via Matlab and IDL routines, which allow compatibility with Apple, Windows, LINUX and UNIX platforms.
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| 2016-10-28T00:29:06 |
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|
https://par.nsf.gov/biblio/10349837-dark-energy-survey-y3-results-blending-shear-redshift-biases-image-simulations
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This content will become publicly available on November 30, 2022
Dark Energy Survey Y3 results: blending shear and redshift biases in image simulations
ABSTRACT As the statistical power of galaxy weak lensing reaches per cent level precision, large, realistic, and robust simulations are required to calibrate observational systematics, especially given the increased importance of object blending as survey depths increase. To capture the coupled effects of blending in both shear and photometric redshift calibration, we define the effective redshift distribution for lensing, nγ(z), and describe how to estimate it using image simulations. We use an extensive suite of tailored image simulations to characterize the performance of the shear estimation pipeline applied to the Dark Energy Survey (DES) Year 3 data set. We describe the multiband, multi-epoch simulations, and demonstrate their high level of realism through comparisons to the real DES data. We isolate the effects that generate shear calibration biases by running variations on our fiducial simulation, and find that blending-related effects are the dominant contribution to the mean multiplicative bias of approximately $-2{{\ \rm per\ cent}}$. By generating simulations with input shear signals that vary with redshift, we calibrate biases in our estimation of the effective redshift distribution, and demonstrate the importance of this approach when blending is present. We provide corrected effective redshift distributions that incorporate statistical and systematic uncertainties, ready for use more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10349837
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
509
Issue:
3
Page Range or eLocation-ID:
3371 to 3394
ISSN:
0035-8711
National Science Foundation
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Weak lensing measurements suffer from well-known shear estimation biases, which can be partially corrected for with the use of image simulations. In this work we present an analysis of simulated images that mimic Hubble Space Telescope/Advance Camera for Surveys observations of high-redshift galaxy clusters, including cluster specific issues such as non-weak shear and increased blending. Our synthetic galaxies have been generated to have similar observed properties as the background-selected source samples studied in the real images. First, we used simulations with galaxies placed on a grid to determine a revised signal-to-noise-dependent ( S / N KSB ) correction for multiplicative shear measurement bias, and to quantify the sensitivity of our KSB+ bias calibration to mismatches of galaxy or PSF properties between the real data and the simulations. Next, we studied the impact of increased blending and light contamination from cluster and foreground galaxies, finding it to be negligible for high-redshift ( z > 0.7) clusters, whereas shear measurements can be affected at the ∼1% level for lower redshift clusters given their brighter member galaxies. Finally, we studied the impact of fainter neighbours and selection bias using a set of simulated images that mimic the positions and magnitudes of galaxies inmore »
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3. ABSTRACT Measurements of large-scale structure are interpreted using theoretical predictions for the matter distribution, including potential impacts of baryonic physics. We constrain the feedback strength of baryons jointly with cosmology using weak lensing and galaxy clustering observables (3 × 2pt) of Dark Energy Survey (DES) Year 1 data in combination with external information from baryon acoustic oscillations (BAO) and Planck cosmic microwave background polarization. Our baryon modelling is informed by a set of hydrodynamical simulations that span a variety of baryon scenarios; we span this space via a Principal Component (PC) analysis of the summary statistics extracted from these simulations. We show that at the level of DES Y1 constraining power, one PC is sufficient to describe the variation of baryonic effects in the observables, and the first PC amplitude (Q1) generally reflects the strength of baryon feedback. With the upper limit of Q1 prior being bound by the Illustris feedback scenarios, we reach $\sim 20{{\ \rm per\ cent}}$ improvement in the constraint of $S_8=\sigma _8(\Omega _{\rm m}/0.3)^{0.5}=0.788^{+0.018}_{-0.021}$ compared to the original DES 3 × 2pt analysis. This gain is driven by the inclusion of small-scale cosmic shear information down to 2.5 arcmin, which was excluded in previous DES analyses that did not model baryonicmore »
4. ABSTRACT Determining the distribution of redshifts of galaxies observed by wide-field photometric experiments like the Dark Energy Survey (DES) is an essential component to mapping the matter density field with gravitational lensing. In this work we describe the methods used to assign individual weak lensing source galaxies from the DES Year 3 Weak Lensing Source Catalogue to four tomographic bins and to estimate the redshift distributions in these bins. As the first application of these methods to data, we validate that the assumptions made apply to the DES Y3 weak lensing source galaxies and develop a full treatment of systematic uncertainties. Our method consists of combining information from three independent likelihood functions: self-organizing map p(z) (sompz), a method for constraining redshifts from galaxy photometry; clustering redshifts (WZ), constraints on redshifts from cross-correlations of galaxy density functions; and shear ratios (SRs), which provide constraints on redshifts from the ratios of the galaxy-shear correlation functions at small scales. Finally, we describe how these independent probes are combined to yield an ensemble of redshift distributions encapsulating our full uncertainty. We calibrate redshifts with combined effective uncertainties of σ〈z〉 ∼ 0.01 on the mean redshift in each tomographic bin.
5. ABSTRACT
The combination of galaxy–galaxy lensing (GGL) and galaxy clustering is a powerful probe of low-redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias Alens. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile ΔΣ(rp) and the projected galaxy correlation function wp, gg(rp) in the final (Year 6) DES data set over scales $r_p=0.3\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$. For a $3{{\ \rm per\ cent}}$ prior on Alens we forecast precisions of $1.9{{\ \rm per\ cent}}$, $2.0{{\ \rm per\ cent}}$, and $1.9{{\ \rm per\ cent}}$ on Ωm, σ8, and $S_8 \equiv \sigma _8\Omega _m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as Alens. Adding scales $r_p=0.3\!-\!3.0\, h^{-1} \, \mathrm{Mpc}$ improves the S8 precision by a factor of ∼1.6 relative to a large scale ($3.0\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$) analysis, equivalent to increasing the survey area by a factor of ∼2.6. Sharpening the Alens prior to \$1{{\more »
| 2022-11-30T04:19:28 |
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|
https://indico.fnal.gov/event/16384/contributions/37220/
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Information on precautionary site access restrictions to Fermilab's Batavia site in response to coronavirus/COVID-19
We continue to review all events currently planned for the next sixty days and organizers will be notified if their event must be canceled, postponed, or held remotely. Please, check back on Indico during this time for updates regarding your meeting specifics.
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For public events you may use either https://library.fnal.gov/indico-search/ or your browser's search engine: "your search string" site:indico.fnal.gov
New Perspectives 2018
18-19 June 2018
Fermilab, Wilson Hall
US/Central timezone
Bayesian Hierarchical Models for parameter inference with missing data: Supernova cosmology case study.
Jun 18, 2018, 5:45 PM
15m
One West (Fermilab, Wilson Hall)
One West
Fermilab, Wilson Hall
Oral Presentation
Speaker
Dr Marisa March (U Penn)
Description
Large scale astronomical surveys are going wider and deeper than ever before. However, astronomers, cosmologists and theorists continue to face the perennial issue that their data sets are often incomplete in magnitude space and must be carefully treated in order to avoid Malmquist bias, especially in the field of supernova cosmology. Historically, cosmological parameter inference in supernova cosmology was done using $\chi^2$ methodology; however, recent years have seen a rise in the use of Bayesian Hierarchical Models. In this paper we develop a Bayesian Hierarchical methodology to account for magnitude limited surveys and present a specific application to cosmological parameter inference and model selection in supernova cosmology.
Primary author
Dr Marisa March (U Penn)
Slides
| 2020-07-11T09:30:05 |
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https://repo.scoap3.org/record/30147
|
Blue and violet graviton spectra from a dynamical refractive index
Giovannini, Massimo (Department of Physics, CERN, Geneva 23, 1211, Switzerland) (INFN, Section of Milan-Bicocca, Milan, 20126, Italy)
03 January 2019
Abstract: We show that the spectral energy distribution of relic gravitons mildly increases for frequencies smaller than the μHz and then flattens out whenever the refractive index of the tensor modes is dynamical during a quasi-de Sitter stage of expansion. For a conventional thermal history the high-frequency plateau ranges between the mHz and the audio band but it is supplemented by a spike in the GHz region if a stiff post-inflationary phase precedes the standard radiation-dominated epoch. Even though the slope is blue at intermediate frequencies, it may become violet in the MHz window. For a variety of post-inflationary histories, including the conventional one, a dynamical index of refraction leads to a potentially detectable spectral energy density in the kHz and in the mHz regions while all the relevant phenomenological constraints are concurrently satisfied.
Published in: Physics letters B 789 (2019) 502-507
Published by: Elsevier
DOI: 10.1016/j.physletb.2018.12.068
License: CC-BY-3.0
Fulltext:
XML PDF PDF (PDFA)
| 2019-06-20T19:03:33 |
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|
https://par.nsf.gov/biblio/10354101-exploration-co-sputtered-ta-zro-thin-films-gravitational-wave-detectors
|
Exploration of co-sputtered Ta 2 O 5 –ZrO 2 thin films for gravitational-wave detectors
Abstract We report on the development and extensive characterization of co-sputtered tantala–zirconia (Ta 2 O 5 -ZrO 2 ) thin films, with the goal to decrease coating Brownian noise in present and future gravitational-wave detectors. We tested a variety of sputtering processes of different energies and deposition rates, and we considered the effect of different values of cation ratio η = Zr/(Zr + Ta) and of post-deposition heat treatment temperature T a on the optical and mechanical properties of the films. Co-sputtered zirconia proved to be an efficient way to frustrate crystallization in tantala thin films, allowing for a substantial increase of the maximum annealing temperature and hence for a decrease of coating mechanical loss φ c . The lowest average coating loss was observed for an ion-beam sputtered sample with η = 0.485 ± 0.004 annealed at 800 °C, yielding φ ¯ c = 1.8 × 1 0 − 4 rad. All coating samples showed cracks after annealing. Although in principle our measurements are sensitive to such defects, we found no evidence that our results were affected. The issue could be solved, at least for ion-beam sputtered coatings, by decreasing heating and cooling rates down to 7 °C h more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10354101
Journal Name:
Classical and Quantum Gravity
Volume:
38
Issue:
19
Page Range or eLocation-ID:
195021
ISSN:
0264-9381
1. Optical coatings formed from amorphous oxide thin films have many applications in precision measurements. The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo use coatings of$SiO2$(silica) and$TiO2:Ta2O5$(titania-doped tantala) and post-deposition annealing to 500°C to achieve low thermal noise and low optical absorption. Optical scattering by these coatings is a key limit to the sensitivity of the detectors. This paper describes optical scattering measurements for single-layer, ion-beam-sputtered thin films on fused silica substrates: two samples of$Ta2O5$and two of$TiO2:Ta2O5$. Using an imaging scatterometer at a fixed scattering angle of 12.8°, in-situ changes in the optical scatter of each sample were assessed during post-deposition annealing to 500°C in vacuum. The scatter of three of the four coated optics was observed to decrease during the annealing process, by 25–30% for tantala and up to 74% for titania-doped tantala, while the scatter frommore »
3. Amorphous tantala ($Ta2O5$) thin films were deposited by reactive ion beam sputtering with simultaneous low energy assist$Ar+$or$Ar+/O2+$bombardment. Under the conditions of the experiment, the as-deposited thin films are amorphous and stoichiometric. The refractive index and optical band gap of thin films remain unchanged by ion bombardment. Around 20% improvement in room temperature mechanical loss and 60% decrease in absorption loss are found in samples bombarded with 100-eV$Ar+$. A detrimental influence from low energy$O2+$bombardment on absorption loss and mechanical loss is observed. Low energy$Ar+$bombardment removes excess oxygen point defects, while$O2+$bombardment introduces defects into the tantala films.
4. Mechanical loss of dielectric mirror coatings sets fundamental limits for both gravitational wave detectors and cavity-stabilized optical local oscillators for atomic clocks. Two approaches are used to determine the mechanical loss: ringdown measurements of the coating quality factor and direct measurement of the coating thermal noise. Here we report a systematic study of the mirror thermal noise at 4, 16, 124, and 300 K by operating reference cavities at these temperatures. The directly measured thermal noise is used to extract the mechanical loss for$SiO2/Ta2O5$coatings, which are compared with previously reported values.
| 2022-11-30T04:00:34 |
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|
https://phys.libretexts.org/TextBooks_and_TextMaps/College_Physics/Book%3A_College_Physics_(OpenStax)/21%3A_Circuits%2C_Bioelectricity%2C_and_DC_Instruments/21.0%3A_Prelude_to_Circuits_and_DC_Instruments
|
$$\require{cancel}$$
# 21.0: Prelude to Circuits and DC Instruments
• Page ID
2687
• Electric circuits are commonplace. Some are simple, such as those in flashlights. Others, such as those used in supercomputers, are extremely complex.
Figure $$\PageIndex{1}$$: Electric circuits in a computer allow large amounts of data to be quickly and accurately analyzed.. (credit: Airman 1st Class Mike Meares, United States Air Force)
This collection of modules takes the topic of electric circuits a step beyond simple circuits. When the circuit is purely resistive, everything in this module applies to both DC and AC. Matters become more complex when capacitance is involved. We do consider what happens when capacitors are connected to DC voltage sources, but the interaction of capacitors and other nonresistive devices with AC is left for a later chapter. Finally, a number of important DC instruments, such as meters that measure voltage and current, are covered in this chapter.
## Contributors
• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2018-09-26T13:28:44 |
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https://pdglive.lbl.gov/Particle.action?init=0&node=M151&home=MXXX045
|
BOTTOM MESONS($\mathit B$ = $\pm1$) ${{\mathit B}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit b}}}$, ${{\mathit B}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit b}}}$, ${{\overline{\mathit B}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit b}}$, ${{\mathit B}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit b}}$, similarly for ${{\mathit B}^{*}}$ 's
${{\mathit B}_{{J}}^{*}{(5732)}}$
$I(J^P)$ = $?(?^{?})$
also known as ${{\mathit B}^{**}}$
Signal can be interpreted as stemming from several narrow and broad resonances.
${{\mathit B}_{{J}}^{*}{(5732)}}$ MASS $5698 \pm8$ MeV (S = 1.2)
${{\mathit B}_{{J}}^{*}{(5732)}}$ WIDTH $128 \pm18$ MeV
$\Gamma_{1}$ ${{\mathit B}^{*}}{{\mathit \pi}}{+}$ ${{\mathit B}}{{\mathit \pi}}$ seen
$\Gamma_{2}$ ${{\mathit B}^{*}}{{\mathit \pi}}$ (X) [1] $(85\pm{29})\%$
FOOTNOTES
| 2022-12-09T11:30:43 |
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|
http://trilinos.sandia.gov/packages/docs/r10.4/packages/nox/doc/html/classNOX_1_1StatusTest_1_1NormWRMS.html
|
# NOX::StatusTest::NormWRMS Class Reference
Convergence test based on the weighted root mean square norm fo the solution update between iterations. More...
#include <NOX_StatusTest_NormWRMS.H>
Inheritance diagram for NOX::StatusTest::NormWRMS:
[legend]
Collaboration diagram for NOX::StatusTest::NormWRMS:
[legend]
List of all members.
## Public Member Functions
NormWRMS (double rtol, double atol, double BDFMultiplier=1.0, double tolerance=1.0, double alpha=1.0, double beta=0.5)
Constructor where ATOL is a scalar.
NormWRMS (double rtol, const Teuchos::RCP< const NOX::Abstract::Vector > &atol, double BDFMultiplier=1.0, double tolerance=1.0, double alpha=1.0, double beta=0.5)
Constructor where ATOL is a vector.
virtual ~NormWRMS ()
Destructor.
virtual StatusType checkStatus (const NOX::Solver::Generic &problem, NOX::StatusTest::CheckType checkType)
Test the stopping criterion
virtual StatusType getStatus () const
Return the result of the most recent checkStatus call.
virtual ostream & print (ostream &stream, int indent=0) const
Output formatted description of stopping test to output stream.
virtual double getNormWRMS () const
Returns the value of WRMS norm.
virtual double getTolerance () const
Returns the requested tolerance set in the constructor.
virtual double getRTOL () const
Returns the realative tolerance set in the constructor.
virtual double getATOL () const
Returns the absolute tolerance set in the constructor. If ATOL is a vector, this will return a value of -1.0.
virtual double getBDFMultiplier () const
Returns the value of the BDFMultiplier set in the constructor.
virtual double getAlpha () const
Returns the value of 'alpha' set in the constructor.
virtual double getBeta () const
Returns the value of 'beta' set in the constructor.
## Detailed Description
Convergence test based on the weighted root mean square norm fo the solution update between iterations.
If the number of iterations is zero, then the status is set to NOX::StatusTest::Unconverged and returned. (Also, value is set to 1.0e+12.)
Otherwise, returns NOX::StatusTest::Converged if the three criteria listed below are satisfied. Note that use of Criteria #2 and #3 depend on the options set in the solver.
1. Weigthed root mean square norm is less than a specified tolerance:
where
Here:
• denotes component of nonlinear iterate .
• denotes the number of unknowns
• denotes the relative error tolerance, specified via rtol in the constructor
• denotes the absolution error tolerance, specified via atol in the constructor. This can be a vector or a scalar.
• denotes a weight, specified via the parameter BDFMultiplier in the constructor.
2. If a line search based solver is used, the line search step size, , must be greater than a specified step size value, :
The motivation for this test is to avoid detecting stagnation when in fact the true problem is that the step size is just small.
The value of is set in the constructor via the argument alpha. Setting to zero effectively eliminates this part of the test.
3. The achieved linear solver tolerance, for nonlinear iteration , must be less than a specified tolerance value, ; i.e.,
The motivation for this test is to avoid detecting stagnation when in fact the true problem is that the linear solve tolerance was not accurate enough.
The value of is set in the constructor via the argument beta. Setting to 1.0 effectively eliminates this part of the test.
Note:
This criteria will only be used if the "Achieved Tolerance" parameter (the value of ) is set by the linear solver in the "Newton"/"Linear Solver"/"Output" sublist. The checkStatus() method will search for this parameter.
References:
1. K. E. Brennam, S. L. Cambell, L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics in Applied Mathematics 14, SIAM 1996.
2. G. D. Byrne and A. C. Hindmarch, PVODE, an ODE Solver for Parallel Computers, Technical Report UCRL-JC-132361, Rev. 1, Center for Applied Scientific Computing (CASC), Lawrence Livermore National Lab, May 1999.
## Member Function Documentation
StatusType NormWRMS::checkStatus ( const NOX::Solver::Generic & problem, NOX::StatusTest::CheckType checkType ) [virtual]`
Test the stopping criterion
The test can (and should, if possible) be skipped if checkType is NOX::StatusType::None. If the test is skipped, then the status should be set to NOX::StatusTest::Unevaluated.
Implements NOX::StatusTest::Generic.
The documentation for this class was generated from the following files:
• NOX_StatusTest_NormWRMS.H
• NOX_StatusTest_NormWRMS.C
Generated on Wed Apr 13 09:59:46 2011 for NOX by 1.6.3
| 2013-12-08T18:09:10 |
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|
https://lammps.sandia.gov/doc/fix_lb_viscous.html
|
# fix lb/viscous command
## Syntax
fix ID group-ID lb/viscous
• ID, group-ID are documented in fix command
• lb/viscous = style name of this fix command
## Examples
fix 1 flow lb/viscous
## Description
This fix is similar to the fix viscous command, and is to be used in place of that command when a lattice-Boltzmann fluid is present, and the user wishes to integrate the particle motion using one of the built in LAMMPS integrators.
This fix adds a force, F = - Gamma*(velocity-fluid_velocity), to each atom, where Gamma is the force coupling constant described in the fix lb/fluid command (which applies an equal and opposite force to the fluid).
Note
This fix should only be used in conjunction with one of the built in LAMMPS integrators; it should not be used with the fix lb/pc or fix lb/rigid/pc/sphere integrators, which already include the hydrodynamic forces. These latter fixes should only be used if the force coupling constant has been set by the user (instead of using the default value); if the default force coupling value is used, then this fix provides the only method for adding the hydrodynamic forces to the particles.
For further details, as well as descriptions and results of several test runs, see Mackay et al.. Please include a citation to this paper if this fix is used in work contributing to published research.
Restart, fix_modify, output, run start/stop, minimize info:
As described in the fix viscous documentation:
“No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command.
The forces due to this fix are imposed during an energy minimization, invoked by the minimize command. This fix should only be used with damped dynamics minimizers that allow for non-conservative forces. See the min_style command for details.”
## Restrictions
This fix is part of the USER-LB package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
Can only be used if a lattice-Boltzmann fluid has been created via the fix lb/fluid command, and must come after this command.
This fix should not be used if either the fix lb/pc or fix lb/rigid/pc/sphere integrator is used.
| 2018-10-21T23:19:32 |
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|
https://zbmath.org/authors/?q=ai:gray.andrew
|
## Gray, Andrew
Compute Distance To:
Author ID: gray.andrew Published as: Gray, A.; Gray, Andrew External Links: MacTutor · Wikidata · GND · IdRef
Documents Indexed: 46 Publications since 1887, including 13 Books Biographic References: 1 Publication Co-Authors: 6 Co-Authors with 7 Joint Publications 68 Co-Co-Authors
all top 5
### Co-Authors
39 single-authored 3 Mathews, George Ballard 1 Baynes, R. E. 1 Burbury, Samuel Hawksley 1 Gordon, James Gordon 1 Gray, James Gordon 1 Walker, George W.
all top 5
### Serials
17 Nature, London 4 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, VI. Series 3 Proceedings of the Royal Society of Edinburgh 3 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, V. Series 2 The Mathematical Gazette 1 Science 1 Proceedings of the Edinburgh Mathematical Society
### Fields
1 History and biography (01-XX)
### Citations contained in zbMATH Open
8 Publications have been cited 60 times in 58 Documents Cited by Year
A treatise on Bessel functions and their applications to physics. Zbl 0135.28002
Gray, A.; Mathews, G. B.
1966
A treatise on Bessel functions and their applications to physics. $$2^{\text{d}}$$ edition, prepared by A. Gray and T. M. Mac Robert. JFM 48.0423.05
Gray, A.; MacRobert, T. M.
1922
A treatise on Bessel’s functions and its applications to physics. JFM 25.0836.01
Gray, A.; Mathews, G. B.
1895
Absolute measurements in electricity and magnetism. 2d edition, rewritten and extended. JFM 48.0883.15
Gray, A.
1921
Notes on Hydrodynamics. II. Determination of translation velocity of a vortex ring of small cross-section. JFM 45.1093.01
Gray, A.
1914
Lord Kelvin, an account of his scientific life and work. JFM 39.0031.05
Gray, Andrew
1908
Lord Kelvin. JFM 27.0027.02
Gray, A.
1896
Absolute measurements in electricity and magnetism. $$2^{\text{nd}}$$ Ed. JFM 21.1177.11
Gray, A.
1889
A treatise on Bessel functions and their applications to physics. Zbl 0135.28002
Gray, A.; Mathews, G. B.
1966
A treatise on Bessel functions and their applications to physics. $$2^{\text{d}}$$ edition, prepared by A. Gray and T. M. Mac Robert. JFM 48.0423.05
Gray, A.; MacRobert, T. M.
1922
Absolute measurements in electricity and magnetism. 2d edition, rewritten and extended. JFM 48.0883.15
Gray, A.
1921
Notes on Hydrodynamics. II. Determination of translation velocity of a vortex ring of small cross-section. JFM 45.1093.01
Gray, A.
1914
Lord Kelvin, an account of his scientific life and work. JFM 39.0031.05
Gray, Andrew
1908
Lord Kelvin. JFM 27.0027.02
Gray, A.
1896
A treatise on Bessel’s functions and its applications to physics. JFM 25.0836.01
Gray, A.; Mathews, G. B.
1895
Absolute measurements in electricity and magnetism. $$2^{\text{nd}}$$ Ed. JFM 21.1177.11
Gray, A.
1889
all top 5
### Cited by 93 Authors
2 Ifantis, Evangelos K. 2 Vargas, Vincent 1 Abbasova, Khatira E. 1 Ahmed, Najma 1 Akin, Omer 1 Amsalu, Hafte 1 Arestov, Vitaliĭ Vladimirovich 1 Arinshtein, Édward Abramovich 1 Babenko, Aleksandr Grigor’evich 1 Bagirova, Sevinc M. 1 Bareket, Miriam 1 Barrow-Green, June E. 1 Barvínek, Erich 1 Bérard, Pierre H. 1 Bevilacqua, Giulia 1 Biancalana, V. 1 Bureau, Florent J. 1 Chang, David B. 1 Chernopiskij, D. I. 1 Dancheva, Y. 1 Deikalova, Marina Valer’evna 1 Farmer, M. R. 1 Fatykhov, A. G. 1 Ferreira, Erasmo M. 1 Gatteschi, Luigi 1 Geppert, Harald 1 Ghaffari, Rezvan 1 Gluchoff, Alan D. 1 Gottlieb, H. P. W. 1 Gray, Jeremy John 1 Gupta, S. L. 1 Hejhal, Dennis A. 1 Henriquez, Craig S. 1 Hill, James Murray 1 Hillion, Pierre T. M. 1 Horváth, Ágota P. 1 Huang, Min-Jei 1 Humphreys, Katherine 1 Kerimov, Movlud Kerimovich 1 Khanmamedov, Agil Khanmamed ogly 1 Kirpichnikova, N. Ya. 1 Kong, Fanze 1 Kouris, Christos B. 1 Kouris, Demitris A. 1 Kravanja, Peter 1 Lewis, Steven M. 1 Lin, Qionggui 1 Lin, Sheng Hsiung 1 Lu, Wenfa 1 MacRobert, Thomas Murray 1 Mansour, Toufik 1 Mardanov, R. Sh. 1 Meleshko, V’yacheslav Volodymyrovych 1 Meyer, Daniel 1 Mi, Changwen 1 Mitchell, Daniel Jon 1 Moi, L. 1 Mukhametzyanov, F. M. 1 Nisar, Kottakkaran S. 1 Ovchinnikova, S. N. 1 Patras, Frédéric 1 Philippov, Vjacheslav Borisovish 1 Pickard, William F. 1 Prabha, Saroj 1 Purohit, Sunil Dutt 1 Ragab, Fouad M. 1 Ragos, Omiros 1 Rhodes, Rémi 1 Robert, Raoul 1 Sarikaya, Mehmet Zeki 1 Saygili, Kemal 1 Sesma, Javier 1 Shah, Nehad Ali 1 Sherstyukov, Vladimir Borisovich 1 Siafarikas, Panayiotis D. 1 Sicbaldi, Pieralberto 1 Sørensen, Thomas Østergaard 1 Sumin, E. V. 1 Suthar, Daya Lal 1 Svirkina, L. A. 1 Taherifar, Somaye 1 Taqqu, Murad S. 1 Trayanova, Natalia A. 1 Trlifaj, Ladislav 1 Veillette, Mark S. 1 Veklich, N. A. 1 Vrahatis, Michael N. 1 Yildirim, Huseyin 1 Young, Allan C. 1 Yudovich, Viktor Iosifovich 1 Zafiropoulos, F. A. 1 Zaman, Fiazud Din 1 Zotter, B.
all top 5
### Cited in 43 Serials
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Mathematical Physics 3 Mathematical Biosciences 3 Journal of Computational and Applied Mathematics 3 Computational Mathematics and Mathematical Physics 2 Fluid Dynamics 2 Journal of Mathematical Analysis and Applications 2 Aplikace Matematiky 2 Historia Mathematica 1 Analysis Mathematica 1 Archive for History of Exact Sciences 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 International Journal of Engineering Science 1 Journal d’Analyse Mathématique 1 Physics Letters. B 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Theoretical and Computational Fluid Dynamics 1 Chaos, Solitons and Fractals 1 Prikladnaya Matematika i Mekhanika 1 Soviet Applied Mechanics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal of Statistical Planning and Inference 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 SIAM Journal on Mathematical Analysis 1 Stochastic Processes and their Applications 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Mathematics and Mechanics of Solids 1 The Ramanujan Journal 1 Communications in Nonlinear Science and Numerical Simulation 1 Methodology and Computing in Applied Probability 1 Lobachevskii Journal of Mathematics 1 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 The Bulletin of Mathematical Biophysics 1 Probability Surveys 1 Azerbaijan Journal of Mathematics
all top 5
### Cited in 30 Fields
14 Special functions (33-XX) 9 Partial differential equations (35-XX) 6 Fluid mechanics (76-XX) 6 Biology and other natural sciences (92-XX) 4 History and biography (01-XX) 4 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 3 Ordinary differential equations (34-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Numerical analysis (65-XX) 3 Mechanics of deformable solids (74-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-07-06T19:30:20 |
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|
http://www.popflock.com/learn?s=Passer_rating
|
Passer Rating
Get Passer Rating essential facts below. View Videos or join the Passer Rating discussion. Add Passer Rating to your PopFlock.com topic list for future reference or share this resource on social media.
Passer Rating
Passer rating (also known as quarterback rating, QB rating, or passing efficiency in college football) is a measure of the performance of passers, primarily quarterbacks, in gridiron football.[1] There are two formulas currently in use: one used by both the National Football League (NFL) and Canadian Football League (CFL), and the other used in NCAA football. Passer rating is calculated using a player's passing attempts, completions, yards, touchdowns, and interceptions. Passer rating in the NFL is on a scale from 0 to 158.3. Passing efficiency in college football is on a scale from -731.6 to 1261.6.
Since 1973, passer rating has been the official formula used by the NFL to determine its passing leader.[2]
## History
Before the development of the passer rating, the NFL struggled with how to crown a passing leader. In the mid-1930s, it was the quarterback with the most passing yardage. From 1938 to 1940, it was the quarterback with the highest completion percentage. In 1941, a system was created that ranked the league's quarterbacks relative to their peers' performance. Over the next thirty years the criteria used to crown a passing leader changed several times, but the ranking system made it impossible to determine a quarterback's rank until all the other quarterbacks were done playing that week, or to compare quarterback performances across multiple seasons. In 1971, NFL commissioner Pete Rozelle asked the league's statistical committee to develop a better system.[3] The committee was headed by Don Smith of the Pro Football Hall of Fame, Seymour Siwoff of the Elias Sports Bureau, and NFL executive Don Weiss. Smith and Siwoff established passing performance standards based on data from all qualified pro football passers between 1960 and 1970, and used those data to create the passer rating. The formula was adopted by the NFL in 1973.[2]
## NFL and CFL formula
The NFL passer rating formula includes five variables: pass attempts, completions, passing yards, touchdowns passes, and interceptions. Each of those variables is scaled to a value between 0 and 2.375, with 1.0 being statistically average (based on league data between 1960-1970). When the formula was first created, a 66.7 rating indicated an average performance, and a 100+ rating indicated an excellent performance.[3] However, passing performance has improved steadily since then and in 2017 the league average rating was 88.6.[4]
The four separate calculations can be expressed in the following equations:
${\displaystyle a=\left({{\text{COMP}} \over {\text{ATT}}}-.3\right)\times 5}$
${\displaystyle b=\left({{\text{YDS}} \over {\text{ATT}}}-3\right)\times 0.25}$
${\displaystyle c=\left({{\text{TD}} \over {\text{ATT}}}\right)\times 20}$
${\displaystyle d=2.375-\left({{\text{INT}} \over {\text{ATT}}}\times 25\right)}$
where
ATT = Number of passing attempts
COMP = Number of completions
YDS = Passing yards
TD = Touchdown passes
INT = Interceptions
If the result of any calculation is greater than 2.375, it is set to 2.375. If the result is a negative number, it is set to zero.
Then, the above calculations are used to complete the passer rating:
${\displaystyle {\text{Passer Rating}}=\left({a+b+c+d \over 6}\right)\times 100}$
A perfect passer rating (158.33) requires at least:[1] A minimum rating (0.0) requires at best:
77.5% completion percentage (31 completions in 40 attempts)
12.5 yards per attempt
11.875% TD/ATT (1 TD/8.421ATT)
No interceptions
30.0% completion percentage
3.0 yards per attempt
No touchdowns
9.5% INT/ATT (1INT/10.526ATT)
## NCAA formula
The NCAA passing efficiency formula is similar to that of the NFL passer rating, but does not impose limits on the four components:[5]
${\displaystyle {\text{Passer Rating}}_{\text{NCAA}}={(8.4\times {\text{YDS}})+(330\times {\text{TD}})+(100\times {\text{COMP}})-(200\times {\text{INT}}) \over {\text{ATT}}}}$
where
ATT = Number of passing attempts
COMP = Number of completions
YDS = Passing yards
TD = Touchdown passes
INT = Interceptions
The NCAA passer rating has an upper limit of 1,261.6 (every attempt is a 99-yard completion for a touchdown), and a lower limit of -731.6 (every attempt is completed, but results in a 99-yard loss). A passer who throws only interceptions will have a -200 rating, as would a passer who only throws completed passes losing an average of 35.714 yards.
## Advantages
In 2011, Sports Illustrated published an article by Kerry Byrne of Cold Hard Football Facts highlighting the importance of passer rating in determining a team's success.[6] "Put most simply," the article states, "you cannot be a smart football analyst and dismiss passer rating. In fact, it's impossible to look at the incredible correlation of victory to passer rating and then dismiss it. You might as well dismiss the score of a game when determining a winner. [...] Few, if any, are more indicative of wins and losses than passer rating. Teams that posted a higher passer rating went 203-53 (.793) in 2010 and an incredible 151-29 (.839) after Week 5." Byrne made an expanded defense of the passer rating and its importance for the Pro Football Researchers Association in 2012.[7] The study showed that all of the eight teams since 1940 that led the league in both offensive passer rating and defensive passer rating won championships.[8]
## Flaws
The biggest criticism of passer rating is that it is too simple a stat that fails to take into account more the full scope of a quarterback's contributions to the team's performance. For example, the equation does not take into account a quarterback's rushing yards, rushing touchdowns, sacks, or fumbles and favors quarterbacks that are efficient over effective.[9]Pro Football Focus writer Nathan Jahnke provides a good example of this phenomenon in the following scenario of two different quarterbacks:
Average NFL passer rating by year. Data from: Pro Football Reference
If Quarterback A completes three passes for three yards in a row, then they would have a passer rating of 79.17.
Meanwhile, Quarterback B throws three straight passes, with the first two falling incomplete, while the third is caught for a 30-yard gain. The quarterback's passer rating in this circumstance is 43.75.[10]
Albeit, Quarterback A does have a greater completion rate and is more efficient than Quarterback B, they still failed to gain 10 yards on the play and reward their team with a first down. On the other hand, Quarterback B wasn't necessarily efficient in his throws, but on their last throw, they were able to make a completion of 30 yards and effectively gives their offense a new set of downs and are now likely on their opponent's half of the field as well.
Due to new rules that favor NFL offenses, such as the roughing the passer penalty, an increase in the number of games, most recently in 1978, and teams opting to pass more than ever, almost all of the passer rating leaders are quarterbacks from the past two decades. Since 1950, there have been 93 quarterbacks who have finished the season with a passer rating of greater than 100.0, yet 9 of those seasons happened in 2018 alone. Moreover, Steve Young and Joe Montana are the only two quarterbacks whose careers ended prior to 2000 and are among the top 25 passer ratings in NFL history. The graph on the right shows a good visual representation of the passer rating inflation since 1950.[9]
Therefore, passer rating is not a valid stat when comparing quarterbacks from two different eras. However, within an era and season itself, passer rating is a much more accurate and reliable stat to measure the true effectiveness of a quarterback.
## Other Measurements
### Total Quarterback Rating (QBR)
ESPN's Total Quarterback Rating is a proprietary statistic that was first introduced in 2011 and is designed to measure the total effectiveness and performance of a quarterback. The metric takes into account all of a quarterback's contribution to a game, including: passing, rushing, sacks, penalties, touchdowns, and turnovers.[11] Moreover, each play is weighted based on its "difficulty", the context of the game, and the strength of the opposing defense. This means that statistics in garbage time of a blowout game hold less merit than statistics in a close game. Also, a quarterback who throws for four touchdowns and 300 yards against a strong defense will have a higher QBR than a quarterback who has the same stat line against the worst defense in the NFL.[11]
QBR functions on a 0-100 scale, where an average NFL quarterback typically has around a 50 QBR, while a Pro Bowl caliber quarterback will have approximately a 75. This scale also represents a percentile of overall quarterback performances since 2006. Meaning that if a quarterback has a QBR of 90, then their performance in that game is, on average, better than 90% of other quarterback performances.[12]
It is also very common for there to be significant differences between QBR and passer rating leaders, especially since passer rating favors yardage and pure volume of passing attempts rather than efficiency and performance. For example, in 2019 Lamar Jackson had a league leading QBR of 83.0 and earned MVP honors. However, Jackson finished 3rd in passer rating (113.3) behind Ryan Tannehill (117.5) and Drew Brees (116.3) who finished 9th and 3rd for QBR.
### PFF Player Grades
Pro Football Focus (PFF) is a football website that conducts in-depth analysis on NFL and NCAA games and players. Part of this analysis is assigning each football player in the NFL and NCAA teams in the Power Five a grade that indicates the performance of said player.[13]
According to the PFF website, the group's algorithm analyzes every play for each individual player and measures the impact that said player has while on the field. A player's impact is then given a grade between -2 to +2 in 0.5 increments.[13] Each position has a scale with a unique algorithm and rules. The scale also takes into account game context, so a strong play in the fourth quarter of a close matchup will be graded higher than one in the 2nd quarter of a blowout game.
A 0 player grade on any given play represents any position player performing at an expected level and in a manner that neither positively nor negatively impacts their team. An example of this is a running back taking a carry through the correct hole and picking up 3 - 4 yards on first and ten. Meanwhile, a +2 represents an incredible performance on a play that shifts the dynamic of a game in favor of the player's team. Brandon Graham's, a defensive end for the Philadelphia Eagles, strip sack on Tom Brady in Super Bowl LII would have easily been a +2 rating.[13] On the other hand a -2 is a play that catastrophically hinders a team's chance of winning, such as a quarterback throwing a pick-six in the fourth quarter of a close game. Ambiguous plays where the outcome is unclear on how a player impacted their team are typically given a 0.
The sum of these plus-minuses are then converted on a 0-100 scale and produce a grade for a single game. However, a player's season grade is not the average of the 16 grades a player receives each game. Instead, PFF credits a player's entire body of work and longevity throughout the season. It is, therefore, possible for a player to have a higher season grade than any individual grade that a player received in any game he played in.[13]
## Records
### NFL
Wide receiver Antwaan Randle El, with a passer rating of 157.5 from 21 completed passes of a possible 26, has the highest career rating of any non-QB with more than twenty attempts.[16]Ben Roethlisberger and Peyton Manning hold the record for the most games with a perfect passer rating (4). As of 2019, 74 NFL quarterbacks have completed a game with a perfect passer rating of 158.3, and seven have done so multiple times. Phil Simms holds the record for the highest passer rating in a Super Bowl, at 150.92 in Super Bowl XXI.
### All-Time NFL Passer Rating Leaders
+ means Hall of Famer.
1 2 3 4 Patrick Mahomes 108.7 2017-2020 KC Deshaun Watson 104.5 2017-2020 HOU Aaron Rodgers 103.9 2005-2020 GB Russell Wilson 101.7 2012-2020 SEA Drew Brees 98.7 2001-2020 2TM Dak Prescott 97.3 2016-2020 DAL Tony Romo 97.1 2004-2016 DAL Tom Brady 97 2000-2020 2TM Kirk Cousins 96.8 2012-2020 2TM Steve Young+ 96.8 1985-1999 2TM Peyton Manning+ 96.5 1998-2015 2TM Philip Rivers 95 2004-2020 2TM Matt Ryan 94.8 2008-2020 ATL Ben Roethlisberger 94.3 2004-2020 PIT Kurt Warner+ 93.7 1998-2009 3TM Jared Goff 92.3 2016-2020 LAR Joe Montana+ 92.3 1979-1994 2TM Derek Carr 92.1 2014-2020 LV Ryan Tannehill 91.2 2012-2020 2TM Chad Pennington 90.1 2000-2010 2TM Carson Wentz 90.1 2016-2020 PHI Marcus Mariota 89.6 2015-2019 2TM Andrew Luck 89.5 2012-2018 IND Matt Schaub 89.5 2004-2019 4TM Matthew Stafford 89.5 2009-2020 DET
[17]
## References
1. ^ a b "NFL.com - NFL Quarterback Rating Formula". Archived from the original on August 14, 2011. Retrieved 2011.
2. ^ a b "NFL's Passer Rating". Pro Football Hall of Fame Official Site. NFL. January 1, 2005. Archived from the original on October 3, 2015. Retrieved 2016.
3. ^ a b "QB Rating story / GQ magazine / by Don Steinberg". bluedonut.com. Archived from the original on September 18, 2013. Retrieved 2018.
4. ^ SteelersFan, Tim (July 23, 2009). "Did NFL Passer Ratings Spike in 2004 Or Have They Risen Steadily?". bleacher report. Bleacher Report, Inc. Archived from the original on December 28, 2016. Retrieved 2016.
5. ^ "NCAA and NFL Passing Efficiency computation". Football.stassen.com. Archived from the original on November 10, 2011. Retrieved 2011.
6. ^ "Kerry J. Byrne: In defense of passer rating". si.com. Archived from the original on December 11, 2017. Retrieved 2018.
7. ^ Cold Hard Football Facts: 40 and Fabulous: in praise of passer rating Archived August 17, 2012, at the Wayback Machine
8. ^
9. ^ a b Paine, Neil (January 4, 2019). "Kirk Cousins Is Not Better Than Joe Montana. So Let's Fix Passer Rating". FiveThirtyEight. Retrieved 2020.
10. ^ Jahnke, Nathan (March 25, 2011). "Stat Sheet Misconceptions: Passer Rating | PFF News & Analysis". PFF. Retrieved 2020.
11. ^ a b "ESPN Introduces The Total Quarterback Rating". ESPN Press Room U.S. August 2, 2011. Retrieved 2020.
12. ^ "How is Total QBR calculated? We explain our quarterback rating". ESPN.com. September 8, 2016. Retrieved 2020.
13. ^ a b c d "PFF Player Grades". PFF. Retrieved 2020.
14. ^ "NFL Passer Rating Career Stats". Pro Football Reference. Retrieved 2020.
15. ^ "Player Game Finder Query Results". Pro Football Reference. Retrieved 2018.
16. ^ King, Peter (November 15, 2010). "Patriots? Jets? Giants? There are no super NFL teams this season". Sports Illustrated. Archived from the original on December 7, 2010. Retrieved 2011.
17. ^ "NFL Passer Rating Career Leaders". Pro-Football-Reference.com. Retrieved 2020.
18. ^ "Tua Tagovailoa College Stats". College Football at Sports-Reference.com. Retrieved 2020.
19. ^ "Passing Efficiency Rating Single Season Leaders and Records - College Football at Sports-Reference.com". College Football at Sports-Reference.com. Retrieved 2020.
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.
| 2021-04-13T03:42:37 |
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|
https://mfix.netl.doe.gov/doc/vvuq-manual/main/html/fluid/fld-02.html
|
# 3.2. FLD02: Steady, 1D heat conduction¶
## 3.2.1. Description¶
Steady-state, one-dimensional heat conduction occurs across a rectangular plane-shaped slab of length $$L$$ with constant material properties. As shown in Fig. 3.4, two opposing slab boundaries are maintained at constant temperatures. All other faces are perfectly insulated such that the heat flux along these boundaries is zero. Without heat generation, heat transfer through the $$x = 0$$ face must equal that through the $$x = L$$ face.
Fig. 3.4 Plane slab with constant material properties and no internal heat generation is shown with constant temperatures specified on opposing faces. The slab is assumed to be perfectly insulated along all other faces.
For constant thermal conductivity, the energy equation reduces to a second order ODE with Dirichlet boundary conditions as given by :eq:fld02eq1. The analytical solution for temperature distribution within the slab follows a line as given by :eq:fld02eq2.
(3.3)$\frac{d}{\text{dx}}\left( \lambda_{g}\frac{\text{dT}}{\text{dx}} \right) = 0; T\left( x = 0 \right) = T_{1}; T\left( x = L \right) = T_{2}$
(3.4)$T\left( x \right) = T_{1} + \frac{\left( T_{2} - T_{1} \right)}{L}$
## 3.2.2. Setup¶
########################################################################
# #
# Author: Aniruddha Choudhary Date: May 2015 #
# Steady-state 1D heat conduction through a plane slab. #
# #
# Default walls are used for the north/south boundaries as they are #
# adiabatic. The termperature is specified for the east/west walls. #
########################################################################
RUN_NAME = 'FLD02'
DESCRIPTION = 'Steady, 1D heat conduction'
#_______________________________________________________________________
# RUN CONTROL SECTION
UNITS = 'SI'
RUN_TYPE = 'NEW'
MOMENTUM_X_EQ = .F.
MOMENTUM_Y_EQ = .F.
ENERGY_EQ = .T.
SPECIES_EQ(0) = .F.
GRAVITY = 0.0
CALL_USR = .T.
#_______________________________________________________________________
# NUMERICAL SECTION
Max_nit = 200000
TOL_RESID_T = 1.0E-16
LEQ_PC(6) = 'NONE'
#_______________________________________________________________________
# GEOMETRY SECTION
COORDINATES = 'CARTESIAN'
ZLENGTH = 1.00 NO_K = .T.
XLENGTH = 1.00 IMAX = 8
YLENGTH = 1.00 JMAX = 8
#_______________________________________________________________________
# GAS-PHASE SECTION
RO_g0 = 1.0 ! (kg/m3)
MU_g0 = 1.0 ! (Pa.s)
C_Pg0 = 1.0 ! (J/kg.K)
K_g0 = 1.0 ! (W/m.K)
#_______________________________________________________________________
# SOLIDS-PHASE SECTION
MMAX = 0
#_______________________________________________________________________
# INITIAL CONDITIONS SECTION
IC_X_w(1) = 0.0 ! (m)
IC_X_e(1) = 1.0 ! (m)
IC_Y_s(1) = 0.0 ! (m)
IC_Y_n(1) = 1.0 ! (m)
IC_EP_g(1) = 1.0
IC_P_g(1) = 0.0 ! (Pa)
IC_T_g(1) = 350.0 ! (K)
IC_U_g(1) = 0.0 ! (m/sec)
IC_V_g(1) = 0.0 ! (m/sec)
#_______________________________________________________________________
# BOUNDARY CONDITIONS SECTION
! Specified temperatures at west and east walls
!---------------------------------------------------------------------//
BC_X_w(1:2) = 0.0 1.0 ! (m)
BC_X_e(1:2) = 0.0 1.0 ! (m)
BC_Y_s(1:2) = 0.0 0.0 ! (m)
BC_Y_n(1:2) = 1.0 1.0 ! (m)
BC_TYPE(1:2) = 'NSW' 'NSW'
BC_Tw_g(1:2) = 400.0 300.0 ! (K)
#_______________________________________________________________________
# OUTPUT CONTROL SECTION
RES_DT = 1.0 ! (sec)
SPX_DT(1:9) = 9*1.0 ! (sec)
FULL_LOG = .T.
RESID_STRING = 'T0'
#_______________________________________________________________________
# DMP SETUP
! NODESI = 1 NODESJ = 1 NODESK = 1
## 3.2.3. Results¶
The analytical and numerical solutions for temperature, $$T_{g}$$, are shown in Fig. 3.5. Only a subset of the numerical solution data points are plotted causing the appearance of a slight shift in presented data points. The largest observed absolute error is bounded above by $$10^{- 12}$$ and occurs for the finest mesh. This error is attributed to convergence criteria of the linear equation solver.
Fig. 3.5 Steady, 1D heat-conduction. (Left) numerical solution vs analytical solution, and (right) absolute error between the analytical and numerical solutions.
| 2022-07-03T17:53:23 |
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https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_Conceptual_Physics_(Crowell)/03._Conservation_of_Momentum/3.2_Force_In_One_Dimension
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$$\require{cancel}$$
# 3.2 Force In One Dimension
### 3.2.1 Momentum transfer
For every conserved quantity, we can define an associated rate of flow. An open system can have mass transferred in or out of it, and we can measure the rate of mass flow, $$d{}m/d{}t$$ in units of kg/s. Energy can flow in or out, and the rate of energy transfer is the power, $$P=d{}E/d{}t$$, measured in watts.3 The rate of momentum transfer is called force,
$\begin{equation*} F = \frac{d{}p}{d{}t} \text{[definition of force]} . \end{equation*}$
The units of force are $$\text{kg}\!\cdot\!\text{m}/\text{s}^2$$, which can be abbreviated as newtons, $$1\ \text{N}=\text{kg}\!\cdot\!\text{m}/\text{s}^2$$. Newtons are unfortunately not as familiar as watts. A newton is about how much force you'd use to pet a dog. The most powerful rocket engine ever built, the first stage of the Saturn V that sent astronauts to the moon, had a thrust of about 30 million newtons. In one dimension, positive and negative signs indicate the direction of the force --- a positive force is one that pushes or pulls in the direction of the positive $$x$$ axis.
a / Power and force are the rates at which energy and momentum are transferred.
Example 20: Walking into a lamppost
$$\triangleright$$ Starting from rest, you begin walking, bringing your momentum up to 100 $$\text{kg}\!\cdot\!\text{m}/\text{s}$$. You walk straight into a lamppost. Why is the momentum change of $$-100\ \text{kg}\!\cdot\!\text{m}/\text{s}$$ so much more painful than the change of $$+100\ \text{kg}\!\cdot\!\text{m}/\text{s}$$ when you started walking?
$$\triangleright$$ The forces are not really constant, but for this type of qualitative discussion we can pretend they are, and approximate $$d{} p/d{} t$$ as $$\Delta{} p/\Delta{} t$$. It probably takes you about 1 s to speed up initially, so the ground's force on you is $$F=\Delta{} p/\Delta{} t\approx100\ \text{N}$$. Your impact with the lamppost, however, is over in the blink of an eye, say 1/10 s or less. Dividing by this much smaller $$\Delta{} t$$ gives a much larger force, perhaps thousands of newtons (with a negative sign).
This is also the principle of airbags in cars. The time required for the airbag to decelerate your head is fairly long: the time it takes your face to travel 20 or 30 cm. Without an airbag, your face would have hit the dashboard, and the time interval would have been the much shorter time taken by your skull to move a couple of centimeters while your face compressed. Note that either way, the same amount of momentum is transferred: the entire momentum of your head.
b / The airbag increases $$\Delta t$$ so as to reduce $$F=\Delta p/\Delta t$$.
Force is defined as a derivative, and the derivative of a sum is the sum of the derivatives. Therefore force is additive: when more than one force acts on an object, you add the forces to find out what happens. An important special case is that forces can cancel. Consider your body sitting in a chair as you read this book. Let the positive $$x$$ axis be upward. The chair's upward force on you is represented with a positive number, which cancels out with the earth's downward gravitational force, which is negative. The total rate of momentum transfer into your body is zero, and your body doesn't change its momentum.
Example 21: Finding momentum from force
$$\triangleright$$ An object of mass $$m$$ starts at rest at $$t=t_\text{o}$$. A force varying as $$F=bt^{-2}$$, where $$b$$ is a constant, begins acting on it. Find the greatest speed it will ever have.
$$\triangleright$$
\begin{align*} F &= \frac{dp}{dt} \\ dp &= F dt \\ p &= \int F dt + p_\text{o}\\ &= -\frac{b}{t}+p_\text{o} , \end{align*}
where $$p_\text{o}$$ is a constant of integration. The given initial condition is that $$p=0$$ at $$t=t_\text{o}$$, so we find that $$p_\text{o}=b/t_\text{o}$$. The negative term gets closer to zero with increasing time, so the maximum momentum is achieved by letting $$t$$ approach infinity. That is, the object will never stop speeding up, but it will also never surpass a certain speed. In the limit $$t\rightarrow\infty$$, we identify $$p_\text{o}$$ as the momentum that the object will approach asymptotically. The maximum velocity is $$v=p_\text{o}/m=b/mt_\text{o}$$.
### Discussion Question
◊ Many collisions, like the collision of a bat with a baseball, appear to be instantaneous. Most people also would not imagine the bat and ball as bending or being compressed during the collision. Consider the following possibilities:
1. The collision is instantaneous.
2. The collision takes a finite amount of time, during which the ball and bat retain their shapes and remain in contact.
3. The collision takes a finite amount of time, during which the ball and bat are bending or being compressed.
How can two of these be ruled out based on energy or momentum considerations?
### 3.2.2 Newton's laws
Although momentum is the third conserved quantity we've encountered, historically it was the first to be discovered. Isaac Newton formulated a complete treatment of mechanical systems in terms of force and momentum. Newton's theory was based on three laws of motion, which we now think of as consequences of conservation of mass, energy, and momentum.
c / Isaac Newton (1643-1727).
Newton’s laws in one dimension: Newton’s first law: If there is no force acting on an object, it stays in the same state of motion. Newton’s second law: The sum of all the forces acting on an object determines the rate at which its momentum changes,Ftotalderpdert. Newton’s third law: Forces occur in opposite pairs. If object A interacts with object B, then A’s force on B and B’s force on A are related byFAB = − FBA.
The second law is the definition of force, which we've already encountered.4 The first law is a special case of the second law --- if $$d{}p/d{}t$$ is zero, then $$p=mv$$ is a constant, and since mass is conserved, constant $$p$$ implies constant $$v$$. The third law is a restatement of conservation of momentum: for two objects interacting, we have constant total momentum, so $$0=\frac{d}{d{}t}(p_A+p_B) =F_{BA}+F_{AB}$$.
Example 22: Ia=F/m
Many modern textbooks restate Newton's second law as $$a= F/ m$$, i.e., as an equation that predicts an object's acceleration based on the force exerted on it. This is easily derived from Newton's original form as follows: $$a=\text{d} v/\text{d} t=(\text{d} p/\text{d} t)/ m= F/ m$$.
Example 23: Gravitational force related to g
As a special case of the previous example, consider an object in free fall, and let the $$x$$ axis point down. Then $$a=+g$$, and $$F= ma= mg$$. For example, the gravitational force on a 1 kg mass at the earth's surface is about 9.8 N. Even if other forces act on the object, and it isn't in free fall, the gravitational force on it is still the same, and can still be calculated as $$mg$$.
Example 24: Changing frames of reference
Suppose we change from one frame reference into another, which is moving relative to the first one at a constant velocity $$u$$. If an object of mass $$m$$ is moving at velocity $$v$$ (which need not be constant), then the effect is to change its momentum from $$mv$$ in one frame to $$mv+mu$$ in the other. Force is defined as the derivative of momentum with respect to time, and the derivative of a constant is zero, so adding the constant $$mu$$ has no effect on the result. We therefore conclude that observers in different inertial frames of reference agree on forces.
#### Using the third law correctly
If you've already accepted Galilean relativity in your heart, then there is nothing really difficult about the first and second laws. The third law, however, is more of a conceptual challenge. The first hurdle is that it is counterintuitive. Is it really true that if a fighter jet collides with a mosquito, the mosquito's force on the jet is just as strong as the jet's force on the mosquito? Yes, it is true, but it is hard to believe at first. That amount of force simply has more of an effect on the mosquito, because it has less mass.
A more humane and practical experiment is shown in figure d. A large magnet and a small magnet are weighed separately, and then one magnet is hung from the pan of the top balance so that it is directly above the other magnet. There is an attraction between the two magnets, causing the reading on the top scale to increase and the reading on the bottom scale to decrease. The large magnet is more “powerful” in the sense that it can pick up a heavier paperclip from the same distance, so many people have a strong expectation that one scale's reading will change by a far different amount than the other. Instead, we find that the two changes are equal in magnitude but opposite in direction, so the upward force of the top magnet on the bottom magnet is of the same magnitude as the downward force of the bottom magnet on the top magnet.
d / Two magnets exert forces on each other.
To students, it often sounds as though Newton's third law implies nothing could ever change its motion, since the two equal and opposite forces would always cancel. As illustrated in figure e, the fallacy arises from assuming that we can add things that it doesn't make sense to add. It only makes sense to add up forces that are acting on the same object, whereas two forces related to each other by Newton's third law are always acting on two different objects. If two objects are interacting via a force and no other forces are involved, then both objects will accelerate --- in opposite directions, as shown in figure f!
e / It doesn't make sense for the man to talk about the woman's money canceling out his bar tab, because there is no good reason to combine his debts and her assets.
f / Newton's third law does not mean that forces always cancel out so that nothing can ever move. If these two ice skaters, initially at rest, push against each other, they will both move.
Here are some suggestions for avoiding misapplication of Newton's third law:
1. It always relates exactly two forces, not more.
2. The two forces involve exactly two objects, in the pattern A on B, B on A.
3. The two forces are always of the same type, e.g., friction and friction, or gravity and gravity.
#### Directions of forces
We've already seen that momentum, unlike energy, has a direction in space. Since force is defined in terms of momentum, force also has a direction in space. For motion in one dimension, we have to pick a coordinate system, and given that choice, forces and momenta will be positive or negative. We've already used signs to represent directions of forces in Newton's third law, $$F_{AB}=-F_{BA}$$.
g / A swimmer doing the breast stroke pushes backward against the water. By Newton's third law, the water pushes forward on him.
There is, however, a complication with force that we were able to avoid with momentum. If an object is moving on a line, we're guaranteed that its momentum is in one of two directions: the two directions along the line. But even an object that stays on a line may still be subject to forces that act perpendicularly to the line. For example, suppose a coin is sliding to the right across a table, h, and let's choose a positive $$x$$ axis that points to the right. The coin's motion is along a horizontal line, and its momentum is positive and decreasing. Because the momentum is decreasing, its time derivative $$dp/dt$$ is negative. This derivative equals the horizontal force of friction $$F_1$$, and its negative sign tells us that this force on the coin is to the left.
h / A coin slides across a table. Even for motion in one dimension, some of the forces may not lie along the line of the motion.
But there are also vertical forces on the coin. The Earth exerts a downward gravitational force $$F_2$$ on it, and the table makes an upward force $$F_3$$ that prevents the coin from sinking into the wood. In fact, without these vertical forces the horizontal frictional force wouldn't exist: surfaces don't exert friction against one another unless they are being pressed together.
To avoid mathematical complication, we want to postpone the full three-dimensional treatment of force and momentum until section 3.4. For now, we'll limit ourselves to examples like the coin, in which the motion is confined to a line, and any forces perpendicular to the line cancel each other out.
##### Discussion Questions
◊ Criticize the following incorrect statement:
“If an object is at rest and the total force on it is zero, it stays at rest. There can also be cases where an object is moving and keeps on moving without having any total force on it, but that can only happen when there's no friction, like in outer space.”
x (m) t (s) 10 1.84 20 2.86 30 3.80 40 4.67 50 5.53 60 6.38 70 7.23 80 8.10 90 8.96 100 9.83
Discussion question B. ”
◊ The table gives laser timing data for Ben Johnson's 100 m dash at the 1987 World Championship in Rome. (His world record was later revoked because he tested positive for steroids.) How does the total force on him change over the duration of the race?”
◊ You hit a tennis ball against a wall. Explain any and all incorrect ideas in the following description of the physics involved: “According to Newton's third law, there has to be a force opposite to your force on the ball. The opposite force is the ball's mass, which resists acceleration, and also air resistance.”
◊ Tam Anh grabs Sarah by the hand and tries to pull her. She tries to remain standing without moving. A student analyzes the situation as follows. “If Tam Anh's force on Sarah is greater than her force on him, he can get her to move. Otherwise, she'll be able to stay where she is.” What's wrong with this analysis?”
### 3.2.3 What force is not
Violin teachers have to endure their beginning students' screeching. A frown appears on the woodwind teacher's face as she watches her student take a breath with an expansion of his ribcage but none in his belly. What makes physics teachers cringe is their students' verbal statements about forces. Below I have listed several dicta about what force is not.
#### Force is not a property of one object.
A great many of students' incorrect descriptions of forces could be cured by keeping in mind that a force is an interaction of two objects, not a property of one object.
Incorrect statement: “That magnet has a lot of force.”
If the magnet is one millimeter away from a steel ball bearing, they may exert a very strong attraction on each other, but if they were a meter apart, the force would be virtually undetectable. The magnet's strength can be rated using certain electrical units $$(\text{ampere}-\text{meters}^2)$$, but not in units of force.
#### Force is not a measure of an object's motion.
If force is not a property of a single object, then it cannot be used as a measure of the object's motion.
Incorrect statement: “The freight train rumbled down the tracks with awesome force.”
Force is not a measure of motion. If the freight train collides with a stalled cement truck, then some awesome forces will occur, but if it hits a fly the force will be small.
#### Force is not energy.
Incorrect statement: “How can my chair be making an upward force on my rear end? It has no power!”
Power is a concept related to energy, e.g., a 100-watt lightbulb uses up 100 joules per second of energy. When you sit in a chair, no energy is used up, so forces can exist between you and the chair without any need for a source of power.
#### Force is not stored or used up.
Because energy can be stored and used up, people think force also can be stored or used up.
Incorrect statement: “If you don't fill up your tank with gas, you'll run out of force.”
Energy is what you'll run out of, not force.
#### Forces need not be exerted by living things or machines.
Transforming energy from one form into another usually requires some kind of living or mechanical mechanism. The concept is not applicable to forces, which are an interaction between objects, not a thing to be transferred or transformed.
Incorrect statement: “How can a wooden bench be making an upward force on my rear end? It doesn't have any springs or anything inside it.”
No springs or other internal mechanisms are required. If the bench didn't make any force on you, you would obey Newton's second law and fall through it. Evidently it does make a force on you!
#### A force is the direct cause of a change in motion
I can click a remote control to make my garage door change from being at rest to being in motion. My finger's force on the button, however, was not the force that acted on the door. When we speak of a force on an object in physics, we are talking about a force that acts directly. Similarly, when you pull a reluctant dog along by its leash, the leash and the dog are making forces on each other, not your hand and the dog. The dog is not even touching your hand.
self-check:
Which of the following things can be correctly described in terms of force?
1. A nuclear submarine is charging ahead at full steam.
2. A nuclear submarine's propellers spin in the water.
3. A nuclear submarine needs to refuel its reactor periodically.
##### Discussion Questions
◊ Criticize the following incorrect statement: “If you shove a book across a table, friction takes away more and more of its force, until finally it stops.”
◊ You hit a tennis ball against a wall. Explain any and all incorrect ideas in the following description of the physics involved: “The ball gets some force from you when you hit it, and when it hits the wall, it loses part of that force, so it doesn't bounce back as fast. The muscles in your arm are the only things that a force can come from.”
### 3.2.4 Forces between solids
Conservation laws are more fundamental than Newton's laws, and they apply where Newton's laws don't, e.g., to light and to the internal structure of atoms. However, there are certain problems that are much easier to solve using Newton's laws. As a trivial example, if you drop a rock, it could conserve momentum and energy by levitating, or by falling in the usual manner.5 With Newton's laws, however, we can reason that $$a=F/m$$, so the rock must respond to the gravitational force by accelerating.
i / Static friction: the tray doesn't slip on the waiter's fingers.
Less trivially, suppose a person is hanging onto a rope, and we want to know if she will slip. Unlike the case of the levitating rock, here the no-motion solution could be perfectly reasonable if her grip is strong enough. We know that her hand's interaction with the rope is fundamentally an electrical interaction between the atoms in the surface of her palm and the nearby atoms in the surface of the rope. For practical problem-solving, however, this is a case where we're better off forgetting the fundamental classification of interactions at the atomic level and working with a more practical, everyday classification of forces. In this practical scheme, we have three types of forces that can occur between solid objects in contact:
A normal force,Fn, is perpendicular to the surface of contact, and prevents objects from passing through each other by becoming as strong as necessary (up to the point where the objects break). “Normal” means perpendicular. Static friction,Fs, is parallel to the surface of contact, and prevents the surfaces from starting to slip by becoming as strong as necessary, up to a maximum value ofFs,max. “Static” means not moving, i.e., not slipping. Kinetic friction,Fk, is parallel to the surface of contact, and tends to slow down any slippage once it starts. “Kinetic” means moving, i.e., slipping.
self-check:
Can a frictionless surface exert a normal force? Can a frictional force exist without a normal force?
If you put a coin on this page, which is horizontal, gravity pulls down on the coin, but the atoms in the paper and the coin repel each other electrically, and the atoms are compressed until the repulsion becomes strong enough to stop the downward motion of the coin. We describe this complicated and invisible atomic process by saying that the paper makes an upward normal force on the coin, and the coin makes a downward normal force on the paper. (The two normal forces are related by Newton's third law. In fact, Newton's third law only relates forces that are of the same type.)
If you now tilt the book a little, static friction keeps the coin from slipping. The picture at the microscopic level is even more complicated than the previous description of the normal force. One model is to think of the tiny bumps and depressions in the coin as settling into the similar irregularities in the paper. This model predicts that rougher surfaces should have more friction, which is sometimes true but not always. Two very smooth, clean glass surfaces or very well finished machined metal surfaces may actually stick better than rougher surfaces would, the probable explanation being that there is some kind of chemical bonding going on, and the smoother surfaces allow more atoms to be in contact.
Finally, as you tilt the book more and more, there comes a point where static friction reaches its maximum value. The surfaces become unstuck, and the coin begins to slide over the paper. Kinetic friction slows down this slipping motion significantly. In terms of energy, kinetic friction is converting mechanical energy into heat, just like when you rub your hands together to keep warm. One model of kinetic friction is that the tiny irregularities in the two surfaces bump against each other, causing vibrations whose energy rapidly converts to heat and sound --- you can hear this sound if you rub your fingers together near your ear.
For dry surfaces, experiments show that the following equations usually work fairly well:
$\begin{equation*} F_{s,max} \approx \mu_sF_n , \end{equation*}$
and
$\begin{equation*} F_k \approx \mu_kF_n , \end{equation*}$
where $$\mu_s$$, the coefficient of static friction, and $$\mu_k$$, the coefficient of kinetic friction, are constants that depend on the properties of the two surfaces, such as what they're made of and how rough they are.
self-check:
1. When a baseball player slides in to a base, is the friction static, or kinetic?
2. A mattress stays on the roof of a slowly accelerating car. Is the friction static, or kinetic?
3. Does static friction create heat? Kinetic friction?
Example 25: Maximum acceleration of a car
$$\triangleright$$ Rubber on asphalt gives $$\mu_k\approx0.4$$ and $$\mu_s\approx 0.6$$. What is the upper limit on a car's acceleration on a flat road, assuming that the engine has plenty of power and that air friction is negligible?
$$\triangleright$$ This isn't a flying car, so we don't expect it to accelerate vertically. The vertical forces acting on the car should cancel out. The earth makes a downward gravitational force on the car whose absolute value is $$mg$$, so the road apparently makes an upward normal force of the same magnitude, $$F_n= mg$$.
Now what about the horizontal motion? As is always true, the coefficient of static friction is greater than the coefficient of kinetic friction, so the maximum acceleration is obtained with static friction, i.e., the driver should try not to burn rubber. The maximum force of static friction is $$F_{s,max}=\mu_{s} F_{n} =\mu_s mg$$. The maximum acceleration is $$a= F_s/ m=\mu_{s} g\approx6\ \text{m}/\text{s}^2$$. This is true regardless of how big the tires are, since the experimentally determined relationship $$F_{s,max}=\mu_{s} F_n$$ is independent of surface area.
j / Kinetic friction: the car skids.
self-check:
Find the direction of each of the forces in figure k.
k / 1. The cliff's normal force on the climber's feet. 2. The track's static frictional force on the wheel of the accelerating dragster. 3. The ball's normal force on the bat.
Example 26: Locomotives
Looking at a picture of a locomotive, l, we notice two obvious things that are different from an automobile. Where a car typically has two drive wheels, a locomotive normally has many --- ten in this example. (Some also have smaller, unpowered wheels in front of and behind the drive wheels, but this example doesn't.) Also, cars these days are generally built to be as light as possible for their size, whereas locomotives are very massive, and no effort seems to be made to keep their weight low. (The steam locomotive in the photo is from about 1900, but this is true even for modern diesel and electric trains.)
l / Example 26.
The reason locomotives are built to be so heavy is for traction. The upward normal force of the rails on the wheels, $$F_N$$, cancels the downward force of gravity, $$F_W$$, so ignoring plus and minus signs, these two forces are equal in absolute value, $$F_N=F_W$$. Given this amount of normal force, the maximum force of static friction is $$F_s=\mu_s F_N=\mu_s F_W$$. This static frictional force, of the rails pushing forward on the wheels, is the only force that can accelerate the train, pull it uphill, or cancel out the force of air resistance while cruising at constant speed. The coefficient of static friction for steel on steel is about 1/4, so no locomotive can pull with a force greater than about 1/4 of its own weight. If the engine is capable of supplying more than that amount of force, the result will be simply to break static friction and spin the wheels.
The reason this is all so different from the situation with a car is that a car isn't pulling something else. If you put extra weight in a car, you improve the traction, but you also increase the inertia of the car, and make it just as hard to accelerate. In a train, the inertia is almost all in the cars being pulled, not in the locomotive.
The other fact we have to explain is the large number of driving wheels. First, we have to realize that increasing the number of driving wheels neither increases nor decreases the total amount of static friction, because static friction is independent of the amount of surface area in contact. (The reason four-wheel-drive is good in a car is that if one or more of the wheels is slipping on ice or in mud, the other wheels may still have traction. This isn't typically an issue for a train, since all the wheels experience the same conditions.) The advantage of having more driving wheels on a train is that it allows us to increase the weight of the locomotive without crushing the rails, or damaging bridges.
### 3.2.5 Fluid friction
Try to drive a nail into a waterfall and you will be confronted with the main difference between solid friction and fluid friction. Fluid friction is purely kinetic; there is no static fluid friction. The nail in the waterfall may tend to get dragged along by the water flowing past it, but it does not stick in the water. The same is true for gases such as air: recall that we are using the word “fluid” to include both gases and liquids.
Unlike kinetic friction between solids, fluid friction increases rapidly with velocity. It also depends on the shape of the object, which is why a fighter jet is more streamlined than a Model T. For objects of the same shape but different sizes, fluid friction typically scales up with the cross-sectional area of the object, which is one of the main reasons that an SUV gets worse mileage on the freeway than a compact car.
m / The wheelbases of the Hummer H3 and the Toyota Prius are surprisingly similar, differing by only 10%. The main difference in shape is that the Hummer is much taller and wider. It presents a much greater cross-sectional area to the wind, and this is the main reason that it uses about 2.5 times more gas on the freeway.
##### Discussion Question
◊ Criticize the following analysis: “A book is sitting on a table. I shove it, overcoming static friction. Then it slows down until it has less force than static friction, and it stops.”
### 3.2.6 Analysis of forces
Newton's first and second laws deal with the total of all the forces exerted on a specific object, so it is very important to be able to figure out what forces there are. Once you have focused your attention on one object and listed the forces on it, it is also helpful to describe all the corresponding forces that must exist according to Newton's third law. We refer to this as “analyzing the forces” in which the object participates.
Example 27: A barge
A barge is being pulled along a canal by teams of horses on the shores. Analyze all the forces in which the barge participates.
force acting on barge force related to it by Newton’s third law ropes’ forward normal forces on barge barge’s backward normal force on ropes water’s backward fluid friction force on barge barge’s forward fluid friction force on water planet earth’s downward gravitational force on barge barge’s upward gravitational force on earth water’s upward “floating” force on barge barge’s downward “floating” force on water
Here I've used the word “floating” force as an example of a sensible invented term for a type of force not classified on the tree in the previous section. A more formal technical term would be “hydrostatic force.”
Note how the pairs of forces are all structured as “A's force on B, B's force on A”: ropes on barge and barge on ropes; water on barge and barge on water. Because all the forces in the left column are forces acting on the barge, all the forces in the right column are forces being exerted by the barge, which is why each entry in the column begins with “barge.”
Often you may be unsure whether you have missed one of the forces. Here are three strategies for checking your list:
1. See what physical result would come from the forces you've found so far. Suppose, for instance, that you'd forgotten the “floating” force on the barge in the example above. Looking at the forces you'd found, you would have found that there was a downward gravitational force on the barge which was not canceled by any upward force. The barge isn't supposed to sink, so you know you need to find a fourth, upward force.
2. Whenever one solid object touches another, there will be a normal force, and possibly also a frictional force; check for both.
3. Make a drawing of the object, and draw a dashed boundary line around it that separates it from its environment. Look for points on the boundary where other objects come in contact with your object. This strategy guarantees that you'll find every contact force that acts on the object, although it won't help you to find non-contact forces.
The following is another example in which we can profit by checking against our physical intuition for what should be happening.
Example 28: Rappelling
As shown in the figure below, Cindy is rappelling down a cliff. Her downward motion is at constant speed, and she takes little hops off of the cliff, as shown by the dashed line. Analyze the forces in which she participates at a moment when her feet are on the cliff and she is pushing off.
force acting on Cindy force related to it by Newton’s third law planet earth’s downward gravitational force on Cindy Cindy’s upward gravitational force on earth ropes upward frictional force on Cindy (her hand) Cindy’s downward frictional force on the rope cliff’s rightward normal force on Cindy Cindy’s leftward normal force on the cliff
The two vertical forces cancel, which is what they should be doing if she is to go down at a constant rate. The only horizontal force on her is the cliff's force, which is not canceled by any other force, and which therefore will produce an acceleration of Cindy to the right. This makes sense, since she is hopping off. (This solution is a little oversimplified, because the rope is slanting, so it also applies a small leftward force to Cindy. As she flies out to the right, the slant of the rope will increase, pulling her back in more strongly.)
I believe that constructing the type of table described in this section is the best method for beginning students. Most textbooks, however, prescribe a pictorial way of showing all the forces acting on an object. Such a picture is called a free-body diagram. It should not be a big problem if a future physics professor expects you to be able to draw such diagrams, because the conceptual reasoning is the same. You simply draw a picture of the object, with arrows representing the forces that are acting on it. Arrows representing contact forces are drawn from the point of contact, noncontact forces from the center of mass. Free-body diagrams do not show the equal and opposite forces exerted by the object itself.
##### Discussion Questions
◊ When you fire a gun, the exploding gases push outward in all directions, causing the bullet to accelerate down the barrel. What Newton's-third-law pairs are involved? [Hint: Remember that the gases themselves are an object.]”
◊ In the example of the barge going down the canal, I referred to a “floating” or “hydrostatic” force that keeps the boat from sinking. If you were adding a new branch on the force-classification tree to represent this force, where would it go?”
◊ A pool ball is rebounding from the side of the pool table. Analyze the forces in which the ball participates during the short time when it is in contact with the side of the table.”
◊ The earth's gravitational force on you, i.e., your weight, is always equal to $$mg$$, where $$m$$ is your mass. So why can you get a shovel to go deeper into the ground by jumping onto it? Just because you're jumping, that doesn't mean your mass or weight is any greater, does it?”
3.2.7 Transmission of forces by low-mass objects
You're walking your dog. The dog wants to go faster than you do, and the leash is taut. Does Newton's third law guarantee that your force on your end of the leash is equal and opposite to the dog's force on its end? If they're not exactly equal, is there any reason why they should be approximately equal?
If there was no leash between you, and you were in direct contact with the dog, then Newton's third law would apply, but Newton's third law cannot relate your force on the leash to the dog's force on the leash, because that would involve three separate objects. Newton's third law only says that your force on the leash is equal and opposite to the leash's force on you,
$\begin{equation*} F_{yL} = - F_{Ly} , \end{equation*}$
and that the dog's force on the leash is equal and opposite to its force on the dog
$\begin{equation*} F_{dL} = - F_{Ld} . \end{equation*}$
Still, we have a strong intuitive expectation that whatever force we make on our end of the leash is transmitted to the dog, and vice-versa. We can analyze the situation by concentrating on the forces that act on the leash, $$F_{dL}$$ and $$F_{yL}$$. According to Newton's second law, these relate to the leash's mass and acceleration:
$\begin{equation*} F_{dL} + F_{yL} = m_La_L . \end{equation*}$
The leash is far less massive then any of the other objects involved, and if $$m_L$$ is very small, then apparently the total force on the leash is also very small, $$F_{dL}$$ + $$F_{yL}\approx 0$$, and therefore
$\begin{equation*} F_{dL}\approx - F_{yL} . \end{equation*}$
Thus even though Newton's third law does not apply directly to these two forces, we can approximate the low-mass leash as if it was not intervening between you and the dog. It's at least approximately as if you and the dog were acting directly on each other, in which case Newton's third law would have applied.
In general, low-mass objects can be treated approximately as if they simply transmitted forces from one object to another. This can be true for strings, ropes, and cords, and also for rigid objects such as rods and sticks.
n / If we imagine dividing a taut rope up into small segments, then any segment has forces pulling outward on it at each end. If the rope is of negligible mass, then all the forces equal $$+T$$ or $$-T$$, where $$T$$, the tension, is a single number.
If you look at a piece of string under a magnifying glass as you pull on the ends more and more strongly, you will see the fibers straightening and becoming taut. Different parts of the string are apparently exerting forces on each other. For instance, if we think of the two halves of the string as two objects, then each half is exerting a force on the other half. If we imagine the string as consisting of many small parts, then each segment is transmitting a force to the next segment, and if the string has very little mass, then all the forces are equal in magnitude. We refer to the magnitude of the forces as the tension in the string, $$T$$.
The term “tension” refers only to internal forces within the string. If the string makes forces on objects at its ends, then those forces are typically normal or frictional forces (example 29).
Example 29: Types of force made by ropes
$$\triangleright$$ Analyze the forces in figures o/1 and o/2.
$$\triangleright$$ In all cases, a rope can only make “pulling” forces, i.e., forces that are parallel to its own length and that are toward itself, not away from itself. You can't push with a rope!
o / Example 29. The forces between the rope and other objects are normal and frictional forces.
In o/1, the rope passes through a type of hook, called a carabiner, used in rock climbing and mountaineering. Since the rope can only pull along its own length, the direction of its force on the carabiner must be down and to the right. This is perpendicular to the surface of contact, so the force is a normal force.
force acting on Cindy force related to it by Newton’s third law planet earth’s downward gravitational force on Cindy Cindy’s upward gravitational force on earth ropes upward frictional force on Cindy (her hand) Cindy’s downward frictional force on the rope cliff’s rightward normal force on Cindy Cindy’s leftward normal force on the cliff
(There are presumably other forces acting on the carabiner from other hardware above it.)
In figure o/2, the rope can only exert a net force at its end that is parallel to itself and in the pulling direction, so its force on the hand is down and to the left. This is parallel to the surface of contact, so it must be a frictional force. If the rope isn't slipping through the hand, we have static friction. Friction can't exist without normal forces. These forces are perpendicular to the surface of contact. For simplicity, we show only two pairs of these normal forces, as if the hand were a pair of pliers.
force acting on Cindy force related to it by Newton’s third law planet earth’s downward gravitational force on Cindy Cindy’s upward gravitational force on earth ropes upward frictional force on Cindy (her hand) Cindy’s downward frictional force on the rope cliff’s rightward normal force on Cindy Cindy’s leftward normal force on the cliff
(There are presumably other forces acting on the person as well, such as gravity.)
If a rope goes over a pulley or around some other object, then the tension throughout the rope is approximately equal so long as the pulley has negligible mass and there is not too much friction. A rod or stick can be treated in much the same way as a string, but it is possible to have either compression or tension.
##### Discussion Question
◊ When you step on the gas pedal, is your foot's force being transmitted in the sense of the word used in this section?”
### 3.2.8 Work
#### Energy transferred to a particle
To change the kinetic energy, $$K=(1/2)mv^2$$, of a particle moving in one dimension, we must change its velocity. That will entail a change in its momentum, $$p=mv$$, as well, and since force is the rate of transfer of momentum, we conclude that the only way to change a particle's kinetic energy is to apply a force.6 A force in the same direction as the motion speeds it up, increasing the kinetic energy, while a force in the opposite direction slows it down.
Consider an infinitesimal time interval during which the particle moves an infinitesimal distance $$d{}x$$, and its kinetic energy changes by $$d{}K$$. In one dimension, we represent the direction of the force and the direction of the motion with positive and negative signs for $$F$$ and $$d{}x$$, so the relationship among the signs can be summarized as follows: \begin{center}
F > 0 dx>0 dK>0 F < 0 dx<0 dK>0 F > 0 dx<0 dK<0 F < 0 dx>0 dK<0
\end{center} This looks exactly like the rule for determining the sign of a product, and we can easily show using the chain rule that this is indeed a multiplicative relationship:
\begin{align*} d{}K &= \frac{d{}K}{d{}v}\frac{d{}v}{d{}t}\frac{d{}t}{d{}x}d{}x \text{[chain rule]} \\ &= (mv)(a)(1/v)d{}x \\ & = m\,a\,d{}x \\ & = F\,d{}x \ \text{[Newton's second law]} \\ &\text{We can verify that force multiplied by distance has units of energy:} \\ &\text{N}\!\cdot\!\text{m} = \frac{\text{kg}\!\cdot\!\text{m}/\text{s}}{\text{s}}\times\text{m} \\ &= \text{kg}\!\cdot\!\text{m}^2/\text{s}^2 \\ &= \text{J} \end{align*}
Example 30: A TV picture tube
$$\triangleright$$ At the back of a typical TV's picture tube, electrical forces accelerate each electron to an energy of $$5\times10^{-16}\ \text{J}$$ over a distance of about 1 cm. How much force is applied to a single electron? (Assume the force is constant.) What is the corresponding acceleration?
$$\triangleright$$ Integrating
\begin{align*} d{} K &= Fd{} x , \quad \text{we find} \quad K_{f}- K_{i}= F( x_{f}- x_{i}) \\ &\text{or} \\ \Delta K &= F\Delta x . \\ &\text{The force is} F = \Delta K/\Delta x \\ &= \frac{5\times10^{-16}\ \text{J}}{ 0.01\ \text{m}} \\ & = 5\times10^{-14}\ \text{N} . \\ &\text{This may not sound like an impressive force,} \\ &\text{but it's enough to supply an electron with a spectacular acceleration.} \\ &\text{Looking up the mass of an electron on p. 943, we find} \quad a = F/ m \\ &= 5\times10^{16}\ \text{m}/\text{s}^2 . \end{align*}
Example 31: An air gun
{
p / A simplified drawing of an airgun.
$$\triangleright$$ An airgun, figure p, uses compressed air to accelerate a pellet. As the pellet moves from $$x_1$$ to $$x_2$$, the air decompresses, so the force is not constant. Using methods from chapter 5, one can show that the air's force on the pellet is given by $$F= bx^\text{-7/5}$$. A typical high-end airgun used for competitive target shooting has
\begin{align*} x_1 &= 0.046\ \text{m} , \\ x_2 &= 0.41\ \text{m} , \\ \text{and} b &= 4.4\ \text{N}\!\cdot\!\text{m}^\text{7/5} . \end{align*}
What is the kinetic energy of the pellet when it leaves the muzzle? (Assume friction is negligible.)
$$\triangleright$$ Since the force isn't constant, it would be incorrect to do $$F = \Delta K/\Delta x$$. Integrating both sides of the equation $$d{} K= Fd{} x$$, we have
\begin{align*} \Delta K &= \int_{ x_{1}}^{ x_{2}} Fd{} x \\ &= -\frac{5 b}{2}\left( x_2^\text{-2/5} - x_1^\text{-2/5}\right) \\ &= 22\ \text{J} \end{align*}
In general, when energy is transferred by a force,7 we use the term work to refer to the amount of energy transferred. This is different from the way the word is used in ordinary speech. If you stand for a long time holding a bag of cement, you get tired, and everyone will agree that you've worked hard, but you haven't changed the energy of the cement, so according to the definition of the physics term, you haven't done any work on the bag. There has been an energy transformation inside your body, of chemical energy into heat, but this just means that one part of your body did positive work (lost energy) while another part did a corresponding amount of negative work (gained energy).
#### Work in general
I derived the expression $$Fd{}x$$ for one particular type of kinetic-energy transfer, the work done in accelerating a particle, and then defined work as a more general term. Is the equation correct for other types of work as well? For example, if a force lifts a mass $$m$$ against the resistance of gravity at constant velocity, the increase in the mass's gravitational energy is $$d{}(mgy)=mgd{}y=Fd{}y$$, so again the equation works, but this still doesn't prove that the equation is always correct as a way of calculating energy transfers.
q / The black box does work by reeling in its cable.
Imagine a black box8, containing a gasoline-powered engine, which is designed to reel in a steel cable, exerting a certain force $$F$$. For simplicity, we imagine that this force is always constant, so we can talk about $$\Delta{}x$$ rather than an infinitesimal $$d{}x$$. If this black box is used to accelerate a particle (or any mass without internal structure), and no other forces act on the particle, then the original derivation applies, and the work done by the box is $$W=F\Delta{}x$$. Since $$F$$ is constant, the box will run out of gas after reeling in a certain amount of cable $$\Delta{}x$$. The chemical energy inside the box has decreased by $$-W$$, while the mass being accelerated has gained $$W$$ worth of kinetic energy.9
Now what if we use the black box to pull a plow? The energy increase in the outside world is of a different type than before; it takes the forms of (1) the gravitational energy of the dirt that has been lifted out to the sides of the furrow, (2) frictional heating of the dirt and the plowshare, and (3) the energy needed to break up the dirt clods (a form of electrical energy involving the attractions among the atoms in the clod). The box, however, only communicates with the outside world via the hole through which its cable passes. The amount of chemical energy lost by the gasoline can therefore only depend on $$F$$ and $$\Delta{}x$$, so it is the same $$-W$$ as when the box was being used to accelerate a mass, and thus by conservation of energy, the work done on the outside world is again $$W$$.
This is starting to sound like a proof that the force-times-distance method is always correct, but there was one subtle assumption involved, which was that the force was exerted at one point (the end of the cable, in the black box example). Real life often isn't like that. For example, a cyclist exerts forces on both pedals at once. Serious cyclists use toe-clips, and the conventional wisdom is that one should use equal amounts of force on the upstroke and downstroke, to make full use of both sets of muscles. This is a two-dimensional example, since the pedals go in circles. We're only discussing one-dimensional motion right now, so let's just pretend that the upstroke and downstroke are both executed in straight lines. Since the forces are in opposite directions, one is positive and one is negative. The cyclist's total force on the crank set is zero, but the work done isn't zero. We have to add the work done by each stroke, $$W=F_1\Delta{}x_1+F_2\Delta{}x_2$$. (I'm pretending that both forces are constant, so we don't have to do integrals.) Both terms are positive; one is a positive number multiplied by a positive number, while the other is a negative times a negative.
This might not seem like a big deal --- just remember not to use the total force --- but there are many situations where the total force is all we can measure. The ultimate example is heat conduction. Heat conduction is not supposed to be counted as a form of work, since it occurs without a force. But at the atomic level, there are forces, and work is done by one atom on another. When you hold a hot potato in your hand, the transfer of heat energy through your skin takes place with a total force that's extremely close to zero. At the atomic level, atoms in your skin are interacting electrically with atoms in the potato, but the attractions and repulsions add up to zero total force. It's just like the cyclist's feet acting on the pedals, but with zillions of forces involved instead of two. There is no practical way to measure all the individual forces, and therefore we can't calculate the total energy transferred.
To summarize, $$\sum{F_jd{}x_j}$$ is a correct way of calculating work, where $$F_j$$ is the individual force acting on particle $$j$$, which moves a distance $$d{}x_j$$. However, this is only useful if you can identify all the individual forces and determine the distance moved at each point of contact. For convenience, I'll refer to this as the work theorem. (It doesn't have a standard name.)
There is, however, something useful we can do with the total force. We can use it to calculate the part of the work done on an object that consists of a change in the kinetic energy it has due to the motion of its center of mass. The proof is essentially the same as the proof on p. 161, except that now we don't assume the force is acting on a single particle, so we have to be a little more delicate. Let the object consist of $$n$$ particles. Its total kinetic energy is $$K=\sum_{j=1}^n{(1/2)m_jv_j^2}$$, but this is what we've already realized can't be calculated using the total force. The kinetic energy it has due to motion of its center of mass is
\begin{align*} K_{cm} &= \frac{1}{2}m_{total}v_{cm}^2 . \end{align*}
r / The wheel spinning in the air has $$K_{cm}=0$$. The space shuttle has all its kinetic energy in the form of center of mass motion, $$K=K_{cm}$$. The rolling ball has some, but not all, of its energy in the form of center of mass motion, $$K_{cm}\lt K$$. (Space Shuttle photo by NASA)
Figure r shows some examples of the distinction between $$K_{cm}$$ and $$K$$. Differentiating $$K_{cm}$$, we have
\begin{align*} d{}K_{cm} &= m_{total}v_{cm}d{}v_{cm} \\ &= m_{total}v_{cm} \frac{d{}v_{cm}}{d{}t}\frac{d{}t}{d{}x_{cm}}d{}x_{cm} \text{[chain rule]} \\ &= m_{total}\frac{d{}v_{cm}}{d{}t}d{}x_{cm} \text{[d{}t/d{}x_{cm}=1/v_{cm}]} \\ &= \frac{d{}p_{total}}{d{}t}d{}x_{cm} \text{[p_{total}=m_{total}v_{cm}]} \\ &= F_{total}d{}x_{cm} \end{align*}
I'll call this the kinetic energy theorem --- like the work theorem, it has no standard name.
Example 32: An ice skater pushing off from a wall
The kinetic energy theorem tells us how to calculate the skater's kinetic energy if we know the amount of force and the distance her center of mass travels while she is pushing off.
The work theorem tells us that the wall does no work on the skater, since the point of contact isn't moving. This makes sense, because the wall does not have any source of energy.
Example 33: Absorbing an impact without recoiling?
$$\triangleright$$ Is it possible to absorb an impact without recoiling? For instance, if a ping-pong ball hits a brick wall, does the wall “give” at all?
$$\triangleright$$ There will always be a recoil. In the example proposed, the wall will surely have some energy transferred to it in the form of heat and vibration. The work theorem tells us that we can only have an energy transfer if the distance traveled by the point of contact is nonzero.
Example 34: Dragging a refrigerator at constant velocity
The fridge's momentum is constant, so there is no net momentum transfer, and the total force on it must be zero: your force is canceling the floor's kinetic frictional force. The kinetic energy theorem is therefore true but useless. It tells us that there is zero total force on the refrigerator, and that the refrigerator's kinetic energy doesn't change.
The work theorem tells us that the work you do equals your hand's force on the refrigerator multiplied by the distance traveled. Since we know the floor has no source of energy, the only way for the floor and refrigerator to gain energy is from the work you do. We can thus calculate the total heat dissipated by friction in the refrigerator and the floor.
Note that there is no way to find how much of the heat is dissipated in the floor and how much in the refrigerator.
Example 35: Accelerating a cart
If you push on a cart and accelerate it, there are two forces acting on the cart: your hand's force, and the static frictional force of the ground pushing on the wheels in the opposite direction.
Applying the work theorem to your force tells us how to calculate the work you do.
Applying the work theorem to the floor's force tells us that the floor does no work on the cart. There is no motion at the point of contact, because the atoms in the floor are not moving. (The atoms in the surface of the wheel are also momentarily at rest when they touch the floor.) This makes sense, because the floor does not have any source of energy.
The kinetic energy theorem refers to the total force, and because the floor's backward force cancels part of your force, the total force is less than your force. This tells us that only part of your work goes into the kinetic energy associated with the forward motion of the cart's center of mass. The rest goes into rotation of the wheels.
##### Discussion Questions
◊ Criticize the following incorrect statement: “A force doesn't do any work unless it's causing the object to move.”
◊ To stop your car, you must first have time to react, and then it takes some time for the car to slow down. Both of these times contribute to the distance you will travel before you can stop. The figure shows how the average stopping distance increases with speed. Because the stopping distance increases more and more rapidly as you go faster, the rule of one car length per 10 m.p.h. of speed is not conservative enough at high speeds. In terms of work and kinetic energy, what is the reason for the more rapid increase at high speeds?
s / Discussion question B.
## 3.2.9 Simple Machines
Conservation of energy provided the necessary tools for analyzing some mechanical systems, such as the seesaw on page 85 and the pulley arrangements of the homework problems on page 120, but we could only analyze those machines by computing the total energy of the system. That approach wouldn't work for systems like the biceps/forearm machine on page 85, or the one in figure t, where the energy content of the person's body is impossible to compute directly. Even though the seesaw and the biceps/forearm system were clearly just two different forms of the lever, we had no way to treat them both on the same footing. We can now successfully attack such problems using the work and kinetic energy theorems.
Example 36: Constant tension around a pulley
t / The force is transmitted to the block.
$$\triangleright$$ In figure t, what is the relationship between the force applied by the person's hand and the force exerted on the block?
$$\triangleright$$ If we assume the rope and the pulley are ideal, i.e., frictionless and massless, then there is no way for them to absorb or release energy, so the work done by the hand must be the same as the work done on the block. Since the hand and the block move the same distance, the work theorem tells us the two forces are the same.
Similar arguments provide an alternative justification for the statement made in section 3.2.7 that show that an idealized rope exerts the same force, the tension, anywhere it's attached to something, and the same amount of force is also exerted by each segment of the rope on the neighboring segments. Going around an ideal pulley also has no effect on the tension.
This is an example of a simple machine, which is any mechanical system that manipulates forces to do work. This particular machine reverses the direction of the motion, but doesn't change the force or the speed of motion.
Example 38: Inclined plane and wedge
v / An inclined plane.
In figure v, the force applied by the hand is equal to the one applied to the load, but there is a mechanical advantage compared to the force that would have been required to lift the load straight up. The distance traveled up the inclined plane is greater by a factor of 1/sin $$\theta$$, so by the work theorem, the force is smaller by a factor of sin $$\theta$$, and we have M.A.=1/sin $$\theta$$. The wedge, w, is similar.
w / A wedge.
Example 39: Archimedes' screw
In one revolution, the crank travels a distance $$2\pi{} b$$, and the water rises by a height $$h$$. The mechanical advantage is $$2\pi{} b/ h$$.
x / Archimedes' screw
### 3.2.10 Force related to interaction energy
In section 2.3, we saw that there were two equivalent ways of looking at gravity, the gravitational field and the gravitational energy. They were related by the equation $$d{}U=mgd{}r$$, so if we knew the field, we could find the energy by integration, $$U=\int{mgd{}r}$$, and if we knew the energy, we could find the field by differentiation, $$g=(1/m)d{}U/d{}r$$.
The same approach can be applied to other interactions, for example a mass on a spring. The main difference is that only in gravitational interactions does the strength of the interaction depend on the mass of the object, so in general, it doesn't make sense to separate out the factor of $$m$$ as in the equation $$d{}U=mgd{}r$$. Since $$F=mg$$ is the gravitational force, we can rewrite the equation in the more suggestive form $$d{}U=Fd{}r$$. This form no longer refers to gravity specifically, and can be applied much more generally. The only remaining detail is that I've been fairly cavalier about positive and negative signs up until now. That wasn't such a big problem for gravitational interactions, since gravity is always attractive, but it requires more careful treatment for nongravitational forces, where we don't necessarily know the direction of the force in advance, and we need to use positive and negative signs carefully for the direction of the force.
In general, suppose that forces are acting on a particle --- we can think of them as coming from other objects that are “off stage” --- and that the interaction between the particle and the off-stage objects can be characterized by an interaction energy, $$U$$, which depends only on the particle's position, $$x$$. Using the kinetic energy theorem, we have $$d{}K=Fd{}x$$. (It's not necessary to write $$K_{cm}$$, since a particle can't have any other kind of kinetic energy.) Conservation of energy tells us $$d{}K+d{}U=0$$, so the relationship between force and interaction energy is $$d{}U=-Fd{}x$$, or
$\begin{equation*} F = -\frac{d{}U}{d{}x} \text{[relationship between force and interaction energy]} . \end{equation*}$
Example 40: Force exerted by a spring
$$\triangleright$$ A mass is attached to the end of a spring, and the energy of the spring is $$U=(1/2) kx^2$$, where $$x$$ is the position of the mass, and $$x=0$$ is defined to be the equilibrium position. What is the force the spring exerts on the mass? Interpret the sign of the result.
$$\triangleright$$ Differentiating, we find
\begin{align*} F &= -\frac{d{} U}{d{} x} \\ &= - kx . \end{align*}
If $$x$$ is positive, then the force is negative, i.e., it acts so as to bring the mass back to equilibrium, and similarly for $$x\lt0$$ we have $$F>0$$.
Most books do the $$F=- kx$$ form before the $$U=(1/2) kx^2$$ form, and call it Hooke's law. Neither form is really more fundamental than the other --- we can always get from one to the other by integrating or differentiating.
Example 41: Newton's law of gravity
$$\triangleright$$ Given the equation $$U=- Gm_1 m_{2}/ r$$ for the energy of gravitational interactions, find the corresponding equation for the gravitational force on mass $$m_2$$. Interpret the positive and negative signs.
$$\triangleright$$ We have to be a little careful here, because we've been taking $$r$$ to be positive by definition, whereas the position, $$x$$, of mass $$m_2$$ could be positive or negative, depending on which side of $$m_1$$ it's on.
For positive $$x$$, we have $$r= x$$, and differentiation gives
\begin{align*} F &= -\frac{d{} U}{d{} x} \\ &= - Gm_1 m_{2}/ x^2 . \end{align*}
As in the preceding example, we have $$F\lt0$$ when $$x$$ is positive, because the object is being attracted back toward $$x=0$$.
When $$x$$ is negative, the relationship between $$r$$ and $$x$$ becomes $$r=- x$$, and the result for the force is the same as before, but with a minus sign. We can combine the two equations by writing
$\begin{equation*} | F| = Gm_1 m_{2}/ r^2 , \end{equation*}$
and this is the form traditionally known as Newton's law of gravity. As in the preceding example, the $$U$$ and $$F$$ equations contain equivalent information, and neither is more fundamental than the other.
Example 42: Equilibrium
I previously described the condition for equilibrium as a local maximum or minimum of $$U$$. A differentiable function has a zero derivative at its extrema, and we can now relate this directly to force: zero force acts on an object when it is at equilibrium.
### Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
| 2019-01-22T05:05:52 |
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|
https://leagueoflegends.fandom.com/wiki/Champions_(Teamfight_Tactics)
|
4,611 Pages
Champions are units in the Teamfight Tactics game mode that fight in arenas to protect the Little Legend. Players can buy, sell, reposition, and equip items on champions.
## Stats and Mechanics
• Health
• Champions are removed from combat when their health reaches 0. With exception:
• Slain champions will respawn next round.
• Health is shown above a unit's heads as a green bar that is separated once for every 300 health the unit has.
• Basic attacks - Each champion has a basic attack. Basic attacks deal physical damage.
• Attack damage is the amount of damage a champion will do with each basic attack.
• Attack speed is measured in attacks per second. All attack speed increases are percentage-based, and affect each champion based on their base attack speed. Attack speed slows are based on total attack speed. Attack speed is capped at 5.0 attacks per second.
• Attack range is measured in hexes.
• 1 Attack range means a champion can only attack enemies in adjacent hexes.
• Armor reduces the damage taken from physical damage. Armor works in exactly the same as it works in the main game, using this formula:
$\pagecolor{Black}\color{White}{\rm Damage\ multiplier}= {100 \over 100+{\it Armor}}$
• Basic attacks have a chance to critically strike to deal 50% bonus damage, determined by critical strike chance. Every champion starts with 25% critical strike chance. The bonus damage is further increased by critical strike damage.
• Special Ability - Each champion has one ability. Active abilities require mana to cast, and automatically cast when a champion reaches maximum mana. Special abilities deal magic damage, with the exceptions of attack-modifiers.
• Mana is generated by basic attacking and taking damage. Basic attacks generate mana on-attack, even if the triggering attack misses or is parried. Both abilities and basic attacks cause the damaged champion to generate mana.
• Ability power increases the power of a champion's Special Ability by a percentage. Ability power affects magic damage, true damage, shielding and healing.
• Magic resistance reduces the damage taken from magic damage. Magic Resistance works in exactly the same as it works in the main game, using this formula:
$\pagecolor{Black}\color{White}{\rm Damage\ multiplier}= {100 \over 100+{\it MR}}$
• Star-level
• All champions starting with Star-level are 1-star.
• Three 1-star champions can be combined to create a stronger 2-star champion. Three 2-star champions can be combined to create an even stronger 3-star champion.
• 2-star and 3-star champion have respectively 180% and 324% of the maximum health and attack damage of the 1-star version of the champion. The ability also becomes stronger by an amount specific to the champion.
• With , a champion can be reduced to a 0-Star unit with 70% of maximum health and attack damage.
• is the only champion interact with Star-level, which deals massive damage to champions with a lower Star level by his Special Ability.
• The effect of , , , increases according to the Star-level of the wearer.
• Other mechanics:
• Banish temporarily removes the target from the battlefield. The target is unable to do anything, and cannot be attacked by enemy team during this duration.
• .
• is a damage over time that also reduces healing.
• Disarm prevents the target using basic attacks.
• .
• causes incoming attacks to miss (deal no damage and do not apply spell or item effects).
• True damage is a rarely-used damage type that bypasses resistances.
• Stealth temporarily makes the target invisible and untargetable.
• prevents the target from gaining mana.
• .
• prevents the target from moving, attacking and activating their Special Ability.
• prevents the target from moving.
• moves in a specified direction or to a specific point. For the duration the target is unable to move, declare attacks or cast their Special Ability.
• units able to the items equipped.
### Calculations
Critical strike damage
• Formula to calculate the value of critical strike damage:
• Critical strike damage = 150% + + ( × 125%).
• Example: With 1 and = 150% + + (1 × ) = 425% critical strike damage.
Ability Power
• Formula to calculate the amount of :
• Ability Power = (AP from items + + ) × (1 + ( × 0.75)).
• Example: With 2 and = ( + ) × (1 + (2 × 0.75)) = 300 AP = 300% increased ability effects.
## Resources
The two main resources of any champion is health and mana.
### Health
• A champion begins combat with full health. If health is reduced to 0, the champion is removed from the current round. However, if equipped with , the champion will be revived after its first death.
• A champion can be healed by items like or , or by ally abilities, such as .
• The maximum health of a champion can be increased through equipped items built from . Currently, the only champion that can increase maximum health is .
• Many origins, classes and champions interact with health.
• instantly kill enemies with his Special Ability if the target is below 35% health.
• shield scales with maximum health.
• and gain maximum health by meeting certain conditions.
• restores health every period of time.
• grant on-hit healing.
• heal for 25% of their maximum health when a Light unit dies.
• reduces an enemy champion's current health at the start of each fight.
• instantly kill enemies they damage who are below 25% health.
• grant their summoned units bonus health.
• gains damage immunity for a few seconds when they are reduced below 50% health.
### Mana
• Most champions use mana as resource for their Special Ability. Mana is generated by basic attacking and when taking damage.
• Basic attacks can generate up to 12 mana per attack.[1]
• 1-Star units generate 8 mana per attack.
• 2-Star units generate 10 mana per attack.
• 3-Star units generate 12 mana per attack.
• and generate twice as much mana per basic attack, and double the cap to 20 per attack.
• Mana from taking damage is pre-mitigated damage, capped at 50 per damage source.[2]
• Champions with mana automatically use their Special Abilities when their mana bar is full.
• After casting their Special Ability, champions can't accumulate mana for the second thereafter. Some champions are mana-locked for longer (e.g. and ).
• Five out of six champions are locked from mana gain permanently after using abilities. This is because their abilities lasts longer than a round, making mana on them useless once transformed. However, Shapeshifters using revive in their original form. They need to refill their mana after revival.
• Some champions do not utilize mana, or use it in a different way:
• Set 1:
• charges his axes with mana and can keep using them even without it.
• , , and have no mana.
• Set 2:
• , , and have no mana.
• Mana generation can be prevented with the effect.
• Some champions can self- themselves, like .
• There is a stat called Starting Mana. Champions using mana have that amount of mana at the start of the game. Higher starting mana allows champion to cast their first special ability sooner, but does not effect on later usages.
• Some champions interact with mana in even more ways. This is partially why monsters have mana without any Special Abilities.
• basic attacks consume enemy mana and convert it into a shield.
• restores mana with his Special Ability.
• restores mana when at least one enemy killed with her Special Ability.
• has a chance to grant mana to himself and allies.
• units gain the chance to burn enemy mana and fill up some of their own.
• units restore mana every period of time.
• units apply Neurotoxin when they deal damage, increasing the mana cost of the target's spell by 50%.
### Special Abilities
• On patch V9.15, it was indicated that most ability cast are 0.5 seconds. [3]
• Almost all Special Abilities deal magic damage, with some exceptions:
• Set 1:
• - it deals true damage.
• deals both magic damage and true damage.
• Set 2:
• , , , and , which deal physical damage.
• and - it deals true damage.
• A Special Ability's effect can be increased using . There are some exception champions does not have any benefit from [4]:
• Set 1: , , , , , , , and .
• Set 2: , , , , , , , , .
## Trivia
• There are Teamfight Tactics champions that are manaless in League of Legends, However, they do use mana in Teamfight Tactics. Those champions are: , , , , , , , , , , , , and .
• Conversely, there are Teamfight Tactics champions that use mana in League of Legends that do not in Teamfight Tactics - these are: , , , , , and
• The icon takes after the logo for Riot Games Inc.
• Oftentimes, champions in Teamfight Tactics will use custom skins on champions to make them better fit their traits:
• In Set 1, most champions use their default skin. Some champions use one of their skins, and cannot be seen without that skin. This is presumably in order for champions to better fit their given Origins.
• appears as .
• appears as .
• appears as .
• appears as in his normal form and in his transformation.
• appears as , however, her shop card uses splash art instead.
• appears as .
• appears as .
• appears as .
• appears as .
• Unlike in Set 1, the champion pool in Set 2 has more champions in one of their custom skins than in their default skin, and cannot be seen without that skin. This is presumably in order for champions to better fit their given Elements.
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appear as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
• appears as .
## References
v · e
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-01-21T02:38:45 |
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|
http://www-cdf.fnal.gov/physics/new/top/2007/singletop/ME1_5fb/index.html
|
## Evidence for Single Top Quark Production in L=1.51 fb-1of CDF Run II Data using the Matrix Element Technique
Florencia Canelli (FNAL), Peter Dong (UCLA), Bernd Stelzer (UCLA), Rainer Wallny (UCLA)
$&sigma$single top = 3.0+1.2-1.1pb, (Mtop = 175 GeV/c2)
Abstract Event selection Analysis Method Validation of the method Systematic uncertainties Results Single Top Signal Features Interesting Cross Checks References Summer 2007 Conference Note
To view GIF format with full resolution, right-click and select "View Image."
## Abstract
We present a search for electroweak single top quark production using 1.51 fb-1 of CDF II data collected between February 2002 and January 2007 at the Tevatron in proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. The analysis employs a matrix-element technique which calculates event probability densities for signal and background hypotheses. We combine the probabilities to form a discriminant variable which is evaluated for signal and background Monte Carlo events. The resulting template distributions are fit to the data using a binned likelihood approach. We search for a combined single top s- and t-channel signal and measure a cross section of 3.0+1.2-1.1pb, assuming a top quark mass of 175 GeV/c2. The probability that the observed excess originated from a background fluctuation (p-value) is 0.09% and the expected (median) p-value in pseudo-experiments is 0.13%. We use the cross section measurement to directly determine the CKM matrix element Vtb and measure $|V$tb| = 1.02 ± 0.18experiment ± 0.07theory.
## Event Selection
This analysis uses events from leptonic decay of the W boson. We require a single, well isolated high-transverse-energy lepton, large missing transverse energy (from the neutrino), and exactly two high-transverse-energy jets. Of these jets, we require at least one to be identified as originating from a b-quark by secondary vertex tagging. The secondary vertex tag identifies tracks associated with the jet originating from a vertex displaced from the primary vertex. We further require the missing transverse energy and the jets not to be collinear for low values of missing transverse energy. This requirement removes a large fraction of the non-W background while retaining most of the signal.
Our major backgrounds come from W + heavy flavor jets, Wbb-bar, Wcc-bar, and Wc+jet; mistags which are W + light quark/gluon events that are mistakenly tagged as b-jets due to detector resolution effects; Non-W, which are mostly multijet events in which a jet is mistakenly identified as a lepton and jets are mismeasured, providing a false missing transverse energy signature; and top pair production events in which one lepton or two jets are lost due to detector acceptance.
Predicted event yield with 1.51 fb-1
s-channel 23.9 ± 6.1
t-channel 37.0 ± 5.4
Single top 60.9 ± 11.5
W+bottom 319.6 ± 112.3
W+charm 324.2 ± 115.8
Mistags 214.6 ± 27.3
tt-bar 85.3 ± 17.8
Diboson/Z+jets 54.5 ± 6.0
Non-W 44.5 ± 17.8
Total background 1042.8 ± 218.2
Total prediction 1103.7 ± 230.9
Observed 1078
Jet multiplicity distribution for signal and background processes. We compare the predicted number of events in each W+jet bin to the number of events observed in data. Uncertainty on the data are statistical; the hatch marks represent systematic errors in the background estimate.
## Analysis Method
This analysis is based on a Matrix-Element method in order to maximize the use of information in the events [2,3]. We calculate event probability densities under the signal and background hypotheses as follows. Given a set of measured variables of each event (the 4-vectors of the lepton and the two jets), we calculate the probability densities that these variables could result from a given underlying interaction (signal and background). The probability is constructed by integrating over the parton-level differential cross-section, which includes the matrix element for the process, the parton distribution functions, and the detector resolutions. This analysis calculates probabilities for four different underlying processes: s-channel, t-channel, Wbb-bar, Wcc-bar, and Wc+jet.
Transfer functions are used to include detector effects. Lepton quantities and jet angles are considered to be well measured. However, jet energies are not, and their resolution is parameterized from Monte Carlo simulation to create a jet resolution transfer function. We integrate over the quark energies and over the z-momentum of the neutrino to create a final probability density.
We use the probabilities to construct a discriminant variable for each event. The two single-top channels are combined to form a single signal probability. We also introduce extra non-kinematic information by using the output (b) of a neural network b-tagger which assigns a probability (0 < b < 1) for each b-tagged jet to originate from a b quark. The event probability discriminant variable (EPD) is then constructed as:
To quantify the single top content in the data, we perform a binned maximum likelihood fit. We fit a linear combination of signal and background shapes of the event probability discriminant to the data. The background normalization are Gaussian constraint in the fit. The fit determines the most probable value of the single-top cross section. All sources of systematic uncertainty are included as nuisance parameters in the likelihood function. Sources of systematic uncertainties can affect the normalization and shape for a given process. Correlations between both are taken into account through a common nuisance parameter (&deltai).
Here &betaj; is the template fit parameter for each process, indexed by j; &deltai; are the nuisance parameters for each systematic effect, with (relative) normalization uncertainty &epsilonji; and (relative) shape uncertainty &kappajik;, indexed by ji;k indexes the bins of the event probability discriminant. H(&deltai) denotes the Heavyside function to treat asymmetric uncertainties properly.
## Validation of the Method
Several tests have been performed for this analysis. We compare the distribution of many kinematic variables predicted by Monte Carlo simulation for signal and background to the data. In particular, we compare the distributions of the input variables to ensure the data matches the Monte Carlo prediction. We evaluate the event probability discriminant in the untagged W + 2 jets sample, a high-statistics control sample with very little single-top content (<0.5%). We also evaluate the event probability discriminant in the tagged dipleton + 2 jets sample (using only the most energetic lepton) and in tagged lepton + 4 jets sample (using only the two most energetic jets as input to the discriminant), which should agree well with tt-bar Monte Carlo. In all control samples, the data agrees well with the Monte Carlo prediction.
Evaluation of the event probability discriminant in the high statistics taggable but untagged W + 2 jets control sample.
The discriminants evaluated in the tagged dilepton + 2jets sample (0.95 fb-1 sample) and the tagged lepton + 4jets sample (1.51 fb-1), both of which are mostly composed of tt-bar events.
The input variables to the signal and background event probability calculations in the b-tagged W + 2 jet data sample.
## Systematic Uncertainties
Each source of systematic uncertainty can posses a normalization uncertainty and a shape uncertainty. The normalization uncertainty includes changes to the event yield due to the systematic effect, and the shape uncertainty includes changes to the template histograms. Both of these effects are included in the likelihood function as shown above.
Listed below are systematic uncertainties estimated from various Monte Carlo samples.
• The jet energy scale systematic is obtained by changing the jet energy scale by 1 standard deviation (SD) and recalculating the event yield and the discriminant template histograms. This affects both normalization and shape.
• We increase or decrease the amount of initial state radiation in the Monte Carlo to assign a systematic from this effect.
• We increase or decrease the amount of final state radiation in the Monte Carlo to assign a systematic from this effect.
• We vary the eigenvectors in the CTEQ parton distribution function tables to determine the uncertainty from this effect. We also include the effect of using different versions of CTEQ and of using MRST with different values of &LambdaQCD.
• We include a systematic error to account for the modeling of the single top sample (MadEvent).
• We include an uncertainty on event detection efficiency due to the scale factors that we apply to our Monte Carlo samples (mainly b-tagging and lepton ID scale factors)
• We include a 6% uncertainty on our measured luminosity.
• We include a systematic which accounts for systematic variation of the neural network b tagger output.
• We use an alternative model for our mistag model and use the difference to the default model as a systematic uncertainty.
• We use an alternate model to model our non-W background. We also assign a systematic effect to the flavor composition of the background, which is necessary to include for the neural-net b tagger to run.
• We vary the factorization and renormalization scele (Q2) in the Monte Carlo samples that have been created with the ALPGEN Monte Carlo program.
Systematic uncertainty Rate Shape Jet energy scale -0.3% / -0.2% X Initial state radiation +3.2% / - 1.0% X Final state radiation +5.3% / -1.5% X Parton distribution functions +1.1% / -1.4% X Monte Carlo generator ±1.6% Event detection efficiency ±5.0% Luminosity ±6.0% Neural-net b tagger N/A X Mistag model N/A X Non-W model N/A X Q2 scale in Alpgen MC N/A X W+bottom normalization 36% W+charm normalization 36% Mistag normalization 15% tt-bar normalization 23%
Systematic uncertainties. The numbers here are given for the combined single-top channel. Jet energy scale and neural network b tagger systematics are applied to all processes (not shown here).
## Results
1. Cross Section Measurement
The result of the binned maximum likelihood fit is shown below. All sources of systematic uncertainties (normalization and shape) are included in this fit.
Event probability discriminant distribution for signal and background processes. All templates are normalized to the best fit value of the maximum likelihood fit result. The inset shows the most sensitive bins of the analysis (EPD>0.7).
Results from full dataset (1078 candidate events):
### $&sigma$single top =3.0+1.2-1.1pb
2. Vtb Measurement:
We use the measured single top cross section to directly measure the CKM matrix element $|V$tb|$that describes the strength of the$Wtb vertex. $|V$tb|$is directly proportional to \left(&sigma$single top)2 so we can extract Vtb from the posterior probability density. This measurement assumes |Vtd|2 +|Vts|2 ≪ |Vtb|2. The theory uncertainties arrise from the cross-section dependence on the top quark mass, the Factorization and Renormalization scales, parton distribution functions and alpha_s [1].
### $|V$tb| = 1.02 ± 0.18experiment ± 0.07theory
3. Hypothesis Test:
We have calculate the signal significance of this result using a standard likelihood ratio technique [4]. In this approach, pseudo-experiments are generated from background only events. The likelihood ratio is used as the test statistic. We then calculate the p-value which is the probability of the background only hypothesis (b) to fluctuate to the observed result in data. We estimate the expected p-value, by taking the median of the test hypothesis (signal + background) distribution as the 'observed' value (dashed red line).
Expected p-value: 0.13% (3.02σ)
Observed p-value: 0.09% (3.1σ)
## Single Top Signal Features
We enrich the sample with signal events by making increasing cuts on our event probability discriminant (EPD) and look for characteristic changes in these sensitive variables. Although the uncertainties are large, there is a good agreement between data and the Monte Carlo simulation including single top.
Increasing cuts on the EPD for the product of the lepton charge and the pseudo-rapidity of the untagged jet, a variable known to be sensitive to t-channel (left) and the invariant mass of the W and the b-tagged jet, a quantity which is close to the top quark mass. The top row includes the last three bins of the EPD discriminant (EPD>0.9) and the bottom row includes the last bin of the EPD discriminant (EPD>0.966).
## Interesting Cross Check Analyses
Separate Search for t-channel and s-channel Single Top:
We also let the s-channel and t-channel templates float independently in the likelihood fit to measure the most likely s-channel and t-channel single top content in data.
We obtain a s-channel and t-channel single top cross-section very consistent with the Standard Model prediction.
### $&sigma$t-channel =1.9+1.0-0.9pb
Unconstrained Likelihood Fit:
As a cross-check, we evaluate how sensitive the outcome of the measurement is on the Gaussian constraints of the backgrounds. For this purpose, we perform a five parameter likelihood fit with all Gaussian constraints removed. The result is shown below. The measurement is less precise (uncertainty is increased by about 20%) but the central value remains almost unchanged.
## Conclusions
We have updated our search for single top using a Matrix-Element based analysis and applied it to 1.51 fb-1 of data taken by the CDF experiment. We include rate and shape systematic uncertainties in our analysis method. We measure a single top cross-section of $&sigma$single top =3.0+1.2-1.1pb. We use a likelihood ratio method to calculate the signal significance. The observed p-value in 1.51 fb-1 of CDF data is 0.09% (3.1 SD). The expected (median) p-value in pseudo-experiments is 0.13% (3.0 SD). The cross section measurement is used to directly determine the CKM matrix element Vtb and we measure $|V$tb| = 1.02±0.18experiment ± 0.07theory.
## Analysis Changes Since DPF2006
• New Alpgen V2 W + Jets Monte Carlo samples with minimum bias overlay
• Improved Neural Network b-tagger (jet-flavor separator)
• Updated background estimate with W+heavy flavor calibration using tagged W + 1 jet events (KHF=1.4+-0.4)
• Separate treatment of single and double b-tagged events
• More refined Transfer Functions (jet pseudo-rapidity dependent)
• CDF Top group wide transition to select events based on hadron level jets (include jet correction to account for calorimeter response)
## References
1. Understanding single-top-quark production, Z. Sullivan, Phys. Rev. D 70, 114012 (2004)
2. B. Stelzer, PhD Thesis, University of Toronto, FERMILAB-THESIS-2005-79
3. D&empty Collaboration, V.M. Abazov, et, al., Nature 429 (2004); D&empty Collaboration, V.M. Abazov, et. al., Phys. Lett. B 617 (2005); F. Canelli, PhD thesis, University of Rochester (2003).
4. T. Junk, Nucl. Instrum. Meth. A 434, 435 (1999), L. Read, J.Phys.G 28, 2693 (2002), Website
| 2013-05-26T00:34:19 |
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|
https://zbmath.org/authors/?q=ai%3Aspencer.thomas-c
|
## Spencer, Thomas C.
Compute Distance To:
Author ID: spencer.thomas-c Published as: Spencer, Thomas; Spencer, T.; Spencer, Thomas C. more...less Homepage: https://www.ias.edu/scholars/spencer External Links: MGP · Wikidata · IdRef · theses.fr
Documents Indexed: 43 Publications since 1975 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 24 Co-Authors with 28 Joint Publications 912 Co-Co-Authors
all top 5
### Co-Authors
14 single-authored 9 Fröhlich, Jürg Martin 3 Disertori, Margherita 3 Jaffe, Arthur Michael 2 Brydges, David C. 2 Conlon, Joseph G. 2 Dodson, Benjamin G. 2 Glimm, James G. 2 Soffer, Avraham 2 Wayne, Clarence Eugene 2 Zirnbauer, Martin R. 1 Albanese, Claudio 1 Chayes, Jennifer Tour 1 Chayes, Lincoln 1 Chulaevsky, Victor 1 Constantinescu, Florin 1 Imbrie, John Z. 1 Martinelli, Fabio 1 Naddaf, Ali 1 Pfister, Charles-Edouard 1 Pinson, Haru T. 1 Scoppola, Elisabetta 1 Shamis, Mira 1 Sheffield, Scott 1 Simon, Barry 1 Sorets, Eugene 1 Wittwer, Peter
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### Serials
18 Communications in Mathematical Physics 5 Journal of Statistical Physics 2 Journal of Mathematical Physics 1 International Journal of Modern Physics B 1 Physica A 1 Transactions of the American Mathematical Society 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the American Mathematical Society 1 IAS/Park City Mathematics Series
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### Fields
28 Statistical mechanics, structure of matter (82-XX) 19 Probability theory and stochastic processes (60-XX) 14 Quantum theory (81-XX) 10 Partial differential equations (35-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 4 Dynamical systems and ergodic theory (37-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Difference and functional equations (39-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX)
### Citations contained in zbMATH Open
35 Publications have been cited 1,200 times in 905 Documents Cited by Year
Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Zbl 0519.60066
Fröhlich, Jürg; Spencer, Thomas
1983
Constructive proof of localization in the Anderson tight binding model. Zbl 0573.60096
Fröhlich, J.; Martinelli, F.; Scoppola, E.; Spencer, T.
1985
Diffusion of directed polymers in a random environment. Zbl 1084.82595
Imbrie, J. Z.; Spencer, T.
1988
Localization for a class of one dimensional quasi-periodic Schrödinger operators. Zbl 0722.34070
Fröhlich, J.; Spencer, T.; Wittwer, P.
1990
Self-avoiding walk in 5 or more dimensions. Zbl 0575.60099
Brydges, David; Spencer, Thomas
1985
On homogenization and scaling limit of some gradient perturbations of a massless free field. Zbl 0871.35010
1997
The phase transition in the one-dimensional Ising model with $$1/r^2$$ interaction energy. Zbl 1110.82302
Fröhlich, Jürg; Spencer, Thomas
1982
Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials. Zbl 0745.34046
Sorets, Eugene; Spencer, Thomas
1991
Phase transitions for $$\phi_2^4$$ quantum fields. Zbl 0956.82501
Glimm, James; Jaffe, Arthur; Spencer, Thomas
1975
Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105
Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene
1986
Trace class perturbations and the absence of absolutely continuous spectra. Zbl 0684.47010
Simon, Barry; Spencer, Thomas
1989
Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model. Zbl 1203.82018
Disertori, M.; Spencer, T.; Zirnbauer, M. R.
2010
Localization for random and quasiperiodic potentials. Zbl 1086.82547
Spencer, Thomas
1988
Density of states for random band matrices. Zbl 1019.15014
Disertori, M.; Pinson, H.; Spencer, T.
2002
Anderson localization for a supersymmetric sigma model. Zbl 1203.82017
Disertori, M.; Spencer, T.
2010
Analyticity of the density of states and replica method for random Schrödinger operators on a lattice. Zbl 0591.60060
Constantinescu, F.; Fröhlich, J.; Spencer, T.
1984
Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions. Zbl 1102.81047
Spencer, T.; Zirnbauer, M. R.
2004
Strong convergence to the homogenized limit of elliptic equations with random coefficients. Zbl 1283.81102
Conlon, Joseph G.; Spencer, Thomas
2014
Random banded and sparse matrices. Zbl 1236.15074
Spencer, Thomas
2011
Positive Lyapunov exponents for a class of deterministic potentials. Zbl 0821.60070
Chulaevsky, Victor; Spencer, Thomas
1995
SUSY statistical mechanics and random band matrices. Zbl 1267.82070
Spencer, Thomas
2012
Periodic solutions of some infinite-dimensional Hamiltonian systems associated with nonlinear partial difference equations. II. Zbl 0699.35242
Albanese, Claudio; Fröhlich, Jürg; Spencer, Thomas
1988
A strong central limit theorem for a class of random surfaces. Zbl 1291.82019
Conlon, Joseph G.; Spencer, Thomas
2014
Ergodic Schrödinger operators. Zbl 0813.47046
Spencer, Thomas
1990
Correlation length bounds for disordered Ising ferromagnets. Zbl 0658.60137
Chayes, J. T.; Chayes, L.; Fisher, Daniel S.; Spencer, T.
1989
Brydges, David; Spencer, Thomas
2012
The nonlinear Schrödinger equation on Z and R with bounded initial data: examples and conjectures. Zbl 1446.35181
Dodson, Benjamin; Soffer, Avraham; Spencer, Thomas
2020
The Schrödinger equation with a random potential. A mathematical review. Zbl 0655.60050
Spencer, Thomas C.
1986
SUSY statistical mechanics and random band matrices. Zbl 1291.82029
Spencer, Thomas
2012
Duality, statistical mechanics, and random matrices. Zbl 1292.82006
Spencer, Thomas
2013
Bounds on the Lyapunov exponent via crude estimates on the density of states. Zbl 1358.37065
Shamis, Mira; Spencer, Thomas
2015
Phase transitions in $$P(\varphi)_2$$ quantum fields. Zbl 0367.60113
Glimm, J.; Jaffe, A.; Spencer, T.
1976
Some rigorous results for random and quasi-periodic potentials. Zbl 0667.60103
Spencer, Thomas
1986
Mathematical aspects of Anderson localization. Zbl 1228.82046
Spencer, Thomas
2010
Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in $$L^p$$-based Sobolev spaces. Zbl 1476.35233
Dodson, Benjamin; Soffer, Avraham; Spencer, Thomas
2021
Global well-posedness for the cubic nonlinear Schrödinger equation with initial data lying in $$L^p$$-based Sobolev spaces. Zbl 1476.35233
Dodson, Benjamin; Soffer, Avraham; Spencer, Thomas
2021
The nonlinear Schrödinger equation on Z and R with bounded initial data: examples and conjectures. Zbl 1446.35181
Dodson, Benjamin; Soffer, Avraham; Spencer, Thomas
2020
Bounds on the Lyapunov exponent via crude estimates on the density of states. Zbl 1358.37065
Shamis, Mira; Spencer, Thomas
2015
Strong convergence to the homogenized limit of elliptic equations with random coefficients. Zbl 1283.81102
Conlon, Joseph G.; Spencer, Thomas
2014
A strong central limit theorem for a class of random surfaces. Zbl 1291.82019
Conlon, Joseph G.; Spencer, Thomas
2014
Duality, statistical mechanics, and random matrices. Zbl 1292.82006
Spencer, Thomas
2013
SUSY statistical mechanics and random band matrices. Zbl 1267.82070
Spencer, Thomas
2012
Brydges, David; Spencer, Thomas
2012
SUSY statistical mechanics and random band matrices. Zbl 1291.82029
Spencer, Thomas
2012
Random banded and sparse matrices. Zbl 1236.15074
Spencer, Thomas
2011
Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model. Zbl 1203.82018
Disertori, M.; Spencer, T.; Zirnbauer, M. R.
2010
Anderson localization for a supersymmetric sigma model. Zbl 1203.82017
Disertori, M.; Spencer, T.
2010
Mathematical aspects of Anderson localization. Zbl 1228.82046
Spencer, Thomas
2010
Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions. Zbl 1102.81047
Spencer, T.; Zirnbauer, M. R.
2004
Density of states for random band matrices. Zbl 1019.15014
Disertori, M.; Pinson, H.; Spencer, T.
2002
On homogenization and scaling limit of some gradient perturbations of a massless free field. Zbl 0871.35010
1997
Positive Lyapunov exponents for a class of deterministic potentials. Zbl 0821.60070
Chulaevsky, Victor; Spencer, Thomas
1995
Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials. Zbl 0745.34046
Sorets, Eugene; Spencer, Thomas
1991
Localization for a class of one dimensional quasi-periodic Schrödinger operators. Zbl 0722.34070
Fröhlich, J.; Spencer, T.; Wittwer, P.
1990
Ergodic Schrödinger operators. Zbl 0813.47046
Spencer, Thomas
1990
Trace class perturbations and the absence of absolutely continuous spectra. Zbl 0684.47010
Simon, Barry; Spencer, Thomas
1989
Correlation length bounds for disordered Ising ferromagnets. Zbl 0658.60137
Chayes, J. T.; Chayes, L.; Fisher, Daniel S.; Spencer, T.
1989
Diffusion of directed polymers in a random environment. Zbl 1084.82595
Imbrie, J. Z.; Spencer, T.
1988
Localization for random and quasiperiodic potentials. Zbl 1086.82547
Spencer, Thomas
1988
Periodic solutions of some infinite-dimensional Hamiltonian systems associated with nonlinear partial difference equations. II. Zbl 0699.35242
Albanese, Claudio; Fröhlich, Jürg; Spencer, Thomas
1988
Localization in disordered, nonlinear dynamical systems. Zbl 0629.60105
Fröhlich, Jürg; Spencer, Thomas; Wayne, C. Eugene
1986
The Schrödinger equation with a random potential. A mathematical review. Zbl 0655.60050
Spencer, Thomas C.
1986
Some rigorous results for random and quasi-periodic potentials. Zbl 0667.60103
Spencer, Thomas
1986
Constructive proof of localization in the Anderson tight binding model. Zbl 0573.60096
Fröhlich, J.; Martinelli, F.; Scoppola, E.; Spencer, T.
1985
Self-avoiding walk in 5 or more dimensions. Zbl 0575.60099
Brydges, David; Spencer, Thomas
1985
Analyticity of the density of states and replica method for random Schrödinger operators on a lattice. Zbl 0591.60060
Constantinescu, F.; Fröhlich, J.; Spencer, T.
1984
Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Zbl 0519.60066
Fröhlich, Jürg; Spencer, Thomas
1983
The phase transition in the one-dimensional Ising model with $$1/r^2$$ interaction energy. Zbl 1110.82302
Fröhlich, Jürg; Spencer, Thomas
1982
Phase transitions in $$P(\varphi)_2$$ quantum fields. Zbl 0367.60113
Glimm, J.; Jaffe, A.; Spencer, T.
1976
Phase transitions for $$\phi_2^4$$ quantum fields. Zbl 0956.82501
Glimm, James; Jaffe, Arthur; Spencer, Thomas
1975
all top 5
### Cited by 832 Authors
32 Klein, Abel 23 Chulaevsky, Victor 19 Jitomirskaya, Svetlana Yakovlevna 18 Slade, Gordon 18 Spencer, Thomas C. 17 Fröhlich, Jürg Martin 14 Simon, Barry 12 Erdős, László 12 van der Hofstad, Remco W. 12 Wang, Wei-Min 11 Bourgain, Jean 11 Otto, Felix 10 Hara, Takashi 10 Yau, Horng-Tzer 9 Damanik, David 9 Disertori, Margherita 9 Kozma, Gady 9 Mourrat, Jean-Christophe 8 Aizenman, Michael 8 Bauerschmidt, Roland 8 Bjerklöv, Kristian 8 Elgart, Alexander 8 Gloria, Antoine 8 Last, Yoram 8 Martinelli, Fabio 8 Molchanov, Stanislav Alekseevich 8 Sadel, Christian 8 Sakai, Akira 8 Shcherbina, Tatyana 8 van Enter, Aernout C. D. 8 You, Jiangong 8 Yuan, Xiaoping 7 Comets, Francis M. 7 Geng, Jiansheng 7 Germinet, François 7 Imbrie, John Z. 7 Jaffe, Arthur Michael 7 Lacoin, Hubert 7 Mastropietro, Vieri 7 Sabot, Christophe 7 Schlag, Wilhelm 7 Veselić, Ivan 6 Cassandro, Marzio 6 Conlon, Joseph G. 6 Constantinescu, Florin 6 Goldstein, Michael 6 Klopp, Frédéric 6 Knowles, Antti 6 Picco, Pierre 6 Schenker, Jeffrey H. 6 Sodin, Sasha 6 Tarrès, Pierre 5 Albanese, Claudio 5 Andres, Sebastian 5 Biskup, Marek 5 Chayes, Lincoln 5 De Roeck, Wojciech 5 Duminil-Copin, Hugo 5 Ekanga, Trésor 5 Endo, Eric Ossami 5 Helmuth, Tyler 5 Liu, Wencai 5 Merkl, Franz 5 Miller, Jason P. 5 Nakano, Fumihiko 5 Neukamm, Stefan 5 Niedermaier, Max R. 5 Puig, Joaquim 5 Rolles, Silke W. W. 5 Shcherbina, Mariya 5 Sheffield, Scott 5 Shi, Yunfeng 5 Stolz, Gunter 5 Tautenhahn, Martin 5 Ueki, Naomasa 5 Warzel, Simone 5 Zeng, Xiaolin 4 Armstrong, Scott N. 4 Berti, Massimiliano 4 Bolthausen, Erwin 4 Brydges, David C. 4 Campanino, Massimo 4 Chayes, Jennifer Tour 4 Combes, Jean-Michel 4 Cosco, Clément 4 Deuschel, Jean-Dominique 4 Exner, Pavel 4 Figotin, Alexander 4 Ge, Lingrui 4 Goldsheid, Ilya Ya. 4 Gordon, Alexander Ya. 4 Gu, Yu 4 Han, Rui 4 Heydenreich, Markus 4 Huveneers, François 4 Johnson, Russell Allan 4 Le Ny, Arnaud 4 Magnen, Jacques 4 Merola, Immacolata 4 Newman, Charles Michael ...and 732 more Authors
all top 5
### Cited in 157 Serials
185 Communications in Mathematical Physics 126 Journal of Statistical Physics 43 Journal of Mathematical Physics 34 Journal of Functional Analysis 31 Probability Theory and Related Fields 29 The Annals of Probability 25 Annales Henri Poincaré 18 Reviews in Mathematical Physics 13 Electronic Journal of Probability 13 Mathematical Physics, Analysis and Geometry 12 Stochastic Processes and their Applications 12 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 11 Journal of Spectral Theory 10 Journal of the European Mathematical Society (JEMS) 9 Duke Mathematical Journal 8 Communications on Pure and Applied Mathematics 8 Acta Mathematica 8 Inventiones Mathematicae 8 Journal of Differential Equations 8 Ergodic Theory and Dynamical Systems 7 Journal of Mathematical Analysis and Applications 7 Letters in Mathematical Physics 7 Bulletin of the American Mathematical Society. New Series 7 Annals of Mathematics. Second Series 6 Archive for Rational Mechanics and Analysis 5 Nuclear Physics. B 5 Journal of Theoretical Probability 5 Communications in Partial Differential Equations 5 Annales de l’Institut Henri Poincaré. Physique Théorique 4 Modern Physics Letters B 4 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 4 Physica D 4 The Annals of Applied Probability 4 Geometric and Functional Analysis. GAFA 4 Journal of Dynamics and Differential Equations 4 Electronic Communications in Probability 4 Journal of High Energy Physics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Statistical Mechanics: Theory and Experiment 4 Stochastic and Partial Differential Equations. Analysis and Computations 3 Nonlinearity 3 Theoretical and Mathematical Physics 3 Advances in Mathematics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Functional Analysis and its Applications 3 Journal of Soviet Mathematics 3 Advances in Applied Mathematics 3 Acta Applicandae Mathematicae 3 Journal of the American Mathematical Society 3 Annals of Physics 3 Journal of Mathematical Sciences (New York) 3 Random Operators and Stochastic Equations 3 Journal of Difference Equations and Applications 3 Discrete and Continuous Dynamical Systems 3 Chaos 3 Physical Review Letters 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Frontiers of Mathematics in China 2 Applicable Analysis 2 Journal d’Analyse Mathématique 2 Physics Reports 2 Annales de l’Institut Fourier 2 Integral Equations and Operator Theory 2 Journal of Combinatorial Theory. Series A 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Calculus of Variations and Partial Differential Equations 2 Combinatorics, Probability and Computing 2 St. Petersburg Mathematical Journal 2 Regular and Chaotic Dynamics 2 Nonlinear Analysis. Real World Applications 2 Milan Journal of Mathematics 2 Oberwolfach Reports 2 Bulletin of the American Mathematical Society 2 Operators and Matrices 2 Advances in Mathematical Physics 2 Science China. Mathematics 2 Random Matrices: Theory and Applications 2 Journal de l’École Polytechnique – Mathématiques 1 International Journal of Modern Physics A 1 International Journal of Modern Physics B 1 International Journal of Theoretical Physics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational Physics 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Wave Motion 1 Arkiv för Matematik 1 Chaos, Solitons and Fractals 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Illinois Journal of Mathematics ...and 57 more Serials
all top 5
### Cited in 47 Fields
498 Statistical mechanics, structure of matter (82-XX) 397 Probability theory and stochastic processes (60-XX) 224 Quantum theory (81-XX) 190 Partial differential equations (35-XX) 175 Operator theory (47-XX) 120 Dynamical systems and ergodic theory (37-XX) 73 Ordinary differential equations (34-XX) 47 Linear and multilinear algebra; matrix theory (15-XX) 36 Difference and functional equations (39-XX) 25 Combinatorics (05-XX) 19 Functional analysis (46-XX) 15 Global analysis, analysis on manifolds (58-XX) 13 Mechanics of particles and systems (70-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 10 Numerical analysis (65-XX) 10 Optics, electromagnetic theory (78-XX) 9 Measure and integration (28-XX) 8 Potential theory (31-XX) 7 Fluid mechanics (76-XX) 6 Real functions (26-XX) 6 Mechanics of deformable solids (74-XX) 5 Statistics (62-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Relativity and gravitational theory (83-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 2 Sequences, series, summability (40-XX) 2 Integral transforms, operational calculus (44-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Biology and other natural sciences (92-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 $$K$$-theory (19-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Systems theory; control (93-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-10-06T12:55:05 |
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|
https://par.nsf.gov/biblio/10249402-sensitivity-neutrinos-from-solar-cno-cycle-borexino
|
Sensitivity to neutrinos from the solar CNO cycle in Borexino
Abstract Neutrinos emitted in the carbon, nitrogen, oxygen (CNO) fusion cycle in the Sun are a sub-dominant, yet crucial component of solar neutrinos whose flux has not been measured yet. The Borexino experiment at the Laboratori Nazionali del Gran Sasso (Italy) has a unique opportunity to detect them directly thanks to the detector’s radiopurity and the precise understanding of the detector backgrounds. We discuss the sensitivity of Borexino to CNO neutrinos, which is based on the strategies we adopted to constrain the rates of the two most relevant background sources, $$pep$$ pep neutrinos from the solar pp -chain and $$^{210}$$ 210 Bi beta decays originating in the intrinsic contamination of the liquid scintillator with $$^{210}$$ 210 Pb. Assuming the CNO flux predicted by the high-metallicity Standard Solar Model and an exposure of 1000 days $$\times$$ × 71.3 t, Borexino has a median sensitivity to CNO neutrino higher than 3 $$\sigma$$ σ . With the same hypothesis the expected experimental uncertainty on the CNO neutrino flux is 23%, provided the uncertainty on the independent estimate of the $$^{210}\text {Bi}$$ 210 Bi interaction rate is 1.5 $$\hbox {cpd}/100~\hbox {ton}$$ cpd / 100 ton . Finally, we evaluated the expected uncertainty of the more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10249402
Journal Name:
The European Physical Journal C
Volume:
80
Issue:
11
ISSN:
1434-6044
1. Abstract We detail the sensitivity of the proposed liquid xenon DARWIN observatory to solar neutrinos via elastic electron scattering. We find that DARWIN will have the potential to measure the fluxes of five solar neutrino components: pp , $$^7$$ 7 Be, $$^{13}$$ 13 N, $$^{15}$$ 15 O and pep . The precision of the $$^{13}$$ 13 N, $$^{15}$$ 15 O and pep components is hindered by the double-beta decay of $$^{136}$$ 136 Xe and, thus, would benefit from a depleted target. A high-statistics observation of pp neutrinos would allow us to infer the values of the electroweak mixing angle, \sinmore »
| 2022-06-29T10:16:37 |
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http://mathonline.wikidot.com/the-supremum-and-infimum-of-the-bounded-set-a-s
|
The Supremum and Infimum of The Bounded Set (a + S)
Table of Contents
# The Supremum and Infimum of The Bounded Set (a + S)
Recall from The Supremum and Infimum of a Bounded Set page the following definitions:
Definition: Let $S$ be a set that is bounded above. We say that the supremum of $S$ denoted $\sup S = u$ is a number $u$ that satisfies the conditions that $u$ is an upper bound of $S$ and $u$ is the least upper bound of $S$, that is for any $v$ that is also an upper bound of $S$ then $u \leq v$.
Definition: Let $S$ be a set that is bounded below. We say that the infimum of $S$ denoted $\inf S = w$ is a number $w$ that satisfies the conditions that $w$ is a lower bound of $S$ and $w$ is the greatest lower bound of $S$, that is for any $t$ that is also a lower bound of $S$ then $t \leq w$.
Now let $a \in \mathbb{R}$ and define the set $(a + S) := \{ a + x : x \in \mathbb{S} \}$. We will now look at some important supremum and infimum theorems regarding this set. Be sure to check out the The Supremum and Infimum of The Bounded Set (aS) as well for similar proofs.
Theorem 1: Let $S$ be a nonempty bounded subset of $\mathbb{R}$. Then $\sup (a + S) = a + \sup S$.
• Proof: Let $S \subset \mathbb{R}$ that is nonempty and bounded and let $u = \sup S$. Then we know that $\forall x \in S$, $x ≤ u = \sup S$. By adding $a$ to both sides of this inequality we get that $a + x ≤ a + u$ and so $a + u$ is an upper bound for the set $(a + S)$ and so $\sup (a + S) ≤ a + u$.
• Now suppose that $v$ is any upper bound to the set $(a + S)$ and then so $\forall x \in S$, $a + x ≤ v$ which implies that $x ≤ v - a$. Therefore $v - a$ is an upper bound to the set $S$ and so $\sup S = u ≤ v - a$ or rather just $u ≤ v - a$ which implies that $a + u ≤ v$. Since $v$ is any upper bound of the set $(a + S)$ we can replace it in this inequality to get that $a + u ≤ \sup (a + S)$.
• Since $\sup (a + S) ≤ a + u$ and $a + u ≤ \sup (a + S)$ then it follows that $\sup (a + S) = a + u = a + \sup S$. $\blacksquare$.
Theorem 2: Let $S$ be a nonempty bounded subset of $\mathbb{R}$. Then $\inf (a + S) = a + \inf S$.
• Proof: Let $S \subset \mathbb{R}$ that is nonempty and bounded and let $w = \inf S$. Then we know that $\forall x \in S$, $\inf S = w ≤ x$. By adding $a$ to both sides of this inequality we get that $a + w ≤ a + x$ and so $a + w$ is a lower bound for the set $(a + S)$ and so $a + w ≤ \inf (a + S)$.
• Now suppose that $t$ is any lower bound to the set $(a + S)$ and then so $\forall x \in S$, $t ≤ a + x$ which implies that $t - a ≤ x$. Therefore $t - a$ is a lower bound to the set $S$ and so $t - a ≤ w = \inf S$ or rather just $t - a ≤ w$ which implies that $t ≤ a + w$. Since $t$ is any lower bound to the set $(a + S)$ we can replace it in this inequality to get that $\inf (a + S) ≤ a + w$.
• Since $a + w ≤ \inf (a + S)$ and $\inf (a + S) ≤ a + w$ then it follows that $\inf (a + S) = a + w = a + \inf S$. $\blacksquare$
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2018-12-11T09:51:02 |
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|
http://www.scstatehouse.gov/sess120_2013-2014/SJ13/20130605.htm
|
South Carolina General Assembly
120th Session, 2013-2014
Journal of the Senate
Wednesday, June 5, 2013
(Statewide Session)
Indicates Matter Stricken
Indicates New Matter
The Senate assembled at 10:00 A.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT.
A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows:
As we recall, the man and the woman hid themselves in the garden.
"But the Lord God called to the man, 'Where are you?' "
(Genesis 3:9)
Let us pray:
Here at the midpoint of this first week of June it is appropriate, O God, to ask: "Where are we?" Where, indeed? These Senators have accomplished much, to be sure, yet there are still many matters which continue to be unresolved here near the end of this year's Session. So Lord, we pray that You will lead these dedicated servants in order that they might yet attain some of those remaining goals which are important to them and to the people of South Carolina. Grant every Senator all the necessary stamina and wisdom they need to bring about significant good for our State. In Your loving name we ask this, Lord. Amen.
The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers.
Doctor of the Day
Senators LOURIE and JACKSON introduced Dr. Patricia Witherspoon, of Columbia, S.C., along with Dr. Danesh Ghiassi, 2nd year Medical Resident, and Marissa Barmine, rising senior and medical student from USC, Doctor of the Day.
Leave of Absence
On motion of Senator JOHNSON, at 10:32 A.M., Senator McELVEEN was granted a leave of absence until 2:00 P.M.
Leave of Absence
At 3:15 P.M., Senator O'DELL requested a leave of absence until 10:00 A.M. in the morning.
Leave of Absence
At 6:30 P.M., Senator CROMER requested a leave of absence beginning at 7:00 P.M. and lasting until 10:00 P.M. this evening.
Expression of Personal Interest
Senator CLEARY rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator BRIGHT rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator HUTTO rose for an Expression of Personal Interest.
Expression of Personal Interest
Senator PEELER rose for an Expression of Personal Interest.
Senator COURSON moved that when the Senate adjourns today, it stand adjourned to meet at 10:00 A.M. tomorrow.
S. 185 (Word version) Sens. Young, Turner
RECESS
At 11:55 A.M., on motion of Senator COURSON, the Senate receded from business for the purpose of attending the Joint Assembly.
Joint Assembly
The PRESIDENT announced that elections were in order to elect successors to Boards of Trustees of State Colleges and Universities.
Election to the Board of Trustees for the
Coastal Carolina University, 5th Congressional District, Seat #5
The PRESIDENT announced that nominations were in order to elect a successor to a position on the Board of Trustees for Coastal Carolina University, 5th Congressional District, Seat #5.
Senator PEELER, Chairman of the Committee to Screen Candidates for State Colleges and Universities, indicated that Charles E. Lewis had been screened and found qualified to serve and placed his name in nomination.
Senator PEELER moved that the nominations be closed and, with unanimous consent, the vote was taken by acclamation, resulting in the election of the nominee.
Whereupon, the PRESIDENT announced that the Honorable Charles E. Lewis was elected to a position on the Board of Trustees for Coastal Carolina University, 5th Congressional District, Seat #5 for the term prescribed by law.
Medical University of South Carolina
6th Congressional District, Lay Member Position
The PRESIDENT announced that nominations were in order to elect to the lay position on the Board of Trustees for the Medical University of South Carolina, 6th Congressional District.
Senator PEELER, Chairman of the Committee to Screen Candidates for State Colleges and Universities, indicated that Ms. Barbara Johnson-Williams had been screened and found qualified to serve and placed her name in nomination.
Senator PEELER moved that the nominations be closed and, with unanimous consent, the vote was taken by acclamation, resulting in the election of the nominee.
Whereupon, the PRESIDENT announced that the Honorable Barbara Johnson-Williams was elected to the lay position on the Board of Trustees for Medical University of South Carolina, 6th Congressional District for the term prescribed by law.
The purposes of the Joint Assembly having been accomplished, the PRESIDENT declared it adjourned, whereupon the Senate returned to its Chamber and was called to order by the PRESIDENT.
RECESS
At 12:06 P.M, on motion of Senator COURSON, with unanimous consent, the Senate receded from business until 1:30 P.M.
AFTERNOON SESSION
The Senate reassembled at 1:39 P.M. and was called to order by the PRESIDENT.
On motion of Senator ALEXANDER, with unanimous consent, Senators MASSEY, SHEHEEN and ALEXANDER were granted leave to attend a meeting and were granted leave to vote from the balcony.
RECALLED
H. 3998 (Word version) -- Rep. Mitchell: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE PORTION OF UNION STREET IN SPARTANBURG COUNTY FROM ITS INTERSECTION WITH CEDAR SPRINGS ROAD TO ITS INTERSECTION WITH SOUTHPORT ROAD "SCHP PATROLMAN NORRIS NETTLES MEMORIAL HIGHWAY" AND ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS STREET THAT CONTAIN THE WORDS "SCHP PATROLMAN NORRIS NETTLES MEMORIAL HIGHWAY".
Senator GROOMS asked unanimous consent to make a motion to recall the Concurrent Resolution from the Committee on Transportation.
The Resolution was recalled from the Committee on Transportation and ordered placed on the Calendar for consideration tomorrow.
INTRODUCTION OF BILLS AND RESOLUTIONS
The following were introduced:
S. 774 (Word version) -- Senator Setzler: A SENATE RESOLUTION TO RECOGNIZE AND HONOR CAYCE UNITED METHODIST CHURCH FOR ITS MINISTRY IN THE COMMUNITY AND TO CONGRATULATE THE PASTOR AND THE CONGREGATION UPON THE CHURCH'S CENTENNIAL ANNIVERSARY.
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S. 775 (Word version) -- Senators Turner, Allen, Fair, L. Martin, Verdin and Corbin: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE INTERCHANGE LOCATED AT THE INTERSECTION OF INTERSTATE HIGHWAY 85 AND INTERSTATE HIGHWAY 385 IN GREENVILLE COUNTY "LT. GOVERNOR NICK AND EMILIE THEODORE INTERCHANGE" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS INTERCHANGE THAT CONTAIN THE WORDS "LT. GOVERNOR NICK AND EMILIE THEODORE INTERCHANGE".
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The Concurrent Resolution was introduced and referred to the Committee on Transportation.
S. 776 (Word version) -- Senator Sheheen: A CONCURRENT RESOLUTION TO EXPRESS THE PROFOUND SORROW OF THE MEMBERS OF THE SOUTH CAROLINA GENERAL ASSEMBLY UPON THE PASSING OF LEONARD PRICE OF KERSHAW AND TO EXTEND THE DEEPEST SYMPATHY TO HIS FAMILY AND MANY FRIENDS.
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The Concurrent Resolution was adopted, ordered sent to the House.
S. 777 (Word version) -- Senators Shealy, Hembree and Bennett: A BILL TO AMEND SECTION 16-27-80 OF THE 1976 CODE, RELATING TO THE EXEMPTIONS OF CERTAIN ACTIVITIES FROM THE ANIMAL FIGHTING AND BAITING ACT, TO DELETE THE EXEMPTION OF "BEAR-BAYING"; AND TO AMEND SECTION 50-11-430, RELATING TO BEAR HUNTING AND UNLAWFUL ACTS IN REGARD TO BEARS INCLUDING A PROVISION THAT IT IS UNLAWFUL TO POSSESS A CAPTIVE BEAR EXCEPT BY PERMIT ISSUED BY THE DEPARTMENT OF NATURAL RESOURCES, TO PROVIDE THAT A CAPTIVE BEAR FOR WHICH A PERMIT HAS BEEN ISSUED AND WHICH UPON INFORMATION AND BELIEF OF THE DEPARTMENT HAS BEEN OR IS BEING USED FOR THE PURPOSE OF "BEAR-BAYING" MUST BE TAKEN INTO CUSTODY BY THE DEPARTMENT, AND TO PROVIDE THAT THE DEPARTMENT SHALL MAKE EVERY EFFORT TO PLACE THESE BEARS IN A SUITABLE ENVIRONMENT, INCLUDING ZOOS OR ANIMAL PARKS WITHIN OR OUTSIDE THIS STATE.
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Read the first time and referred to the Committee on Fish, Game and Forestry.
S. 778 (Word version) -- Senator Hembree: A BILL TO AMEND SECTION 56-5-2953(A), THE CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE VIDEO RECORDING OF A PERSON WHO VIOLATES SECTION 56-5-2930, 56-5-2922, OR 56-5-2945, SO AS TO PROVIDE THAT A VIDEO RECORDING AT A BREATH TEST SITE DOES NOT HAVE TO INCLUDE A PERSON'S CONDUCT DURING THE REQUIRED TWENTY-MINUTE PRE-TEST WAITING PERIOD IF THE PERSON REFUSES TO TAKE THE TEST.
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Read the first time and referred to the Committee on Judiciary.
S. 779 (Word version) -- Senator Davis: A BILL TO AMEND CHAPTER 19, TITLE 16 OF THE 1976 CODE, RELATING TO GAMBLING AND LOTTERIES, BY ADDING SECTION 16-19-60, TO PROVIDE THAT CERTAIN SOCIAL CARD AND DICE GAMES ARE NOT UNLAWFUL.
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Read the first time and referred to the Committee on Judiciary.
S. 780 (Word version) -- Senator Nicholson: A SENATE RESOLUTION TO PROCLAIM THE MONTH OF JUNE AS THE SALVATION ARMY OF GREENWOOD MONTH IN RECOGNITION OF THE CORPS' SEVENTY-FIFTH YEAR OF SERVICE TO THE COMMUNITY.
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S. 781 (Word version) -- Senator Pinckney: A SENATE RESOLUTION TO CONGRATULATE QUINCY PRUITT KNIGHTON OF BEAUFORT COUNTY, UPON THE OCCASION OF HER ONE HUNDREDTH BIRTHDAY, AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND MANY MORE YEARS OF CONTINUED HEALTH AND HAPPINESS.
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S. 782 (Word version) -- Senators Malloy and McElveen: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE INTERCHANGE LOCATED AT EXIT 120 ALONG UNITED STATES HIGHWAY 20 IN LEE COUNTY "STATE REPRESENTATIVE GRADY A. BROWN INTERCHANGE" AND ERECT APPROPRIATE MARKERS OR SIGNS AT THIS EXIT THAT CONTAIN THE WORDS "STATE REPRESENTATIVE GRADY A. BROWN INTERCHANGE".
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On motion of Senator MALLOY, with unanimous consent, the Concurrent Resolution was adopted and ordered sent to the House.
S. 783 (Word version) -- Senator McElveen: A SENATE RESOLUTION TO CONGRATULATE ANGELINE LONEY OF SUMTER COUNTY ON THE OCCASION OF HER ONE HUNDREDTH BIRTHDAY, AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND MANY YEARS OF CONTINUED HEALTH AND HAPPINESS.
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Message from the House
Columbia, S.C., June 4, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has confirmed the reappointment:
Master-in-Equity Reappointment
Reappointment, Georgetown County Master-in-Equity, with the term to commence December 31, 2013, and to expire December 31, 2019
Joe M. Crosby, 405 Dozier Street, Georgetown, SC 29440
Very respectfully,
Speaker of the House
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 484 (Word version) -- Senator Setzler: A BILL TO AMEND SECTION 9-11-80, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DISABILITY RETIREMENT FOR MEMBERS OF THE POLICE OFFICERS RETIREMENT SYSTEM, SO AS TO DELETE THE REQUIREMENT THAT CERTAIN MEMBERS BE ELIGIBLE FOR, AND PROVIDE PROOF OF, SOCIAL SECURITY BENEFITS TO CONTINUE TO RECEIVE A DISABILITY BENEFIT.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 308 (Word version) -- Senators Bennett, Shealy, Grooms, Hembree, L. Martin, Massey, Campbell, Turner, Thurmond, Bryant, Verdin, S. Martin, Davis, Bright, Corbin, Campsen, Fair and Cromer: A BILL TO AMEND SECTION 16-23-465 OF THE 1976 CODE, RELATING TO THE CARRYING OF A CONCEALED WEAPON IN A BUSINESS THAT SELLS ALCOHOL TO BE CONSUMED ON THE PREMISES, TO PERMIT THE POSSESSION OF A WEAPON UNLESS NOTICE OF A PROHIBITION IS PROVIDED BY THE BUSINESS, TO PROHIBIT THE CONSUMPTION OF ALCOHOLIC BEVERAGES IN A BUSINESS BY SOMEONE CARRYING A FIREARM, AND TO REDUCE THE PENALTIES FOR VIOLATIONS.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
S. 707 (Word version) -- Senator Lourie: A BILL TO PROVIDE FOR THE AUTHORITY OF THE CITY OF COLUMBIA TO APPOINT AND COMMISSION FIREFIGHTERS TO SERVE AS CERTIFIED LAW ENFORCEMENT OFFICERS WHO HAVE THE FULL POWERS AS CERTIFIED LAW ENFORCEMENT OFFICERS AND TO REQUIRE FIREFIGHTERS TO MEET CERTAIN QUALIFICATIONS TO BE COMMISSIONED AS A CERTIFIED LAW ENFORCEMENT OFFICER.
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Bill to the Senate with amendments:
H. 3710--GENERAL APPROPRIATIONS BILL
Respectfully submitted,
Speaker of the House
The Bill was ordered placed on the Calendar for consideration tomorrow.
Message from the House
Columbia, S.C., June 5, 2013
Mr. President and Senators:
The House respectfully informs your Honorable Body that it has returned the following Joint Resolution to the Senate with amendments:
H. 3711 (Word version) -- Ways and Means Committee: A JOINT RESOLUTION TO APPROPRIATE MONIES FROM THE CAPITAL RESERVE FUND FOR FISCAL YEAR 2012-2013, AND TO ALLOW UNEXPENDED FUNDS APPROPRIATED TO BE CARRIED FORWARD TO SUCCEEDING FISCAL YEARS AND EXPENDED FOR THE SAME PURPOSES.
Respectfully submitted,
Speaker of the House
The Joint Resolution was ordered placed on the Calendar for consideration tomorrow.
THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR.
ORDERED ENROLLED FOR RATIFICATION
The following Bills and Joint Resolution were read the third time and, having received three readings in both Houses, it was ordered that the titles be changed to that of Acts and enrolled for Ratification:
H. 3960 (Word version) -- Rep. Sandifer: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 38-41-35 SO AS TO REQUIRE EMPLOYERS PARTICIPATING IN A MULTIPLE EMPLOYER SELF-INSURED HEALTH PLAN TO EXECUTE HOLD HARMLESS AGREEMENTS IN WHICH THE EMPLOYER AGREES TO PAY ALL UNPAID PORTIONS OF INSURED CLAIMS, AND TO REQUIRE THE DEPARTMENT OF INSURANCE TO PROVIDE FORMS THAT MUST BE USED FOR THESE AGREEMENTS, AMONG OTHER THINGS.
H. 3099 (Word version) -- Reps. Nanney and Long: A BILL TO AMEND SECTION 63-17-2310, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ENTITIES REQUIRED TO PROVIDE INFORMATION TO THE DEPARTMENT OF SOCIAL SERVICES FOR THE PURPOSE OF ESTABLISHING, MODIFYING, AND ENFORCING CHILD SUPPORT OBLIGATIONS, SO AS TO ALSO REQUIRE THESE ENTITIES TO PROVIDE THIS INFORMATION TO CLERKS OF COURT FOR THE SAME PURPOSE IN CASES NOT BEING ADMINISTERED PURSUANT TO TITLE IV-D OF THE SOCIAL SECURITY ACT BY THE DEPARTMENT OF SOCIAL SERVICES; AND TO MAKE TECHNICAL CORRECTIONS.
Senator MASSEY explained the Bill.
H. 3378 (Word version) -- Reps. Sandifer, Whitmire and Gambrell: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 6-1-90 SO AS TO ENACT THE "VOLUNTEER SERVICE PERSONNEL APPRECIATION ACT" AND TO ALLOW THE GOVERNING BODY OF A LOCAL GOVERNMENT TO AUTHORIZE THE DISTRIBUTION OF CERTAIN REWARDS TO THREE ENUMERATED CATEGORIES OF VOLUNTEER SERVICE PERSONNEL SO LONG AS ALL PERSONNEL IN A RESPECTIVE CATEGORY ARE TREATED EQUALLY.
H. 3502 (Word version) -- Reps. Murphy, Vick, Goldfinch, K.R. Crawford, Harrell, Horne, M.S. McLeod and Owens: A BILL TO AMEND SECTION 59-121-55, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE TRANSFER OF FUNDS OR PROPERTY BY THE CITADEL BOARD OF VISITORS TO A NONPROFIT ELEEMOSYNARY CORPORATION ESTABLISHED BY THE BOARD, SO AS TO REMOVE A LIMIT ON THE AMOUNT OF FUNDS OR PROPERTY THAT THE BOARD MAY TRANSFER TO THE CORPORATION.
H. 3752 (Word version) -- Rep. Patrick: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, SO AS TO ENACT THE "EXPANDED VIRTUAL LEARNING ACT"; TO AMEND SECTION 59-16-15, RELATING TO THE SOUTH CAROLINA VIRTUAL SCHOOL PROGRAM, SO AS TO RESTYLE THE PROGRAM AS A VIRTUAL EDUCATION PROGRAM AND TO REMOVE LIMITS ON THE NUMBER OF ONLINE CREDITS A STUDENT MAY BE AWARDED UNDER THE PROGRAM; AND TO AMEND SECTION 59-40-65, RELATING TO ENROLLMENT OF CHARTER SCHOOL STUDENTS IN THE SOUTH CAROLINA VIRTUAL SCHOOL PROGRAM, SO AS TO MAKE A CONFORMING CHANGE.
Senator HAYES explained the Bill.
H. 3870 (Word version) -- Reps. Gambrell, Bowen, D.C. Moss, Gagnon, Putnam, Sandifer and White: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 23-49-65 SO AS TO PROVIDE IN THE "FIREFIGHTER MOBILIZATION ACT OF 2000" THAT THE SOUTH CAROLINA LAW ENFORCEMENT DIVISION (SLED) HAS SPECIFIC AND EXCLUSIVE JURISDICTION ON BEHALF OF THE STATE IN MATTERS PERTAINING TO THE RESPONSE TO AND CRISIS MANAGEMENT OF ACTS OF TERRORISM AND EMERGENCY EVENT MANAGEMENT OF EXPLOSIVE DEVICES; TO AMEND SECTION 23-49-20, RELATING TO THE SOUTH CAROLINA FIREFIGHTER MOBILIZATION OVERSIGHT COMMITTEE, SO AS TO ADD THE CHIEF OF SLED TO THE COMMITTEE AND TO CORRECT OBSOLETE REFERENCES; TO AMEND SECTION 23-49-50, RELATING TO THE SOUTH CAROLINA FIREFIGHTER MOBILIZATION PLAN, SO AS TO RENAME THE COMMITTEE AS THE SOUTH CAROLINA FIREFIGHTER MOBILIZATION AND EMERGENCY RESPONSE TASK FORCE PLAN, TO ADD THE TASK FORCE TO THOSE RESOURCES THAT THE PLAN IS INTENDED TO OFFER, AND TO PROVIDE THE PLAN IS OPERATIONAL WHEN THE CHIEF OF SLED DIRECTS A RESPONSE TO A TERRORIST OR EXPLOSIVE DEVICE EVENT; TO AMEND SECTION 23-49-60, RELATING TO THE DUTIES OF THE COMMITTEE, SO AS TO PROVIDE THE COMMITTEE SHALL DEVELOP GUIDELINES FOR USING RESOURCES ALLOCATED TO THE TASK FORCE AT THE STATE AND REGIONAL LEVEL; TO AMEND SECTION 23-49-70, RELATING TO STATE AND REGIONAL COORDINATORS APPOINTED BY THE COMMITTEE TO EXECUTE THE PLAN, SO AS TO MAKE A CONFORMING CHANGE TO THE NAME OF THE PLAN, TO REQUIRE THE OFFICE OF STATE FIRE MARSHAL TO PROVIDE ADMINISTRATIVE SUPPORT AS REQUIRED BY THE COMMITTEE TO PERFORM ITS PRESCRIBED FUNCTIONS, AND TO PROVIDE THAT THE STATE COORDINATOR APPOINTED BY THE COMMITTEE SHALL REPORT TO THE STATE FIRE MARSHAL AND PROVIDE ADMINISTRATIVE SUPPORT TO THE COMMITTEE; TO AMEND SECTION 23-49-80, RELATING TO INFORMATION REQUIRED OF THE SOUTH CAROLINA STATE FIREMEN'S ASSOCIATION, SO AS TO CORRECT OBSOLETE LANGUAGE; AND TO AMEND SECTION 23-49-110, RELATING TO DEFINITIONS, SO AS TO DEFINE ADDITIONAL TERMS.
H. 3956 (Word version) -- Reps. Horne and Whipper: A BILL TO AMEND SECTION 61-6-20, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS IN THE ALCOHOLIC BEVERAGE CONTROL ACT, SO AS TO REVISE THE DEFINITION OF "FURNISHING LODGING" TO PROVIDE FOR AT LEAST EIGHTEEN INSTEAD OF TWENTY ROOMS THAT A BUSINESS MUST OFFER FOR ACCOMMODATIONS ON A REGULAR BASIS.
Senator CAMPBELL explained the Bill.
H. 4204 (Word version) -- Rep. Delleney: A BILL TO AMEND SECTION 7-7-170, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF PRECINCTS IN CHESTER COUNTY, SO AS TO REDESIGNATE CERTAIN PRECINCTS, TO DESIGNATE A MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD, AND TO CORRECT ARCHAIC LANGUAGE.
H. 3557 (Word version) -- Reps. Cobb-Hunter, White, Bannister, Rutherford, Harrell, Merrill, Simrill, Stavrinakis, Loftis, Horne, Weeks, Mitchell, Ott, Sellers, Hodges and Whipper: A BILL TO AMEND SECTION 12-6-3375, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE TAX CREDIT FOR PORT CARGO VOLUME INCREASE, SO AS TO EXPAND THE TYPES OF BUSINESSES THAT QUALIFY FOR THE CREDIT, TO GIVE THE COORDINATING COUNCIL FOR ECONOMIC DEVELOPMENT DISCRETION IN AWARDING CREDITS, TO FURTHER DEFINE TERMS, TO PROVIDE THAT TAXPAYERS ENGAGED IN THE MOVEMENT OF GOODS IMPORTED OR EXPORTED THROUGH SOUTH CAROLINA'S PORT FACILITIES MAY BE ELIGIBLE FOR THE CREDIT IF THE CARGO SUPPORTS A PRESENCE IN THE STATE AND MEETS OTHER JOB AND CAPITAL INVESTMENT REQUIREMENTS, AND TO PROVIDE THAT A TAXPAYER THAT FAILS TO MEET THE REQUIREMENTS OF THE CREDIT MUST REPAY A PRO RATA PORTION OF THE CREDIT.
Senator O'DELL explained the Bill.
H. 3944 (Word version) -- Reps. Goldfinch, Hardwick and H.A. Crawford: A BILL TO AMEND SECTION 4-23-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BOARD OF FIRE CONTROL FOR THE MURRELL'S INLET - GARDEN CITY FIRE DISTRICT IN GEORGETOWN AND HORRY COUNTIES, SO AS TO PROVIDE THAT THE MEMBERS OF THAT BOARD REPRESENTING GEORGETOWN COUNTY MUST BE APPOINTED BY THE GOVERNOR UPON THE RECOMMENDATION OF A MAJORITY OF THE GEORGETOWN COUNTY LEGISLATIVE DELEGATION NOTWITHSTANDING THE PROVISIONS OF ACT 515 OF 1996 DEVOLVING THAT APPOINTMENT AUTHORITY ON THE GOVERNING BODY OF GEORGETOWN COUNTY AND TO DELETE OBSOLETE LANGUAGE.
H. 4133 (Word version) -- Medical, Military, Public and Municipal Affairs Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE BOARD OF COSMETOLOGY, RELATING TO REQUIREMENTS OF LICENSURE IN THE FIELD OF COSMETOLOGY (EDUCATIONAL REQUIREMENTS), DESIGNATED AS REGULATION DOCUMENT NUMBER 4336, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE.
Senator CLEARY explained the Joint Resolution.
HOUSE BILLS RETURNED
The following House Bills were read the third time and ordered returned to the House with amendments:
H. 3847 (Word version) -- Reps. Hiott and Hardwick: A BILL TO AMEND SECTION 48-60-20, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS FOR TERMS USED IN THE SOUTH CAROLINA MANUFACTURER RESPONSIBILITY AND CONSUMER CONVENIENCE INFORMATION TECHNOLOGY EQUIPMENT COLLECTION AND RECOVERY ACT OF 2010, SO AS TO ADD, AMONG OTHER DEFINITIONS, TERMS RELATED TO COMPUTER MONITORS; TO AMEND SECTION 48-60-30, RELATING TO REQUIREMENTS OF CERTAIN MANUFACTURERS TO PROVIDE LABELS ON DEVICES INDICATING THE BRAND, SO AS TO REQUIRE COMPUTER MONITOR MANUFACTURERS TO DO SO; TO AMEND SECTION 48-60-50, RELATING TO THE REQUIREMENT FOR TELEVISION MANUFACTURERS TO PROVIDE A RECOVERY PROGRAM FOR RECYCLING TELEVISIONS, SO AS TO REQUIRE COMPUTER MONITOR MANUFACTURERS TO DO SO; BY ADDING SECTION 48-60-55 SO AS TO PROVIDE FOR THE CREATION AND OPERATION OF STATEWIDE CONSUMER ELECTRONIC DEVICE STEWARDSHIP PROGRAMS AND THE DEVELOPMENT AND IMPLEMENTATION OF RELATED RECOVERY PLANS, INCLUDING REQUIREMENTS FOR APPROVAL OF PLANS BY THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, AND TO ESTABLISH OTHER RESPONSIBILITIES AND AUTHORITY OF THE DEPARTMENT AND REQUIREMENTS OF REGULATED MANUFACTURERS; TO AMEND SECTION 48-60-60, RELATING TO PROTECTION FROM LIABILITY FOR CERTAIN DAMAGES, SO AS TO APPLY TO COMPUTER MONITOR MANUFACTURERS; TO AMEND SECTION 48-60-70, RELATING TO RETAILER SALE REQUIREMENTS, SO AS TO PROHIBIT RETAILERS FROM SELLING DEVICES MADE BY MANUFACTURERS WHO DO NOT COMPLY WITH THE REQUIREMENTS OF SECTION 48-60-55; TO AMEND SECTION 48-60-90, RELATING TO DISCARDING OR PLACING COVERED DEVICES IN A WASTE STREAM, TO PROHIBIT COMPONENTS OF COVERED DEVICES; TO AMEND SECTION 48-60-100, RELATING TO RECOVERY PROCESS FEES, SO AS TO LIMIT THE ABILITY OF LOCAL GOVERNMENTS TO CHARGE CERTAIN FEES; TO AMEND SECTION 48-60-140, RELATING TO REQUIREMENTS THAT RECOVERY PROCESSES COMPLY WITH STATE AND FEDERAL LAW, SO AS TO REQUIRE RECYCLING OR REUSE FACILITIES TO MAINTAIN CERTIFICATION, TO IDENTIFY APPROVED CERTIFICATION PROGRAMS, AND TO REQUIRE MANUFACTURERS AND GOVERNMENTS ONLY TO USE FACILITIES THAT HAVE APPROPRIATE CERTIFICATION; TO AMEND SECTION 48-60-150, RELATING TO THE DEPARTMENT'S PROMULGATION OF REGULATIONS, SO AS TO ELIMINATE THE RIGHT TO CHARGE CERTAIN FEES TO MANUFACTURERS; BY ADDING SECTION 48-60-160 SO AS TO PROVIDE FOR CERTAIN FEES AND PENALTIES; BY ADDING SECTION 48-60-170 SO AS TO SET FORTH THE PURPOSES OF THE CHAPTER AND CERTAIN LIMITATIONS ON LIABILITY; TO PROVIDE EXPIRATION DATES FOR REGULATIONS PROMULGATED PURSUANT TO THIS CHAPTER, AND TO MAKE TECHNICAL CORRECTIONS; AND TO REPEAL SECTION 48-60-50 JUNE 30, 2014, AND CERTAIN OTHER PROVISIONS JUNE 30, 2020.
Senator VERDIN explained the Bill.
H. 3847--Recorded Vote
Senators BRIGHT, CORBIN, DAVIS and SHANE MARTIN desired to be recorded as voting against the third reading of the Bill.
H. 3033 (Word version) -- Rep. G.M. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 132 TO CHAPTER 3 OF TITLE 56 SO AS TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ISSUE SPECIAL LICENSE PLATES TO RECIPIENTS OF THE DISTINGUISHED FLYING CROSS.
H. 3184 (Word version) -- Reps. Pope, R.L. Brown, M.S. McLeod, Weeks, Bales, Gilliard, Whipper, W.J. McLeod and Mitchell: A BILL TO AMEND SECTION 22-5-910, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EXPUNGEMENT OF CRIMINAL RECORDS, SO AS TO PROVIDE THAT A PERSON MAY BE ELIGIBLE FOR EXPUNGEMENT OF A FIRST OFFENSE CRIME WHICH CARRIES A FINE OF ONE THOUSAND DOLLARS RATHER THAN FIVE HUNDRED DOLLARS.
Senator MASSEY explained the Bill.
H. 3632 (Word version) -- Reps. G.M. Smith, White, Sandifer, J.R. Smith, Bannister and Lucas: A BILL TO AMEND SECTION 42-5-190, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE MAINTENANCE TAX IMPOSED BY THE WORKERS' COMPENSATION COMMISSION ON SELF INSURERS, SO AS TO PROVIDE THAT THE COMMISSION SHALL RETAIN A PORTION OF THE ANNUAL MAINTENANCE TAX REVENUE TO PAY THE SALARIES AND EXPENSES OF THE COMMISSION AND TO PROVIDE THAT THE COMMISSION SHALL RETAIN ONE-HALF OF THE INTEREST CHARGED ON DELINQUENT MAINTENANCE TAX FOR THE SAME PURPOSE.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
The Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
Recorded Vote
Senators ALLEN, COLEMAN, DAVIS, HAYES, HUTTO, MALLOY, MASSEY, McELVEEN, RANKIN, SETZLER, SHEHEEN and YOUNG wished the Journal to reflect that they abstained from consideration of and voting on H. 3632.
H. 3962 (Word version) -- Reps. Pitts, Parks and Riley: A BILL TO AMEND SECTION 7-7-290, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN GREENWOOD COUNTY, SO AS TO ADD CERTAIN PRECINCTS AND TO DESIGNATE A MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD.
H. 4192 (Word version) -- Reps. Merrill, Crosby, Daning, Jefferson, Rivers and Southard: A BILL TO AMEND SECTION 7-7-120, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN BERKELEY COUNTY, SO AS TO ADD FOUR PRECINCTS AND TO REDESIGNATE THE MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD.
H. 3093 (Word version) -- Reps. J.E. Smith, W.J. McLeod and Whipper: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 67 TO TITLE 12 SO AS TO ENACT THE "SOUTH CAROLINA ABANDONED BUILDINGS REVITALIZATION ACT", TO PROVIDE THAT A TAXPAYER MAKING INVESTMENTS OF A CERTAIN SIZE IN REHABILITATING AN ABANDONED BUILDING BASED ON THE POPULATION OF THE POLITICAL SUBDIVISION IN WHICH THE BUILDING IS LOCATED MAY AT THE TAXPAYER'S OPTION RECEIVE SPECIFIED INCOME TAX CREDITS OR CREDITS AGAINST THE PROPERTY TAX LIABILITY.
H. 3505 (Word version) -- Reps. Loftis, Bannister, Harrell, J.R. Smith, Brannon, Huggins, Kennedy, Ballentine, Cole, Hixon, McCoy, G.R. Smith, Hamilton, Tallon, Henderson, Forrester, Whipper and Hodges: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 44 TO TITLE 11 SO AS TO ENACT THE "HIGH GROWTH SMALL BUSINESS ACCESS TO CAPITAL ACT OF 2013" BY PROVIDING FOR STATE NONREFUNDABLE INCOME TAX CREDITS FOR QUALIFIED INVESTMENTS IN BUSINESSES MEETING CERTAIN CRITERIA AND PRIMARILY ENGAGED IN MANUFACTURING, PROCESSING, WAREHOUSING, WHOLESALING, SOFTWARE DEVELOPMENT, INFORMATION TECHNOLOGY SERVICES, RESEARCH AND DEVELOPMENT OR OTHER NONPROHIBITED SERVICES, TO ESTABLISH THE CRITERIA AND PROCEDURES FOR THE CREDIT, TO MAKE THE CREDIT TRANSFERABLE, AND TO PROVIDE FOR CERTAIN ADJUSTED NET CAPITAL GAIN AND LOSS COMPUTATIONS FOR INVESTOR TAXPAYERS WHO RECOGNIZE SUCH A GAIN OR LOSS ON THE SALE OF CREDIT ASSETS AS DEFINED IN THIS CHAPTER.
H. 3974 (Word version) -- Reps. Loftis, Brannon, Burns, Erickson, Bannister, Barfield, Hamilton, Harrell, Henderson, Hosey, Murphy, G.M. Smith, G.R. Smith and J.R. Smith: A BILL TO AMEND SECTION 12-54-240, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DISCLOSURE OF RECORDS AND RETURNS FILED WITH THE DEPARTMENT OF REVENUE, SO AS TO ALLOW THE DISCLOSURE OF CERTAIN INFORMATION TO THE SECRETARY OF STATE ABOUT A TAXPAYER WHO FILED AN INITIAL OR FINAL CORPORATE RETURN; AND BY ADDING SECTION 12-58-165 SO AS TO ALLOW THE DEPARTMENT OF REVENUE TO EXPUNGE THE RECORDING OF A LIEN ONCE THE LIEN IS FULLY PAID AND SATISFIED.
RETURNED TO THE HOUSE
H. 3360 (Word version) -- Reps. Owens, Daning, Hiott, Skelton, Simrill, Anthony, Bedingfield, Clemmons, Delleney, Hardwick, Henderson, Hixon, Limehouse, Nanney, Ott, Pope, G.R. Smith, J.E. Smith, Sottile, Stringer, Tallon, Taylor and Bales: A BILL TO AMEND SECTIONS 57-5-10, 57-5-70, AND 57-5-80, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE COMPOSITION OF THE STATE HIGHWAY SYSTEM, ADDITIONS TO THE STATE HIGHWAY SECONDARY SYSTEM, AND THE DELETION AND REMOVAL OF ROADS FROM THE STATE HIGHWAY SECONDARY SYSTEM, SO AS TO PROVIDE THAT ALL HIGHWAYS WITHIN THE STATE HIGHWAY SYSTEM SHALL BE CONSTRUCTED TO THE DEPARTMENT OF TRANSPORTATION STANDARDS, TO PROVIDE THE FUNDING SOURCES THAT THE DEPARTMENT USES TO CONSTRUCT AND MAINTAIN THESE HIGHWAYS, TO REVISE THE PROCEDURE AND WHEREBY ENTITIES TO WHICH THE DEPARTMENT MAY TRANSFER ROADS WITHIN THE STATE HIGHWAY SECONDARY SYSTEM; AND TO REVISE THE PROCEDURE WHEREBY THE DEPARTMENT MAY ADD A ROAD FROM THE COUNTY OR MUNICIPAL ROAD TO THE STATE HIGHWAY SYSTEM; AND TO REPEAL SECTION 57-5-90 RELATING TO THE ESTABLISHMENT AND MAINTENANCE OF BELT LINES AND SPURS.
Senator LEATHERMAN asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator LEATHERMAN asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Senator LEATHERMAN proposed the following amendment (NBD\3360C002.NBD.VR13), which was adopted:
Amend the bill, as and if amended, by adding an appropriately numbered new SECTION to read:
/SECTION __. Section 11-43-165 of the 1976 Code, as added by this act, takes effect July 1, 2013. Implementation of Section 11-43-165 is contingent upon fifty million dollars being appropriated to the South Carolina Department of Transportation in the 2013-2014 general appropriations act for the purposes provided for in Section 11-43-165./
Renumber sections to conform.
Amend title to conform.
Senator LEATHERMAN explained the amendment.
The question then was the third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 39; Nays 4
AYES
Alexander Allen Bennett
Campbell Campsen Cleary
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Hutto
Jackson Johnson Leatherman
Lourie Malloy Martin, Larry
Massey Matthews McElveen
McGill Nicholson Peeler
Pinckney Rankin Reese
Scott Setzler Shealy
Sheheen Thurmond Turner
Verdin Williams Young
Total--39
NAYS
Bright Bryant Corbin
Martin, Shane
Total--4
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
RETURNED TO THE HOUSE
H. 3464 (Word version) -- Reps. Allison, Brannon, Erickson, Bedingfield, Taylor, Kennedy, Clyburn, Anderson, G.A. Brown, Clemmons, H.A. Crawford, Douglas, Forrester, Goldfinch, Hamilton, Hardwick, Hixon, Horne, Hosey, Nanney, Pope, Powers Norrell, G.R. Smith, J.R. Smith, Stringer, Wood, Felder, Cobb-Hunter and Gilliard: A BILL TO AMEND SECTION 63-7-730, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EXPEDITED RELATIVE PLACEMENTS OF CHILDREN AT THE PROBABLE CAUSE HEARING, SO AS TO ENCOURAGE PLACEMENT OF THE CHILD WITH A GRANDPARENT OR OTHER RELATIVE OF THE FIRST OR SECOND DEGREE UNDER CERTAIN CIRCUMSTANCES; TO SET FORTH CRITERIA FOR THE COURT TO CONSIDER WHEN DECIDING WHETHER TO PLACE A CHILD WITH A GRANDPARENT OR OTHER RELATIVE OF THE FIRST OR SECOND DEGREE AT THE PROBABLE CAUSE HEARING; AND TO PROVIDE THAT IF THE COURT PLACES A CHILD WITH A GRANDPARENT OR OTHER RELATIVE OF THE FIRST OR SECOND DEGREE AT THE PROBABLE CAUSE HEARING, THE INDIVIDUAL MUST BE ADDED AS A PARTY TO THE ACTION FOR THE DURATION OF THE CASE OR UNTIL FURTHER ORDER OF THE COURT.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator BRYANT asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Senators LARRY MARTIN, MALLOY, COLEMAN and SHEALY proposed the following amendment (JUD3464.001), which was adopted:
Amend the bill, as and if amended, by striking SECTION 1 in its entirety and inserting:
/ SECTION 1. Section 63-7-730 of the 1976 Code is amended to read:
"Section 63-7-730. (A) If the court orders the child to remain in the legal custody of the department at the probable cause hearing finds at the probable cause hearing that the department made reasonable efforts to prevent removal of the child and that continuation of the child in the home would be contrary to the welfare of the child, the family court may order expedited placement of the child with a grandparent or other relative of the first or second degree. In making this expedited placement decision, the court shall consider the totality of the circumstances including, but not limited to, the individual's suitability, fitness, and willingness to serve as a placement for the child. A parent who complies with these requirements must be the first relative considered by the court for expedited placement. The court shall require the department to check the names of all adults in the home against the Central Registry of Child Abuse and Neglect, other relevant records of the department, county sex abuse registers, and records for the preceding five years of law enforcement agencies in the jurisdiction in which the person resides and, to the extent reasonably possible, jurisdictions in which the person has resided during that period. The court may hold open the record of the probable cause hearing for up to twenty-four hours to receive the these reports and based on these reports and other information introduced at the probable cause hearing, the court may order expedited placement of the child in the home of the relative. Nothing in this section precludes the department from requesting or the court from ordering pursuant to the department's request either a full study of the individual's home before placement or the licensing or approval of the individual's home before placement.
(B) If the court orders expedited placement of the child with a grandparent or other relative of the first or second degree, the individual may be added as a party to the action for the duration of the case or until further order of the court." /
Renumber sections to conform.
Amend title to conform.
Senator BRYANT explained the amendment.
The question then was the third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 45; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hembree
Hutto Jackson Johnson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Massey
Matthews McElveen McGill
Nicholson O'Dell Peeler
Pinckney Rankin Reese
Scott Setzler Shealy
Sheheen Thurmond Turner
Verdin Williams Young
Total--45
NAYS
Total--0
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
RETURNED TO THE HOUSE
H. 3602 (Word version) -- Reps. Weeks, Cobb-Hunter, Clemmons, Pope, Kennedy, M.S. McLeod, Tallon, Murphy, Crosby, McCoy, Dillard, Long, Bowen, Munnerlyn, Sellers, Limehouse, Brannon, Gilliard, Bales, Barfield, Bowers, Branham, G.A. Brown, R.L. Brown, Daning, Delleney, Edge, Funderburk, Henderson, Horne, Howard, Huggins, Jefferson, Loftis, Lowe, W.J. McLeod, Merrill, D.C. Moss, Norman, Powers Norrell, Quinn, Sandifer, Simrill, G.M. Smith, Spires, Taylor, Wells, Whipper, Wood, Newton, Riley, Anderson and Erickson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 16-13-131 SO AS TO CREATE AN OFFENSE RELATING TO STEALING GOODS OR MERCHANDISE FROM A MERCHANT BY AFFIXING A PRODUCT CODE AND TO PROVIDE A PENALTY; BY ADDING SECTION 16-13-135 SO AS TO DEFINE NECESSARY TERMS, CREATE AN OFFENSE RELATING TO RETAIL THEFT, AND TO PROVIDE A PENALTY; TO AMEND SECTION 16-13-440, RELATING TO THE USE OF A FALSE OR FICTITIOUS NAME OR ADDRESS TO OBTAIN A REFUND FROM A BUSINESS ESTABLISHMENT FOR MERCHANDISE, SO AS TO INCLUDE USING A FALSE OR ALTERED IDENTIFICATION CARD TO COMMIT CERTAIN RETAIL THEFT OFFENSES; TO AMEND SECTION 16-13-180, AS AMENDED, RELATING TO RECEIVING STOLEN GOODS, SO AS TO INCLUDE RECEIVING OR POSSESSING STOLEN GOODS WHEN THE PERSON IS ON NOTICE BY LAW ENFORCEMENT THAT THE GOODS ARE STOLEN; TO AMEND SECTION 17-25-323, RELATING TO DEFAULT ON COURT-ORDERED PAYMENTS INCLUDING RESTITUTION BY PERSONS ON PROBATION OR PAROLE AND CIVIL JUDGMENTS AND LIENS, SO AS TO INCLUDE DEFENDANTS WHO DEFAULT ON THE VARIOUS MAGISTRATES COURT OR MUNICIPAL COURT-ORDERED PAYMENTS INCLUDING RESTITUTION IN THE PURVIEW OF THE STATUTE AND TO PROVIDE THAT A FILING FEE OR OTHER FEE MAY NOT BE REQUIRED WHEN SEEKING A CIVIL JUDGMENT; TO AMEND SECTION 14-25-65, AS AMENDED, RELATING TO PENALTIES THE MAGISTRATES COURT MAY IMPOSE, RESTITUTION, AND CONTEMPT, SO AS TO ALLOW A MAGISTRATE TO CONVERT CERTAIN UNPAID COURT-ORDERED PAYMENTS TO A CIVIL JUDGMENT; AND TO AMEND SECTION 22-3-550, AS AMENDED, RELATING TO THE JURISDICTION OF THE MAGISTRATES COURT OVER MINOR OFFENSES, RESTITUTION, AND CONTEMPT, SO AS TO ALLOW A MAGISTRATE TO CONVERT CERTAIN UNPAID COURT-ORDERED PAYMENTS TO A CIVIL JUDGMENT AND TO INCLUDE VIOLATIONS OF SECTIONS 16-13-180 AND 16-13-440 IN THOSE OFFENSES FOR WHICH A MAGISTRATE HAS THE POWER TO SENTENCE A PERSON TO CONSECUTIVE TERMS OF IMPRISONMENT TOTALING MORE THAN NINETY DAYS.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Senator MALLOY proposed the following amendment (JUD3602.002), which was adopted:
Amend the bill, as and if amended, page 7, by striking lines 24-36, and inserting:
/ (B) However, a A magistrate shall does not have the power to sentence any a person to consecutive terms of imprisonment totaling more than ninety thirty days except for convictions resulting from violations of Chapter 11 of Title 34, pertaining to fraudulent checks, or violations of Section 16-13-110(B)(1), relating to shoplifting. Further, a A magistrate must shall specify an amount of restitution in damages at the time of sentencing as an alternative to any imprisonment of more than ninety thirty days which is lawfully imposed. The provisions of this subsection do not affect the transfer of criminal matters from the general sessions court made pursuant to Section 22-3-545." /
Renumber sections to conform.
Amend title to conform.
Senator MALLOY explained the amendment.
The question then was the third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 43; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Coleman
Corbin Courson Cromer
Davis Fair Gregory
Grooms Hayes Hembree
Hutto Johnson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey Matthews
McElveen McGill Nicholson
O'Dell Peeler Pinckney
Reese Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--43
NAYS
Total--0
The Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
RETURNED TO THE HOUSE
H. 3735 (Word version) -- Reps. Goldfinch, Hardwick, H.A. Crawford, Huggins, Hardee, Clemmons, Vick, Finlay, Chumley, Hamilton, Herbkersman, Hiott, Hixon, V.S. Moss, Owens, Pitts, Sottile, Wells, Wood, Powers Norrell, Knight and McCoy: A BILL TO AMEND SECTION 50-5-2730, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE STATE'S ADOPTION OF CERTAIN FEDERAL LAWS AND REGULATIONS THAT REGULATE THE TAKING OF FISH IN STATE WATERS, SO AS TO PROVIDE THAT LAWS AND REGULATIONS DO NOT APPLY TO BLACK SEA BASS (CENTROPRIATES STRIATA), TO PROVIDE A LAWFUL CATCH LIMIT AND SIZE FOR THIS SPECIES OF FISH, AND TO PROVIDE THAT THERE IS NO CLOSED SEASON ON THE CATCHING OF BLACK SEA BASS (CENTROPRIATES STRIATA).
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator CAMPSEN asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Senator CAMPSEN proposed the following amendment (NBD\3735C001.NBD.VR13), which was adopted:
Amend the bill, as and if amended, by deleting Section 50-5-2730(B) and inserting:
/ (B) This provision does not apply to Black Sea Bass (Centropristis striata) whose lawful catch limit is five fish per person per day or the same as the federal limit for Black Sea Bass, whichever is higher. The lawful minimum size is thirteen inches total length. Additionally, there is no closed season on the catching of Black Sea Bass (Centropristis striata). /
Renumber sections to conform.
Amend title to conform.
Senator CAMPSEN explained the amendment.
The question then was the third reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 40; Nays 1
AYES
Allen Bennett Bryant
Campbell Campsen Cleary
Coleman Corbin Courson
Cromer Davis Gregory
Grooms Hayes Hembree
Hutto Jackson Johnson
Lourie Malloy Martin, Larry
Martin, Shane Massey Matthews
McElveen McGill Nicholson
O'Dell Peeler Pinckney
Reese Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--40
NAYS
Bright
Total--1
There being no further amendments, the Bill was read the third time, passed and ordered returned to the House of Representatives with amendments.
The following Bills were read the third time and ordered sent to the House of Representatives:
S. 699 (Word version) -- Senator Verdin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 46-25-815 SO AS TO IMPOSE AN INSPECTION FEE OF ONE DOLLAR A TON ON THE DISTRIBUTION OR SALE OF COMMERCIAL FERTILIZER IN THIS STATE, TO PROVIDE THAT THIS FEE MUST BE REPORTED, PAID, AND ENFORCED IN THE SAME MANNER THAT THE EXISTING FIFTY CENTS A TON INSPECTION TAX ON THE SALE OF COMMERCIAL FERTILIZER IS REPORTED, PAID, AND ENFORCED, TO PROVIDE THAT THE REVENUES OF THIS INSPECTION FEE MUST BE RETAINED AND EXPENDED BY THE DIVISION OF REGULATORY AND PUBLIC SERVICE PROGRAMS OF CLEMSON UNIVERSITY (CLEMSON PSA) FOR THE SUPPORT OF THE DIVISION'S PROGRAMS, AND TO PROVIDE THAT UNEXPENDED FEE REVENUES AT THE END OF A FISCAL YEAR CARRY FORWARD TO THE SUCCEEDING FISCAL YEAR AND MUST BE USED FOR THE SAME PURPOSES.
Senator VERDIN explained the Bill.
S. 699--Recorded Vote
Senators SHANE MARTIN and BRIGHT desired to be recorded as voting against the third reading of the Bill.
S. 437 (Word version) -- Senators Cleary, Reese, Rankin, Campsen, Hembree, Davis, McGill, Thurmond, Campbell, Cromer and Ford: A BILL TO AMEND SECTION 12-43-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO VALUATION AND CLASSIFICATION OF PROPERTY FOR PURPOSES OF THE PROPERTY TAX, SO AS TO PROVIDE THAT THE OWNER-OCCUPANT OF RESIDENTIAL PROPERTY QUALIFIES FOR THE FOUR PERCENT ASSESSMENT RATIO ALLOWED OWNER-OCCUPIED RESIDENTIAL PROPERTY, IF THE OWNER IS OTHERWISE QUALIFIED AND THE RESIDENCE IS NOT RENTED FOR MORE THAN ONE HUNDRED DAYS A YEAR, AND TO DELETE OTHER REFERENCES TO RENTAL OF THESE RESIDENCES; AND TO AMEND SECTION 12-54-240, RELATING TO DISCLOSURE OF RECORDS, REPORTS, AND RETURNS WITH THE DEPARTMENT OF REVENUE, SO AS TO PROVIDE VERIFICATION THAT THE FEDERAL SCHEDULE E CONFORMS WITH THE SAME DOCUMENT REQUIRED BY A COUNTY ASSESSOR IS NOT PROHIBITED.
S. 160 (Word version) -- Senators Malloy, Cleary, Jackson, Shealy, Verdin, Fair, Alexander, L. Martin, Nicholson, Johnson, Lourie, Cromer, Reese, Thurmond, Massey, Rankin, Turner, Corbin, Setzler, Hayes and Hembree: A BILL TO AMEND CHAPTER 32, TITLE 59 OF THE 1976 CODE, RELATING TO THE COMPREHENSIVE HEALTH EDUCATION PROGRAM, BY ADDING SECTION 59-32-35 TO REQUIRE INSTRUCTION IN CARDIOPULMONARY RESUSCITATION AND THE USE OF AN AUTOMATED EXTERNAL DEFIBRILLATOR TO ALL STUDENTS ENROLLED IN THE SCHOOL DISTRICT AS A REQUIREMENT FOR GRADUATION FROM HIGH SCHOOL.
Senator HAYES explained the Bill.
S. 671 (Word version) -- Senator Massey: A BILL TO AMEND SECTION 7-7-240, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN EDGEFIELD COUNTY, SO AS TO REVISE CERTAIN PRECINCTS AND TO DESIGNATE A MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD.
S. 474 (Word version) -- Senator Setzler: A BILL TO AMEND SECTION 12-21-2420, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EXEMPTIONS FROM THE ADMISSIONS LICENSE TAX, SO AS TO EXEMPT ADMISSIONS CHARGED BY THE STATE MUSEUM.
S. 502 (Word version) -- Senator O'Dell: A BILL TO AUTHORIZE THE STARR-IVA WATER AND SEWER DISTRICT IN ANDERSON COUNTY TO PROVIDE WATER SERVICE TO A SPECIFIED AREA OF ABBEVILLE COUNTY, UPON THE CONSENT OF THE GOVERNING BODY OF ABBEVILLE COUNTY, TO SOLVE A CRITICAL WATER SERVICE PROBLEM.
The following Bill, having been read the second time, was ordered placed on the Third Reading Calendar:
Senator MALLOY asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 40; Nays 0; Present 1
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Corbin
Courson Cromer Davis
Fair Grooms Hayes
Hembree Hutto Jackson
Johnson Leatherman Martin, Larry
Martin, Shane Massey Matthews
McElveen McGill Nicholson
Peeler Pinckney Rankin
Reese Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--40
NAYS
Total--0
PRESENT
Malloy
Total--1
The Bill was read the second time, passed and ordered placed on the Third Reading Calendar.
H. 3717 (Word version) -- Reps. Quinn, Bannister, Allison, Sandifer, Sellers, Clemmons, Ballentine, Atwater, Toole, Kennedy, Vick, Erickson, Long, Bernstein, Munnerlyn, Horne, Funderburk, Brannon, Henderson, Wood, Dillard, M.S. McLeod, Whipper and R.L. Brown: A BILL TO AMEND SECTION 16-3-1700, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS FOR PURPOSES OF THE OFFENSES OF HARASSMENT AND STALKING, SO AS TO INCLUDE IN THE PURVIEW OF THE OFFENSES PERSONS WHO COMMIT THE OFFENSES WHILE SUBJECT TO THE TERMS OF A RESTRAINING ORDER ISSUED BY THE FAMILY COURT; AND TO AMEND SECTIONS 16-3-1710, 16-3-1720, AND 16-3-1730, ALL AS AMENDED, RELATING TO PENALTIES FOR HARASSMENT IN THE SECOND DEGREE, HARASSMENT IN THE FIRST DEGREE, AND STALKING, RESPECTIVELY, ALL SO AS TO INCLUDE PERSONS SUBJECT TO A RESTRAINING ORDER ISSUED BY THE FAMILY COURT.
Senator RANKIN asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator LARRY MARTIN proposed the following amendment (JUD3717.001), which was adopted:
Amend the bill, as and if amended, page 1, by striking lines 34-40, and inserting:
/ "( ) A person who commits the offense of harassment in any degree or stalking, as defined in this section, while subject to the terms of a restraining order issued by the family court may be charged with a violation of this article and, upon conviction, may be sentenced pursuant to the provisions of Section 16-3-1710, 16-3-1720, or 16-3-1730." /
Renumber sections to conform.
Amend title to conform.
Senator LARRY MARTIN explained the amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 43; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Hutto
Jackson Johnson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey Matthews
McElveen McGill Nicholson
Peeler Pinckney Rankin
Reese Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--43
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
H. 3342 (Word version) -- Reps. Hart and King: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 17-15-175 SO AS TO PROVIDE THAT A JUDGE MAY NOT ISSUE A BENCH WARRANT FOR FAILURE TO APPEAR UNLESS THE SOLICITOR OR CLERK OF COURT HAS PROVIDED NOTICE TO THE ATTORNEY OF RECORD BEFORE ISSUING THE BENCH WARRANT.
Senator HEMBREE asked unanimous consent to take the Bill up for immediate consideration.
There was no objection.
Senators ALLEN and HEMBREE proposed the following amendment (JUD3342.003), which was adopted:
Amend the bill, as and if amended, page 1, by striking SECTION 1 in its entirety and inserting:
/ SECTION 1. Chapter 15, Title 17 of the 1976 Code is amended by adding:
"Section 17-15-175. After an initial appearance, a circuit court judge may not issue a general sessions court bench warrant for failure to appear in court upon motion by a solicitor, unless the solicitor has conspicuously posted a list of potential bench warrants at the appropriate courthouse and on the solicitor's Internet website at least forty-eight hours before the bench warrant is requested. This section does not apply if the presiding judge sua sponte issues the bench warrant for failure to appear or the person has been personally served with an appearance date." /
Renumber sections to conform.
Amend title to conform.
Senator HEMBREE explained the amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 43; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Hutto
Jackson Johnson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey Matthews
McElveen McGill Nicholson
Peeler Pinckney Rankin
Reese Scott Setzler
Shealy Sheheen Thurmond
Turner Verdin Williams
Young
Total--43
NAYS
Total--0
The Bill was read the second time, passed and ordered to a third reading.
H. 4216 (Word version) -- Reps. Bales, Ballentine and Neal: A BILL TO AMEND SECTION 7-7-465, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF PRECINCTS IN RICHLAND COUNTY, SO AS TO REVISE AND ADD CERTAIN PRECINCTS, TO REDESIGNATE A MAP NUMBER ON WHICH THE NAMES OF THESE PRECINCTS MAY BE FOUND AND MAINTAINED BY THE OFFICE OF RESEARCH AND STATISTICS OF THE STATE BUDGET AND CONTROL BOARD, TO CORRECT REFERENCES, AND TO PROVIDE FOR ALTERNATE PRECINCT POLLING PLACES UNDER SPECIFIED CONDITIONS.
The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill.
Senator SCOTT proposed the following amendment (MS\4216C001.MS.AHB13), which was adopted:
Amend the bill, as and if amended, by deleting SECTION 2 in its entirety and inserting:
/ SECTION 2. This act takes effect on January 1, 2014. /
Renumber sections to conform.
Amend title to conform.
Senator SCOTT explained the amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 42; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Hutto
Jackson Johnson Leatherman
Lourie Malloy Martin, Larry
Martin, Shane Massey McElveen
McGill Nicholson Peeler
Pinckney Rankin Reese
Scott Setzler Shealy
Sheheen Thurmond Turner
Verdin Williams Young
Total--42
NAYS
Total--0
There being no further amendments, the Bill was read the second time, passed and ordered to a third reading.
PREVIOUSLY PROPOSED AMENDMENT TABLED
H. 3774 (Word version) -- Reps. Loftis, Hardwick, Clemmons, Hamilton, Huggins, J.R. Smith, Goldfinch, Hixon, Ryhal, Sottile and Spires: A JOINT RESOLUTION TO SUSPEND THE RUNNING OF CERTAIN GOVERNMENT APPROVALS AFFECTING THE DEVELOPMENT OF REAL PROPERTY WITHIN THE STATE FOR THE PERIOD BEGINNING JANUARY 1, 2013 AND ENDING DECEMBER 31, 2017; AND TO PROVIDE GOVERNMENTAL ENTITIES ISSUING SUCH APPROVALS SHALL PUBLISH NOTICE IN THE STATE REGISTER LISTING THE TYPES OF THESE APPROVALS IT ISSUES AND NOTING THE SUSPENSION OF THE RUNNING OF THE PERIOD OF THE APPROVAL AND TO PROVIDE AN EXCEPTION FOR UNITS OF LOCAL GOVERNMENT.
The Senate proceeded to a consideration of the Joint Resolution, the question being the adoption of the previously proposed amendment as follows.
Senator HUTTO proposed the following amendment (3774MW1), which was tabled:
Amend the joint resolution, as and if amended, page 4, by striking lines 41-42.
Renumber sections to conform.
Amend title to conform.
Senator HUTTO explained the amendment.
Senator VERDIN moved to lay the amendment on the table.
The amendment was laid on the table.
Senator VERDIN proposed the following amendment (3774R001.DBV), which was adopted:
Amend the joint resolution, as and if amended, page 4, by striking lines 41-42 and inserting:
/ (h) a coastal zone consistency certification issued by the department's Office of Ocean and Coastal Resource Management;
(i) a critical area permit issued by the department's Office of Ocean and Coastal Resource Management. /
Amend the joint resolution further, as and if amended, page 5, by striking lines 32-35 and inserting:
/ federal law or program;
(8) affect a Certificate of Need issued pursuant to Article 3, Chapter 7, Title 44 or a Demonstration of Need issued pursuant to Article 2, Chapter 96, Title 44; or
(9) affect SCDHEC-OCRM permits issued pursuant to R.30-12(N) Access to Coastal Islands. /
Renumber sections to conform.
Amend title to conform.
Senator VERDIN explained the amendment.
Senator VERDIN proposed the following amendment (3774R002.DBV), which was adopted:
Amend the joint resolution, as and if amended, page 5, by striking line 12 and inserting:
/ December 31, 2016. /
Amend the joint resolution, further, as and if amended, page 5, by striking line 27 and inserting:
/ of this joint resolution to December 31, 2016; /
Renumber sections to conform.
Amend title to conform.
Senator VERDIN explained the amendment.
The question then was second reading of the Bill.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 41; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Coleman
Corbin Cromer Davis
Fair Grooms Hayes
Hembree Hutto Johnson
Leatherman Lourie Malloy
Martin, Larry Martin, Shane Massey
Matthews McElveen McGill
Nicholson Peeler Pinckney
Rankin Reese Scott
Setzler Shealy Sheheen
Thurmond Turner Verdin
Williams Young
Total--41
NAYS
Total--0
There being no further amendments, the Joint Resolution was read the second time, passed and ordered to a third reading.
AMENDMENT PROPOSED
OBJECTION TO FURTHER CONSIDERATION OF THE BILL
H. 3014 (Word version) -- Reps. J.E. Smith, Bernstein, M.S. McLeod, McEachern, Weeks, Hart and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 29 TO TITLE 14 SO AS TO ENACT THE "VETERANS TREATMENT COURT PROGRAM ACT", TO REQUIRE THE CREATION AND ADMINISTRATION OF A VETERANS TREATMENT COURT PROGRAM IN EACH JUDICIAL CIRCUIT BY THE ATTORNEY GENERAL, TO PROVIDE FOR THE APPOINTMENT, POWERS, AND DUTIES OF A VETERANS TREATMENT COURT JUDGE, AND TO PROVIDE FOR REQUIREMENTS FOR AN OFFENDER TO QUALIFY FOR ADMISSION TO A VETERANS TREATMENT COURT PROGRAM.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary.
Senator MASSEY proposed the following amendment (JUD3014.003), which was adopted:
Amend the committee report, as and if amended, by striking lines 36-37 in their entirety, on page [3014-1] and inserting:
/ (7) receive training provided for this service through organizations which offer this type of training as determined by the solicitor's office; and /
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the perfecting amendment.
The Judiciary Committee proposed the following amendment (JUD3014.002), which was adopted:
Amend the bill, as and if amended, page 2, by striking line 29, in Section 14-29-30, as contained in SECTION 1, and inserting therein the following:
/ funds. Each circuit solicitor that accepts state funding for the /
Amend the bill further, as and if amended, page 3, by striking lines 6-8, in Section 14-29-40(B)(4) as contained in SECTION 1, and inserting therein the following:
/ (4) receive an allowance for mileage, subsistence, and per diem paid by the solicitor's office when engaged in the exercise of duties as a veterans treatment court judge; /
Amend the bill further, as and if amended, page 3, by striking line 15, in Section 14-29-40(B)(7) as contained in SECTION 1, and inserting therein the following:
/ (7) receive training provided for this service by organizations which offer this type of training; and /
Amend the bill further, as and if amended, page 3, by striking line 36, in Section 14-29-40(C)(5) as contained in SECTION 1, and inserting therein the following:
/ solicitor, a certified or licensed drug and alcohol counselor, a veterans affairs counselor, /
Amend the bill further, as and if amended, page 8, by striking lines 1-19, in Sections 14-29-70(A) and (B), as contained in SECTION 1, and inserting therein the following:
/ Section 14-29-70. (A) The transfer of an offender from the custody and jurisdiction of the circuit court to custody and jurisdiction of the veterans treatment court must be made by issue of a written order from the circuit court in response to the approval of the application by the veterans treatment court. This order must provide for the deferment of the offender's sentence pending the conclusion of the veterans treatment court program. The veterans treatment court then shall control and be responsible for the custody of the offender upon entry of the circuit court's order.
(B) Where a person fails to successfully complete the program and is consequently dismissed from the program, the veterans treatment court must transfer custody of the person to the circuit court for the imposition of the sentence. A court may not reduce a sentence for time spent participating in a veterans treatment court program and other conditions of the sentence. /
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the committee amendment.
Senator MASSEY proposed the following amendment (JUD3014.004):
Amend the bill, as and if amended, by striking Section 14-29-90 in its entirety, on page 8 and inserting:
/ Section 14-29-90. The General Assembly shall appropriate funds annually to an account to be maintained by the South Carolina Commission on Prosecution Coordination for the payment of mileage, subsistence, and per diem for veterans treatment court judges as provided by this chapter." /
Renumber sections to conform.
Amend title to conform.
Senator MASSEY explained the amendment.
Senator HAYES objected to further consideration of the Bill, as amended.
AMENDED, OBJECTION TO FURTHER CONSIDERATION
S. 387 (Word version) -- Senators O'Dell, Campbell, Cromer, Hembree, Setzler, McGill, Johnson and Ford: A BILL TO AMEND SECTION 12-10-95, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREDIT AGAINST WITHHOLDING FOR RETRAINING, SO AS TO INCREASE THE CREDIT, TO SPECIFY ELIGIBLE EMPLOYEES AND PROGRAMS, TO PROVIDE THAT A BUSINESS MAY NOT CLAIM THE CREDIT IF THE EMPLOYEE IS REQUIRED TO REIMBURSE OR PAY FOR THE COSTS OF THE RETRAINING, TO INCREASE THE MATCH AMOUNT FOR THE BUSINESS, AND TO PROVIDE THE PROGRAMS ARE SUBJECT TO REVIEW BY THE DEPARTMENT OF REVENUE AND THE STATE BOARD OF TECHNICAL AND COMPREHENSIVE EDUCATION; TO AMEND SECTION 12-10-105, AS AMENDED, RELATING TO THE ANNUAL FEE FOR A BUSINESS CLAIMING THE CREDIT, SO AS TO PROVIDE THAT THE ANNUAL FEE IS NOT APPLICABLE TO THE RETRAINING CREDIT; AND TO AMEND SECTION 12-20-105, AS AMENDED, RELATING TO THE CREDIT AGAINST THE LICENSE TAX FOR CERTAIN INFRASTRUCTURE EXPENSES, SO AS TO PROVIDE THAT AN ELIGIBLE PROJECT MAY BE OWNED OR CONSTRUCTED BY A GOVERNMENTAL ENTITY IF THE PROJECT IS EXPECTED TO CONTRIBUTE TO THE ECONOMIC DEVELOPMENT OF THE GOVERNMENTAL ENTITY, TO FURTHER SPECIFY ELIGIBLE INFRASTRUCTURE, AND TO PROVIDE THAT A GOVERNMENTAL ENTITY MAY SELL THE PROJECT AFTER THE COMPANY PAYS FOR THE INFRASTRUCTURE.
The Senate proceeded to a consideration of the Bill, the question being the third reading of the Bill.
Motion Under Rule 26B
Senator HEMBREE asked unanimous consent to make a motion to take up further amendments pursuant to the provisions of Rule 26B.
There was no objection.
Senator HEMBREE proposed the following amendment (NBD\387C001.NBD.VR13), which was adopted:
Amend the bill, as and if amended, by adding an appropriately numbered SECTION to read:
/SECTION __. A. Section 12-20-105(B) of the 1976 Code, as last amended by Act 290 of 2010, is further amended by adding a new item at the end to read:
"(3) In a county in which at least five million dollars in state accommodations tax imposed pursuant to Section 12-36-920 has been collected in at least one fiscal year, a county or municipality owned multiuse sports and recreational complex is considered an 'eligible project' promoting economic development for all purposes of the credit allowed pursuant to this section."
B. Section 12-20-105 of the 1976 Code, as last amended by Act 187 of 2012, is further amended by adding a new subsection at the end to read:
"(I) For the purposes of this section, for a qualifying project pursuant to subsection (B)(3), infrastructure includes all applicable provisions of subsection (C) applying to the development and construction of the sports and recreational complex and further includes costs of land acquisition and preparation, construction of facilities and venues in the complex, improvements and upgrades to existing facilities and venues, and any other capital costs incurred in the acquisition, construction, and operation of the complex."
C. This section takes effect upon approval by the Governor and applies for contributions made for a multiuse sports and recreational complex placed in service after 2011. /
Renumber sections to conform.
Amend title to conform.
Senator HEMBREE explained the amendment.
Senator BRYANT objected to further consideration of the Bill, as amended.
OBJECTION
H. 3412 (Word version) -- Reps. Harrell, Lucas, Clemmons, Herbkersman, Loftis, Barfield, Huggins, Bowen, K.R. Crawford, Allison, Merrill, Ballentine, McCoy, Wood, Erickson, Putnam, Bannister, Branham, Taylor, Limehouse, Southard, Atwater, Bingham, Brannon, Chumley, Cole, Crosby, Daning, Delleney, Gagnon, Gambrell, Goldfinch, Henderson, Hiott, Hixon, Kennedy, Lowe, D.C. Moss, V.S. Moss, Murphy, Newton, Owens, Patrick, Pitts, Pope, Rivers, Ryhal, Sandifer, G.M. Smith, G.R. Smith, J.R. Smith, Sottile, Spires, Stringer, Tallon, Thayer, Toole, White, Whitmire, Willis, Hardwick, Quinn, Hamilton, Forrester and Edge: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 12-36-2647 SO AS TO PROVIDE THAT THE SALES, USE, AND CASUAL EXCISE TAX REVENUES IN A FISCAL YEAR FROM THE SALE, USE, OR TITLING OF A VEHICLE REQUIRED TO BE REGISTERED AND LICENSED BY THE SOUTH CAROLINA DEPARTMENT OF MOTOR VEHICLES MUST BE CREDITED TO THE STATE NON-FEDERAL AID HIGHWAY FUND, AND TO PROVIDE FOR THE USE OF THESE REVENUES.
Senator SETZLER asked unanimous consent to take the Bill up for immediate consideration.
Senator HAYES objected.
OBJECTION
Senator MALLOY objected to the Bill.
S. 731 (Word version) -- Senator Leatherman: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 11-43-165 SO AS TO REQUIRE THE SOUTH CAROLINA DEPARTMENT OF TRANSPORTATION (DOT) TO TRANSFER TO THE SOUTH CAROLINA TRANSPORTATION INFRASTRUCTURE BANK (SIB) FROM NON-TAX SOURCES AN AMOUNT EQUAL TO THE AMOUNT OF GENERAL FUND REVENUE APPROPRIATED TO DOT IN THE ANNUAL GENERAL APPROPRIATIONS ACT FOR "HIGHWAY ENGINEERING PERMANENT IMPROVEMENTS", TO PROVIDE THAT THE AMOUNT APPROPRIATED TO DOT IN THE ANNUAL GENERAL APPROPRIATIONS ACT FOR "HIGHWAY ENGINEERING PERMANENT IMPROVEMENTS" ARE NOT SUBJECT TO ANY ACROSS THE BOARD REDUCTIONS, TO REQUIRE SIB TO USE THE TRANSFERRED FUNDS SOLELY TO FINANCE BRIDGE REPLACEMENT, REHABILITATION PROJECTS, AND EXPANSION AND IMPROVEMENTS TO EXISTING MAINLINE INTERSTATES, TO PROVIDE THAT DOT SHALL SUBMIT A LIST OF APPROPRIATE PROJECT RECOMMENDATIONS TO SIB, AND TO PROVIDE THAT THE FUNDS TRANSFERRED PURSUANT TO THIS SECTION MAY NOT BE EXPENDED ON ANY PROJECT APPROVED BY SIB BEFORE JULY 1, 2013.
Senator CLEARY objected to the Bill.
PREVIOUSLY PROPOSED AMENDMENT TABLED
AMENDMENT PROPOSED
OBJECTION TO FURTHER CONSIDERATION OF THE BILL
H. 3161 (Word version) -- Reps. Spires and Toole: A BILL TO AMEND SECTION 40-43-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS IN THE SOUTH CAROLINA PHARMACY PRACTICE ACT, SO AS TO DEFINE ADDITIONAL TERMS; TO AMEND SECTION 40-43-86, RELATING TO COMPOUNDING PHARMACIES, SO AS TO REVISE MINIMUM GOOD COMPOUNDING PRACTICES, TO PROVIDE A PHARMACIST MUST PERFORM A FINAL CHECK ON A PRODUCT COMPOUNDED BY A PHARMACY TECHNICIAN, TO MODIFY REQUIREMENTS FOR AN AREA USED FOR COMPOUNDING IN A PHARMACY, TO PROVIDE PHARMACISTS SHALL ENSURE CERTAIN EXPECTED FEATURES OF INGREDIENTS USED IN A FORMULATION, TO PROVIDE A MEANS FOR DETERMINING THE MAXIMUM BEYOND-USE DATE OF AN EXCESS AMOUNT OF A SPECIFIC COMPOUND IN CERTAIN CIRCUMSTANCES, TO REQUIRE CERTAIN WRITTEN POLICIES AND PROCEDURES APPLICABLE TO A COMPOUNDING AREA, AND TO PROVIDE THAT MATERIAL DATA SAFETY MUST BE READILY ACCESSIBLE TO PHARMACY PERSONNEL WHO WORK WITH DRUG SUBSTANCES OR BULK CHEMICALS, AND TO DELETE OBSOLETE LANGUAGE; AND TO AMEND SECTION 40-43-88, RELATING TO THE HANDLING OF STERILE PRODUCTS BY PHARMACIES, SO AS TO REVISE ASSOCIATED STANDARDS AND TO BROADEN THE APPLICATION OF THESE STANDARDS TO INCLUDE OTHER FACILITIES PERMITTED BY THE BOARD, AMONG OTHER THINGS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of the previously proposed amendment as follows.
Senator BRYANT proposed the following amendment (AGM\3161C003.AGM.AB13), which was tabled:
Amend the bill, as and if amended, by adding an appropriately numbered penultimate SECTION to read:
/ SECTION ___. Section 40-43-130(B) and (G)(1) of the 1976 Code is amended to read:
"(B) Each licensed pharmacist, as a condition of an active status license renewal, shall complete fifteen hours (1.5 CEU's) of American Council on Pharmaceutical Education (ACPE) accredited continuing pharmacy education or continuing medical education (CME), Category I, or both, each license year. Of The fifteen hours, a minimum of six hours must may be obtained through any combination of online courses and attendance at lectures, seminars, or workshops. At least fifty percent of the total number of hours required must be in drug therapy or patient management.
(G)(1) As a condition of registration renewal, a registered pharmacy technician shall complete ten hours of American Council on Pharmaceutical Education or CME I approved continuing education each year, beginning with the next renewal period after June 30, 2003. A minimum of four hours of the total These hours must be obtained through any combination of online courses and attendance at lectures, seminars, or workshops." /
Renumber sections to conform.
Amend title to conform.
Senator BRYANT explained the amendment.
Senator SETZLER moved to lay the amendment on the table.
The amendment was laid on the table.
Senator BRYANT proposed the following amendment (AGM\3161C001.AGM.AB13):
Amend the bill, as and if amended, SECTION 2, by deleting the SECTION in its entirety and inserting:
/ SECTION 2. Section 40-43-86(B)(4)(b) and (CC) of the 1976 Code is amended to read:
"(b) The pharmacist-in-charge shall develop and implement written policies and procedures to specify the duties to be performed by pharmacy technicians. The duties and responsibilities of these personnel shall must be consistent with their training and experience. These policies and procedures shall, at a minimum, specify that pharmacy technicians are to be personally supervised by a licensed pharmacist who has the ability to control and who is responsible for the activities of pharmacy technicians and that pharmacy technicians are not assigned duties that may be performed only by a licensed pharmacist. One pharmacist may not supervise more than three pharmacy technicians at a time; through June 30, 2006, at least one of these three technicians must be state-certified, and after June 30, 2006, at least two of these three technicians must be state-certified. If a pharmacist supervises only one or two pharmacy technicians, these technicians are not required to be state-certified. Pharmacy technicians do not include personnel in the prescription area performing only clerical functions, including data entry up to the point of dispensing, as defined in Section 40-43-30(14).
(CC)(1) The provisions of this subsection only apply to the compounding of medication by pharmacies permitted in the State of South Carolina.
(2) The following are the minimum current good compounding practices for the preparation of medications by pharmacists licensed in the State for dispensing or administering, or both, to humans or animals:
(a) Pharmacists engaged in the compounding of drugs shall operate in conformance with applicable laws regulating the practice of pharmacy;
(b) Based on the existence of a pharmacist/patient/practitioner relationship and the presentation of a valid prescription, or in anticipation of prescription medication orders based on routine, regularly observed prescribing patterns, pharmacists may compound, for an individual patient medications that are commercially available in the market place for which the components are commercially available;
(c) Pharmacists shall receive, store, or use drug substances for compounding that meet official compendia requirements, or of a chemical grade in one of the following categories: chemically pure (CP), analytical reagent (AR), American Chemical Society (ACS), or, if other than this, drug substances that meet the accepted standard of the practice of pharmacy;
(d) Pharmacists may compound drugs before receiving a valid prescription based on a history of receiving valid prescriptions that have been generated solely within an established pharmacist/patient/practitioner relationship, for all such products compounded at the pharmacy as required by the Board of Pharmacy A compounder shall first attempt to use components manufactured in an FDA-registered facility. When components cannot be obtained from an FDA-registered facility, a compounder shall use his professional judgment in selecting an acceptable and reliable source and shall establish purity and safety by reasonable means, to include Certificate of Analysis, manufacturer reputation, and reliability of source.
(e) For components that do not have expiration dates assigned by the manufacturer or supplier, a compounder shall label the container with the date of receipt and assign a conservative expiration date, not to exceed three years after receipt of the component based on the nature of the component and its degradation mechanism, the container in which it is packaged, and the storage conditions;
(ef) Pharmacists may not offer compounded medications to other pharmacies for resale; however, pharmacists may compound products preparations based on an order from a practitioner for use by practitioners for patient use administration to a patient in institutional or office settings. Compounding pharmacies/pharmacists may advertise or otherwise promote the fact that they provide prescription compounding services, e.g., chemicals, devices, and information, when requested; however, they may not solicit business by promoting to compound specific drug products, e.g., like a manufacturer;
(fg) The compounding of legend drugs in anticipation of receiving prescriptions without a historical basis or the distribution of compounded products preparations without a patient/practitioner/pharmacist relationship is considered manufacturing.
(h) Physicians who administer compounded medications in an office or licensed ambulatory surgical facility setting shall be allowed to order and purchase those medications from the compounding pharmacy, store them in the office for future use but not for resale, and administer those medications according to their usual physician/patient/pharmacy practice relationship. A prescription for an individual patient for each administration of the drug shall not be required.
(i) Institutional pharmacies may order and store compounded preparations, both sterile and nonsterile, from compounding pharmacies in anticipation of patient orders based on the existence of a pharmacist/patient/practitioner relationship for regularly observed prescribing patterns. A chart order from a practitioner will be required for administration in a institutional facility.
(3)(a) Pharmacists engaging in compounding shall maintain proficiency through current awareness and training. Continuing education shall include training in the art and science of compounding and the rules and regulations of compounding.
(b) Pharmacy technicians may assist the pharmacist in compounding. The pharmacist is responsible for training and monitoring the pharmacy technician. The pharmacy technician's duties must be consistent with the training received. The pharmacist must perform the final check of the compound preparation to determine if the preparation is ready to dispense.
(c) Personnel engaged in the compounding of medications shall wear clean clothing appropriate to the operation being performed. Protective apparel, such as coats, jackets, aprons, gowns, hand or arm coverings, or masks must be worn as necessary to protect personnel from chemical exposure and medication or chemical contamination.
(d) Only personnel authorized by the responsible pharmacist may be in the immediate vicinity of the drug compounding operation. A person shown at any time, either by medical examination or pharmacist determination, to have an apparent illness or open lesions that may adversely affect the safety or quality of a drug product preparation being compounded must be excluded from direct contact with components, medication containers, closures, in-process materials, and medication products preparations until the condition is corrected or determined by competent medical personnel not to jeopardize the safety or quality of the products preparations being compounded. All personnel who assist the pharmacists in compounding procedures must be instructed to report to the pharmacist any health conditions that may have an adverse effect on drug products preparations.
(4)(a) Pharmacists engaging in compounding shall have a specifically designated and an adequate area (space) for the orderly complexity level of compounding of prescriptions that is maintained in a good state of repair for the placement of material and equipment. Sterile compounding must be performed in a separate area in compliance with Section 40-43-88.
(b) Bulk medications and other chemicals or materials used in the compounding of medication must be stored in adequately labeled containers in a clean, dry, and temperature-controlled area or, if required, under proper refrigeration.
(c) Adequate lighting and ventilation must be provided in all drug compounding areas. Potable water must be supplied under continuous positive pressure in a plumbing system free of defects that could contribute contamination to a compounded drug product preparation. Adequate washing facilities, easily accessible to the compounding areas of the pharmacy, must be provided. These facilities shall include, but are not limited to, hot and cold water, soap or detergent, and air-dryers or single-use towels.
(d) The area used for the compounding of drugs must be maintained in a clean and sanitary condition. It must be free of infestation by insects, rodents, and other vermin. Trash must be held and disposed of in a timely and sanitary manner. Sewage and other refuse in and from the pharmacy and immediate medication compounding areas must be disposed of in a safe and sanitary manner.
(e) If sterile products preparations are being compounded, the pharmacist shall comply with Section 40-43-88 as applicable to the procedure.
(f) If radiopharmaceuticals are being compounded, the pharmacist shall comply with Section 40-43-87 as applicable to the procedure.
(g) If drug products with special precautions for contamination, such as penicillin or hazardous drugs, are involved in a compounding procedure, appropriate measures, including either the dedication of equipment or meticulous cleaning of contaminated equipment before its use for the preparation of other drugs, must be utilized in order to prevent cross-contamination.
(5)(a) Equipment and utensils used for compounding must be of appropriate design and capacity and stored in a manner to protect from contamination. In addition, all equipment and utensils must be cleaned and sanitized before use to prevent contamination that would alter the safety or quality of the drug product preparation beyond that desired. The pharmacist is responsible for determining suitability for use. In the case of sterile compounding, the pharmacist shall comply with Section 40-43-88 as applicable to equipment and utensils.
(b) Automatic, mechanical, electronic, or other equipment used in compounding must be routinely inspected, calibrated, if necessary, or checked to ensure proper performance.
(c) The pharmacist shall ensure that the proper container is selected to dispense the finished compounded prescription, whether sterile or nonsterile.
(6)(a) The pharmacist shall ensure that there are formulas and logs maintained either electronically or manually. Formulas must be comprehensive and include ingredients, amounts, methodology, and equipment, if needed, and special information regarding sterile compounding.
(b) The pharmacist shall ensure that components used in compounding are accurately weighed, measured, or subdivided as appropriate at each stage of the compounding procedure to conform to the formula being prepared. Any chemical transferred to a container from the original container must be labeled with the same information as on the original container and the date of transfer placed on the label.
(c) The pharmacist shall establish and conduct procedures so as to monitor the output of compounded prescriptions, i.e., capsule weight variation, adequacy of mixing, clarity, pH of solutions, and, where appropriate, procedures to prevent microbial contamination of medications purported to be sterile.
(7)(a) The pharmacist shall label any excess compounded product preparation so as to reference it to the formula used and the assigned control number and the estimated beyond-use date based on the pharmacist's professional judgment, appropriate testing, or published data. In the absence of stability information applicable to the specific compound, the maximum BUD must be determined by:
(i) the type of formulation, such as nonaqueous, water containing, or topical; and
(ii) professional judgment.
(b) The product preparation must be stored appropriately.
(c) At the completion of compounding the prescription, the pharmacist shall examine the prescription for correct labeling.
(8) The pharmacist shall keep records of all compounded products preparations for a period of time as other prescriptions as required by the Board of Pharmacy. These records must be readily available for authorized inspection during the retention period at the establishment. These records are subject to duplication by photocopying or other means of reproduction as part of the inspection.
(9) All significant procedures performed in the compounding area must be covered in written policies and procedures. These procedures must be developed for the facility, equipment, personnel, preparation, packaging, and storage of compounded preparations and ingredients to ensure accountability, accuracy, quality safety, and uniformity in compounding as appropriate for the level of compounding performed at the facility.
(10) Material Data Safety should be readily accessible from an internet website or otherwise to all personnel working with drug substances or bulk chemicals located on the compounding facility premises, and personnel should be instructed on how to retrieve needed information." /
Renumber sections to conform.
Amend title to conform.
Senator BRYANT explained the amendment.
Senator SCOTT moved to lay the amendment on the table.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 20; Nays 23
AYES
Allen Cleary Cromer
Gregory Hayes Hutto
Jackson Johnson Lourie
Matthews McElveen McGill
Nicholson Pinckney Rankin
Reese Scott Setzler
Sheheen Williams
Total--20
NAYS
Alexander Bennett Bright
Bryant Campbell Campsen
Corbin Courson Davis
Fair Grooms Hembree
Leatherman Malloy Martin, Larry
Martin, Shane Massey Peeler
Shealy Thurmond Turner
Verdin Young
Total--23
The Senate refused to lay the amendment on the table.
Senator SCOTT argued contra to the amendment.
Senator BRYANT objected to further consideration of the Bill.
CARRIED OVER
H. 3540 (Word version) -- Reps. Harrell, J.E. Smith, Bales, Hosey, Cobb-Hunter, Bannister, J.R. Smith, Patrick, Brannon, Erickson, Taylor, Huggins, Kennedy, Ballentine, Bernstein, Sellers, Williams, Jefferson, M.S. McLeod, Atwater, Bowers, R.L. Brown, Cole, Douglas, George, Hixon, Long, McCoy, Mitchell, Pitts, Pope, G.R. Smith, Tallon, Wood, Weeks, Knight and Hart: A BILL TO AMEND SECTION 1-3-240, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE REMOVAL OF OFFICERS BY THE GOVERNOR, SO AS TO ADD THE ADJUTANT GENERAL TO THE LIST OF OFFICERS OR ENTITIES THE GOVERNING BOARD OF WHICH MAY BE REMOVED BY THE GOVERNOR ONLY FOR CERTAIN REASONS CONSTITUTING CAUSE; TO AMEND SECTION 25-1-320, RELATING TO THE STATE ADJUTANT GENERAL, SO AS TO PROVIDE THAT BEGINNING UPON THE EXPIRATION OF THE TERM OF THE ADJUTANT GENERAL SERVING IN OFFICE ON THE DATE OF THE 2014 GENERAL ELECTION, THE ADJUTANT GENERAL MUST BE APPOINTED BY THE GOVERNOR UPON THE ADVICE AND CONSENT OF THE SENATE FOR A FOUR-YEAR TERM COMMENCING ON THE FIRST WEDNESDAY FOLLOWING THE SECOND TUESDAY IN JANUARY THAT FOLLOWS THE GENERAL ELECTION THAT MARKS THE MIDTERM OF THE GOVERNOR, EXCEPT THAT THE INITIAL TERM OF THE FIRST ADJUTANT GENERAL APPOINTED PURSUANT TO THIS ACT MUST BE FOR TWO YEARS SO AS TO ALLOW SUBSEQUENT TERMS TO BE STAGGERED WITH THAT OF THE GOVERNOR, AND TO ESTABLISH CERTAIN QUALIFICATIONS FOR THE OFFICE OF ADJUTANT GENERAL; TO AMEND SECTION 25-1-340, AS AMENDED, RELATING TO VACANCIES IN THE OFFICE OF ADJUTANT GENERAL, SO AS TO DELETE A REFERENCE TO THE ELIGIBILITY REQUIREMENTS OF CONSTITUTIONAL OFFICERS; AND TO PROVIDE THAT THE ABOVE PROVISIONS ARE EFFECTIVE UPON THE RATIFICATION OF AMENDMENTS TO SECTION 7, ARTICLE VI, AND SECTION 4, ARTICLE XIII OF THE CONSTITUTION OF THIS STATE DELETING THE REQUIREMENT THAT THE STATE ADJUTANT GENERAL BE ELECTED BY THE QUALIFIED ELECTORS OF THIS STATE.
On motion of Senator MASSEY, the Bill was carried over.
H. 3459 (Word version) -- Reps. Sandifer, Bales, J.E. Smith and Erickson: A BILL TO AMEND SECTION 40-2-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE SOUTH CAROLINA BOARD OF ACCOUNTANCY, SO AS TO PROVIDE THE DEPARTMENT OF LABOR, LICENSING AND REGULATION SHALL DESIGNATE CERTAIN PERSONNEL FOR THE EXCLUSIVE USE OF THE BOARD, TO PROHIBIT THE DEPARTMENT FROM ASSIGNING OTHER WORK TO THESE PERSONNEL WITHOUT APPROVAL OF THE BOARD, AND TO PROVIDE THESE PERSONNEL MAY BE TERMINATED BY THE DIRECTOR OF A MAJORITY OF THE BOARD; TO AMEND SECTION 40-2-30, RELATING TO THE PRACTICE OF ACCOUNTANCY, SO AS TO PROVIDE A CERTIFIED PUBLIC ACCOUNTANT LICENSED BY THE BOARD IS EXEMPT FROM LICENSURE REQUIREMENTS OF PRIVATE SECURITY AND INVESTIGATION AGENCIES; AND TO AMEND SECTION 40-2-70, RELATING TO POWERS AND DUTIES OF THE BOARD, SO AS TO PROVIDE THE BOARD MAY CONDUCT PERIODIC INSPECTIONS OF LICENSEES OR FIRMS; AND TO AMEND SECTION 40-2-80, RELATING TO INVESTIGATIONS OF ALLEGED VIOLATIONS, SO AS TO PROVIDE THE DEPARTMENT SHALL DIRECT THE INVESTIGATOR ASSIGNED TO THE BOARD TO INVESTIGATE AN ALLEGED VIOLATION TO DETERMINE THE EXISTENCE OF PROBABLE CAUSE MERITING FURTHER PROCEEDINGS.
On motion of Senator MALLOY, the Bill was carried over.
H. 3878 (Word version) -- Reps. Murphy, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H.A. Crawford, K.R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Munnerlyn, Nanney, Neal, Newton, Norman, Ott, Owens, Parks, Patrick, Pitts, Pope, Powers Norrell, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G.M. Smith, G.R. Smith, J.E. Smith, J.R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO MEMORIALIZE THE FULL COMMITTEE OF THE INTERNATIONAL OLYMPIC COMMITTEE TO OPPOSE THE DECISION OF ITS EXECUTIVE BOARD AND REINSTATE WRESTLING AS A CORE SPORT OF THE SUMMER OLYMPIC GAMES.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4149 (Word version) -- Rep. Erickson: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION AND BEAUFORT COUNTY ERECT APPROPRIATE SIGNS OR MARKERS ALONG UNITED STATES HIGHWAY 21 IN BEAUFORT COUNTY AS IT ENTERS ST. HELENA ISLAND FROM BOTH LADY'S ISLAND AND HUNTING ISLAND THAT CONTAIN THE WORDS "ST. HELENA ISLAND-HOME OF THE 2013 AMERICAN IDOL WINNER CANDICE GLOVER".
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4200 (Word version) -- Rep. Howard: A CONCURRENT RESOLUTION TO RECOGNIZE THE DEVASTATING EFFECTS CAUSED BY MENINGOCOCCAL DISEASE AND RAISE PUBLIC AWARENESS OF ITS SERIOUS IMPACT ON CITIZENS AND COMMUNITIES IN THE PALMETTO STATE.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4201 (Word version) -- Reps. G.R. Smith, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bannister, Barfield, Bedingfield, Bernstein, Bingham, Bowen, Bowers, Branham, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, H.A. Crawford, K.R. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Edge, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hardwick, Harrell, Hart, Hayes, Henderson, Herbkersman, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Kennedy, King, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Munnerlyn, Murphy, Nanney, Neal, Newton, Norman, Ott, Owens, Parks, Patrick, Pitts, Pope, Powers Norrell, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sabb, Sandifer, Sellers, Simrill, Skelton, G.M. Smith, J.E. Smith, J.R. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Toole, Vick, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Wood: A CONCURRENT RESOLUTION TO RECOGNIZE AUGUST 20, 2013, AS DIABETIC PERIPHERAL NEUROPATHY DAY AT THE STATE CAPITOL TO RAISE AWARENESS OF THE DELETERIOUS EFFECTS OF NERVE DAMAGE DUE TO DIABETIC PERIPHERAL NEUROPATHY.
The Concurrent Resolution was adopted, ordered returned to the House.
H. 4268 (Word version) -- Reps. D.C. Moss, V.S. Moss, Pope and King: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF TRANSPORTATION NAME THE PORTION OF SOUTH CAROLINA HIGHWAY 55 IN YORK COUNTY FROM ITS INTERSECTION WITH THE YORK/CHEROKEE COUNTY LINE TO ITS INTERSECTION WITH SOUTH CAROLINA HIGHWAY 161 "STATE REPRESENTATIVE HUGH J. LOVE HIGHWAY" AND ERECT APPROPRIATE MARKERS OR SIGNS ALONG THIS PORTION OF HIGHWAY THAT CONTAIN THE WORDS "STATE REPRESENTATIVE HUGH J. LOVE HIGHWAY".
The Concurrent Resolution was adopted, ordered returned to the House.
THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD.
On motion of Senator PEELER, the Senate agreed to dispense with the Motion Period.
HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF REPORTS OF COMMITTEES OF CONFERENCE AND FREE CONFERENCE.
SUBSTITUTION OF SENATE CONFEREE
H. 3638 (Word version) -- Reps. Harrell, Stavrinakis, Limehouse and Gilliard: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 55-1-80 SO AS TO AUTHORIZE THE APPOINTMENT OF ADDITIONAL MEMBERS TO COUNTY AVIATION COMMISSIONS AND TO PROVIDE THAT IN COUNTIES WITH TWO MUNICIPALITIES WITH A POPULATION IN EXCESS OF FIFTY THOUSAND, THE MAYORS OF THESE MUNICIPALITIES SHALL SERVE, EX OFFICIO, AS MEMBERS OF THE COMMISSION.
On motion of Senator COURSON, with unanimous consent, the Senate appointed Senator PINCKNEY in lieu of Senator FORD on the Committee of Conference to H. 3638 and a message was sent to the House accordingly.
S. 2--REPORT OF THE
S. 2 (Word version) -- Senators Campsen, L. Martin, Cromer, Hayes and Grooms: A BILL TO ESTABLISH THE "EQUAL ACCESS TO THE BALLOT ACT", BY AMENDING SECTION 8-13-1356, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE FILING OF A STATEMENT OF ECONOMIC INTERESTS BY A CANDIDATE, TO PROVIDE THAT A CANDIDATE WHO IS NOT A PUBLIC OFFICIAL AND A CANDIDATE WHO IS A PUBLIC OFFICIAL SHALL ELECTRONICALLY FILE OR UPDATE A STATEMENT OF ECONOMIC INTERESTS, AS APPLICABLE, PRIOR TO FILING A STATEMENT OF INTENTION OF CANDIDACY OR NOMINATION FOR PETITION; TO AMEND SECTION 7-11-15, TO PROVIDE THAT THE FILING PERIOD RUNS FROM MARCH TWENTY-THIRD TO MARCH THIRTIETH, TO REQUIRE THAT THE PARTY EXECUTIVE COMMITTEE NOT ACCEPT A STATEMENT OF INTENTION OF CANDIDACY UNLESS THE COMMITTEE VERIFIES THAT THE CANDIDATE FILED AN ELECTRONIC STATEMENT OF ECONOMIC INTEREST, AND TO PROVIDE THAT INTENTIONS OF CANDIDACY ARE TO BE SUBMITTED TO THE APPROPRIATE ELECTION COMMISSION BY NOON ON THE FIFTH DAY AFTER THE FILING DEADLINE.
On motion of Senator CAMPSEN, with unanimous consent, the Report of the Committee of Conference was taken up for immediate consideration.
Senator CAMPSEN spoke on the report.
The question then was adoption of the Report of the Committee of Conference.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 40; Nays 0
AYES
Alexander Allen Bennett
Bright Bryant Campbell
Campsen Cleary Coleman
Corbin Courson Cromer
Davis Fair Hayes
Hembree Hutto Jackson
Johnson Leatherman Lourie
Malloy Martin, Larry Martin, Shane
Massey Matthews McGill
Nicholson O'Dell Peeler
Pinckney Reese Scott
Setzler Shealy Sheheen
Thurmond Turner Williams
Young
Total--40
NAYS
Total--0
The Report of the Conference Committee was adopted as follows:
S. 2--Conference Report
The General Assembly, Columbia, S.C., May 31, 2013
The COMMITTEE OF CONFERENCE, to whom was referred:
S. 2 (Word version) -- Senators Campsen, L. Martin, Cromer, Hayes and Grooms: A BILL TO ESTABLISH THE "EQUAL ACCESS TO THE BALLOT ACT", BY AMENDING SECTION 8-13-1356, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE FILING OF A STATEMENT OF ECONOMIC INTERESTS BY A CANDIDATE, TO PROVIDE THAT A CANDIDATE WHO IS NOT A PUBLIC OFFICIAL AND A CANDIDATE WHO IS A PUBLIC OFFICIAL SHALL ELECTRONICALLY FILE OR UPDATE A STATEMENT OF ECONOMIC INTERESTS, AS APPLICABLE, PRIOR TO FILING A STATEMENT OF INTENTION OF CANDIDACY OR NOMINATION FOR PETITION; TO AMEND SECTION 7-11-15, TO PROVIDE THAT THE FILING PERIOD RUNS FROM MARCH TWENTY-THIRD TO MARCH THIRTIETH, TO REQUIRE THAT THE PARTY EXECUTIVE COMMITTEE NOT ACCEPT A STATEMENT OF INTENTION OF CANDIDACY UNLESS THE COMMITTEE VERIFIES THAT THE CANDIDATE FILED AN ELECTRONIC STATEMENT OF ECONOMIC INTEREST, AND TO PROVIDE THAT INTENTIONS OF CANDIDACY ARE TO BE SUBMITTED TO THE APPROPRIATE ELECTION COMMISSION BY NOON ON THE FIFTH DAY AFTER THE FILING DEADLINE.
Beg leave to report that they have duly and carefully considered the same and recommend:
That the same do pass with the following amendments:
Amend the bill, as and if amended, by striking all after the enacting words and inserting:
/ SECTION 1. Section 7-11-10 of the 1976 Code, as last amended by Act 419 of 1982, is further amended to read: "Section 7-11-10. Nominations for candidates for the offices to be voted on in a general or special election may be by political party primary, by political party convention, or by petition; provided however, no a person who was defeated as a candidate for nomination to an office in a party primary or party convention shall not have his name placed on the ballot for the ensuing general or special election, except that this proviso shall does not prevent a defeated candidate from later becoming his party's nominee for that office in that election if the candidate first selected as the party's nominee dies, resigns, is disqualified, or otherwise ceases to become the party's nominee for such that office before the election is held."
SECTION 2. Section 7-11-15 of the 1976 Code is amended to read:
"Section 7-11-15. (A) In order to qualify as a candidate to run in the general election, all candidates seeking nomination by political party primary or political party convention must file a statement of intention of candidacy and party pledge and submit any filing fees between noon on March sixteenth and noon on March thirtieth as provided in this section.
(1) Candidates Except as otherwise provided in this section, candidates seeking nomination for a statewide, congressional, or district office that includes more than one county must file their statements of intention of candidacy, and party pledge and submit any filing fees with the state executive committee of their respective party State Election Commission.
(2) Candidates seeking nomination for the State Senate or House of Representatives must file their statements of intention of candidacy and party pledge and submit any filing fees with the county executive committee of their respective party election commission in the county of their residence. The county committees must, within five days of the receipt of the statements, transmit the statements along with the applicable filing fees to the respective state executive committees. However, the county committees must report all filings to the state committees no later than five p.m. on March thirtieth. The state executive committees must certify candidates pursuant to Section 7-13-40.
(3) Candidates seeking nomination for a countywide or less than countywide office shall file their statements of intention of candidacy and party pledge and submit any filing fees with the county executive committee of their respective party election commission in the county of their residence.
(B) Except as provided herein, the county executive committee of any political party election commission with whom statements of intention of candidacy the documents in subsection (A) are filed must file, in turn, provide a copy of all statements of intention of candidacy, the party pledge, receipt with the county election commission by noon on the tenth and filing fees, to the appropriate political party executive committee within two days following the deadline for filing statements by candidates. If the tenth second day falls on Saturday, Sunday, or a legal holiday, the statements statement of intention of candidacy, party pledge, and filing fee must be filed by noon the following day that is not a Saturday, Sunday, or legal holiday. The state executive committee of any political party with whom statements of intention of candidacy are filed must file, in turn, all the statements of intention of candidacy with the State Election Commission by noon on the tenth day following the deadline for filing statements by candidates. If the tenth day falls on Saturday, Sunday, or a legal holiday, the statements must be filed by noon the following day. No candidate's name may appear on a primary election ballot, convention slate of candidates, general election ballot, or special election ballot, except as otherwise provided by law, if (1) the candidate's statement of intention of candidacy and party pledge has not been filed with the County Election Commission or State Election Commission, as the case may be, as well as any filing fee, by the deadline and (2) the candidate has not been certified by the appropriate political party as required by Sections 7-13-40 and 7-13-350, as applicable. The candidate's name must appear if the candidate produces the signed and dated copy of his timely filed statement of intention of candidacy. An error or omission by a person seeking to qualify as a candidate pursuant to this section that is not directly related to a constitutional or statutory qualification for that office must be construed in a manner that favors the person's access to the ballot.
(C) The statement of intention of candidacy required in this section and in Section 7-13-190(B) must be on a form designed and provided by the State Election Commission. This form, in addition to all other information, must contain an affirmation that the candidate meets, or will meet by the time of the general election, or as otherwise required by law, the qualifications for the office sought. It must be filed in triplicate by the candidate The candidate must file three signed copies and the political party committee election commission with whom it is filed must stamp it each copy with the date and time received, sign it, keep one copy, return one copy to the candidate, and send one copy to either the county election commission or the State Election Commission, as the case may be the appropriate political party executive committee.
(D) The candidate must file three signed copies of the party pledge, as required pursuant to Section 7-11-210, and the election commission with whom it is filed must stamp each copy with the date and time received, return one copy to the candidate, and send one copy to the appropriate political party executive committee.
(E) The candidate must sign a receipt for the filing fee, and the election commission with whom it is filed must stamp the receipt with the date and time the filing fee was received, provide one copy to the candidate and provide one copy to the appropriate political executive party. The filing fee must be made payable to the appropriate political party.
(F) If, after the closing of the time for filing statements of intention of candidacy the documents required pursuant to this section, there are not more than two candidates for any one office and one or more of the candidates dies, or withdraws, the state or county committee, as the case may be, if the nomination is by political party primary or political party convention only may, in its discretion, afford opportunity for the entry of other candidates for the office involved; however, for the office of State House of Representatives or State Senator, the discretion must be exercised by the state committee.
(G) The county chairman of a political party and the chairman of the state executive committee of a political party may designate a person to observe the filings made at the election commission pursuant to this section.
(H) The provisions of this section do not apply to nonpartisan school trustee elections in any school district where local law provisions provide for other dates and procedures for filing statements of candidacy or petitions, and to the extent the provisions of this section and the local law provisions conflict, the local law provisions control."
SECTION 3. Section 7-11-30 of the 1976 Code, as last amended by Act 403 of 1984, is further amended to read:
"Section 7-11-30. If a party nominates candidates by conventions, the state convention shall nominate the party's candidate for Governor, Lieutenant Governor, and all other statewide officers and United States Senators, members of Congress, and circuit solicitors, and the county conventions shall nominate the party's candidates for all county offices. No convention shall make nominations for candidates for offices unless the decision to use the convention method is reached by a three-fourths vote of the total membership of the convention, except the office of state Senator and of member of the House of Representatives. The nomination of the party's candidates for the office of the state Senator and of member of the House of Representatives must be made in the manner determined by the state committee. If a party determines that nomination for the office of state Senator and of member of the House of Representatives must be by convention, these nominations must be made by the state convention. No convention shall make nominations for one or more offices at the convention and order primaries for other offices to be filled during the same election year. Conventions for political parties not nominating candidates in primaries may be called by state and county committees on other dates than those given in this title for conventions after three weeks' published notices of the calls. Any political party nominating candidates by party convention shall nominate the party candidates and make the nominations public not later than the time for certifying candidates to the authority charged by law with preparing ballots for the general or special election.
(A) A party may choose to nominate candidates for all offices, including but not limited to Governor, Lieutenant Governor, United States Senator, United States House of Representatives, circuit solicitor, state Senator, and members of the state House of Representatives if:
(1) there is a three-fourths vote of the total membership of the convention to use the convention nomination process; and
(2) a majority of voters in that party's next primary election approve the use of the convention nomination process.
(B) A party may not choose to nominate by party convention for an election cycle in which the filing period for candidates has begun.
(C) A political party nominating candidates by party convention shall nominate the party candidates and make the nominations public not later than the time for certifying candidates to the authority charged by law with preparing ballots for the general or special election."
SECTION 4. Section 7-11-210 of the 1976 Code is amended to read:
"Section 7-11-210. Every candidate for selection as a nominee of any political party for any state office, United States Senator, member of Congress, or solicitor, to be voted for in any party primary election or political party convention, shall file with and place in the possession of the treasurer of the state committee appropriate election commission, pursuant to Section 7-11-15 by twelve o'clock noon on March thirtieth a notice or party pledge in the following form, the blanks being properly filled in and the notice or party pledge signed by the candidate: 'I hereby file my notice as a candidate for the nomination as __________ in the primary election or convention to be held on __________. I affiliate with the __________ Party, and I hereby pledge myself to abide by the results of the primary or convention. I shall not authorize my name to be placed on the general election ballot by petition and will not offer or campaign as a write-in candidate for this office or any other office for which the party has a nominee. I authorize the issuance of an injunction upon ex parte application by the party chairman, as provided by law, should I violate this pledge by offering or campaigning in the ensuing general election for election to this office or any other office for which a nominee has been elected in the party primary election, unless the nominee for the office has become deceased or otherwise disqualified for election in the ensuing general election. I hereby affirm that I meet, or will meet by the time of the general or special election, or as otherwise required by law, the qualifications for this office'.
Every candidate for selection in a primary election as the nominee of any political party for member of the Senate, member of the House of Representatives, and all county and township offices shall file with and place in the possession of the county chairman election commission of the county in which they reside or other officer as may be named by the county committee of the county in which they reside by twelve o'clock noon on March thirtieth a like notice and party pledge.
The notice of candidacy party pledge required by this section to be filed by a candidate in a primary must be signed personally by the candidate, and the signature of the candidate must be signed in the presence of the county chairman or other officer as may be named by the county committee with whom the candidate is filing, or a candidate must have his signature on the notice of the candidacy acknowledged and certified by any officer authorized to administer an oath an individual authorized by the election commission director. Any notice of candidacy party pledge of any candidate signed by an agent in behalf of a candidate shall not be valid.
In the event that a person who was defeated as a candidate for nomination to an office in a party's primary election shall thereafter offer or campaign as a candidate against any nominee for election to any office in the ensuing general election, the state chairman of the party which held the primary (if the office involved is one voted for in the general election by the electors of more than one county), or the county chairman of the party which held the primary (in the case of all other offices), shall forthwith institute an action in a court of competent jurisdiction for an order enjoining the person from so offering or campaigning in the general election, and the court is hereby empowered upon proof of these facts to issue an order."
SECTION 5. Section 7-13-40 of the 1976 Code is amended to read:
"Section 7-13-40. In the event that a party nominates candidates by party primary, a party primary must be held by the party and conducted by the State Election Commission and the respective county election commissions on the second Tuesday in June of each general election year, and a second and third primary each two weeks successively thereafter, if necessary. Written certification of the names of all candidates to be placed on primary ballots must be made by the political party chairman, vice chairman, or secretary to the State Election Commission or the county election commission, whichever is responsible under law for preparing the ballot, not later than twelve o'clock noon on April ninth fifth, or if April ninth fifth falls on a Saturday or Sunday, not later than twelve o'clock noon on the following Monday. Political parties nominating candidates by party primary must verify the qualifications of those candidates prior to certification to the appropriate election commission of the names of candidates to be placed on primary ballots. The written verification required by this section must contain a statement that each candidate certified meets, or will meet by the time of the general election, or as otherwise required by law, the qualifications for office for which he has filed. Political parties must not accept the filing of A political party must not certify any candidate who does not or will not by the time of the general election, or as otherwise required by law, meet the qualifications for the office for which the candidate desires to file has filed, and such candidate's name shall not be placed on a primary ballot. The filing fees for all candidates filing to run in all primaries, except municipal primaries, must be transmitted by the respective political parties to the State Election Commission and placed by the executive director of the commission in a special account designated for use in conducting primary elections and must be used for that purpose. The filing fee for each office is one percent of the total salary for the term of that office or one hundred dollars, whichever amount is greater."
SECTION 6. Section 7-13-45 of the 1976 Code is amended to read:
"Section 7-13-45. (A) In every general election year, the county chairman executive director of the State Election Commission and the director of each county election commission shall:
(1) designate a specified place other than a private residence where persons may file a statement of intention of candidacy;
(2) designate a specified place other than a private residence where persons may file as candidates;
(3)(1) establish regular hours of not less than four hours a day during the final seventy-two hours of the filing period in which he the director or some person he designates must be present at the designated place to accept filings as required by Section 7-11-15;
(4)(2) place an advertisement to appear two weeks before the filing period begins in a newspaper of general circulation in the county at least five by seven inches in size that notifies the public of the dates of the filing periods, the offices which may be filed for, the place and street address where filings may be made, and the hours that an authorized person will be present to receive filings."
SECTION 7. Section 8-13-365 of the 1976 Code is amended to read:
"Section 8-13-365. (A) The commission shall establish a system of electronic filing for all disclosures and reports required pursuant to Chapter 13, Title 8, and Chapter 17, Title 2 from all persons and entities subject to its jurisdiction except for forms and reports required pursuant to Article 9, Chapter 13, Title 8. These disclosures and reports must be filed using an Internet-based filing system as prescribed by the commission. Reports and disclosures filed with the Ethics Committees of the Senate and House of Representatives for legislative offices must be in a format such that these filings can be forwarded to the State Ethics Commission using an Internet-based system. The information contained in the reports and disclosure forms, with the exception of social security numbers, campaign bank account numbers, and tax ID numbers, must be publicly accessible, searchable, and transferable.
(B) The Ethics Commission must submit to the General Assembly a report no later than one year after implementation of subsection (A), concerning the effectiveness of mandatory electronic filing, and must make recommendations as to the implementation of mandatory filing for all other candidates and entities."
SECTION 8. Section 8-13-1140 of the 1976 Code is amended to read:
"Section 8-13-1140. A person required to file a statement of economic interests under this chapter shall annually file, pursuant to Section 8-13-365, an updated statement for the previous calendar year with the appropriate supervisory office annually, no later than April fifteenth noon on March thirtieth of each calendar year, listing any addition, deletion, or change in his economic status with respect to which information is required to be supplied under this article. If the person has filed the description by name, amount, and schedule of payments of a continuing arrangement relating to an item required to be reported under this article, an updating statement need not be filed for each payment under the continuing arrangement, but only if the arrangement is terminated or altered."
SECTION 9. Section 8-13-1356 of the 1976 Code is amended to read:
"Section 8-13-1356. (A) This section does not apply to a public official who has a current disclosure statement on file with the appropriate supervisory office pursuant to Sections 8-13-1110 or 8-13-1140.
(B)A person who becomes a candidate by filing a statement of intention of candidacy seeking nomination by political party primary or political party convention must electronically file a statement of economic interests for the preceding calendar year at the same time and with the same official with whom the candidate files pursuant to Section 8-13-365 prior to the close of filing for the particular office a declaration of candidacy or petition for nomination.
(B) A person who becomes a candidate by filing a petition for nomination must electronically file a statement of economic interests for the preceding calendar year pursuant to Section 8-13-365 within fifteen days of submitting the petition pursuant to Section 7-11-70 or 7-11-71.
(C) A person who becomes a write-in candidate must electronically file a statement of economic interests for the preceding calendar year within twenty-four hours of filing an initial campaign finance report pursuant to Section 8-13-1308(A) or before taking the oath of office, whichever occurs earlier.
(C) The official with whom the candidate files a declaration of candidacy or petition for nomination, no later than five business days after candidacy books close, must file a copy of the statement with the appropriate supervisory office.
(D) An individual who becomes a candidate other than by filing must, no later than fifteen business days after becoming a candidate, file a statement of economic interests for the preceding calendar year with the appropriate supervisory office.
(E) An officer authorized to receive declarations of candidacy and petitions for nominations under the provisions of Chapter 11 of Title 7 may not accept a declaration of candidacy or petition for nomination unless the declaration or petition is accompanied by a statement of economic interests. If the candidate's name inadvertently appears on the ballot, the officer authorized to receive declarations of candidacy or petitions for nomination must not certify the candidate subsequent to the election.
(F) If the candidate files for office before January first of the year in which the election is held, he must file a supplementary statement covering the preceding calendar year no later than April first of the year in which the election is held.
(G)(D) A candidate who is not a public official otherwise filing a statement has the same disclosure requirements as a public official with the exception of reporting gifts.
(H) The State Ethics Commission must furnish to each clerk of court in the State forms on which the statement of economic interests shall be filed.
(E) The appropriate supervisory office shall access a civil penalty pursuant to Section 8-13-1510 against a candidate who fails to timely file a statement of economic interests as required by this section."
SECTION 10. Section 7-11-220 of the 1976 Code is repealed.
SECTION 11. In order to educate various parties regarding the provisions contained in this act, the following notifications must be made:
(1) The State Election Commission must notify each county election commission of the provisions of this act.
(2) The State Election Commission must post the provisions of this act on its website.
(3) Each state party executive committee must notify their respective county executive parties of the provisions of this act.
SECTION 12. The General Assembly finds that all the provisions contained in this act relate to one subject as required by Section 17, Article III of the South Carolina Constitution in that each provision relates directly to or in conjunction with other sections to the subject of election reform as stated in the title. The General Assembly further finds that a common purpose or relationship exists among the sections, representing a potential plurality but not disunity of topics, notwithstanding that reasonable minds might differ in identifying more than one topic contained in this act.
SECTION 13. The provisions of this act are severable. If any section, subsection, paragraph, subparagraph, item, subitem, sentence, clause, phrase, or word of this act is for any reason held to be unconstitutional or invalid, such holding shall not affect the constitutionality or validity of the remaining portions of the act, the General Assembly hereby declaring that it would have passed each and every section, subsection, paragraph, subparagraph, item, subitem, sentence, clause, phrase, and word thereof, irrespective of the fact that any one or more other sections, subsections, paragraphs, subparagraphs, items, subitems, sentences, clauses, phrases, or words hereof may be declared to be unconstitutional, invalid, or otherwise ineffective.
SECTION 14. This act takes effect upon preclearance approval by the United States Department of Justice or approval by a declaratory judgment issued by the United States District Court for the District of Columbia, whichever occurs first. /
Amend title to conform.
/s/Sen. George E. Campsen III /s/Rep. F. Gregory Delleney, Jr.
/s/Sen. John L. Scott, Jr. /s/Rep. Alan D. Clemmons
/s/Sen. Paul Thurmond /s/Rep. J. David Weeks
On Part of the Senate. On Part of the House.
, and a message was sent to the House accordingly.
THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE.
CARRIED OVER
S. 75 (Word version) -- Senator Cromer: A BILL TO AMEND SECTION 40-57-130, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO LICENSE RENEWALS FOR REAL ESTATE BROKERS AND SALESMEN, SO AS TO REQUIRE A CRIMINAL BACKGROUND CHECK FROM A SOURCE APPROVED BY THE DEPARTMENT OF LABOR, LICENSING AND REGULATION; AND BY ADDING SECTION 40-57-245 SO AS TO REQUIRE THAT THE DEPARTMENT ASSIGN ONE INVESTIGATOR FOR EVERY TWO THOUSAND FIVE HUNDRED LICENSEES TO ENSURE COMPLAINTS ARE PROCESSED AND CONSIDERED IN AN EXPEDITIOUS MANNER.
The House returned the Bill with amendments.
Point of Order
Senator SHANE MARTIN raised a Point of Order under Rule 24A that the House amendments were out of order inasmuch as they were not germane to the Bill.
The PRESIDENT overruled the Point of Order.
Point of Order
Senator SHANE MARTIN raised a Point of Order under Rule 32C that the House amendments contained matter that was not germane to the Bill and, therefore, the Bill should be referred to the Committee on Labor, Commerce and Industry.
The PRESIDENT overruled the Point of Order.
Senator PEELER spoke on the Bill.
Senator ALEXANDER spoke on the Bill.
Senator MALLOY spoke on the Bill.
Senator PEELER moved to carry over the Bill.
Senator MALLOY moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 14; Nays 26
AYES
Allen Hutto Jackson
Johnson Malloy Matthews
McElveen McGill Nicholson
Pinckney Reese Scott
Setzler Williams
Total--14
NAYS
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hembree Martin, Larry Martin, Shane
Massey Peeler Rankin
Shealy Thurmond Turner
Verdin Young
Total--26
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 29; Nays 14
AYES
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Leatherman
Martin, Larry Martin, Shane Massey
Peeler Rankin Shealy
Sheheen Thurmond Turner
Verdin Young
Total--29
NAYS
Allen Hutto Jackson
Johnson Malloy Matthews
McElveen McGill Nicholson
Pinckney Reese Scott
Setzler Williams
Total--14
The Bill was carried over.
CARRIED OVER
S. 127 (Word version) -- Senators Alexander and Ford: A BILL TO AMEND CHAPTER 38, TITLE 44 OF THE 1976 CODE, RELATING TO HEAD AND SPINAL CORD INJURIES, BY ADDING ARTICLE 6 TO CREATE THE SOUTH CAROLINA BRAIN INJURY LEADERSHIP COUNCIL, TO PROVIDE FOR THE RESPONSIBILITIES AND DUTIES OF THE COUNCIL, TO PROVIDE FOR THE COMPOSITION AND APPOINTMENT OF THE COUNCIL, AND TO PROVIDE FOR THE POWERS AND AUTHORITY OF THE COUNCIL.
The House returned the Bill with amendments.
Senator PEELER moved to carry over the Bill.
Senator MALLOY moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 15; Nays 28
AYES
Allen Coleman Hutto
Jackson Johnson Malloy
Matthews McElveen McGill
Nicholson Pinckney Reese
Scott Setzler Williams
Total--15
NAYS
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hembree Leatherman Martin, Larry
Martin, Shane Massey Peeler
Rankin Shealy Sheheen
Thurmond Turner Verdin
Young
Total--28
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 29; Nays 12
AYES
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Coleman Corbin
Courson Cromer Davis
Fair Gregory Grooms
Hayes Hembree Leatherman
Martin, Larry Martin, Shane Massey
Peeler Rankin Shealy
Sheheen Thurmond Turner
Verdin Young
Total--29
NAYS
Allen Johnson Malloy
Matthews McElveen McGill
Nicholson Pinckney Reese
Scott Setzler Williams
Total--12
The Bill was carried over.
CARRIED OVER
The House returned the Bill with amendments.
Senator PEELER moved to carry over the Bill.
Senator NICHOLSON moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 13; Nays 27
AYES
Allen Coleman Hutto
Johnson Malloy Matthews
McGill Nicholson Pinckney
Reese Scott Setzler
Williams
Total--13
NAYS
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Corbin Courson
Cromer Davis Fair
Gregory Grooms Hembree
Martin, Larry Martin, Shane Massey
McElveen Peeler Rankin
Shealy Sheheen Thurmond
Turner Verdin Young
Total--27
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
The Bill was carried over.
CARRIED OVER
S. 348 (Word version) -- Senator L. Martin: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 6-10-35 SO AS TO PROVIDE FOR REQUIREMENTS FOR FIREPLACES IN LIEU OF REQUIREMENTS OF THE 2009 EDITION OF THE INTERNATIONAL ENERGY CONSERVATION CODE.
The House returned the Bill with amendments.
Senator PEELER moved to carry over the Bill.
Senator MATTHEWS moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 15; Nays 25
AYES
Allen Bryant Coleman
Hutto Jackson Johnson
Malloy Matthews McGill
Nicholson Pinckney Reese
Scott Setzler Williams
Total--15
NAYS
Alexander Bennett Bright
Cleary Corbin Courson
Cromer Davis Fair
Gregory Grooms Hayes
Hembree Martin, Larry Martin, Shane
Massey McElveen Peeler
Rankin Shealy Sheheen
Thurmond Turner Verdin
Young
Total--25
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
The Bill was carried over.
CARRIED OVER
S. 590 (Word version) -- Senator Campsen: A BILL TO AMEND SECTION 50-5-1705 OF THE 1976 CODE, RELATING TO CATCH LIMITS, TO PROVIDE THAT IT IS UNLAWFUL FOR A PERSON TO TAKE OR POSSESS MORE THAN ONE TARPON IN ANY ONE DAY OR A TARPON OF LESS THAN SEVENTY-SEVEN INCHES IN FORK LENGTH.
The House returned the Bill with amendments.
Senator PEELER moved to carry over the Bill.
Senator MATTHEWS moved to table the motion to carry over.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 13; Nays 25
AYES
Allen Coleman Hutto
Jackson Johnson Matthews
McGill Nicholson Pinckney
Reese Scott Setzler
Williams
Total--13
NAYS
Alexander Bennett Bright
Bryant Campbell Campsen
Cleary Corbin Courson
Cromer Fair Grooms
Hayes Hembree Martin, Larry
Martin, Shane Massey McElveen
Peeler Shealy Sheheen
Thurmond Turner Verdin
Young
Total--25
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
The Bill was carried over.
NONCONCURRENCE
H. 3710 -- Ways and Means Committee: A BILL TO MAKE APPROPRIATIONS AND TO PROVIDE REVENUES TO MEET THE ORDINARY EXPENSES OF STATE GOVERNMENT FOR THE FISCAL YEAR BEGINNING JULY 1, 2013, TO REGULATE THE EXPENDITURE OF SUCH FUNDS, AND TO FURTHER PROVIDE FOR THE OPERATION OF STATE GOVERNMENT DURING THIS FISCAL YEAR AND FOR OTHER PURPOSES.
The House returned the Bill with amendments.
On motion of Senator LEATHERMAN, with unanimous consent, the Senate nonconcurred in the House amendments and a message was sent to the House accordingly.
NONCONCURRENCE
H. 3711 (Word version) -- Ways and Means Committee: A JOINT RESOLUTION TO APPROPRIATE MONIES FROM THE CAPITAL RESERVE FUND FOR FISCAL YEAR 2012-2013, AND TO ALLOW UNEXPENDED FUNDS APPROPRIATED TO BE CARRIED FORWARD TO SUCCEEDING FISCAL YEARS AND EXPENDED FOR THE SAME PURPOSES.
The House returned the Joint Resolution with amendments.
On motion of Senator LEATHERMAN, with unanimous consent, the Senate nonconcurred in the House amendments and a message was sent to the House accordingly.
THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE.
AMENDMENT PROPOSED, DEBATE INTERRUPTED
H. 3945 (Word version) -- Reps. G.M. Smith, Harrell, Lucas, Bannister, Toole, Stringer, Hamilton, Sottile, Barfield, Bingham, Spires, Hardwick, Owens, Hiott, Long, Erickson, Murphy, Horne, Willis, Gagnon, Simrill, Funderburk and Henderson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 4 TO CHAPTER 13, TITLE 8 SO AS TO ESTABLISH THE SOUTH CAROLINA COMMISSION ON ETHICS ENFORCEMENT AND DISCLOSURE, TO PROVIDE FOR ITS POWERS, DUTIES, PROCEDURES, AND JURISDICTION, AND TO PROVIDE PENALTIES FOR CERTAIN VIOLATIONS; TO REPEAL ARTICLE 3, CHAPTER 13, TITLE 8 RELATING TO THE STATE ETHICS COMMISSION; TO REPEAL ARTICLE 5, CHAPTER 13, TITLE 8 RELATING TO THE HOUSE OF REPRESENTATIVES AND SENATE ETHICS COMMITTEES; TO AMEND SECTION 8-13-100, AS AMENDED, RELATING TO DEFINITIONS IN REGARD TO ETHICS, GOVERNMENT ACCOUNTABILITY, AND CAMPAIGN REFORM, SO AS TO REVISE CERTAIN DEFINITIONS; TO AMEND SECTION 8-13-700, AS AMENDED, RELATING TO USE OF AN OFFICIAL POSITION OR OFFICE FOR FINANCIAL GAIN, SO AS TO PROVIDE THAT IF A MEMBER OF THE GENERAL ASSEMBLY DETERMINES THAT HE HAS A CONFLICT OF INTEREST, HE MUST COMPLY WITH CERTAIN REQUIREMENTS BEFORE ABSTAINING FROM ALL VOTES ON THE MATTER, AND TO PROVIDE FOR WHEN A PUBLIC OFFICIAL WHO IS REQUIRED TO RECUSE HIMSELF FROM A MATTER MUST DO SO; TO AMEND SECTION 8-13-740, AS AMENDED, RELATING TO REPRESENTATION OF ANOTHER PERSON BY A PUBLIC OFFICIAL BEFORE A GOVERNMENTAL ENTITY, SO AS TO FURTHER DELINEATE WHAT IS CONSIDERED A CONTESTED CASE WHEN REPRESENTATION BY A MEMBER OF THE GENERAL ASSEMBLY IS PERMITTED; TO AMEND SECTION 8-13-745, RELATING TO PAID REPRESENTATION OF CLIENTS AND CONTRACTING BY A MEMBER OF THE GENERAL ASSEMBLY OR AN ASSOCIATE IN PARTICULAR SITUATIONS, SO AS TO DELETE A PROHIBITION AGAINST CERTAIN CONTRACTS WITH AN ENTITY FUNDED WITH GENERAL FUNDS; TO AMEND SECTION 8-13-1120, AS AMENDED, RELATING TO CONTENTS OF STATEMENTS OF ECONOMIC INTEREST, SO AS TO FURTHER PROVIDE FOR THESE CONTENTS; TO AMEND SECTION 8-13-1300, AS AMENDED, RELATING TO DEFINITIONS IN REGARD TO CAMPAIGN PRACTICES, SO AS TO REVISE CERTAIN DEFINITIONS; TO AMEND SECTION 8-13-1318, RELATING TO ACCEPTANCE OF CONTRIBUTIONS TO RETIRE CAMPAIGN DEBTS, SO AS TO REQUIRE ANY SUCH CONTRIBUTIONS TO BE USED FOR THIS PURPOSE ONLY; TO AMEND SECTION 8-13-1338, RELATING TO PERSONS WHO MAY NOT SOLICIT CONTRIBUTIONS, SO AS TO INCLUDE THE HEAD OF ANY STATE AGENCY WHO IS SELECTED BY THE GOVERNOR, THE GENERAL ASSEMBLY, OR AN APPOINTED OR ELECTED BOARD; TO AMEND SECTION 8-13-1340, AS AMENDED, RELATING TO RESTRICTIONS ON CONTRIBUTIONS BY ONE CANDIDATE TO ANOTHER OR THROUGH COMMITTEES CONTROLLED BY A CANDIDATE, SO AS TO DELETE AN EXCEPTION FOR A COMMITTEE CONTROLLED BY A CANDIDATE IF IT IS THE ONLY SUCH COMMITTEE, AND TO MAKE CONFORMING CHANGES; TO AMEND SECTIONS 8-13-1510 AND 8-13-1520, BOTH AS AMENDED, RELATING TO PENALTIES FOR ETHICAL AND OTHER VIOLATIONS, AND BY ADDING SECTION 8-13-1530 SO AS TO FURTHER PROVIDE FOR THE PENALTIES FOR VIOLATIONS AND FOR WHERE CERTAIN WILFUL VIOLATIONS MUST BE TRIED; AND TO REPEAL SECTIONS 8-13-710 AND 8-13-715 RELATING TO REPORTING OF PARTICULAR GIFTS AND AUTHORIZED REIMBURSEMENTS FOR SPEAKING ENGAGEMENTS.
The Senate proceeded to a consideration of the Bill, the question being the adoption of Amendment No. 1 (JUD3945.078) proposed by Senators CAMPSEN, MALLOY, HUTTO and MASSEY and printed in the Journal of June 4, 2013.
Senator CAMPSEN explained the amendment.
ACTING PRESIDENT PRESIDES
At 6:22 P.M., Senator LARRY MARTIN assumed the Chair.
Senator CAMPSEN explained the amendment.
Senator RANKIN spoke on the amendment.
Remarks by Senator RANKIN
Thank you, Mr. PRESIDENT.
I just wanted to take a few minutes to kindly share with you my perspective on where we are, and to tip my hat to those who feel compelled to vote for this Bill. Y'all know my experience, my education and my profession as a lawyer. I was trained at the University of South Carolina Law School, and you have heard me invoke that perhaps in talking about this Bill.
I say this with the perspective that, we sitting as a full subcommittee or full committee, sit like jurors. We must decide if a burden of proof has been established, that there is something wrong, something that needs to be fixed, or that the subject, Bill or amendment we are asked to consider fixes what is broken. In a sense, you've got to prove it. Don't just tell me. Prove to me that something is wrong or something is broken. This applies to me in what I am called to do as one member of this Senate on anything I am asked to vote on. The question becomes, "Is it broken?" And, does what I am being asked to support fix or address what is broken?
We are told we have a crisis. I am using that term though it has probably not been stated by the main proponent of this Bill, but by those championing this Bill. Effectively, we are told we are on the cusp of dramatic reform, the likes of which if we fail to embrace this, will set our State back.
There was great work done by the commission assembled to take a look at this reform -- Attorneys General Medlock and McMaster, great work. I am sure you all have heard and read the report. They liken this to a job creator, an enhancement for our State. Selfishly we are told it will enhance our self esteem, because the public does not trust us.
I quipped with them, especially Attorney General McMaster, particularly at the initial presentation. If he is listening, I hope he is not offended. I like the way he sold it, as the next best thing to penicillin -- to the likes that cancer would be removed and the skies would be bluer if we pass this reform. He went on to say this is good for South Carolina. We have to do it. If we don't, we will be held in low regard by the industry and by those who selfishly look at people like us as corrupt, distrustful, and out for myself.
The subcommittee got its work done, and got through the marathon full Judiciary Committee meeting, chaired by the Senator from Pickens, Senator LARRY MARTIN. Some strange things came in the wee hours of that effort. Ultimately, those with different backgrounds, and perhaps different perspectives, all said this is what we need.
My question to you as a juror is, "Is it broken?" Is it? Or has it been affected? What has happened since all of this broke out -- again Senator from Richland talked about the impetus of this. Has it been fixed? I would suggest to you that the real fix has been affected. In December, the House did what they should have done a long time ago and created an exact model for their committee. Between December and January they adopted rules for their committee do what our committee does.
I don't have to remind everyone of the history. Again, we know why we are here. We know what was broken. Is the effort perhaps gubernatorial politics or is it the desire to have better, cleaner, and more transparent government with Rules that apply to everyone? With Rules that keep me from making my constituents think that I am in this for personal gain? Rule 4.16 in the House created a bipartisan committee that copied our Rule.
Senator from York, Senator WES HAYES, was the Chairman of Ethics when we changed our Rule, which made us able to do what we did last week. So is the system broken in the Senate? I think last week's hearing is the perfect and best evidence to say to you, "No." The Senate does not take care of their own. The Senate provided full disclosure, full eyes for anyone that wanted to see it in person, to watch it stream live on ETV, or read the complaint filed, answers received and every bit of evidence that will be made available tomorrow for all to see. We did it right.
Some have said, "Oh, we have been taken off the hook because there was a resignation." Folks, had there not been a resignation, you would be sitting here as jurors of a member in which there was overwhelming, compelling, and competent evidence that violations had occurred. Does the Senate protect its own? I am looking to my right, at the Senators from Orangeburg and from Richland. You have heard the pain they had to endure. It wasn't just a personal history they shared. I served with the Senator from Charleston for twenty years until last Friday. We all had a relationship here. But did that relationship skew their charge to do what had to justly be done?
"Love and mercy walk with thy God," from Micah 6:8. I use it all of time. Last Thursday and Friday we held a member of this Senate to the standard that we weren't going to take care of our own, or take us off the hard task of holding him in judgment. We did it, so now is the Senate broken? No. Is the House broken? I'm not a member over there. You can read the paper. You can see what allegations have been bandied about the paper. They have had a tough task over there.
I wasn't aware of this, but according to today's paper, twenty-three years ago was the last time a sitting member of the House was the subject of an Ethics Committee investigation, that came after an indictment, not before. So again, the House governs its own. You might say in the past they swept things under the rug until they changed their Rule to model ours. Maybe the outcome in several of the issues brought before them would have been dramatically different had they had what they have now under the Rule -- an equally divided membership with the same power, authority, latitude, and discretion afforded to the sitting committee.
I am looking forward. I have listened to the conversation and argument at the subcommittee and full committee level. Again, not to undo the work of those who want to see Super PACS register in South Carolina, that want to see that folks are not profiting from their companies for their positions on issues. I want to see some of the changes we have in this Bill as well -- for example, the Public Integrity Unit. The Attorney General's office has called it the number one desire to have. Which by the way as of this past week, if not this week, it will go forward with a memorandum of understanding.
There is nothing that precludes the collaboration of all agencies of South Carolina from doing what they have done and what they are going to do outside of this law. So what is it that we really can point to here that is broken? Super PACS, clearly. A number of us have had untold hundreds of thousands of dollars poured into campaigns against us. I fortunately have not been the subject of that, but I have an idea and know that it isn't right. If you are going to spend the money and try to defeat someone, then be man enough to tell who you are. Clearly this ought to be changed. Clearly this is broken and we should fix it.
So do we scrap a system in this Senate that has worked, just to satisfy the whim of proponents who want a Bill so they can check it off on their campaign to say look what we have done? To give the Governor credit? I don't blame her for wanting to move past this so she can rightly say she has been exonerated, that she did nothing wrong, and that this was her change. That this was her epiphany, her road to Damascus; an event that says not that I was guilty, but the perception was that I was, so we need change right now. If we don't fix this, not only will I or any other elected officeholder be held in low regard, but it will affect how we conduct business in this State. Is that reason enough, folks, to scrap our system in this Senate? Is it reason enough to scrap what their House has done by Rule?
Maybe they can change it when the tides turn and the cameras go off, but folks, people are not talking to me in Horry County about ethics reform, but about infrastructure and education. They are not talking to me about how industry is not coming to Horry County or the NISA region because our politicians look to be in it for themselves. They aren't talking about this. They want to talk about jobs. The Chamber of Commerce wants to talk about jobs.
What does this satisfy to you as a juror sitting in judgment of this proposal? What does it fix? That is the question to me. So I say, Senator from York, change, fix, put into law the definition of the super PACs. Make them register. Let's pass the substantial expenditure language. With regard to the Public Integrity Unit, we don't need to do it, but let's do it. Regarding the disclosure requirement, the Senator from Charleston wanted to cure the blackout period. I don't think we can do that, but there a lot of things we do need to fix it. Creating a panel made up of eight members; two appointed by the Governor of his or her party, two by the other party, two by -- I almost want to start singing the song of Noah, trampling in the park two by two. But to do what? Make people trust them because they don't trust us? That is what we are doing. We are passing it on, looking holier than thou. Are there blood and sins in this Chamber we don't cure and we don't right? Ya'll have to decide that.
Thank you.
On motion of Senator SETZLER, with unanimous consent, the remarks of Senator RANKIN were ordered printed in the Journal.
PRESIDENT PRESIDES
At 7:03 P.M., the PRESIDENT assumed the Chair.
Senator RANKIN spoke on the amendment.
Senator LARRY MARTIN spoke on the amendment.
Senator MALLOY spoke on the amendment.
Objection
With Senator MALLOY retaining the floor, Senator HUTTO asked unanimous consent to make a motion to carry over H. 3945, take up for immediate consideration H. 3101, proceed to a consideration of Amendment No. 1C to H. 3101 proposed by Senator DAVIS, then proceed to a vote on second reading on H. 3101, carrying over all remaining amendments to third reading.
Senator MASSEY objected.
Senator MALLOY spoke on the amendment.
Objection
Senator CROMER asked unanimous consent to make a motion, to give H. 3945 a second reading and to carry over all amendments to third reading.
Senator WILLIAMS objected.
Objection
Senator SHANE MARTIN asked unanimous consent to make a motion, to give H. 3945 and H. 3101 a second reading and to carry over all amendments to third reading.
Senator WILLIAMS objected.
Senator MALLOY made the motion to carry over H. 3945.
Senator LARRY MARTIN moved to lay the the motion to carry over H. 3945 on the table.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 15; Nays 27
AYES
Alexander Campbell Campsen
Courson Cromer Gregory
Hembree Martin, Larry Massey
Peeler Shealy Sheheen
Thurmond Turner Young
Total--15
NAYS
Allen Bennett Bright
Bryant Cleary Coleman
Corbin Davis Grooms
Hutto Jackson Johnson
Leatherman Lourie Malloy
Martin, Shane Matthews McElveen
McGill Nicholson Pinckney
Rankin Reese Scott
Setzler Verdin Williams
Total--27
The Senate refused to table the motion to carry over. The question then was the motion to carry over.
At 9:08 P.M., Senator MASSEY moved that the Senate stand adjourned.
Point of Order
Senator MALLOY raised a Point of Order that the Senator was not at his seat when the motion was made.
The PRESIDENT sustained the Point of Order.
At 9:09 P.M., Senator COURSON moved that the Senate stand adjourned.
The "ayes" and "nays" were demanded and taken, resulting as follows:
Ayes 23; Nays 19
AYES
Alexander Bennett Coleman
Courson Gregory Hayes
Hembree Hutto Jackson
Johnson Leatherman Lourie
Martin, Larry Massey Matthews
McElveen McGill Nicholson
Peeler Pinckney Reese
Scott Williams
Total--23
NAYS
Allen Bright Bryant
Campbell Campsen Cleary
Corbin Cromer Davis
Grooms Malloy Martin, Shane
Rankin Shealy Sheheen
Thurmond Turner Verdin
Young
Total--19
| 2014-07-23T07:55:31 |
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https://ikapedia.fandom.com/wiki/Espi%C3%A3o
|
553 Páginas
Espião
Requisitos
Nenhum
Custo
Nenhum
## Informação geral Editar
Assim que construir a Espionagem, poderá treinar espiões. Para cada fase de expansão, é permitido treinar um espião adicional.
Para implantar um espião, vá no mapa da ilha e clique na cidade que deseja espionar. A opção de implantar um espião aparece no menu à esquerda. Quando selecionar esta opção, um de seus espiões vai tentar se infiltrar na cidade.
## A matemática Editar
Adicionar base de risco missão de risco atual, subtraia defendendo / alvo nível prefeitura multiplicado por 2, subtrair o nível de ataque esconderijo multiplicado por 2, adicione o risco gerado por espiões defendendo que trabalham na defesa / cidade alvo multiplicado por 5.
Se o valor calculado é entre 5 e 95, então este é o risco total, se for inferior a 5, em seguida, Risco Total é de 5%, se for acima de 95, em seguida, Risco Total é de 95%.
O algoritmo:
$Calculated Risk = C + M + 5s + 2e - 2t - 2h$
$If Calculated Risk < 5\%, Total Risk = 5\%$
$If Calculated Risk > 95\%, Total Risk = 95\%$
onde $C$ é igual ao risco atual (ver seção Riscos abaixo); $M$ é igual à Missão de Risco Base de Dados; $s$ é o risco gerado pelo número de espiões que trabalham em defesa na defesa / cidade-alvo; $e$ é igual ao nível do esconderijo / alvo; $t$ é igual ao nível de defesa da cidade / alvo; $h$ é igual ao nível de ataque de esconderijo.
Uma versão simplificada do algoritmo acima pode ser usado para determinar o risco calculado de travar ou parar um espião atacar, fazendo certas suposições úteis:
• All of the spies in the defending/target hideout are working in defense: $s = e$
• The attacking hideout level is 32 (most large towns have this): $h = 32$
• An attacking player will wait til attacking spy's Current Risk is 0: $C = 0$
Thus the simplified algorithm for defense:
$Calculated Risk = M + 7e - 2t - 64$
### Risks Editar
There are three different kinds of risks calculated in this game.
• Calculated Risk
This is the intermediate risk after performing the calculations in the formula above. This number can have a wide range of values from -255% up to 255%. There currently is a bug where if calculated risk is above 255%, the total risk shows 0% with a full bar. This is instant death for the spy.
• Current Risk
This is the risk associated after a successful Spy action. This is usually the number seen on the bar that slowly decreases. There is actually a number behind the scene that counts down past 5% total risk seen on the bar. This value is always between 0% and 95%
• Total Risk
This is the risk seen when you look at the spy. No matter what this risk % is, your spy can not be caught. Only by performing actions can a spy be caught. This ranges from 5% to 95%
### Risk Levels Editar
Risk 1 Base
5% - Infiltrate Town
Risk 2 Base
24% - Spy out treasure chamber
Risk 3 Base
30% - Inspect Warehouse, Recall Spy
Risk 4 Base
40% - Spy out level of research
Risk 5 Base
50% - Online status
Risk 6 Base
70% - Spy out garrison
Risk 7 Base
80% - Observe fleet and troop movements
Risk 8 Base
90% - Observe communication
### Example Editar
The algorithm:
$Calculated Risk = C + M + 5s + 2e -2t -2h$
Current risk: None $C=0\%$
Mission: Spy out garrison $M=70\%$
Enemy Spies: One spy in defense $s=1$
Level of target town's Hideout: Level 1 $e=1$
Level of target town: Town hall Level 6 $t=6$
Level of your Hideout: $h=2$
$0 + 70 + 5\cdot1 + 2\cdot1 -2\cdot6 -2\cdot2 = 61$
• The risk for the mission is then: $61\%$
Current risk is increased every time a spy performs an espionage mission; but it cannot be greater than 95%. Current risk drops gradually until it reaches 0% (5% total risk still visible).
If current risk is high, it can make even easy missions (like checking online status) hard to perform; so it is advisable to wait a certain amount of time until current risk drops to a lower level.
## Town Spy Defense Editar
Remember the previous simplified algorithm:
$Calculated Risk = M + 7e - 2t - 64$
For Spy Infiltration: $M = 5$
With this information we can calculate what level of hideout you need to prevent spies from infiltrating your town or how much protection you are getting from your current level of hideout. The following table uses the formula above with its assumptions that the attacking hideout is level 32 and all of the spies in your defensive hideout are working in defense. It visually shows you what the percentage chance of catching a spy is, for a given defending town level and its hideout level.
The column at far left shows in ascending order the level of the defensive hideout. The remaining columns represent the defending town's level, $t$. The numbers in the middle of the table represent the percentage Risk for catching a spy that is attempting to infiltrate.
To determine the level of hideout you need, trace over to the current level of your town. Then trace down that column until you reach your desired percentage chance of stopping the spy. Trace over to the left on the same row until you reach the far left column, and this number will be your required defensive hideout level, assuming all of its spies are working in defense.
For example, if you have a level 6 town, and you want to stop a spy from infiltrating at least 75% of the time, you need go to the column at the top that says, $t=6$. Then scroll down that column until you reach a number that is 75 or higher. In this case it is $76$. Then trace over to the left on the same row until you reach the far left column, and you will see that you need a hideout level of $21$.
To determine your current % protection from infiltration, with one finger find your town level, $t$, at the top, and trace down that column. With the other finger find the row with your current hideout level at the left, and trace across to the right until both fingers meet. The box, where your two fingers meet, will show you what your current % protection from infiltration is.
To determine your level of protection if some of your spies are not working in defense (i.e. spying on other people), then simply subtract 2% for every spy on a mission from the number in the box.
The two exceptions to this rule are when the number in the box is 5 or 95. If it is 5, it will always remain at 5. If it is 95, then you can use the formula below:
$Calculated Risk = 7e - 2a - 2t - 59$
Where $a$ is the number of spies who are not working in defense (i.e. spying on other people).
$e=$
$t=$
3 4 5 6 7 8 9 10 11 12 13 14 15
10 5 5 5 5 5 5 5 5 5 5 5 5 5
11 12 10 8 6 5 5 5 5 5 5 5 5 5
12 19 17 15 13 11 9 7 5 5 5 5 5 5
13 26 24 22 20 18 16 14 12 10 8 6 5 5
14 33 31 29 27 25 23 21 19 17 15 13 11 9
15 40 38 36 34 32 30 28 26 24 22 20 18 16
16 47 45 43 41 39 37 35 33 31 29 27 25 23
17 54 52 50 48 46 44 42 40 38 36 34 32 30
18 61 59 57 55 53 51 49 47 45 43 41 39 37
19 68 66 64 62 60 58 56 54 52 50 48 46 44
20 75 73 71 69 67 65 63 61 59 57 55 53 51
21 82 80 78 76 74 72 70 68 66 64 62 60 58
22 89 87 85 83 81 79 77 75 73 71 69 67 65
23 95 94 92 90 88 86 84 82 80 78 76 74 72
24 95 95 95 95 95 93 91 89 87 85 83 81 79
25 95 95 95 95 95 95 95 95 94 92 90 88 86
26 95 95 95 95 95 95 95 95 95 95 95 95 93
27 95 95 95 95 95 95 95 95 95 95 95 95 95
28 95 95 95 95 95 95 95 95 95 95 95 95 95
29 95 95 95 95 95 95 95 95 95 95 95 95 95
30 95 95 95 95 95 95 95 95 95 95 95 95 95
31 95 95 95 95 95 95 95 95 95 95 95 95 95
32 95 95 95 95 95 95 95 95 95 95 95 95 95
## Caught spies Editar
Occasionally, spies are being caught due to high level of spy out chance. However, the level of spy out chance will decrease after a certain amount of time and will increase again after another mission.
If unfortunate, you may get a report like this:
This means that your spy has been caught and executed , so he won't be able to return to your town. Based on a random chance, he may give a report as shown in the above section, so the player you wanted to spy may be informed of what he was trying to do, how many resources you have in your town, how many workers you have assigned on your island or how many and what units are stationed in your town. There also a chance that they may receive no information other than the spy's capture. You will need to train and deploy a new spy as a replacement.
Some times you may also get a report like this:
• Status: Mission aborted...
Report: Your spy was discovered, but could flee in time. He is now returning to your home town. You should give him a little rest...
The player you wanted to spy will be informed about your spy that has been caught and maybe the mission he was trying to complete.
Spy Caught Report Wine is used, but sometimes... they can get rowdy
## Usefulness of some abilities Editar
Due to certain mechanics of the game, the player can automatically observe the wealth of another by looking in the highscores, opposed to risking the chance of a spy being lost and wasting gold .
Also, observing communications can also be quite futile, as the only things the spy can get is who the enemy is communicating to, and what the subject is, which itself is only limited to certain options.
## Outros(as) Misc
O conteúdo da comunidade está disponível sob CC-BY-SA salvo indicação em contrário.
| 2019-11-22T00:33:20 |
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|
https://ftp.mcs.anl.gov/pub/fathom/moab-docs/classMBMesquite_1_1AWSizeNB1.html
|
MOAB: Mesh Oriented datABase (version 5.3.1)
MBMesquite::AWSizeNB1 Class Reference
#include <AWSizeNB1.hpp>
Inheritance diagram for MBMesquite::AWSizeNB1:
Collaboration diagram for MBMesquite::AWSizeNB1:
## Public Member Functions
virtual MESQUITE_EXPORT ~AWSizeNB1 ()
virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqError &err)
Evaluate $$\mu(A,W)$$.
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqMatrix< 2, 2 > &deriv_wrt_A, MsqError &err)
Gradient of $$\mu(A,W)$$ with respect to components of A.
virtual MESQUITE_EXPORT bool evaluate_with_hess (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqMatrix< 2, 2 > &deriv_wrt_A, MsqMatrix< 2, 2 > second_wrt_A[3], MsqError &err)
Hessian of $$\mu(A,W)$$ with respect to components of A.
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqError &err)
Evaluate $$\mu(A,W)$$.
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqMatrix< 3, 3 > &deriv_wrt_A, MsqError &err)
Gradient of $$\mu(A,W)$$ with respect to components of A.
virtual MESQUITE_EXPORT bool evaluate_with_hess (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqMatrix< 3, 3 > &deriv_wrt_A, MsqMatrix< 3, 3 > second_wrt_A[6], MsqError &err)
Hessian of $$\mu(A,W)$$ with respect to components of A.
## Detailed Description
$$(\alpha - \omega)^2$$
Definition at line 42 of file AWSizeNB1.hpp.
## Constructor & Destructor Documentation
MBMesquite::AWSizeNB1::~AWSizeNB1 ( ) [virtual]
Definition at line 46 of file AWSizeNB1.cpp.
{}
## Member Function Documentation
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate ( const MsqMatrix< 2, 2 > & A, const MsqMatrix< 2, 2 > & W, double & result, MsqError & err ) [virtual]
Evaluate $$\mu(A,W)$$.
Parameters:
A 2x2 active matrix W 2x2 target matrix result Output: value of function
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate ( const MsqMatrix< 3, 3 > & A, const MsqMatrix< 3, 3 > & W, double & result, MsqError & err ) [virtual]
Evaluate $$\mu(A,W)$$.
Parameters:
A 3x3 active matrix W 3x3 target matrix result Output: value of function
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate_with_grad ( const MsqMatrix< 2, 2 > & A, const MsqMatrix< 2, 2 > & W, double & result, MsqMatrix< 2, 2 > & deriv_wrt_A, MsqError & err ) [virtual]
Gradient of $$\mu(A,W)$$ with respect to components of A.
Parameters:
A 2x2 active matrix W 2x2 target matrix result Output: value of function deriv_wrt_A Output: partial deriviatve of $$\mu$$ wrt each term of A, evaluated at passed A. $\left[\begin{array}{cc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} \\ \end{array}\right]$
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate_with_grad ( const MsqMatrix< 3, 3 > & A, const MsqMatrix< 3, 3 > & W, double & result, MsqMatrix< 3, 3 > & deriv_wrt_A, MsqError & err ) [virtual]
Gradient of $$\mu(A,W)$$ with respect to components of A.
Parameters:
A 3x3 active matrix W 3x3 target matrix result Output: value of function deriv_wrt_A Output: partial deriviatve of $$\mu$$ wrt each term of A, evaluated at passed A. $\left[\begin{array}{ccc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} & \frac{\partial\mu}{\partial A_{0,2}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} & \frac{\partial\mu}{\partial A_{1,2}} \\ \frac{\partial\mu}{\partial A_{2,0}} & \frac{\partial\mu}{\partial A_{2,1}} & \frac{\partial\mu}{\partial A_{2,2}} \end{array}\right]$
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate_with_hess ( const MsqMatrix< 2, 2 > & A, const MsqMatrix< 2, 2 > & W, double & result, MsqMatrix< 2, 2 > & deriv_wrt_A, MsqMatrix< 2, 2 > second_wrt_A[3], MsqError & err ) [virtual]
Hessian of $$\mu(A,W)$$ with respect to components of A.
Parameters:
A 2x2 active matrix W 2x2 target matrix result Output: value of function deriv_wrt_A Output: partial deriviatve of $$\mu$$ wrt each term of A, evaluated at passed A. second_wrt_A Output: 4x4 matrix of second partial deriviatve of $$\mu$$ wrt each term of A, in row-major order. The symmetric matrix is decomposed into 2x2 blocks and only the upper diagonal blocks, in row-major order, are returned. $\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial A_{0,0}^2} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}^2} \\ \end{array}\right]$
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
virtual MESQUITE_EXPORT bool MBMesquite::AWSizeNB1::evaluate_with_hess ( const MsqMatrix< 3, 3 > & A, const MsqMatrix< 3, 3 > & W, double & result, MsqMatrix< 3, 3 > & deriv_wrt_A, MsqMatrix< 3, 3 > second_wrt_A[6], MsqError & err ) [virtual]
Hessian of $$\mu(A,W)$$ with respect to components of A.
Parameters:
A 3x3 active matrix W 3x3 target matrix result Output: value of function deriv_wrt_A Output: partial deriviatve of $$\mu$$ wrt each term of A, evaluated at passed A. second_wrt_A Output: 9x9 matrix of second partial deriviatve of $$\mu$$ wrt each term of A, in row-major order. The symmetric matrix is decomposed into 3x3 blocks and only the upper diagonal blocks, in row-major order, are returned. $\left[\begin{array}{ccc|ccc|ccc} \frac{\partial^{2}\mu}{\partial A_{0,0}^2} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,2}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,2}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,2}^2} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,2}} \\ \hline & & & \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}^2} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,2}^2} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,2}} \\ \hline & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}^2} & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{2,1}^2} & \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} & \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} & \frac{\partial^{2}\mu}{\partial A_{2,2}^2} \\ \end{array}\right]$
Returns:
false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.
Reimplemented from MBMesquite::AWMetric.
std::string MBMesquite::AWSizeNB1::get_name ( ) const [virtual]
Reimplemented from MBMesquite::AWMetricNonBarrier.
Definition at line 41 of file AWSizeNB1.cpp.
{
return "AWSizeNB1";
}
List of all members.
The documentation for this class was generated from the following files:
| 2021-12-02T13:11:10 |
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|
https://par.nsf.gov/biblio/10095848-search-top-quark-partners-charge-same-sign-dilepton-single-lepton-final-states-proton-proton-collisions-sqrt-tev
|
Search for top quark partners with charge 5/3 in the same-sign dilepton and single-lepton final states in proton-proton collisions at s = 13 $$\sqrt{s}=13$$ TeV
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10095848
Journal Name:
Journal of High Energy Physics
Volume:
2019
Issue:
3
ISSN:
1029-8479
| 2022-08-08T22:53:06 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_astpre/sec_cu3pre_cali/ssec_cu3pre_cali_ccdbias.html
|
# 2.3.5 CCD bias and bias non-uniformity
Author(s): Nigel Hambly
As is usual in imaging systems that employ charge-coupled devices (CCDs) and analogue-to-digital converters (ADCs), the input to the initial amplification stage of the latter is offset by a small, constant voltage to prevent thermal noise at low signal levels from causing wrap-around across zero digitised units. The Gaia CCDs and associated electronic controllers and amplifiers are described in detail in Kohley et al. (2012). The readout registers of each Gaia CCD incorporate 14 prescan pixels (i.e., those having no corresponding columns of pixels in the main light-sensitive array; Figure 1.3). These enable monitoring of the prescan levels, and the video chain noise fluctuations for zero photo-electric signal, at a configurable frequency and for configurable across-scan (AC) hardware sampling. In practice, the acquisition of prescan data is limited to the standard un-binned (1 pixel AC) and fully binned (2, 10, or 12 pixel AC depending on instrument and mode) and to a burst of 1024 one-millisecond samples each once every 70 minutes in order that the volume of prescan data handled on board and telemetred to the ground does not impact significantly on the science data telemetry budget.
## Video chain offset levels and total detection noise
The read noise (or, more correctly, the video chain total detection noise including noise contributions from CCD readout noise, ADC and quantisation noise, etc.) can be assessed from the short timescale fluctuations measured in the prescan levels. Figure 2.4 shows the offset levels and measured total detection noise for the FPA science devices. Table 2.1 gives a summary of the required and measured noise properties of the various instrument video chains. From the sample-to-sample fluctuations measured in the 1 second prescan bursts, all devices are operating well within the requirements. All devices are operating nominally as regards their offset and read noise properties.
## Offset stability
The approximately hourly monitoring of the prescan pixels is suitable for characterising any longer timescale drifts in the offsets characteristics. For example, Figure 2.5 shows the total video chain detection noise as measured from prescan fluctuations over an extended period of over 1000 revolutions (corresponding to more than 250 days). Over this period (July 2014 to May 2015) there is no discernible degradation in the video chain performance. This remains true up to the day of writing (February 2018).
Figure 2.6 shows the long timescale stability of one device in the Gaia focal plane. In this case (device AF2 on row 4 of the FPA), the long term drift over more than 100 days is $\sim 1$ ADU, apart from the electronic disturbance near OBMT revolution 1320 (this was caused by payload module heaters being activated during a ‘de-contamination’ period in September 2014; Table 1.6). The roughly hourly monitoring of the offsets via the prescan data allows the calibration of the additive signal bias early in the daily processing chain, including the effects of long timescale drift and any electronic disturbances of the kind illustrated in Figure 2.6. The ground segment receives the bursts of prescan data for all devices and distils them into ‘bias records’ containing one or more bursts per device. These provide robustly estimated mean levels along with dispersion statistics for noise performance monitoring. Spline interpolation amongst these values is used to provide an offset model at arbitrary times within a processing period. Figure 2.7 shows a detailed example around the large excursion seen in Figure 2.6.
Figure 2.6 illustrates the small offset difference between the un-binned and fully binned sample modes for the device in question. In fact, there are various subtle features in the behaviour of the offsets for each Gaia CCD associated with the operational mode and electronic environment. These manifest themselves as small (typically a few ADU for non-RVS video chains, but up to $\sim$100 ADU in the worst-case RVS devices), very short timescale ($\sim$10 $\mu$s) perturbations to the otherwise highly stable offsets. The features are known collectively as ‘offset non-uniformities’ and, because the effect presumably originates somewhere in the CCD–PEM coupling, it is also known as the ‘PEM–CCD offset anomaly’. The effect requires a separate calibration process and a correction procedure that involves the on-ground reconstruction of the readout timing of every sample read by the CCDs since they are a complex function of the sample readout sequencing. This procedure is beyond the time-limited resources of the near real-time daily processing chain and is left to the offline cyclic data reductions at the Data Processing Centres associated with each of the three main Gaia instruments. For a detailed description of the characteristics of these non-uniformities along with their calibration and correction, see Hambly et al. (2018).
| 2019-05-20T14:48:57 |
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|
https://deathstranding.fandom.com/wiki/Q-pid
|
## FANDOM
115 Pages
A Q-pid is a necklace bearing a series of tag-engraved physics equations, containing all of the necessary security and operations protocols to integrate a terminal location into the Chiral Network. All established strand points are accessible to those bearing the required equations.
Sam is given a Q-pid upon undertaking his expedition across America.
## List of equations Edit
Inscribed equations are processed in the following order, and include:
1. $\partial_t q = \underline{\underline{D}} \,\nabla^2 q + R(q)$
Reaction-diffusion equation, represented in the general form.
2. $i \gamma^\mu \partial_\mu \psi(x) - m \psi(x) = 0$
Dirac equation, a part of quantum mechanics relating to Einstein's special relativity. It predicted the existence of antimatter.
3. $\phi = (\frac{\phi_1}{\phi_2})$
Higgs field equation, in a simplified form.
4. $G_\mu + \Lambda g_{\mu\nu} = \kappa T_{\mu\nu}$
Einstein field equation, which describes gravitation, and notably uses Einstein's gravitational constant $\kappa$.
5. Quantum entanglement state.
6. $r_g = \frac{2 G M}{c^2}$
Schwartzschild radius, the radius to which an object would have to be compressed (i.e., increasing its density without losing any of its mass) in order to turn it into a black hole.
After the above equations are processed, the Schrödinger equation and an equation related to Lagrangian density, along with others, are then additionally loaded and displayed.
## Edit
Community content is available under CC-BY-SA unless otherwise noted.
| 2019-10-16T09:44:26 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S017NOS&home=sumtabB
|
# LIMIT ON ${{\boldsymbol n}}{{\boldsymbol n}^{\,'}}$ OSCILLATIONS INSPIRE search
Lee and Yang (LEE 1956 ) proposed the existence of mirror world in an attempt to restore global parity symmetry. See BEREZHIANI 2006 for a recent discussion.
VALUE (s) CL% DOCUMENT ID TECN COMMENT
$\bf{> 414}$ 90
2008
CNTR UCN, B field on $\&$ off
• • • We do not use the following data for averages, fits, limits, etc. • • •
$> 12$ 95 1
2009 A
CNTR UCN, scan 0${}\leq{}B{}\leq{}$12.5 $\mu$T
$> 103$ 95
2007
CNTR UCN, B field on $\&$ off
1 Losses of neutrons due to oscillations to mirror neutrons would be maximal when the magnetic fields ${{\mathit B}}$ and ${{\mathit B}^{\,'}}$ in the two worlds were equal. Hence the scan over ${{\mathit B}}$ by ALTAREV 2009A: the limit applies for any ${{\mathit B}^{\,'}}$ over the given range. At ${{\mathit B}^{\,'}}$ = 0, the limit is 141 s (95$\%$ CL).
References:
ALTAREV 2009A
PR D80 032003 Neutron to Mirror-Neutron Oscillations in the Presence of Mirror Magnetic Fields
SEREBROV 2008
PL B663 181 Experimental Search for Neutron$−$Mirror Neutron Oscillations using Storage of Ultracold Neutrons
BAN 2007
PRL 99 161603 Direct Experimental Limit on Neutron$−$Mirror-Neutron Oscillations
BEREZHIANI 2006
PRL 96 081801 Neutron$−$Mirror-Neutron Oscillations: How Fast Might They Be?
LEE 1956
PR 104 254 Question of Parity Conservation in Weak Interactions
| 2019-04-19T08:26:47 |
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|
http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/DM/DMPlexSetAdjacencyUseClosure.html
|
petsc-master 2016-07-22
Report Typos and Errors
Define adjacency in the mesh using the transitive closure
Synopsis
#include "petscdmplex.h"
#include "petscdmlabel.h"
Input Parameters
dm - The DM object useClosure - Flag to use the closure
Notes
FEM: Two points p and q are adjacent if q \in closure(star(p)), useCone = PETSC_FALSE, useClosure = PETSC_TRUE
FVM: Two points p and q are adjacent if q \in support(p+cone(p)), useCone = PETSC_TRUE, useClosure = PETSC_FALSE
FVM++: Two points p and q are adjacent if q \in star(closure(p)), useCone = PETSC_TRUE, useClosure = PETSC_TRUE
| 2016-07-23T15:41:39 |
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|
http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ordplot.htm
|
Dataplot Vol 1 Vol 2
# ORD PLOT
Name:
ORD PLOT
Type:
Graphics Command
Purpose:
Generates an Ord plot.
Description:
An Ord plot can be used to distinguish whether a data set follows a Poisson, binomial, negative binomial, or logarithmic series distribution.
If x and nx denote the class value and the corresponding class frequency, then the Ord plot is a plot of
$$\frac{x n_{x}} {n_{x-1}}$$ versus x
If this plot is approximately linear, then it can help distinguish between these four distributions based on the following table:
Distribution Slope
b
Intercept
a
Parameter Estimate
Poisson 0 + $$\lambda$$ = a
Binomial - + p = b/(b-1)
Negative Binomial + + p = 1 - b
Logarithmic Series + - $$\theta$$ = -a
The slope and intercept can be determined by fitting a line to the plotted points. We follow the suggestion of Friendly of using the weights
$$w_{x} = \sqrt{n_{x} - 1}$$
This compensates for the fact that classes with small frequency have large variance.
The primary disadvantage of this plot is that a discrepant frequency affects the points for both x and x+1. For this reason, the Ord plot does not have good resistance properties.
Syntax 1:
ORD PLOT <y> <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax is used for the case where you have raw data. Dataplot will automatically create the frequency table.
Syntax 2:
ORD PLOT <y> <x> <SUBSET/EXCEPT/FOR qualification>
where <y> is a variable containing frequencies;
<x> is a variable containing the class value;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax is used for the case where your data is already in the form of a frequency table.
Examples:
ORD PLOT Y
ORD PLOT Y X
Note:
The appearance of the plot can be controlled with the LINE and CHARACTER commands. The first setting is for the plot points and the second setting is for the fitted line. This is demonstrated with the sample plot below.
Note:
The following internal parameters are saved by this plot:
PPA0 - the intercept of the fitted line
PPA1 - the slope of the fitted line
Default:
None
Synonyms:
None
Related Commands:
POSSION PLOT = Generates a Poisson plot. PROBABILITY PLOT = Generates a probability plot. PPCC PLOT = Generates a ppcc plot. KS PLOT = Generates a Kolmogorov-Smirnov (or chi-square) plot. ORD PLOT = Generate an Ord plot. HISTOGRAM = Generates a histogram. LINES = Sets the type for plot lines. CHARACTER = Sets the type for plot characters.
References:
Friendly (2000), "Visualizing Categorical Data", SAS Publishing Inc., Cary, NC, pp. 49-56.
Applications:
Distributional Modeling
Implementation Date:
2007/5
Program:
. Data from p. 47 of Friendly
0 109
1 65
2 22
3 3
4 1
end of data
.
title case asis
title offset 2
label case asis
title Ord Plot
y1label Frequency Ratio
x1label x
.
tic offset units screen
tic offset 3 3
xlimits 1 4
major xtic mark number 4
minor xtic mark number 0
.
character x blank
line blank dotted
.
ord plot y x
NIST is an agency of the U.S. Commerce Department.
Date created: 7/25/2007
Last updated: 10/13/2015
| 2017-10-24T00:20:18 |
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|
https://mooseframework.inl.gov/modules/porous_flow/tutorial_01.html
|
# Porous Flow Tutorial Page 01. A single fluid
This tutorial page describes how PorousFlow can be used to solve a very simple fluid-flow problem. The physics are described by the equation (1) This is the simplest type of equation that PorousFlow solves. It is often used in thermo-poro-elasticity, but PorousFlow is often employed to solve much more complex equations. See governing equations for further details, and PorousFlowFullySaturatedMassTimeDerivative and PorousFlowFullySaturatedDarcyBase for the derivation of Eq. (1) from the general governing equations. In this equation:
• is the fluid porepressure (units of Pa)
• an over-dot represents a time derivative
• is the Biot Modulus (units of Pa)
• is the Biot coefficient (dimensionless)
• is the rate of volumetric strain of the solid rock (units s)
• is the effective volumetric thermal expansion coefficient (units K)
• is the temperature (units K)
• represents a spatial derivative
• is the permeability tensor (units m)
• is the fluid viscosity (units Pa.s)
• is the fluid density (units kg.m)
• is the gravitational acceleration (units m.s)
The units suggested here are not manditory: any consistent unit system may be used in MOOSE. For instance, in reservoir physics it is often convenient to express everything in MPa and years rather than Pa and seconds.
The Biot modulus is (2) and the effective volumetric thermal expansion coefficient is (3) In these equations
• is the porosity (dimensionless)
• is the bulk modulus of the fluid (units Pa)
• is the bulk modulus of the drained porous skeleton (units Pa)
• is the volumetric thermal expansion coefficient of the drained porous skeleton (units K)
• is the volumetric thermal expansion coefficient of the fluid (units K)
The derivation of Eq. (1) from the full PorousFlow equations assumes that and are constant.
In this tutorial page we will be solving fluid flow only, so the and in Eq. Eq. (1) are ignored (set to zero).
All PorousFlow input files must contain a PorousFlowDictator, and almost all PorousFlow objects (Kernels, Materials, etc) require the PorousFlowDictator to be provided. This enables PorousFlow to make consistency checks on the number of fluid phases, components, chemical reactants, etc. Therefore, most input files specify its name in the Globals block:
[GlobalParams]
PorousFlowDictator = dictator
[]
(modules/porous_flow/examples/tutorial/01.i)
Most PorousFlow simulations require fluid properties to be supplied. In this instance, the SimpleFluidProperties are used, which assume a constant fluid bulk modulus and viscosity:
[Modules]
[./FluidProperties]
[./the_simple_fluid]
type = SimpleFluidProperties
bulk_modulus = 2E9
viscosity = 1.0E-3
density0 = 1000.0
[../]
[../]
[]
(modules/porous_flow/examples/tutorial/01.i)
The DE of Eq. (1) is implemented in the following way
[Variables]
[./porepressure]
[../]
[]
[PorousFlowBasicTHM]
porepressure = porepressure
coupling_type = Hydro
gravity = '0 0 0'
fp = the_simple_fluid
[]
(modules/porous_flow/examples/tutorial/01.i)
There is just one variable — the porepressure — and there is no coupling with heat or mechanics. Gravity is set to zero. The PorousFlowBasicTHM has other optional inputs that you are encouraged to explore, including setting the temperature to a non-default value, or to the value of an AuxVariable (your fluid properties may depend on temperature, even in an isothermal situation).
In this tutorial page, the only boundary condition is to fix the porepressure to 1MPa at the injection area (the other boundaries default to zero flux):
[BCs]
[./constant_injection_porepressure]
type = PresetBC
variable = porepressure
value = 1E6
boundary = injection_area
[../]
[]
(modules/porous_flow/examples/tutorial/01.i)
The porosity, Biot modulus and permeability are defined through the Materials block:
[Materials]
[./porosity]
type = PorousFlowPorosity
porosity_zero = 0.1
[../]
[./biot_modulus]
type = PorousFlowConstantBiotModulus
biot_coefficient = 0.8
solid_bulk_compliance = 2E-7
fluid_bulk_modulus = 1E7
[../]
[./permeability_aquifer]
type = PorousFlowPermeabilityConst
block = aquifer
permeability = '1E-14 0 0 0 1E-14 0 0 0 1E-14'
[../]
[./permeability_caps]
type = PorousFlowPermeabilityConst
block = caps
permeability = '1E-15 0 0 0 1E-15 0 0 0 1E-16'
[../]
[]
(modules/porous_flow/examples/tutorial/01.i)
The result is shown in Figure 1
Figure 1: Porepressure evolution in the borehole-aquifer-caprock system.
| 2019-05-23T12:53:04 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=Q007STX
|
# t-channel Single ${{\boldsymbol t}}$ Production Cross Section in ${{\boldsymbol p}}{{\boldsymbol p}}$ Collisions at $\sqrt {s }$ = 13$~$TeV INSPIRE search
VALUE (pb) DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$130$ $\pm1$ $\pm19$ 1
2020 D
CMS ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}$, ${{\mathit \ell}}+\not E_T$+ ${}\geq{}$2 ${{\mathit j}}$
$77$ $\pm1$ $\pm12$ 1
2020 D
CMS ${\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$, ${{\mathit \ell}}+\not E_T$+ ${}\geq{}$2 ${{\mathit j}}$
$156$ $\pm5$ $\pm27$ $\pm3$ 2
2017 H
ATLS ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}$, ${{\mathit \ell}}+\not E_T$+2 j (1${{\mathit b}}$, 1 forward j)
$91$ $\pm4$ $\pm18$ $\pm2$ 2
2017 H
ATLS ${\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$, ${{\mathit \ell}}+\not E_T$+2 j (1${{\mathit b}}$, 1 forward j)
$154$ $\pm8$ $\pm9$ $\pm19$ $\pm4$ 3
2017 AA
CMS ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}$, ${{\mathit \mu}}+{}\geq{}$2 j (1${{\mathit b}}$)
$85$ $\pm10$ $\pm4$ $\pm11$ $\pm2$ 3
2017 AA
CMS ${\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$, ${{\mathit \mu}}+{}\geq{}$2 j (1${{\mathit b}}$)
1 SIRUNYAN 2020D based on 35.9 fb${}^{-1}$ of data. Different categories of jet and b jet multiplicity and multivariate discriminators are used to separate signal and background events. The cross section ratio is measured to be ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}/{\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$ = $1.68$ $\pm0.02$ $\pm0.05$. CKM matrix element is obtained as $\vert$f$_{LV}\mathit V_{\mathit tb}\vert$ = $0.98$ $\pm0.07$(exp)$\pm0.02$(theo) where f$_{LV}$ is an anomalous form factor. All results are in agreement with the SM.
2 AABOUD 2017H based on 3.2 fb${}^{-1}$ of data. A maximum-likelihood fit to neural-network discriminant distributions is used to separate signal and background events. The third error is for luminosity. The cross section ratio is measured to be ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}/{\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$ = $1.72$ $\pm0.09$ $\pm0.18$. A lower limit $\vert \mathit V_{\mathit tb}\vert$ $>$ 0.84 (95$\%$ CL) is obtained. All results are in agreement with the SM.
3 SIRUNYAN 2017AA based on 2.2 fb${}^{-1}$ of data. A multivariate discriminator is used to separate signal and background events. The four errors are from statitics, experimental systematics, theory, and luminosity. The cross section ratio is measured to be ${\mathit \sigma (}$ ${{\mathit t}}{{\mathit q}}{)}/{\mathit \sigma (}$ ${{\overline{\mathit t}}}{{\mathit q}}{)}$ = $1.81$ $\pm0.18$ $\pm0.15$. CKM matrix element is obtained as $\vert \mathit V_{\mathit tb}\vert$ = $1.05$ $\pm0.07$(exp)$\pm0.02$(theo). All results are in agreement with the SM.
References:
SIRUNYAN 2020D
PL B800 135042 Measurement of the single top quark and antiquark production cross sections in the $t$ channel and their ratio in proton-proton collisions at $\\sqrt{s}=$ 13 TeV
AABOUD 2017H
JHEP 1704 086 Measurement of the Inclusive Cross-Sections of Single top-Quark and top-Antiquark ${\mathit {\mathit t}}$-Channel Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
SIRUNYAN 2017AA
PL B772 752 Cross Section Measurement of ${\mathit {\mathit t}}$-Channel Single Top Quark Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV
| 2020-09-21T09:13:58 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=Q007TX7
|
# ${{\boldsymbol t}}{{\overline{\boldsymbol t}}}$ Production Cross Section in ${{\boldsymbol p}}{{\boldsymbol p}}$ Collisions at $\sqrt {s }$ = 7 TeV INSPIRE search
Unless otherwise noted the first quoted error is from statistics, the second from systematic uncertainties, and the third from luminosity. If only two errors are quoted the luminosity is included in the systematic uncertainties.
VALUE (pb) DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$161.7$ $\pm6.0$ $\pm12.0$ $\pm3.6$ 1
2017 B
CMS ${{\mathit \ell}}+\not E_T+{}\geq{}$4j (${}\geq{}1{{\mathit b}}$)
$173.6$ $\pm2.1$ ${}^{+4.5}_{-4.0}$ $\pm3.8$ 2
2016 AW
CMS ${{\mathit e}}$ + ${{\mathit \mu}}$ + $\not E_T$ + ${}\geq{}$0j
$181.2$ $\pm2.8$ ${}^{+10.8}_{-10.6}$ 3
2015 BO
ATLS ${{\mathit e}}$ + ${{\mathit \mu}}$ + $\not E_T$ + ${}\geq{}$0j
$178$ $\pm3$ $\pm16$ $\pm3$ 4
2015 CC
ATLS ${{\mathit \ell}}$+jets, ${{\mathit \ell}}{{\mathit \ell}}$ +jets, ${{\mathit \ell}}{{\mathit \tau}_{{h}}}$ +jets
5
2015 R
LHCB ${{\mathit \mu}}+{}\geq{}$1j(${{\mathit b}}$-tag) forward region
$182.9$ $\pm3.1$ $\pm6.4$ 6
2014 AY
ATLS ${{\mathit e}}$ + ${{\mathit \mu}}$ + 1 or 2${{\mathit b}}$ jets
$194$ $\pm18$ $\pm46$ 7
2013 X
ATLS ${{\mathit \tau}_{{h}}}$ + $\not E_T$ + ${}\geq{}$5j (${}\geq{}2{{\mathit b}}$)
$139$ $\pm10$ $\pm26$ 8
2013 AY
CMS ${}\geq{}$6 jets with 2 b-tags
$158.1$ $\pm2.1$ $\pm10.8$ 9
2013 BB
CMS ${{\mathit \ell}}$ + $\not E_T$ + jets(${}\geq{}$1 b-tag)
$152$ $\pm12$ $\pm32$ 10
2013 BE
CMS ${{\mathit \tau}_{{h}}}$+ $\not E_T$+ ${}\geq{}$4 jets (${}\geq{}$1 b)
$177$ $\pm20$ $\pm14$ $\pm7$ 11
2012 B
$176$ $\pm5$ ${}^{+14}_{-11}$ $\pm8$ 12
2012 BF
ATLS ${{\mathit \ell}}{{\mathit \ell}}$ +$\not E_T+{}\geq{}$2j
$187$ $\pm11$ ${}^{+18}_{-17}$ $\pm6$ 13
2012 BO
ATLS ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$ 3j with ${{\mathit b}}$-tag
$186$ $\pm13$ $\pm20$ $\pm7$ 14
2012 CG
ATLS ${{\mathit \ell}}$ + ${{\mathit \tau}_{{h}}}$+ $\not E_T+{}\geq{}$2j (${}\geq{}1{{\mathit b}}$)
$143$ $\pm14$ $\pm22$ $\pm3$ 15
2012 AC
CMS ${{\mathit \ell}}$ + ${{\mathit \tau}_{{h}}}$+ $\not E_T+{}\geq{}$2j (${}\geq{}1{{\mathit b}}$)
$161.9$ $\pm2.5$ ${}^{+5.1}_{-5.0}$ $\pm3.6$ 16
2012 AX
CMS ${{\mathit \ell}}{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$ 2${{\mathit b}}$
$145$ $\pm31$ ${}^{+42}_{-27}$ 17
2011 A
ATLS ${{\mathit \ell}}+\not E_T+{}\geq{}$4j, ${{\mathit \ell}}{{\mathit \ell}}$ +$\not E_T+{}\geq{}$2j
$173$ ${}^{+39}_{-32}$ $\pm7$ 18
2011 AA
CMS ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$3 jets
$168$ $\pm18$ $\pm14$ $\pm7$ 19
2011 F
CMS ${{\mathit \ell}}{{\mathit \ell}}$ + $\not E_T$ + jets
$154$ $\pm17$ $\pm6$ 20
2011 Z
CMS Combination
$194$ $\pm72$ $\pm24$ $\pm21$ 21
2011 A
CMS ${{\mathit \ell}}{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$2 jets
1 KHACHATRYAN 2017B based on 5.0 fb${}^{-1}$ of data, using a binned likelihood fit of templates to the data. Also the ratio ${\mathit \sigma (}$ ${{\mathit t}}{{\overline{\mathit t}}}$ ; 8 TeV${)}/{\mathit \sigma (}$ ${{\mathit t}}{{\overline{\mathit t}}}$ ; 7 TeV${)}$ = $1.43$ $\pm0.04$ $\pm0.07$ $\pm0.05$ is reported. The results are in agreement with NNLO SM predictions.
2 KHACHATRYAN 2016AW based on 5.0 fb${}^{-1}$ of data, using a binned likelihood fit to differential distributions of ${{\mathit b}}$-tagged and non-${{\mathit b}}$-tagged jets. The result is in good agreement with NNLO SM predictions.
3 Based on 4.6 fb${}^{-1}$ of data. Uses a template fit to distributions of $\not E_T$ and jet multiplicities to measure simultaneously ${{\mathit t}}{{\overline{\mathit t}}}$ , ${{\mathit W}}{{\mathit W}}$ , and ${{\mathit Z}}$/ ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}$ cross sections, assuming ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
4 AAD 2015CC based on 4.6 fb${}^{-1}$ of data. The event selection criteria are optimized for the ${{\mathit \ell}}{{\mathit \tau}_{{h}}}$ + jets channel. Using only this channel $183$ $\pm9$ $\pm23$ $\pm3$ pb is derived for the cross section.
5 AAIJ 2015R, based on 1.0 fb${}^{-1}$ of data, reports $0.239$ $\pm0.053$ $\pm0.033$ $\pm0.024$ pb cross section for the forward fiducial region ${{\mathit p}_{{T}}}({{\mathit \mu}}$) $>$ 25 GeV, 2.0 $<$ ${{\mathit \eta}}({{\mathit \mu}}$) $<$ 4.5, 50 GeV $<$ ${{\mathit p}_{{T}}}$ (${{\mathit b}}$) $<$ 100 GeV, 2.2 $<$ ${{\mathit \eta}}({{\mathit b}}$) $<$ 4.2, ${{\mathit \Delta}}{{\mathit R}}({{\mathit \mu}},{{\mathit b}}$) $>$ 0.5, and ${{\mathit p}_{{T}}}({{\mathit \mu}}+{{\mathit b}}$) $>$ 20 GeV. The three errors are from statistics, systematics, and theory. The result agrees with the SM NLO prediction.
6 AAD 2014AY reports $182.9$ $\pm3.1$ $\pm4.2$ $\pm3.6$ $\pm3.3$ pb value based on 4.6 fb${}^{-1}$ of data. The four errors are from statistics, systematic, luminosity, and the 0.66$\%$ beam energy uncertainty. We have combined the systematic uncertainties in quadrature. The result is for ${\mathit m}_{{{\mathit t}}}$ = 172.5GeV; for other ${\mathit m}_{{{\mathit t}}}$, ${\mathit \sigma (}{\mathit m}_{{{\mathit t}}}{)}$ = $\sigma$(172.5GeV)${\times }[1-0.0028{\times }({\mathit m}_{{{\mathit t}}}-172.5$GeV)]. The result is consistent with the SM prediction at NNLO.
7 Based on 1.67 fb${}^{-1}$ of data. The result uses the acceptance for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
8 Based on 3.54 fb${}^{-1}$ of data.
9 Based on 2.3 fb${}^{-1}$ of data.
10 Based on 3.9 fb${}^{-1}$ of data.
11 Based on 35 pb${}^{-1}$ of data for an assumed top quark mass of ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
12 Based on 0.70 fb${}^{-1}$ of data. The 3 errors are from statistics, systematics, and luminosity. The result uses the acceptance for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
13 Based on 35 pb${}^{-1}$ of data. The 3 errors are from statistics, systematics, and luminosity. The result uses the acceptance for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV and $173$ $\pm17$ ${}^{+18}_{-16}$ $\pm6$ pb is found without the ${{\mathit b}}$-tag.
14 Based on 2.05 fb${}^{-1}$ of data. The hadronic ${{\mathit \tau}}$ candidates are selected using a BDT technique. The 3 errors are from statistics, systematics, and luminosity. The result uses the acceptance for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
15 Based on 2.0 fb${}^{-1}$ and 2.2 fb${}^{-1}$ of data for ${{\mathit \ell}}$ = ${{\mathit e}}$ and ${{\mathit \ell}}$ = ${{\mathit \mu}}$, respectively. The 3 errors are from statistics, systematics, and luminosity. The result uses the acceptance for ${\mathit m}_{{{\mathit t}}}$ = 172.5 GeV.
16 Based on 2.3 fb${}^{-1}$ of data. The 3 errors are from statistics, systematics, and luminosity. The result uses the profile likelihood-ratio (PLB) method and an assumed ${\mathit m}_{{{\mathit t}}}$ of 172.5 GeV.
17 Based on 2.9 pb${}^{-1}$ of data. The result for single lepton channels is $142$ $\pm34$ ${}^{+50}_{-31}$ pb, while for the dilepton channels is $151$ ${}^{+78}_{-62}{}^{+37}_{-24}$ pb.
18 Result is based on 36 pb${}^{-1}$ of data. The first uncertainty corresponds to the statistical and systematic uncertainties, and the second corresponds to the luminosity.
19 Based on 36 pb${}^{-1}$ of data. The ratio of ${{\mathit t}}{{\overline{\mathit t}}}$ and ${{\mathit Z}}/{{\mathit \gamma}^{*}}$ cross sections is measured as ${\mathit \sigma (}$ ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}{)}/{\mathit \sigma (}$ ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}$ / ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ / ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{)}$ = $0.175$ $\pm0.018$(stat)$\pm0.015$(syst) for 60 $<$ ${\mathit m}_{\mathrm { {{\mathit \ell}} {{\mathit \ell}} }}<$ 120 GeV, for which they use an NNLO prediction for the denominator cross section of $972$ $\pm42$ pb.
20 Result is based on 36 pb${}^{-1}$ of data. The first error is from statistical and systematic uncertainties, and the second from luminosity. This is a combination of a measurement in the dilepton channel (CHATRCHYAN 2011F) and the measurement in the ${{\mathit \ell}}$ + jets channel (CHATRCHYAN 2011Z) which yields $150$ $\pm9$ $\pm17$ $\pm6$ pb.
21 Result is based on $3.1$ $\pm0.3$ pb${}^{-1}$ of data.
References:
KHACHATRYAN 2017B
EPJ C77 15 Measurements of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in Lepton+Jets Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at 8 TeV and Ratio of 8 to 7 TeV Cross Sections
KHACHATRYAN 2016AW
JHEP 1608 029 Measurement of the ${\mathit {\mathit t}}−{\mathit {\overline{\mathit t}}}$ Production Cross Section in the ${{\mathit e}}−{{\mathit \mu}}$ Channel in Proton-Proton Collisions at $\sqrt {s }$ = 7 and 8 TeV
PR D91 052005 imultaneous Measurements of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$, ${{\mathit W}^{+}}{{\mathit W}^{-}}$, and ${{\mathit Z}}$ $/$ ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}$ Production Cross-Sections in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
PR D92 072005 Measurements of the Top Quark Branching Ratios into Channels with Leptons and Quarks with the ATLAS Detector
AAIJ 2015R
PRL 115 112001 First Observation of Top Quark Production in the Forward Region
EPJ C74 3109 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross-Section using ${{\mathit e}}{{\mathit \mu}}$ Events with ${\mathit {\mathit b}}$-Tagged Jets in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 and 8 TeV with the ATLAS Detector
EPJ C73 2328 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in the tau + Jets Channel using the ATLAS Detector
CHATRCHYAN 2013BB
PL B720 83 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with Lepton + Jets Final States
CHATRCHYAN 2013AY
JHEP 1305 065 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in the All-Jet Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
CHATRCHYAN 2013BE
EPJ C73 2386 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in the ${{\mathit \tau}}$+jets Channel in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
JHEP 1205 059 Measurement of the Cross Section for Top-Quark Pair Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector using Final States with Two High-${{\mathit p}_{{T}}}$ Leptons
PL B707 459 Measurement of the Top Quark Pair Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7$~$TeV in Dilepton Final States with ATLAS
PL B711 244 Measurement of the Top Quark Pair Production Cross-Section with ATLAS in the Single Lepton Channel
PL B717 89 Measurement of the Top Quark Pair Cross Section with ATLAS in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV using Final States with an Electron or a Muon and a Hadronically Decaying ${{\mathit \tau}}$ Lepton
CHATRCHYAN 2012AC
PR D85 112007 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV in Dilepton Final States Containing a ${{\mathit \tau}}$
CHATRCHYAN 2012AX
JHEP 1211 067 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in the Dilepton Channel in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
EPJ C71 1577 Measurement of the Top Quark-Pair Production Cross Section with ATLAS in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
PR D84 092004 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at 7 TeV in Lepton+Jets Events using ${\mathit {\mathit b}}$-Quark Jet Identification
JHEP 1107 049 Measurement of the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production Cross Section and the Top Quark Mass in the Dilepton Channel in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
EPJ C71 1721 Measurement of the ${{\mathit t}}{{\overline{\mathit t}}}$ Production Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV using the Kinematic Properties of Events with Leptons and Jets
PL B695 424 First Measurement of the Cross Section for top-Quark Pair Production in Proton-Proton Collisions at $\sqrt {s }$ = 7 TeV
| 2020-09-21T10:45:41 |
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http://www.legisquebec.gouv.qc.ca/en/version/cs/V-1.2%20?code=se:59_1&history=20211204
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### V-1.2 - Act respecting off-highway vehicles
59.1. A person who operates an off-highway vehicle at a speed in excess of the prescribed maximum speed is guilty of an offence and is liable to a fine of \$30 plus,
(1) if the speed exceeds the speed limit by 1 to 20 km/h, \$15 for each 5 km/h by which the speed exceeds the speed limit;
(2) if the speed exceeds the speed limit by 21 to 30 km/h, \$20 for each 5 km/h by which the speed exceeds the speed limit;
(3) if the speed exceeds the speed limit by 31 to 45 km/h, \$25 for each 5 km/h by which the speed exceeds the speed limit;
(4) if the speed exceeds the speed limit by 46 to 60 km/h, \$30 for each 5 km/h by which the speed exceeds the speed limit;
(5) if the speed exceeds the speed limit by 61 km/h or more, \$35 for each 5 km/h by which the speed exceeds the speed limit.
2006, c. 12, s. 22; 2014, c. 12, s. 38.
59.1. A person who operates an off-highway vehicle at a speed in excess of the prescribed maximum speed is guilty of an offence and is liable to a fine of \$25 plus,
(1) if the speed exceeds the speed limit by 1 to 20 km/h, \$10 for each 5 km/h by which the speed exceeds the speed limit;
(2) if the speed exceeds the speed limit by 21 to 30 km/h, \$15 for each 5 km/h by which the speed exceeds the speed limit;
(3) if the speed exceeds the speed limit by 31 to 45 km/h, \$20 for each 5 km/h by which the speed exceeds the speed limit;
(4) if the speed exceeds the speed limit by 46 to 60 km/h, \$25 for each 5 km/h by which the speed exceeds the speed limit;
(5) if the speed exceeds the speed limit by 61 km/h or more, \$30 for each 5 km/h by which the speed exceeds the speed limit.
2006, c. 12, s. 22.
| 2022-01-24T14:34:56 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/8164/4972
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Imaging sensors operating in infrared (IR) region of electromagnetic spectrum are gaining importance in airborne automatic target recognition (ATR) applications due to their passive nature of operation. IR imaging sensors exploit the unintended IR radiation emitted by the targets of interest for detection. The ATR systems based on the passive IR imaging sensors employ a set of signal processing algorithms for processing the image information in real-time. The real-time execution of signal processing algorithms provides the sufficient reaction time to the platform carrying ATR system to react upon the target of interest. These set of algorithms include detection, tracking, and classification of low-contrast, small sized-targets. Paper explained a signal processing framework developed to detect and track moving point targets from the acquired IR image sequences in real-time.
The main functionality of infrared (IR) imaging-based airborne automatic target recognition (ATR) systems is to detect, track, and identify the threats by processing the image information. These ATR systems employ wide field of view imaging sensors operating in MWIR (3 µm - 5 µm) or LWIR (8 µm - 12 µm) regions of the electromagnetic spectrum to exploit the IR scene surrounded by platform. The target is expected to be a point size (pixel size) in the image plane due to the wide field of view of imaging sensors. The less spatial extent (point, small) nature of the target pixels relative to the background pixels makes the signal processing algorithm design more challenging for these applications. The specifications of ATR system is highly demanding in terms of probability of detection and false alarm rate. This calls for highly sophisticated signal processing algorithms. Figure 1, depicts the signal processing data flow in a generic imaging-based ATR system1,2. The important stages in signal processing data flow include: Image pre-processing, clutter-rejection, tracking and association, and discrimination.
1.1 Image Pre-processing
The pre-processing handles problems related with the IR Imagery. The IR Imagery generally consists of significant level of noise. The noise is usually associated with the non-uniform response of the detector elements. The non-uniformities can be handled to a certain extent by calibrating each detector element. The problem still exists in handling the pixels, either dead (no response) or saturated (excess photo-current). The localised non-uniformities are within one or two pixels in size. The target size in the image is expected to be within a pixel. The elimination of non-uniformities can improve the system performance. There exists a requirement to identify these pixels and to eliminate them for further processing. In recent developments, the imaging sensors are made to realise the image pre-processing as part of sensor rather than part of ATR system.
Figure 1. Algorithmic data flow in an ATR system.
1.2 Clutter-Rejection
The input to clutter-rejection phase of algorithm is the pre-processed raw image to reject clutter (unwanted signals originated from background). The output image after clutter- rejection stage should ideally contain possible targets. The main goal of clutter-rejection algorithm is to estimate the background and suppress the background clutter level to zero at the same time preserving the signal level. Clutter-rejection (CR) stage operates on every image frame and generates set of detections.
1.3 Tracking and Association
The tracking and association (TA) phase operates on the detections provided by the clutter-rejection module for grouping the detections originated from the same spatial source into single track. TA phase carries out; track initiation, track association, and track-smoothing functionalities.
1.4 Discrimination
Discrimination phase of the algorithm operates on the track database created by tracking and association module. The function of the discrimination module is to identify the track whether it belongs to true target or a false target.
The current work focuses on an algorithm framework for real-time detection and tracking of target of interest with minimal information available related to the target. The paper discusses a clutter-rejection, and tracking algorithm designed for detection and tracking moving point targets from IR image sequences.
Clutter-rejection (CR) stage processes large amount of pixel data from the imaging sensor as a frame to identify few pixels that might contain targets. Clutter-rejection stage has to process the image frames at sensor frame rate for real- time detection of targets. For example if a IR imaging sensor operating at 60 HZ,it can provide one image frame at every 16 ms. In this case the CR stage should process an image frame within 16 ms to identify the pixels that might contain targets.
CR stage identifies the pixels with targets by comparing pixel information with the estimated background information. The large deviation of pixel information from the background information probably due to the presence of a target. There exists several techniques in literature for the detection of point targets from IR image sequences. These techniques can be broadly categorized into:
• Spatial filtering techniques.
• Temporal filtering techniques.
2.1 Spatial Filtering Techniques
The spatial filtering techniques uses the spatial information, in neighbourhood surrounded by pixel under test (PUT) for estimating the background information.
The background information from spatial neighbourhood piexls can be estimated by simple mean or median filtering3,4. Figure 2, depicts a 5x5 spatial neighbourhood surrounded by a PUT ‘S1’. The mean, median filtering schemes are easier to implement but will result very less SNR due to the background estimation inaccuracies. These inaccuracies are due to non-uniform and de-correlated backgrounds that are present surrounded by PUT. This is a common case in wide FOV sensors with less spatial resolution. However there exists other spatial filtering techniques, viz., image morphology based techniques5, Wavelet based decomposition techiques6,7, they require significant information related to target. These techniques can also cause significant loss of target signature in the process of filtering. This can make detection of very low SNR targets difficult. If ATR systems require good detection range then spatial filtering schemes are not the obvious choice for target detection.
Figure 2. Spatial filtering neighbourhood surrounded by pixel under test.
2.2 Temporal Filtering Techniques
Temporal filtering schemes8,9 use information from a set of previous frames for estimating the background information at PUT. The temporal filtering schemes can provide the better estimate for the background due to high correlation between successively sampled images. Figure 3 depicts a temporal neighbourhood surrounded by a PUT.
Figure 3. Temporal filtering neighbourhood surrounded by pixel under test.
For using temporal filtering scheme, the temporal images participating in background estimation process need to be co-registered with sub-pixel accuracy. The more the number of frames used for background estimation will yield better noise filtering. But, too many previous frames can make the background estimation inaccurate due to increase in registration errors.
There exists various other techniques, viz., hypothesis testing10,11, track before detect12-14, techniques that use both the spatial and temporal information15,16 surrounded by PUT for accurately estimating the background information. Hypothesis testing methods are probabilistic techniques that use predefined models for the background to identify target pixels. These techniques have limited applications due to difficulty in modelling the IR clutter using a particular type of distribution. The airborne ATR system has to detect the targets against various backgrounds, like sky, vegetation, sea, industrial, rural, etc. Modelling these wide variety of backgrounds under wide variety of atmospheric conditions is highly impractical. Track before detect (TBD) techniques, on the other hand, require some a priori information related to target (like the target velocity in image plane). The target motion in image plane depends on the aspect angle, and it is highly variable. The TBD techniques uses multiple filter banks for various target velocities in the process of tracking. The tracking in image plane may fail in case of large manoeuvrability of platform carrying the ATR system. These limitations make TBD techniques difficult to implement.
In the present work authors have proposed a method for real-time target detection based on the change detection. The underlying principle behind the proposed approach is that a moving target can introduce certain change from one image to the other image due to its motion or variation in its signature. Figure 4 depicts the proposed clutter-rejection framework.
Figure 4. Proposed clutter-rejection approach
The proposed approach involves a background-estimation process and thresholding the residual image for identifying the possible target pixels.
2.3 Background Estimation
In our approach, the background is estimated by the temporal method. The temporal method uses the moving property of the target, and similarity of the background for two consecutive frames. The main challenge involved in the change-detection method is to align two consecutive frames over time for observing the change. In the present work the two consecutive frames were aligned using a registration process proposed18.
The selected image registration approach requires the platform motion to align the previous frame to the current frame. The platform motion data can be obtained using an onboard inertial navigation system. The registered previous image can give the better estimate for background due to stationary nature of background within one frame acquisition time. Following the registration process, the aligned images are subjected to subtraction for eliminating the background. The residual image is further subjected to threshold operation.
2.4 Threshold
The residual background image will be subjected to threshold operation to identify the pixels with significantly high residual values. The pixels with significantly high signal-to-noise ratio (SNR) values in residual image can be possibly due to the presence of the target. The noise statistics were estimated using neighbourhood pixels surrounded by PUT. Figure 5 depicts the local neighbourhood used for estimating the noise statistics.
Figure 5. Neighbourhood pixels surrounded by PUT for noise statistics estimation.
The pixels values having significant SNR metric are declared as detections in a frame.
$\begin{array}{l}SNR=\frac{\sum _{i=1}^{9}{S}_{i}}{{\text{σ}}_{noise}}\hfill \\ {\text{σ}}_{noise}=std\left({N}_{1}......{N}_{16}\right)\hfill \end{array}$
The tracking and association phase operate on the detections provided by the clutter-rejection module. The goal of tracking and association module17 is to associate detections into the existing tracks and to estimate, maintain (deletion, creation) the track states. The track state estimation can be performed using various prediction filters, viz., fixed gain α-β-γ filter, variable-gain Kalman filter, and particle filters, etc. The tracking and association phase also handles missing detections due to occlusions or target intensity variations for tracking with minimum error. The output from tracking and association phase is database of tracks. A track in the tracks database contains all the information related to the target.
The framework for the tracking module is depicted in Fig. 6. The tracking of the detections need to be performed independent of platform motion. In our approach, inertial coordinate system used is local level local north (LLLN). The clutter-rejection phase provides the detection locations as image coordinates (row, column). In the detection-transformation block, the detection locations are transformed from image coordinate (row, column) to inertial space (azimuth, elevation). The tracking and association module handles the detections efficiently by tracking continuously the targets even in the presence of platform manoeuvres, missing detections, handling sensor noise and track separation or loss conditions.
Figure 6. Various stages of Tracking and Association module.
3.1 Track Initiation Phase
The initiation phase is executed only once when detection set is received for the first time and initialises the track structure, viz., gate width, gate centre, prediction filter. The gate is a region around the predicted detection position where the detection is expected to appear in the next frame. The tracking space is expressed in inertial coordinate (azimuth, elevation) system.
3.2 Track Association
The track association phase associates the detections to their respective gates. The gate is defined as a cone in the inertial space. The detection is associated to a track provided the angle between the gate centre and detection is less than the gate size. The association algorithm implemented is nearest- neighbour approach. The various association rules considered in our approach are
• Associating single detection in a single gate,
• Single detection in multiple gates,
• Multiple detection within a single gate, and
• Multiple detections within multiple gates.
3.3 Track Update Phase
The track update phase estimates target state variables (position, velocity, acceleration) using Kalman Filter17. The target-tracking process is defined through various track states as track undefined, track init, tracking mode and monitoring. The track is initially in undefined state, upon reception of first detection enters to init mode and a gate is initialised. The tracking mode starts after receiving the next detection, wherein the position, velocity, and acceleration are predicted, corrected, and estimated by Kalman filter. The track enters into monitoring state if it stops receiving a valid detection. The track not receiving a valid detection consequently for a defined period is switched to an undefined state.
The large track loss condition occurs due to non-availability of the initial target state (angular rate) information of the target. This causes initial tracking error to be large before the filter reaches steady state. In our proposed approach the initial estimate of the target state (angular rates) is estimated using the first two detections of the track. Initializing the filter with rough estimate of target angular rates can significantly reduce the filter convergence time.
Performance evaluation of algorithms is a challenging task, as it is difficult to obtain data sets representing all the target occurrence scenarios practically. In the present work, to evaluate the algorithms for all possible target occurrence scenarios, a synthetic data set generation module has been developed. This module uses the scene-rendering technique to implant the targets into recorded background videos. Figure 7 demonstrates block diagram of target implantation module. The target implanted video recordings are used for the algorithm evaluation.
The proposed target detection approach is evaluated on background recordings with simulated targets. Figures 8 and 9 demonstrate the effectiveness of the proposed detection process and background estimation approach. Figure 8(a) presents the current image; Fig. 8(b) presents the registered previous image into current image. Figure 9, presents the residual current image after background suppression. From change detection map presented in Fig. 9, it is obvious that residual image after background suppression contains minimal amount of clutter information (almost zero). This approach effectively reduces the clutter and improves the target SNR significantly.
Figure 7. Synthetic data set generation module.
Figure 8. (a) Current image (b) Previous registered image.
Figure 9. Residual image after background filtering using proposed approach.
The proposed target detection approach based on the temporal information has been compared with various other spatial filtering techniques using receiver operating characteristics (ROC). For any given detector, the trade-off between probability of detection (Pd) and probability of false alarm (Pf) can be described using ROC curves. The ROC curve plots, Pd(η) and Pf(η) as function of all possible values of threshold (η). Terms commonly used in ROC analysis are given by
True positives (TP) = Number of correct detections.
True negatives (TN) = Number of correct rejections.
False alarm (FA) = Number of false detections.
False negatives (FN) = Number of missed detections.
Probability of detection (Pd) = TP/(TP+FN)
Probability of false alarm (Pf) = FA/(FA+TN)
From the ROC curves presented in Fig. 10, it is observed that proposed temporal filtering approach is exhibiting significantly high Pd than other spatial filtering techniques for the same amount of false alarm. This improvement is mainly due to improved SNR achieved using the proposed temporal background subtraction approach.
Figure 10. Performance comparison of proposed temporal filtering approach with other spatial filtering approaches.
The tracking performance was tested on synthetic data, generated by implanting targets into collected background recordings. The track loss rate was significantly reduced using proposed work compared to classical Kalman filter (KF) with nearest neighbour association (NNA). The performance achieved with the proposed tracking algorithm is presented in Table 1. Targets are implanted into collected background video recordings at various ranges from platform.
Table 1. Performance comparison between proposed tracking framework and classical KF+NNA.
From the Table 1 it is concluded that proposed approach can track the targets present at various ranges without track loss. Whereas the conventional KF+NNA is having significant track loss, the significant improvement in tracking performance with the proposed approach is mainly due to the initialization of filter states with rough estimate of target angular rates.
The detection tracks generated by tracking association module will be classified into true target track or false target track by extracting various features related to target. As the paper’s main focus is on detection and tracking of targets from images, feature extraction and discrimination is not discussed by authors in detail. The feature extraction and discrimination is very subjective to application and target of interest.
The paper explains the importance of ATR systems based on the IR imaging. Analgorithmic framework for real time target detection and tracking is presented in the paper. The various algorithmic stages and their functions are presented. The algorithm framework is modeled using MATLAB tool. The data set for evaluating the algorithm components were generated by implanting targets in the background recording. The results obtained at various stages of the algorithm have been also discussed.
1. Brown, W. & Swonger, C. A prospectus for automatic target recognition. IEEE Trans. Aero. Electro. Sys., 1989, 25,401-410. doi: 10.1109/7.30795
2. Bhanu, B. Automatic target recognition: State-of-the-art survey. IEEE Trans. Aero. Electro. Sys., AES-22, 1986, (4), 364-379. doi: 10.1109/taes.1986.310772
3. Suyog, D.D.; Meng, H.E.; Ronda, V. & Philip, C. Max- mean and Max-median filters for detection of small targets. In Proceeding SPIE 3809, Signal and Data Processing of Small Targets. 1999, 74. doi: 10.1117/12.364049
4. Soni, T.; Zeidler, J.R. & Ku, W.H. Adaptive whitening filters for small target detection. In Proceeding SPIE 1698, Signal and Data Processing of Small Targets, 21, 1992. doi: 10.1117/12.139383
5. Victor, T.; Tamar, P. ; May, L. & Bondary, K. Morphology- based algorithm for point target detection in infrared backgrounds. In Proceeding of SPIE, Signal and Data Processing of Small Targets, 1993, 1954, pp. 2-11. doi: 10.1117/12.157758
6. Wang, Y. & Zhang, J. Dim target detection system based on DSP. In Proceeding Second symposium on International Computer Science and Computational Technology, Academy Publisher, 2009.
7. Marco, S. Del & Agaian, S. The design of wavelets for image enhancement and target detection. In Proceeding SPIE, Mobile Multimedia/Image Processing, Security, and Applications. 2009, 7351, pp.12-26.
8. Blostein, S.A. Detecting small moving objects in image sequences using sequential hypothesis testing. IEEE Trans. Signal Process., 1991, 39, 1611-1629. doi: 10.1109/78.134399
9. Ralph, J.F.; Smith M.I. & Heather, J.P. Motion-based detection, identification, and tracking for missile warning system applications. In Proceeding SPIE 5809, Signal Processing, Sensor Fusion, and Target Recognition XIV, 2005, 54. doi: 10.1117/12.603320
10. Tzannes, A.P. & Mooney, J.M. Point target detection in IR image sequences using spatio-temporal hypothesis testing. Air Force Research Laboratory, Hanscom AFB, MA, 1999.
11. Silverman, J.; Caefer, C.E.; DiSalvo, S. & Vickers, V.E. Temporal filtering for point target detection in staring IR imagery: II. Recursive variance filter. In Proceeding SPIE 3373, Signal and Data Processing of Small Targets 1998, 44. doi: 10.1117/12.324648
12. Kligys, S.; Rozovsky, B. & Tartakovsky, A. Detection algorithm and track before detect architecture based on non linear filtering for infrared search and track systems. Centre for applied mathematical sciences, University of southern california, Los Angeles, CA, 1998.
13. Warren, R.C. A bayesian track before detect algorithm for IR point target detection. Weapons Systems Division, Aeronautical and Maritime Research Laboratory, Victoria, Austalia, 2002. doi: 10.1007/978-3-7908-1782-9_39
14. Geo, S. & Shui, P.L. Method for moving point target detection in image sequences based on directional cumulation. In Proceeding SPIE 6795, 2I-1-6795 2I-6, 2007.
15. Tartakovsky, A.G. & Blazek, R.B. Effective adaptive spatial-temporal technique for clutter-rejection in IRST. In Proceeding SPIE 4048, Signal and Data Processing of Small Targets 2000, 85. doi: 10.1117/12.392023
16. Aridgides, T.; Fernandez, M.F.; Randolph, D. & Bray, D. Adaptive three-dimensional spatio-temporal filtering techniques for infrared clutter suppression. In Proceeding SPIE 1305, Signal and Data Processing of Small Targets 1990, 63. doi: 10.1117/12.21580
17. Brookner, E. Tracking and Kalman filtering made easy. John Wiley Sons Inc, New York, 1998. doi: 10.1002/0471224197
18. Shankar, Ravi & Raji, R. Registration of airborne IR images using platform attitude information. Def. Sci. J., 2014, 64(2),130-135. doi: 10.14429/dsj.64.5460
Authors thank Ms J. Manjula Outstanding Scientist and Director, Defence Avionics Research Establishment and Mr P.M. Soundar Rajan, DRDO Fellow, for their constant guidance and encouragement for carrying out the work reported here.
R. Anand Raji has designed the algorithm frame work and formulated a methodology for testing the functionality of algorithms. By surveying the literature author brought out the existing methods or approaches for the stated problem and limitations of the same in real time implementation. Author also structured of paper to effectively express the designed methodology. Mr Ravishankar Chekuri has modelled the conceptual approach in MATLAB and tested the approach by generating the input data set that replicates actual scenario. The author also contributed in explaining simulation results. Mr Ravi Kumar has modelled the tracking and association algorithm in MATLAB and tested the approach by generating the input data set. The author carried out literature survey in tracking and association algorithm and contributed towards technical writing part of the paper. Mr Reghu Kumar has reviewed the work at each and every development stage and given valuable inputs in fine tuning the frame work for feasible real time implementation. The author also reviewed technical writing of the paper and suggested modifications to effectively communicate the designed methodology.
| 2021-12-04T07:34:43 |
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|
http://pdglive.lbl.gov/ParticleGroup.action?init=0&node=M201
|
# Non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ Candidates
For a review on gluonium and other non- ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ candidatessee PDG 2006 , Journal of Physics G33 1 (2006).See also the Note on scalar mesons'' in the ${{\mathit f}_{{0}}{(500)}}$ Particle Listings, our noteNew charmonium-like states'' in PDG 2008 , Physics Letters B667 1 (2008), and the extensive chapter on Spectroscopy in N. Brambilla $\mathit et~al.$ (Quarkonium Working Group),The European Physical Journal C71 1534 (2011).
See related review: Non-${\mathit {\mathit q}}{\mathit {\overline{\mathit q}}}$ Mesons
| 2019-02-19T01:28:36 |
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|
https://www.cabq.gov/planning/plans-publications/area-sector-development-plans
|
# Area & Sector Development Plans
These Area & Sector Development Plans are included in the ABC Comprehensive Plan as Appendix D for reference as historical documents.
These Area & Sector Development Plans were adopted between 1970 and 2015. Some were updated multiple times; some were never updated.
• Policies from these plans were incorporated into the 2017 update of the ABC Comprehensive Plan, and the plans themselves became Appendix D.
• Regulations from the Sector Development Plans were incorporated into the Integrated Development Ordinance in 2017.
• See Table II for an alphabetical index of small area regulations carried over from Sector Development Plans.
• These Rank II and Rank III Plans were rescinded as standalone documents in 2017 per Resolution 17-213 (R-17-213).
• See the ABC-Z project webpage for more information.
| 2022-12-07T06:50:04 |
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|
https://par.nsf.gov/biblio/10362007-simultaneous-constraints-star-formation-history-nucleosynthesis-sculptor-dsph
|
Simultaneous Constraints on the Star Formation History and Nucleosynthesis of Sculptor dSph
Abstract
We demonstrate that using up to seven stellar abundance ratios can place observational constraints on the star formation histories (SFHs) of Local Group dSphs, using Sculptor dSph as a test case. We use a one-zone chemical evolution model to fit the overall abundance patterns ofαelements (which probe the core-collapse supernovae that occur shortly after star formation),s-process elements (which probe AGB nucleosynthesis at intermediate delay times), and iron-peak elements (which probe delayed Type Ia supernovae). Our best-fit model indicates that Sculptor dSph has an ancient SFH, consistent with previous estimates from deep photometry. However, we derive a total star formation duration of ∼0.9 Gyr, which is shorter than photometrically derived SFHs. We explore the effect of various model assumptions on our measurement and find that modifications to these assumptions still produce relatively short SFHs of duration ≲1.4 Gyr. Our model is also able to compare sets of predicted nucleosynthetic yields for supernovae and AGB stars, and can provide insight into the nucleosynthesis of individual elements in Sculptor dSph. We find that observed [Mn/Fe] and [Ni/Fe] trends are most consistent with sub-MChType Ia supernova models, and that a combination of “prompt” (delay times similar to core-collapse supernovae) and “delayed” (minimum delay more »
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10362007
Journal Name:
The Astrophysical Journal
Volume:
925
Issue:
1
Page Range or eLocation-ID:
Article No. 66
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
We derive empirical constraints on the nucleosynthetic yields of nitrogen by incorporating N enrichment into our previously developed and empirically tuned multizone galactic chemical evolution model. We adopt a metallicity-independent (‘primary’) N yield from massive stars and a metallicity-dependent (‘secondary’) N yield from AGB stars. In our model, galactic radial zones do not evolve along the observed [N/O]–[O/H] relation, but first increase in [O/H] at roughly constant [N/O], then move upward in [N/O] via secondary N production. By t ≈ 5 Gyr, the model approaches an equilibrium [N/O]–[O/H] relation, which traces the radial oxygen gradient. Reproducing the [N/O]–[O/H] trend observed in extragalactic systems constrains the ratio of IMF-averaged N yields to the IMF-averaged O yield of core-collapse supernovae. We find good agreement if we adopt $y_\text{N}^\text{CC}/y_\text{O}^\text{CC}=0.024$ and $y_\text{N}^\text{AGB}/y_\text{O}^\text{CC} = 0.062(Z/Z_\odot)$. For the theoretical AGB yields we consider, simple stellar populations release half their N after only ∼250 Myr. Our model reproduces the [N/O]–[O/H] relation found for Milky Way stars in the APOGEE survey, and it reproduces (though imperfectly) the trends of stellar [N/O] with age and [O/Fe]. The metallicity-dependent yield plays the dominant role in shaping the gas-phase [N/O]–[O/H] relation, but the AGB time-delay is required to match the stellar age andmore »
| 2023-03-21T17:48:02 |
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|
https://indico.bnl.gov/event/11335/
|
High Energy / Nuclear Theory / RIKEN seminars
# [NT/RBRC seminar] Single Transverse-Spin Asymmetry and Sivers Function on Lattice
## by Dr Feng Yuan (Lawrence Berkeley National Lab)
US/Eastern
https://bnl.zoomgov.com/j/1608484735?pwd=b1FUSXM4d1ExRkR0SStXYWgyMERhQT09
#### https://bnl.zoomgov.com/j/1608484735?pwd=b1FUSXM4d1ExRkR0SStXYWgyMERhQT09
Description
This is not a lattice talk. Instead, I will present our recent development on how to formulate the quark Sivers function on Lattice based on the so-called large momentum effective theory. In particular, we argue the spin asymmetry defined as the ratio of the quark Sivers function over the spin averaged distribution can be directly calculated in terms of the relevant quasi distributions with the soft functions and perturbative matching kernels cancelling out. We will give explicit results at one-loop order, which reduces to a collinear expansion at twist-three level. This may lead to an alternative way to simulate the quark-gluon-quark correlation function (twist-3 distribution) on lattice. Reference: 2011.13397 [hep-ph]
| 2021-09-19T03:58:52 |
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|
https://wiki.cosmos.esa.int/planck-legacy-archive/index.php/TOI_processing_LFI
|
# TOI processing
## Overview
The LFI Level 2 Pipeline analyses data from each horn of the instrument separately, one pointing period at a time, and stores the results in an object the length of an OD. Each diode of the horn is corrected for systematic effects. Next, measurements of the sky and the 4-K load are differenced, then the signals from one diode are combined with signals from the complementary diode in the same radiometer. Finally, photometric calibration is applied for each horn.
### Pre-processing
Before the Level 2 pipeline is run, the Mission information and data sampling divisions are stored in the database, in order to improve the analysis.
The Mission information is a set of objects, one for each Operational Day (OD, as defined in the glossary), in which are stored pointing period data: the DPC pointing ID (where 1 is the first pointing of the nominal mission); PSO pointing ID; start OBT of the pointing manoeuvre; start OBT of the stable pointing period; OBT of the end of the stable pointing period; and spin axis ecliptic longitude and latitude.
The sampling information is a set of objects, one for each LFI frequency, in which are stored for each pointing ID: the start OBT of the pointing manoeuvre; th start OBT of the stable pointing period; the end OBT of the pointing period; the number of samples of the pointing, number of stable samples of the pointing; the starting sample of the stable pointing period; and the sample number from the start of the nominal mission. Valid samples and OBTs are defined to be those where any of the radiometers in a frequency band contain valid data.
During the analysis of LFI date, a systematic effect was discovered that was common to both white noise and calibration. This turned out to be a nonlinearity in the analogue-to-digital converter (ADC) on board, as discussed further in Planck-2013-II[1], Planck-2013-III[2], Planck-2015-A03[3], Planck-2015-A04[4] and Planck-2020-A2[5].
### Evaluation
The mathematical model represents the digital ADC output as:
,
where V is the voltage input, γ is the DAE gain, Δ is the DAE offset and x0 is the DAE Tzero.
We can model the non-linearity as a function of the input voltage R(V). So we have the apparent inferred voltage V' and we can link it to the actual input voltage with:
,
so that
.
Since V >> Δ and V γ >> x0, we can use the much simpler relation
,
and we expect this to be very near to unity for all V.
To find the response curve we have only the apparent voltage to work with, so we had to use the inverse response function R'(V') and replace the real input voltage with Tsys times the time varying gain factor G(t):
.
If we introduce a small signal on top of Tsys, which leads to increased detected voltage and corresponding apparent voltage increment, then
,
so carrying out the differentiation with respect to V' of the relation between true and apparent signal voltage leads to
.
We now assume Tsys and δT are fixed and that the variations are due to slow drifts in the gain. Then we can isolate the terms
,
.
Combining the equations to remove the gain factor, we have
.
Rearranging and setting a = δT/Tsys gives
.
We see the expected direct proportionality of δV' to V', based on the assumption that the variations in voltage are due to overall gain drift, so that the amplitude of voltage and signal will vary together. Then there is the additional differential term, which will pull the signal amplitude away from the linear relationship. So if we plot measured white noise or dipole gain factor against recovered voltage, we should see a linear curve with variations due to local slope changes at particular voltages. The linear part can be taken out and the differential part fitted. This was numerically integrated to obtain the inverse response curve, which is then used to convert the measured voltages to corrected voltages.
### Application
In the 2015 release we fit white noise amplitudes binned with respect to detector voltage with a simple spline curve and we translate results into a correction curve as described in Planck-2015-A03[3]. Instead, the fit now relies on a more physically motivated function based on voltage steps (see Planck-2020-A2[5] for futher details). We compared the results between this method and the previous one by means of null-maps, checking the consistency of the resulting new gain solution with the new ADC correction applied. This was done by computing the rms scatter from the 8 different survey maps taking into account pixel hits and zero levels. A goodness" parameter can then be derived from the mean level of the masked null-map made between these survey scatter maps. The 70 and 44 GHz null-maps failed to show significant improvements but this was not the case at 30 GHz. Inspecting the ADC solutions it became clear that the higher noise per radiometer and low ADC non-linearity at 70 GHz did not allow for a good fit. Meanwhile the ADC effect was so large at 44 GHz that new model could not reproduce some of the details, and so led to some small residuals. The 30 GHz system has much lower noise and less thermal drift in the gain, meaning that more voltage levels were revisited more often thus yielding a more consistent ADC model curve. It was therefore decided to keep this new solution only for the 30 GHz channels. The other two channels thus have the same correction for ADC non-linearity as in the previous release.
## Spike removal
Some of the LFI receivers exhibit a small artefact with exactly 1-s period, that produces effects visible in the power spectra. The effect is a set of spikes at 1 Hz and harmonics. The spurious signal can be well modelled and is removed from the timelines. More information can be found in Planck-2013-II[1], Planck-2013-III[2], Planck-2015-A03[3], Planck-2015-A04[4] and Planck-2020-A2[5].
### Modelling
The cause of the spikes at 1 Hz and harmonics is a tiny 1-s square-wave embedded in signals from the affected channels. The method used to estimate the 1-Hz signal is to build a template in the time domain, synchronized with the spurious signal. The first step is to divide each second of data into time bins using OBT. The number of bins is computed using
where fsamp is the sampling frequency and is 136 Hz at 70 GHz, 80 at 44 GHz, and 56 at 30 GHz. Then the vector of bins is initialized with time intervals. To avoid aliasing effects, the template resolution is √3. We can write the process adding indices to the time sample; here a lower index denotes the particular time sample, while the upper index labels the bin into which the sample falls. The linear filter can be written as
.
Here Δx(ti) is the filter weight, which is determined by where the sample lies within the bin. If we use tj with only an upper index to denote the start of each bin, then we can write the filter weight as
.
In other words, the filter weight is the time sample value minus the start of the bin divided by the width of the bin.
We must estimate the parameters aj from the data. With the assumption that the instrument has stable noise properties, we can use a least squares algorithm to estimate the bin values:
.
This can be represented in the matrix equation
,
with the following definitions:
;
;
;
;
.
With these definitions we have to make use of periodic boundary conditions to obtain the correct results, such that if k = 0, then k-1 = n-1 and if k = n-1, then k+1 = 0. Once this is done, we have a symmetric tridiagonal matrix with additional values at the upper right and lower left corners. The matrix can be solved with LU decomposition. In order to be certain of the numerical accuracy of the result, we can perform a simple iteration. The solving of the linear system and the iterative improvement of the solution are implemented as suggested in Numerical Recipes (Press et al., Cambridge University Press, 2007).
### Application
For each of the 44 LFI diodes there is a corresponding object in the Database. After studying the amplitude of the spikes at other LFI frequencies, we chose to apply the correction only to the 44 GHz radiometers. Each object contains three columns: the bins start time vector; the sky amplitudes; and the reference amplitudes.
For each sample the value to be subtracted is computed using
,
where k is the index of the bins at a given time.
## Filling gaps in the data
During the mission, a small number of data packets were lost (Planck-2013-II[1], Planck-2015-A03[3] and Planck-2020-A2[5]). Moreover, in two different and very peculiar situations, LFI was shut down and restarted, giving inconsistencies in data sampling. None of these data are used for scientific purposes, but to avoid discrepancies in data analysis all of the radiometers at the same frequency must have the same number of samples.
To ensure this, we compare the length of the data stream to be reduced in a specific pointing period to the data stored in the sample information object. If the length is not the same, the OBT vector is filled with missing sample times, the data vector is filled with zeros, and in the flag column the bit for "gap" is entered.
## Gain modulation factor
The pseudo-correlation design of the LFI radiometers allows for a dramatic reduction of 1/f noise when the Vsky and Vload outputs are differenced (see LFI instrument description). The two streams are slightly unbalanced, since one looks at the 2.7-K sky and the other looks at the 4.5-K reference load. To force the mean of the difference to zero, the load signal is multiplied by the gain modulation factor (R). For each pointing period this factor is computed using (see equation (3) in LFI description)
.
Then the data are differenced using
.
This value for R minimizes both the 1/f noise and the white noise in the difference timestream. The i index represents the diode and can be 0 or 1.
At this point, we also set the manoeuvre flag bit to identify those samples that have missing data, using the information stored in the sampling information object. This identifies which data to ignore in the next step of the Pipeline.
The R values are stored in the database. At the same time the mean values of Vsky and Vload are stored, so they can be used in other steps of the analysis.
## Diode combination
The two complementary diodes of each radiometer are combined. The relative weights of the diodes in the combination are chosen for optimal noise. We assign relative weights to the uncalibrated diode streams based on their first-order calibrated noise.
### Evaluation
From first-order calibration we compute an absolute gain G0 and G1, subtract an estimated sky signal and calculate the calibrated white noise σ0 and σ1, for the pair of diodes (see equation 6 in LFI description). The weights for the two diodes (i = 0 or 1) are
,
where the weighted calibration constant is given by
.
The weights are fixed to a single value per diode for the entire data set. Small variations in the relative noise of the diodes would in principle require that we recalculate the weights on shorter timescales; however, we decided that a time-varying weight could possibly induce more significant (and hard to model) systematics, so we chose a single best estimate for the weights for each diode pair.
Weights used in combining diodes.
### Application
The weights in the table above are used in the formula
.
## Planet flagging
### Extraction method
Measurements of planets have been formed from samples containing flux from the planet, plus a surrounding region, projected onto a grid (microstripes), by assuming an elliptical Gaussian beam using parameters from instrument database.
Microstripes are a way to extract and store relevant samples for planet detection. Here relevant samples are those affected by the planet plus samples in the neighbourhood (to establish a background level). The search radius for selecting samples as relevant is 5° around the planet's position, computed at the pointing period mid-time. For each sample we store SCET (Spacecraft Event Time), pointing directions, and calibrated temperature. Destriping is applied during the application of this procedure.
Random errors are estimated by taking the variance of samples entering each micromap pixel. This method is fast but not exact, since the variance is larger near a bright source. This can cause the noise to be overestimated by a factor of 2; however, given the large S/N for planetary observations, that is not a major drawback.
The apparent position of a planet as seen from Planck at a given time is derived from JPL Horizons. Positions are tabulated in steps of 15 minutes and then linearly interpolated at the sampling frequency of each detector. JPL Horizons tables allow us also to derive other quantities such as the planet-Planck distance and the planet-Sun distance, as well as the planet angular diameter, which affects the apparent brightness of the planet.
The antenna temperature is a function of the dilution factor, according to
,
where Tant,obs and Tant,1 are the observed and reduced Tant, θ is the instantaneous angular diameter of the planet, and bFWHM the beam full-width at half-maximum.
With the above definition Tant,1 could be considered as the Tant for a planet with bFWHM = θ, but a more convenient view is to take a reference dilution factor D0, as the dilution factor for a standardized angular diameter for the planet and fiducial FWHM beam bFWHM, θ0, to have
,
leading to the following definition of a standardized Tant:
.
This has the advantage of removing variations among different detectors and transits, while keeping the value of Tant similar to that seen by the instrument and then allowing a prompt comparison of signals and sensitivities.
### Application
The OBT vectors found by the searches are saved in a set of objects, one for each horn. In the Level 2 pipeline those OBTs are compared with the OBT vector of the data to set the planet bit flag where needed.
## Photometric calibration
Photometric calibration is the procedure used to convert data from volts to kelvins. The source of the calibration is the well understood CMB dipole, caused by the motion of the Solar System with respect to the CMB reference frame. To this signal we add the modulation induced by the orbital motion of Planck around the Sun. The resulting signal is then convoluted with the horn beam to obtain the observed dipole. For details refer to Planck-2015-A06[6] and Planck-2020-A2[5].
In the 2018 release we decided to include the sky signal in the calibration process, on the same footing as the orbital and Solar dipole, including both temperature and polarization fluctuations. Unfortunately, this is non-trivial, since the purpose of the experiment, in this case, is precisely to measure the polarized emission from the sky. A good approximation, however, can be estalished through an iterative process that alternates between gain calibration, map making and astrophysical component separation:
1. Let T(sky) be the full best-fit Planck2015 astrophysical sky model, including CMB, synchrotron, free-free, thermal and spinning dust and CO emission for temperature maps, and CMB, synchrotron and thermal dust in polarization.
2. Estimate G explicitly including the temperature and polarization component of T(sky) in the calibrator on the same footing as teh orbital and Solar Dipole.
3. Compute frequency maps with these new gains.
4. Estimate new astrophysical model from updated frequency maps using Commander. (At the moment the sky model is adjusted only for LFI frequencies.)
5. Iterate (2)--(4).
Since the true sky signal is stationary on the sky, while the spurious gain fluctuations are not, this process will in principle converge, essentially corresponding to a generalized map-maker in which the G is estimated jointly with the sky maps (see Planck-2020-A2[5] for further details).
### Beam-convolved dipole
In computing the beam-convolved dipole we used an elegant algorithm to save time and computing power. In computing the cosmological dipole signal it is common to assume a pencil-like beam acting as a Dirac delta function. In this case a dipole timeline is defined as
where PE(t) is the pointing direction in the observer reference frame and DE(t) is the dipole axis scaled by the dipole amplitude, again in the same reference frame (here the label "E" is for "Ecliptic").
In general the true signal would have to be convolved with the beam pattern of the given radiometer, usually described as a fixed map in the beam reference frame or as a time-dependent map in the observer reference frame. In this case it is easiest to describe the convolution in the beam reference frame, since the function to be convolved then can be described by a single vector.
Denoting by the matrix converting from the observer to the beam reference frame, so that
,
the instantaneous dipole direction in the beam reference frame is
.
By denoting with a pointing direction in the beam reference frame, then
,
where N is a normalization constant defined through
.
Denoting with Px, Py, and Pz the three Cartesian components of P, the integral of the dot product can be decomposed into three independent integrals:
;
;
.
These integrals define a time independent vector characteristic of each radiometer and constant over the mission.
Detector ID
LFI18S 4.64653×10-3 -1.32712×10-3 9.95771×10-1
LFI18M 2.84449×10-3 -8.95117×10-4 9.97353×10-1
LFI19S 4.29488×10-3 -1.40378×10-3 9.96128×10-1
LFI19M 4.50970×10-3 -1.62551×10-3 9.95733×10-1
LFI20S 5.27978×10-3 -1.94793×10-3 9.95146×10-1
LFI20M 4.74206×10-3 -1.84621×10-3 9.95483×10-1
LFI21S 5.23772×10-3 1.93375×10-3 9.95176×10-1
LFI21M 4.37131×10-3 1.70755×10-3 9.95851×10-1
LFI22S 3.62730×10-3 1.20309×10-3 9.96790×10-1
LFI22M 3.18177×10-3 1.13834×10-3 9.97055×10-1
LFI23S 3.25825×10-3 9.10802×10-4 9.97061×10-1
LFI23M 2.63850×10-3 8.05452×10-4 9.97552×10-1
LFI24S 1.20077×10-3 -2.98774×10-7 9.98979×10-1
LFI24M 1.19670×10-3 -1.35903×10-6 9.98945×10-1
LFI25S -2.10060×10-4 4.42870×10-4 9.99657×10-1
LFI25M -2.51334×10-4 5.58031×10-4 9.99546×10-1
LFI26S -1.97667×10-4 -4.22022×10-4 9.99670×10-1
LFI26M -2.54267×10-4 -5.74267×10-4 9.99521×10-1
LFI27S 5.85555×10-3 1.81753×10-3 9.94483×10-1
LFI27M 4.99628×10-3 1.57663×10-3 9.95292×10-1
LFI28S 6.37507×10-3 -1.96172×10-3 9.93966×10-1
LFI28M 4.78777×10-3 -1.54429×10-3 9.95517×10-1
Characteristic vectors for each LFI detector.
By using this characteristic vector the calculation of the convolved dipole is simply defined by a dot product of the vector and the dipole axis rotated in the beam reference frame:
.
### Binning
In order to simplify the computation and to reduce the amount of data used in the calibration procedure, the data are phase binned into maps with Nside=256. During phase binning all the data are neglected that are flagged for manoeuvres, planets, and gaps, as well as those flagged in Level 1 analysis as not recoverable.
### Fit
The first-order calibration values are given by a least squares fit between the signal and the dipole. For each pointing gain gk and offset bk values are computed by minimizing
,
where the sum includes only samples outside a Galactic mask.
### DaCapo
The largest source of error in the fit arises from unmodelled sky signal ΔTa from CMB anisotropy. The procedure adopted to correct this effect (DaCapo) is described below.
The uncalibrated TOI yi belonging to a pointing period k is modelled as
,
where the unknowns si, gk, and bk are, respectively, the signal per OBT, the gain per PID, and the offset per PID, and where di is the total dipole.
This is a nonlinear χ2 minimization problem. It can be linearized using an iterative procedure: for each iteration step a linearized model TOI is built as
,
where gk(-1) and si(-1) are the gain and sky signal computed at the previous iteration step.
A linear fit is performed between yi and yi,model to obtain the new gk and si values. The procedure is iterated until convergence. To reduce the impact of the noise during the iterative procedure the sky estimation is built using data from both radiometers of the same horn.
### Smoothing
To improve accuracy given by the iterative algorithm and remove noise from the solution a smoothing algorithm must be applied.
#### OSGTV
OSGTV is a 3-step smoothing algorithm, implemented with a C++ code.
The gain reconstructed with DaCapo can be expressed as
,
where the T(t) function represents temperature fluctuations of the Focal Plane. The time dependence of the "real" gain Gtrue is modelled as the superposition of a "slow" component, with a timescale of about 3 months, and a "fast" component with a timescale of a few PIDs:
.
The slow component takes into account the seasonal variations of the thermal structure of the spacecraft due to the orbital motion, while the "fast" component describes the thermal effects of the electronics and compressors, as well as single events like the sorption cooler switchover.
To disentangle the components of Gtrue, we apply a parametric "hybrid" approach in three steps.
Step 1. For each PID i, we used the 4-K total-power Vload(i) and the signal from temperature detectors in the focal plane Ti, subsampled at 1 sample/PID, to track gain changes. This is implemented through a linear fit between Vload(i) × Graw and Ti:
,
where the window length MW of the moving average is proportional to the variance of the dipole in the PID being considered. The resulting gain is
.
Step 2. The "fast" component Gfast is recovered as follows: we define a maximum moving average window length WLmax,and for each PID we compute the variance σ2i of Gi in this window. We define a percentile on the ordered variance array and we compute the corresponding value of the variance σ2p. The window length for each PID is then computed as
.
If WLi > WLmax we impose WLi = WLmax. With these window lengths a moving window average is performed on Gi. The averaged gain vector is subtracted from the raw hybrid gain to obtain Gfast.
Step 3. We perform a moving window average on Gi and we compute the variances of the smoothed array. The window length is computed with a linear interpolation between a minimum length WLmin defined in the dipole minima and a maximum WLmax defined in the dipole maxima. The array of gain variances is weighted with the variance of the dipole. We set a percentile on the variance array and we find the corresponding variance value σ2p. Around this value we search for local maxima of the variance array, and we split the domain of the gain into subsets between consecutive maxima. For each subset we perform a moving average with the corresponding window length. The "slow" component Gslow is given by the union of these subsets.
### Gain application
The last step in TOI processing is the creation of the calibrated stream. For each sample we have
,
where t is the time and k is the pointing period, "convDip" is the CMB dipole convolved with the beam, and Tstray is the stray light.
## Noise
The aim of this pipeline step is the reconstruction of the noise parameters from calibrated flight TOI. The goal is two-fold. On the one hand we need to know the actual noise properties of our instrument in order to properly take them into account, especially during later processing and analysis steps, such as map-making and power spectrum estimation. On the other hand, evaluation of noise properties during the instrument lifetime is a way to track down possible variations, anomalies, and general deviations from the expected behaviour.
### Operations
Noise estimation is performed on calibrated data; since we would like to track possible noise variations through the mission lifetime, we select data in chunks of five ODs (Operational Days). These data are processed by the ROMA iterative generalized least-squares (IGLS) mapmaking algorithm, which includes a noise estimation tool. In general IGLS mapmaking is a quite costly in terms of time and resources required. However, the length of the data is such that it can run on the DPC cluster in a very short time (around 1-2 minutes).
The method implemented can be summerized as follows. We model the calibrated TOI as
,
where n is the noise vector and P is the pointing matrix that links a pixel in the map m with a sample in the TOI d. The initial estimation of the signal is obtained by simply rebinning the TOI into a map. Then an iterative approach follows in which both signal and noise are estimated according to
,
where Ni is the noise covariance matrix in the time domain resulting from iteration i. We find that convergence is achieved after three iterations.
We then perform an FFT (Fast Fourier Transform) on the noise timestream output from from the iterative approach, and fit the resulting spectrum.
### Fitting pipeline
As already done in the 2013 and 2015 release, we estimate the parameters of the noise properties (i.e., white noise level, knee-frequency, and slope of the low-frequency noise component) by means of an MCMC approach. Therefore for the spectra just described we first compute the white noise level by taking the mean of the last 10% of the data (at 30 GHz due to the higher value of the knee-frequency this quantity is reduced to 5%). Once the white noise level has been determined we proceed with the actual fitting of the knee-frequency and slope. The resulting values reported are the medians of the fitted values for our 5-OD chunks, through the whole mission lifetime.
Horn White noise M [K s] White noise S [K s] Knee-frequency M [mHz] Knee-frequency S [mHz] Slope M Slope S
18 512.5±2.0 466.7±2.3 14.8±2.1 17.8±1.5 -1.06±0.08 -1.18±0.10
19 578.9±2.1 554.2±2.2 11.7±1.1 13.7±1.3 -1.21±0.23 -1.10±0.13
20 586.9±1.9 620.0±2.7 7.9±1.5 5.6±1.0 -1.19±0.27 -1.30±0.33
21 450.4±1.4 559.8±1.8 37.9±5.7 13.1±1.3 -1.24±0.08 -1.20±0.08
22 490.1±1.3 530.9±2.2 9.5±1.7 14.3±6.7 -1.41±0.25 -1.23±0.27
23 503.9±1.6 539.1±1.7 29.6±1.1 58.9±1.6 -1.07±0.02 -1.21±0.02
24 462.8±1.3 400.5±1.1 26.9±1.0 89.6±13.8 -0.94±0.01 -0.91±0.01
25 415.2±1.3 395.0±3.1 19.7±1.0 46.8±1.9 -0.85±0.01 -0.90±0.01
26 482.6±1.9 422.9±2.5 64.4±1.8 70.7±18.7 -0.92±0.01 -0.75±0.07
27 281.5±2.0 302.8±1.8 173.7±3.1 109.6±2.5 -0.93±0.01 -0.91±0.01
28 317.9±2.4 286.1±2.1 128.5±10.9 44.1±2.2 -0.93±0.01 -0.90±0.02
Time variations of noise parameters are a good tracer of possible modifications in the instrument behaviour and we know that some events capable of affecting instrument behaviour happened during the mission. Variations of the physical temperature of the instrument due to the transition in the operations from the first sorption cooler to the second one, as well as the observed degradation in the performances of the first cooler, are events that clearly show their imprints in the variation of the noise spectra.
In the following figure we report a representative sample of noise spectra, one for each frequency channel (from left to right LFI 18M, LFI 25S, and LFI 27M), covering the whole mission lifetime. The white noise is extremely stable at the level of 0.1%. As already noted in the 2013 and 2015 release, knee-frequencies and slopes are stable until OD 326 and show clear variations and deviations from the simple one knee-frequency and one slope model. This is a sign of the degradation of the first cooler inducing thermal variations, with a characteristic knee-frequency (different from the radiometric one) and with a steeper slope. Once the second cooler became operational and performed as expected, the noise spectra gradually returned to the original shape at the beginning of the mission. This behaviour is visible, although not identical, at each frequency for several reasons e.g., intrinsic thermal susceptibility and position on the focal plane that determines the actual thermal transfer function.
Noise power spectra for selected LFI radiometers.
## References
1. Planck 2013 results. II. Low Frequency Instrument data processing, Planck Collaboration, 2014, A&A, 571, A2.
2. Planck 2013 results. III. Low Frequency Instrument systematic uncertainties, Planck Collaboration, 2014, A&A, 571, A3.
3. Planck 2015 results. II. LFI processing, Planck Collaboration, 2016, A&A, 594, A2.
4. Planck 2015 results. III. LFI systematics, Planck Collaboration, 2016, A&A, 594, A3.
5. Planck 2018 results. II. Low Frequency Instrument data processing, Planck Collaboration, 2020, A&A, 641, A2.
6. Planck 2015 results. V. LFI calibration, Planck Collaboration, 2016, A&A, 594, A5.
(Planck) Low Frequency Instrument
Operation Day definition is geometric visibility driven as it runs from the start of a DTCP (satellite Acquisition Of Signal) to the start of the next DTCP. Given the different ground stations and spacecraft will takes which station for how long, the OD duration varies but it is basically once a day.
Data Processing Center
Planck Science Office
On-Board Time
analog to digital converter
LFI Data Acquisition Electronics
Full-Width-at-Half-Maximum
Cosmic Microwave background
| 2020-10-26T18:30:49 |
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|
http://dlmf.nist.gov/9.5
|
# §9.5(i) Real Variable
9.5.1 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}% \mathop{\cos\/}\nolimits\!\left(\tfrac{1}{3}t^{3}+xt\right)dt.$
9.5.2 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(-x\right)=\frac{x^{\ifrac{1}{2}}}{\pi}% \int_{-1}^{\infty}\mathop{\cos\/}\nolimits\!\left(x^{\ifrac{3}{2}}(\tfrac{1}{3% }t^{3}+t^{2}-\tfrac{2}{3})\right)dt,$ $x>0$.
9.5.3 $\mathop{\mathrm{Bi}\/}\nolimits\!\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}% \mathop{\exp\/}\nolimits\!\left(-{\tfrac{1}{3}}t^{3}+xt\right)dt+\frac{1}{\pi}% \int_{0}^{\infty}\mathop{\sin\/}\nolimits\!\left(\tfrac{1}{3}t^{3}+xt\right)dt.$
9.5.4 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(z\right)=\frac{1}{2\pi i}\int_{\infty e% ^{-\pi i/3}}^{\infty e^{\pi i/3}}\mathop{\exp\/}\nolimits\!\left(\tfrac{1}{3}t% ^{3}-zt\right)dt,$
9.5.5 $\mathop{\mathrm{Bi}\/}\nolimits\!\left(z\right)=\frac{1}{2\pi}\int_{-\infty}^{% \infty e^{\pi i/3}}\mathop{\exp\/}\nolimits\!\left(\tfrac{1}{3}t^{3}-zt\right)% dt+\dfrac{1}{2\pi}\int_{-\infty}^{\infty e^{-\pi i/3}}\mathop{\exp\/}\nolimits% \!\left(\tfrac{1}{3}t^{3}-zt\right)dt.$
9.5.6 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(z\right)=\frac{\sqrt{3}}{2\pi}\int_{0}^% {\infty}\mathop{\exp\/}\nolimits\!\left(-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}% \right)dt.$
9.5.7 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(z\right)=\frac{e^{-\zeta}}{\pi}\int_{0}% ^{\infty}\mathop{\exp\/}\nolimits\!\left(-z^{\ifrac{1}{2}}t^{2}\right)\mathop{% \cos\/}\nolimits\!\left(\tfrac{1}{3}t^{3}\right)dt,$ $|\mathop{\mathrm{ph}\/}\nolimits z|<\pi$.
9.5.8 $\mathop{\mathrm{Ai}\/}\nolimits\!\left(z\right)=\frac{e^{-\zeta}\zeta^{\ifrac{% -1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\mathop{\Gamma\/}\nolimits\!\left(\frac{% 5}{6}\right)}\int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}% \right)^{-\ifrac{1}{6}}dt,$ $|\mathop{\mathrm{ph}\/}\nolimits z|<\frac{2}{3}\pi$.
In (9.5.7) and (9.5.8) $\zeta=\frac{2}{3}z^{\ifrac{3}{2}}$.
| 2015-07-31T01:06:06 |
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|
http://lammps.sandia.gov/doc/pair_awpmd.html
|
# pair_style awpmd/cut command
## Syntax
pair_style awpmd/cut Rc keyword value ...
• Rc = global cutoff, -1 means cutoff of half the shortest box length
• zero or more keyword/value pairs may be appended
• keyword = hartree or dproduct or uhf or free or pbc or fix or harm or ermscale or flex_press
hartree value = none
dproduct value = none
uhf value = none
free value = none
pbc value = Plen
Plen = periodic width of electron = -1 or positive value (distance units)
fix value = Flen
Flen = fixed width of electron = -1 or positive value (distance units)
harm value = width
width = harmonic width constraint
ermscale value = factor
factor = scaling between electron mass and width variable mass
flex_press value = none
## Examples
pair_style awpmd/cut -1
pair_style awpmd/cut 40.0 uhf free
pair_coeff * *
pair_coeff 2 2 20.0
## Description
This pair style contains an implementation of the Antisymmetrized Wave Packet Molecular Dynamics (AWPMD) method. Need citation here. Need basic formulas here. Could be links to other documents.
Rc is the cutoff.
The pair_style command allows for several optional keywords to be specified.
The hartree, dproduct, and uhf keywords specify the form of the initial trial wave function for the system. If the hartree keyword is used, then a Hartree multielectron trial wave function is used. If the dproduct keyword is used, then a trial function which is a product of two determinants for each spin type is used. If the uhf keyword is used, then an unrestricted Hartree-Fock trial wave function is used.
The free, pbc, and fix keywords specify a width constraint on the electron wavepackets. If the free keyword is specified, then there is no constraint. If the pbc keyword is used and Plen is specified as -1, then the maximum width is half the shortest box length. If Plen is a positive value, then the value is the maximum width. If the fix keyword is used and Flen is specified as -1, then electrons have a constant width that is read from the data file. If Flen is a positive value, then the constant width for all electrons is set to Flen.
The harm keyword allow oscillations in the width of the electron wavepackets. More details are needed.
The ermscale keyword specifies a unitless scaling factor between the electron masses and the width variable mass. More details needed.
If the flex_press keyword is used, then a contribution from the electrons is added to the total virial and pressure of the system.
This potential is designed to be used with atom_style wavepacket definitions, in order to handle the description of systems with interacting nuclei and explicit electrons.
The following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, or by mixing as described below:
• cutoff (distance units)
For awpmd/cut, the cutoff coefficient is optional. If it is not used (as in some of the examples above), the default global value specified in the pair_style command is used.
Mixing, shift, table, tail correction, restart, rRESPA info:
The pair_modify mix, shift, table, and tail options are not relevant for this pair style.
This pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file.
This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.
none
## Default
These are the defaults for the pair_style keywords: hartree for the initial wavefunction, free for the wavepacket width.
| 2018-02-21T03:31:43 |
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https://www.lessonplanet.com/teachers/testing-a-solution-for-a-system-of-equations
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# Testing a solution for a system of equations
Can students use an ordered pair test a solution for a system of equations? Sal says you can, if you plug the x and y numbers into each equation. He shows that while the ordered pair does satisfy one equation, it does not satisfy the other. He also shows that to be the correct ordered pair it would have to satisfy both equations.
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| 2019-04-24T21:58:59 |
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https://zbmath.org/authors/?q=ai%3Abensoussan.alain
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## Bensoussan, Alain
Compute Distance To:
Author ID: bensoussan.alain Published as: Bensoussan, Alain; Bensoussan, A. Homepage: http://www.cityu.edu.hk/seem/abensous/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Documents Indexed: 359 Publications since 1967, including 20 Books 21 Contributions as Editor · 5 Further Contributions Biographic References: 2 Publications Co-Authors: 159 Co-Authors with 291 Joint Publications 4,686 Co-Co-Authors
all top 5
### Co-Authors
88 single-authored 58 Lions, Jacques-Louis 41 Frehse, Jens 28 Sethi, Suresh P. 24 Yam, Sheung Chi Phillip 16 Çakanyıldırım, Metin 13 Papanicolaou, George C. 12 Hoe, SingRu 8 Mertz, Laurent 8 Proth, Jean-Marie 7 Boccardo, Lucio 7 Crouhy, Michel G. 7 Mitter, Sanjoy K. 7 Turi, Janos 6 Menaldi, Jose-Luis 6 Tapiero, Charles S. 5 Blankenship, Gilmer L. 5 Galai, Dan 5 Nagai, Hideo 5 Temam, Roger Meyer 5 Yan, ZhongFeng 4 Chau, Man Ho Michael 4 Chen, Shaokuan 4 Delfour, Michel Claude 4 Elliott, Robert James 4 Friedman, Avner 4 Glowinski, Roland 4 Kantarcioglu, Murat 4 Liu, Jingzhen 4 Murat, François 4 Rascanu, Aurel 4 Yiu, Ka Fai Cedric 3 Aubin, Jean-Pierre 3 Brouste, Alexandre 3 Da Prato, Giuseppe 3 Li, Meng 3 Minjárez-Sosa, J. Adolfo 3 Peng, Shige 3 Shi, Ruixia 3 Siu, Chi Chung 3 Wong, Kwok Chuen 2 Baras, John S. 2 Benkherouf, Lakdere 2 Bertrand, Pierre Raphael 2 Borkar, Vivek Shripad 2 Breit, Dominic 2 Bulíček, Miroslav 2 Chevalier-Roignant, Benoît 2 Chow, Pao-Liu 2 Chutani, Anshuman 2 Delarue, François 2 Diltz, J. David 2 Ekeland, Ivar 2 Goursat, Maurice 2 Grün, Christine 2 Julien, Hugues 2 Kleindorfer, Paul R. 2 Kokotovic, Petar V. 2 Koo, Hyeng Keun 2 Rivera, Alejandro 2 Royal, Andrew J. 2 Runggaldier, Wolfgang J. 2 Skaaning, Sonny 2 Song, Huaming 2 Sung, K. C. J. 2 Viot, Michel 2 Vogelgesang, Jens 2 Yang, Hui 2 Yung, Siu Pang 1 Acharya, Subas 1 Ackermann, Juergen E. 1 Aggoun, Lakhdar 1 Ąkanyildirim, Metin 1 Anderson, Brian David Outram 1 Åström, Karl Johan 1 Balchen, Jens Glad 1 Barmish, B. Ross 1 Başar, Tamer 1 Blondel, Vincent D. 1 Bossavit, Alain 1 Bouleau, Nicolas 1 Brézis, Haïm 1 Bultez, Alain V. 1 Byrnes, Christopher Ian 1 Cadenillas, Abel 1 Caines, Peter Edwin 1 Cartiaux, F. B. 1 Cass, Thomas Richard 1 Chandrasekaran, Keerthi 1 Chandrasekharan, Keerthi 1 Curtain, Ruth Frances 1 Davis, Mark Herbert Ainsworth 1 Davison, Edward Joseph 1 Delebecque, Francois 1 Derzko, Nicolas A. 1 Djehiche, Boualem 1 Evstigneev, Igor V. 1 Feau, Cyril 1 Feng, Xinwei 1 Fernández de Luco, Marina 1 Fhima, Mehdi ...and 91 more Co-Authors
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### Serials
19 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 18 SIAM Journal on Control and Optimization 15 Applied Mathematics and Optimization 10 Lecture Notes in Control and Information Sciences 8 IEEE Transactions on Automatic Control 6 Journal of Optimization Theory and Applications 6 Comptes Rendus de l’Académie des Sciences. Série I 5 Discrete and Continuous Dynamical Systems. Series B 5 Communications in Information and Systems 5 SIAM Journal on Financial Mathematics 4 Stochastics 4 Operations Research 4 Chinese Annals of Mathematics. Series B 4 Acta Applicandae Mathematicae 4 Asymptotic Analysis 4 Mathematical Finance 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Mathematical Analysis and Applications 3 Journal für die Reine und Angewandte Mathematik 3 Systems & Control Letters 3 Stochastic Processes and their Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Systems & Control: Foundations & Applications 3 Risk and Decision Analysis 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Computation 2 Automatica 2 Commentationes Mathematicae Universitatis Carolinae 2 Journal of Functional Analysis 2 Journal of the Mathematical Society of Japan 2 Management Science 2 Le Matematiche 2 Mathematics of Operations Research 2 RAIRO, Automatique, Systems Analysis and Control 2 Operations Research Letters 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 RAIRO. Automatique-Productique, Informatique Industrielle 2 Stochastics and Stochastics Reports 2 Journal of Convex Analysis 2 Applied Mathematical Finance 2 Finance and Stochastics 2 Communications on Pure and Applied Analysis 2 Journal of Industrial and Management Optimization 2 Stochastics 2 SIAM Journal on Control 2 Studies in Probability, Optimization and Statistics 2 Dynamic Games and Applications 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 IMA Journal of Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of the Franklin Institute 1 Russian Mathematical Surveys 1 Conferenze del Seminario di Matematica dell’Università di Bari 1 INFOR. Information Systems and Operational Research 1 Kybernetika 1 Mathematics and Computers in Simulation 1 Naval Research Logistics 1 Numerical Functional Analysis and Optimization 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Ricerche di Matematica 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Large Scale Systems 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Stochastic Analysis and Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Computers & Operations Research 1 Journal of Economic Dynamics & Control 1 Mathematical and Computer Modelling 1 CWI Quarterly 1 Stochastic Hydrology and Hydraulics 1 Annals of Operations Research 1 Mathematica Bohemica 1 Communications in Partial Differential Equations 1 European Journal of Operational Research 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Matemática Aplicada e Computacional 1 Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică 1 Philosophical Transactions of the Royal Society of London. Series A 1 Georgian Mathematical Journal 1 Obozrenie Prikladnoĭ i Promyshlennoĭ Matematiki 1 Discrete and Continuous Dynamical Systems 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 European Journal of Control 1 Communications in Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Markov Processes and Related Fields 1 Journal of Applied Statistics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Journal of Evolution Equations 1 AMRX. Applied Mathematics Research eXpress 1 Communications in Mathematical Sciences 1 Rendiconti di Matematica, VI. Serie 1 Revue Française d’Informatique et de Recherche Opérationnelle 1 Advanced Series in Management ...and 14 more Serials
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### Fields
180 Systems theory; control (93-XX) 132 Calculus of variations and optimal control; optimization (49-XX) 116 Probability theory and stochastic processes (60-XX) 103 Partial differential equations (35-XX) 99 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 81 Operations research, mathematical programming (90-XX) 22 General and overarching topics; collections (00-XX) 17 Ordinary differential equations (34-XX) 16 Statistics (62-XX) 14 Numerical analysis (65-XX) 8 History and biography (01-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Mechanics of deformable solids (74-XX) 6 Operator theory (47-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Computer science (68-XX) 4 Mechanics of particles and systems (70-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 2 Measure and integration (28-XX) 2 Functional analysis (46-XX) 1 Combinatorics (05-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
266 Publications have been cited 5,384 times in 4,342 Documents Cited by Year
Asymptotic analysis for periodic structures. Zbl 0404.35001
Bensoussan, Alain; Lions, Jacques-Louis; Papanicolaou, George
1978
Boundary layer analysis in homogeneization of diffusion equations with Dirichlet conditions in the half space. Zbl 0411.60078
Bensoussan, A.; Lions, J. L.; Papanicolaou, G.
1978
Mean field games and mean field type control theory. Zbl 1287.93002
Bensoussan, Alain; Frehse, Jens; Yam, Phillip
2013
Applications des inéquations variationnelles en contrôle stochastique. Zbl 0411.49002
Bensoussan, A.; Lions, J.-L.
1978
Representation and control of infinite dimensional systems. 2nd ed. Zbl 1117.93002
Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K.
2007
Equations stochastiques du type Navier-Stokes. Zbl 0265.60094
Bensoussan, A.; Temam, R.
1973
Stochastic control of partially observable systems. Zbl 0776.93094
Bensoussan, Alain
1992
Lectures on stochastic control. I: Variational methods in stochastic control. Zbl 0505.93078
Bensoussan, A.
1982
Contrôle impulsionnel et inéquations quasi variationnelles. Zbl 0491.93002
Bensoussan, A.; Lions, J. L.
1982
Boundary layers and homogenization of transport processes. Zbl 0408.60100
Bensoussan, Alain; Lions, Jacques L.; Papanicolaou, George C.
1979
Stochastic Navier-Stokes equations. Zbl 0836.35115
Bensoussan, A.
1995
Applications of variational inequalities in stochastic control. Transl. from the French. Zbl 0478.49002
Bensoussan, Alain; Lions, Jacques-Louis
1982
On a nonlinear partial differential equation having natural growth terms and unbounded solution. Zbl 0696.35042
Bensoussan, A.; Boccardo, L.; Murat, F.
1988
Asymptotic analysis for periodic structures. Reprint of the 1978 original with corrections and bibliographical additions. Zbl 1229.35001
Bensoussan, Alain; Lions, Jacques-Louis; Papanicolaou, George
2011
Stochastic control by functional analysis methods. Zbl 0474.93002
Bensoussan, Alain
1982
Representation and control of infinite dimensional systems. Volume I. Zbl 0781.93002
Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K.
1992
Linear-quadratic mean field games. Zbl 1343.91010
Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P.; Yung, S. P.
2016
Nouvelle formulation de problèmes de contrôle impulsionnel et applications. Zbl 0266.49007
Bensoussan, Alain; Lions, Jacques-Louis
1973
On the theory of option pricing. Zbl 0554.90019
Bensoussan, A.
1984
Contrôle impulsionnel et inéquations quasi-variationnelles stationnaires. Zbl 0264.49004
Bensoussan, Alain; Goursat, Maurice; Lions, Jacques-Louis
1973
Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Zbl 0516.60072
Bensoussan, A.
1983
Perturbation methods in optimal control. Transl. from the French by C. Tomson. Zbl 0648.49001
Bensoussan, Alain
1988
Stochastic maximum principle for distributed parameter systems. Zbl 0519.93042
Bensoussan, A.
1983
Nouvelles méthodes en contrôle impulsionnel. Zbl 0339.93033
Bensoussan, A.; Lions, J. L.
1975
Regularity results for nonlinear elliptic systems and applications. Zbl 1055.35002
Bensoussan, Alain; Frehse, Jens
2002
Points de Nash dans le cas de fonctionnelles quadratiques et jeux différentiels linéaires à N personnes. Zbl 0254.90066
Bensoussan, A.
1974
Equations aux dérivées partielles stochastiques non linéaires. I. Zbl 0241.35009
Bensoussan, A.; Temam, R.
1972
Optimal impulse and continuous control: Method of nonlinear quasi- variational inequalities. Zbl 0324.49005
Bensoussan, A.; Lions, J. L.
1975
Optimality of $$(s,S)$$ policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. Zbl 1151.90304
Bensoussan, Alain; Liu, R. H.; Sethi, Suresh P.
2006
The master equation in mean field theory. Zbl 1325.35232
Bensoussan, Alain; Frehse, Jens; Yam, Sheung Chi Phillip
2015
Management applications of modern control theory. Zbl 0343.90001
Bensoussan, A.; Hurst, E. Gerald jun.; Näslund, B.
1974
Optimal control of partially observable stochastic systems with an exponential-of-integral performance index. Zbl 0574.93067
Bensoussan, A.; van Schuppen, J. H.
1985
A class of non-zero-sum stochastic differential investment and reinsurance games. Zbl 1297.93180
Bensoussan, Alain; Siu, Chi Chung; Yam, Sheung Chi Phillip; Yang, Hailiang
2014
Filtrage optimal des systèmes linéaires. (Optimal filtering of linear systems). Zbl 0231.93022
Bensoussan, Alain
1971
Nonlinear variational inequalities and differential games with stopping times. Zbl 0297.90120
Bensoussan, Alain; Friedman, Avner
1974
Nonzero-sum stochastic differential games with stopping times and free boundary problems. Zbl 0368.93029
Bensoussan, Alain; Friedman, Avner
1977
Time-consistent portfolio selection under short-selling prohibition: from discrete to continuous setting. Zbl 1348.60096
Bensoussan, A.; Wong, K. C.; Yam, S. C. P.; Yung, S. P.
2014
Optimal impulse and continuous control: Method of nonlinear quasi- variational inequalities. Zbl 0373.49004
Bensoussan, A.; Lions, J.-L.
1977
Hybrid control and dynamic programming. Zbl 0897.49022
Bensoussan, A.; Menaldi, J. L.
1997
Representation and control of infinite dimensional systems. Vol. 2. Zbl 0790.93016
Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K.
1993
Mathematical theory of production planning. Zbl 0564.90010
Bensoussan, Alain; Crouhy, Michel; Proth, Jean-Marie
1983
Some existence results for stochastic partial differential equations. Zbl 0793.60067
Bensoussan, A.
1992
On the interpretation of the master equation. Zbl 1379.60063
Bensoussan, A.; Frehse, J.; Yam, S. C. P.
2017
Stochastic inertial manifold. Zbl 0854.60059
Bensoussan, Alain; Flandoli, Franco
1995
On Bellman equations of ergodic control in $$\mathbb{R}{}^ n$$. Zbl 0779.35038
Bensoussan, A.; Frehse, J.
1992
Approximation of some stochastic differential equations by the splitting up method. Zbl 0745.65089
Bensoussan, A.; Glowinski, R.; Rǎşcanu, A.
1992
The maximum principle for global solutions of stochastic Stackelberg differential games. Zbl 1320.91042
Bensoussan, Alain; Chen, Shaokuan; Sethi, Suresh P.
2015
Mean field games with a dominating player. Zbl 1348.49031
Bensoussan, A.; Chau, M. H. M.; Yam, S. C. P.
2016
Nonlinear elliptic systems in stochastic game theory. Zbl 0531.93052
Bensoussan, A.; Frehse, J.
1984
Contrôle impulsionnel et inéquations quasi-variationnelles d’évolution. Zbl 0264.49005
Bensoussan, Alain; Lions, Jacques-Louis
1973
Stochastic variational inequalities in infinite dimensional spaces. Zbl 0887.60063
Bensoussan, Alain; Rascanu, Aurel
1997
Mean field Stackelberg games: aggregation of delayed instructions. Zbl 1320.91028
Bensoussan, A.; Chau, M. H. M.; Yam, S. C. P.
2015
Stochastic games for $$N$$ players. Zbl 0977.91006
Bensoussan, A.; Frehse, J.
2000
Problèmes de temps d’arret optimal et inéquations variationnelles paraboliques. Zbl 0341.60032
Bensoussan, A.; Lions, J. L.
1973
Impulsive control in management: Prospects and applications. Zbl 0465.90022
Bensoussan, A.; Tapiero, C. S.
1982
Dynamic programming and inventory control. Zbl 1252.90001
Bensoussan, Alain
2011
Optimal consumption and portfolio decisions with partially observed real prices. Zbl 1168.91375
Bensoussan, Alain; Keppo, Jussi; Sethi, Suresh P.
2009
Regularity theory for systems of partial differential equations with Neumann boundary conditions. Zbl 1140.35407
Bensoussan, A.; Frehse, J.
2002
Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and $$H^ 1$$ regularity. Zbl 0851.35079
Bensoussan, A.; Frehse, J.
1996
Survey on the state of systems and control. Zbl 1177.93001
Blondel, Vincent; Gevers, Michel; Lindquist, Anders
1995
Stochastic production planning with production constraints. Zbl 0561.90044
Bensoussan, A.; Sethi, S. P.; Vickson, R.; Derzko, N.
1984
Linear-quadratic mean field Stackelberg games with state and control delays. Zbl 1372.91021
Bensoussan, A.; Chau, M. H. M.; Lai, Y.; Yam, S. C. P.
2017
Well-posedness of mean-field type forward-backward stochastic differential equations. Zbl 1327.60114
Bensoussan, A.; Yam, S. C. P.; Zhang, Z.
2015
Optimality of an $$(s,S)$$ policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach. Zbl 1194.93215
Benkherouf, Lakdere; Bensoussan, Alain
2009
Approximation of the Zakai equation by the splitting up method. Zbl 0726.60040
Bensoussan, A.; Glowinski, R.; Rascanu, A.
1990
Dynamic observers as asymptotic limits of recursive filters: Special cases. Zbl 0658.93017
Baras, J. S.; Bensoussan, A.; James, M. R.
1988
$$H$$ convergence for quasi-linear elliptic equations with quadratic growth. Zbl 0795.35008
Bensoussan, A.; Boccardo, L.; Murat, F.
1992
Nonlinear systems of elliptic equations with natural growth conditions and sign conditions. Zbl 1077.35046
Bensoussan, Alain; Boccardo, Lucio
2002
Sur quelques phénomènes asymptotiques stationnaires. Zbl 0309.35007
Bensoussan, Alain; Lions, Jacques-Louis; Papanicolaou, Georges
1975
Systems of partial differential equations and stochastic control. Zbl 0548.35037
Bensoussan, A.
1981
Differential games with mixed leadership: The open-loop solution. Zbl 1198.91039
Başar, Tamer; Bensoussan, Alain; Sethi, Suresh P.
2010
Homogenization of elliptic equations with principal part not in divergence form and Hamiltonian with quadratic growth. Zbl 0602.35030
Bensoussan, A.; Boccardo, L.; Murat, F.
1986
Local solutions for stochastic Navier-Stokes equations. Zbl 0972.76021
Bensoussan, Alain; Frehse, Jens
2000
Optimal control of stochastic linear distributed parameter systems. Zbl 0276.93058
Bensoussan, A.; Viot, M.
1975
Difference equations on weighted graphs. Zbl 1068.05039
Bensoussan, Alain; Menaldi, José-Luis
2005
Optimum inventory and product quality control with deterministic and stochastic deterioration - an application of distributed parameters control systems. Zbl 0301.93072
Bensoussan, Alain; Nissen, Georges; Tapiero, Charles S.
1975
Stochastic hybrid control. Zbl 0967.93097
Bensoussan, A.; Menaldi, J. L.
2000
Existence and uniqueness of solutions for Bertrand and Cournot mean field games. Zbl 1382.35141
Graber, P. Jameson; Bensoussan, Alain
2018
Threshold-type policies for real options using regime-switching models. Zbl 1255.91444
Bensoussan, Alain; Yan, ZhongFeng; Yin, G.
2012
Smooth solutions of systems of quasilinear parabolic equations. Zbl 1078.35022
Bensoussan, Alain; Frehse, Jens
2002
Linear-quadratic time-inconsistent mean field games. Zbl 1314.91040
Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P.
2013
Some results on risk-sensitive control with full observation. Zbl 0896.93035
Bensoussan, A.; Frehse, J.; Nagai, H.
1998
A paradox in time-consistency in the mean-variance problem? Zbl 1426.91240
Bensoussan, Alain; Wong, Kwok Chuen; Yam, Sheung Chi Phillip
2019
Optimal sensor scheduling in nonlinear filtering of diffusion processes. Zbl 0683.49001
Baras, John S.; Bensoussan, Alain
1989
Singular perturbations in stochastic control. Zbl 0622.93076
Bensoussan, A.; Blankenship, G. L.
1987
On the support of the solution of some variational inequalities of evolution. Zbl 0341.49026
Bensoussan, A.; Lions, J. L.
1976
A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality. Zbl 0474.49013
Bensoussan, A.; Frehse, J.; Mosco, U.
1982
Partially observed inventory systems: The case of zero-balance walk. Zbl 1190.90015
Bensoussan, Alain; Ąkanyildirim, Metin; Sethi, Suresh P.
2007
A finite-dimensional risk-sensitive control problem. Zbl 0841.93081
Bensoussan, Alain; Elliott, Robert J.
1995
Unemployment risks and optimal retirement in an incomplete market. Zbl 1348.91247
Bensoussan, Alain; Jang, Bong-Gyu; Park, Seyoung
2016
Asymptotic behaviour of Norton-Hoff’s law in plasticity theory and $$H^ 1$$ regularity. Zbl 0831.35047
Bensoussan, A.; Frehse, J.
1993
Impulse control with random reaction periods: a central bank intervention problem. Zbl 1258.90030
Bensoussan, Alain; Long, Hongwei; Perera, Sandun; Sethi, Suresh
2012
Control and Nash games with mean field effect. Zbl 1264.49028
Bensoussan, Alain; Frehse, Jens
2013
On the Hamilton-Jacobi approach for the optimal control of diffusion processes with jumps. Zbl 0446.93052
Bensoussan, A.
1978
On the optimal control of partially observed inventory systems. Zbl 1134.90303
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.
2005
Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049
Kolokoltsov, V. N.; Bensoussan, A.
2016
A multiperiod newsvendor problem with partially observed demand. Zbl 1279.90008
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.
2007
Controlled diffusions in a random medium. Zbl 0666.93131
Bensoussan, A.; Blankenship, G.
1988
An ultra weak finite element method as an alternative to a Monte Carlo method for an elasto-plastic problem with noise. Zbl 1210.37060
Bensoussan, Alain; Mertz, Laurent; Pironneau, Olivier; Turi, Janos
2009
Homogenization of a class of stochastic partial differential equations. Zbl 0737.60054
Bensoussan, A.
1991
Linear-quadratic-Gaussian mean-field-game with partial observation and common noise. Zbl 1471.91026
Bensoussan, Alain; Feng, Xinwei; Huang, Jianhui
2021
Does performance-sensitive debt mitigate debt overhang? Zbl 1475.91394
Bensoussan, Alain; Chevalier-Roignant, Benoît; Rivera, Alejandro
2021
Mean-field-type games with jump and regime switching. Zbl 1437.91050
Bensoussan, Alain; Djehiche, Boualem; Tembine, Hamidou; Yam, Sheung Chi Phillip
2020
Mean field games with parametrized followers. Zbl 1483.91031
Bensoussan, Alain; Cass, Thomas; Chau, Man Ho Michael; Yam, Sheung Chi Phillip
2020
Optimal periodic replenishment policies for spectrally positive Lévy demand processes. Zbl 1461.60032
Pérez, José-Luis; Yamazaki, Kazutoshi; Bensoussan, Alain
2020
A paradox in time-consistency in the mean-variance problem? Zbl 1426.91240
Bensoussan, Alain; Wong, Kwok Chuen; Yam, Sheung Chi Phillip
2019
Sequential capacity expansion options. Zbl 1455.91268
Bensoussan, Alain; Chevalier-Roignant, Benoît
2019
Feedback Stackelberg-Nash equilibria in mixed leadership games with an application to cooperative advertising. Zbl 1427.49045
Bensoussan, Alain; Chen, Shaokuan; Chutani, Anshuman; Sethi, Suresh P.; Siu, Chi Chung; Phillip Yam, Sheung Chi
2019
Control problem on space of random variables and master equation. Zbl 1450.35305
Bensoussan, Alain; Yam, Sheung Chi Phillip
2019
A mean-variance approach to capital investment optimization. Zbl 1411.91481
Bensoussan, Alain; Hoe, SingRu (Celine); Yan, Zhongfeng
2019
Existence and uniqueness of solutions for Bertrand and Cournot mean field games. Zbl 1382.35141
Graber, P. Jameson; Bensoussan, Alain
2018
Mean field control and mean field game models with several populations. Zbl 1406.35416
Bensoussan, Alain; Huang, Tao; Laurière, Mathieu
2018
Estimation and control of dynamical systems. Zbl 1401.37001
Bensoussan, Alain
2018
Optimal inventory control with jump diffusion and nonlinear dynamics in the demand. Zbl 1378.35176
Liu, Jingzhen; Cedric Yiu, Ka Fai; Bensoussan, Alain
2018
Backward stochastic dynamics with a subdifferential operator and non-local parabolic variational inequalities. Zbl 1381.37063
Bensoussan, Alain; Li, Yiqun; Yam, Sheung Chi Phillip
2018
Ergodic control for a mean reverting inventory model. Zbl 1412.35187
Liu, Jingzhen; Yiu, Ka Fai Cedric; Bensoussan, Alain
2018
On the interpretation of the master equation. Zbl 1379.60063
Bensoussan, A.; Frehse, J.; Yam, S. C. P.
2017
Linear-quadratic mean field Stackelberg games with state and control delays. Zbl 1372.91021
Bensoussan, A.; Chau, M. H. M.; Lai, Y.; Yam, S. C. P.
2017
Real options with competition and regime switching. Zbl 1414.91403
Bensoussan, Alain; Hoe, Singru; Yan, Zhongfeng; Yin, George
2017
Optimality of $$(s,S)$$ policies with nonlinear processes. Zbl 1360.90016
Liu, Jingzhen; Yiu, Ka Fai Cedric; Bensoussan, Alain
2017
Base stock list price policy in continuous time. Zbl 1360.93767
Bensoussan, Alain; Skaaning, Sonny
2017
Linear-quadratic mean field games. Zbl 1343.91010
Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P.; Yung, S. P.
2016
Mean field games with a dominating player. Zbl 1348.49031
Bensoussan, A.; Chau, M. H. M.; Yam, S. C. P.
2016
Unemployment risks and optimal retirement in an incomplete market. Zbl 1348.91247
Bensoussan, Alain; Jang, Bong-Gyu; Park, Seyoung
2016
Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049
Kolokoltsov, V. N.; Bensoussan, A.
2016
Parabolic Bellman-systems with mean field dependence. Zbl 1342.35054
Bensoussan, Alain; Breit, Dominic; Frehse, Jens
2016
Nonlocal boundary value problems of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise. Zbl 1456.74061
Bensoussan, A.; Mertz, L.; Yam, S. C. P.
2016
Preface: In memory of A. V. Balakrishnan. Zbl 1341.01041
2016
The optimal mean variance problem with inflation. Zbl 1327.90362
Liu, Jingzhen; Yiu, Ka Fai Cedric; Bensoussan, Alain
2016
The master equation in mean field theory. Zbl 1325.35232
Bensoussan, Alain; Frehse, Jens; Yam, Sheung Chi Phillip
2015
The maximum principle for global solutions of stochastic Stackelberg differential games. Zbl 1320.91042
Bensoussan, Alain; Chen, Shaokuan; Sethi, Suresh P.
2015
Mean field Stackelberg games: aggregation of delayed instructions. Zbl 1320.91028
Bensoussan, A.; Chau, M. H. M.; Yam, S. C. P.
2015
Well-posedness of mean-field type forward-backward stochastic differential equations. Zbl 1327.60114
Bensoussan, A.; Yam, S. C. P.; Zhang, Z.
2015
Entrepreneurial decisions on effort and project with a nonconcave objective function. Zbl 1329.90071
Bensoussan, Alain; Cadenillas, Abel; Koo, Hyeng Keun
2015
Degenerate Dirichlet problems related to the ergodic property of an elasto-plastic oscillator excited by a filtered white noise. Zbl 1328.35235
Mertz, Laurent; Bensoussan, Alain
2015
An analytical approach for the growth rate of the variance of the deformation related to an elasto-plastic oscillator excited by a white noise. Zbl 1337.60148
Bensoussan, Alain; Feau, Cyril; Mertz, Laurent; Yam, Sheung Chi Phillip
2015
Technical note: Managing nonperishable inventories with learning about demand arrival rate through stockout times. Zbl 1327.90005
Bensoussan, Alain; Guo, Pengfei
2015
Future perspectives in risk models and finance. Zbl 1304.91010
2015
A class of non-zero-sum stochastic differential investment and reinsurance games. Zbl 1297.93180
Bensoussan, Alain; Siu, Chi Chung; Yam, Sheung Chi Phillip; Yang, Hailiang
2014
Time-consistent portfolio selection under short-selling prohibition: from discrete to continuous setting. Zbl 1348.60096
Bensoussan, A.; Wong, K. C.; Yam, S. C. P.; Yung, S. P.
2014
Feedback Stackelberg solutions of infinite-horizon stochastic differential games. Zbl 1296.91063
Bensoussan, Alain; Chen, Shaokuan; Sethi, Suresh P.
2014
Mean-variance pre-commitment policies revisited via a mean-field technique. Zbl 1314.91189
Bensoussan, A.; Wong, K. C.; Yam, S. C. P.
2014
Optimal decision making in multi-product dual sourcing procurement with demand forecast updating. Zbl 1348.90042
Song, Hua-ming; Yang, Hui; Bensoussan, Alain; Zhang, Ding
2014
Control and Nash games with mean field effect. Zbl 1331.49036
Bensoussan, Alain; Frehse, Jens
2014
Stochastic differential games with a varying number of players. Zbl 1307.91032
Bensoussan, Alain; Frehse, Jens; Grün, Christine
2014
Mean field games and mean field type control theory. Zbl 1287.93002
Bensoussan, Alain; Frehse, Jens; Yam, Phillip
2013
Linear-quadratic time-inconsistent mean field games. Zbl 1314.91040
Bensoussan, A.; Sung, K. C. J.; Yam, S. C. P.
2013
Control and Nash games with mean field effect. Zbl 1264.49028
Bensoussan, Alain; Frehse, Jens
2013
Linear quadratic differential games with mixed leadership: the open-loop solution. Zbl 1262.91010
Bensoussan, Alain; Chen, Shaokuan; Sethi, Suresh P.
2013
Optimal inventory control with shrinkage and observed sales. Zbl 1302.90009
Bensoussan, Alain; Çakanyıldırım, Metin; Li, Meng; Sethi, Suresh P.
2013
Optimizing production and inventory decisions in a supply chain with lot size, production rate and lead time interactions. Zbl 1334.90014
Song, Hua-Ming; Yang, Hui; Bensoussan, Alain
2013
Real options, ambiguity, risk and insurance. Zbl 1272.91002
2013
Threshold-type policies for real options using regime-switching models. Zbl 1255.91444
Bensoussan, Alain; Yan, ZhongFeng; Yin, G.
2012
Impulse control with random reaction periods: a central bank intervention problem. Zbl 1258.90030
Bensoussan, Alain; Long, Hongwei; Perera, Sandun; Sethi, Suresh
2012
Existence and compactness for weak solutions to Bellman systems with critical growth. Zbl 1255.35106
Bensoussan, Alain; Bulíček, Miroslav; Frehse, Jens
2012
An analytic approach to the ergodic theory of a stochastic variational inequality. Zbl 1248.60078
Bensoussan, Alain; Mertz, Laurent
2012
Long cycle behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise. Zbl 1310.74011
Bensoussan, Alain; Mertz, Laurent; Yam, S. C. P.
2012
Nash and Stackelberg differential games. Zbl 1254.91051
Bensoussan, Alain; Frehse, Jens; Vogelgesang, Jens
2012
Asymptotic analysis for periodic structures. Reprint of the 1978 original with corrections and bibliographical additions. Zbl 1229.35001
Bensoussan, Alain; Lions, Jacques-Louis; Papanicolaou, George
2011
Dynamic programming and inventory control. Zbl 1252.90001
Bensoussan, Alain
2011
Average cost optimality in inventory models with dynamic information delays. Zbl 1368.90005
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.; Wang, Mingzheng; Zhang, Hanqin
2011
Filtering for discrete-time Markov processes and applications to inventory control with incomplete information. Zbl 1228.60051
Bensoussan, A.; Çakanyıldırım, M.; Sethi, S. P.
2011
Computation of approximate optimal policies in a partially observed inventory model with rain checks. Zbl 1234.90003
Bensoussan, Alain; Cakanyildirim, Metin; Sethi, Suresh P.; Shi, Ruixia
2011
Differential games with mixed leadership: The open-loop solution. Zbl 1198.91039
Başar, Tamer; Bensoussan, Alain; Sethi, Suresh P.
2010
Systems of Bellman equations to stochastic differential games with non-compact coupling. Zbl 1191.35275
Bensoussan, Alain; Frehse, Jens; Vogelgesang, Jens
2010
Real options games in complete and incomplete markets with several decision makers. Zbl 1203.91319
Bensoussan, Alain; Diltz, J. David; Hoe, SingRu
2010
Inventory control with an order-time constraint: optimality, uniqueness and significance. Zbl 1229.90007
Bensoussan, Alain; Moussawi-Haidar, Lama; Çakanyıldırım, Metin
2010
A game-theoretical approach for finding optimal strategies in a botnet defense model. Zbl 1298.91058
Bensoussan, Alain; Kantarcioglu, Murat; Hoe, SingRu (Celine)
2010
On a class of partial differential equations with nonlocal Dirichlet boundary conditions. Zbl 1195.35107
Bensoussan, Alain; Turi, Janos
2010
An incomplete information inventory model with presence of inventories or backorders as only observations. Zbl 1217.90008
Bensoussan, A.; Çakanyıldırım, M.; Minjárez-Sosa, J. A.; Sethi, S. P.; Shi, R.
2010
Singular control and impulse control: a common approach. Zbl 1181.49033
Bensoussan, Alain; Liu, John; Yuan, Jiguang
2010
When do firms invest in privacy-preserving technologies? Zbl 1298.91064
Kantarcioglu, Murat; Bensoussan, Alain; Hoe, SingRu (Celine)
2010
Optimal control of variational inequalities. Zbl 1214.49008
Bensoussan, Alain; Chandrasekaran, Keerthi; Turi, Janos
2010
Optimal consumption and portfolio decisions with partially observed real prices. Zbl 1168.91375
Bensoussan, Alain; Keppo, Jussi; Sethi, Suresh P.
2009
Optimality of an $$(s,S)$$ policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach. Zbl 1194.93215
Benkherouf, Lakdere; Bensoussan, Alain
2009
An ultra weak finite element method as an alternative to a Monte Carlo method for an elasto-plastic problem with noise. Zbl 1210.37060
Bensoussan, Alain; Mertz, Laurent; Pironneau, Olivier; Turi, Janos
2009
Optimal cash management under uncertainty. Zbl 1182.91189
Bensoussan, Alain; Chutani, Anshuman; Sethi, Suresh P.
2009
On diagonal elliptic and parabolic systems with super-quadratic Hamiltonians. Zbl 1152.35361
Bensoussan, Alain; Frehse, Jens
2009
A note on “The censored newsvendor and the optimal acquisition of information”. Zbl 1233.90010
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.
2009
Bayesian and adaptive controls for a newsvendor facing exponential demand. Zbl 05794652
Bensoussan, Alain; Çakanyıldırım, Metin; Royal, Andrew; Sethi, Suresh P.
2009
Diagonal elliptic Bellman systems for stochastic differential games with discount control and noncompact coupling. Zbl 1196.35082
Bensoussan, Alain; Frehse, Jens
2009
Censored newsvendor model revisited with unnormalized probabilities. Zbl 1185.93123
Bensoussan, Alain; Çakanyildirim, Metin; Sethi, Suresh P.
2009
Degenerate Dirichlet problems related to the invariant measure of elasto-plastic oscillators. Zbl 1168.60029
Bensoussan, Alain; Turi, Janos
2008
Partially observed inventory systems: the case of rain checks. Zbl 1170.90003
Bensoussan, Alain; ÇAkanyildirim, Metin; Minjárez-Sosa, J. Adolfo; Sethi, Suresh P.; Shi, Ruixia
2008
Systems of Bellman equations to stochastic differential games with discount control. Zbl 1190.49045
Bensoussan, Alain; Frehse, Jens
2008
Inventory problems with partially observed demands and lost sales. Zbl 1190.90014
Bensoussan, A.; Çakanyıldırım, M.; Minjárez-Sosa, J. A.; Royal, A.; Sethi, S. P.
2008
Impulse control in discrete time. Zbl 1151.49029
Bensoussan, Alain
2008
Representation and control of infinite dimensional systems. 2nd ed. Zbl 1117.93002
Bensoussan, Alain; Da Prato, Giuseppe; Delfour, Michel C.; Mitter, Sanjoy K.
2007
Partially observed inventory systems: The case of zero-balance walk. Zbl 1190.90015
Bensoussan, Alain; Ąkanyildirim, Metin; Sethi, Suresh P.
2007
A multiperiod newsvendor problem with partially observed demand. Zbl 1279.90008
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.
2007
The machine maintenance and sale age model of Kamien and Schwartz revisited. Zbl 1232.90164
Bensoussan, Alain; Sethi, Suresh P.
2007
Optimality of $$(s,S)$$ policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. Zbl 1151.90304
Bensoussan, Alain; Liu, R. H.; Sethi, Suresh P.
2006
Optimality of base-stock and $$(s,S)$$ policies for inventory problems with information delays. Zbl 1184.90006
Bensoussan, A.; Çakanyildirim, M.; Sethi, S. P.
2006
Stochastic variational inequalities for elasto-plastic oscillators. Zbl 1111.60050
Bensoussan, Alain; Turi, Janos
2006
Explicit solutions of linear quadratic differential games. Zbl 1136.91330
Bensoussan, A.
2006
Difference equations on weighted graphs. Zbl 1068.05039
Bensoussan, Alain; Menaldi, José-Luis
2005
On the optimal control of partially observed inventory systems. Zbl 1134.90303
Bensoussan, Alain; Çakanyıldırım, Metin; Sethi, Suresh P.
2005
Penalty approximation and analytical characterization of the problem of super-replication under portfolio constraints. Zbl 1109.91021
Bensoussan, Alain; Touzi, Nizar; Menaldi, José Luis
2005
Homogenization of systems of partial differential equations. Zbl 1128.35016
Bensoussan, A.
2005
Some remarks on linear filtering theory for infinite dimensional systems. Zbl 1042.93056
Bensoussan, Alain
2003
...and 166 more Documents
all top 5
### Cited by 4,795 Authors
82 Bensoussan, Alain 35 Suslina, Tat’yana Aleksandrovna 32 Menaldi, Jose-Luis 29 Abdulle, Assyr 27 Cui, Junzhi 27 Lions, Pierre-Louis 26 Allaire, Grégoire 26 Wu, Zhen 25 Sethi, Suresh P. 24 Frehse, Jens 24 Yam, Sheung Chi Phillip 23 Cao, Liqun 20 Murat, François 20 Sango, Mamadou 20 Temam, Roger Meyer 19 Piatnitski, Andrey L. 18 Tachim Medjo, Theodore 17 Donato, Patrizia 17 Pham, Huyên 17 Raymond, Jean-Pierre 17 Razafimandimby, Paul André 16 Boccardo, Lucio 16 Deugoue, Gabriel 16 Noor, Muhammad Aslam 16 Yong, Jiongmin 15 Gozzi, Fausto 15 Huang, Jianhui 15 Laurière, Mathieu 15 Le Bris, Claude 15 Legoll, Frédéric 15 Pastukhova, Svetlana Evgenievna 14 Carmona, René A. 14 Conca, Carlos 14 Kolpakov, Alexander G. 14 Shi, Jingtao 13 Elliott, Robert James 13 Flandoli, Franco 13 Meng, Qingxin 13 Morimoto, Hiroaki 13 Pardoux, Etienne 13 Robin, Maurice 13 Rodríguez-Ramos, Reinaldo 13 Vanninathan, Muthusamy 12 Briane, Marc 12 Hu, Ying 12 Wang, Guangchen 12 Xiong, Jie 11 Bayraktar, Erhan 11 Borkar, Vivek Shripad 11 Ghosh, Mrinal Kanti 11 Li, Qin 10 Bessaih, Hakima 10 Bravo-Castillero, Julián 10 Cherednichenko, Kirill D. 10 Federico, Salvatore 10 Fuhrman, Marco 10 Haiour, Mohamed 10 Hintermüller, Michael 10 Huang, Minyi 10 Jin, Zhuo 10 Kalamkarov, Alexander L. 10 Peng, Shige 10 Qiu, Jinniao 10 Rautenberg, Carlos N. 10 Spiliopoulos, Konstantinos V. 10 Tang, Shanjian 10 Tessitore, Gianmario 10 Visintin, Augusto 9 Auriault, Jean-Louis 9 Averboukh, Yuriĭ Vladimirovich 9 Başar, Tamer 9 Blanc, Xavier 9 Capuzzo Dolcetta, Italo 9 Da Prato, Giuseppe 9 Friedman, Avner 9 Glatt-Holtz, Nathan E. 9 Hata, Hiroaki 9 Huang, Nan-Jing 9 Kolokoltsov, Vassili N. 9 Kunisch, Karl 9 Li, Xun 9 Marchi, Claudio 9 Pavliotis, Grigorios A. 9 Stettner, Łukasz 9 Tapiero, Charles S. 9 Tucsnak, Marius 9 Woźniak, Czesław 9 Xin, Jack X. 9 Yang, Zhiqiang 8 Achdou, Yves 8 Arrieta, José M. 8 Badra, Mehdi 8 Bal, Guillaume 8 Boulbrachene, Messaoud 8 Breit, Dominic 8 Cardaliaguet, Pierre 8 Charalambous, Charalambos D. 8 Cirant, Marco 8 De Angelis, Tiziano 8 Delarue, François ...and 4,695 more Authors
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### Cited in 533 Serials
146 Journal of Mathematical Analysis and Applications 143 Applied Mathematics and Optimization 104 SIAM Journal on Control and Optimization 99 Journal of Optimization Theory and Applications 98 Journal of Differential Equations 93 Stochastic Processes and their Applications 85 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 71 Computer Methods in Applied Mechanics and Engineering 65 Systems & Control Letters 64 Stochastic Analysis and Applications 62 Automatica 61 European Journal of Operational Research 52 Archive for Rational Mechanics and Analysis 46 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 46 Multiscale Modeling & Simulation 42 International Journal of Engineering Science 41 Applied Mathematics and Computation 41 Journal de Mathématiques Pures et Appliquées. Neuvième Série 40 Computers & Mathematics with Applications 40 Journal of Computational Physics 38 Journal of Computational and Applied Mathematics 38 The Annals of Applied Probability 37 Journal of the Mechanics and Physics of Solids 37 SIAM Journal on Mathematical Analysis 36 Communications in Partial Differential Equations 34 Journal of Functional Analysis 34 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 33 Discrete and Continuous Dynamical Systems 32 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 32 Comptes Rendus. Mathématique. Académie des Sciences, Paris 31 The Annals of Probability 31 Insurance Mathematics & Economics 31 European Journal of Mechanics. A. Solids 30 Annali di Matematica Pura ed Applicata. Serie Quarta 28 Calculus of Variations and Partial Differential Equations 28 Dynamic Games and Applications 28 Nonlinear Analysis. Theory, Methods & Applications 27 RAIRO. Modélisation Mathématique et Analyse Numérique 27 Journal of Mathematical Sciences (New York) 26 St. Petersburg Mathematical Journal 26 NoDEA. Nonlinear Differential Equations and Applications 25 International Journal of Control 25 Probability Theory and Related Fields 24 Journal of Statistical Physics 23 SIAM Journal on Applied Mathematics 23 Mathematical Control and Related Fields 21 Stochastics 21 Mathematics of Operations Research 21 Acta Applicandae Mathematicae 21 Journal of Economic Dynamics & Control 21 Stochastics and Dynamics 20 Applicable Analysis 20 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 19 Communications in Mathematical Physics 19 International Journal of Systems Science 19 Mathematical Notes 19 Transactions of the American Mathematical Society 19 MCSS. Mathematics of Control, Signals, and Systems 19 SIAM Journal on Scientific Computing 19 Abstract and Applied Analysis 19 Journal of Industrial and Management Optimization 18 Physica D 18 Annals of Operations Research 18 Mathematical Methods of Operations Research 17 Acta Mechanica 17 Mathematics of Computation 17 Journal of Global Optimization 17 Mathematics and Mechanics of Solids 17 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 16 Journal of Mathematical Physics 16 Numerische Mathematik 16 Operations Research Letters 16 Mathematical and Computer Modelling 16 Mathematical Problems in Engineering 16 Journal of Evolution Equations 15 Journal of the Franklin Institute 14 Wave Motion 14 Acta Mathematicae Applicatae Sinica. English Series 14 Applications of Mathematics 14 Finance and Stochastics 14 Mathematical Finance 14 Stochastics 14 Stochastic and Partial Differential Equations. Analysis and Computations 13 Computational Mechanics 13 Applied Mathematics Letters 13 Journal of Scientific Computing 13 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 13 Discrete and Continuous Dynamical Systems. Series B 13 Journal of Systems Science and Complexity 13 Communications on Pure and Applied Analysis 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 SIAM Journal on Numerical Analysis 12 Chinese Annals of Mathematics. Series B 12 Applied Numerical Mathematics 12 Journal of Elasticity 12 Journal of Inequalities and Applications 12 Nonlinear Analysis. Real World Applications 11 International Journal of Solids and Structures 11 Functional Analysis and its Applications 11 Numerical Functional Analysis and Optimization ...and 433 more Serials
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### Cited in 50 Fields
1,810 Partial differential equations (35-XX) 1,215 Probability theory and stochastic processes (60-XX) 1,049 Systems theory; control (93-XX) 1,011 Calculus of variations and optimal control; optimization (49-XX) 811 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 588 Mechanics of deformable solids (74-XX) 497 Numerical analysis (65-XX) 408 Fluid mechanics (76-XX) 387 Operations research, mathematical programming (90-XX) 211 Operator theory (47-XX) 146 Ordinary differential equations (34-XX) 142 Statistical mechanics, structure of matter (82-XX) 105 Dynamical systems and ergodic theory (37-XX) 89 Optics, electromagnetic theory (78-XX) 82 Biology and other natural sciences (92-XX) 63 Statistics (62-XX) 55 Integral equations (45-XX) 54 Functional analysis (46-XX) 50 Classical thermodynamics, heat transfer (80-XX) 36 Quantum theory (81-XX) 34 Geophysics (86-XX) 32 Global analysis, analysis on manifolds (58-XX) 29 Mechanics of particles and systems (70-XX) 23 Computer science (68-XX) 19 Potential theory (31-XX) 18 Real functions (26-XX) 17 Information and communication theory, circuits (94-XX) 16 Approximations and expansions (41-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 12 Measure and integration (28-XX) 9 Combinatorics (05-XX) 9 General topology (54-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Functions of a complex variable (30-XX) 6 Topological groups, Lie groups (22-XX) 5 General and overarching topics; collections (00-XX) 5 Difference and functional equations (39-XX) 5 Convex and discrete geometry (52-XX) 5 Differential geometry (53-XX) 5 Astronomy and astrophysics (85-XX) 4 Mathematical logic and foundations (03-XX) 3 Nonassociative rings and algebras (17-XX) 3 Special functions (33-XX) 3 Abstract harmonic analysis (43-XX) 3 Integral transforms, operational calculus (44-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX)
### Wikidata Timeline
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| 2022-05-20T06:56:22 |
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https://drupal.star.bnl.gov/STAR/blog/slhuang/measurements-v2-v3-pau-dau-and-3heau-collisions-%C2%AD200-gev-star-collaboration
|
# Measurements of v2, v3 in p+Au, d+Au and 3He+Au collisions at 200 GeV from STAR collaboration
Title: Measurements of v2, v3 in central p+Au, d+Au and 3He+Au collisions at 200 GeV from STAR collaboration
PA: Shengli Huang, Zhenyu Chen, Jiangyong Jia, Roy Lacey, Pengfei Liu, Maowu Nie, Yuri Sato, Chunjian Zhang
Target Journal: Physical Review Letter
Paper Draft:
Draft for PWGC review
drupal.star.bnl.gov/STAR/system/files/starsmallshort_5.pdf
Draft for PWG review:
drupal.star.bnl.gov/STAR/system/files/starsmallshort-6_0.pdf
Analysis Note:
PWGC review
presentation:
drupal.star.bnl.gov/STAR/blog/slhuang/small-system-pwgc-review-request
Abstract:
In this paper, the flow coefficients \$v_2\$ and \$v_3\$ are extracted by four kinds of subtraction methods from long-range two-particle azimuthal angular correlations with \$|\Deta|>\$1.0, as a function of transversal momentum in central p/d/\$^3\$He+Au collisions at \$\sqrtsNN\$ = 200 GeV. At comparable centralities, a universal scaling has been found for \$v_3\$ from \$p\$/\$d\$/\$^3\$He+Au collisions at RHIC to those in \$p\$+Pb at the LHC. Comparing with several hydro-calculations with different assumptions on the initial conditions indicates the initial geometry in small system may be dominated by sub-nucleon fluctuations, while the window is still open for contributions from initial momentum anisotropy and pre-equilibrium dynamics.
Fig.1:Two-particle per-trigger yield distributions for \$^3\$He/\$d\$/\$p\$+Au and \pp collisions at \$\sqrtsNN\$ = 200 as indicated; the trigger and associated particles are both selected from the range \$0.2 <p_{T}< 2.0\$~GeV/c. An illustration of the template fitting procedure are also shown, which employs the MB \pp correlator to estimate the non-flow contributions and to extract the \$v_2\$ and \$v_3\$ flow coefficients.
Fig.2:The \$v_2\$ and \$v_3\$ before and after subtraction in 0\%-2\% \$p\$+Au, 0\%-10\% \$d\$+Au and \$^{3}\$He+Au collisions. Four kinds of subtraction methods have been employed and the detail can be found in text.
Fig.3:Comparing with \$v_2\$ and \$v_3\$ in \$p\$/\$d\$/\$^{3}\$He+Au collisions at 200 GeV from RHIC with that measured in \$p\$+Pb at 5.02 TeV from the LHC. A universal scaling has been found for \$v_3\$ from RHIC to LHC.
Fig.4:Comparison of \$v_2\$ and \$v_3\$ measured central \pau, \dau and \heau collisions with calculations from several hydrodynamical models. Sonic model with initial geometry eccentricity from Nucleon Glauber has been found under-predict \$v_3\$ in all systems. By including the “pre-flow”, supersonic model can match the \$v_2\$ and \$v_3\$ better. IP-Glasma+Hydro that includes sub-nucleonic fluctuations + initial momentum correlation over predicts \$v_2\$ but reproduces \$v_3\$ well.
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http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S2007-09342018000601193&lng=es&nrm=iso&tlng=en
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## Articulo
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## versión impresa ISSN 2007-0934
### Rev. Mex. Cienc. Agríc vol.9 no.6 Texcoco ago./sep. 2018
#### https://doi.org/10.29312/remexca.v9i6.1584
Articles
Credit as a strategy for rural development: credit union Mixta Plan Puebla
1Postgraduate College-Postgraduate in Rural Development. Campus Montecillo. Mexico-Texcoco Highway, km 36.5, Montecillo, Texcoco, State of Mexico. CP. 56230. ([email protected], [email protected], [email protected]).
Abstract
The financing through the credit allows to increase the productive activities of the farmers and the opportunities of access to the market, their income and in this way to improve the quality of life of the families. The objective of this paper was to analyze the distribution of credits made by the Credit Union ‘Mixta Plan Puebla’ (UCMPP) from 1993 to 2005, with the purpose of knowing if these have been destined to the less developed municipalities where its area of greatest dispersion and if the loans granted were tracked. To achieve this purpose, a field investigation was carried out that consisted of the application of 86 surveys to the partners, as well as the preparation of a historical database of the municipalities. Within the results, it is observed that 61% of the credits are distributed in urban communities, while 39% in rural communities, of which 56% are of medium marginalization and 59% of low migration.
Keywords: index of human development; marginalization; migration; rurality
Resumen
Palabras clave: índice de desarrollo humano; marginación; migración; ruralidad
Introduction
The agricultural sector faces a series of risks that mean that it is not sufficiently attended to in its credit needs, for which reason it lacks financial services; however, there are institutions that support rural productive development, for example, financial intermediaries. Muños et al. (2002) states that they are the fundamental mechanism of operations of financial markets, it can be said that basically financial markets are markets where companies, individuals and institutions (savers), place their surplus liquidity with financial intermediaries in exchange of the payment of an interest.
Mexico has several financial institutions regulated by the government, which provide credit and savings services, mainly to people who have a formal job and a certain level of income. However, not all people comply with this profile and access to these institutions is restricted, that is why some resort to means that provide credit facilities, named as informal financial system such as: runs with family and friends, lenders, pawnshops, independent boxes, among others. However, as Remigio (2013) points out, these are not recommended, have low profitability and security, carry a risk and charge very high interest rates, which can cause the debt to increase and become more complicated to liquidate, even impossible face it in addition, the fact that these processes are not subject to formal regulation makes users of this medium more vulnerable.
On the other hand, there are several regulated financial intermediaries, depending on the type of service they provide, for example: banks, savings banks, exchange houses, insurers, credit unions, among others. Being the credit institutions or bank, the best known. Banks offer their services to the public and are an essential part of the payment system. There are two types of banks, the first are the banks that are private banks and the second are the development banks, which are owned by the government. These intermediaries are regulated by the law of credit institutions; in turn, each of the development banks is regulated by its own organic law (BANXICO, 2017).
Considering the scarcity of financial services in rural areas, the UCMPP was very relevant, since it offered access to credit and with them the possibility of undertaking productive projects that would contribute to improving the living conditions of families. The objective of this research was to analyze the distribution of credits that this institution has made, it is centered in 34 municipalities of the state of Puebla, the observation period is from 1993 in which began operations as a financial intermediary until 2005, in order to know if these were destined to the less developed municipalities, with high rates of marginalization, migration and rural areas, where it was their most dispersed area. These municipalities constituted the initial area of influence of the ‘Puebla Plan’, being the main reason why this study area was chosen.
Materials and methods
The study area is located in the Central West region of the state of Puebla, is made up of 34 municipalities, in which there are 109 urban locations and 882 rural locations. In Figure 1, the location of said municipalities is observed.
The research was developed in two stages, the first consisted in making a historical database with bibliographic information of the municipalities with data on the human development index, marginalization index, rurality index and the absolute index of migratory intensity.
In a second stage, the fieldwork was carried out, which consisted in the application of a survey through stratified sampling, this being a probabilistic sampling technique where the entire population is divided into different strata. Therefore, a classification of the municipalities was made, selecting those where there was greater influence on the part of the Mixed Credit Union Plan Puebla; resulting in 9 municipalities in which 80% of the capital is concentrated, 78% of the loans, 48% of the communities and 77% of the members. Subsequently, it was stratified according to the amount of the partners, to determine the size of the sample; that is, the number of surveys that were conducted, with a total of 874 partners, the following statistical formula was applied according to Rendón (2015).
n=Zα/22NiSniN2d2+Zα/22NiSni22
Where: Z= 95% confidence coefficient = 1.96; N= universe or total population = 874; Sni2= sample variance of the stratum; d= precision = 10%; and n= sample size = 86.
n=1.962(71 298 392)2(874)211 825.305312+1.962(31 077 230 552 181)
n=19 528 622 826 797 700226 205 063 031 105
n= 86
Obtaining a total of 86 surveys that represent the target population of the study area. Finally, the final subjects of the different strata were randomly selected proportionally. The information obtained in the surveys was processed in IBM SPSS Statistics 22.0.
Results and discussion
According to the agricultural census 2007, it is observed in Table 1 that there is a total of 4 067 633 production units at the national level, where the state of Puebla concentrates 23.11% of these and the study area (34 municipalities) has 22.4 % at the state level.
Table 1 Situation of financing for agricultural and forestry activities.
Concept Mexican Republic Puebla
Total Regarding the country (%) Regarding the section (%) Total Regarding the country (%) Regarding the state (%) Regarding the section (%)
Production units 4 067 633 940 192 23.11
Contract only credit 146 437 3.6 5 510 0.59
Contract only insurance 13 257 0.33 912 0.1
Contract credit and insurance 12 891 0.32 154 0.02
No contract credit and insurance 3 895 048 95.76 324 638 34.53
Funding source
Commercial Bank 14 318 8.99 919 16.68
SOFOL 1 861 1.17 71 1.29
Financiera Rural 28 006 17.58 456 8.28
Credit union 14 078 8.84 356 6.46
Another source 103 492 64.96 3 914 71.03
FIRA 37 869 23.77 617 11.2
Does not know 58 991 37.02 2 211 40.13
Supply credit
Production units 104 992 71.7 2 322 42.14
Until 10 000 42 415 40.4 1 548 66.67
10 000 a 50 000 35 026 33.36 626 26.96
50 000 a 100 000 15 107 14.39 72 3.1
More of 100 000 12 444 11.85 76 3.27
Refactionary credit
Production units 13 102 8.22 416 7.55
Until 10 000 5 891 44.96 230 55.29
10 000 a 50 000 3 810 29.08 109 26.2
50 000 a 100 000 1 120 8.55 19 4.57
More of 100 000 2 281 17.41 58 13.94
Other type of credit
Production units 34 400 21.59 1 658 30.09
Until 10 000 22 478 65.34 1 240 74.79
10 000 a 50 000 8 442 24.54 329 26.53
50 000 a 100 000 1 785 5.19 53 16.11
More of 100 000 1 695 4.93 36 67.92
They allocate part of the income to savings institutions
Production units 119 048 2.93 5 953 0.63
Commercial Bank 45 244 38 1 928 32.39
Public banking BANSEFI 4 275 3.59 171 2.87
Credit union 1 680 1.41 63 1.06
Savings bank 24 458 20.54 926 15.56
Another institution 44 279 37.19 2 865 48.13
Grouped for supports
Production units 100 210 2.46 171 316 18.22
Grouped for financing 5 663 5.65 5 607 3.27
Source: elaborated with data from the agro-livestock census 2007.
It should be noted that 95.79% nationwide did not take credit or insurance to finance their agricultural activities, at the state level it represents 34.5% and in the study area 35.6%. Among the institutions that contracted credit, it was observed that neither the commercial banks, nor the government institutions, nor the credit unions are the main source of financing; this reflects that the sector lacks financial services. Buchenau and Del Ángel (2007), point out that the structure of the supply of financial services to the agricultural and rural sector is characterized by low penetration levels of commercial banks, a high multiplicity of organizations and financing mechanisms and a strong presence of programs of the State that affect the financing mechanisms.
In the broadest sense, they continue to have low or no banking levels, little access to financial services, and an uncertain future. The main source of financing for the 3 areas is not specified and they have the following percentage: 65% for the national, 71% for the national and 73% for the municipalities. Since the main sources of financing within the formal banking system are not specified, it is deduced that the informal financing (usurers, tandas) is the one that provides this service.
The most requested credits are the supply, both national, state and study area: 2.6%, 0.25% and 0.22% respectively. Only 13 102 production units, at a national level, contracted refactional credit, 416 at the state level and 90 at the municipality level. Only 2.9% of the units allocate part of their income to savings and 2.5% are grouped to request funding support at the national level. Almeraya (2011), points out that, if the most requested loan were the refactionary, the producers would be more focused on the growth of their projects or activities, because this type of credit refers to the acquisition of machinery, real estate or repair of facilities. Within the sample, it was found that 43% were accorded credits, followed by 31.4% of refactionary credit.
Distribution of credits by the UCMPP
Selecting the members without balance and with balance, it was found that 61% of the credits are distributed in urban communities, while 39% in rural communities. The distribution of credits was more oriented to urban communities, leaving a large number of rural communities without access to credit. There are still obstacles that prevent families and producers in rural areas from gaining access to financial services. In this sense, Rajdeep (2008) points out that there is a belief that granting loans to peasants presupposes a risk because they are not desirable subjects to be granted loans, because they do not have the necessary skills to make the best use of them. the funds loaned.
Human development index (IDH). In 44% of the municipalities in the sample, the IDH increased from 2000 to 2010, measuring the index of life expectancy, education and income; the level of human development is the set of opportunities for people to achieve or carry out actions they consider valuable (PNUD, 2016); therefore, the increase can be due to one of these three factors. So there was a positive change in human development, because they have a long and healthy life, acquired knowledge and enjoy a decent standard of living.
Degree of marginalization (GM). According to CONAPO (2011), marginalization is a multidimensional and structural phenomenon, originated in the last instance by the economic production model expressed in the unequal distribution of progress, in the productive structure and in the exclusion of diverse social groups, both in the process as of the benefits of development. They are grouped into five grades: very low, low, medium, high and very high. The 24% of the municipalities in the sample had a positive change (high marginalization on average) from 1990 to 2010, the rest remained stable, in 2010 there are 56% of municipalities in middle marginalization, 15% high, 21% in low and 9% in very low. It was observed that 56% of the population is improving in terms of goods and services that are fundamental for social welfare.
Degree of rurality (GR). The 56% of the municipalities in the sample had a change from urban to rural semi-urban from 2000 to 2010 the rest did not change significantly. On the other hand, according to the OCDE (2010) the 56% of the municipalities in rural semi-urban, 29% in intermediate urban, 12% in dispersed rural and 3% in urban metropolitan. The classification depends on the population fraction: dispersed rural (less than 2 500 inhabitants), semi-urban rural (between 2 500 and 15 000), intermediate urban (between 15 000 and 100 000) and urban or urban metropolitan (more than 100 000) (OCDE, 2007).
Degree of migratory intensity (GIM). The 53% of the municipalities changed from 2000 to 2010; finding that 24% of the municipalities went from very low-low, 9% high-medium, 9% low-medium, 6% medium-high, 3% medium-low and 3% high-low, which reflects a decrease in this index. In 2010, it was 59% low, 32% medium, 6% high and 3% very high. Therefore, by decreasing the migration indicates that there are sources of employment in the municipalities, which improves the income of families and consequently the quality of life. As mentioned by Sobrino (2010), among the causes of economic migration are the search for opportunities and better incomes, with the aim of transforming individual or family economic conditions and increasing the standard of living. Likewise, García (2007) indicates that migration rather than an individual strategy is a familiar alternative to diversify sources of income, face risks, gather resources of different kinds and try to replicate the success stories of other migrants.
On the other hand, carrying out an analysis of the 4 indices described above (IDH, GM, GR, GIM) has 44% of the municipalities where the human development index increased, the degree of marginalization is between 29% on average and 6% in high, in the same way, there are semi-urban rural areas with 26%, scattered rural areas with 9%; the degree of migratory intensity 26% medium and 15% low. As noted, communities do not necessarily have to be urban in order for their IDH to be high; likewise, 56% of the municipalities had an IDH decrease, in which the degree of marginalization in the last year was 26% average and 15% low; 29% in rural semi-urban, 21% in intermediate urban and 44% in low migration (Table 2). Therefore, according to these indexes, the most benefited municipalities with credits were the semi-urban rural areas, with a medium marginalization and low migration.
Table 2 Comparison of the different indices.
Index 2010
IDH increase IDH decreased
(44%) (56%)
Degree of marginalization
High 9% 6%
Medium 29% 27%
Low 6% 15%
Very low 0% 9%
Degree of rurality
Urban metropolitan 0% 3%
Intermediate urban 9% 21%
Rural semi-urban 27% 29%
Dispersed rural 9% 3%
Degree of migratory intensity
High 0% 6%
Medium 27% 6%
Low 15% 44%
Very high 3% 0%
Source: elaborated in 2017.
On the other hand, according to the survey carried out, the following information is obtained:
General data of the interviewees
The average age is 64 years. The 40.7% of the interviewees are in the range of 55 to 65 years. The foregoing indicates that the members of the UCMPP are people with tendencies towards aging; it is therefore advisable to carry out a renewal of the partners, through promotion to more productive age groups, as mentioned by ENA (2014), 40.5% of the rural population is 60 years of age or older, so they at risks personal physical and social that temporarily or permanently truncate their capacity or productive possibility. On the other hand, 89.5% are men; therefore, productive activities and resource management continue to be an activity that men perform. However, the role of women in the UCMPP is very important, in the board of directors of 1996-1999 its president was a peasant woman.
The 70.9% have completed the basic (primary) school level therefore, the degree of education is minimal. CONAPO (2011), points out that education is a factor in accessing better paid jobs, it is also related to the capacity of workers and this is related to the production of goods and services with higher added value and increased productivity, innovations and economic competitiveness. On the other hand, 29.1% speak indigenous language, being Nahuatl the spoken dialect, which shows that there is a percentage of the population considered indigenous who obtained some credit from the UCMPP. According to the FAO (2011), indigenous communities continue to be among the most vulnerable population, suffering high levels of poverty and discrimination and having less access to education, health, land tenure and credit; which is observed in the study area.
Productive activity
The results of the analysis show that 24 years ago, 98.8% of the respondents worked, dedicating themselves mainly with 57% to agriculture, 24.4% workers on their own (people who have their own business), 16.3% in livestock activities, services, employees and workers, the remaining 2.4% is concentrated in other activities. The most outstanding changes are observed in that currently 76.7% work, which indicates that there is a decrease in the labor force. Of the people who work, 58% are engaged in agricultural activity, 23.2% are workers on their own, 14.4% livestock activities, services, employees and workers. So, the main activity is still agriculture, hence its importance as a source of employment.
Credit situation
The 97.7% of the respondents are members of the UCMPP, of which 53.5% have between one and five shares; however, 30.2% do not remember the number of shares. The above, suggests that there is lack of attention and monitoring of partners.
The length of stay indicates that 77.9% were founding members covering the period from 1990 to 1993. The 68.6% mention that they learned about the UCMPP from a friend or acquaintance, 31.4%, through their staff.
The 97.7% of the partners interviewed obtained credit from these 84.9% requested between one to three credits. Of which 88.4% were individually and only 8.1% as a group.
The way in which they received the loan 82.6% indicated that it was in cash, 10.5% in implements and 3.5% in inputs and 3.5% in others. The main destination of the loan was the acquisition or purchase of raw material with 32.6%, followed by the purchase of a vehicle or tractor for work, 31.4% (Table 3).
Table 3 Granting of credit by the UCMPP.
Received the credit (%) Destination of credit (%) Benefit with
credit (%)
Cash Implements Inputs Other Acquire or buy raw material Purchase of vehicle or tractor for work Acquire or buy merchandise Other Yes No
82.6 10.5 3.5 3.5 32.6 31.4 19.8 16.2 89.5 10.5
Source: elaborated in 2017.
On the other hand, 89.5% obtained some benefit with the credit, as, for example: increased sales, improved the quality of their products, increased profits, facilitated the use of machinery, cost reduction, started a business, obtained economic resources.
In terms of credit sufficiency, 88.4% mentioned that the credit granted was sufficient, 11.6% mentioned that it was not enough, since it needed more economic resources, but it was the amount that was granted.
In the problems in obtaining the loan, 91.9% said they had no problem. Likewise, 79.1% made the payment of the credit on time; however, 20.9% did not pay within the agreed term, although the borrowers indicated that they were not in the past due portfolio. It is indicating lack of ignorance of the partners on their credit standing, hence the importance of monitoring partners by the UCMPP.
On the other hand, 40.7% of the interviewees indicate that, if the UCMPP had not granted the loan, they would not have resorted to another source of financing because they had not met the requirements requested in most cases. This shows the importance of the UCMPP as a financing option for these producers, since to obtain a credit it is necessary to prove that there is income and demonstrate that there is an acceptable probability that such income will be sustained over time (Raphael, 2012).
Members with credit without balance and with balance
During the period analyzed (1993-2005) it was found that the UCMPP dispersed a total of 4 753 credits, with an amount of $129 973 628.00 pesos in 124 communities, benefiting 1 142 members, as well, in the sample (9 municipalities) a total of 3 709 credits were obtained, with an amount of$103 353 168.00 pesos in 60 communities, granted to 874 members (Table 4).
Table 4 Data of the members with credit without balance of the UCMPP.
Municipality Capital Credits Community Partners
Acajete 5 693 547 252 9 80
Chiautzingo 9 104 035 368 5 68
Huejotzingo 13 386 989 396 5 82
Puebla 31 747 473 940 8 250
San Martin Texmelucan 8 759 151 309 9 63
San Salvador the Verde 9 092 183 279 5 55
Tecali of Herrera 2 457 691 105 4 35
Tepatlaxco of Hidalgo 3 451 513 153 1 54
Tlahuapan 19 660 586 907 14 187
Total sample 103 353 168 3 709 60 874
Percentage of the sample with respect to the total 80% 78% 48% 77%
Total 129 973 628 4753 124 1142
Source: elaborated in 2017.
On the other hand, as shown in Table 5, with respect to the members with outstanding balance to be paid, that is to say in the past due portfolio, there were 321, with a total of 532 credits, with a total capital amount of $16 564 899.00 pesos, with an interest of$7 587 301.00 pesos. The amount of the overdue portfolio represents 13% of the total dispersed in the analysis period this situation reflects the little follow-up that the UCMPP gave to the credits granted. Díaz (2011) mentions that the process of supervision and follow-up is intentional in order to anticipate incidents in the portfolio, making visits, calls and information requirements to the borrower, to supervise the use of credit -management of business- continuity and solidity in their activities, as well as their roots.
Table 5 Expired portfolio of UCMPP members.
Municipality Capital Interest Mora Credit Community Partner
Acajete 671 328 218 348 493 340 31 5 19
Chiautzingo 324 951 102 614 28 986 7 4 7
Huejotzingo 1 179 965 481 162 443 757 31 5 19
Puebla 4 755 297 2 073 698 3 483 515 140 5 85
San Martin Texmelucan 717 338 100 154 1 276 938 26 6 17
San Salvador the Verde 2 364 164 1 731 250 1 313 241 38 5 25
Tecali of Herrera 72 106 22 295 6 545 4 2 4
Tepatlaxco of Hidalgo 464 847 105 771 68 263 15 1 11
Tlahuapan 4 228 251 2 169 688 1 885 642 143 11 80
Total sample 14 77 247 7 004 980 9 000 227 435 44 267
Percentage of the sample with respect to the total 89% 92% 87% 81% 62% 83%
Total 16 564 899 7 587 301 10 387 882 532 71 321
Source: elaborated in 2017.
Conclusions
The objective of this research was to analyze the distribution of credits made by the Credit Union ‘Mixta Plan Puebla’ from the period 1993 to 2005. The hypothesis was that the credit was allocated to the municipalities of rural areas with high marginalization, high migration and areas dispersed rural. However, the results allowed to reject the hypothesis, since the opposite effect was found. The impact in rural areas of the ‘Mixta Plan Puebla’ credit union was low, due to the fact that 61% of its loans were granted to urban communities with medium marginalization, with rurality level: ‘semi-urban-urban’ and low migration.
Therefore, the granting of loans by UCMPP should be extended to rural communities with a high degree of marginalization and poor accessibility, as Deugd et al. (2006), there is a strong demand for financial services, especially in the rural sector; as well as the lack of financial intermediaries to cover said demand; the commercial banking system has a limited interest in the sector; and it only operates in it when there are subsidies from the State. However, this must be accompanied by technical assistance, technological support, training in administrative services for organization and marketing, including financial education for producers in the rural sector.
It is necessary to follow the credits of the partners that are part of the Credit Union ‘Mixta Plan Puebla’, as well as to implement financial education courses as indicated by Amezcua et al. (2014), if you do not have an adequate financial culture, you will have problems in the scarce or no use of financial products and services; in bad habits at the moment of acquiring them, in the ignorance of their rights and obligations, as well as in the lack of financial planning, which negatively impacts on their well-being and quality of life, at the same time that it does not help financial institutions to reach the levels of competitiveness required and that the economic development of the country be promoted.
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PNUD. 2016. Programa de las Naciones Unidas para el Desarrollo. Informe sobre Desarrollo Humano. Communications Development Incorporated. Washington DC. Estados Unidos. http://hdr.undp.org/sites/default/files/hdr2016-sp-overview-web.pdf. [ Links ]
Rajdeep, S. y Craig, P. A. 2008. La revolución de las microfinanzas: una visión general. Boletín del CEMLA. 64-83 pp. [ Links ]
Raphael, M. R. 2012. Reporte sobre la discriminación en México 2012: crédito. Consejo Nacional para prevenir la discriminación. México, DF. [ Links ]
Remigio, M. J. 2013. Finanzas populares en México. Universidad Nacional Autónoma de México. México. [ Links ]
Sobrino, J. 2010. Migración interna en México durante el siglo XX. CONAPO. México, DF. [ Links ]
Received: June 2018; Accepted: September 2018
§Corresponding author: [email protected].
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
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https://zbmath.org/authors/?q=ai%3Awhite.brian-cabell
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# zbMATH — the first resource for mathematics
## White, Brian Cabell
Compute Distance To:
Author ID: white.brian-cabell Published as: White, B.; White, Brian Homepage: https://profiles.stanford.edu/brian-white External Links: MGP · Wikidata
Documents Indexed: 81 Publications since 1979
all top 5
#### Co-Authors
53 single-authored 8 Hoffman, David A. 4 Ilmanen, Thomas 4 Meeks, William Hamilton III 3 Martín, Francisco 2 Gulliver, Robert D. II 2 Hershkovits, Or 2 Micallef, Mario J. 1 Choi, Hyeong In 1 Colding, Tobias Holck 1 Drachman, Jordan 1 Ekholm, Tobias 1 Minicozzi, William Philip II 1 Schulze, Felix 1 Solomon, Bruce 1 Traizet, Martin 1 Wienholtz, Daniel
all top 5
#### Serials
13 Journal of Differential Geometry 6 Communications in Analysis and Geometry 5 Bulletin of the American Mathematical Society. New Series 5 Annals of Mathematics. Second Series 4 Acta Mathematica 4 Commentarii Mathematici Helvetici 4 Calculus of Variations and Partial Differential Equations 3 Indiana University Mathematics Journal 3 Inventiones Mathematicae 3 Journal für die Reine und Angewandte Mathematik 3 Journal of the American Mathematical Society 3 The Journal of Geometric Analysis 2 Duke Mathematical Journal 1 Communications on Pure and Applied Mathematics 1 The Mathematical Intelligencer 1 Mathematische Annalen 1 Proceedings of the American Mathematical Society 1 Topology 1 IMRN. International Mathematics Research Notices 1 Notices of the American Mathematical Society 1 Geometry & Topology 1 Cambridge Journal of Mathematics
all top 5
#### Fields
61 Differential geometry (53-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 30 Global analysis, analysis on manifolds (58-XX) 4 Algebraic topology (55-XX) 3 Measure and integration (28-XX) 3 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 History and biography (01-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX)
#### Citations contained in zbMATH Open
74 Publications have been cited 1,028 times in 672 Documents Cited by Year
The nature of singularities in mean curvature flow of mean-convex sets. Zbl 1027.53078
White, Brian
2003
The size of the singular set in mean curvature flow of mean-convex sets. Zbl 0961.53039
White, Brian
2000
A local regularity theorem for mean curvature flow. Zbl 1091.53045
White, Brian
2005
Homotopy classes in Sobolev spaces and the existence of energy minimizing maps. Zbl 0647.58016
White, Brian
1988
The space of minimal submanifolds for varying Riemannian metrics. Zbl 0742.58009
White, Brian
1991
Infima of energy functionals in homotopy classes of mappings. Zbl 0588.58017
White, Brian
1986
Stratification of minimal surfaces, mean curvature flows, and harmonic maps. Zbl 0874.58007
White, Brian
1997
The structure of branch points in minimal surfaces and in pseudoholomorphic curves. Zbl 0873.53038
Micallef, Mario J.; White, Brian
1995
Rectifiability of flat chains. Zbl 0965.49024
White, Brian
1999
Complete surfaces of finite total curvature. Zbl 0631.53007
White, Brian
1987
The space of $$m$$-dimensional surfaces that are stationary for a parametric elliptic functional. Zbl 0770.58005
White, Brian
1987
Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals. Zbl 0615.53044
White, B.
1987
The deformation theorem for flat chains. Zbl 0980.49035
White, Brian
1999
Tangent cones to two-dimensional area-minimizing integral currents are unique. Zbl 0538.49030
White, Brian
1983
The round sphere minimizes entropy among closed self-shrinkers. Zbl 1278.53069
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P. II.; White, Brian
2013
Subsequent singularities in mean-convex mean curvature flow. Zbl 1325.53090
White, Brian
2015
A strong maximum principle for varifolds that are stationary with respect to even parametric elliptic functionals. Zbl 0711.49059
Solomon, Bruce; White, Brian
1989
Embeddedness of minimal surfaces with total boundary curvature at most $$4\pi$$. Zbl 1017.53013
Ekholm, Tobias; White, Brian; Wienholtz, Daniel
2002
A strong minimax property of nondegenerate minimal submanifolds. Zbl 0808.49037
White, Brian
1994
Minimal surfaces bounded by convex curves in parallel planes. Zbl 0731.53004
Meeks, William H. III; White, Brian
1991
Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds. Zbl 0737.53009
White, Brian
1991
Evolution of curves and surfaces by mean curvature. Zbl 1036.53045
White, Brian
2002
The maximum principle for minimal varieties of arbitrary codimension. Zbl 1226.53061
White, Brian
2010
A new proof of the compactness theorem for integral currents. Zbl 0706.49028
White, Brian
1989
On the bumpy metrics theorem for minimal submanifolds. Zbl 1379.53084
White, Brian
2017
Existence of least-energy configurations of immiscible fluids. Zbl 0853.49030
White, Brian
1996
Mappings that minimize area in their homotopy classes. Zbl 0566.57018
White, Brian
1984
Which ambient spaces admit isoperimetric inequalities for submanifolds? Zbl 1179.53061
White, Brian
2009
The topology of hypersurfaces moving by mean curvature. Zbl 0858.58047
White, Brian
1995
A rigidity theorem for properly embedded minimal surfaces in $$R^ 3$$. Zbl 0704.53008
Choi, Hyeong In; Meeks, William H. III; White, Brian
1990
The rate of convergence of a harmonic map at a singular point. Zbl 0645.58018
Gulliver, Robert; White, Brian
1989
Graphical translators for mean curvature flow. Zbl 1416.53062
Hoffman, D.; Ilmanen, T.; Martín, F.; White, B.
2019
Partial regularity of mean-convex hypersurfaces flowing by mean curvature. Zbl 0818.53081
White, Brian
1994
The least area bounded by multiples of a curve. Zbl 0529.49023
White, Brian
1984
Existence of least-area mappings of N-dimensional domains. Zbl 0526.49029
White, Brian
1983
The structure of minimizing hypersurfaces mod 4. Zbl 0431.49044
White, Brian
1979
Currents and flat chains associated to varifolds, with an application to mean curvature flow. Zbl 1161.49043
White, Brian
2009
Genus-one helicoids from a variational point of view. Zbl 1161.53009
Hoffman, David; White, Brian
2008
The mathematics of F. J. Almgren, jun. Zbl 0955.01020
White, Brian
1998
New applications of mapping degrees to minimal surface theory. Zbl 0638.58005
White, Brian
1989
Controlling area blow-up in minimal or bounded mean curvature varieties. Zbl 1341.53094
White, Brian
2016
Sequences of embedded minimal disks whose curvatures blow up on a prescribed subset of a line. Zbl 1244.53010
Hoffman, David; White, Brian
2011
Nonunique tangent maps at isolated singularities of harmonic maps. Zbl 0774.49028
White, Brian
1992
A local regularity theorem for mean curvature flow with triple edges. Zbl 1431.53101
Schulze, Felix; White, Brian
2020
Topological change in mean convex mean curvature flow. Zbl 1266.53064
White, Brian
2013
Sharp lower bounds on density for area-minimizing cones. Zbl 1341.53012
Ilmanen, Tom; White, Brian
2015
The bridge principle for stable minimal surfaces. Zbl 0830.49025
White, Brian
1994
The space of minimal annuli bounded by an extremal pair of planar curves. Zbl 0854.53009
Meeks, William H. III; White, Brian
1993
Some recent developments in differential geometry. Zbl 0701.53004
White, Brian
1989
Regularity of area-minimizing hypersurfaces at boundaries with multiplicity. Zbl 0528.53051
White, Brian
1983
On the compactness theorem for embedded minimal surfaces in $$3$$-manifolds with locally bounded area and genus. Zbl 1394.53065
White, Brian
2018
Helicoidal minimal surfaces of prescribed genus. Zbl 1356.53010
Hoffman, David; Traizet, Martin; White, Brian
2016
Introduction to minimal surface theory. Zbl 1354.49091
White, Brian
2016
Properly embedded, area-minimizing surfaces in hyperbolic 3-space. Zbl 1295.53066
Martín, Francisco; White, Brian
2014
Soap films bounded by non-closed curves. Zbl 0959.58018
Drachman, Jordan; White, Brian
1998
The bridge principle for unstable and for singular minimal surfaces. Zbl 0860.58009
White, Brian
1994
Sharp entropy bounds for self-shrinkers in mean curvature flow. Zbl 1418.53072
Hershkovits, Or; White, Brian
2019
Curvatures of embedded minimal disks blow up on subsets of $$C^1$$ curves. Zbl 1335.53011
White, Brian
2015
Axial minimal surfaces in $$\mathbf {S}^2 \times\mathbb R$$ are helicoidal. Zbl 1229.53065
Hoffman, David; White, Brian
2011
On the number of minimal surfaces with a given boundary. Zbl 1184.53012
Hoffman, David; White, Brian
2008
A new proof of Federer’s structure theorem for $$k$$-dimensional subsets of $$\mathbf{R}^{N}$$. Zbl 0904.28004
White, Brian
1998
Classical area minimizing surfaces with real-analytic boundaries. Zbl 0955.53008
White, Brian
1997
Half of Enneper’s surface minimizes area. Zbl 1039.53018
White, Brian
1996
Some questions of De Giorgi about mean curvature flow of triply-periodic surfaces. Zbl 0807.53045
White, Brian
1994
On the topological type of minimal submanifolds. Zbl 0767.53043
White, Brian
1992
Minimal surfaces bounded by a pair of convex planar curves. Zbl 0752.53007
Meeks, William H. III; White, Brian
1991
Every three-sphere of positive Ricci curvature contains a minimal embedded torus. Zbl 0689.53003
White, Brian
1989
Correction to ”Complete surfaces of finite total curvature”. Zbl 0687.53037
White, Brian
1988
Correction to: “Graphical translators for mean curvature flow”. Zbl 1440.53108
Hoffman, D.; Ilmanen, T.; Martín, F.; White, B.
2019
The geometry of genus-one helicoids. Zbl 1168.53006
Hoffman, David; White, Brian
2009
On the structure of branch points of minimizing disks. Zbl 0645.53034
Micallef, Mario J.; White, Brian
1987
The space of m-dimensional surfaces that are stationary for a parametric elliptic functional. Zbl 0613.58009
White, Brian
1987
Regularity of the singular sets in immiscible fluid interfaces and solutions to other Plateau-type problems. Zbl 0606.49029
White, Brian
1986
Homotopy classes in Sobolev spaces and energy minimizing maps. Zbl 0595.58011
White, Brian
1985
A local regularity theorem for mean curvature flow with triple edges. Zbl 1431.53101
Schulze, Felix; White, Brian
2020
Graphical translators for mean curvature flow. Zbl 1416.53062
Hoffman, D.; Ilmanen, T.; Martín, F.; White, B.
2019
Sharp entropy bounds for self-shrinkers in mean curvature flow. Zbl 1418.53072
Hershkovits, Or; White, Brian
2019
Correction to: “Graphical translators for mean curvature flow”. Zbl 1440.53108
Hoffman, D.; Ilmanen, T.; Martín, F.; White, B.
2019
On the compactness theorem for embedded minimal surfaces in $$3$$-manifolds with locally bounded area and genus. Zbl 1394.53065
White, Brian
2018
On the bumpy metrics theorem for minimal submanifolds. Zbl 1379.53084
White, Brian
2017
Controlling area blow-up in minimal or bounded mean curvature varieties. Zbl 1341.53094
White, Brian
2016
Helicoidal minimal surfaces of prescribed genus. Zbl 1356.53010
Hoffman, David; Traizet, Martin; White, Brian
2016
Introduction to minimal surface theory. Zbl 1354.49091
White, Brian
2016
Subsequent singularities in mean-convex mean curvature flow. Zbl 1325.53090
White, Brian
2015
Sharp lower bounds on density for area-minimizing cones. Zbl 1341.53012
Ilmanen, Tom; White, Brian
2015
Curvatures of embedded minimal disks blow up on subsets of $$C^1$$ curves. Zbl 1335.53011
White, Brian
2015
Properly embedded, area-minimizing surfaces in hyperbolic 3-space. Zbl 1295.53066
Martín, Francisco; White, Brian
2014
The round sphere minimizes entropy among closed self-shrinkers. Zbl 1278.53069
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P. II.; White, Brian
2013
Topological change in mean convex mean curvature flow. Zbl 1266.53064
White, Brian
2013
Sequences of embedded minimal disks whose curvatures blow up on a prescribed subset of a line. Zbl 1244.53010
Hoffman, David; White, Brian
2011
Axial minimal surfaces in $$\mathbf {S}^2 \times\mathbb R$$ are helicoidal. Zbl 1229.53065
Hoffman, David; White, Brian
2011
The maximum principle for minimal varieties of arbitrary codimension. Zbl 1226.53061
White, Brian
2010
Which ambient spaces admit isoperimetric inequalities for submanifolds? Zbl 1179.53061
White, Brian
2009
Currents and flat chains associated to varifolds, with an application to mean curvature flow. Zbl 1161.49043
White, Brian
2009
The geometry of genus-one helicoids. Zbl 1168.53006
Hoffman, David; White, Brian
2009
Genus-one helicoids from a variational point of view. Zbl 1161.53009
Hoffman, David; White, Brian
2008
On the number of minimal surfaces with a given boundary. Zbl 1184.53012
Hoffman, David; White, Brian
2008
A local regularity theorem for mean curvature flow. Zbl 1091.53045
White, Brian
2005
The nature of singularities in mean curvature flow of mean-convex sets. Zbl 1027.53078
White, Brian
2003
Embeddedness of minimal surfaces with total boundary curvature at most $$4\pi$$. Zbl 1017.53013
Ekholm, Tobias; White, Brian; Wienholtz, Daniel
2002
Evolution of curves and surfaces by mean curvature. Zbl 1036.53045
White, Brian
2002
The size of the singular set in mean curvature flow of mean-convex sets. Zbl 0961.53039
White, Brian
2000
Rectifiability of flat chains. Zbl 0965.49024
White, Brian
1999
The deformation theorem for flat chains. Zbl 0980.49035
White, Brian
1999
The mathematics of F. J. Almgren, jun. Zbl 0955.01020
White, Brian
1998
Soap films bounded by non-closed curves. Zbl 0959.58018
Drachman, Jordan; White, Brian
1998
A new proof of Federer’s structure theorem for $$k$$-dimensional subsets of $$\mathbf{R}^{N}$$. Zbl 0904.28004
White, Brian
1998
Stratification of minimal surfaces, mean curvature flows, and harmonic maps. Zbl 0874.58007
White, Brian
1997
Classical area minimizing surfaces with real-analytic boundaries. Zbl 0955.53008
White, Brian
1997
Existence of least-energy configurations of immiscible fluids. Zbl 0853.49030
White, Brian
1996
Half of Enneper’s surface minimizes area. Zbl 1039.53018
White, Brian
1996
The structure of branch points in minimal surfaces and in pseudoholomorphic curves. Zbl 0873.53038
Micallef, Mario J.; White, Brian
1995
The topology of hypersurfaces moving by mean curvature. Zbl 0858.58047
White, Brian
1995
A strong minimax property of nondegenerate minimal submanifolds. Zbl 0808.49037
White, Brian
1994
Partial regularity of mean-convex hypersurfaces flowing by mean curvature. Zbl 0818.53081
White, Brian
1994
The bridge principle for stable minimal surfaces. Zbl 0830.49025
White, Brian
1994
The bridge principle for unstable and for singular minimal surfaces. Zbl 0860.58009
White, Brian
1994
Some questions of De Giorgi about mean curvature flow of triply-periodic surfaces. Zbl 0807.53045
White, Brian
1994
The space of minimal annuli bounded by an extremal pair of planar curves. Zbl 0854.53009
Meeks, William H. III; White, Brian
1993
Nonunique tangent maps at isolated singularities of harmonic maps. Zbl 0774.49028
White, Brian
1992
On the topological type of minimal submanifolds. Zbl 0767.53043
White, Brian
1992
The space of minimal submanifolds for varying Riemannian metrics. Zbl 0742.58009
White, Brian
1991
Minimal surfaces bounded by convex curves in parallel planes. Zbl 0731.53004
Meeks, William H. III; White, Brian
1991
Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds. Zbl 0737.53009
White, Brian
1991
Minimal surfaces bounded by a pair of convex planar curves. Zbl 0752.53007
Meeks, William H. III; White, Brian
1991
A rigidity theorem for properly embedded minimal surfaces in $$R^ 3$$. Zbl 0704.53008
Choi, Hyeong In; Meeks, William H. III; White, Brian
1990
A strong maximum principle for varifolds that are stationary with respect to even parametric elliptic functionals. Zbl 0711.49059
Solomon, Bruce; White, Brian
1989
A new proof of the compactness theorem for integral currents. Zbl 0706.49028
White, Brian
1989
The rate of convergence of a harmonic map at a singular point. Zbl 0645.58018
Gulliver, Robert; White, Brian
1989
New applications of mapping degrees to minimal surface theory. Zbl 0638.58005
White, Brian
1989
Some recent developments in differential geometry. Zbl 0701.53004
White, Brian
1989
Every three-sphere of positive Ricci curvature contains a minimal embedded torus. Zbl 0689.53003
White, Brian
1989
Homotopy classes in Sobolev spaces and the existence of energy minimizing maps. Zbl 0647.58016
White, Brian
1988
Correction to ”Complete surfaces of finite total curvature”. Zbl 0687.53037
White, Brian
1988
Complete surfaces of finite total curvature. Zbl 0631.53007
White, Brian
1987
The space of $$m$$-dimensional surfaces that are stationary for a parametric elliptic functional. Zbl 0770.58005
White, Brian
1987
Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals. Zbl 0615.53044
White, B.
1987
On the structure of branch points of minimizing disks. Zbl 0645.53034
Micallef, Mario J.; White, Brian
1987
The space of m-dimensional surfaces that are stationary for a parametric elliptic functional. Zbl 0613.58009
White, Brian
1987
Infima of energy functionals in homotopy classes of mappings. Zbl 0588.58017
White, Brian
1986
Regularity of the singular sets in immiscible fluid interfaces and solutions to other Plateau-type problems. Zbl 0606.49029
White, Brian
1986
Homotopy classes in Sobolev spaces and energy minimizing maps. Zbl 0595.58011
White, Brian
1985
Mappings that minimize area in their homotopy classes. Zbl 0566.57018
White, Brian
1984
The least area bounded by multiples of a curve. Zbl 0529.49023
White, Brian
1984
Tangent cones to two-dimensional area-minimizing integral currents are unique. Zbl 0538.49030
White, Brian
1983
Existence of least-area mappings of N-dimensional domains. Zbl 0526.49029
White, Brian
1983
Regularity of area-minimizing hypersurfaces at boundaries with multiplicity. Zbl 0528.53051
White, Brian
1983
The structure of minimizing hypersurfaces mod 4. Zbl 0431.49044
White, Brian
1979
all top 5
#### Cited by 653 Authors
20 White, Brian Cabell 14 Colding, Tobias Holck 13 De Lellis, Camillo 13 Minicozzi, William Philip II 13 Morgan, Frank 11 Brendle, Simon 10 Marchese, Andrea 10 Meeks, William Hamilton III 9 Arroja Neves, André 9 Giaquinta, Mariano 9 Mucci, Domenico 9 Piccione, Paolo 8 Hardt, Robert M. 8 Haslhofer, Robert 8 Li, Jiayu 8 Spadaro, Emanuele Nunzio 8 Spolaor, Luca 7 Bethuel, Fabrice 7 Martín, Francisco 7 Rivière, Tristan 6 Ambrosio, Luigi 6 Bernstein, Jacob 6 Carlotto, Alessandro 6 Hershkovits, Or 6 Marques, Fernando Codá 6 Novaga, Matteo 6 Stuvard, Salvatore 5 Brézis, Haïm 5 Chambolle, Antonin 5 De Philippis, Guido 5 Guang, Qiang 5 Hoffman, David A. 5 Isobe, Takeshi 5 Lin, Fang Hua 5 Mironescu, Petru 5 Orlandi, Giandomenico 5 Pérez Muñoz, Joaquín 5 Ros, Antonio 5 Schulze, Felix 5 Tonegawa, Yoshihiro 5 Young, Robert 4 Bellettini, Costante 4 Bergner, Matthias 4 Breiner, Christine 4 Chodosh, Otis 4 Colombo, Maria 4 Coskunuzer, Baris 4 Duzaar, Frank 4 Fröhlich, Steffen 4 Fusco, Nicola 4 Hajłasz, Piotr 4 Han, Xiaoli 4 Lopez Camino, Rafael 4 Massaccesi, Annalisa 4 Modica, Giuseppe 4 Nakauchi, Nobumitsu 4 Sharp, Ben 4 Sinestrari, Carlo 4 Soucek, Jiri 4 Van Schaftingen, Jean 4 Velichkov, Bozhidar 4 Wickramasekera, Neshan 4 Zhou, Xin 3 Aiolfi, Ari J. 3 Alías, Luis J. 3 Ambrozio, Lucas C. 3 Anderson, Michael T. 3 Angenent, Sigurd Bernardus 3 Bellettini, Giovanni 3 Bögelein, Verena 3 Bousquet, Pierre 3 Caraballo, David G. 3 Cheeger, Jeff 3 Cheung, Leung-Fu 3 De Pauw, Thierry 3 De Rosa, Antonio 3 Ding, Qi 3 Eliashberg, Yakov Matveevich 3 Ghiraldin, Francesco 3 Giga, Yoshikazu 3 Hirsch, Jonas 3 Huisken, Gerhard 3 Ilmanen, Thomas 3 Ju, Hongjie 3 Julin, Vesa 3 Katz, Mikhail G. 3 Ketover, Daniel 3 Kleiner, Bruce 3 Liu, Yannan 3 Lotay, Jason Dean 3 Maggi, Francesco 3 Magni, Annibale 3 Mantegazza, Carlo 3 Mramor, Alexander 3 Naber, Aaron C. 3 Nguyen, Huy The 3 Pigola, Stefano 3 Rigoli, Marco 3 Ripoll, Jaime Bruck 3 Ritoré, Manuel ...and 553 more Authors
all top 5
#### Cited in 139 Serials
59 Calculus of Variations and Partial Differential Equations 46 The Journal of Geometric Analysis 26 Inventiones Mathematicae 26 Transactions of the American Mathematical Society 23 Duke Mathematical Journal 20 Advances in Mathematics 20 Mathematische Annalen 16 Manuscripta Mathematica 16 Mathematische Zeitschrift 16 Annals of Mathematics. Second Series 15 Journal of Functional Analysis 15 Proceedings of the American Mathematical Society 14 Journal für die Reine und Angewandte Mathematik 14 Geometric and Functional Analysis. GAFA 14 Bulletin of the American Mathematical Society. New Series 13 Archive for Rational Mechanics and Analysis 13 Geometriae Dedicata 12 Geometry & Topology 10 Annals of Global Analysis and Geometry 9 Journal of Mathematical Analysis and Applications 9 Acta Mathematica 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Communications on Pure and Applied Mathematics 8 Communications in Partial Differential Equations 7 Differential Geometry and its Applications 6 Communications in Mathematical Physics 6 Tohoku Mathematical Journal. Second Series 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Israel Journal of Mathematics 5 Memoirs of the American Mathematical Society 5 Pacific Journal of Mathematics 5 Zeitschrift für Analysis und ihre Anwendungen 5 Chinese Annals of Mathematics. Series B 5 Journal of the American Mathematical Society 5 Journal of the European Mathematical Society (JEMS) 5 Acta Mathematica Sinica. English Series 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 5 Advances in Calculus of Variations 4 Annales de l’Institut Fourier 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Journal of Differential Equations 4 SIAM Journal on Mathematical Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Publications Mathématiques 3 Nagoya Mathematical Journal 3 Revista Matemática Iberoamericana 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Communications in Contemporary Mathematics 3 Algebraic & Geometric Topology 3 Journal of Fixed Point Theory and Applications 2 Bulletin of the Australian Mathematical Society 2 Journal d’Analyse Mathématique 2 Arkiv för Matematik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Archiv der Mathematik 2 Illinois Journal of Mathematics 2 Journal of Differential Geometry 2 Monatshefte für Mathematik 2 Ricerche di Matematica 2 Probability Theory and Related Fields 2 International Journal of Mathematics 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Experimental Mathematics 2 Journal of Mathematical Sciences (New York) 2 NoDEA. Nonlinear Differential Equations and Applications 2 Interfaces and Free Boundaries 2 Journal of Evolution Equations 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Mediterranean Journal of Mathematics 2 Frontiers of Mathematics in China 2 Groups, Geometry, and Dynamics 2 Journal of Topology and Analysis 2 Nonlinear Analysis. Theory, Methods & Applications 2 Journal de l’École Polytechnique – Mathématiques 2 Geometric Flows 2 Bollettino dell’Unione Matematica Italiana 1 International Journal of Modern Physics A 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Anais da Academia Brasileira de Ciências 1 The Annals of Statistics 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Indiana University Mathematics Journal 1 Journal of Geometry 1 Journal of the Mathematical Society of Japan 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matemàtico e Fisico di Milano ...and 39 more Serials
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#### Cited in 44 Fields
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#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-06-15T17:18:19 |
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|
https://www.usgs.gov/center-news/new-monitoring-instruments-mount-rainier-have-their-roots-hvos-history
|
# New Monitoring Instruments at Mount Rainier Have Their Roots in HVO's History
Release Date:
The Cascades Volcano Observatory, one of the Hawaiian Volcano Observatory's sister observatories, has worked in the past two weeks to install new monitoring equipment at two sites on Mount Rainier.
Mount Rainier, Washington, as seen on flight to Mount St. Helens. View is from the south. USGS Photograph taken on December 28, 2004, by Jim Vallance and Stephanie Konfal.
(Public domain.)
Rainier is the third largest of Cascade Range volcanoes and the highest peak in Washington state (4,392 m, 14,410 ft). Its slopes pack more snow and ice than any other volcano within the lower 48 states.
Mount Rainier has the added hazard of having shed huge lahars (slurries of mud and boulders) into surrounding valleys during the past few thousand years. These events, which begin as large landslides, may be unrelated to volcanism, because they can originate simply by failure of weak, clay-altered rock in the volcano's core. Similar large landslides today would be costly to infrastructure and deadly to many living in communities as far west as Tacoma, 80 km (50 miles) distant. About 80,000 people and their homes are at risk in Mount Rainier's lahar-hazard zones.
The monitoring sites installed recently are located at Observation Rock, on the volcano's north flank, and St. Andrews Rock, high on the west flank. The installations include tools well known to followers of Hawaiian volcanism. For example, each site has a seismometer to track small earthquakes that might occur at shallow depths within the volcano. Additionally, the seismometer at Observation Rock is capable of recording across a broader frequency range (or longer period), which makes it useful to better understand the source and energy of low-frequency, as well as larger, earthquakes. Such "broadband" seismometers play an increasingly important role in modern seismologic interpretation.
Each site hosts a continuously operating GPS receiver. This instrument consists of an antenna mounted on a mast, from which it receives signals from satellites within its line of sight. The resulting data allow pinpoint positioning, as accurate as a few millimeters (a tenth of an inch or so). The goal is to track changes resulting from incipient landsliding or volcanic deformation.
Our wintertime experience at Mount St. Helens has taught us that GPS antennae deflect slightly as snow and ice build on them, leading to shifting positions that have nothing to do with landslide or volcanic hazards. To master this shortcoming, we needed a second tool sheltered from, and unaffected by, winter weather. Therefore a borehole tiltmeter was added to each of the new Mount Rainier monitoring sites.
Each tiltmeter, about the length and diameter of an adult's arm, is placed vertically about 3 m (10 ft) deep, to shield it from the surficial effects of day/night warming and freezing. The instrument is remarkably sensitive, recording in units of angular rotation known as microradians. One microradian (0.000057 of a degree) is the amount of tilt that results if a board 1 km long were displaced at one end by only a dime's thickness. Modern tiltmeters are 10 to 100 times more precise. In the dime-beneath-board analogy, we must sliver the dime to visualize the precision of the tiltmeter.
Those familiar with Mount Rainier will realize that these two new installations were a substantial undertaking. The sites are in roadless areas, so equipment was flown in by helicopter. The data from each site must be collected and radioed to stations 50-100 km (30-60 mi) distant and then relayed to the corresponding seismic or volcano observatory. Solar panels and batteries maintain operation through prolonged stormy weather. Each installation was built to withstand substantial snow load and high winds.
Volcano monitoring is a business of experimentation, of trial and error. Much of its modern instrumentation has its roots at the Hawaiian Volcano Observatory and the work conducted there since the early 20th century. The new Mount Rainier sites include well-known workhorses, like seismometers, but also tools that have become common in only the past decade, like GPS receivers and borehole tiltmeters. At the heart of these experiments lies the goal of warning the populace when nearby volcanoes become restless.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
Kīlauea Volcano continues to be active. A vent in Halemaumau Crater is erupting elevated amounts of sulfur dioxide gas and very small amounts of ash. Resulting high concentrations of sulfur dioxide in downwind air have closed the south part of Kīlauea caldera and produced occasional air quality alerts in more distant areas, such as Pahala and communities adjacent to Hawaii Volcanoes National Park, during kona wind periods. On September 5, scientists observed a 50-m - (160 ft) diameter lava lake about 100 m (330 ft) below the vent rim on the floor of Halemaumau; the lava cannot be seen from the rim of Halemaumau Crater or Jaggar Museum Overlook. There have been several small ash-emission events from the vent, lasting only minutes, in the last week.
Puu Ōō continues to produce sulfur dioxide at even higher rates than the vent in Halemaumau Crater. Trade winds tend to pool these emissions along the West Hawaii coast, while Kona winds blow these emissions into communities to the north, such as Mountain View, Volcano, and Hilo.
Lava continues to erupt from fissure D of the July 21, 2007, eruption and flows toward the ocean through a well-established lava tube. A small, short-lived breakout, probably near the ocean entry delta, was active on Monday, September 15; otherwise, no significant surface flows have been observed this past week. Lava continues to flow into the ocean at Waikupanaha.
Be aware that active lava deltas can collapse at any time, potentially generating large explosions. This may be especially true during times of rapidly changing lava supply conditions. Do not venture onto the lava deltas. Even the intervening beaches are susceptible to large waves generated during delta collapse; avoid these beaches. In addition, steam plumes rising from ocean entries are highly acidic and laced with glass particles. Check Civil Defense Web site or call 961-8093 for viewing hours.
Mauna Loa is not erupting. Two earthquakes were located beneath the summit this past week. Continuing extension between locations spanning the summit indicates slow inflation of the volcano.
Three earthquakes beneath Hawaii Island were reported felt within the past week. A magnitude-2.1 earthquake occurred at 12:02 p.m., H.s.t., on Friday, September 12, 2008, and was located 6 km (4 miles) southwest of Holualoa, at a depth of 9 km (5 miles). A magnitude-3.1 earthquake occurred at 4:57 p.m. on Monday, September 15, 2008, and was located 14 km (9 miles) northwest of Kailua at a depth of 11 km (7 miles). A magnitude-2.2 earthquake occurred at 1:51 p.m. on Wednesday, September 17, 2008, and was located 2 km (1 mile) north of Kaena Point at a depth of 8 km (5 miles).
Visit our Web site for daily Kīlauea eruption updates, a summary of volcanic events over the past year, and nearly real-time Hawaii earthquake information. Kīlauea daily update summaries are also available by phone at (808) 967-8862. Questions can be emailed to [email protected]. skip past bottom navigational bar
| 2020-01-26T14:03:04 |
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|
https://indico.fnal.gov/event/12423/?ovw=True
|
Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/
#### This search is only for public events. Restricted events are not available.
INDICO will be UPGRADED to version 3.0.3 on
Saturday January 22nd starting at 9 a.m. Central Time.
Please email ASAP [email protected] for any conflicts.
# Santa Fe Jets and Heavy Flavor Workshop
13-15 February 2017
US/Mountain timezone
The Santa Fe Jets and Heavy Flavor workshop will take place February 13-15, 2017. This year the workshop will directly follow Quark Matter 2017. This will allow for a broad international representation of the experimental and theoretical communities that will come together and discuss the recent developments in the field at this workshop.
Recent years have brought about important advances in the experimental measurements and theoretical understanding of jets and heavy flavor production in hadronic and nuclear collisions. With new results from the Relativistic Heavy Ion Collider (RHIC) and run II measurements at the Large Hadron Collider (LHC) in proton and heavy ion collisions, this is the opportune time for a focused discussion between the high energy and nuclear physics communities on the interpretation of the data.
This workshop will bring together senior researchers, postdoctoral fellows and talented graduate students to discuss the exciting recent developments and future directions in high energy and nuclear science. The purpose of the 2017 Santa Fe Jets and Heavy Flavor workshop is to summarize the accomplishments and provide guidance for the community effort in the areas of hadronic jets, quarkonia and open heavy flavor, with emphasis on perturbative Quantum Chromodynamics (pQCD) and Soft Collinear Effective Theory (SCET). The theory is closely tied to experiments at the leading nuclear and particle physics facilities in the US and abroad, such as the RHIC at Brookhaven National Lab and the LHC complex at CERN. The workshop is also central to the physics goals of the next-generation nuclear physics facility in the US, the Electron Ion Collider (EIC).
This is the second year for this workshop following a very successful 2016 Santa Fe Jets & Heavy Flavor Workshop with more than 60 attendees form the US and abroad.
Hosted by Los Alamos National Laboratory.
Local organizing committee: Ivan Vitev (chair), Cesar da Silva, Zhongbo Kang, Christopher Lee, Mike McCumber, Duff Neill, Felix Ringer.
Sponsors: DOE Office of Science and Early Career Research Program, and LANL.
Local workshop webpage including registration links.
Starts
Ends
US/Mountain
Banquet Registration is now open (deadline Feb 13). Dinner Tuesday evening Feb 14 at Maria's New Mexican Kitchen. Pay $30 cash, check or PayPal (Send to "Friends or family") to Christopher Lee ([email protected]) Link to banquet registration form. Registration: A conference fee of$100 will cover breakfast and coffee breaks. Please follow the link here (also left sidebar). Deadline: January 12, 2017
Hotel: conference hotel is the Inn and Spa at Loretto, which offers a highly discounted rate of \$99 per night, plus tax. The deadline to use this rate is January 12, 2017We have reserved a block of rooms and made arrangements with the hotel to allow attendees to stay for a few days before and/or after the conference. To reserve a room, please follow the link here (The site will ask you to agree to a "resort fee" in order to make a reservation; however, the hotel has agreed to waive the resort, internet, and parking fees for guests in our block upon your arrival.)
Abstract submission: Follow the left sidebar (Registration and Abstract). Abstract submission is part of the registration process. You can also log in after you register to submit an abstract before the deadline. To do that, simply click "Already registered?" link on the registration page. Deadline: December 19, 2016
Invitation Letter for US visa purpose: In case you need an invitation letter to apply for a US visa to come to the workshop, please send a request to the organizers at [email protected].
For further information please email the organizers at [email protected].
| 2022-01-18T05:19:56 |
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|
http://pdglive.lbl.gov/Particle.action?node=B080&home=sumtabB
|
${{\boldsymbol \Sigma}}$ BARYONS($\boldsymbol S$ = $-1$, $\boldsymbol I$ = 1) ${{\mathit \Sigma}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$, ${{\mathit \Sigma}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit s}}$ INSPIRE search
# ${{\boldsymbol \Sigma}{(1560)}}$ Bumps $I(J^P)$ = $1(?^{?})$
This entry lists peaks reported in mass spectra around 1560 MeV without implying that they are necessarily related. DIONISI 1978B observes a 6 standard-deviation enhancement at 1553 MeV in the charged ${{\mathit \Lambda}}$ /${{\mathit \Sigma}}{{\mathit \pi}}$ mass spectra from ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ( ${{\mathit \Lambda}}$ /${{\mathit \Sigma}}$) ${{\mathit \pi}}{{\mathit K}}{{\overline{\mathit K}}}$ at 4.2 ${\mathrm {GeV/}}\mathit c$. In a CERN ISR experiment, LOCKMAN 1978 reports a narrow 6 standard-deviation enhancement at 1572 MeV in ${{\mathit \Lambda}}{{\mathit \pi}^{\pm}}$ from the reaction ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit X}}$ . These enhancements are unlikely to be associated with the ${{\mathit \Sigma}{(1580)}}$ (which has not been confirmed by several recent experiments -- see the next entry in the Listings). CARROLL 1976 observes a bump at 1550 MeV (as well as one at 1580 MeV) in the isospin-$1{}^{}{}^{}$ ${{\overline{\mathit K}}}{{\mathit N}}$ total cross section, but uncertainties in cross section measurements outside the mass range of the experiment preclude estimating its significance. See also MEADOWS 1980 for a review of this state.
${{\mathit \Sigma}{(1560)}}$ MASS (PRODUCTION EXPERIMENTS) $\approx1560$ MeV
${{\mathit \Sigma}{(1560)}}$ WIDTH (PRODUCTION EXPERIMENTS)
$\Gamma_{1}$ ${{\mathit \Lambda}}{{\mathit \pi}}$ seen 363
$\Gamma_{2}$ ${{\mathit \Sigma}}{{\mathit \pi}}$ 304
| 2019-03-20T05:52:20 |
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|
http://lammps.sandia.gov/doc/pair_lj_sf.html
|
# pair_style lj/sf/omp command
## Syntax
pair_style lj/sf cutoff
• cutoff = global cutoff for Lennard-Jones interactions (distance units)
## Examples
pair_style lj/sf 2.5
pair_coeff * * 1.0 1.0
pair_coeff 1 1 1.0 1.0 3.0
## Description
Style lj/sf computes a truncated and force-shifted LJ interaction (Shifted Force Lennard-Jones), so that both the potential and the force go continuously to zero at the cutoff (Toxvaerd):
The following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, or by mixing as described below:
• epsilon (energy units)
• sigma (distance units)
• cutoff (distance units)
The last coefficient is optional. If not specified, the global LJ cutoff specified in the pair_style command is used.
Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed in Section 5 of the manual. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.
These accelerated styles are part of the GPU, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Making LAMMPS section for more info.
You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.
See Section 5 of the manual for more instructions on how to use the accelerated styles effectively.
Mixing, shift, table, tail correction, restart, rRESPA info:
For atom type pairs I,J and I != J, the epsilon and sigma coefficients and cutoff distance for this pair style can be mixed. Rin is a cutoff value and is mixed like the cutoff. The default mix value is geometric. See the “pair_modify” command for details.
The pair_modify shift option is not relevant for this pair style, since the pair interaction goes to 0.0 at the cutoff.
The pair_modify table option is not relevant for this pair style.
This pair style does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure, since the energy of the pair interaction is smoothed to 0.0 at the cutoff.
This pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file.
This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.
## Restrictions
This pair style is part of the USER-MISC package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.
| 2017-03-28T17:37:39 |
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|
https://pdglive.lbl.gov/DataBlock.action?node=M261W&home=MXXX025
|
#### ${{\mathit \chi}_{{c1}}{(4685)}}$ WIDTH
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$126$ $\pm15$ ${}^{+37}_{-41}$ 24k 1
2021 E
LHCB ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \phi}}{{\mathit K}^{+}}$
1 From an amplitude analysis of the decay ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \phi}}{{\mathit K}^{+}}$ with a significance of 15 $\sigma$.
References:
AAIJ 2021E
PRL 127 082001 Observation of New Resonances Decaying to $J/\psi K^+$+ and $J/\psi \phi$
| 2022-08-12T11:22:33 |
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|
http://lammps.sandia.gov/doc/compute_msd_chunk.html
|
# compute msd/chunk command
## Syntax
compute ID group-ID msd/chunk chunkID
• ID, group-ID are documented in compute command
• msd/chunk = style name of this compute command
• chunkID = ID of compute chunk/atom command
## Examples
compute 1 all msd/chunk molchunk
## Description
Define a computation that calculates the mean-squared displacement (MSD) for multiple chunks of atoms.
In LAMMPS, chunks are collections of atoms defined by a compute chunk/atom command, which assigns each atom to a single chunk (or no chunk). The ID for this command is specified as chunkID. For example, a single chunk could be the atoms in a molecule or atoms in a spatial bin. See the compute chunk/atom doc page and Section 6.23 for details of how chunks can be defined and examples of how they can be used to measure properties of a system.
Four quantities are calculated by this compute for each chunk. The first 3 quantities are the squared dx,dy,dz displacements of the center-of-mass. The 4th component is the total squared displacement, i.e. (dx*dx + dy*dy + dz*dz) of the center-of-mass. These calculations include all effects due to atoms passing thru periodic boundaries.
Note that only atoms in the specified group contribute to the calculation. The compute chunk/atom command defines its own group; atoms will have a chunk ID = 0 if they are not in that group, signifying they are not assigned to a chunk, and will thus also not contribute to this calculation. You can specify the “all” group for this command if you simply want to include atoms with non-zero chunk IDs.
The slope of the mean-squared displacement (MSD) versus time is proportional to the diffusion coefficient of the diffusing chunks.
The displacement of the center-of-mass of the chunk is from its original center-of-mass position, calculated on the timestep this compute command was first invoked.
Note
The number of chunks Nchunk calculated by the compute chunk/atom command must remain constant each time this compute is invoked, so that the displacement for each chunk from its original position can be computed consistently. If Nchunk does not remain constant, an error will be generated. If needed, you can enforce a constant Nchunk by using the nchunk once or ids once options when specifying the compute chunk/atom command.
Note
This compute stores the original position (of the center-of-mass) of each chunk. When a displacement is calculated on a later timestep, it is assumed that the same atoms are assigned to the same chunk ID. However LAMMPS has no simple way to insure this is the case, though you can use the ids once option when specifying the compute chunk/atom command. Note that if this is not the case, the MSD calculation does not have a sensible meaning.
Note
The initial coordinates of the atoms in each chunk are stored in “unwrapped” form, by using the image flags associated with each atom. See the dump custom command for a discussion of “unwrapped” coordinates. See the Atoms section of the read_data command for a discussion of image flags and how they are set for each atom. You can reset the image flags (e.g. to 0) before invoking this compute by using the set image command.
Note
If you want the quantities calculated by this compute to be continuous when running from a restart file, then you should use the same ID for this compute, as in the original run. This is so that the fix this compute creates to store per-chunk quantities will also have the same ID, and thus be initialized correctly with chunk reference positions from the restart file.
The simplest way to output the results of the compute com/msd calculation to a file is to use the fix ave/time command, for example:
compute cc1 all chunk/atom molecule
compute myChunk all com/msd cc1
fix 1 all ave/time 100 1 100 c_myChunk[*] file tmp.out mode vector
Output info:
This compute calculates a global array where the number of rows = the number of chunks Nchunk as calculated by the specified compute chunk/atom command. The number of columns = 4 for dx,dy,dz and the total displacement. These values can be accessed by any command that uses global array values from a compute as input. See this section for an overview of LAMMPS output options.
The array values are “intensive”. The array values will be in distance^2 units.
none
| 2018-02-20T21:33:11 |
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|
https://par.nsf.gov/biblio/10331447-challenges-ahead-multimessenger-analyses-gravitational-waves-kilonova-case-study-gw190425
|
This content will become publicly available on December 1, 2022
The Challenges Ahead for Multimessenger Analyses of Gravitational Waves and Kilonova: A Case Study on GW190425
Abstract In recent years, there have been significant advances in multimessenger astronomy due to the discovery of the first, and so far only confirmed, gravitational wave event with a simultaneous electromagnetic (EM) counterpart, as well as improvements in numerical simulations, gravitational wave (GW) detectors, and transient astronomy. This has led to the exciting possibility of performing joint analyses of the GW and EM data, providing additional constraints on fundamental properties of the binary progenitor and merger remnant. Here, we present a new Bayesian framework that allows inference of these properties, while taking into account the systematic modeling uncertainties that arise when mapping from GW binary progenitor properties to photometric light curves. We extend the relative binning method presented in Zackay et al. to include extrinsic GW parameters for fast analysis of the GW signal. The focus of our EM framework is on light curves arising from r -process nucleosynthesis in the ejected material during and after merger, the so-called kilonova, and particularly on black hole−neutron star systems. As a case study, we examine the recent detection of GW190425, where the primary object is consistent with being either a black hole or a neutron star. We show quantitatively how improved mapping more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10331447
Journal Name:
The Astrophysical Journal
Volume:
922
Issue:
2
Page Range or eLocation-ID:
269
ISSN:
0004-637X
4. ABSTRACT The association of GRB170817A with a binary neutron star (BNS) merger has revealed that BNSs produce at least a fraction of short gamma-ray bursts (SGRBs). As gravitational wave (GW) detectors push their horizons, it is important to assess coupled electromagnetic (EM)/GW probabilities and maximize observational prospects. Here, we perform BNS population synthesis calculations with the code mobse, seeding the binaries in galaxies at three representative redshifts, $z$ = 0.01, 0.1, and 1 of the Illustris TNG50 simulation. The binaries are evolved and their locations numerically tracked in the host galactic potentials until merger. Adopting the microphysics parameters of GRB170817A, wemore »
| 2022-08-11T05:03:30 |
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|
https://par.nsf.gov/biblio/10310553-adaptive-newton-sketch-linear-time-optimization-quadratic-convergence-effective-hessian-dimensionality
|
Adaptive Newton Sketch: Linear-time Optimization with Quadratic Convergence and Effective Hessian Dimensionality
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a random projection of the Hessian. Our first contribution is to show that, at each iteration, the embedding dimension (or sketch size) can be as small as the effective dimension of the Hessian matrix. Leveraging this novel fundamental result, we design an algorithm with a sketch size proportional to the effective dimension and which exhibits a quadratic rate of convergence. This result dramatically improves on the classical linear-quadratic convergence rates of state-of-theart sub-sampled Newton methods. However, in most practical cases, the effective dimension is not known beforehand, and this raises the question of how to pick a sketch size as small as the effective dimension while preserving a quadratic convergence rate. Our second and main contribution is thus to propose an adaptive sketch size algorithm with quadratic convergence rate and which does not require prior knowledge or estimation of the effective dimension: at each iteration, it starts with a small sketch size, and increases it until quadratic progress is achieved. Importantly, we show that the embedding dimension remains proportional more »
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10310553
Journal Name:
Preceedings of the 38th International Conference on Machine Learning
| 2022-11-30T01:20:41 |
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|
http://wikimechanics.org/banner-internal-energy
|
Banner: Internal Energy
Adjective Definition Internal Energy \begin{align} U \equiv \sum_{i \, \sf{=1}}^{N} \varepsilon_{\it{i}} \hat{E}_{\it{i}} \end{align} 4-7
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License
| 2020-07-12T17:18:48 |
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|
https://www.ctcms.nist.gov/potentials/iprPy/calculation/dislocation_periodic_array/calc.html
|
# calc_dislocation_periodic_array.py
## Calculation script functions
anneal_info(temperature=0.0, runsteps=None, randomseed=None, units='metal')
Generates LAMMPS commands for thermo anneal.
Parameters
• temperature (float, optional) – The temperature to relax at (default is 0.0).
• randomseed (int or None, optional) – Random number seed used by LAMMPS in creating velocities and with the Langevin thermostat. (Default is None which will select a random int between 1 and 900000000.)
• units (str, optional) – The LAMMPS units style to use (default is ‘metal’).
Returns
The generated LAMMPS input lines for performing a dynamic relax. Will be ‘’ if temperature==0.0.
Return type
str
disl_relax(lammps_command, system, potential, mpi_command=None, annealtemp=0.0, annealsteps=None, randomseed=None, etol=0.0, ftol=1e-06, maxiter=10000, maxeval=100000, dmax=0.01)
Sets up and runs the disl_relax.in LAMMPS script for relaxing a dislocation monopole system.
Parameters
• lammps_command (str) – Command for running LAMMPS.
• system (atomman.System) – The system to perform the calculation on.
• potential (atomman.lammps.Potential) – The LAMMPS implemented potential to use.
• mpi_command (str, optional) – The MPI command for running LAMMPS in parallel. If not given, LAMMPS will run serially.
• annealtemp (float, optional) – The temperature to perform a dynamic relaxation at. Default is 0.0, which will skip the dynamic relaxation.
• annealsteps (int, optional) – The number of time steps to run the dynamic relaxation for. Default is None, which will run for 10000 steps if annealtemp is not 0.0.
• randomseed (int or None, optional) – Random number seed used by LAMMPS in creating velocities and with the Langevin thermostat. Default is None which will select a random int between 1 and 900000000.
• etol (float, optional) – The energy tolerance for the structure minimization. This value is unitless. Default is 0.0.
• ftol (float, optional) – The force tolerance for the structure minimization. This value is in units of force. Default is 0.0.
• maxiter (int, optional) – The maximum number of minimization iterations to use default is 10000.
• maxeval (int, optional) – The maximum number of minimization evaluations to use default is 100000.
• dmax (float, optional) – The maximum distance in length units that any atom is allowed to relax in any direction during a single minimization iteration default is 0.01 Angstroms.
Returns
Dictionary of results consisting of keys:
• ’logfile’ (str) - The name of the LAMMPS log file.
• ’dumpfile’ (str) - The name of the LAMMPS dump file for the relaxed system.
• ’E_total’ (float) - The total potential energy for the relaxed system.
Return type
dict
dislocationarray(lammps_command, ucell, potential, C, burgers, ξ_uvw, slip_hkl, mpi_command=None, m=[0, 1, 0], n=[0, 0, 1], sizemults=None, amin=None, bmin=None, cmin=None, shift=None, shiftscale=False, shiftindex=None, tol=1e-08, etol=0.0, ftol=0.0, maxiter=10000, maxeval=100000, dmax=0.01, annealtemp=0.0, annealsteps=None, randomseed=None, boundaryshape='cylinder', boundarywidth=0.0, boundaryscale=False, cutoff=None, linear=False)
Creates and relaxes a dislocation monopole system.
Parameters
• lammps_command (str) – Command for running LAMMPS.
• ucell (atomman.System) – The unit cell to use as the seed for generating the dislocation monopole system.
• potential (atomman.lammps.Potential) – The LAMMPS implemented potential to use.
• C (atomman.ElasticConstants) – The elastic constants associated with the bulk crystal structure for ucell.
• burgers (array-like object) – The dislocation’s Burgers vector given as a Miller or Miller-Bravais vector relative to ucell.
• ξ_uvw (array-like object) – The dislocation’s line direction given as a Miller or Miller-Bravais vector relative to ucell.
• slip_hkl (array-like object) – The dislocation’s slip plane given as a Miller or Miller-Bravais plane relative to ucell.
• mpi_command (str or None, optional) – The MPI command for running LAMMPS in parallel. If not given, LAMMPS will run serially.
• m (array-like object, optional) – The m unit vector for the dislocation solution. m, n, and ξ (dislocation line) should be right-hand orthogonal. Default value is [0,1,0] (y-axis).
• n (array-like object, optional) – The n unit vector for the dislocation solution. m, n, and ξ (dislocation line) should be right-hand orthogonal. Default value is [0,0,1] (z-axis). n is normal to the dislocation slip plane.
• sizemults (tuple, optional) – The size multipliers to use when generating the system. Values are limited to being positive integers. The multipliers for the two non-periodic directions must be even. If not given, the default multipliers will be 2 for the non-periodic directions and 1 for the periodic direction.
• amin (float, optional) – A minimum thickness to use for the a box vector direction of the final system. Default value is 0.0. For the non-periodic directions, the resulting vector multiplier will be even. If both amin and sizemults is given, then the larger multiplier for the two will be used.
• bmin (float, optional) – A minimum thickness to use for the b box vector direction of the final system. Default value is 0.0. For the non-periodic directions, the resulting vector multiplier will be even. If both bmin and sizemults is given, then the larger multiplier for the two will be used.
• cmin (float, optional) – A minimum thickness to use for the c box vector direction of the final system. Default value is 0.0. For the non-periodic directions, the resulting vector multiplier will be even. If both cmin and sizemults is given, then the larger multiplier for the two will be used.
• shift (float, optional) – A rigid body shift to apply to the rotated cell prior to inserting the dislocation. Should be selected such that the ideal slip plane does not correspond to any atomic planes. Is taken as absolute if shiftscale is False, or relative to the rotated cell’s box vectors if shiftscale is True. Cannot be given with shiftindex. If neither shift nor shiftindex is given then shiftindex = 0 is used.
• shiftindex (float, optional) – The index of the identified optimum shifts based on the rotated cell to use. Different values allow for the selection of different atomic planes neighboring the slip plane. Note that shiftindex values only apply shifts normal to the slip plane; best shifts for non-planar dislocations (like bcc screw) may also need a shift in the slip plane. Cannot be given with shiftindex. If neither shift nor shiftindex is given then shiftindex = 0 is used.
• shiftscale (bool, optional) – If False (default), a given shift value will be taken as absolute Cartesian. If True, a given shift will be taken relative to the rotated cell’s box vectors.
• tol (float) – A cutoff tolerance used with obtaining the dislocation solution. Only needs to be changed if there are issues with obtaining a solution.
• etol (float, optional) – The energy tolerance for the structure minimization. This value is unitless. Default is 0.0.
• ftol (float, optional) – The force tolerance for the structure minimization. This value is in units of force. Default is 0.0.
• maxiter (int, optional) – The maximum number of minimization iterations to use. Default is 10000.
• maxeval (int, optional) – The maximum number of minimization evaluations to use. Default is 100000.
• dmax (float, optional) – The maximum distance in length units that any atom is allowed to relax in any direction during a single minimization iteration. Default is 0.01 Angstroms.
• annealtemp (float, optional) – The temperature to perform a dynamic relaxation at. Default is 0.0, which will skip the dynamic relaxation.
• annealsteps (int, optional) – The number of time steps to run the dynamic relaxation for. Default is None, which will run for 10000 steps if annealtemp is not 0.0.
• randomseed (int or None, optional) – Random number seed used by LAMMPS in creating velocities and with the Langevin thermostat. Default is None which will select a random int between 1 and 900000000.
• boundarywidth (float, optional) – The width of the boundary region to apply. Default value is 0.0, i.e. no boundary region. All atoms in the boundary region will have their atype values changed.
• boundaryscale (bool, optional) – If False (Default), the boundarywidth will be taken as absolute. If True, the boundarywidth will be taken relative to the magnitude of the unit cell’s a box vector.
• linear (bool, optional) – If True, then only linear displacements will be used and not the dislocation solution. Using only linear displacements is useful for screw dislocations and dislocations with large stacking fault distances. If False (default) then the dislocation solution will be used for the middle displacements and linear displacements only in the boundary region.
• cutoff (float, optional) – Cutoff distance to use for identifying duplicate atoms to remove. For dislocations with an edge component, applying the displacements creates an extra half-plane of atoms that will have (nearly) identical positions with other atoms after altering the boundary conditions. Default value is 0.5 Angstrom.
Returns
Dictionary of results consisting of keys:
• ’dumpfile_base’ (str) - The filename of the LAMMPS dump file for the relaxed base system.
• ’symbols_base’ (list of str) - The list of element-model symbols for the Potential that correspond to the base system’s atypes.
• ’dumpfile_disl’ (str) - The filename of the LAMMPS dump file for the relaxed dislocation monopole system.
• ’symbols_disl’ (list of str) - The list of element-model symbols for the Potential that correspond to the dislocation monopole system’s atypes.
• ’dislocation’ (atomman.defect.Dislocation) - The Dislocation object used to generate the monopole system.
• ’E_total_disl’ (float) - The total potential energy of the dislocation monopole system.
Return type
dict
main(*args)
Main function called when script is executed directly.
process_input(input_dict, UUID=None, build=True)
Processes str input parameters, assigns default values if needed, and generates new, more complex terms as used by the calculation.
Parameters
• input_dict (dict) – Dictionary containing the calculation input parameters with string values. The allowed keys depends on the calculation style.
• UUID (str, optional) – Unique identifier to use for the calculation instance. If not given and a ‘UUID’ key is not in input_dict, then a random UUID4 hash tag will be assigned.
• build (bool, optional) – Indicates if all complex terms are to be built. A value of False allows for default values to be assigned even if some inputs required by the calculation are incomplete. (Default is True.)
| 2022-01-25T08:41:24 |
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|
http://dlmf.nist.gov/26.3
|
# §26.3(i) Definitions
$\binom{m}{n}$ is the number of ways of choosing $n$ objects from a collection of $m$ distinct objects without regard to order. $\binom{m+n}{n}$ is the number of lattice paths from $(0,0)$ to $(m,n)$. The number of lattice paths from $(0,0)$ to $(m,n)$, $m\leq n$, that stay on or above the line $y=x$ is $\binom{m+n}{m}-\binom{m+n}{m-1}.$
26.3.1 $\binom{m}{n}=\binom{m}{m-n}=\frac{m!}{(m-n)!\,n!},$ $m\geq n$,
26.3.2 $\binom{m}{n}=0,$ $n>m$.
For numerical values of $\binom{m}{n}$ and $\binom{m+n}{n}$ see Tables 26.3.1 and 26.3.2.
# §26.3(ii) Generating Functions
26.3.3 $\sum_{n=0}^{m}\binom{m}{n}x^{n}=(1+x)^{m},$ $m=0,1,\ldots$,
26.3.4 $\sum_{m=0}^{\infty}\binom{m+n}{m}x^{m}=\frac{1}{(1-x)^{n+1}},$ $|x|<1$. Symbols: $\binom{m}{n}$: binomial coefficient, $x$: real variable, $m$: nonnegative integer and $n$: nonnegative integer A&S Ref: 24.1.1 (in slightly different form) Permalink: http://dlmf.nist.gov/26.3.E4 Encodings: TeX, pMML, png
# §26.3(iii) Recurrence Relations
26.3.5 $\displaystyle\binom{m}{n}$ $\displaystyle=\binom{m-1}{n}+\binomial{m-1}{n-1},$ $m\geq n\geq 1$, Symbols: $\binom{m}{n}$: binomial coefficient, $m$: nonnegative integer and $n$: nonnegative integer A&S Ref: 24.1.1 Permalink: http://dlmf.nist.gov/26.3.E5 Encodings: TeX, pMML, png 26.3.6 $\displaystyle\binom{m}{n}$ $\displaystyle=\frac{m}{n}\binom{m-1}{n-1}$ $\displaystyle=\frac{m-n+1}{n}\binom{m}{n-1},$ $m\geq n\geq 1$,
26.3.7 $\binom{m+1}{n+1}=\sum_{k=n}^{m}\binom{k}{n},$ $m\geq n\geq 0$,
26.3.8 $\binom{m}{n}=\sum_{k=0}^{n}\binom{m-n-1+k}{k},$ $m\geq n\geq 0$.
# §26.3(iv) Identities
26.3.9 $\binom{n}{0}=\binom{n}{n}=1,$ Symbols: $\binom{m}{n}$: binomial coefficient and $n$: nonnegative integer A&S Ref: 24.1.1 Permalink: http://dlmf.nist.gov/26.3.E9 Encodings: TeX, pMML, png
26.3.10 $\binom{m}{n}=\sum_{k=0}^{n}(-1)^{n-k}\binom{m+1}{k},$ $m\geq n\geq 0$,
26.3.11 $\binom{2n}{n}=\frac{2^{n}(2n-1)(2n-3)\cdots 3\cdot 1}{n!}.$ Symbols: $\binom{m}{n}$: binomial coefficient, $!$: $n!$: factorial and $n$: nonnegative integer A&S Ref: 24.1.1 Permalink: http://dlmf.nist.gov/26.3.E11 Encodings: TeX, pMML, png
26.3.12 $\binom{2n}{n}\sim\frac{4^{n}}{\sqrt{\pi n}},$ $n\to\infty$. Symbols: $\binom{m}{n}$: binomial coefficient, $\sim$: asymptotic equality and $n$: nonnegative integer Referenced by: §26.5(iv) Permalink: http://dlmf.nist.gov/26.3.E12 Encodings: TeX, pMML, png
| 2014-08-23T05:34:14 |
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|
https://indico.fnal.gov/event/22303/contributions/241399/
|
# Seattle Snowmass Summer Meeting 2022
Jul 16 – 26, 2022
US/Pacific timezone
## Higgs boson decay width and couplings at muon collider
Jul 18, 2022, 7:00 PM
2h 20m
211 South Ballroom (HUB)
### Speaker
Luca Giambastiani (University and INFN, Padova)
### Description
Among the facilities proposed for the next generation of particle accelerators for High Energy Physics, the muon collider represents a unique machine, which would be able to provide leptonic collisions at energies of several TeV.
Muons collisions at such energy scale holds a remarkable physic potential, both for searches of phenomena beyond the Standard Model, and precision measurements of known processes.
In particular, in the multi-TeV regime, Higgs production rates are so high that Higgs physics measurements, such as its couplings to bosons and fermions and its decay width, can be achieved with unprecedented precision.
This contribution aims to give an overview of the results obtained so far on Higgs couplings and width by studying single Higgs boson production occurring by vector boson fusion (VBF).
All the studies have been performed simulating the relevant physics processes at a 3 TeV muon collider, taking into account the effects of the Beam Induced Background on the detector performance.
The indirect measurement of the Higgs width is possible thanks to the simultaneous search for on-shell and off-shell Higgs boson decaying to a pair of vector bosons ($H \rightarrow WW$ and $H \rightarrow ZZ$), an analysis strategy already used by LHC experiments.
The knowledge of the Higgs width allows to determine, in a model-independent way, all Higgs boson couplings from $\sigma(\mu^+ \mu^- \rightarrow H) \cdot BR(H \rightarrow xx)$ measurements.
In-person or Virtual? In-person
### Primary author
Luca Giambastiani (University and INFN, Padova)
### Presentation materials
PosterGiambastiani.pdf VideoGiambastiani.mp4
| 2022-11-29T00:32:32 |
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|
https://par.nsf.gov/biblio/10093378
|
First Data Release of the COSMOS LyA Mapping and Tomography Observations: 3D LyA Forest Tomography at 2.05
Faint star-forming galaxies at z∼2–3 can be used as alternative background sources to probe the Lyα forest in addition to quasars, yielding high sightline densities that enable 3D tomographic reconstruction of the foreground absorption field. Here, we present the first data release from the COSMOS Lyα Mapping And Tomography Observations (CLAMATO) Survey, which was conducted with the LRIS spectrograph on the Keck I telescope. Over an observational footprint of 0.157 deg2 within the COSMOS field, we used 240 galaxies and quasars at 2.17<z<3.00, with a mean comoving transverse separation of 2.37 h-1 Mpc, as background sources probing the foreground Lyα forest absorption at 2.05<z<2.55. The Lyα forest data was then used to create a Wiener- filtered tomographic reconstruction over a comoving volume of 3.15 ́ 105 h-3 Mpc3 with an effective smoothing scale of 2.5 h-1 Mpc. In addition to traditional figures, this map is also presented as a virtual-reality visualization and manipulable interactive figure. We see large overdensities and underdensities that visually agree with the distribution of coeval galaxies from spectroscopic redshift surveys in the same field, including overdensities associated with several recently discovered galaxy protoclusters in the volume. Quantitatively, the map signal-to- noise is S Nwiener » 3.4 more »
Authors:
; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10093378
Journal Name:
Astrophysical journal. Supplement series
Volume:
237
Page Range or eLocation-ID:
31
ISSN:
1538-4365
Our understanding of reionization has advanced considerably over the past decade, with several results now demonstrating that the intergalactic medium transitioned from substantially neutral at z = 7 to largely reionized at z = 6. However, little remains known about the sizes of ionized bubbles at z ≳ 7 as well as the galaxy overdensities which drive their growth. Fortunately, rest-ultraviolet (UV) spectroscopic observations offer a pathway towards characterizing these ionized bubbles thanks to the resonant nature of Lyman-alpha photons. In a previous work, we presented Ly α detections from three closely separated Lyman-break galaxies at z ≃ 6.8, suggesting the presence of a large (R > 1 physical Mpc) ionized bubble in the 1.5 deg2 COSMOS field. Here, we present new deep Ly α spectra of 10 UV-bright ($\mathrm{\mathit{ M}}_{\mathrm{UV}}^{} \le -20.4$) z ≃ 6.6–6.9 galaxies in the surrounding area, enabling us to better characterize this potential ionized bubble. We confidently detect (S/N > 7) Ly α emission at z = 6.701–6.882 in nine of ten observed galaxies, revealing that the large-scale volume spanned by these sources (characteristic radius R = 3.2 physical Mpc) traces a strong galaxy overdensity (N/〈N〉 ≳ 3). Our data additionally confirm that the Lymore »
| 2022-12-03T22:05:10 |
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https://it.overleaf.com/latex/templates/why-poisson-why-exponential/nydscrgwgpyv
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# Why Poisson? Why Exponential?
Author
L.Z.
License
Creative Commons CC BY 4.0
Abstract“过去十年一涝，未来十年不涝的概率是？” Answer: 36.8% Though Poisson & Exponential are commonly used, few people understand why. This note exlpains why we use these two distribution.
| 2021-01-21T02:38:32 |
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https://www.usgs.gov/center-news/volcano-watch-first-historical-eruption-anatahan-volcano-northern-mariana-islands
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# Volcano Watch - First Historical Eruption of Anatahan Volcano, Northern Mariana Islands
Release Date:
For the past week, a billowing column of dark volcanic ash has been erupting from Anatahan Volcano in the Northern Mariana Islands, burying parts of the volcano with more than 45 cm (18 inches) of ash and sending a dilute eruption cloud more than 1000 km (600 miles) to the west.
Eruption cloud, from the east crater of Anatahan Volcano, rising to a height of about 15,000 feet, on May 10, 2003. View from the NE side of the island, looking in a southwesterly direction.
(Public domain.)
This is the first eruption from the volcano in historical time, but it didn't come as much of a surprise to people familiar with Anatahan, especially to scientists of the Hawaiian Volcano Observatory (HVO) who worked there in 2001 with personnel from the Emergency Management Office (EMO) of the Commonwealth of the Northern Mariana Islands.
Anatahan Volcano is a small volcanic island located 320 km (200 miles) north of Guam. The island is about 9 km (5.6 miles) long and 3 km (2 miles) wide. Anatahan is a stratovolcano that consists of the largest known caldera in the Northern Mariana Islands. In 1990, when geologists from HVO, EMO, and the University of Hawaii examined the rock layers of Anatahan, they discovered abundant evidence of ancient explosive eruptions that sent fast-moving flows of hot ash and rocks across the island.
The eruption began suddenly on the evening of May 10. No one was directly threatened by the initial activity-residents had long before evacuated the volcano, but not because of recent warnings from the volcano or officials from EMO. Most residents were evacuated in 1990 after a shallow earthquake swarm hinted at the possibility of volcanic activity; another swarm of earthquakes occurred in 1993. Any remaining residents on the island were likely driven away by destructive typhoons of the past year.
Within hours of the eruption's onset, a towering column of volcanic ash and gas rose to more than 10 km (33,000 feet) above sea level, and the prevailing wind blew the ash westward. An immediate concern that was felt far beyond the Western Pacific was the potential for the tiny abrasive ash fragments to damage aircraft passing nearby and downwind from the volcano.
Commercial flights between Hawaii and the Philippines and Hong Kong, and between Japan, Saipan, Guam, Australia, and New Zealand, pass over volcanoes of the Northern Mariana Islands. When an explosive eruption from these islands sends volcanic ash and gas high enough to affect aircraft, it is extremely important for pilots already in the air, and airline dispatchers on the ground, to receive immediate notification of the activity and location of the resulting eruption cloud.
Engines of jet aircraft have failed within minutes of encountering a thick cloud of volcanic ash particles, and many aircraft surfaces and internal electronics can suffer severe damage from ash. More than 80 commercial aircraft have unexpectedly encountered volcanic ash in flight and at airports in the past 20 years.
The job of tracking eruption clouds from the Northern Mariana Islands is the responsibility of the Washington Volcanic Ash Advisory Center (VAAC) in Camp Springs, Maryland. The Washington VAAC issued a series of Volcanic Ash Advisories that identified the estimated location of the eruption cloud based on satellite images and pilot reports. The advisories are distributed through several global networks and served on the Internet.
The Washington VAAC also issued forecasts of where the eruption cloud was likely to go, based on predicted winds. These forecasts, called a Volcanic Ash Forecast Transport and Dispersion model, estimate the location of the eruption cloud at different elevations above sea level for 12-hour time intervals after the eruption began.
No one knows how this eruption may proceed in the next few weeks to months. Very little is known about Anatahan's eruptive history, and the volcano is not currently monitored with real-time volcano sensors that scientists need in order to track the intensity of an ongoing eruption.
In the 1980s and 1990s, HVO scientists assisted the EMO in installing one or two seismometers on several of the volcanoes of the Northern Mariana Islands, including Anatahan, but the single station on the volcano was not operating before the eruption. As scientists have learned elsewhere, a robust volcano-monitoring program is necessary to evaluate the potential for stronger volcanic activity in the near future.
### Volcano Activity Update
Eruptive activity at the Puu O`o vent of Kilauea Volcano continued unabated during the past week. Streams of lava are still visible on Pulama pali and Paliuli. The lava breaks out of the main Mother's Day tube above Pulama pali and wends it way to the coastal flat in a series of open channels and tubes. Surface flows are found near the base of Paliuli, and the National Park Service has marked a trail out to the closest activity. Ocean entry activity at the West Highcastle delta was weak and intermittent during the week. Another active lobe of the Mother's Day flow is approaching the ocean and is within 150 meters (500 ft) of the coast at Highcastle.
The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The steam clouds are highly acidic and laced with glass particles. The National Park Service has erected a rope barricade to delineate the edge of the restricted area. Do not venture beyond this rope boundary and onto the lava deltas and benches.
No earthquakes were reported felt during the past week.
Mauna Loa is not erupting. The summit region continues to inflate. Seismic activity remains low with only 1 earthquake located in the summit area during the last seven days.
| 2019-11-14T07:32:00 |
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|
https://zbmath.org/authors/?q=ai:olver.peter-j
|
# zbMATH — the first resource for mathematics
## Olver, Peter John
Compute Distance To:
Author ID: olver.peter-j Published as: Olver, P.; Olver, P. J.; Olver, Peter; Olver, Peter J. Homepage: http://www-users.math.umn.edu/~olver/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · dblp · GND
Documents Indexed: 202 Publications since 1977, including 20 Books
all top 5
#### Co-Authors
74 single-authored 23 Kamran, Niky 11 González-López, Artemio 11 Pohjanpelto, Juha 8 Qu, Changzheng 8 Tannenbaum, Allen Robert 7 Shakiban, Chehrzad 5 Li, Yi A. 5 Liu, Xiaochuan 4 Fels, Mark E. 4 Kang, Jing 4 Rosenau, Philip S. 4 Sapiro, Guillermo 3 Kogan, Irina A. 3 Liu, Yue 3 Valiquette, Francis 3 Winternitz, Pavel 2 Anderson, Ian M. 2 Chen, Gong 2 Clarkson, Peter A. 2 Finkel, Federico 2 Foursov, Mikhail V. 2 Hoff, Daniel J. 2 Kichenassamy, Satyanad 2 Levi, Decio 2 Lewis, Debra 2 Marí Beffa, Gloria 2 McLeod, John Bryce 2 Muriel, Concepción 2 Nutku, Yavuz 2 Sanders, Jan A. 2 Sheils, Natalie E. 2 Sokolov, Vladimir Vyacheslavovich 2 Wang, Jingping 1 Acosta Humánez, Primitivo Belén 1 Adams, Scot 1 Angulo-Umaña, Pedro 1 Arik, Metin 1 Aronson, Donald G. 1 Ball, John M. 1 Benjamin, Thomas Brooke 1 Berchenko, Irina 1 Bloch, Anthony M. 1 Bozhkov, Yuri Dimitrov 1 Brinkman, Daniel 1 Calabi, Eugenio 1 Calder, Jeff 1 Cheh, Jeongoo 1 Chen, Jeongoo 1 Cucker, Felipe 1 Currie, J. C. 1 DeVore, Ronald A. 1 Fernandez, Oscar E. 1 Fokas, Athanassios S. 1 Georgiou, Tryphon T. 1 Gómez-Ullate, David 1 Grinberg, Darij 1 Guha, Partha 1 Gui, Guilong 1 Gunney, Brian T. N. 1 Hatfield, Gary A. 1 Hernández Heredero, Rafael 1 Hessburg, Bo 1 Hubert, Evelyne 1 Hurtubise, Jacques C. 1 Iserles, Arieh 1 Itskov, Vladimir 1 Jodeit, Max jun. 1 Kac, Victor G. 1 Kaup, David J. 1 Kim, Pilwon 1 Kumar, Arun M. 1 Levine, Howard Allen 1 Lewis, Mark Alun 1 Li, Bingtuan 1 Li, Hongbo 1 Lui, Roger 1 Maliakas, Mihalis 1 Malkoun, Joseph 1 Miller, Willard jun. 1 Milson, Robert 1 Neyzi, Fahrünisa 1 Nigam, Nilima 1 O’Neill, Riley C. W. 1 Özer, Teoman 1 Petitot, Michel 1 Polat, Gülden Gün 1 Quispel, Reinout 1 Ramani, Alfred 1 Raphael, Robert M. 1 Reyes, Enrique G. 1 Rodríguez, Miguel Angel 1 Romero, Juan Luis 1 Ruiz, Adrián Tonatiuh 1 Santosa, Fatil 1 Sattinger, David H. 1 Shigesada, Nanako 1 Sivaloganathan, Jeyabal 1 Smith, David Andrew 1 Solé, Patrick 1 Sommer, Gerald ...and 13 more Co-Authors
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#### Serials
7 Journal of Mathematical Physics 6 Advances in Mathematics 6 Acta Applicandae Mathematicae 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 5 Archive for Rational Mechanics and Analysis 5 Journal of Differential Equations 5 SIAM Journal on Mathematical Analysis 4 Communications in Mathematical Physics 4 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal of Mathematical Analysis and Applications 3 Nonlinearity 3 Advances in Applied Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Journal of Lie Theory 3 Discrete and Continuous Dynamical Systems 3 Regular and Chaotic Dynamics 3 Foundations of Computational Mathematics 3 Graduate Texts in Mathematics 2 Proceedings of the London Mathematical Society. Third Series 2 Results in Mathematics 2 Journal of Symbolic Computation 2 Differential Geometry and its Applications 2 SIAM Journal on Applied Mathematics 2 Journal of Mathematical Imaging and Vision 2 Selecta Mathematica. New Series 2 Transformation Groups 2 Communications in Contemporary Mathematics 2 Lobachevskii Journal of Mathematics 2 Contemporary Mathematics 2 The IMA Volumes in Mathematics and its Applications 2 London Mathematical Society Lecture Note Series 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of Geometric Mechanics 2 Undergraduate Texts in Mathematics 1 American Mathematical Monthly 1 Archives of Mechanics 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Physics Letters. A 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Arkiv för Matematik 1 American Journal of Mathematics 1 Canadian Journal of Mathematics 1 Journal of Algebra 1 Journal of Differential Geometry 1 Journal of Functional Analysis 1 Mathematische Annalen 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Real Analysis Exchange 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 Applied Numerical Mathematics 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Nonlinear Science 1 Communications in Analysis and Geometry 1 Symmetry: Culture and Science 1 RIMS Kokyuroku 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Lie Groups and their Applications 1 Journal of Nonlinear Mathematical Physics 1 Portugaliae Mathematica. Nova Série 1 Analysis and Applications (Singapore) 1 CRM Proceedings & Lecture Notes 1 Lecture Notes in Computer Science 1 London Mathematical Society Student Texts 1 SIAM Journal on Imaging Sciences 1 Forum of Mathematics, Sigma 1 Springer Proceedings in Mathematics & Statistics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 SIAM Journal on Applied Algebra and Geometry 1 Journal of Integrable Systems
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#### Fields
84 Partial differential equations (35-XX) 69 Global analysis, analysis on manifolds (58-XX) 58 Differential geometry (53-XX) 33 Dynamical systems and ergodic theory (37-XX) 27 Topological groups, Lie groups (22-XX) 19 Ordinary differential equations (34-XX) 18 Computer science (68-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 14 Mechanics of particles and systems (70-XX) 13 Nonassociative rings and algebras (17-XX) 13 Numerical analysis (65-XX) 13 Mechanics of deformable solids (74-XX) 13 Fluid mechanics (76-XX) 13 Quantum theory (81-XX) 10 General and overarching topics; collections (00-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 5 Number theory (11-XX) 5 Commutative algebra (13-XX) 5 Operator theory (47-XX) 4 Group theory and generalizations (20-XX) 4 Manifolds and cell complexes (57-XX) 3 Field theory and polynomials (12-XX) 3 Algebraic geometry (14-XX) 3 Real functions (26-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Combinatorics (05-XX) 2 Convex and discrete geometry (52-XX) 2 General topology (54-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)
#### Citations contained in zbMATH Open
172 Publications have been cited 6,695 times in 4,640 Documents Cited by Year
Applications of Lie groups to differential equations. Zbl 0588.22001
Olver, Peter J.
1986
Applications of Lie groups to differential equations. 2nd ed. Zbl 0785.58003
Olver, Peter J.
1993
Noether’s theorems and systems of Cauchy-Kovalevskaya type. Zbl 0656.58039
Olver, P. J.
1986
Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. Zbl 0958.35119
Li, Yi A.; Olver, Peter J.
2000
Equivalence, invariants, and symmetry. Zbl 0837.58001
Olver, Peter J.
1995
Evolution equations possessing infinitely many symmetries. Zbl 0348.35024
Olver, Peter J.
1977
Moving coframes. II: Regularization and theoretical foundations. Zbl 0937.53013
Fels, Mark; Olver, Peter J.
1999
Classical invariant theory. Zbl 0971.13004
Olver, Peter J.
1999
Applications of Lie groups to differential equations. Paperback ed. Zbl 0937.58026
Olver, Peter J.
2000
Null Lagrangians, weak continuity, and variational problems of arbitrary order. Zbl 0459.35020
Ball, J. M.; Currie, J. C.; Olver, P. J.
1981
Wave-breaking and peakons for a modified Camassa-Holm equation. Zbl 1263.35186
Gui, Guilong; Liu, Yue; Olver, Peter J.; Qu, Changzheng
2013
Euler operators and conservation laws of the BBM equation. Zbl 0387.35050
Olver, Peter J.
1979
Group-invariant solutions of differential equations. Zbl 0621.35007
Olver, Peter J.; Rosenau, Philip
1987
Moving coframes. I: A practical algorithm. Zbl 0937.53012
Fels, Mark; Olver, Peter J.
1998
Existence and nonexistence of solitary wave solutions to higher-order model evolution equations. Zbl 0755.76023
1992
Hamiltonian structure, symmetries and conservation laws for water waves. Zbl 0511.76020
Benjamin, T. Brooke; Olver, P. J.
1982
The construction of special solutions to partial differential equations. Zbl 0937.35501
Olver, Peter; Rosenau, Philip
1986
Integrable evolution equations on associative algebras. Zbl 0908.35124
Olver, Peter J.; Sokolov, Vladimir V.
1998
Generating differential invariants. Zbl 1124.53006
Olver, Peter J.
2007
Differential invariants of conformal and projective surfaces. Zbl 1141.53010
Hubert, Evelyne; Olver, Peter J.
2007
Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons. Zbl 0949.35118
Li, Y. A.; Olver, P. J.
1997
Direct reduction and differential constraints. Zbl 0814.35003
Olver, Peter J.
1994
Symmetry groups and path-independent integrals. Zbl 0591.73024
Olver, P. J.
1985
Moving frames: a brief survey. Zbl 1076.53018
Olver, Peter J.
2001
Applications of Lie groups to differential equations. (Prilozheniya grupp Li k differentsial’nym uravneniyam). Transl. from the English I. G. Shcherbak. Transl. ed. and with a preface by A. B. Shabat. Zbl 0743.58003
Olver, P.
1989
Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators. Zbl 0767.35052
González-López, Artemio; Kamran, Niky; Olver, Peter J.
1993
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
1996
The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of Painleve type. Zbl 0518.35075
McLeod, J. B.; Olver, P. J.
1983
A nonlinear Hamiltonian structure for the Euler equations. Zbl 0534.76035
Olver, Peter J.
1982
Invariant Euler–Lagrange equations and the invariant variational bicomplex. Zbl 1034.53015
Kogan, Irina A.; Olver, Peter J.
2003
Hamiltonian structures for systems of hyperbolic conservation laws. Zbl 0697.35084
Olver, Peter J.; Nutku, Yavuz
1988
Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II: Complex analytic behavior and convergence to non-analytic solutions. Zbl 0959.35157
Li, Y. A.; Olver, P. J.
1998
Lie algebras of vector fields in the real plane. Zbl 0872.17022
González-López, Artemio; Kamran, Niky; Olver, Peter J.
1992
On the Hamiltonian structure of evolution equations. Zbl 0445.58012
Olver, Peter J.
1980
On the blow-up of solutions to the integrable modified Camassa-Holm equation. Zbl 1302.35074
Liu, Yue; Olver, Peter J.; Qu, Changzheng; Zhang, Shuanghu
2014
Conformal curvature flows: from phase transitions to active vision. Zbl 0937.53029
Kichenassamy, Satyanad; Kumar, Arun; Olver, Peter; Tannenbaum, Allen; Yezzi, Anthony jun.
1996
Lie algebras of differential operators and Lie-algebraic potentials. Zbl 0693.34021
Kamran, Niky; Olver, Peter J.
1990
Invariant submanifold flows. Zbl 1146.53040
Olver, Peter J.
2008
Conservation laws in elasticity. II: Linear homogeneous isotropic elastostatics. Zbl 0582.73024
Olver, Peter J.
1984
Moving frames for Lie pseudo-groups. Zbl 1160.53006
Olver, Peter J.; Pohjanpelto, Juha
2008
Hamiltonian perturbation theory and water waves. Zbl 0521.76018
Olver, Peter
1984
Joint invariant signatures. Zbl 1001.53004
Olver, Peter J.
2001
Internal, external, and generalized symmetries. Zbl 0809.58044
Anderson, Ian M.; Kamran, Niky; Olver, Peter J.
1993
Geometric foundations of numerical algorithms and symmetry. Zbl 0982.65135
Olver, Peter J.
2001
Differential invariant algebras of Lie pseudo-groups. Zbl 1194.58018
Olver, Peter J.; Pohjanpelto, Juha
2009
On multivariate interpolation. Zbl 1145.41311
Olver, Peter J.
2006
Lie algebras of differential operators in two complex variables. Zbl 0781.17011
González-López, Artemio; Kamran, Niky; Olver, Peter J.
1992
Multi-Hamiltonian structure of the Born-Infeld equation. Zbl 0850.70173
Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.
1989
Conservation laws in elasticity. I: General results. Zbl 0559.73019
Olver, Peter J.
1984
Maurer-Cartan forms and the structure of Lie pseudo-groups. Zbl 1091.58014
Olver, Peter J.; Pohjanpelto, Juha
2005
Classification of integrable one-component systems on associative algebras. Zbl 1033.37035
Olver, Peter J.; Wang, Jing Ping
2000
Variational $$C^{\infty}$$-symmetries and Euler–Lagrange equations. Zbl 1085.70016
Muriel, C.; Romero, J. L.; Olver, P. J.
2006
Geometric integration via multi-space. Zbl 1068.65092
Kim, Pilwon; Olver, Peter J.
2004
Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems. Zbl 0969.35038
Kamran, Niky; Milson, Robert; Olver, Peter J.
2000
Moving frames and singularities of prolonged group actions. Zbl 0966.57037
Olver, Peter J.
2000
Conservation laws and null divergences. Zbl 0556.35021
Olver, Peter J.
1983
Algorithms for differential invariants of symmetry groups of differential equations. Zbl 1183.58016
Cheh, Jeongoo; Olver, Peter J.; Pohjanpelto, Juha
2008
Non-analytic solutions of nonlinear wave models. Zbl 0940.35176
Li, Yi A.; Olver, Peter J.; Rosenau, Philip
1999
Hamiltonian and non-Hamiltonian models for water waves. Zbl 0583.76014
Olver, Peter J.
1984
Applications of Lie groups to differential equations. Lecture Notes. Zbl 0599.58050
Olver, Peter J.
1980
Introduction to partial differential equations. Zbl 1295.35001
Olver, Peter J.
2014
Affine geometry, curve flows, and invariant numerical approximations. Zbl 0973.53006
Calabi, Eugenio; Olver, Peter J.; Tannenbaum, Allen
1996
Non-associative local Lie groups. Zbl 0862.22005
Olver, Peter J.
1996
Quasi-exactly solvable Lie algebras of differential operators in two complex variables. Zbl 0760.17021
González-López, Artemio; Kamran, Niky; Olver, Peter J.
1991
Symmetry groups and group invariant solutions of partial differential equations. Zbl 0437.58024
Olver, Peter J.
1979
A plethora of integrable bi-Hamiltonian equations. Zbl 0865.35121
Fokas, A. S.; Olver, P. J.; Rosenau, P.
1997
Symmetry and explicit solutions of partial differential equations. Zbl 0777.35017
Olver, Peter J.
1992
Darboux’ theorem for Hamiltonian differential operators. Zbl 0651.47036
Olver, Peter J.
1988
Transvectants, modular forms, and the Heisenberg algebra. Zbl 1041.11026
Olver, Peter J.; Sanders, Jan A.
2000
Equivalence of differential operators. Zbl 0715.47032
Kamran, Niky; Olver, Peter J.
1989
The structure of null Lagrangians. Zbl 0662.49016
Olver, P. J.; Sivaloganathan, J.
1988
Invariant theory and differential equations. Zbl 0646.35003
Olver, Peter J.
1987
Moving frames and differential invariants in centro-affine geometry. Zbl 1260.53024
Olver, P. J.
2010
Poisson structures for geometric curve flows in semi-simple homogeneous spaces. Zbl 1229.22018
Marí Beffa, G.; Olver, P. J.
2010
Moving frames and joint differential invariants. Zbl 1014.53013
Olver, P. J.
1999
Equivalence problems for first order Lagrangians on the line. Zbl 0677.49034
Kamran, Niky; Olver, Peter J.
1989
Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy. Zbl 1344.37075
Kang, Jing; Liu, Xiaochuan; Olver, Peter J.; Qu, Changzheng
2016
Recursive moving frames. Zbl 1254.22014
Olver, Peter J.
2011
Geodesic flow and two (super) component analog of the Camassa-Holm equation. Zbl 1095.53058
Guha, Partha; Olver, Peter J.
2006
A survey of moving frames. Zbl 1078.53507
Olver, Peter J.
2005
Symmetries of polynomials. Zbl 0970.15023
Berchenko, Irina; Olver, Peter J.
2000
Non-abelian integrable systems of the derivative nonlinear Schrödinger type. Zbl 0915.35097
Olver, P. J.; Sokolov, V. V.
1998
Hyperjacobians, determinantal ideals and weak solutions to variational problems. Zbl 0562.49005
Olver, Peter J.
1983
Internal symmetries of differential equations. Zbl 0723.58045
Olver, Peter J.
1991
A resolution of the Euler operator. I. Zbl 0395.49002
1978
Lectures on moving frames. Zbl 1235.53016
Olver, Peter J.
2011
Differential invariants of surfaces. Zbl 1164.53002
Olver, Peter J.
2009
Geometric integration algorithms on homogeneous manifolds. Zbl 1018.22017
Lewis, Debra; Olver, Peter J.
2002
New quasi-exactly solvable Hamiltonians in two dimensions. Zbl 0811.35106
González-López, Artemio; Kamran, Niky; Olver, Peter J.
1994
Canonical elastic moduli. Zbl 0658.73014
Olver, Peter J.
1988
On the structure of Lie pseudo-groups. Zbl 1241.58008
Olver, Peter J.; Pohjanpelto, Juha; Valiquette, Francis
2009
Real Lie algebras of differential operators and quasi-exactly solvable potentials. Zbl 0872.17021
González-López, Artemio; Kamran, Niky; Olver, Peter
1996
Equivalence and the Cartan form. Zbl 0794.49041
Olver, Peter J.
1993
Liouville correspondences between integrable hierarchies. Zbl 1366.37133
Kang, Jing; Liu, Xiaochuan; Olver, Peter J.; Qu, Changzheng
2017
Orbital stability of peakons for a generalization of the modified Camassa-Holm equation. Zbl 1307.35035
Liu, Xiaochuan; Liu, Yue; Olver, Peter J.; Qu, Changzheng
2014
Dispersion of discontinuous periodic waves. Zbl 1371.35246
Chen, Gong; Olver, Peter J.
2013
Extensions of invariant signatures for object recognition. Zbl 1276.68137
Hoff, Daniel J.; Olver, Peter J.
2013
Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics, Jairo Charris Seminar 2010, Santa Maria, Colombia, August 2010. Zbl 1234.81013
Acosta-Humánez, Primitivo B. (ed.); Finkel, Federico (ed.); Kamran, Niky (ed.); Olver, Peter J. (ed.)
2012
Moving frames – in geometry, algebra, computer vision, and numerical analysis. Zbl 0981.53010
Olver, Peter J.
2001
Invariant geometric evolutions of surfaces and volumetric smoothing. Zbl 0874.35044
Olver, Peter J.; Sapiro, Guillermo; Tannenbaum, Allen
1997
Applied linear algebra. 2nd edition, previously published by Pearson/Prentice Hall 2006. Zbl 1402.15001
2018
Normal forms for submanifolds under group actions. Zbl 1426.22014
Olver, Peter J.
2018
Prolonged analytic connected group actions are generically free. Zbl 1432.22025
2018
On the commutator of $$\mathcal C^\infty$$-symmetries and the reduction of Euler-Lagrange equations. Zbl 1391.49018
Ruiz, A.; Muriel, C.; Olver, P. J.
2018
Liouville correspondences between integrable hierarchies. Zbl 1366.37133
Kang, Jing; Liu, Xiaochuan; Olver, Peter J.; Qu, Changzheng
2017
Bäcklund transformations for tri-Hamiltonian dual structures of multi-component integrable systems. Zbl 1403.37080
Kang, Jing; Liu, Xiaochuan; Olver, Peter J.; Qu, Changzheng
2017
Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy. Zbl 1344.37075
Kang, Jing; Liu, Xiaochuan; Olver, Peter J.; Qu, Changzheng
2016
The symmetry groupoid and weighted signature of a geometric object. Zbl 1341.53027
Olver, Peter J.
2016
Invariants of objects and their images under surjective maps. Zbl 1332.53021
Kogan, I. A.; Olver, P. J.
2015
On the blow-up of solutions to the integrable modified Camassa-Holm equation. Zbl 1302.35074
Liu, Yue; Olver, Peter J.; Qu, Changzheng; Zhang, Shuanghu
2014
Introduction to partial differential equations. Zbl 1295.35001
Olver, Peter J.
2014
Orbital stability of peakons for a generalization of the modified Camassa-Holm equation. Zbl 1307.35035
Liu, Xiaochuan; Liu, Yue; Olver, Peter J.; Qu, Changzheng
2014
Automatic solution of jigsaw puzzles. Zbl 1361.68291
Hoff, Daniel J.; Olver, Peter J.
2014
Numerical simulation of nonlinear dispersive quantization. Zbl 1358.35152
Chen, Gong; Olver, Peter J.
2014
Wave-breaking and peakons for a modified Camassa-Holm equation. Zbl 1263.35186
Gui, Guilong; Liu, Yue; Olver, Peter J.; Qu, Changzheng
2013
Dispersion of discontinuous periodic waves. Zbl 1371.35246
Chen, Gong; Olver, Peter J.
2013
Extensions of invariant signatures for object recognition. Zbl 1276.68137
Hoff, Daniel J.; Olver, Peter J.
2013
Algebraic aspects of Darboux transformations, quantum integrable systems and supersymmetric quantum mechanics, Jairo Charris Seminar 2010, Santa Maria, Colombia, August 2010. Zbl 1234.81013
Acosta-Humánez, Primitivo B. (ed.); Finkel, Federico (ed.); Kamran, Niky (ed.); Olver, Peter J. (ed.)
2012
Invariant histograms. Zbl 1266.53003
Brinkman, Daniel; Olver, Peter J.
2012
Persistence of freeness for Lie pseudogroup actions. Zbl 1260.58010
Olver, Peter J.; Pohjanpelto, Juha
2012
Variational integrators for hamiltonizable nonholonomic systems. Zbl 1262.65193
Fernandez, Oscar E.; Bloch, Anthony M.; Olver, P. J.
2012
Recursive moving frames. Zbl 1254.22014
Olver, Peter J.
2011
Lectures on moving frames. Zbl 1235.53016
Olver, Peter J.
2011
Differential invariant algebras. Zbl 1232.53021
Olver, Peter J.
2011
Lie completion of pseudo-groups. Zbl 1257.22004
Itskov, Vladimir; Olver, Peter J.; Valiquette, Francis
2011
Pohozhaev and Morawetz identities in elastostatics and elastodynamics. Zbl 1244.35143
Bozhkov, Yuri; Olver, Peter J.
2011
Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Zbl 1218.39002
Levi, Decio (ed.); Olver, Peter (ed.); Thomova, Zora (ed.); Winternitz, Pavel (ed.)
2011
Moving frames and differential invariants in centro-affine geometry. Zbl 1260.53024
Olver, P. J.
2010
Poisson structures for geometric curve flows in semi-simple homogeneous spaces. Zbl 1229.22018
Marí Beffa, G.; Olver, P. J.
2010
Recent advances in the theory and application of Lie pseudo-groups. Zbl 1330.81112
Olver, Peter
2010
Differential invariant algebras of Lie pseudo-groups. Zbl 1194.58018
Olver, Peter J.; Pohjanpelto, Juha
2009
Differential invariants of surfaces. Zbl 1164.53002
Olver, Peter J.
2009
On the structure of Lie pseudo-groups. Zbl 1241.58008
Olver, Peter J.; Pohjanpelto, Juha; Valiquette, Francis
2009
Local symplectic invariants for curves. Zbl 1176.53032
Kamran, Niky; Olver, Peter; Tenenblat, Keti
2009
Equivalence, invariants, and symmetry. Reprint of the 1995 hardback ed. Zbl 1156.58002
Olver, Peter J.
2009
Invariant submanifold flows. Zbl 1146.53040
Olver, Peter J.
2008
Moving frames for Lie pseudo-groups. Zbl 1160.53006
Olver, Peter J.; Pohjanpelto, Juha
2008
Algorithms for differential invariants of symmetry groups of differential equations. Zbl 1183.58016
Cheh, Jeongoo; Olver, Peter J.; Pohjanpelto, Juha
2008
Moving frames and differential invariants for Lie pseudo-groups. Zbl 1146.58010
Olver, Peter; Pohjanpelto, Juha
2008
Pseudo-groups, moving frames, and differential invariants. Zbl 1144.58013
Olver, Peter J.; Pohjanpelto, Juha
2008
Generating differential invariants. Zbl 1124.53006
Olver, Peter J.
2007
Differential invariants of conformal and projective surfaces. Zbl 1141.53010
Hubert, Evelyne; Olver, Peter J.
2007
Differential invariants for Lie pseudo-groups. Zbl 1133.58009
Olver, Peter; Pohjanpelto, Juha
2007
Generalized transvectants and Siegel modular forms. Zbl 1221.11117
Olver, P. J.; Petitot, M.; Solé, P.
2007
On multivariate interpolation. Zbl 1145.41311
Olver, Peter J.
2006
Variational $$C^{\infty}$$-symmetries and Euler–Lagrange equations. Zbl 1085.70016
Muriel, C.; Romero, J. L.; Olver, P. J.
2006
Geodesic flow and two (super) component analog of the Camassa-Holm equation. Zbl 1095.53058
Guha, Partha; Olver, Peter J.
2006
Applied linear algebra. Zbl 1076.15001
2006
Maurer-Cartan forms and the structure of Lie pseudo-groups. Zbl 1091.58014
Olver, Peter J.; Pohjanpelto, Juha
2005
A survey of moving frames. Zbl 1078.53507
Olver, Peter J.
2005
Maurer-Cartan equations for Lie symmetry pseudogroups of differential equations. Zbl 1076.37054
Chen, Jeongoo; Olver, Peter J.; Pohjanpelto, Juha
2005
Regularity of pseudogroup orbits. Zbl 1136.58304
Olver, Peter J.; Pohjanpelto, Juha
2005
Computer algebra and geometric algebra with applications. 6th international workshop, IWMM 2004, Shanghai, China, May 19–21, 2004 and international workshop, GIAE 2004, Xian, China, May 24–28, 2004. Revised selected papers. Zbl 1073.68007
Li, Hongbo (ed.); Olver, Peter J. (ed.); Sommer, Gerald (ed.)
2005
Connections for general group actions. Zbl 1086.58006
Lewis, Debra; Nigam, Nilima; Olver, Peter J.
2005
Geometric integration via multi-space. Zbl 1068.65092
Kim, Pilwon; Olver, Peter J.
2004
Nonlocal symmetries and ghosts. Zbl 1072.35193
Olver, Peter J.
2004
Invariant Euler–Lagrange equations and the invariant variational bicomplex. Zbl 1034.53015
Kogan, Irina A.; Olver, Peter J.
2003
Moving frames. Zbl 1076.53017
Olver, Peter J.
2003
Mathematical methods in computer vision. Papers presented at the IMA workshops: “Image processing and low level vision”, October 16–20, 2000, and “Image analysis and high level vision”, November 13–17, 2000, Minneapolis, MN, USA. Zbl 1103.68009
Olver, Peter J. (ed.); Tannenbaum, Allen (ed.)
2003
Geometric integration algorithms on homogeneous manifolds. Zbl 1018.22017
Lewis, Debra; Olver, Peter J.
2002
Moving frames: a brief survey. Zbl 1076.53018
Olver, Peter J.
2001
Joint invariant signatures. Zbl 1001.53004
Olver, Peter J.
2001
Geometric foundations of numerical algorithms and symmetry. Zbl 0982.65135
Olver, Peter J.
2001
Moving frames – in geometry, algebra, computer vision, and numerical analysis. Zbl 0981.53010
Olver, Peter J.
2001
On formal integrability of evolution equations and local geometry of surfaces. Zbl 1019.37044
Foursov, Mikhail V.; Olver, Peter J.; Reyes, Enrique G.
2001
The invariant variational bicomplex. Zbl 1004.58009
Kogan, Irina A.; Olver, Peter J.
2001
Classification of symmetry-integrable evolution equations. Zbl 0995.35005
Olver, Peter J.; Sanders, Jan A.; Wang, Jing Ping
2001
Moving frames and coframes. Zbl 1037.53007
Fels, Mark; Olver, Peter J.
2001
Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. Zbl 0958.35119
Li, Yi A.; Olver, Peter J.
2000
Applications of Lie groups to differential equations. Paperback ed. Zbl 0937.58026
Olver, Peter J.
2000
Classification of integrable one-component systems on associative algebras. Zbl 1033.37035
Olver, Peter J.; Wang, Jing Ping
2000
Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems. Zbl 0969.35038
Kamran, Niky; Milson, Robert; Olver, Peter J.
2000
Moving frames and singularities of prolonged group actions. Zbl 0966.57037
Olver, Peter J.
2000
Transvectants, modular forms, and the Heisenberg algebra. Zbl 1041.11026
Olver, Peter J.; Sanders, Jan A.
2000
Symmetries of polynomials. Zbl 0970.15023
Berchenko, Irina; Olver, Peter J.
2000
Moving coframes. II: Regularization and theoretical foundations. Zbl 0937.53013
Fels, Mark; Olver, Peter J.
1999
Classical invariant theory. Zbl 0971.13004
Olver, Peter J.
1999
Non-analytic solutions of nonlinear wave models. Zbl 0940.35176
Li, Yi A.; Olver, Peter J.; Rosenau, Philip
1999
Moving frames and joint differential invariants. Zbl 1014.53013
Olver, P. J.
1999
Affine invariant detection: Edge maps, anisotropic diffusion, and active contours. Zbl 1005.53010
Olver, Peter J.; Sapiro, Guillermo; Tannenbaum, Allen
1999
Differential invariants for parametrized projective surfaces. Zbl 0949.53012
Marí Beffa, Gloria; Olver, Peter J.
1999
Solitary waves in the critical surface-tension model. Zbl 0934.76012
Gunney, Brian T. N.; Li, Yi A.; Olver, Peter J.
1999
Moving coframes. I: A practical algorithm. Zbl 0937.53012
Fels, Mark; Olver, Peter J.
1998
Integrable evolution equations on associative algebras. Zbl 0908.35124
Olver, Peter J.; Sokolov, Vladimir V.
1998
Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II: Complex analytic behavior and convergence to non-analytic solutions. Zbl 0959.35157
Li, Y. A.; Olver, P. J.
1998
Non-abelian integrable systems of the derivative nonlinear Schrödinger type. Zbl 0915.35097
Olver, P. J.; Sokolov, V. V.
1998
Canonical forms and conservation laws in linear elastostatics. Zbl 0940.74008
Hatfield, G.; Olver, P. J.
1998
Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons. Zbl 0949.35118
Li, Y. A.; Olver, P. J.
1997
A plethora of integrable bi-Hamiltonian equations. Zbl 0865.35121
Fokas, A. S.; Olver, P. J.; Rosenau, P.
1997
Invariant geometric evolutions of surfaces and volumetric smoothing. Zbl 0874.35044
Olver, Peter J.; Sapiro, Guillermo; Tannenbaum, Allen
1997
On relative invariants. Zbl 0877.57019
Fels, Mark; Olver, Peter J.
1997
Quasi-exact solvability in the real domain. Zbl 0905.17024
González-López, A.; Kamran, N.; Olver, P. J.
1997
Symmetry and the Chazy equation. Zbl 0842.34010
Clarkson, Peter A.; Olver, Peter J.
1996
Conformal curvature flows: from phase transitions to active vision. Zbl 0937.53029
Kichenassamy, Satyanad; Kumar, Arun; Olver, Peter; Tannenbaum, Allen; Yezzi, Anthony jun.
1996
Affine geometry, curve flows, and invariant numerical approximations. Zbl 0973.53006
Calabi, Eugenio; Olver, Peter J.; Tannenbaum, Allen
1996
Non-associative local Lie groups. Zbl 0862.22005
Olver, Peter J.
1996
Real Lie algebras of differential operators and quasi-exactly solvable potentials. Zbl 0872.17021
González-López, Artemio; Kamran, Niky; Olver, Peter
1996
Lie algebras of differential operators and partial integrability. Zbl 0928.58035
Finkel, Federico; González-López, Artemio; Kamran, Niky; Olver, Peter J.; Rodríguez, Miguel A.
1996
Classification of invariant wave equations. Zbl 0871.35005
Hernández Heredero, Rafael; Olver, Peter J.
1996
Equivalence, invariants, and symmetry. Zbl 0837.58001
Olver, Peter J.
1995
...and 72 more Documents
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#### Cited by 4,517 Authors
69 Olver, Peter John 59 Qu, Changzheng 52 Khalique, Chaudry Masood 47 Kara, Abdul Hamid 46 Gandarias Núñez, Maria Luz 42 Bruzón, Maria Santos 40 Yin, Zhaoyang 39 Popovych, Roman O. 38 Sophocleous, Christodoulos 37 Mahomed, Fazal M. 33 Li, Jibin 32 Anco, Stephen C. 31 Ma, Wen-Xiu 30 Gaeta, Giuseppe 30 Liu, Yue 28 Nadjafikhah, Mehdi 28 Wazwaz, Abdul-Majid Abdul-Rahman 27 Zhang, Hongqing 26 Leach, Peter Gavin Lawrence 25 Llibre, Jaume 25 Özer, Teoman 24 Tian, Lixin 24 Winternitz, Pavel 23 Bluman, George W. 22 Freire, Igor Leite 22 Govinder, Keshlan Sathasiva 20 Himonas, A. Alexandrou 20 Liu, Hanze 20 Qiao, Zhijun 18 Hernández-Bermejo, Benito 18 Kamran, Niky 18 Lai, Shaoyong 18 Oliveri, Francesco 18 Zhdanov, Renat Z. 17 Bihlo, Alexander 17 Cheviakov, Alexei F. 17 Clarkson, Peter A. 17 Moitsheki, Raseelo J. 17 Sergyeyev, Artur 17 Valiquette, Francis 17 Wang, Jingping 16 Cherniha, Roman M. 16 Meleshko, Sergey V. 16 Morozov, Oleg I. 16 Nucci, Maria Clara 15 Anderson, Ian M. 15 Chen, Yong 15 Grundland, Alfred Michel 15 Guha, Partha 15 Mansfield, Elizabeth Louise 15 Sahadevan, Ramajayam 15 Vulpe, Nicolae I. 14 Biswas, Anjan 14 Bozhkov, Yuri Dimitrov 14 Dağ, İdris 14 Gordoa, Pilar Ruiz 14 Morando, Paola 14 Mustafa, Muhammad Tahir 14 Pickering, Andrew 14 Shen, Shoufeng 13 Bokhari, Ashfaque H. 13 Cicogna, Giampaolo 13 Fu, Ying 13 Fushchych, Vil’gel’m Illich 13 Hu, Qiaoyi 13 Kumar, Sachin 13 Lakshmanan, Muthusamy 13 Lou, Senyue 13 Marí Beffa, Gloria 13 Naeem, Imran 13 Pohjanpelto, Juha 13 Reyes, Enrique G. 13 Senthilvelan, Murugaian 13 Tracinà, Rita 13 Vitolo, Raffaele F. 13 Zhang, Zhiyong 12 Fokas, Athanassios S. 12 Ivanova, Nataliya M. 12 Liu, Xingxing 12 Mu, Chunlai 12 Vaneeva, Olena O. 12 Zaman, Fiazud Din 12 Zhou, Shouming 11 Azad, Hassan 11 Dorodnitsyn, Vladimir A. 11 Jamal, Sameerah 11 Kozlov, Roman 11 Luo, Shaokai 11 Mikula, Karol 11 Muriel, Concepción 11 Rosenhaus, Vladimir 11 Sanders, Jan A. 11 Smirnov, Roman G. 11 Yan, Wei 11 Zharinov, Victor Victorovich 10 Carillo, Sandra 10 Huang, Dingjiang 10 Kudryashov, Nikolaĭ Alekseevich 10 Li, Yongsheng 10 Mi, Yongsheng ...and 4,417 more Authors
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#### Cited in 487 Serials
313 Journal of Mathematical Physics 201 Applied Mathematics and Computation 194 Journal of Mathematical Analysis and Applications 134 Journal of Nonlinear Mathematical Physics 117 Physics Letters. A 113 Communications in Nonlinear Science and Numerical Simulation 112 Journal of Geometry and Physics 112 Journal of Differential Equations 95 Chaos, Solitons and Fractals 90 Physica D 90 Nonlinear Dynamics 73 Theoretical and Mathematical Physics 70 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 70 Acta Applicandae Mathematicae 68 Nonlinear Analysis. Real World Applications 62 Reports on Mathematical Physics 58 Abstract and Applied Analysis 52 Applied Mathematics Letters 50 International Journal of Theoretical Physics 48 Computers & Mathematics with Applications 46 Discrete and Continuous Dynamical Systems 45 Archive for Rational Mechanics and Analysis 44 Journal of Computational and Applied Mathematics 44 Studies in Applied Mathematics 40 Communications in Mathematical Physics 38 Letters in Mathematical Physics 34 Mathematical Methods in the Applied Sciences 34 International Journal of Geometric Methods in Modern Physics 33 Differential Geometry and its Applications 32 International Journal of Engineering Science 32 Advances in Mathematical Physics 31 Journal of Symbolic Computation 28 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 27 Journal of Elasticity 26 Applicable Analysis 26 Applied Numerical Mathematics 25 Mathematical and Computer Modelling 25 Mathematical Problems in Engineering 24 General Relativity and Gravitation 24 Journal of Computational Physics 24 Journal of Fluid Mechanics 24 Journal of Applied Mathematics 23 Computer Physics Communications 23 Journal of Mathematical Sciences (New York) 22 Advances in Mathematics 22 Journal of Nonlinear Science 22 Journal of Physics A: Mathematical and Theoretical 21 Transactions of the American Mathematical Society 21 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 20 Acta Mechanica 19 Applied Mathematics and Mechanics. (English Edition) 19 Symmetry 18 Discrete and Continuous Dynamical Systems. Series S 17 International Journal of Modern Physics B 17 Journal of Engineering Mathematics 17 Journal of Functional Analysis 17 Applied Mathematical Modelling 16 Physica A 16 Automatica 16 Regular and Chaotic Dynamics 16 Journal of High Energy Physics 15 Ukrainian Mathematical Journal 15 Wave Motion 15 Annals of Physics 15 International Journal of Computer Mathematics 15 Linear Algebra and its Applications 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Mathematics and Computers in Simulation 14 Proceedings of the American Mathematical Society 14 Lobachevskii Journal of Mathematics 14 Foundations of Computational Mathematics 13 European Journal of Applied Mathematics 13 Calculus of Variations and Partial Differential Equations 12 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Acta Mathematicae Applicatae Sinica. English Series 12 Advances in Difference Equations 11 Modern Physics Letters A 11 Mathematical Notes 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Rocky Mountain Journal of Mathematics 11 Quaestiones Mathematicae 11 Advances in Applied Mathematics 11 Communications in Partial Differential Equations 11 Acta Mathematica Sinica. English Series 10 Computer Methods in Applied Mechanics and Engineering 10 Nonlinearity 10 Nuclear Physics. B 10 Journal of Mathematical Imaging and Vision 10 Physical Review Letters 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Science China. Mathematics 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Duke Mathematical Journal 9 Mathematische Annalen 9 Monatshefte für Mathematik 9 Results in Mathematics 9 Systems & Control Letters 9 SIAM Journal on Mathematical Analysis 9 Nonlinear Analysis. Theory, Methods & Applications 8 International Journal of Modern Physics A ...and 387 more Serials
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#### Cited in 59 Fields
2,570 Partial differential equations (35-XX) 1,123 Dynamical systems and ergodic theory (37-XX) 607 Fluid mechanics (76-XX) 535 Ordinary differential equations (34-XX) 508 Global analysis, analysis on manifolds (58-XX) 371 Mechanics of particles and systems (70-XX) 354 Numerical analysis (65-XX) 335 Differential geometry (53-XX) 266 Quantum theory (81-XX) 239 Mechanics of deformable solids (74-XX) 185 Topological groups, Lie groups (22-XX) 170 Nonassociative rings and algebras (17-XX) 164 Computer science (68-XX) 142 Calculus of variations and optimal control; optimization (49-XX) 134 Relativity and gravitational theory (83-XX) 83 Statistical mechanics, structure of matter (82-XX) 80 Systems theory; control (93-XX) 71 Biology and other natural sciences (92-XX) 69 Algebraic geometry (14-XX) 66 Commutative algebra (13-XX) 61 Difference and functional equations (39-XX) 59 Special functions (33-XX) 47 Probability theory and stochastic processes (60-XX) 45 Optics, electromagnetic theory (78-XX) 44 Operator theory (47-XX) 42 Real functions (26-XX) 40 Number theory (11-XX) 40 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 39 Functional analysis (46-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 37 Geophysics (86-XX) 35 Classical thermodynamics, heat transfer (80-XX) 34 Several complex variables and analytic spaces (32-XX) 32 Field theory and polynomials (12-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 23 Manifolds and cell complexes (57-XX) 23 Information and communication theory, circuits (94-XX) 22 Functions of a complex variable (30-XX) 21 Combinatorics (05-XX) 19 Associative rings and algebras (16-XX) 17 Astronomy and astrophysics (85-XX) 15 Group theory and generalizations (20-XX) 15 Approximations and expansions (41-XX) 15 Integral equations (45-XX) 12 General topology (54-XX) 11 History and biography (01-XX) 11 Geometry (51-XX) 11 Algebraic topology (55-XX) 10 General and overarching topics; collections (00-XX) 10 Operations research, mathematical programming (90-XX) 9 Abstract harmonic analysis (43-XX) 7 Mathematical logic and foundations (03-XX) 7 Measure and integration (28-XX) 7 Statistics (62-XX) 5 Category theory; homological algebra (18-XX) 5 Integral transforms, operational calculus (44-XX) 4 Convex and discrete geometry (52-XX) 3 $$K$$-theory (19-XX) 3 Potential theory (31-XX)
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| 2021-06-19T11:41:14 |
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|
https://fallout.fandom.com/wiki/Fallout_76_cultural_references?oldid=3141436
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## FANDOM
33,861 Pages
This page lists all cultural references in Fallout 76. The content is not described in full detail on this page. For details, please see the respective articles. For cultural references in other Fallout games, please see "Cultural reference." For an overview of Fallout 76 content, please refer to "Portal:Fallout 76."
## Alien
In the AVR Medical Center, one can find a Jangles the Moon Monkey doll lying on a stretcher with a toy alien attached to its face on the first floor, reminiscent of a facehugger from the Alien franchise.
## Albert Einstein
Inside the doghouse of the isolated cabin is a mathematical formula written in chalk: $R_{\mu \nu} – \tfrac{1}{2} R g_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G} {c^4} T_{\mu \nu}$. This is an Einstein field equation, first published by Albert Einstein in 1915.
## Alice in Wonderland
• Behind the counter at the Giant Teapot, there is a series of wooden blocks that spell out "LATE" next to a scrap of paper with "10/6" written on it. These are references to the Lewis Carroll novel Alice in Wonderland.
• Another Alice in Wonderland reference can be found east of the Tyler County fairgrounds, with a table in the woods reminiscent of the Mad Hatter's tea party.
## Beowulf
The tale of the "nightstalker" wendigo at the Sons of Dane compound mirrors the Old English epic Beowulf, in which Hrothgar, King of the Danes, and his men are repeatedly attacked by a foreboding creature while dining.
Just north of Sugar Grove, there are several partially buried blue barrels with money on top of them and a skeleton nearby in a lab coat. This references the scene from Breaking Bad in which Walter White buries barrels full of money in the desert.
## Charlie and the Chocolate Factory
Willie is a deceased ghoul in Appalachia whose body holds The Golden Holotape, a reference to the Roald Dahl novel Charlie and the Chocolate Factory. Willie's name is similar to that of Willy Wonka, the owner of the chocolate factory, and the "Golden Holotape" replaces the "Golden Ticket" needed to enter the factory.
In the glassed cavern, there is a small area full of ultracite ores and a series of wooden blocks that spell out the word "PLUGH." This is a reference to Colossal Cave Adventure, a text adventure game from the 1970s. One scenario from the game involves the player character hearing the word "plugh" coming from a hollow voice in a dark pit.
## Distant Drums
The memetic "Wilhelm Scream" is briefly heard in a promotional video for Fallout 76.
## Doom
A set of wooden blocks in the apartment building with the Nuka-Cola billboard on the east side of Morgantown spells out "BFG," a reference to the weapon first appearing in the Doom franchise, published by Bethesda Softworks since 2010.
## dril
The final line of the note Skeleton extraction guide is a reference to a well-known tweet from popular Twitter user @dril, stating that "if your grave doesnt say "rest in peace" on it you are automatically drafted into the skeleton war."
## The Elder Scrolls V: Skyrim
• The raid decals used by the raiders are strikingly similar to the Shadow marks used by the Thieves Guild in Skyrim, down to sharing the "loot" and "empty" marks.
• At the Mount Blair trainyard, there is a series of wooden blocks that spell out "WE KNO" next to a framed picture with a bloody handprint on it. This is a reference to the Dark Brotherhood's mysterious note in Skyrim.
• On a path west of Vault 96, there is a carriage carrying three dead settlers that resembles the intro scene of Skyrim. It is a possible location to wake up at after drinking Nukashine.
• One question in the Medic Pioneer Scout exam involves a patient that has been shot in the knee. One incorrect answer is to "advise Ricky to give up on adventuring," a reference to the memetic line "I used to be an adventurer like you. Then I took an arrow in the knee..."
## Fallout: New Vegas
One of the raider tribes that previously existed in Appalachia was the Gourmands. This appears to be a reference to the White Glove Society and their restaurant The Gourmand, that previously appeared in New Vegas, given the preference of both groups for eating human flesh.
## Harley-Davidson
Harley Wheeler, a prisoner at Eastern Regional Penitentiary, was sentenced to seven years imprisonment for five counts of grand theft auto. Considering their name and crime, Harley is most likely a reference to Harley-Davidson, Inc., a motorcycle manufacturing company.
Headlight fluid, a trolling bait and meme used to send someone on a search for something that doesn't exist, is referenced in the R&G Processing Services terminal entries, when Manager Jarrett Delgado suggests giving a job to Pat Rhodes involving the nonexistent item. Headlight fluid was popularized through its appearances on radio shows and the Rooster Teeth series Red vs. Blue.
The random encounter with two Mr. Handies talking back and forth in an endless loop is a reference to a January 2017 video stream of two Google Home devices (also named Mia and Vlad) stuck in a loop asking each other questions.[1]
## It
Inside of a fridge at the Whitespring golf club, there is a clown holding a red balloon in reference to Pennywise the Clown from Stephen King's It, who is often menacingly portrayed with a red balloon.
## Jesco White
Jesse "The Dancin' Bandit" White, a pre-War country singer who had a set list for a concert at The Rusty Pick, is a reference to Jesco "The Dancing Outlaw" White, a folk dancer from West Virginia. The set list also contains a number of real-life country songs, including ones by Jason Isbell and Jamey Johnson, among others.
## Jim Croce
Leroy Brown, a guard at Eastern Regional Penitentiary, shares a name with a character in the song "Bad, Bad Leroy Brown" by Jim Croce.
## The Kids in the Hall
The Garrahan Mining Headquarters terminal entries mention a Family Fun Day event featuring the band Rod Torfulson's Armada. This is a reference to the Canadian sketch comedy show The Kids in the Hall, which featured a rock band with the same name.
## Killing Them Softly
The perk card design for Enforcer parodies a poster for the 2012 film Killing Them Softly, in which Brad Pitt plays a mafia enforcer named Jackie Cogan.
## The Legend of Zelda
Vendor bot Raiders reference a famous line in The Legend of Zelda, saying "it's dangerous to go alone."
## Loss.jpg
There is a picnic table at a campsite west of the pumpkin house with seven beer bottles on it that are positioned in reference to "Loss," an infamous comic that often takes a minimalist form in Internet memes, using just seven lines in a sequence.
## The Magic School Bus
In a parking lot outside of Camden Park, there is a school bus with a series of wooden blocks spelling out "MAGIC" lying on the dashboard. In the driver's seat is an orange tie Mr. Fuzzy with a clipboard and a clown hat, a reference to Ms. Frizzle from the educational cartoon The Magic School Bus.
## The Mist
The fog crawlers could be an allusion to the arachni-lobster creature from Stephen King's novella The Mist. The similarities include a mysterious crustacean, which dwells in an unnatural fog.
## Monster Factory
Near the Kanawha Nuka-Cola plant, there is a house the references the webseries Monster Factory by Polygon. There are several characters from their Fallout 4 series at the house.[2]
## Monty Python
The lumberjack protectrons at Gilman lumber mill will occasionally say "Lumberjack protectron works all night and also works all day," a variation on a line from "The Lumberjack Song."
## The Most Dangerous Game
The holotape The Addington's Dangerous Game references "The Most Dangerous Game," a short story by Richard Connell in which the protagonist is stranded on a Caribbean island, where he is hunted by an aristocratic big game hunter, a similar situation to the proposal Westley Addington makes.
## Murdoch Mysteries
At the Top of the World, there is a customer comment terminal. One of the entries contains references to the CBC mystery show Murdoch Mysteries. The heading reads "W. Murdock & J. Ogdin," which are references to the titular character of the television show (William Murdoch) and his wife, Dr. Julia Ogden. The text also refers to a "Crab-tree Burger," which is a reference to another character on the show, George Crabtree. Finally, one of the burger ingredients is listed as "Canadian Bacon," which is a nod to the show's origin and shooting location.
## The Office
In the Camden Park terminal entries, Marty Porkins is promoted to the position of Assistant to the Park Manager, before the title is changed to Assistant Park Manager. This is a reference to a running gag from The Office, in which Dwight Schrute (in the U.S. version) or Gareth Keenan (in the U.K. version) repeatedly claims that he is the Assistant Regional Manager, forcing others to correct him with his actual position, the Assistant to the Regional Manager, a much less valuable title.
## One Flew Over the Cuckoo's Nest
At Fort Defiance, there is a room with a skeleton lying in bed, wearing a nightcap and a pillow over its face. This is a reference to the ending of One Flew Over the Cuckoo's Nest, where McMurphy is smothered with a pillow while in an asylum.
## Peanuts
In the woods near Vault 76, there is a doghouse with a skeleton sprawled on its roof, baseball items lying on the ground outside and a birdhouse on a nearby tree. These are references to Snoopy, Woodstock and other characters from the comic strip Peanuts.
## Pied Piper
The Eyebot Pied Piper random encounter is a reference to the story of the Pied Piper of Hamelin, who leads rodents by playing music to clear out a town's rat infestation.
## Rebel Wilson
Pre-War prisoner "Rebel" Wilson shares a name with Rebel Wilson, an Australian actress and writer best known for her portrayal of the character Fat Amy in the Pitch Perfect film series.
## Record scratch - freeze frame
The note My story, found at the Tyler County fairgrounds, is a reference to an Internet meme about a movie cliché in which a record scratch is played while the film freezes on a particular frame, followed by a character explaining how they got themselves in a particular situation. It was first popularized on 4chan's /tv/ board in 2015.[3]
## The Shining
Torrance House contains multiple references to The Shining, including the "redrum" scene, the fire axe and the hedge maze. The name itself is also a reference to the main characters of the film.
## The Simpsons
Dick Shale's audio tour of Uncanny Caverns references a running gag in The Simpsons, where character Troy McClure greets his viewers with "Hi, I'm Troy McClure. You may remember me from such [films, educational videos, voiceovers, etc.] as..."
## Star Trek: The Next Generation
Tanagra Town and the "Darmok + Jalad" graffiti in the bus stop are references to the Star Trek: The Next Generation episode "Darmok."
## Throw Momma from the Train
The note Untitled is a reference to the opening scene of Throw Momma from the Train, in which character Larry Donner suffers from writer's block and can only come up with "The night was" on his typewriter.
## Titanic
In the middle of the dry lake east of the lakeside cabins, there is a female skeleton lying on a door, reaching out to a disconnected skeleton arm. The scene mimics the characters Rose and Jack from the 1997 film Titanic.
## Toy Story
East of Bleeding Kate's Grindhouse, there is a Comrade Chubs teddy bear sitting on the front of a truck on the highway. This is a reference to the ending of Toy Story 3, where the antagonist, teddy bear Lotso, is found by a trucker and tied to the front of his vehicle.
## We Bare Bears
In a tower at the Palace of the Winding Path, where the child's note is found, there is a stack of three teddy bear variants that resembles the main characters of We Bare Bears, an animated television series that began airing in 2015.[4]
## Willow
In the movie Willow a character named Madmartigan is found in a crow's cage - a single occupant suspended cage. This is similar to how Hank Madigan dies at Top of the World.
## The Wizard of Oz
In a terminal entry found in Harpers Ferry, Ella Ames writes that "We're not in Kansas anymore!" which is Dorothy's first line upon arriving in Oz.
## References
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-04-04T00:40:57 |
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https://par.nsf.gov/biblio/10386259-phangs-jwst-first-results-spurring-star-formation-jwst-reveals-localized-star-formation-spiral-arm-spur-ngc
|
PHANGS-JWST First Results: Spurring on Star Formation: JWST Reveals Localized Star Formation in a Spiral Arm Spur of NGC 628
Abstract
We combine JWST observations with Atacama Large Millimeter/submillimeter Array CO and Very Large Telescope MUSE Hαdata to examine off-spiral arm star formation in the face-on, grand-design spiral galaxy NGC 628. We focus on the northern spiral arm, around a galactocentric radius of 3–4 kpc, and study two spurs. These form an interesting contrast, as one is CO-rich and one CO-poor, and they have a maximum azimuthal offset in MIRI 21μm and MUSE Hαof around 40° (CO-rich) and 55° (CO-poor) from the spiral arm. The star formation rate is higher in the regions of the spurs near spiral arms, but the star formation efficiency appears relatively constant. Given the spiral pattern speed and rotation curve of this galaxy and assuming material exiting the arms undergoes purely circular motion, these offsets would be reached in 100–150 Myr, significantly longer than the 21μm and Hαstar formation timescales (both < 10 Myr). The invariance of the star formation efficiency in the spurs versus the spiral arms indicates massive star formation is not only triggered in spiral arms, and cannot simply occur in the arms and then drift away from the wave pattern. These early JWST results show that in situ star formation likely more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10386259
Journal Name:
The Astrophysical Journal Letters
Volume:
941
Issue:
2
Page Range or eLocation-ID:
Article No. L27
ISSN:
2041-8205
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
More Like this
1. ABSTRACT
Star formation histories (SFHs) are integral to our understanding of galaxy evolution. We can study recent SFHs by comparing the star formation rate (SFR) calculated using different tracers, as each probes a different time-scale. We aim to calibrate a proxy for the present-day rate of change in SFR, dSFR/dt, which does not require full spectral energy distribution (SED) modelling and depends on as few observables as possible, to guarantee its broad applicability. To achieve this, we create a set of models in cigale and define an SFR change diagnostic as the ratio of the SFR averaged over the past 5 and 200 Myr, $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$, probed by the H α–FUV colour. We apply $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ to the nearby spiral NGC 628 and find that its star formation activity has overall been declining in the recent past, with the spiral arms, however, maintaining a higher level of activity. The impact of the spiral arm structure is observed to be stronger on $\langle SFR_{\rm {5}} \rangle \big / \langle SFR_{\rm {200}} \rangle$ than on the star formation efficiency. In addition, increasing disc pressure tends to increase recent starmore »
2. Abstract
We present a high-resolution view of bubbles within the Phantom Galaxy (NGC 628), a nearby (∼10 Mpc), star-forming (∼2Myr−1), face-on (i∼ 9°) grand-design spiral galaxy. With new data obtained as part of the Physics at High Angular resolution in Nearby GalaxieS (PHANGS)-JWST treasury program, we perform a detailed case study of two regions of interest, one of which contains the largest and most prominent bubble in the galaxy (the Phantom Void, over 1 kpc in diameter), and the other being a smaller region that may be the precursor to such a large bubble (the Precursor Phantom Void). When comparing to matched-resolution Hαobservations from the Hubble Space Telescope, we see that the ionized gas is brightest in the shells of both bubbles, and is coincident with the youngest (∼1 Myr) and most massive (∼105M) stellar associations. We also find an older generation (∼20 Myr) of stellar associations is present within the bubble of the Phantom Void. From our kinematic analysis of the HI, H2(CO), and Hiigas across the Phantom Void, we infer a high expansion speed of around 15 to 50 km s−1. The large size and high expansion speed of the Phantom Void suggest that the driving mechanism ismore »
3. Abstract
Large-scale bars can fuel galaxy centers with molecular gas, often leading to the development of dense ringlike structures where intense star formation occurs, forming a very different environment compared to galactic disks. We pair ∼0.″3 (30 pc) resolution new JWST/MIRI imaging with archival ALMA CO(2–1) mapping of the central ∼5 kpc of the nearby barred spiral galaxy NGC 1365 to investigate the physical mechanisms responsible for this extreme star formation. The molecular gas morphology is resolved into two well-known bright bar lanes that surround a smooth dynamically cold gas disk (Rgal∼ 475 pc) reminiscent of non-star-forming disks in early-type galaxies and likely fed by gas inflow triggered by stellar feedback in the lanes. The lanes host a large number of JWST-identified massive young star clusters. We find some evidence for temporal star formation evolution along the ring. The complex kinematics in the gas lanes reveal strong streaming motions and may be consistent with convergence of gas streamlines expected there. Indeed, the extreme line widths are found to be the result of inter-“cloud” motion between gas peaks;ScousePydecomposition reveals multiple components with line widths of 〈σCO,scouse〉 ≈ 19 km s−1and surface densities of, similar to the properties observed throughout the rest of the central molecular gas structure. Tailored hydrodynamical simulations exhibit many of the observed properties and imply that the observed structures are transient and highly time-variable. From our study of NGC 1365, we conclude that it is predominantly the high gas inflow triggered by the bar that is setting the star formation in its CMZ.
4. Abstract
We use PHANGS–James Webb Space Telescope (JWST) data to identify and classify 1271 compact 21μm sources in four nearby galaxies using MIRI F2100W data. We identify sources using a dendrogram-based algorithm, and we measure the background-subtracted flux densities for JWST bands from 2 to 21μm. Using the spectral energy distribution (SED) in JWST and HST bands plus ALMA and MUSE/VLT observations, we classify the sources by eye. Then we use this classification to define regions in color–color space and so establish a quantitative framework for classifying sources. We identify 1085 sources as belonging to the ISM of the target galaxies with the remainder being dusty stars or background galaxies. These 21μm sources are strongly spatially associated with Hiiregions (>92% of sources), while 74% of the sources are coincident with a stellar association defined in the HST data. Using SED fitting, we find that the stellar masses of the 21μm sources span a range of 102–104Mwith mass-weighted ages down to 2 Myr. There is a tight correlation between attenuation-corrected Hαand 21μm luminosity forLν,F2100W> 1019W Hz−1. Young embedded source candidates selected at 21μm are found below this threshold and haveM< 103M.
5. Abstract We present a high-resolution analysis of the host galaxy of fast radio burst (FRB) 190608, an SB(r)c galaxy at z = 0.11778 (hereafter HG 190608), to dissect its local environment and its contributions to the FRB properties. Our Hubble Space Telescope Wide Field Camera 3 ultraviolet and visible light image reveals that the subarcsecond localization of FRB 190608 is coincident with a knot of star formation (Σ SFR = 1.5 × 10 −2 M ⊙ yr −1 kpc −2 ) in the northwest spiral arm of HG 190608. Using H β emission present in our Keck Cosmic Web Imager integral field spectrum of the galaxy with a surface brightness of μ H β = ( 3.36 ± 0.21 ) × 10 − 17 erg s − 1 cm − 2 arcsec − 2 , we infer an extinction-corrected H α surface brightness and compute a dispersion measure (DM) from the interstellar medium of HG 190608 of DM Host,ISM = 94 ± 38 pc cm −3 . The galaxy rotates with a circular velocity v circ = 141 ± 8 km s −1 at an inclination i gas = 37° ± 3°, giving a dynamical mass M halo dyn ≈more »
| 2023-03-31T07:35:47 |
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http://dlmf.nist.gov/33.18
|
# §33.18 Limiting Forms for Large $\ell$
As $\ell\to\infty$ with $\epsilon$ and $r$ ($\neq 0$) fixed,
33.18.1 $\displaystyle\mathop{f\/}\nolimits\!\left(\epsilon,\ell;r\right)$ $\displaystyle\sim\frac{(2r)^{\ell+1}}{(2\ell+1)!},$ $\displaystyle\mathop{h\/}\nolimits\!\left(\epsilon,\ell;r\right)$ $\displaystyle\sim\frac{(2\ell)!}{\pi(2r)^{\ell}}.$
| 2014-07-28T16:25:17 |
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https://math.libretexts.org/Courses/University_of_California%2C_Davis/UCD_Mat_21A%3A_Differential_Calculus/2%3A_Limits_and_Continuity/2.4%3A_One-Sided_Limits
|
# 2.4: One-Sided Limits
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
We introduced the concept of a limit gently, approximating their values graphically and numerically. Next came the rigorous definition of the limit, along with an admittedly tedious method for evaluating them. The previous section gave us tools (which we call theorems) that allow us to compute limits with greater ease. Chief among the results were the facts that polynomials and rational, trigonometric, exponential and logarithmic functions (and their sums, products, etc.) all behave "nicely.'' In this section we rigorously define what we mean by "nicely.''
In Section 1.1 we explored the three ways in which limits of functions failed to exist:
1. The function approached different values from the left and right,
2. The function grows without bound, and
3. The function oscillates.
In this section we explore in depth the concepts behind #1 by introducing the one-sided limit. We begin with formal definitions that are very similar to the definition of the limit given in Section 1.2, but the notation is slightly different and "$$x\neq c$$'' is replaced with either "$$x<c$$'' or "$$x>c$$.''
Definition 2: One Sided Limits
Left-Hand Limit
Let $$I$$ be an open interval containing $$c$$, and let $$f$$ be a function defined on $$I$$, except possibly at $$c$$. The limit of $$f(x)$$, as $$x$$ approaches $$c$$ from the left, is $$L$$, or, the left--hand limit of $$f$$ at $$c$$ is $$L$$, denoted by
$\lim\limits_{x\rightarrow c^-} f(x) = L,$
means that given any $$\epsilon > 0$$, there exists $$\delta > 0$$ such that for all $$x< c$$, if $$|x - c| < \delta$$, then $$|f(x) - L| < \epsilon$$.
Right-Hand Limit
Let $$I$$ be an open interval containing $$c$$, and let $$f$$ be a function defined on $$I$$, except possibly at $$c$$. The limit of $$f(x)$$, as $$x$$ approaches $$c$$ from the right, is $$L$$, or, the right--hand limit of $$f$$ at $$c$$ is $$L$$, denoted by
$\lim\limits_{x\rightarrow c^+} f(x) = L,$
means that given any $$\epsilon > 0$$, there exists $$\delta > 0$$ such that for all $$x> c$$, if $$|x - c| < \delta$$, then $$|f(x) - L| < \epsilon$$.
Practically speaking, when evaluating a left-hand limit, we consider only values of $$x$$ "to the left of $$c$$,'' i.e., where $$x<c$$. The admittedly imperfect notation $$x\to c^-$$ is used to imply that we look at values of $$x$$ to the left of $$c$$. The notation has nothing to do with positive or negative values of either $$x$$ or $$c$$. A similar statement holds for evaluating right-hand limits; there we consider only values of $$x$$ to the right of $$c$$, i.e., $$x>c$$. We can use the theorems from previous sections to help us evaluate these limits; we just restrict our view to one side of $$c$$.
We practice evaluating left and right-hand limits through a series of examples.
Example 17: Evaluating one sided limits
Let $$f(x) = \left\{\begin{array}{cc} x & 0\leq x\leq 1 \\ 3-x & 1<x<2\end{array},\right.$$ as shown in Figure 1.21. Find each of the following:
1. $$\lim\limits_{x\to 1^-} f(x)$$
2. $$\lim\limits_{x\to 1^+} f(x)$$
3. $$\lim\limits_{x\to 1} f(x)$$
4. $$f(1)$$
5. $$\lim\limits_{x\to 0^+} f(x)$$
6. $$f(0)$$
7. $$\lim\limits_{x\to 2^-} f(x)$$
8. $$f(2)$$
$$\text{FIGURE 1.21}$$: A graph of $$f$$ in Example 17.
Solution:
For these problems, the visual aid of the graph is likely more effective in evaluating the limits than using $$f$$ itself. Therefore we will refer often to the graph.
1. As $$x$$ goes to 1 from the left, we see that $$f(x)$$ is approaching the value of 1. Therefore $$\lim\limits_{x\to 1^-} f(x) =1.$$
2. As $$x$$ goes to 1 from the right, we see that $$f(x)$$ is approaching the value of 2. Recall that it does not matter that there is an "open circle'' there; we are evaluating a limit, not the value of the function. Therefore $$\lim\limits_{x\to 1^+} f(x)=2$$.
3. The limit of $$f$$ as $$x$$ approaches 1 does not exist, as discussed in the first section. The function does not approach one particular value, but two different values from the left and the right.
4. Using the definition and by looking at the graph we see that $$f(1) = 1$$.
5. As $$x$$ goes to 0 from the right, we see that $$f(x)$$ is also approaching 0. Therefore $$\lim\limits_{x\to 0^+} f(x)=0$$. Note we cannot consider a left-hand limit at 0 as $$f$$ is not defined for values of $$x<0$$.
6. Using the definition and the graph, $$f(0) = 0$$.
7. As $$x$$ goes to 2 from the left, we see that $$f(x)$$ is approaching the value of 1. Therefore $$\lim\limits_{x\to 2^-} f(x)=1.$$
8. The graph and the definition of the function show that $$f(2)$$ is not defined.
Note how the left and right-hand limits were different at $$x=1$$. This, of course, causes the limit to not exist. The following theorem states what is fairly intuitive: the limit exists precisely when the left and right-hand limits are equal.
Theorem 7: Limits and One Sided Limits
Let $$f$$ be a function defined on an open interval $$I$$ containing $$c$$. Then $\lim\limits_{x\to c}f(x) = L$if, and only if, $\lim\limits_{x\to c^-}f(x) = L \quad \text{and} \quad \lim\limits_{x\to c^+}f(x) = L.$
The phrase "if, and only if'' means the two statements are equivalent: they are either both true or both false. If the limit equals $$L$$, then the left and right hand limits both equal $$L$$. If the limit is not equal to $$L$$, then at least one of the left and right-hand limits is not equal to $$L$$ (it may not even exist).
One thing to consider in Examples 17 - 20 is that the value of the function may/may not be equal to the value(s) of its left/right-hand limits, even when these limits agree.
Example 18: Evaluating limits of a piecewise-defined function
Let $$f(x) = \left\{\begin{array}{cc} 2-x & 0<x<1 \\ (x-2)^2 & 1<x<2 \end{array},\right.$$ as shown in Figure 1.22. Evaluate the following.
1. $$\lim\limits_{x\to 1^-} f(x)$$
2. $$\lim\limits_{x\to 1^+} f(x)$$
3. $$\lim\limits_{x\to 1} f(x)$$
4. $$f(1)$$
5. $$\lim\limits_{x\to 0^+} f(x)$$
6. $$f(0)$$
7. $$\lim\limits_{x\to 2^-} f(x)$$
8. $$f(2)$$
$$\text{FIGURE 1.22}$$: A graph of $$f$$ from Example 18.
Solution:
Again we will evaluate each using both the definition of $$f$$ and its graph.
1. As $$x$$ approaches 1 from the left, we see that $$f(x)$$ approaches 1. Therefore $$\lim\limits_{x\to 1^-} f(x)=1.$$
2. As $$x$$ approaches 1 from the right, we see that again $$f(x)$$ approaches 1. Therefore $$\lim\limits_{x\to 1+} f(x)=1$$.
3. The limit of $$f$$ as $$x$$ approaches 1 exists and is 1, as $$f$$ approaches 1 from both the right and left. Therefore $$\lim\limits_{x\to 1} f(x)=1$$.
4. $$f(1)$$ is not defined. Note that 1 is not in the domain of $$f$$ as defined by the problem, which is indicated on the graph by an open circle when $$x=1$$.
5. As $$x$$ goes to 0 from the right, $$f(x)$$ approaches 2. So $$\lim\limits_{x\to 0^+} f(x)=2$$.
6. $$f(0)$$ is not defined as $$0$$ is not in the domain of $$f$$.
7. As $$x$$ goes to 2 from the left, $$f(x)$$ approaches 0. So $$\lim\limits_{x\to 2^-} f(x)=0$$.
8. $$f(2)$$ is not defined as 2 is not in the domain of $$f$$.
Example 19: Evaluating limits of a piecewise-defined function
Let $$f(x) = \left\{\begin{array}{cc} (x-1)^2 & 0\leq x\leq 2, x\neq 1\\ 1 & x=1\end{array},\right.$$ as shown in Figure 1.23. Evaluate the following.
1. $$\lim\limits_{x\to 1^-} f(x)$$
2. $$\lim\limits_{x\to 1^+} f(x)$$
3. $$\lim\limits_{x\to 1} f(x)$$
4. $$f(1)$$
$$\text{FIGURE 1.23}$$: Graphing $$f$$ in Example 19.
It is clear by looking at the graph that both the left and right-hand limits of $$f$$, as $$x$$ approaches 1, is 0. Thus it is also clear that the limit is 0; i.e., $$\lim\limits_{x\to 1} f(x) = 0$$. It is also clearly stated that $$f(1) = 1$$.
Example 20: Evaluating limits of a piecewise-defined function
Let $$f(x) = \left\{\begin{array}{cc} x^2 & 0\leq x\leq 1 \\ 2-x & 1<x\leq 2\end{array},\right.$$ as shown in Figure 1.24. Evaluate the following.
1. $$\lim\limits_{x\to 1^-} f(x)$$
2. $$\lim\limits_{x\to 1^+} f(x)$$
3. $$\lim\limits_{x\to 1} f(x)$$
4. $$f(1)$$
$$\text{FIGURE 1.24}$$: Graphing $$f$$ in Example 20.
Solution:
It is clear from the definition of the function and its graph that all of the following are equal:
$\lim\limits_{x\to 1^-} f(x) = \lim\limits_{x\to 1^+} f(x) =\lim\limits_{x\to 1} f(x) =f(1) = 1.$
In Examples 17 - 20 we were asked to find both $$\lim\limits_{x\to 1}f(x)$$ and $$f(1)$$. Consider the following table:
$\begin{array}{ccc} & \lim\limits_{x\to 1}f(x) & f(1) \\ \hline \text{Example 17} & \text{does not exist} & 1 \\ \text{Example 18} & 1 & \text{not defined} \\ \text{Example 19} & 0 & 1 \\ \text{Example 20} & 1 & 1 \\ \end{array}$
Only in Example 20 do both the function and the limit exist and agree. This seems "nice;'' in fact, it seems "normal.'' This is in fact an important situation which we explore in the next section, entitled "Continuity.'' In short, a continuous function is one in which when a function approaches a value as $$x\rightarrow c$$ (i.e., when $$\lim\limits_{x\to c} f(x) = L$$), it actually attains that value at $$c$$. Such functions behave nicely as they are very predictable.
## Contributors
• Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/
| 2019-06-17T17:29:53 |
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http://www.like2do.com/learn?s=Portal:Logic
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Portal:Logic
Get Portal:Logic essential facts below. View Videos or join the Portal:Logic discussion. Add Portal:Logic to your Like2do.com topic list for future reference or share this resource on social media.
Portal:Logic
The Logic Portal a portal for Wikipedia's Logic resources.
Article · Category · List · Outline · WikiProject
## Logic
Logic (from Classical Greek logos; meaning 'speech/word') is the study of the principles and criteria of valid inference and demonstration. The term "logos" was also believed by the Greeks to be the universal power by which all reality was sustained and made coherent and consistent.
As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. [1]
Traditionally, logic is studied as a branch of philosophy, one part of the classical trivium, which consisted of grammar, logic, and rhetoric. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics. In 1910 Bertrand Russell and Alfred North Whitehead attempted to establish logic as the cornerstone of mathematics formally with the publication of Principia Mathematica. However, the system of Principia is no longer much used, having been largely supplanted by set theory. The development of formal logic and its implementation in computing machinery is the foundation of computer science.
## Selected article
In the formal languages used in mathematical logic and computer science, a well-formed formula or simply formula[3] (often abbreviated wff, pronounced "wiff" or "wuff") is an idea, abstraction or concept which is expressed using the symbols and formation rules (also called the formal grammar) of a particular formal language. To say that a string of symbols ${\displaystyle \ S}$ is a wff with respect to a given formal grammar ${\displaystyle \ G}$ is equivalent to saying that ${\displaystyle \ S}$ belongs to the language generated by ${\displaystyle \ G}$. A formal language can be identified with the set of its wffs.
...Archive/Nominations
## Selected biography
Aristotle (Greek: , Aristotél?s) (384 BC - 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote on many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, politics, government, ethics, biology and zoology.
Together with Plato and Socrates (Plato's teacher), Aristotle is one of the most important founding figures in Western philosophy. He was the first to create a comprehensive system of Western philosophy, encompassing morality and aesthetics, logic and science, politics and metaphysics. Aristotle's views on the physical sciences profoundly shaped medieval scholarship, and their influence extended well into the Renaissance, although they were ultimately replaced by Newtonian Physics. In the biological sciences, some of his observations were confirmed to be accurate only in the nineteenth century. His works contain the earliest known formal study of logic, which was incorporated in the late nineteenth century into modern formal logic. In metaphysics, Aristotelianism had a profound influence on philosophical and theological thinking in the Islamic and Jewish traditions in the Middle Ages, and it continues to influence Christian theology, especially Eastern Orthodox theology, and the scholastic tradition of the Roman Catholic Church. All aspects of Aristotle's philosophy continue to be the object of active academic study today.
...Archive/Nominations
## Things to do
Here are some tasks awaiting attention: Article requests : Anonymous authority o Anti-Procreation Movement o Appeal to classical allusions o Archimedean Fulcrum o Asserting an alternative o Bad reasons fallacy o Cartesian logic o Common thread reasoning o Conjunctive forks o Converting a conditional o Doctrine of Unexpected Consequences o Dream logic o Equivocity o Fallacy of assuming a common cause o Fallacy of biased generalization o Conflicting conditions o Failure to elucidate o Too broad o Too narrow o Fallacies of distraction o Fallacies of explanation o Limited depth o Limited scope o Non-support o Subverted support o Untestability o Fallacy of personal preference assumptions o Fallacy of quantificational logic o Fallacy of reverse causation o Fallacy of the alternative syllogism o Fallacy of the disjunctive syllogism o Fallacy of the propositional logic o Free time (fallacy) o Futurist extrapolation o Heads in the sand critique o Ignoring common cause o Illicit process o Improper disjunctive syllogism o Improper transposition o Inferring from a metaphor o Intuitionistic modal logic o Jactication o Kicking the problem upstairs o Lennon/McCartney fallacy o Liminocentricity o List of valid argument forms Done o List of invalid argument forms o Logical notation o Meinongian arguments o Mereological arguments o Negating antecedent and consequent o Neutrality Schmeutrality o One-sidedness o Open Block Logic o Oppositional logic o Perfectly rigorous o Physiological Egoism o Plurivocity o Postmodern mathematics o Prejudicial language o Pseudorefutation o Quote-name o Repetition (fallacy) o Science fiction moralizing o Significant difference reasoning o Some are/some are not o Sublime experience o Superalternation o Swiftian logic o Tendentious appeal to possibilities o truth-apt o Truthmapping o Unwarranted contrast o Upwards inherited o Volitive o Weaseler o John Arrington Woodward Other : Add links to this portal by placing {{Portal|Logic}} in the See also sections of relevant articles
## References
1. ^ J. Robert Cox and Charles Arthur Willard, eds. Advances in Argumentation Theory and Research, Southern Illinois University Press, 1983 ISBN 0809310503, ISBN-13 978-0809310500
2. ^ Godel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter
3. ^ Because non-well-formed formulas are rarely considered, some authors ignore them altogether. For these authors, "formula" and "well-formed formula" are synonyms. Other authors use the term "formula" for any string of symbols in the language; certain of these strings are then singled out as the well-formed formulas.
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This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.
| 2017-11-18T06:49:16 |
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http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3672.htm
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2. Measurement Process Characterization
2.3. Calibration
2.3.6. Instrument calibration over a regime
2.3.6.7. Uncertainties of calibrated values
## Uncertainty for linear calibration using check standards
Check standards provide a mechanism for calculating uncertainties The easiest method for calculating type A uncertainties for calibrated values from a calibration curve requires periodic measurements on check standards. The check standards, in this case, are artifacts at the lower, mid-point and upper ends of the calibration curve. The measurements on the check standard are made in a way that randomly samples the output of the calibration procedure.
Calculation of check standard values The check standard values are the raw measurements on the artifacts corrected by the calibration curve. The standard deviation of these values should estimate the uncertainty associated with calibrated values. The success of this method of estimating the uncertainties depends on adequate sampling of the measurement process.
Measurements corrected by a linear calibration curve As an example, consider measurements of linewidths on photomask standards, made with an optical imaging system and corrected by a linear calibration curve. The three control measurements were made on reference standards with values at the lower, mid-point, and upper end of the calibration interval.
Compute the calibration standard deviation For the linewidth data, the regression equation from the calibration experiment is $$Y = a + bX + \epsilon$$ and the estimated regression coefficients are the following. $$\hat{a} = 0.2357$$ $$\hat{b} = 0.9870$$ Next, we calculate the difference between the "predicted" $$X$$ from the regression fit and the observed $$X$$. $$W_i = \frac{(Y_i - \hat{a})}{\hat{b}} - X_i$$ Finally, we find the calibration standard deviation by calculating the standard deviation of the computed differences. $$S = \sqrt{\frac{\sum \left( W_i - \overline{W} \right)^2}{n-1}}$$ The calibration standard deviation for the linewidth data is 0.119 µm.
The calculations in this section can be completed using Dataplot code and R code.
Comparison with propagation of error The standard deviation, 0.119 µm, can be compared with a propagation of error analysis.
Other sources of uncertainty In addition to the type A uncertainty, there may be other contributors to the uncertainty such as the uncertainties of the values of the reference materials from which the calibration curve was derived.
| 2014-11-01T08:51:43 |
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https://mooseframework.inl.gov/source/postprocessors/InterfaceIntegralVariableValuePostprocessor.html
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# InterfaceIntegralVariableValuePostprocessor
## Description !syntax description /Postprocessors/InterfaceIntegralVariableValuePostprocessor
This post-processor is used to compute an integral value of variable on an interface. The type of average to compute is selected by changing the interface_value_type parameter. If the parameter interface_value_type is omitted it defaults to compute the average value between the two input variables across the interface. The various types of averages that can be computed are describe in more details in InterfaceValueTools.
## Example Input File Syntax
listing test/tests/postprocessors/interface_value/interface_integral_variable_value_postprocessor.i block=Postprocessors/diffusivity_average
## Input Parameters
• variableThe name of the variable on the master side of the interface
C++ Type:std::vector
Options:
Description:The name of the variable on the master side of the interface
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
### Required Parameters
• neighbor_variableThe name of the variable on the slave side of the interface. By default the same variable name is used for the slave side
C++ Type:std::vector
Options:
Description:The name of the variable on the slave side of the interface. By default the same variable name is used for the slave side
• execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM TRANSFER
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
• interface_value_typeaverageType of value we want to compute
Default:average
C++ Type:MooseEnum
Options:average jump_master_minus_slave jump_slave_minus_master jump_abs master slave
Description:Type of value we want to compute
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
• allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
| 2019-05-24T03:28:40 |
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https://www.federalreserve.gov/newsevents/speech/brainard20210224a.htm
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February 24, 2021
### How Should We Think about Full Employment in the Federal Reserve's Dual Mandate?
Governor Lael Brainard
At the Ec10, Principles of Economics, Lecture, Faculty of Arts and Sciences, Harvard University, Cambridge, Massachusetts (via webcast)
I want to thank Jason Furman and David Laibson for inviting me to join your economics class. I often found it difficult in introductory economics to connect the abstract concepts in the textbooks to the real-world issues I cared about. So the one message I hope you remember from today is that economics provides powerful tools to enable you to analyze and affect the issues that matter most to you.1
With jobs down by 10 million relative to pre-pandemic levels, one issue that matters fundamentally to all of us is achieving full employment. So today I want to talk about both the Federal Reserve's responsibilities with regard to full employment and different approaches to assessing where we are relative to that goal.
The belief that the federal government has a responsibility for full employment has its roots in the Great Depression. It was given statutory expression at the end of the Second World War when policymakers and legislators feared that the millions of American soldiers returning to the labor market would face Depression-era conditions.2 In the Employment Act of 1946, the Congress directed the federal government as a whole to pursue "conditions under which there will be afforded useful employment for those able, willing, and seeking work, and to promote maximum employment, production, and purchasing power."3
The postwar policy discussion raised important issues surrounding the definition and measurement of full employment. In 1950, the Review of Economics and Statistics published a symposium titled "How Much Unemployment?" which debated the accuracy of the Census Bureau's value for unemployment.4 Dr. Palmer was a critical contributor to the symposium. Palmer was a professor at Wharton, a fellow of the American Statistical Association, a worldwide expert on manpower and labor mobility, and a consultant with the Office of Statistical Standards.5 She argued that "a single figure of unemployment, regardless of how it is defined or derived, is inadequate as a basis for selection among [policy] programs. Inherent in the phenomena being measured are so many degrees and kinds of labor force activity that no single definition or classification can adequately summate them."6
With concerns about employment again on the rise, in 1976, Senator Hubert Humphrey joined with Congressman Augustus Hawkins to sponsor legislation promoting full employment.7 An amendment to the Federal Reserve Act in 1977 specifically assigned monetary policy responsibility for promoting "the goals of maximum employment, stable prices, and moderate long-term interest rates," commonly referred to as the dual mandate.8 This amendment was followed by the Humphrey-Hawkins Full Employment and Balanced Growth Act, passed in 1978, requiring that the Federal Reserve regularly report to the Congress on how monetary policy was supporting the goals of the act.9
Congressman Hawkins was a prominent advocate of full employment, emphasizing its importance not only for providing a job to every American seeking work, but also for reducing poverty, inequality, discrimination, and crime and improving the quality of life of all people.10 A congressman from southern California, Hawkins was one of the founders of the Congressional Black Caucus and played a major role in the drafting of the Civil Rights Act of 1964. He was also an undergraduate economics major.
Hawkins's views were influenced by his experience representing the Watts neighborhood in Los Angeles, where depression levels of joblessness persisted even when the nation overall was experiencing good times. He was also influenced by the work of economists such as Robert Browne and Bernard Anderson, which highlighted the persistent disparity between Black and white employment and the connection between elevated Black unemployment and economic challenges facing Black communities.11 Hawkins emphasized that "without genuine full employment it would be impossible to eliminate racial discrimination in the provision of job opportunities."12 The Humphrey-Hawkins Act noted that "increasing job opportunities and full employment would greatly contribute to the elimination of discrimination based upon sex, age, race, color, religion, national origin, handicap, or other improper factors."13
The centrality of achieving full employment for all Americans is as pressing today as it was in 1930, 1946, and 1977. The measurement challenges highlighted by Dr. Gladys Palmer and the racial disparities highlighted by Robert Browne and Bernard Anderson are just as relevant in today's economy. And the statutory dual mandate assigned to monetary policy has ensured an unwavering, strong focus on maximum employment as well as price stability at the Federal Reserve in research and measurement no less than policymaking.
The Federal Reserve recently concluded a review of our monetary policy framework, which included extensive outreach to a broad range of people over the course of 2019. In 14 Fed Listens events in communities around the country, we heard testimonials that would have sounded strikingly familiar to Congressman Hawkins. At a time when the national headline unemployment rate was at a multidecade low, community and labor representatives and educators noted "it's always a recession" in their communities.14 They challenged whether the overall economy could be characterized as at "full employment" while unemployment remained in the double digits in their communities.
Reflecting this input, and in light of persistently below-target inflation, low equilibrium interest rates, and low sensitivity of inflation to resource utilization, we made several important changes to the monetary policy framework. Two changes have particular relevance for the employment leg of the dual mandate.15 The new framework calls for monetary policy to seek to eliminate shortfalls of employment from its maximum level, in contrast to the previous approach that called for policy to minimize deviations when employment is too high as well as too low. The new framework also defines the maximum level of employment as a broad-based and inclusive goal assessed through a wide range of indicators.
So how should we assess this broad-based and inclusive concept of maximum employment? When discussing aggregate indicators about the labor market, people tend to focus on the headline U-3 measure of the unemployment rate.16 Although the unemployment rate is a very informative aggregate indicator, it provides only one narrow measure of where the labor market is relative to maximum employment. Recalling Gladys Palmer's dictum, I would not recommend relying on any single indicator, but rather consulting a variety of indicators that together provide a holistic picture of where we are relative to full employment.
So let us start by seeing what insights we gain by disaggregating the unemployment data into different groups of workers. The unemployment rate has improved very rapidly from its peak of 14.8 percent last April to 6.3 percent today. But this number is closer to 6.8 percent when taking into account a substantial number of people on temporary layoff, who have been misclassified as "employed but on unpaid absence" but instead should be counted as unemployed." 17
Disaggregating the overall unemployment rate reveals that workers in the lowest wage quartile face Depression-era rates of unemployment of around 23 percent.18 In part, this rate likely reflects the concentration of lower-wage jobs in service industries that are strongly reliant on in-person contact, or at least in-person work, while a larger proportion of higher-wage jobs are currently being performed remotely or with reduced levels of in-person contact.
There is also important information in the disaggregation of unemployment by different racial and ethnic groups. Figure 1 shows the prime-age unemployment rate overall and on a disaggregated basis.19 There are notable persistent gaps between different racial and ethnic groups, and the sizes of those gaps tend to vary over the business cycle.
For example, historically, the ratio of the Black unemployment rate to the white unemployment rate is around 2 for prime-age workers. On average, a 1 percentage point increase in the white unemployment rate is accompanied by a 2 percentage point increase in the Black unemployment rate. This gap narrows considerably the longer an expansion progresses. At the beginning of 2015, a time when many economists believed the overall unemployment rate had reached its "normal" rate, the gap between the Black and white prime-age unemployment rates stood just under 5 percentage points, roughly at its average level since 1972. By September 2019, that gap had reached a historical minimum of 1.7 percentage points, and the gap between the Hispanic and white prime-age unemployment rates had fallen to 0.3 percentage point.
The unemployment gaps between racial and ethnic groups widened again during the pandemic. Currently, for prime-age individuals, the gaps between the white unemployment rate and the Black and Hispanic unemployment rates are roughly 4 percentage points and 3 percentage points, respectively.
The unemployment rate obscures important information about people leaving and entering the workforce. Each adult in the population is classified as employed, unemployed, or not in the labor force. The unemployment rate is the number of individuals who are not currently working but are actively looking for a job, divided by the size of the labor force, which includes only those people who are either working or actively seeking work:
$$U = {Unemployed \over Labor Force}.$$
Changes in labor force participation contain important information about the strength of the labor market that is not captured in the unemployment rate. The labor force participation rate (LFPR) is the number of individuals who are either working or are seeking work, divided by the working-age population:
$$LFPR = {Labor Force \over Population}.$$
When we take into consideration the more than 4 million workers who have left the labor force since the pandemic started, as well as misclassification, the unemployment rate is close to 10 percent currently—much higher than the headline unemployment rate of 6.3 percent—and similar to the peak unemployment rate following the financial crisis. This is shown in Figure 2.
A decline in participation by prime-age women is an important contributor to the overall participation decline. Some portion of the decline reflects the increase in caregiving work at home with the shutdown of schools and daycare due to COVID-19. On average over the period from November 2020 to January 2021, the fraction of prime-age respondents with children aged 6 to 17 who were out of the labor force for caregiving was about 14 percent, up 1-3/4 percentage points from a year earlier. For mothers, the fraction who were out of the labor force for caregiving was 22.8 percent, an increase of 2.4 percentage points from a year earlier, while for fathers the fraction was 2.2 percent, an increase of about 0.6 percentage point.20 If not soon reversed, the decline in the participation rate for prime‑age women could have longer-term implications for household incomes and potential growth.21
While there are long-term structural trends in participation, such as population aging, there are also cyclical dynamics that are important for our assessment of maximum employment. The two panels in figure 3 show prime-age unemployment and labor force participation over the previous recession and recovery. Following the onset of the global financial crisis, as the number of unemployed people was rising, the size of the labor force was also contracting, pushing the numerator of the unemployment rate up and the denominator down. When the unemployment rate started to decline at the end of 2010, this decline in part reflected unemployed people dropping out of the labor force through 2013. As the labor market healed further, prime-age LFPR leveled out and started to increase at the end of 2015. The subsequent seemingly modest decline in the unemployment rate from 4.3 at the end of 2015 to 3 percent at the end of 2019 was much more significant, taking into account that more than 3-1/2 million prime-age workers joined or rejoined the labor force during that period.
This brings me to figure 4 and the employment-to-population (EPOP) ratio, which is the number of individuals employed divided by the working-age population:
$$EPOP = {Employed \over Population}.$$
The EPOP ratio synthesizes the information contained in the unemployment rate and LFPR. For instance, as you can see in figure 4, a decline in participation almost entirely offset the decline in unemployment in 2010 and 2011, leaving the prime-age EPOP ratio essentially flat at 75 percent. The EPOP ratio then improved steadily over the subsequent seven years, moving up to 80.4 percent in late 2019.
As the effects of the virus and measures to combat it took hold of the economy, the EPOP ratio plummeted last April, and, after staging a sharp but partial recovery, improvements in the prime-age EPOP ratio have moderated in recent months. A glance back at figure 3 shows that the reductions in employment last spring were accompanied by many prime-age workers leaving the labor force, and the participation rate among prime-age workers has declined further since last May. The prime-age EPOP ratio currently stands at 76.4 percent, well below the 80 percent level that was reached during each of the past two expansions.
Figure 5 shows the patterns in the EPOP ratio for prime-age workers in different racial and ethnic groups.22 Following the Global Financial Crisis, the Black–white EPOP gap opened to more than 10 percentage points in mid-2011 before shrinking to under 5 percentage points as labor markets tightened further during 2018 and 2019. In contrast, the Hispanic–white EPOP gap was smaller than the Black–white gap, and it fluctuated in a much narrower range over the business cycle.
During the pandemic, labor market performance as shown by the EPOP measure has been fairly similar for Black and Hispanic prime-age workers and markedly worse than for white workers. Research indicates that Black and Hispanic workers are overrepresented in industries particularly hard hit by the pandemic, such as hotels and restaurants.23 It also shows that Black and Hispanic workers are overrepresented in essential industries at lower pay, and that they are significantly less likely to be able to telework.24
Figure 6 shows one more EPOP snapshot, this time for prime-age women overall, as well as for Black and white subgroups. Following the financial crisis, a gap opened up between the prime-age EPOP ratios for Black and white women. That gap closed in 2015, and employment for both groups surged over the next four years. Between January 2015 and February 2020, the EPOP ratios for white and Black prime-age women each increased roughly 5 percentage points, reaching historical highs in the months just before the onset of the pandemic. As the pandemic took hold in the subsequent months, once again a gap opened up between the EPOP ratios for white and Black women, though the current gap of roughly 2 percentage points is not as large as in the previous downturn.
While the EPOP ratio is a strong indicator of the extensive margin in the labor market, or how many people are working, there is also important information in the intensive margin—that is, how much work each person is doing. The part-time for economic reasons (PTER) indicator shown in figure 7 measures those who are working part time because they are unable to find a full-time job or whose hours have been reduced and who would prefer full-time employment.25 This indicator is an important measure of labor market slack, which tends to jump rapidly during recessions and improve more slowly than headline unemployment during recoveries. PTER jumped during the financial crisis as workers who were unable to secure full-time employment moved to part-time work, accounting for more than half of the increase in involuntary part-time work during 2008.26
Today there are 6.0 million people working part time who would prefer full-time work, up 1.6 million relative to the pre-COVID level. The Bureau of Labor Statistics has six alternative measures of labor underutilization, the most expansive of which is the U-6 measures, which adds to the headline unemployment rate those employed part time for economic reasons, along with all persons marginally attached to the labor force as a percentage of the civilian labor force. The U-6 measure stood at 11.1 percent in January.27
Figure 8 shows the large amount of cyclical variation across PTER for several racial and ethnic groups. The incidence of involuntary part-time work was especially notable for Hispanic workers at the trough of the Great Recession, nearing 12 percent of employment and almost double its rate before the recession. This gap between Hispanic and white PTER narrowed substantially during the recovery and fell to just above 1 percentage point in the summer of 2019. Research indicates that gaps in involuntary part-time employment rates remain for Blacks, as well as Hispanics, relative to whites after controlling for age, education, marital status, and state of residence, although education and occupation can explain a portion of the gap for Hispanics.28
Before concluding, I would like to point to two other labor market indicators that provide useful evidence of the extent of labor market slack. The quits rate, shown in figure 9, is a measure of voluntary separations that provides information about how confident people are that they will be successful in finding a new job they prefer and, relatedly, of how aggressively firms are pursuing talent.29 Research indicates that the quits rate and wage growth are highly correlated, suggesting that these voluntary job-to-job transitions reflect individuals moving up a "job ladder" to higher-paying jobs.30 The quits rate fell rapidly during the 2008 recession as workers' options became more limited, then recovered slowly, only surpassing its pre–financial crisis level of roughly 2.5 percent in 2018. In contrast, the bounceback from the pandemic trough has been much more robust, with quits already reaching 2.6 percent in December. As undergraduates, the quits rate may soon become relevant to you, as research indicates that job-to-job transitions are most frequent for young workers and that this measure has trended down in recent decades.31
Finally, measures of compensation are closely monitored for evidence on labor market slack. Figure 10 shows the 12-month growth rate of the employment cost index for total compensation for private industry workers (ECI). Just as quits fell during the Great Recession, so did the ECI. About two years after the onset of the financial crisis, the ECI moved up slightly in 2010 and then remained essentially flat at an annual growth rate of 2 percent over a five-year period between 2010 and 2015. There was a pickup of the ECI at the end of 2015, which coincided with the turning point in the prime-age LFPR. Even so, the growth rate of the ECI did not return to the levels experienced before 2008.
Unlike the other indicators I have discussed, the pandemic appears to have made fairly little imprint on the ECI. The ECI declined slightly over the second and third quarters of 2020 and moved up in the fourth quarter. It is difficult to draw any firm conclusions from these developments; while the ECI is not as susceptible to composition effects as some other measures, smaller composition effects are still possible.32
So, what conclusions can we draw from this high-level overview of a variety of labor market indicators, their current readings, and their performance in the previous expansion? First, the headline unemployment rate by itself can obscure important dimensions of labor market slack, so it is important to heed Dr. Palmer's dictum and consult a broad set of aggregated and disaggregated measures. Second, groups that have faced the greatest challenges often make important labor market gains late in an expansion, consistent with Augustus Hawkins's emphasis on the importance of full employment for all Americans.
So where does this leave us today? Jobs are still down by 10 million relative to pre-COVID levels, and COVID has disproportionately harmed certain sectors, groups of workers, businesses, and states and localities, leading to a K-shaped recovery. The fiscal support that is enacted and expected will provide assistance to vulnerable households, small businesses, and localities and a significant boost to activity when vaccinations are sufficiently widespread to support a reopening of in-person services. Monetary policy will continue to provide support by keeping borrowing costs for households and businesses low.
The assessment of shortfalls from broad-based and inclusive maximum employment will be a critical guidepost for monetary policy, alongside indicators of realized and expected inflation. The Federal Open Market Committee has said it expects the policy rate to remain in the current target range until labor market conditions have reached levels consistent with the Committee's assessments of maximum employment and inflation has risen to 2 percent and is on track to moderately exceed 2 percent for some time. It has noted that asset purchases will continue at least at the current pace until substantial further progress has been made toward the maximum-employment and inflation goals.
In assessing substantial further progress, I will be looking for sustained improvements in realized and expected inflation and examining a range of indicators to assess shortfalls from maximum employment. I will be looking for indicators that show the healing in the labor market is broad based, rather than focusing on the narrow aggregate U-3 unemployment rate, in light of the significant decline in labor force participation since the spread of COVID and the extremely elevated unemployment rate for workers in the lowest wage quartile.
For nearly four decades, monetary policy was guided by a strong presumption that accommodation should be reduced preemptively when the unemployment rate nears its normal rate in anticipation that high inflation would otherwise soon follow. But changes in economic relationships over the past decade have led trend inflation to run persistently somewhat below target and inflation to be relatively insensitive to resource utilization. With these changes, our new monetary policy framework recognizes that removing accommodation preemptively as headline unemployment reaches low levels in anticipation of inflationary pressures that may not materialize may result in an unwarranted loss of opportunity for many Americans. It may curtail progress for racial and ethnic groups that have faced systemic challenges in the labor force, which is particularly salient in light of recent research indicating that additional labor market tightening is especially beneficial for these groups when it occurs in already tight labor markets, compared with earlier in the labor market cycle.33 Instead, the shortfalls approach means that the labor market will be able to continue to improve absent high inflationary pressures or an unmooring of inflation expectations to the upside.
Inflation remains very low, and although various measures of inflation expectations have picked up recently, they remain within their recent historical ranges. PCE (personal consumption expenditures) inflation may temporarily rise to or above 2 percent on a 12-month basis in a few months when the low March and April price readings from last year fall out of the 12-month calculation, and we could see transitory inflationary pressures reflecting imbalances if there is a surge of demand that outstrips supply in certain sectors when the economy opens back up. While I will carefully monitor inflation expectations, it will be important to see a sustained improvement in actual inflation to meet our average inflation goal.
Today the economy remains far from our goals in terms of both employment and inflation, and it will take some time to achieve substantial further progress. I look forward to the time when this K-shaped recovery becomes a broad-based and inclusive recovery and when vaccinations are widespread, the services sector springs back to life, and all Americans enjoy the benefits of full employment. I cannot think of a more meaningful time to be studying economics or a more important time to be thinking about the different ways to assess our shared goal of full employment.
1. I am grateful to Kurt Lewis, Mark Carlson, Christopher Nekarda, Edward Nelson, Ivan Vidangos, and Nicholas Zevanove of the Federal Reserve Board for their assistance in preparing these materials. These remarks represent my own views, which do not necessarily represent those of the Federal Reserve Board or the Federal Open Market Committee. Return to text
2. From 1930 to 1940, the unemployment rate averaged 18 percent by one estimate. See G.J. Santoni (1986), "The Employment Act of 1946: Some History Notes," Review (Federal Reserve Bank of St. Louis), vol. 68 (November), pp. 5–16. Return to text
3. The language of the act (quoted text in section 2) is available through FRASER on the Federal Reserve Bank of St. Louis website at https://fraser.stlouisfed.org/title/employment-act-1946-1099. In 1945, the staff at the Federal Reserve Board wrote a series of Postwar Economic Studies on the economic effects of demobilization. The first study notes that "jobs are the main channel through which national welfare reaches the individual." See Emanuel Alexandrovich Goldenweiser (1945), "Jobs," in Frank R. Garfield, Emanuel Alexandrovich Goldenweiser, Everett Einar Hagen, and Board of Governors of the Federal Reserve System, eds., Jobs, Production, and Living Standards (Baltimore: Waverly Press), p. 1. Return to text
4. For an introduction to the symposium, see Seymour E. Harris (1950), "Introduction," Review of Economics and Statistics, vol. 32 (February), p. 49. Return to text
5. See Gertrude Bancroft McNally (1967), "Gladys L. Palmer, 1895–1967," American Statistician, vol. 21 (December), p. 35. Return to text
6. See Gladys L. Palmer (1950), "Unemployment Statistics as a Basis for Employment Policy," Review of Economics and Statistics, vol. 32 (February), pp. 70–74 (quoted text on p. 70). Return to text
7. For a discussion of the evolution of the Federal Reserve's statutory responsibilities, see Ben S. Bernanke (2013), "A Century of U.S. Central Banking: Goals, Frameworks, Accountability," speech delivered at "The First 100 Years of the Federal Reserve: The Policy Record, Lessons Learned, and Prospects for the Future," a conference sponsored by the National Bureau of Economic Research, Cambridge, Mass., July 10. Return to text
8. As noted by Frederic Mishkin, "Because long-term interest rates can remain low only in a stable macroeconomic environment, these goals are often referred to as the dual mandate; that is, the Federal Reserve seeks to promote the two coequal objectives of maximum employment and price stability." See Frederic S. Mishkin (2007) "Monetary Policy and the Dual Mandate," speech delivered at Bridgewater College, Bridgewater, Va., April 10 (quoted text in paragraph 3). Return to text
9. A few other central banks have an explicit employment mandate that has the same weight as their price-stability mandate, such as the Reserve Bank of Australia and the Reserve Bank of New Zealand. For most central banks, price stability is the single objective of monetary policy (Bank of Canada, Riksbank, and Bank of Japan) or the priority objective (for example, European Central Bank and Bank of England). Economic research suggests that inflation outcomes have been as good, or better, in the United States compared with jurisdictions in which employment either is not a monetary policy objective or is subordinate to price stability. See Eric S. Rosengren (2014), "Should Full Employment Be a Mandate for Central Banks?" Journal of Money, Credit and Banking, vol. 46, suppl. 2 (October), pp. 169–82. Return to text
10. See Helen Lachs Ginsburg (2012), "Historical Amnesia: The Humphrey-Hawkins Act, Full Employment and Employment as a Right," Review of Black Political Economy, vol. 39 (October), pp.121–36. Return to text
11. See Bernard E. Anderson (2008), "Robert Browne and Full Employment," Review of Black Political Economy, vol. 35 (January), pp. 91–101. Return to text
12. See Augustus F. Hawkins (1975), "Full Employment to Meet America's Needs," Challenge, vol. 18 (November/December), pp. 20–28. Return to text
13. The complete original language of the act (quoted text in section 2B (4)) is available through FRASER on the Federal Reserve Bank of St. Louis website at https://fraser.stlouisfed.org/title/full-employment-balanced-growth-act-humphrey-hawkins-act-1034. Return to text
14. See Board of Governors of the Federal Reserve System (2020), Fed Listens: Perspectives from the Public (PDF) (Washington: Board of Governors, June). Return to text
15. See Lael Brainard (2021), "Full Employment in the New Monetary Policy Framework," speech delivered at the Inaugural Mike McCracken Lecture on Full Employment, sponsored by the Canadian Association for Business Economics (via webcast), January 13. Return to text
16. This measure is the number of unemployed persons divided by the size of the labor force. People in both categories must be 16 years of age or older. Return to text
17. Since March 2020, the Bureau of Labor Statistics (BLS) has instructed its household survey interviewers to classify employed persons who are absent from work due to temporary, pandemic-related business closures or cutbacks as being unemployed on temporary layoff. During this period, however, some workers affected by the pandemic who should have been classified as unemployed on temporary layoff were instead misclassified as employed but not at work. Each month, the BLS provides an estimate of the likely size of this effect on the unemployment rate. More information is available on the BLS website at https://www.bls.gov/covid19/employment-situation-covid19-faq-january-2021.htm. Return to text
18. For more information on this analysis, see the box "Disparities in Job Loss during the Pandemic" in Board of Governors of the Federal Reserve System (2021), Monetary Policy Report (Washington: Board of Governors, February), pp. 12–14. Return to text
19. Prime age refers to ages 25 to 54. I focus on this age range because of how important those working years are for individuals' overall careers and because labor market metrics calculated over workers in this age range help control for the aging of the population. Return to text
20. The percentages are staff calculations based on the microdata from the January Current Population Survey. For more information on this analysis, see the box "Disparities in Job Loss during the Pandemic" in Board of Governors, Monetary Policy Report, pp. 12–14, in note 19. Return to text
21. See Olivia Lofton, Nicolas Petrosky-Nadeau, and Lily Seitelman (2021) "Parents in a Pandemic Labor Market," Federal Reserve Bank of San Francisco Working Paper 2021-04. (February) (2020), and Lael Brainard, "Achieving a Broad-Based and Inclusive Recovery," speech delivered at "Post-COVID—Policy Challenges for the Global Economy," Society of Professional Economists Annual Online Conference, October 21. Return to text
22. The Bureau of Labor Statistics makes disaggregated EPOP data from the Current Population Survey available through online tools found on the bureau's website at https://www.bls.gov/data. Return to text
23. See Connor Maxwell and Danyelle Solomon (2020), "The Economic Fallout of the Coronavirus for People of Color," Center for American Progress, April 14. Return to text
24. See Hye Jin Rho, Hayley Brown, and Shawn Fremstad (2020), A Basic Demographic Profile of Workers in Frontline Industries (PDF) (Washington: Center for Economic and Policy Research, April). Return to text
25. According to the Bureau of Labor Statistics, this category includes people who gave an economic reason when asked why they worked 1 to 34 hours during the survey's reference week. Their usual hours of work may be either full or part time. Economic reasons include the following: slack work, unfavorable business conditions, inability to find full-time work, and seasonal declines in demand. People who usually work part time and were at work part time during the reference week must indicate that they want and are available for full-time work to be classified as part time for economic reasons. Return to text
26. For more information, see Tomaz Cajner, Dennis Mawhirter, Christopher Nekarda, and David Ratner (2014), "Why Is Involuntary Part-Time Work Elevated?" FEDS Notes (Washington: Board of Governors of the Federal Reserve System, April 14). Return to text
27. Persons marginally attached to the labor force are those who currently are neither working nor looking for work but indicate that they want and are available for a job and have looked for work sometime in the past 12 months. Return to text
28. See Tomaz Cajner, Tyler Radler, David Ratner, and Ivan Vidangos (2017), "Racial Gaps in Labor Market Outcomes in the Last Four Decades and over the Business Cycle (PDF)," Finance and Economics Discussion Series 2017-071 (Washington: Board of Governors of the Federal Reserve System, June). Return to text
29. See the Job Openings and Labor Turnover Survey, which can be found on the Bureau of Labor Statistics website at https://www.bls.gov/jlt/home.htm. Return to text
30. See R. Jason Faberman and Alejandro Justiniano (2015), "Job Switching and Wage Growth," Chicago Fed Letter 337 (Chicago: Federal Reserve Bank of Chicago). Return to text
31. For evidence that job-to-job transition is utilized most when young, and that job dynamism for the young has declined, see Canyon Bosler and Nicolas Petrosky-Nadeau (2016), "Job-to-Job Transitions in an Evolving Labor Market," FRBSF Economic Letter 2016-34 (San Francisco: Federal Reserve Bank of San Francisco, November). Return to text
32. For example, the ECI data are assembled at an industry-occupation level of granularity. If at the outset of the pandemic, firms in a particular industry laid off their newest, lowest-paid staff in a particular occupational category first, the compositional change could lead compensation in that industry and occupation to increase on average. Return to text
33. See Stephanie R. Aaronson, Mary C. Daly, William L. Wascher, and David W. Wilcox (2019), "Okun Revisited: Who Benefits Most from a Strong Economy? (PDF)" Brookings Papers on Economic Activity, Spring, pp. 333–75. Return to text
Last Update: February 24, 2021
| 2021-05-18T08:59:46 |
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http://jde27.uk/blog/horikawa-surfaces.html
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Horikawa surfaces
[2018-02-26 Mon]
Mostly for my own convenience, here is an overview of the geometry of Horikawa surfaces (because I will forget most of this).
Horikawa's work
A Horikawa surface is a minimal surface of general type with geometric genus $$p_g\geq 3$$ which lies on the Noether line $$c_1^2=2p_g-4$$. These all have irregularity zero. This means that the Chern numbers are given in terms of $$p_g$$ by $c_1^2=2p_g-4,\quad c_2=10p_g+16$ These surfaces were studied extensively by Horikawa. Here is a summary of what he proved. Let $$n=p_g-1$$.
• The canonical map $$\Phi_K\colon X\to\mathbf{CP}^n$$ has image a surface $$W=\Phi_K(X)$$ of degree $$n-1$$ in $$\mathbf{CP}^n$$ (Lemma 1.1). Write $$f\colon X\to W$$ for the corestriction; then $$f$$ is a double branched cover. The ramification locus $$R\subset X$$ of $$f$$ satisfies $$K_X=f^*K_W+R$$; the branch locus $$B\subset W$$ is the pushforward $$f_*R$$ and has no multiple component.
• The image $$W$$ of $$f$$ is one of the following (Lemma 1.2):
• "Type (\infty)": ($$n=2$$) the whole of $$\mathbf{CP}^2$$ or ($$n=5$$) the quadratic Veronese surface $$\mathbf{CP}^2\subset\mathbf{CP}^5$$.
• "Type (d)": ($$n\geq 3$$) a Hirzebruch surface $$\mathbf{F}_d$$ where $$d+3\leq n$$ and $$n-d-3$$ is even, embedded into $$\mathbf{CP}^n$$ via the linear system $$\left|\Delta_0+\frac{n-1+d}{2}\Gamma\right|$$ where $$\Gamma$$ is a fibre of $$\mathbf{F}_d\to\mathbf{CP}^1$$ and $$\Delta_0$$ is the unique section with square $$-d$$. In fact, we will see below that $$n\geq\max(d+3,2d-3)$$.
• "Type (d')": ($$n\geq 3$$) the cone $$C_{n-1}$$ on a rational curve of degree $$d=n-1$$ in $$\mathbf{CP}^{n-1}\subset\mathbf{CP}^n$$. In fact, this is only possible for $$n=3,4,5$$.
We will analyse the possible branch curves case-by-case below.
• If $$K^2$$ is not divisible by 8 ($$p_g\neq 2\mod 4$$) then any two Horikawa surfaces with this value of $$K^2$$ can be connected through deformations (i.e. there is a path in the Gieseker moduli space connecting these surfaces: note that this path may connect different irreducible components of the moduli space, but all surfaces along the path are diffeomorphic).
• If $$k\geq 2$$, $$K^2=8k$$ ($$p_g=4k+2$$) then there are two deformation classes of Horikawa surfaces with this value of $$K^2$$ (Theorem 7.1). These comprise, on the one hand, surfaces of type (d) with $$d$$ even and $$d\leq 2k$$, and, on the other, surfaces of type (2k+2).
• If, moreover, $$k$$ is even, then these surfaces are homotopy equivalent.
• If, instead, $$k$$ is odd, then they are distinguished by the second Stiefel-Whitney class (type $$(2k+2)$$ is spin/has even intersection form, the others are not spin/have odd intersection form).
• Finally (Theorem 4.1), if $$K^2=8$$, then there are two deformation classes: surfaces of type (0) and (2) and surfaces of type (\infty) and (4'). Surfaces from different deformation classes are not homotopy equivalent, distinguished by their second Stiefel-Whitney class.
Type ($$\infty$$)
($$n=2$$) The surface $$W$$ is the whole of $$\mathbf{CP}^2$$; the ramification locus is then homologous to $$4f^*H$$ (as $$K_X=f^*H$$ and $$K_W=-3H$$) so the branch locus $$B$$ is a curve of degree 8 in $$\mathbf{CP}^2$$.
($$n=5$$) The surface $$W$$ is the quadratic Veronese surface $$\mathbf{CP}^2\subset\mathbf{CP}^5$$. We have $$K_X=\Phi_K^*H$$, but $$\Phi_K$$ is the composition of $$f$$ with the inclusion of the (degree 2) Veronese surface, so if $$h$$ is the hyperplane class on $$\mathbf{CP}^2$$ we get $$\Phi_K^*H=2f^*h$$. We also have $$f^*K_W=-3g^*h$$, so $$R=5g^*h$$ and the branch locus $$B$$ is a curve of degree 10.
Type ($$d$$)
($$n\geq 3$$) The surface $$W$$ is a Hirzebruch surface $$\mathbf{F}_d$$ where $$n-d-3$$ is a nonnegative even integer, embedded into $$\mathbf{CP}^n$$ via the linear system $$\left|\Delta_0+\frac{n-1+d}{2}\Gamma\right|$$ where $$\Gamma$$ is a fibre of $$\mathbf{F}_d\to\mathbf{CP}^1$$ and $$\Delta_0$$ is the unique section with square $$-d$$.
In this case, if $$i\colon W\to\mathbf{CP}^n$$ is the inclusion, we have $K_X=\Phi_K^*H=(i\circ f)^*H=f^*\left(\Delta_0+\frac{n-1+d}{2}\Gamma\right)$ and $$K_W=-2\Delta_0-(d+2)\Gamma$$, so $$R=f^*\left(3\Delta_0+\frac{n+3d+3}{2}\Gamma\right)$$. Therefore the branch locus $$B$$ is homologous to $$6\Delta_0+(n+3d+3)\Gamma$$. Note that since $$B$$ has no multiple component, its intersection number with $$\Delta_0$$ must be at least $$-d$$ (it equals $$-d$$ if $$B=\Delta_0$$ and it increases for every other component of $$B$$). This means $$\Delta_0\cdot B=n-3d+3\geq -d$$ or $$d\leq \frac{1}{2}(n+3)$$.
When $$d\leq (n+3)/3$$ the generic curves in the class $$B=6\Delta_0+(n+3+3d)\Gamma$$ are smooth and irreducible. When $$(n+3)/2\geq d>(n+3)/3$$, the generic curves in the class $$B$$ are reducible of the form $$\Delta_0+B_0$$ where $$B_0$$ is an irreducible smooth curve which intersects $$\Delta_0$$ transversely at $$n+3-2d$$ points. In particular, when $$n=2d-3$$, $$\Delta_0$$ and $$B_0$$ are disjoint.
Type ($$d'$$)
($$n\geq 3$$) The surface $$W$$ is the cone $$C_{n-1}$$ on a rational curve of degree $$d=n-1$$ in $$\mathbf{CP}^{n-1}\subset\mathbf{CP}^n$$. In this case, $$f$$ factors through the minimal resolution $$\mathbf{F}_{n-1}\to C_{n-1}$$ (Lemma 1.5). The branch locus in $$\mathbf{F}_{n-1}$$ is homologous to $$6\Delta_0+4n\Gamma$$ and, again, $$\Delta_0\cdot B\geq -(n-1)$$. This means $$n\leq 5$$ (in fact the only possibilities are $$n=3,4,5$$).
Fintushel and Stern on Horikawa surfaces
Fintushel and Stern, in their classic paper on rational blowdown, study a family of Horikawa surfaces they call $$H(N)$$ with $$K^2=2N-6$$. This has $$p_g=N-1$$, so $$n=N-2$$. They take a surface of type (0), which is then a branched cover of $$\mathbf{F}_0$$ with branch locus $$B=6\Delta_0+(N+1)\Gamma$$. They point out that, smoothly, this is the same as taking the branched cover of $$\mathbf{F}_{N-3}$$ branched over $$4(\Delta+\Gamma)+2\Delta_0$$ (where $$\Delta=\Delta_0+(N-3)\Gamma$$ is the class of a positive section). At least this makes sense when $$N$$ is odd so that $$\mathbf{F}_{N-3}$$ is diffeomorphic to $$\mathbf{F}_0$$.
Note that the choice of Hirebruch surface they give would correspond to type (N-3) in Horikawa's terminology, which is actually forbidden (the class $$4(\Delta+\Gamma)+2\Delta_0$$ has no reduced holomorphic representative in $$\mathbf{F}_{N-3}$$ as its intersection with $$\Delta_0$$ is too negative). Nonetheless, this rational blow-down construction does have a complex-geometric interpretation due to Lee and Park. More on this below.
Their motivation for choosing this Hirzebruch surface is that they can find a rational homology ball $$B_{N-2,1}$$ in $$\mathbf{F}_{N-3}$$ whose complement contains the branch curve. One can see this explicitly in an almost toric picture for the Hirzebruch surface:
Figure 1: An almost toric picture of the Hirzebruch surface $$\mathbf{F}_{N-3}$$: we have performed a nodal trade at the bottom left corner so that a neighbourhood of the dashed line is a rational homology ball $$B_{N-2,1}$$ (the numbers $$(N-2,1)$$ can be read off from how the dashed line intersects the sloping edge). Note that for this picture to make sense, we need the length of $$\Gamma$$ to be strictly bigger than 1, otherwise the dashed line (with slope 1) will not intersect the sloping edge at an internal point. The length of the long bottom edge is $$N-2$$.
In the branched double cover we can therefore find two disjoint rational homology balls (note that $$N-2$$ is odd, and $$\pi_1(B_{N-2,1})$$ is cyclic of order $$N-2$$, so the rational homology ball lifts in two different ways to the double cover). Fintushel and Stern prove that the result of rationally blowing down these two rational homology balls in $$H(N)$$ is an elliptic surface $$E(N)$$.
Lee and Park on Horikawa surfaces
In an attempt to understand Fintushel and Stern's construction algebro-geometrically, Lee and Park showed that one can construct Horikawa surfaces via $$\mathbf{Q}$$-Gorenstein smoothing. The idea is that there is a singular surface $$X_N$$ with two Wahl singularities of type $$\frac{1}{(N-2)^2}(1,N-3)$$ such that
• the minimal resolution of $$X_N$$ is an elliptic surface,
• $$X_N$$ is QG-smoothable to a Horikawa surface $$H(N)$$ (in the notation of Subsection FS).
Here is how their construction works:
1. Start with a Hirzebruch surface $$\mathbf{F}_N$$. Let $$f$$ be one of the fibres, let $$\Delta_0$$ be the section with square $$-N$$ and let $$\Delta$$ be the homology class of a section with square $$N$$.
2. Find an irreducible curve $$D\subset\mathbf{F}_N$$ in the linear system $$4\Delta$$ such that:
• $$D$$ intersects $$f$$ at two points $$p$$ and $$q$$; $$D$$ has an $$A_1$$ singularity at $$p$$ and an $$A_{2N-9}$$-singularity at $$q$$. In other words, in local coordinates $$(x,y)$$ at $$p$$ (respectively $$q$$) where $$f=(x=0)$$, $$D$$ looks like $$(y-x)(y+x)=0$$ (respectively $$(y-x^{N-4})(y+x^{N-4})=0$$).
• Blow up $$\mathbf{F}_N$$ at $$p$$ and then repeatedly at $$q$$ to separate the branches of $$D$$. The fibre $$f$$ becomes a $$-2$$-curve (it had square zero and is blown up twice). The exceptional curve of the blow-up at $$q$$ is a string of $$(N-5)$$ $$(-2)$$-curves followed by a $$-1$$-curve.
Here is a picture, with $$D$$ and its proper transform drawn in blue, $$-1$$-spheres drawn dotted, and in red, a configuration of curves which, upon contraction, yields a Wahl singularity of type $$\frac{1}{(N-2)^2}(1,N-3)$$.
1. Let $$Z_N$$ be the blown-up Hirzebruch surface and let $$\tilde{D}$$ denote the proper transform of $$D$$. Let $$E$$ be the double cover of $$Z_N$$ branched over $$\tilde{D}$$. The $$-1$$-spheres become $$-2$$-spheres and there are now two disjoint red chains of spheres. The double cover $$E$$ is an elliptic surface: the preimages of the generic fibres of the Hirzebruch surface are elliptic curves (double-covering the rulings of the Hirzebruch surface branched at the four points of intersection with $$D$$). The union of all $$-2$$-spheres forms an affine $$A_{2N-6}$$ fibre (a cycle of $$-2$$-spheres).
Equivalently, we could have taken the double cover of $$\mathbf{F}_N$$ branched over $$D$$ and then $$E$$ is its minimal resolution. We can compute the invariants of $$E$$: if $$L$$ is a line bundle on $$\mathbf{F}_N$$ whose square is $$\mathcal{O}(D)$$ then $$L^2=4N$$ and $$K_{\mathbf{F}_N}\cdot L=-2N-4$$, so, using the formulae from Barth-Hulek-Peters-Van de Ven (Section 22, Eqs 9): \begin{align} K_E^2&=2K_{\mathbf{F}_N}^2+4K_{\mathbf{F}_N}\cdot L+2L\cdot L\\ &=16-8N-16+8N\\ &=0\\ c_2(E)&=2c_2(\mathbf{F}_N)+2K_{\mathbf{F}_N}\cdot L+4L\cdot L\\ &=8-4N-8+16N\\ &=12N\\ \chi(E)&=2\chi(\mathbf{F}_N)+\frac{1}{2}K_{\mathbf{F}_N}\cdot L+\frac{1}{2}L\cdot L\\ &=2-N-2+2N\\ &=N\\ p_g&=p_g(\mathbf{F}_N)+h^0(\mathbf{F}_N,K_{\mathbf{F}_N}\otimes L)\\ &=0+h^0(\mathbf{F}_N,(N-2)f)\\ &=N-1\\ q(E)&=p_q-\chi+1=0. \end{align}
2. Contracting the red chains of spheres we obtain a singular surface $$X_N$$ which Lee and Park prove admits a $$\mathbf{Q}$$-Gorenstein smoothing. Indeed, if we contract the spheres in $$Z_N$$, we get a singular surface $$Y_N$$ which is QG-smoothable; the smoothing of $$X_N$$ is obtained by taking a fibrewise branched double cover of this QG-smoothing of $$Y_N$$.
The most interesting part of this is that the singular surface obtained by contracting only one of the two red chains does not admit a $$\mathbf{Q}$$-Gorenstein smoothing. Indeed, Fintushel and Stern already pointed out that the smooth 4-manifold (in their paper called $$Y(N)$$) obtained by rationally blowing down one of the chains (which would be a model for this smoothing) admits no complex structure (Corollary 7.5):
• it is minimal (by examining its Donaldson invariants),
• it has $$c_1^2=N-3$$ and $$c_2=11N+3$$, so it is neither an elliptic surface (since $$c_1^2$$ is positive) nor a surface of general type (since the Chern numbers violate Noether's inequality), but its geometric genus is $$N-1$$ which is positive, so that exhausts the possibilities for a minimal complex surface with these invariants (by the Enriques-Kodaira classification).
Note that the surface $$X_N$$ is KSBA-stable (in other words, $$K_{X_N}$$ is ample). To see this, we appeal to the Nakai-Moishezon/Kleiman criterion: suppose that there is an irreducible curve $$C'\subset X_N$$ such that $$K_{X_N}\cdot C'\leq 0$$ and let $$C$$ be its proper transform in $$E$$. We have $K_{X_N}\cdot C'=K_E\cdot C-\sum a_jE_j\cdot C-\sum a_jE'_j\cdot C,$ where $$E_1,\ldots,E_{N-3}$$ and $$E'_1,\ldots,E'_{N-3}$$ are the Wahl strings and $$a_j$$ are the discrepancies (if $$E_1^2=-N$$, $$E_j^2=-2$$ for $$j\geq 2$$ then $$a_1=-(N-2)/(N-1)$$, $$a_2=-(N-3)/(N-1)$$,... $$a_1=-1/(N-1)$$). We also have $$K_E\cdot C\geq 0$$ with equality if and only if $$C$$ is contained in a fibre of the elliptic fibration. All the terms in $$K_{X_N}\cdot C'$$ are therefore nonnegative. Moreover, they cannot all vanish: if $$K_E\cdot C=0$$ then $$C$$ is contained in a fibre and so it either:
• intersects the sections $$E_1$$ and $$E'_1$$ positively, or
• coincides with one of the double covers of a $$-1$$-sphere, and hence intersects $$E_2$$ and $$E'_2$$ or $$E_{N-3}$$ and $$E'_{N-3}$$ positively.
In either case, there is a positive term in $$K_{X_N}\cdot C$$.
The famous open problem
The "most interesting case" from the points of view of low-dimensional topology is the case $$K^2=16\ell$$, $$p_g=8\ell+2$$ ($$n=8\ell+1$$). In this case we have two deformation classes of Horikawa surfaces, and we know that the corresponding surfaces are homotopy equivalent. In fact, all known smooth 4-manifold invariants fail to distinguish them, and it is a tantalising open problem to determine whether or not they are diffeomorphic.
• One (type (0)) is given by the branched double cover of $$\mathbf{F}_0=S^2\times S^2$$ branched along a smooth, connected curve in the homology class $$6\Delta_0+(n+3)\Gamma$$. In Fintushel-Stern notation from the previous subsection, this is $$H(8\ell+3)$$.
• The other (type (4\ell+2)) is a branched cover of $$\mathbf{F}_{4\ell+2}$$ branched over a disconnected curve $$\Delta_0\cup B_0$$ where $$B_0=5(\Delta_0+(4\ell+2)\Gamma)=5\Delta$$.
One can also take the canonical symplectic form on these and ask if they are symplectomorphic. The answer is not known; see Auroux's paper on Horikawa surfaces for more discussion about this symplectic version of the question focusing on the smallest case $$\ell=1$$, $$K^2=16$$.
Comments, corrections and contributions are very welcome; please drop me an email at j.d.evans at lancaster.ac.uk if you have something to share.
CC-BY-SA 4.0 Jonny Evans.
| 2020-09-24T09:02:39 |
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|
https://wiki.bnl.gov/rhicspin/Asym_versions
|
# Asym versions
This page has not been updated for a long time because the development of the cnipol had moved to github: https://github.com/rhicspin/cnipol
# To do (proposed)
• enable detector 4 in Yel2 (run.db change...)
• check limits for Gaussian fit of polarization profile
• investigate crashes on earlier data with small number of events, e.g. run 14802.001
• change root tree file creation procedure
• give names to parameters
• add online make process to the overall makefile
• Increase labels font (also move signature up)
• Adjust axis scales: polarization, profile, etc
• Rename RunInfo to MeasurementInfo to reflect the actual (for measurement)
• test online code after changing the compiling procedure
• investigate crashes on 15200.206
# v1.8.8
• Committed revision 1623
# v1.8.0
• In the online part of the code:
• Improved the management of the log file
• The measurement type is now supported and saved in raw data file. Can get it from command line option -T and CDEV
# v1.7.1
• Removed all scale factors from the code. They will be applied directly on the DB results
• Better management of MySQL connections
# v1.6.3
• Added possibility for saving pulser histograms from empty bunches
• Noise and pulser data from empty bunches is subtracted from data from filled bunches
# v1.6.2
• Now save maximum polarization from the P vs I fit in AnaResult
# v1.6.1
• Fixed the bug related to target orientation
# v1.6.0
• Introduced a bug related to target orientation. Some H targets are reported as V ones
• Automatically disable 90 degree detectors for horizontal targets
• Improved control of active and disabled channels
• Added a unique identifier (the suffix option) to allow for easier management of multiple output from the same data analysis
• Added an option to disable channels for specified detectors
# v1.4.1
• The Average TOF length is used to fit the all-channel combined banana data
# v1.4.0
• The average analyzing power is (rougly) scaled back to the level of 100 GeV value. The change is dictated by the scaling to H-jet results. Each polarimeter has its own scale factor
• Added signature to saved plots
• Another attempt to get rid of global variables is made by hiding them in the EventConfig class (aka RunConfig)
• New class RunConfig for storing global run information
• Many good histograms in MAsym...
• Cleaner use of global variable ndelim
# v1.3.13
• Implemented constructors for some of the old structures. Made code much cleaner
# v1.3.11
• Removed the remnants using the text run database (run.db)
• Created an SQL table with run periods for easier tracking of calibration runs and disabled channels/bunches. The corresponding class is MseRunPeriods
• Fixed another bug related to histogram being offset by 1 bin in CnipolProfileHists::Fill
• Redefined the criteria determining the measurement type. Now if the number of step at the same intensity is more than 33% then the measurement is fixed
# v1.3.10
• Implemented communication with MySQL database
• Implemented measurement type. Simple criteria: if 10% of maximum intensity is collected within 1/3 of the total time then the type is sweep, fixed otherwise
• Fixed a division by zero bug in CnipolProfileHists::Fill
• The package now depends on some files containing useful utilities a in local directory ~dsmirnov/root_macros/utils. Not good... Has to be addressed somehow
# v1.3.9
• Restored Igor's changes lost in online/rhic2hbook/ rhic2hbook.f and ramp.kumac
# v1.3.8
• Modified building procedure for online/. It is now compiled with C++ and ROOT libraries. Some improvements in makefiles
• Fixed permissions for root tree output files
• Added more checks for verifying existing calibration files
• Significantly updated the structure of the package, new classes, better management of global varables, simplified makefile
# v1.3.7
• Calculated the R parameter - the ratio of the intensity and polarization profiles
• Added polarization vs intensity histogram/graph in the profiles container
• Constrained the polarization value to be within 0 and 1 in the strip asymmetry fits. The negative polarization values should be taken care of by the phase parameter
• Separated run DB classes: new class DbEntry
• Fixed permissions of the log file stdoe.log such that it is also group writable
• Fixed a bug in fitting the binned beam polarization profile in standardized coordinates
• The offline part of the package (in src/) now uses the same headers as the online part (online/include)
• Added an option to copy the results to the server. See the --copy option
• Changed rectangular cuts to a linearly dependent one for the noise in raw data
• Updated DB file (run.db) so that runs taken with the downstream DAQ outside the tunnel use the appropriate energy calibration files
# v1.3.6
• Default output file permission is 0775. Users within the same group are allowed to overwrite files
• Added profile histograms in unified distance units, i.e. the width of the intensity profile is 1
• Fixed most of the warnings coming from HBOOK routines (const string to char* conversion)
• By default redirected standard output and error streams to a log file (see -l, --log options)
• The --profile mode now also assumes the --target mode as information from the latter is required
• Adjusted timing in online configuration files to move the banana back to the window. Only Y1D is changed. The parameters are now closer to Y2U
• Added Igor's fix in rhicpol to exit gracefully when the stop button in PolarControl is clicked
# v1.3.5
• Minor changes
# v1.3.4
• Minor changes
# v1.3.1
• A new correction factor of 0.823 is now introduced for p-C polarization in both online and offline frameworks
• The plots are now being save automatically at the end of analysis
• Adjusted cuts for BD and YD to cut away the noise in the bottom lower corner of the integration window
• Only saved plots are displayed on the run summary webpage
• In alpha mode fixed a bug
• The output directory has write permission for group
# v1.3.0
• The standard Run9 analyzing power is used to calculate the final polarization at ${\displaystyle {\sqrt {s}}}$ = 500 GeV (i.e. the polarization calculated is NOT scaled by 15% with respect to Run9 values as in the previous release v1.2.0)
# v1.2.0
• The calculated polarization values are scaled down by 15% to address the difference seen between polarization values reported by the H-Jet and pCarbon polarimeters at ${\displaystyle {\sqrt {s}}}$ = 500 GeV in Run9
# v0.0.0
This is a dummy version number for all releases prior to v1.2.0
| 2022-10-05T13:13:07 |
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|
https://www.pnnl.gov/news-media/enriching-science-education-thin-films
|
July 20, 2022
Feature
## Enriching Science Education with Thin Films
Materials scientist Tiffany Kaspar brings PNNL research to the community
PNNL materials scientist Tiffany Kaspar uses a molecular beam epitaxy system to develop and explore ultra-thin films that could have far-reaching effects on a variety of applications.
(Photo by Andrea Starr | Pacific Northwest National Laboratory)
“The instrument,” as it’s called, seems to take up the entire room. The sprawling molecular beam epitaxy (MBE) system is all tubes, bolts, stainless steel components, and air-tight glass. It can create an ultrahigh-vacuum environment, a space nearly devoid of matter, a space similar to that outside the International Space Station.
The main chamber is about the size of a wine barrel and looks as durable as a tank. Tiffany Kaspar, however, makes sure it’s treated with the care befitting an instrument capable of producing high-quality thin films with atomic precision. Knee-high plexiglass surrounds some tubes near the laboratory floor, a precautionary shield created by a colleague. Kaspar values the low-tech device to protect against clumsy feet, especially her own.
Kaspar, a Pacific Northwest National Laboratory (PNNL) materials scientist, was inspecting the MBE instrument one day this spring. Weeks earlier, she and her colleagues had overseen the careful transport of the MBE from a nearby building on PNNL’s Richland campus to its home in the new Energy Sciences Center (ESC).
The instrument is the center of Kaspar’s research universe. Each week she grows perfect crystalline films, a few atoms to a few hundred atoms thick, on a centimeter-wide surface, creating new materials. Kaspar’s work has advanced the discovery and understanding of oxide materials. The thin-film oxide heterostructures have been essential to developments in electronics, quantum computing, and energy production.
“We call it use-inspired research,” said Kaspar. “What we're studying may be very fundamental—the properties of atomically precise films of new materials. But we always have some sort of application in mind as to how these materials could be useful in society.”
From her start on the Richland campus more than 20 years ago, Kaspar has been driven to produce useful science. She’s not necessarily trumpeting the wonders of pulsed laser deposition of epitaxial metallic and metal oxide thin films—her area of expertise (although she does that too). She’s targeting a bigger tent, usually filled with younger faces. It’s the kind of audience that will appreciate seeing a marshmallow puffed large then deflated through the magic of a desktop vacuum chamber. Just maybe, she thinks, her efforts will have as much impact on a young student as she experienced early in life.
## Setting the course in middle school
Kaspar was born not far from the PNNL campus. Her parents were living in Kennewick at the time as her father, a civil engineer, participated in the construction of the cable bridge connecting Pasco and Kennewick. When she was 2, the family moved to Olympia. By her middle school years, they had settled in Arvada, a Denver suburb.
A middle school pond water experiment sparked her interest. “We were able to figure out what was in this jar of stuff that the teacher handed us,” Kaspar said. “We used the skills we had learned over the year to determine the contents. Heating the liquid showed us that first ethanol evaporated off, then water. Salts were left behind. I thought it was fascinating that we could use science to deconstruct a complex mixture into its simple components.”
By junior year of high school, it was a four-way tie for her academic interests: chemistry, physics, English, and history. A teacher with a PhD in chemistry resolved the dilemma by sparking her love of chemistry. “He could’ve taught in college,” Kaspar said, “but found teaching high school students to be rewarding.”
Kaspar earned an undergraduate degree in chemical engineering at the University of Colorado Boulder. While she had a passion for chemistry, she said the engineering major also reflected her concern for job certainty. A couple of years spent assisting graduate students in a laboratory gave her an idea of what it takes to earn a doctoral degree as well as the degree’s career potential. She earned the PhD, also in chemical engineering, at the University of Washington (UW) in Seattle.
Midway through her UW experience, her graduate adviser, J.W. “Bill” Rogers Jr., accepted a management job at PNNL.
“That helped put PNNL on the map for my future career search,” Kaspar said. “Up to that point, I didn’t realize national laboratories existed.”
She started at the Richland lab as a graduate student intern in 2000. After graduation, she remained as a postdoctoral researcher and was hired as a full-time PNNL staff scientist in 2007.
## Growing thin films, one at a time
Colleagues say Kaspar is an expert at growing thin films, carefully adjusting her techniques to achieve different results.
To create a film, Kaspar and colleagues evaporate atoms of metals like iron, titanium, and chromium using immense heat—as high as 1800 degrees Celsius or about 3200 degrees Fahrenheit—near the bottom of the ultraclean MBE chamber. A substrate near the top of the chamber collects the evaporating atoms, creating a crystalline structure that may be no thicker than an atom. One of the most common uses of thin films, made at larger scale, is for computer chip circuitry.
Kaspar “is very patient and systematic in summarizing data,” said Yingge Du, a senior staff scientist in the Materials Group of the Physical and Computational Sciences Directorate. “She pays attention to the details.”
Kaspar has authored or contributed to more than 80 peer-reviewed studies of thin-film creation and characterization.
In a Nano Letters study published in June, Kaspar, the co-lead author, explored the atomic-scale reactions that occur during the deposition of oxide thin films by MBE.
“It can be difficult to measure oxygen diffusion in an oxide because atomically, all oxygen looks the same, whether it has diffused through the oxide crystal lattice or remained stationary,” Kaspar said. “In this study, we achieved greater understanding of the movement of oxygen by experiment with two types of oxygen, each chemically identical but each with different atomic weights.”
Last year, she co-authored another study reporting a new method to measure oxygen diffusion through solids using single crystalline thin films.
“The findings in the study are significant because in order to understand how to grow atomically precise materials, we must understand where and how atoms end up on a predetermined place on a substrate,” said Kaspar. “This will help us control and understand atom deposition.”
## Los Alamos nuclear reactor project
Kaspar’s thin-film expertise also plays a role in a Los Alamos National Laboratory led research project that aims to understand how the extreme conditions encountered by materials in nuclear reactors—radiation, corrosive environments, high stresses, and high temperatures—combine to affect the material properties.
“Her participation is crucial,” said PNNL materials scientist Dan Schreiber, who oversees PNNL’s participation in an Energy Frontier Research Center project called FUTURE (Fundamental Understanding of Transport under Reactor Extremes). The Department of Energy’s (DOE's) Basic Energy Sciences program oversees 41 Energy Frontier Research Center projects in 34 states.
Schreiber has worked with Kaspar since he arrived at the lab in 2011. “She is very methodical in her approach to a problem,” he said. “She approaches it with a very explicit research plan.”
Those characteristics contributed to the DOE selecting her as an official “detailee,” meaning that she provides expert scientific and technical advice to ensure effective management of the Synthesis and Processing Science Program within DOE’s Basic Energy Sciences portfolio.
She also brings her knack for explanation to audiences beyond DOE, with the help of marshmallows.
## A marshmallow whoosh
On a late April day, Kaspar stood behind a display table in the lobby outside her ESC laboratory. The ESC, the $90 million center focused on scientific discovery in chemistry, materials science, and computing, had opened weeks before. On this day, Kaspar was poised in the lobby to help with the groundbreaking festivities for the nearby$75 million Grid Storage Launchpad.
She presented a physics magic trick of sorts that she’d presented many times before. It’s a repeat crowd favorite. Youngsters passing through at PNNL’s Take Our Kids to Work Day have seen it. So have Congressional staff members. Marshmallows are involved. More importantly, so are the basics of an airless chamber.
Kaspar places two marshmallows in a desktop, portable vacuum chamber. She flips a switch to remove air from the chamber. The marshmallows then put on a show. They grow from their modest shape to nearly fill the circumference of the chamber as their internal air pockets expand. These giant marshmallows can’t be enjoyed, though, because the air pressure in the surrounding room is so strong that it’s impossible to remove the clear dome of the airless vacuum chamber. Introducing air back into the chamber, the marshmallows collapse into a shrunken, shriveled shape because their internal air pockets have popped and collapsed.
“Kids love these zombie marshmallows the best,” Kaspar said.
## Contributing to STEM at PNNL
Groundbreaking materials research is Kaspar’s specialty. Conveying science to non-scientists—especially aspiring scientists—is her passion.
Soon after her arrival at PNNL, Kaspar looked for opportunities to work with area students. When PNNL introduced its STEM Ambassadors program, “Tiffany was one of the first persons to raise their hand and say, ‘I want to be part of that,’” said Karen Kniep Blanton, PNNL senior STEM education consultant.
“Tiffany is incredibly dedicated and skilled in sharing her science and work at the lab in engaging and easily understandable ways,” said Blanton. “She is able to adapt what she shares, depending on who is in front of her. So, she’s a hit at Kids Day and her messages equally resonate with sponsors, stakeholders, and other visitors to the lab.”
In 2020, Kaspar was awarded the PNNL Laboratory Director’s Award for Outstanding Contributions to STEM Education: Community Engagement & Outreach. Nomination letters pointed to her track record of science education, including the founding of a Tri-Cities based nonprofit to promote science engagement and outreach in the community as well as staging an annual “Celebration of Science” on Earth Day in 2017, 2018, and 2019 in John Dam Plaza in Richland.
In his nomination letter, PNNL senior research scientist Shuttha Shutthanandan wrote about Kaspar’s outreach efforts.
“I have had the opportunity to work with several scientists and professors,” wrote Shutthanandan, “but I can honestly say that none have exhibited such enthusiasm, devotion, and confidence as Tiffany.”
The award was an honor, Kaspar said, but her participation is “just a part of a larger community effort to introduce the wonder, excitement, and usefulness of science to a broad audience.
“I feel strongly that achieving a large and diverse scientific workforce requires effort all along the talent pipeline, starting with sparking kids’ interest in science from a young age,” she said. “And science won’t thrive in the U.S. unless everyone in the community, regardless of their technical expertise, understands that scientific endeavors underpin almost everything in our daily lives and will enable future U.S. innovation.”
###
About PNNL
Pacific Northwest National Laboratory draws on its distinguishing strengths in chemistry, Earth sciences, biology and data science to advance scientific knowledge and address challenges in sustainable energy and national security. Founded in 1965, PNNL is operated by Battelle for the Department of Energy’s Office of Science, which is the single largest supporter of basic research in the physical sciences in the United States. DOE’s Office of Science is working to address some of the most pressing challenges of our time. For more information, visit https://energy.gov/science. For more information on PNNL, visit PNNL's News Center. Follow us on Twitter, Facebook, LinkedIn and Instagram.
Published: July 20, 2022
| 2022-08-17T07:04:54 |
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|
https://par.nsf.gov/biblio/10361031-return-spin-period-dw-cnc-evidence-new-high-state-outbursts
|
The return of the spin period in DW Cnc and evidence of new high state outbursts
ABSTRACT
DW Cnc is an intermediate polar which has previously been observed in both high and low states. Observations of the high state of DW Cnc have previously revealed a spin period at ∼38.6 min, however, observations from the 2018 to 2019 low state showed no evidence of the spin period. We present results from our analysis of 12 s cadence photometric data collected by Next Generation Transit Survey of DW Cnc during the high state which began in 2019. Following the previously reported suppression of the spin period signal, we identify the return of this signal during the high state, consistent with previous observations of it. We identify this as the restarting of accretion during the high state. We further identified three short outbursts lasting ∼1 d in DW Cnc with a mean recurrence time of ∼60 d and an amplitude of ∼1 mag. These are the first outbursts identified in DW Cnc since 2008. Due to the short nature of these events, we identify them not as a result of accretion instabilities but instead either from instabilities originating from the interaction of the magnetorotational instability in the accretion disc and the magnetic field generated by the white dwarf or the more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
NSF-PAR ID:
10361031
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
510
Issue:
1
Page Range or eLocation-ID:
p. 1002-1009
ISSN:
0035-8711
Publisher:
Oxford University Press
National Science Foundation
##### More Like this
1. Abstract
Since its discovery in 1995, V2400 Ophiuchi (V2400 Oph) has stood apart from most known intermediate polar cataclysmic variables due to its proposed magnetic field strength (9–27 MG) and diskless accretion. To date, the exact accretion mechanism of the system is still unknown, and standard accretion models fail to accurately predict the peculiar behavior of its light curve. We present the K2 Campaign 11 light curve of V2400 Oph recording 74.19 days of photometric data cadenced at 1 minute. The light curve is dominated by aperiodic flickering and quasiperiodic oscillations, which make the beat and spin signals inconspicuous on short timescales. Notably, a log–log full power spectrum shows a break frequency at ∼102cycles d−1similar to some disk-fed systems. Through power-spectral analysis, the beat and spin periods are measured as 1003.4 ± 0.2 s and 927.7 ± 0.1 s, respectively. A power spectrum of the entire K2 observation demonstrates beat period dominance. However, time-resolved power spectra reveal a strong dependence between observation length and the dominant frequency of the light curve. For short observations (2–12 hr) the beat, spin, or first beat harmonic can be observed as the dominant periodic signal. Such incoherence and variability indicate a dynamical accretion systemmore »
2. ABSTRACT In 2019 November, MAXI detected an X-ray outburst from the known Be X-ray binary system RX J0209.6−7427 located in the outer wing of the Small Magellanic Cloud. We followed the outburst of the system with NICER, which led to the discovery of X-ray pulsations with a period of 9.3 s. We analysed simultaneous X-ray data obtained with NuSTAR and NICER, allowing us to characterize the spectrum and provide an accurate estimate of its bolometric luminosity. During the outburst, the maximum broad-band X-ray luminosity of the system reached (1–2) × 1039 erg s−1, thus exceeding by about one order of magnitude the Eddington limit for a typical 1.4 M⊙ mass neutron star (NS). Monitoring observations with Fermi/GBM and NICER allowed us to study the spin evolution of the NS and compare it with standard accretion torque models. We found that the NS magnetic field should be of the order of 3 × 1012 G. We conclude that RX J0209.6−7427 exhibited one of the brightest outbursts observed from a Be X-ray binary pulsar in the Magellanic Clouds, reaching similar luminosity level to the 2016 outburst of SMC X-3. Despite the super-Eddington luminosity of RX J0209.6−7427, the NS appears to have only a moderate magnetic field strength.
3. ABSTRACT
We constrain the orbital period (Porb) distribution of low-mass detached main-sequence eclipsing binaries (EBs) with light-curves from the Zwicky Transient Facility (ZTF), which provides a well-understood selection function and sensitivity to faint stars. At short periods (Porb ≲ 2 d), binaries are predicted to evolve significantly due to magnetic braking (MB), which shrinks orbits and ultimately brings detached binaries into contact. The period distribution is thus a sensitive probe of MB. We find that the intrinsic period distribution of low-mass (0.1 ≲ M1/M⊙ < 0.9) binaries is basically flat (${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rm orb}^0$) from Porb = 10 d down to the contact limit. This is strongly inconsistent with predictions of classical MB models based on the Skumanich relation, which are widely used in binary evolution calculations and predict ${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rm orb}^{7/3}$ at short periods. The observed distributions are best reproduced by models in which the magnetic field saturates at short periods with a MB torque that scales roughly as $\dot{J}\propto P_{\rm orb}^{-1}$, as opposed to $\dot{J} \propto P_{\rm orb}^{-3}$ in the standard Skumanich law. We also find no significant difference between the period distributions of binaries containing fully and partially convective stars. Our results confirmmore »
4. (Ed.)
Electroencephalography (EEG) is a popular clinical monitoring tool used for diagnosing brain-related disorders such as epilepsy [1]. As monitoring EEGs in a critical-care setting is an expensive and tedious task, there is a great interest in developing real-time EEG monitoring tools to improve patient care quality and efficiency [2]. However, clinicians require automatic seizure detection tools that provide decisions with at least 75% sensitivity and less than 1 false alarm (FA) per 24 hours [3]. Some commercial tools recently claim to reach such performance levels, including the Olympic Brainz Monitor [4] and Persyst 14 [5]. In this abstract, we describe our efforts to transform a high-performance offline seizure detection system [3] into a low latency real-time or online seizure detection system. An overview of the system is shown in Figure 1. The main difference between an online versus offline system is that an online system should always be causal and has minimum latency which is often defined by domain experts. The offline system, shown in Figure 2, uses two phases of deep learning models with postprocessing [3]. The channel-based long short term memory (LSTM) model (Phase 1 or P1) processes linear frequency cepstral coefficients (LFCC) [6] features from each EEGmore »
5. Abstract
In the first days of WZ Sge-type dwarf nova (DN) outbursts, the 2 : 1 resonance induces a spiral arm structure in the accretion disk, which is observed as early superhumps in optical light curves. We reports on our optical observations of an eclipsing WZ Sge-type DN PNV J00444033+4113068 during its 2021 superoutburst using the 3.8 m Seimei telescope and through the Variable Star Network collaboration. The eclipse analysis showed that its orbital period was 0.055425534(1) d. Our observations confirmed early superhumps with an amplitude of 0.7 mag, the largest amplitude among known WZ Sge-type DNe. More interestingly, its early superhumps became the reddest around their secondary minimum, whereas other WZ Sge-type DNe show the reddest color around the early superhump maximum. The spectrum around the peak of the outburst showed two double-peaked emission lines of He ii 4686 Å and Hα with a peak separation of ≥700 km s−1, supporting a very high-inclination system. With the early superhump mapping, the unique profile and color of the early superhump are successfully reproduced by an accretion disk with a vertically extended double arm structure. Therefore, a large amplitude and a unique color behavior of the early superhumps in PNV J00444033+4113068 can be explained by the 2 : 1 resonance model along with other WZ Sge-type DNe.
| 2023-02-01T05:04:58 |
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|
https://www.federalreserve.gov/econres/notes/feds-notes/use-of-the-federal-reserves-repo-operations-and-changes-in-dealer-balance-sheets-20210806.htm
|
August 06, 2021
Use of the Federal Reserve's repo operations and changes in dealer balance sheets
Mark Carlson, Zack Saravay, and Mary Tian
Before the 2008 financial crisis, the Federal Reserve (Fed) regularly conducted repurchase agreements (repos) in a fairly modest size with primary dealers to adjust the supply of reserves in the banking system and to keep the federal funds rate at the target set by the FOMC.1 During the economic downturn that followed the financial crisis, the Fed engaged in large scale asset purchases in order to provide additional monetary accommodation, and those purchases significantly increased the supply of reserves and eliminated the need for the Fed to engage in repo operations to increase reserves in the system. In 2015, the FOMC started to normalize monetary policy by raising its target for the federal funds rate. As normalization progressed, the Fed began to reduce the size of its balance sheet in 2017, and its total assets declined from about $4.5 trillion in October 2017 to$3.8 trillion in September 2019. While the size of the balance sheet did decrease slowly, the FOMC indicated in January 2019 that it intended to maintain an ample reserves regime that included a sufficient level of reserves such that repo operations would not be necessary to fine-tune the supply of reserves.
In September 2019, funding markets experienced significant pressures and the federal funds rate printed above the FOMC's target range. In response, the Fed re-started daily repo operations with primary dealers to provide additional reserves to the system, helping ensure that the federal funds rate stayed in the FOMC's target range and supporting the smooth functioning of short-term funding markets. In March 2020, the Fed markedly increased the size of its repo operations, especially term repo operations, in response to disruptions to Treasury market functioning that occurred as market participants reacted to news of the spread of the COVID-19 virus.
In this note, we use supervisory data to understand dealer usage of the Fed's repo operations and how those operations affected dealer balance sheets in the pre-COVID versus post-COVID outbreak periods. We find that usage of Fed repo had different implications for overall dealer repo borrowing behavior in the two periods. During the pre-COVID period, dealer borrowing from Fed repo is strongly associated with increases in the dealers' total repo borrowing and we observe only limited substitution away from other funding sources. This pattern switches in the post-COVID period, as borrowing from the Fed is much more closely associated with a partial reduction in borrowing from other sources than in the pre-COVID period, especially during the high stress period in March 2020. (It should be kept in mind however that these results are correlations and our analysis cannot determine whether dealers borrowed more from the Fed because other funding was not available or whether the dealers reduced borrowing from others because they had access to the Fed.) We also find that, in both periods, increased dealer borrowing from the Fed corresponded with an increase in dealer repo lending to their customers, although the majority of such on-lending in the post-COVID period went to institutions affiliated with the dealers, especially their bank affiliates.
Section 1. Review of the changes in Fed repo operations and dealer usage
Overnight funding markets experienced extreme upward pressure on September 16 and 17th 2019; the federal funds rate printed above the FOMC's target range and the secured overnight financing rate (SOFR) jumped more than 2.5 percentage points to above 5 percent.2 In response, the Fed announced that it was re-starting its repo operations; pressures in overnight funding markets quickly abated following the Fed's announcement on September 17 of a $75 billion repo operation.3 Soon thereafter, the Fed began conducting term repo operations in addition to its overnight operations.4 In October, the Federal Reserve announced that it would "conduct term and overnight repurchase agreement operations at least through January of next year to ensure that the supply of reserves remains ample even during periods of sharp increases in non-reserve liabilities, and to mitigate the risk of money market pressures that could adversely affect policy implementation."5 These Fed repo operations have been cited as stabilizing market conditions. Substantial pressures in funding markets materialized suddenly in early March 2020 as concerns about COVID and the economic impacts of efforts to contain it surged. Simultaneously, liquidity in the Treasury market deteriorated markedly. In response, the Fed announced a series of increases in the size of its repo operations, offering several$500 billion one- and three-month term repo operations during the week of March 12, along with continuing its $175 billion limit on overnight operations.6 As shown in Figure 1, dealer take-up in these operations rose significantly in the following days, peaking at$495 billion on March 17, with notable take-up in both overnight and term repo.7 Over the next few weeks, dealers' participation in overnight operations declined, and dealers allowed some of the shorter-term operations to roll off, bringing total usage of the operations to about $200 billion by April. Use of Fed repo declined further in subsequent months as market functioning normalized.8 Figure 1. Federal Reserve Repo Outstanding A notable change during and after the COVID pressures is that Fed repo operations shifted toward a much higher proportion of term repo (blue portions in Figure 1). As funding market liquidity deteriorated in early March, many market participants found it particularly difficult to obtain term financing. In the first few days after the Fed announced expanded term operations on March 12, there was significant take-up in the three-month term repo operations. As liquidity began to improve in the second half of March, dealers' overnight repo with the Fed declined sharply, and by the end of March, the outstanding balance was almost entirely term repo. Despite the reports of severe liquidity problems in the Treasury market during mid-March, the Fed’s expanded repo operations were undersubscribed. Even during the March 17 peak, the total volume of Fed repo was$495 billion, short of the combined limit for overnight and term repo. Because repo with the Fed increases balance sheet size, it may have been the case that dealers were constrained or were reluctant to increase their usage of the repo operations.
Dealers’ usage of Fed repo operations during March was likely also affected by other Fed actions taken to support market functioning. As the Fed ramped up asset purchases and took other actions to stabilize markets, conditions in the Treasury market began to improve. In particular, asset purchases reduced dealers’ Treasury positions, and conditions in repo markets normalized.9 This was most likely another driver of the reduction in take-up in late March.
Section 2. Comparison of dealer behavior between pre- and post-COVID outbreak periods
In this section, we analyze how dealers' use of the Fed's repo was related to their borrowing and lending in the broader repo market during the pre-COVID and the post-COVID outbreak periods. On the liability side, we examine whether dealers used the Fed's repo operations to expand the size of their repo book, to replace borrowing from other sources, or both. On the asset side, we examine, in particular, whether dealers used the increase in funding obtained from the Fed's repo operations to increase their repo lending to their counterparties.
As we consider the behavior of the individual dealers, we limit our analysis to the dealers that provide daily balance sheet data in the FR 2052A report.10 Being able to associate balance sheet developments at a fairly high frequency with changes in repo usage is key for understanding how the Fed's repo operations related to dealer behavior. Although the total volume of Fed repo increased during mid-March, the dealers who used the operations most heavily remained largely stable and tended to be the dealers with the largest holdings of Treasuries.
To better understand the context of the Fed's repo operations, it is helpful to consider the breakdown of dealers' typical repo counterparties. Figure 2 shows the percentage of dealers' average daily repo that is sourced from each counterparty type, for the period from Jan. 2016 to Sept. 2019.11 During this period, the 10 dealers in our sample averaged about $1.5 trillion in daily outstanding repo volume. The most common repo counterparties were other dealers, asset managers, and banks.12 Figure 2. Average Dealer Repo Volume by Counterparty We start our analysis by examining how dealers' usage of the Fed's repo operations was related to their total borrowing in the repo market. To see how dealers acted, we regress daily changes in the total dollar amount of dealer repo borrowing, as well as borrowing from major counterparty types, on each dealer's daily change in dollars borrowed from the Fed's repo operations. The resulting regression coefficients essentially represent a decomposition of how, on average, each dollar increase in borrowing from the Fed is allocated towards the different components of dealer repo borrowing. We separate the analysis into a pre-COVID outbreak period (September 18, 2019 to February 14, 2020) and a post-COVID outbreak period (February 15, 2020 to April 30, 2020). We also consider separately the "high stress" sub-period of March 12-31, 2020. The results, shown in Table 1, indicate that during the pre-COVID period, dealers used the Fed's repo operations primarily to increase their total repo borrowing and only to a lesser extent to shift borrowing away from other funding sources. In particular, as shown in row 1, for each$1 increase in borrowing from the Fed's repo operations, $0.76 was used to increase dealers' repo book size, while the remainder was used to shift borrowing away from other sources, most notably other dealers.13 During the post-COVID outbreak period, we find that borrowing from the Fed's repo operations continued to be associated with an increase in their total repo borrowing, though to a smaller extent (row 2). However, borrowing from the Fed was associated with a larger decline in borrowing from others post-COVID than pre-COVID, especially dealers' borrowing from other dealers (column 2). Even during the high stress sub-period, not all repo borrowing from the Fed was associated with a substitution away from other counterparties, although substitution was occurring to a greater extent than at other times. Table 1. Results from Dealer Repo Regressions Increase in size of repo book (1) Substitution away from: Observations Dealers (2) Asset managers (3) 0.76*** -0.11* -0.03 -0.05 1010 0.53*** -0.25*** -0.06 0.06 510 0.39*** -0.45*** -0.1 0.05 130 Note. The coefficients in each column are estimated in separate regressions. Dealer repo book size roughly equals the sum of dealer repo borrowing from each counterparty type plus dealer borrowing through Federal Reserve repo (there is also an "other" category not shown in the table). The symbols *** and * indicate statistical significance at the 1 percent and 10 percent levels, respectively. Another way of assessing how the Fed's repo shaped dealer borrowing is to look at how it related to dealer borrowing from affiliated institutions and non-affiliated institutions. When looking at the substitution away from affiliated institutions in this way, we observe that in the pre-COVID period, the substitution away from other counterparties was split roughly evenly between affiliated and unaffiliated counterparties. There was a notable change in behavior in the post-COVID period when virtually all of the substitution was away from unaffiliated counterparties (Table 2, columns 1 and 2). In all periods, the majority of dealers' substitution away from unaffiliated counterparties was from other dealers. Table 2. Dealer Repo–Affiliated vs. Unaffiliated Counterparties Split Total: Affiliated (1) Total: Unaffiliated (2) Observations -0.14*** -0.10* 1010 -0.01 -0.31*** 510 -0.01 -0.53*** 130 Note. The symbols *** and * indicate statistical significance at the 1 percent and 10 percent levels, respectively. A similar exercise looks at the other side of dealers' balance sheets to see how changes in dealers' repo lending were associated with their use of the Fed's repo operations. As dealers appear to have used some of the funds obtained from the Fed to expand their total repo borrowing, this analysis provides insight into how those additional funds were used. The results in Table 3 show that a notable share of funds that dealers borrowed from the Fed did appear to be, in turn, lent by the dealers to their own customers. For instance, in the pre-COVID period (row 1), each$1 increase in dealers' repo borrowing from the Fed corresponds to a $0.55 increase in repo lending by the dealers.14 A decomposition of the increase in repo lending shows that most of it went to banks (column 4). This is particularly true in the high stress sub-period where each$1 increase in repo with the Fed increased repo lending to banks by $0.40. In the pre-COVID period, increased repo borrowing from the Fed by the dealers also corresponded with a notable increase in repo lending to other dealers and asset managers. There is a considerably weaker relationship with lending to these counterparties in the post-COVID period, when each$1 increase in dealers' borrowing from the Fed corresponds to only a $0.39 increase in repo lending. This seems consistent with developments in the Treasury market at that time, when the large-scale selling of off-the-run Treasury securities in March left dealers with increased financing needs and thus increased usage of the Fed's repo operations.15 Table 3. Dealer Reverse Repo Regression Results Total (1) Increase in reverse repo with: Observations Dealers (2) Asset managers (3) 0.55*** 0.17*** 0.10*** 0.29*** 1010 0.39*** 0.08 0.04* 0.29*** 510 0.35*** -0.07 0.02 0.40*** 130 Note. The symbols *** and * indicate statistical significance at the 1 percent and 10 percent levels, respectively. Further analysis in Table 4 sheds light on the share of the increase in dealers' repo lending going to their affiliated versus unaffiliated counterparties. During the pre-COVID period (row 1),$0.29 of the $0.55 of the increase in total repo lending went to affiliated counterparties (column 1), where affiliated banks account for nearly all of this increase (column 3). The remainder ($0.26 of the $0.55) went to unaffiliated counterparties (column 2). In contrast, during the post-COVID period (row 2) and in particular high stress period (row 3), there were signs of pullback from external capital markets—nearly all of the increase in total repo lending went to affiliated counterparties, while the share that went to unaffiliated counterparties was statistically insignificant. While dealers were still on-lending funds received from the Fed during the high stress period, nearly all of the on-lending was to affiliated banks. Table 4. Dealer Reverse Repo–Affiliated vs. Unaffiliated Counterparties Split Total Affiliated (1) Total Unaffiliated (2) Banks Affiliated (3) Banks Unaffiliated (4) Observations 0.29*** 0.26*** 0.28*** 0.01** 1010 0.31*** 0.08 0.28*** 0.01 510 0.46*** -0.11 0.39*** 0.01 130 Note. The symbols ***, **, and * indicate statistical significance at the 1 percent, 5 percent, and 10 percent levels, respectively. 1. In a repo operation, the Federal Reserve lends funds to a dealer against Treasury securities, agency debt securities, or agency mortgage-backed securities. The provision of funds to the dealer is associated with an increase in the account balance maintained by the dealer's commercial bank at the Federal Reserve (i.e. the commercial bank's reserves). Return to text 2. Anbil, Anderson, and Senyuz (2020) provides more detail on the September 2019 money market turmoil. Return to text 6. See for instance, https://www.newyorkfed.org/markets/opolicy/operating_policy_200316. Return to text 7. For comparison, usage at the end of January 2020 was about$170 billion. Return to text
8. Fed repo usage fell to zero shortly after the Desk's announcement on June 11 of an increase in the minimum bid rate on repo operations. Return to text
9. Our analysis shows that total Fed asset purchases have a statistically significant negative association with aggregate Fed repo usage during the post-COVID period. Return to text
10. The FR 2052a report collects quantitative information on selected assets, liabilities, and funding activities at the consolidated holding company level and at the subsidiary level. Foreign Banking Organization Large Institution Supervision Coordinating Committee (LISCC) firms and US Firms with $700 billion or more in total consolidated assets or$10 trillion or more in assets under custody must submit daily reports. For additional detail, see https://www.federalreserve.gov/reportforms/forms/FR_2052a20200630_f.pdf. Return to text
11. Repo volume includes all collateral, though the vast majority is OMO-eligible collateral. Return to text
12. The counterparty types used in this note are representative of broader categories in the FR 2052a report. Dealers represent the "supervised non-bank financial institution" category, asset managers represent the "other financial entity" category, and "banks" are their own category. For more details, see the FR2052a reporting instructions. Return to text
13. For brevity, we only report the three largest counterparty types, by volume, with which dealers engage in repo activity. Return to text
14. The response of total repo lending by the dealers to a \$1 increase in borrowing from the Fed is slightly smaller than the response in total repo borrowing. We do not know how the remaining funds were used. Return to text
15. While the increase in net repo borrowing was smaller per dollar of Fed borrowing in the post-COVID outbreak period, the total volume of repo borrowing, particularly from the Fed, was much greater. Return to text
| 2022-07-06T15:51:22 |
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|
https://www.usgs.gov/center-news/halemaumau-engine-shifts-gears-keeps-chugging
|
Halemaumau Engine Shifts Gears, but Keeps on Chugging
Release Date:
For the past month, Kīlauea's summit eruption has been steadily chugging along.
Photos, taken by HVO's webcam on November 17th illustrate the new behavior of the summit eruption plume, which this week began oscillating between strong and robust (left), and weak and wispy (right).
(Public domain.)
Clattering sounds issue from the Halemaumau vent as gas pulses forth, forming a thick plume that rolls into white billows high above the caldera. On most days, the plume rises and turns above the summit, gently drifting southward and darkening the Kau landscape. In the distance, an endless train of fume wraps around the flanks of Mauna Loa, destined for Kona and other points on the island chain.
Since mid-October, this scene has been relatively steady. But on Monday, November 17th, something changed. The thick white plume that we have become accustomed to seeing suddenly vanished, leaving only transparent trails of fume issuing from the vent. It appeared as though the summit activity had stopped—the chugging engine had seized. But, just as suddenly as it paused, it resumed a few minutes later, and the thick plume returned, puffing high above the caldera. This cycle of robust and wispy plumes occurred several more times on Monday and into the next day.
On Tuesday morning, HVO geologists made their way to the crater's edge and were standing above the vent through four of these plume transitions. Instead of a continuous flow of fume and occasional clatter, they witnessed something far more curious. When the plume became weak and wispy, the faint roar of surf, usually a common sound, was barely audible. Then, suddenly, they heard the loud and intimidating sound of breaking glass, followed by the rushing return of a thick white plume.
During these changes, cameras captured images and instruments recorded temperatures as glow returned to the vent. The glow intensity and associated temperatures were the highest observed since mid-October.
The amount of material ejected onto the crater rim also increased to its highest level since mid-October. This material largely consists of Pele's hair and other glassy fragments suggestive of fresh lava.
So, what is happening at the vent and why has it changed? Our explanations of natural phenomena are always working hypotheses that are refined as more data become available. At this stage, our data suggest that lava may be pistoning (rising and falling) within the vent.
When pistoning occurs, lava rises within the conduit to a level perhaps within 100 meters (300 feet) of the vent rim. As the lava cools, a crust forms on its surface. This crust can impede the flow of gas, causing pressure to build within the lava. When enough pressure is built to break the crust, gas can rush forward. The reduction in gas pressure causes the lava piston to drop down within the vent, and the cycle starts again.
Scientists at HVO have witnessed lava pistoning within vents during other eruptions on Kīlauea. For example, seismic tremor recorded at the summit in recent days is reminiscent of tremor produced at Puu Oo several years ago, when lava filled and drained from vents within its crater.
The sound of breaking glass heard within the vent may be caused by shattering of the glassy crust on the lava-piston's surface. The increase in glassy lava fragments deposited on the rim of Halemaumau is probably the result of this sequence.
Periods of intense glow observed at night could also be explained by the pistoning. When the crust breaks up and the lava level drops, red-hot molten lava and incandescent vent walls are exposed, increasing the intensity of the glow.
An explanation for changes deep within the volcano causing this pistoning behavior is more ambiguous. Whatever the reasons are for the shift in summit activity, we are sure that the engine is still chugging.
————————————————————————————————————————————————————————————————
Volcano Activity Update
Kīlauea Volcano continues to be active. A vent in Halemaumau Crater is erupting elevated amounts of sulfur dioxide gas and very small amounts of ash. Resulting high concentrations of sulfur dioxide in downwind air have closed the south part of Kīlauea caldera and produced occasional air quality alerts in more distant areas, such as Pahala and communities adjacent to Hawaii Volcanoes National Park, during kona wind periods. The have been several small ash-emission events from the vent, lasting only minutes, in the last week. For a few days mid-week, there were several brief periods of decreased plume vigor lasting minutes to hours. During these periods, the plume was the weakest it has been since the vent opened last March.
Puu Ōō continues to produce sulfur dioxide at rates higher than the vent in Halemaumau Crater. Trade winds tend to pool these emissions along the West Hawaii coast, while Kona winds blow these emissions into communities to the north, such as Mountain View, Volcano, and Hilo.
Lava continues to erupt from the Thanksgiving Eve Breakout (TEB) vent and flows toward the ocean through a well-established lava tube. Activity at the Waikupanaha ocean entry has fluctuated over the past week, with periods of small littoral explosions and a voluminous plume, followed by periods of no explosions and a wispy plume. Part of these fluctuations may have occurred in response to a deflation-inflation (DI) event at Kīlauea's summit on November 16-17. A western branch of the tube, which diverges from the main TEB tube at the top of the pali, continues to supply lava to breakouts on the coastal plain. These breakouts are scattered along the western margin of the TEB flow field and are slowly marching southward toward the National Park boundary.
Be aware that active lava deltas can collapse at any time, potentially generating large explosions. This may be especially true during times of rapidly changing lava supply conditions. Do not venture onto the lava deltas. Even the intervening beaches are susceptible to large waves generated during delta collapse; avoid these beaches. In addition, steam plumes rising from ocean entries are highly acidic and laced with glass particles. Check the Civil Defense Web site or call 961-8093 for viewing hours.
Mauna Loa is not erupting. Two earthquakes were located beneath the summit this past week. Continuing extension between locations spanning the summit indicates slow inflation of the volcano.
There were no felt earthquakes reported on Hawaii Island for the past week.
Visit our Web site for daily Kīlauea eruption updates, a summary of volcanic events over the past year, and nearly real-time Hawaii earthquake information. Kīlauea daily update summaries are also available by phone at (808) 967-8862. Questions can be emailed to [email protected].
| 2020-01-27T18:56:19 |
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|
https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc448.htm
|
6. Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
6.4.4. Univariate Time Series Models
## Box-Jenkins Model Diagnostics
Assumptions for a Stable Univariate Process Model diagnostics for Box-Jenkins models is similar to model validation for non-linear least squares fitting.
That is, the error term $$A_t$$ is assumed to follow the assumptions for a stationary univariate process. The residuals should be white noise (or independent when their distributions are normal) drawings from a fixed distribution with a constant mean and variance. If the Box-Jenkins model is a good model for the data, the residuals should satisfy these assumptions.
If these assumptions are not satisfied, we need to fit a more appropriate model. That is, we go back to the model identification step and try to develop a better model. Hopefully the analysis of the residuals can provide some clues as to a more appropriate model.
4-Plot of Residuals As discussed in the EDA chapter, one way to assess if the residuals from the Box-Jenkins model follow the assumptions is to generate a 4-plot of the residuals and an autocorrelation plot of the residuals. One could also look at the value of the Box-Ljung (1978) statistic.
An example of analyzing the residuals from a Box-Jenkins model is given in the Negiz data case study.
| 2018-05-27T16:01:47 |
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|
https://www.khronos.org/registry/vulkan/specs/1.2-extensions/man/html/VkVertexInputRate.html
|
## C Specification
Possible values of VkVertexInputBindingDescription::inputRate, specifying the rate at which vertex attributes are pulled from buffers, are:
// Provided by VK_VERSION_1_0
typedef enum VkVertexInputRate {
VK_VERTEX_INPUT_RATE_VERTEX = 0,
VK_VERTEX_INPUT_RATE_INSTANCE = 1,
} VkVertexInputRate;
## Description
• VK_VERTEX_INPUT_RATE_VERTEX specifies that vertex attribute addressing is a function of the vertex index.
• VK_VERTEX_INPUT_RATE_INSTANCE specifies that vertex attribute addressing is a function of the instance index.
## Document Notes
For more information, see the Vulkan Specification
This page is extracted from the Vulkan Specification. Fixes and changes should be made to the Specification, not directly.
Copyright (c) 2014-2020 The Khronos Group Inc.
SPDX-License-Identifier: CC-BY-4.0
| 2020-07-09T18:30:10 |
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|
https://mfix.netl.doe.gov/doc/vvuq-manual/main/html/mms/index.html
|
# 2. Method of Manufactured Solutions (MMS)¶
Order of accuracy testing (or ‘order testing’) is considered a rigorous method for performing code verification. During order testing, the formal order of accuracy of a numerical scheme is compared to the observed order of accuracy. The observed order is the order at which the discretization error (which is the difference between the numerical solution to the discrete equations and the exact solution to the PDEs) decreases with systematic mesh refinement. However, the exact solution to a PDE is unknown for most practical problems. In this scenario, the Method of Manufactured Solutions (MMS) [23] can be used where a selected analytical function (called a ‘manufactured solution’) is forced to be the exact solution by modifying the PDE through additional source terms.
The MMS test cases presented in this chapter are summarized in Table 2.1. These test cases offer an increasing level of computational complexity to isolate any potential problems in the source code. Three explanatory test cases that employ various simplifying assumptions are provided to assist the reader in understanding the MMS. Additional test cases were selected based upon their ability to invoke various parts of the MFIX code, and present physically acceptable data. All cases are executed in serial mode unless explicitly noted.
Table 2.1 Summary of MMS tests by feature.
EX01
EX02
EX03
01
02
03
04
05
06
Frequency†
X
X
X
M
M
M
M
M
M
Dimension
1D
1D
1D
2D
3D
3D
3D
3D
3D
Multiphase
$${\checkmark}$$
$${\checkmark}$$
Continuity
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
Momentum
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
Thermal Energy
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
$${\checkmark}$$
Species Mass
Granular Energy
$${\checkmark}$$
$${\checkmark}$$
Turbulence
No-slip Wall BC
$${\checkmark}$$
Free-slip Wall BC
$${\checkmark}$$
Pressure Outflow
$${\checkmark}$$
Distributed Memory
Shared Memory
† C-Incorporated into the continuous integration server; M-Monthly; Q-Quarterly; D-Disabled; X-Manual
| 2022-07-03T17:45:10 |
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|
https://www.usgs.gov/news/crack-measurement-old-fashioned-good
|
# Crack measurement-old fashioned but good
May 1, 2003
Most monitoring done by HVO is designed to interpret changes taking place below the surface of the earth.
In general, the deeper the process, the more widely spaced must be the monitoring devices. Consequently, seismometers and GPS receivers are generally kilometers apart, and leveling benchmarks, a few hundred meters. To study shallow features, more closely spaced monitoring is needed. An inclusive monitoring network has some stations located far apart and others close together.
Such a monitoring network is required to study the Koae fault system, which connects the east and southwest rift zones of Kīlauea. We really don't yet know how deeply the faults in the Koae extend, nor do we know whether they remain nearly vertical or flatten at some depth below the earth's surface.
Continuously recording GPS stations and seismometers around the Koae give information of possible deep processes. A network of survey lines about 1 km long spider-webs its way across the Koae and provides information about horizontal movements. Level lines across the Koae have benchmarks spaced from about 1 km (0.6 miles) to about 90 m (300 feet) apart to tell us about vertical changes. But this type of monitoring says little about individual cracks and faults, and the Koae has thousands of them. How can they be monitored?
Very simply--with a tape measure. We use a time-honored method first used at Kīlauea by Thomas Jaggar when HVO was established in 1912. Permanent markers, generally stainless steel carriage bolts, are cemented into the ground on either side of a crack, spaced closely enough so that a 30-m-long (100-feet-long) tape measure can reach between them. At least three such markers are established, two on one side of the crack to form a baseline, and a third across the crack. The first taping of the distances between the markers provides a basis for comparison with future measurements. Subsequent tapings will tell if the crack has remained stable or has opened more.
This type of station, termed a crack station, can also provide information about vertical changes, provided that the markers are surveyed with a level. A complete crack station contains information about both horizontal and vertical changes.
In practice, most crack stations are more than simple triangles. The additional complexity is necessary when the cracks and faults themselves are complicated. There may be a family of cracks spanning a width of several tens of meters, so that a station may need as many as 10 different markers for complete coverage. Some crack stations consist only of a long line of markers rather than connected triangles or other configurations.
Another complexity is the topography. To tape accurately between markers, there can be no obstacle. An intermediate marker may have to be emplaced to get around or over the obstacle.
This kind of monitoring is done on the cheap. No fancy equipment here. But we can't realistically have many crack stations, because it takes a couple of hours to measure a complex one. Currently we have some 20 stations spaced throughout the Koae.
Measurement of crack stations shows that some cracks creep open slowly and then jump during earthquakes or intrusions of magma into the nearby east rift zone.
Two creeping cracks are located at the intersection of the Chain of Craters and Hilina Pali Roads. Since September 20, 1999, these cracks have gradually widened 1-1.5 cm (0.4-0.6 inches). Each probably opened rapidly during an intrusion on September 11 between Mauna Ulu and the Escape Road, for each widened by 1 to 1.5 cm (0.4-0.6 inches) in the one year ending on September 20. These two crack stations, the granddaddies at Kīlauea, were first measured in 1966; since then, one has opened 30 cm (12 inches) and the other 60 cm (24 inches).
Measurement of cracks is not glamorous, but a few can be measured from time to time to provide important information on how the surface of Kīlauea breaks up.
### Volcano Activity Update
Eruptive activity at the Puu Oo vent of Kīlauea Volcano continued unabated during the past week. A string of incandescence stretches from top to bottom of both Pulama pali and Paliuli, and slight glow comes from the base of Paliuli, showing the presence of surface lava there. Surface breakouts are also found along the east edge of the Kohola flow, and the National Park Service has marked a trail out to the closest activity. Ocean entry activity at the two sites on the West Highcastle delta waxed and waned during the week.
The public is reminded that the ocean entry areas are extremely hazardous, with explosions accompanying sudden collapses of the new land. The steam clouds are highly acidic and laced with glass particles. The National Park Service has erected a rope barricade to delineate the edge of the restricted area. Do not venture beyond this rope boundary and onto the lava deltas and benches.
No earthquakes were reported felt during the past week.
Mauna Loa is not erupting. The summit region continues to inflate slowly. Seismic activity remains low with no earthquakes located in the summit area during the last seven days.
| 2023-01-27T22:15:17 |
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|
http://legisquebec.gouv.qc.ca/en/showversion/cr/A-6.002,%20r.%201?code=se:31r4&pointInTime=20200214
|
### A-6.002, r. 1 - Regulation respecting fiscal administration
31R4. After the allocation provided for in section 31R3, the Minister sends to each Minister or body concerned the information listed in the second or third paragraph, as the case may be, concerning the debtor.
Where the debtor is a natural person, the information referred to in the first paragraph is the following:
(a) the information under subparagraphs a to e of the second paragraph of section 31R2; and
(b) the amount allocated to the debt.
Where the debtor is a person other than a natural person, the information referred to in the first paragraph is the following:
(a) the information under subparagraphs a to d of the third paragraph of section 31R2; and
(b) the amount allocated to the debt.
O.C. 80-82, s. 1; O.C. 499-82, s. 4; O.C. 1408-84, s. 3; O.C. 122-2000, s. 4; O.C. 1223-2005, s. 3; O.C. 701-2013, s. 3.
31R4. After the allocation provided for in section 31R3, the Minister sends to each Minister or body concerned the following particulars concerning the debtor:
(a) the information described in paragraphs a to d of section 31R2;
| 2020-05-25T11:23:21 |
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|
https://pvpmc.sandia.gov/modeling-steps/1-weather-design-inputs/plane-of-array-poa-irradiance/calculating-poa-irradiance/poa-beam/
|
The plane of array (POA) beam component of irradiance is calculated by adjusting the direct normal irradiance ($DNI$) by the angle of incidence ($AOI$) in the following manner:
$E{_b}=DNI\times&space;\cos&space;\left&space;(&space;AOI&space;\right&space;)$ .
Content contributed by Sandia National Laboratories
| 2021-01-21T21:28:53 |
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|
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