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http://ndl.iitkgp.ac.in/document/MEtsQUU2M0FnbWNWM1Z2YjdLNkZlZz09
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### Low-$x$ QCD studies with forward jets in proton-proton collisions at $\sqrt{s}$~=~14~TeVLow-$x$ QCD studies with forward jets in proton-proton collisions at $\sqrt{s}$~=~14~TeV
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Author Cerci, Salim ♦ D'Enterria, David Source CERN Document Server Content type Text File Format PDF Date Created 2011-06-15 Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Physics ♦ Modern physics ♦ Technology ♦ Engineering & allied operations ♦ Applied physics Subject Keyword Particle Physics - Experiment ♦ Detectors and Experimental Techniques ♦ PHYSICS Abstract Forward (di)jet measurements are a useful tool to constrain the Parton Distribution Functions (PDFs) at low values of parton momentum fraction x, and to study the possible onset of BFKL or gluon saturation QCD evolutions in the proton. We present studies of jet reconstruction capabilities in the CMS Hadron Forward (HF) calorimeter (3<|eta|<5). The expected sensitivity of the inclusive forward jet p_T spectrum to the proton PDF, as well as the azimuthal decorrelation of Mueller-Navelet jets with a large rapidity separation are presented for p-p collisions at sqrt{s} = 14 TeV. Description Presented at: AIP Conf. Proc. 1105 (2009) 28-32 International Workshop on Diffraction in High-Energy Physics, La Londe-les-Maures, France, 09 - 14 Sep 2008, pp.28-32Collaboration with: for the CMS Learning Resource Type Article Publisher Date 2008-01-01 Rights License Preprint: (License: CC-BY-4.0) Page Count 6
| 2020-10-01T03:53:15 |
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https://zbmath.org/authors/?q=ai%3Agoodman.leo-a
|
Goodman, Leo A.
Compute Distance To:
Author ID: goodman.leo-a Published as: Goodman, Leo A.; Goodman, L. A. External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 73 Publications since 1949, including 3 Books 1 Contribution as Editor Biographic References: 1 Publication Co-Authors: 39 Co-Authors with 16 Joint Publications 948 Co-Co-Authors
all top 5
Co-Authors
57 single-authored 6 Kruskal, William H. 1 Amemiya, Takeshi 1 Anderson, Theodore Wilbur jun. 1 Bahadur, Raghu Raj 1 Bhattacharjee, Manish C. 1 Bickel, Peter John 1 Brillinger, David R. 1 Chernoff, Herman 1 Christ, Carl F. 1 Clogg, Clifford C. 1 Diaconis, Persi Warren 1 Ferguson, Thomas S. 1 Friedman, Milton 1 Griliches, Zvi 1 Grunfeld, Yehuda 1 Haberman, Shelby J. 1 Harberger, Arnold C. 1 Hartley, Hermann Otto 1 Karlin, Samuel 1 Liviatan, Nissan 1 Lo, Albert Y. 1 Lockhart, Richard A. 1 Madansky, Albert 1 Magidson, Jay 1 Mincer, Jacob 1 Mundlak, Yair 1 Nerlove, Marc L. 1 Patinkin, Don 1 Puri, Madan Lal 1 Rolph, John E. 1 Rosenblatt, Murray 1 Roussas, George Gregory 1 Samaniego, Francisco J. 1 Shaffer, Juliet 1 Stigler, Stephen M. 1 Sudderth, William D. 1 Telser, Lester G. 1 Theil, Henri 1 Tucker, Howard G. 1 Wets, Roger Jean-Baptiste 1 Yatracos, Yannis G.
all top 5
Serials
20 Journal of the American Statistical Association 13 Annals of Mathematical Statistics 8 Biometrika 3 Technometrics 3 Journal of the Royal Statistical Society. Series B 2 Annals of Human Genetics 2 Biometrics 2 The Journal of Mathematical Sociology 1 Psychometrika 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Annals of the Institute of Statistical Mathematics 1 The Annals of Statistics 1 International Statistical Review 1 Journal of Statistical Planning and Inference 1 Proceedings of the American Mathematical Society 1 Theoretical Population Biology 1 Statistical Science 1 Notices of the American Mathematical Society 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Sankhyā 1 Springer Series in Statistics
all top 5
Fields
28 Statistics (62-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 History and biography (01-XX) 2 General and overarching topics; collections (00-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Biology and other natural sciences (92-XX)
Citations contained in zbMATH Open
63 Publications have been cited 1,166 times in 930 Documents Cited by Year
Exploratory latent structure analysis using both identifiable and unidentifiable models. Zbl 0281.62057
Goodman, Leo A.
1974
Measures of association for cross classifications. Zbl 0056.12801
Goodman, Leo A.; Kruskal, William H.
1954
Statistical inference about Markov chains. Zbl 0087.14905
Anderson, T. W.; Goodman, Leo A.
1957
The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries. Zbl 0613.62070
Goodman, Leo A.
1985
Some useful extensions of the usual correspondence analysis approach and the usual log-linear models approach in the analysis of contingency tables. Zbl 0611.62060
Goodman, Leo A.
1986
Measures of association for cross classifications. Zbl 0426.62034
Goodman, Leo A.; Kruskal, William H.
1979
The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with or without missing entries. Zbl 0177.46901
Goodman, L. A.
1968
Measures of association for cross classifications. II: Further discussion and references. Zbl 0095.13101
Goodman, Leo A.; Kruskal, William H.
1959
Measures, models, and graphical displays in the analysis of cross-classified data (with comments). Zbl 0850.62093
Goodman, Leo A.
1991
On simultaneous confidence intervals for multinomial proportions. Zbl 0131.17701
Goodman, L. A.
1965
Measures of association for cross classifications. IV: Simplification of asymptotic variances. Zbl 0243.62038
Goodman, Leo A.; Kruskal, William H.
1972
Impartial decision rules and sufficient statistics. Zbl 0048.11902
Bahadur, Raghu Raj; Goodman, Leo A.
1952
Snowball sampling. Zbl 0099.14203
Goodman, Leo A.
1961
Sequential sampling tagging for population size problems. Zbl 0050.14805
Goodman, Leo A.
1953
On the estimation of the number of classes in a population. Zbl 0035.09102
Goodman, Leo A.
1949
A single general method for the analysis of cross-classified data: Reconciliation and synthesis of some methods of Pearson, Yule, and Fisher, and also some methods of correspondence analysis and association analysis. Zbl 0871.62051
Goodman, Leo A.
1996
Association models and the bivariate normal for contingency tables with ordered categories. Zbl 0477.62038
Goodman, Leo A.
1981
Latent structure analysis of a set of multidimensional contingency tables. Zbl 0547.62037
Clogg, Clifford C.; Goodman, Leo A.
1984
Analyzing qualitative/categorical data. Log-linear models and latent- structure analysis. Jay Magidson (ed.). Zbl 0396.92020
Goodman, Leo A.
1978
Stochastic models for the population growth of the sexes. Zbl 0167.48701
Goodman, L. A.
1968
The analysis of multidimensional contingency tables: Stepwise procedures and direct estimation methods for building models for multiple classifications. Zbl 0218.62066
Goodman, Leo A.
1971
On the exact variance of products. Zbl 0099.13603
Goodman, Leo A.
1960
Simultaneous confidence intervals for contrasts among multinomial populations. Zbl 0227.62025
Goodman, Leo A.
1964
The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach. Zbl 0253.62029
Goodman, Leo A.
1973
Partitioning of chi-square, analysis of marginal contingency tables, and estimation of expected frequencies in multidimensional contingency tables. Zbl 0217.51504
Goodman, L. A.
1971
On the sensitivity of the intrinsic growth rate to changes in the age- specific birth and death rates. Zbl 0242.92006
Goodman, Leo A.
1971
Interactions in multidimensional contingency tables. Zbl 0136.40803
Goodman, L. A.
1964
A new model for scaling response patterns: An application of the quasi- independence concept. Zbl 0321.62056
Goodman, Leo A.
1975
The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds. Zbl 0532.62035
Goodman, Leo A.
1983
The analysis of nonadditivity in two-way analysis of variance. Zbl 0702.62064
Goodman, Leo A.; Haberman, Shelby J.
1990
The probabilities of extinction for birth-and-death processes that are age-dependent or phase-dependent. Zbl 0173.19902
Goodman, L. A.
1967
Some multiplicative models for the analysis of cross classified data. Zbl 0248.62032
Goodman, Leo A.
1972
Simultaneous confidence limits for cross-product ratios in contingency tables. Zbl 0129.32304
Goodman, L. A.
1964
Simplified runs tests and likelihood ratio tests for Markoff chains. Zbl 0089.15301
Goodman, Leo A.
1958
Measurement in economics. Studies in mathematical economics and econometrics. In memory of Yehuda Grunfeld. Zbl 0117.00108
Christ, Carl F.; Friedman, Milton; Goodman, Leo A.; Griliches, Zvi; Harberger, Arnold C.; Liviatan, Nissan; Mincer, Jacob; Mundlak, Yair; Nerlove, Marc; Patinkin, Don; Telser, Lester G.; Theil, Henri
1963
The precision of unbiased ratio-type estimators. Zbl 0087.15104
Goodman, Leo A.; Hartley, H. O.
1958
The variance of the product of $$K$$ random variables. Zbl 0102.35505
Goodman, Leo A.
1962
Parameter-free and nonparametric tolerance limits: the exponential case. Zbl 0118.14102
1962
Simple methods for analyzing three-factor interaction in contingency tables. Zbl 0129.33101
Goodman, L. A.
1964
A simple method for improving some estimators. Zbl 0050.14901
Goodman, Leo A.
1953
A note on the estimation of variance. Zbl 0102.35801
Goodman, Leo A.
1960
On quasi-independence and quasi-dependence in contingency tables, with special reference to ordinal triangular contingency tables. Zbl 0825.62497
Goodman, Leo A.
1994
On partitioning $$\chi^2$$ and detecting partial association in three-way contingency tables. Zbl 0186.52303
Goodman, Leo A.
1969
Simple statistical methods for scalogram analysis. Zbl 0083.15103
Goodman, Leo A.
1959
Exact probabilities and asymptotic relationships for some statistics from $$m$$-th order Markov chains. Zbl 0086.12203
Goodman, Leo A.
1958
Empirical evaluation of formal theory. Zbl 0367.92015
Goodman, Leo A.; Kruskal, William
1974
More about empirical evaluation of formal theory. Zbl 0367.92016
Goodman, Leo A.; Kruskal, William
1974
Contributions to the statistical analysis of contingency tables: Notes on quasi-symmetry, quasi-independence, log-linear models, log-bilinear models, and correspondence analysis models. Zbl 1122.62316
Goodman, Leo A.
2002
The analysis of persistence in a chain of multiple events. Zbl 0132.38502
Goodman, L. A.
1964
On the analysis of samples from $$k$$ lists. Zbl 0047.38203
Goodman, Leo A.
1952
On the Poisson-gamma distribution problem. Zbl 0048.10704
Goodman, Leo A.
1952
Some nonparametric tests for comovements between time series. Zbl 0108.15602
Goodman, L. A.; Grunfeld, Y.
1961
How to minimize or maximize the probabilities of extinction in a Galton- Watson process and in some related multiplicative population processes. Zbl 0279.60075
Goodman, Leo A.
1968
On Plackett’s test for contingency table interactions. Zbl 0137.13102
Goodman, L. A.
1963
Correspondence analysis, association analysis, and generalized nonindependence analysis of contingency tables: Saturated and unsaturated models, and appropriate graphical displays. Zbl 0810.62052
Goodman, Leo A.
1993
Studies in econometrics, time series, and multivariate statistics. (In commemoration of T. W. Anderson’s 65th birthday). Zbl 0528.00008
1983
On quasi-independence in triangular contingency tables. Zbl 0413.62040
Goodman, Leo A.
1979
Tests based on the movements in and the comovements between $$m$$-dependent time series. Zbl 0117.15503
Goodman, Leo A.
1963
Some possible effects of birth control on the incidence of disorders and on the influence of birth order. Zbl 0118.14602
Goodman, L. A.
1963
Serial number analysis. Zbl 0048.12104
Goodman, Leo A.
1952
On methods of amalgamation. Zbl 0058.13701
Goodman, Leo A.
1954
Partial tests for partial taus. Zbl 0097.34503
Goodman, Leo A.
1959
Asymptotic distributions of ’psi-squared’ goodness of fit criteria for $$m$$-th order Markov chains. Zbl 0113.12505
Goodman, L. A.
1958
Contributions to the statistical analysis of contingency tables: Notes on quasi-symmetry, quasi-independence, log-linear models, log-bilinear models, and correspondence analysis models. Zbl 1122.62316
Goodman, Leo A.
2002
A single general method for the analysis of cross-classified data: Reconciliation and synthesis of some methods of Pearson, Yule, and Fisher, and also some methods of correspondence analysis and association analysis. Zbl 0871.62051
Goodman, Leo A.
1996
On quasi-independence and quasi-dependence in contingency tables, with special reference to ordinal triangular contingency tables. Zbl 0825.62497
Goodman, Leo A.
1994
Correspondence analysis, association analysis, and generalized nonindependence analysis of contingency tables: Saturated and unsaturated models, and appropriate graphical displays. Zbl 0810.62052
Goodman, Leo A.
1993
Measures, models, and graphical displays in the analysis of cross-classified data (with comments). Zbl 0850.62093
Goodman, Leo A.
1991
The analysis of nonadditivity in two-way analysis of variance. Zbl 0702.62064
Goodman, Leo A.; Haberman, Shelby J.
1990
Some useful extensions of the usual correspondence analysis approach and the usual log-linear models approach in the analysis of contingency tables. Zbl 0611.62060
Goodman, Leo A.
1986
The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries. Zbl 0613.62070
Goodman, Leo A.
1985
Latent structure analysis of a set of multidimensional contingency tables. Zbl 0547.62037
Clogg, Clifford C.; Goodman, Leo A.
1984
The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds. Zbl 0532.62035
Goodman, Leo A.
1983
Studies in econometrics, time series, and multivariate statistics. (In commemoration of T. W. Anderson’s 65th birthday). Zbl 0528.00008
1983
Association models and the bivariate normal for contingency tables with ordered categories. Zbl 0477.62038
Goodman, Leo A.
1981
Measures of association for cross classifications. Zbl 0426.62034
Goodman, Leo A.; Kruskal, William H.
1979
On quasi-independence in triangular contingency tables. Zbl 0413.62040
Goodman, Leo A.
1979
Analyzing qualitative/categorical data. Log-linear models and latent- structure analysis. Jay Magidson (ed.). Zbl 0396.92020
Goodman, Leo A.
1978
A new model for scaling response patterns: An application of the quasi- independence concept. Zbl 0321.62056
Goodman, Leo A.
1975
Exploratory latent structure analysis using both identifiable and unidentifiable models. Zbl 0281.62057
Goodman, Leo A.
1974
Empirical evaluation of formal theory. Zbl 0367.92015
Goodman, Leo A.; Kruskal, William
1974
More about empirical evaluation of formal theory. Zbl 0367.92016
Goodman, Leo A.; Kruskal, William
1974
The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach. Zbl 0253.62029
Goodman, Leo A.
1973
Measures of association for cross classifications. IV: Simplification of asymptotic variances. Zbl 0243.62038
Goodman, Leo A.; Kruskal, William H.
1972
Some multiplicative models for the analysis of cross classified data. Zbl 0248.62032
Goodman, Leo A.
1972
The analysis of multidimensional contingency tables: Stepwise procedures and direct estimation methods for building models for multiple classifications. Zbl 0218.62066
Goodman, Leo A.
1971
Partitioning of chi-square, analysis of marginal contingency tables, and estimation of expected frequencies in multidimensional contingency tables. Zbl 0217.51504
Goodman, L. A.
1971
On the sensitivity of the intrinsic growth rate to changes in the age- specific birth and death rates. Zbl 0242.92006
Goodman, Leo A.
1971
On partitioning $$\chi^2$$ and detecting partial association in three-way contingency tables. Zbl 0186.52303
Goodman, Leo A.
1969
The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with or without missing entries. Zbl 0177.46901
Goodman, L. A.
1968
Stochastic models for the population growth of the sexes. Zbl 0167.48701
Goodman, L. A.
1968
How to minimize or maximize the probabilities of extinction in a Galton- Watson process and in some related multiplicative population processes. Zbl 0279.60075
Goodman, Leo A.
1968
The probabilities of extinction for birth-and-death processes that are age-dependent or phase-dependent. Zbl 0173.19902
Goodman, L. A.
1967
On simultaneous confidence intervals for multinomial proportions. Zbl 0131.17701
Goodman, L. A.
1965
Simultaneous confidence intervals for contrasts among multinomial populations. Zbl 0227.62025
Goodman, Leo A.
1964
Interactions in multidimensional contingency tables. Zbl 0136.40803
Goodman, L. A.
1964
Simultaneous confidence limits for cross-product ratios in contingency tables. Zbl 0129.32304
Goodman, L. A.
1964
Simple methods for analyzing three-factor interaction in contingency tables. Zbl 0129.33101
Goodman, L. A.
1964
The analysis of persistence in a chain of multiple events. Zbl 0132.38502
Goodman, L. A.
1964
Measurement in economics. Studies in mathematical economics and econometrics. In memory of Yehuda Grunfeld. Zbl 0117.00108
Christ, Carl F.; Friedman, Milton; Goodman, Leo A.; Griliches, Zvi; Harberger, Arnold C.; Liviatan, Nissan; Mincer, Jacob; Mundlak, Yair; Nerlove, Marc; Patinkin, Don; Telser, Lester G.; Theil, Henri
1963
On Plackett’s test for contingency table interactions. Zbl 0137.13102
Goodman, L. A.
1963
Tests based on the movements in and the comovements between $$m$$-dependent time series. Zbl 0117.15503
Goodman, Leo A.
1963
Some possible effects of birth control on the incidence of disorders and on the influence of birth order. Zbl 0118.14602
Goodman, L. A.
1963
The variance of the product of $$K$$ random variables. Zbl 0102.35505
Goodman, Leo A.
1962
Parameter-free and nonparametric tolerance limits: the exponential case. Zbl 0118.14102
1962
Snowball sampling. Zbl 0099.14203
Goodman, Leo A.
1961
Some nonparametric tests for comovements between time series. Zbl 0108.15602
Goodman, L. A.; Grunfeld, Y.
1961
On the exact variance of products. Zbl 0099.13603
Goodman, Leo A.
1960
A note on the estimation of variance. Zbl 0102.35801
Goodman, Leo A.
1960
Measures of association for cross classifications. II: Further discussion and references. Zbl 0095.13101
Goodman, Leo A.; Kruskal, William H.
1959
Simple statistical methods for scalogram analysis. Zbl 0083.15103
Goodman, Leo A.
1959
Partial tests for partial taus. Zbl 0097.34503
Goodman, Leo A.
1959
Simplified runs tests and likelihood ratio tests for Markoff chains. Zbl 0089.15301
Goodman, Leo A.
1958
The precision of unbiased ratio-type estimators. Zbl 0087.15104
Goodman, Leo A.; Hartley, H. O.
1958
Exact probabilities and asymptotic relationships for some statistics from $$m$$-th order Markov chains. Zbl 0086.12203
Goodman, Leo A.
1958
Asymptotic distributions of ’psi-squared’ goodness of fit criteria for $$m$$-th order Markov chains. Zbl 0113.12505
Goodman, L. A.
1958
Statistical inference about Markov chains. Zbl 0087.14905
Anderson, T. W.; Goodman, Leo A.
1957
Measures of association for cross classifications. Zbl 0056.12801
Goodman, Leo A.; Kruskal, William H.
1954
On methods of amalgamation. Zbl 0058.13701
Goodman, Leo A.
1954
Sequential sampling tagging for population size problems. Zbl 0050.14805
Goodman, Leo A.
1953
A simple method for improving some estimators. Zbl 0050.14901
Goodman, Leo A.
1953
Impartial decision rules and sufficient statistics. Zbl 0048.11902
Bahadur, Raghu Raj; Goodman, Leo A.
1952
On the analysis of samples from $$k$$ lists. Zbl 0047.38203
Goodman, Leo A.
1952
On the Poisson-gamma distribution problem. Zbl 0048.10704
Goodman, Leo A.
1952
Serial number analysis. Zbl 0048.12104
Goodman, Leo A.
1952
On the estimation of the number of classes in a population. Zbl 0035.09102
Goodman, Leo A.
1949
all top 5
Cited by 1,385 Authors
27 Beh, Eric J. 16 Bartolucci, Francesco 13 Agresti, Alan 13 Kateri, Maria 12 D’Ambra, Luigi 10 Lombardo, Rosaria 9 Vermunt, Jeroen K. 9 Warrens, Matthijs J. 8 D’Ambra, Antonello 8 Fienberg, Stephen Elliot 7 Biernacki, Christophe 7 Goodman, Leo A. 7 Marbac, Matthieu 7 Pandolfi, Silvia 6 Bacci, Silvia 6 Formann, Anton K. 6 Gupal, Anatol M. 6 Montanari, Giorgio Eduardo 6 Sergienko, Ivan Vasylyovych 6 van der Heijden, Peter G. M. 5 De Leeuw, Jan 5 DeSarbo, Wayne S. 5 Misra, Neeraj Kumar 5 Pardo, Leandro 5 Pollak, Edward 5 Rudas, Tamás 5 Sarnacchiaro, Pasquale 5 Simonetti, Biagio 5 Xu, Gongjun 4 Amenta, Pietro 4 Anderson, Carolyn Jane 4 Arshad, Mohd Rizal 4 De Boeck, Paul 4 Denœux, Thierry 4 Eshima, Nobuoki 4 Farcomeni, Alessio 4 Gnaldi, Michela 4 Greenacre, Michael J. 4 Heiser, Willem J. 4 Huang, Guan-Hua 4 Kumar, Somesh 4 Mode, Charles J. 4 Moustaki, Irini 4 Nikoloulopoulos, Aristidis K. 4 Takane, Yoshio 4 Tomizawa, Sadao 4 Vandewalle, Vincent 4 von Eye, Alexander 3 Albatineh, Ahmed N. 3 Anděl, Jiří 3 Bandeen-Roche, Karen J. 3 Bhattacharjee, Debanjan 3 Biswas, Atanu 3 Caussinus, Henri 3 Celeux, Gilles 3 Cho, Hokwon A. 3 Choulakian, Vartan 3 Chung, Hwan 3 Cole, Diana J. 3 Dias, José G. 3 Frank, Ove 3 Ganjali, Mojtaba 3 Ginsberg, Ralph B. 3 Govaert, Gérard 3 Govindarajulu, Zakkula 3 Gu, Yuqi 3 Iliopoulos, George 3 Karlis, Dimitris 3 Kelton, Christina M. L. 3 Kim, Daeyoung 3 Klimova, Anna 3 Lawal, H. Bayo 3 Lee, Mei-Ling Ting 3 Leite, José Galvão 3 Limnios, Nikolaos 3 Lin, Ting Hsiang 3 Martin, Donald E. K. 3 Martín, Nirian 3 Molenberghs, Geert 3 Murphy, Thomas Brendan 3 Nayak, Tapan Kumar 3 Niewiadomska-Bugaj, Magdalena 3 Ntzoufras, Ioannis 3 Pennoni, Fulvia 3 de Bragança Pereira, Carlos Alberto 3 Ranalli, Monia 3 Reiter, Jerome P. 3 Rocci, Roberto 3 Rovine, Michael J. 3 Scaccia, Luisa 3 Sen, Pranab Kumar 3 Siciliano, Roberta 3 Snijders, Tom A. B. 3 Tabata, Minoru 3 Tahata, Kouji 3 Takemura, Akimichi 3 van der Ark, L. Andries 3 Van Mechelen, Iven 3 Vellaisamy, Palaniappan 3 Voda, Viorel Gh. ...and 1,285 more Authors
all top 5
Cited in 168 Serials
86 Psychometrika 65 Computational Statistics and Data Analysis 56 Communications in Statistics. Theory and Methods 38 Journal of Statistical Planning and Inference 30 Journal of Classification 29 Statistics & Probability Letters 27 Journal of Applied Statistics 24 Journal of Multivariate Analysis 23 Biometrics 20 The Journal of Mathematical Sociology 19 Annals of the Institute of Statistical Mathematics 17 Journal of Statistical Computation and Simulation 16 Advances in Data Analysis and Classification. ADAC 14 Mathematical Biosciences 12 Theoretical Population Biology 12 Communications in Statistics. Simulation and Computation 12 European Journal of Operational Research 12 Statistical Methodology 11 Metrika 10 The Canadian Journal of Statistics 10 Journal of Mathematical Psychology 10 Computational Statistics 10 Statistics and Computing 9 Journal of Econometrics 9 Journal of Statistical Theory and Practice 8 The Annals of Statistics 8 Statistica Neerlandica 8 Statistics 8 Sequential Analysis 8 Statistical Papers 8 Australian & New Zealand Journal of Statistics 8 Statistical Methods and Applications 8 The Annals of Applied Statistics 7 Biometrical Journal 7 Journal of the American Statistical Association 7 Statistical Science 6 Metron 6 International Journal of Approximate Reasoning 6 Test 5 Information Sciences 5 Revue de Statistique Appliquée 5 Cybernetics and Systems Analysis 5 Statistical Modelling 5 AStA. Advances in Statistical Analysis 5 Electronic Journal of Statistics 4 Aplikace Matematiky 4 International Statistical Review 4 Kybernetika 4 Trabajos de Estadistica y de Investigacion Operativa 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Bernoulli 4 Mathematical Population Studies 4 Data Mining and Knowledge Discovery 4 Methodology and Computing in Applied Probability 4 Statistical Methods in Medical Research 3 Advances in Applied Probability 3 Scandinavian Journal of Statistics 3 Statistische Hefte. Neue Folge 3 Insurance Mathematics & Economics 3 American Journal of Mathematical and Management Sciences 3 Mathematical and Computer Modelling 3 Annals of Operations Research 3 Economics Letters 3 Pattern Recognition 3 Journal of Nonparametric Statistics 3 Journal of the Korean Statistical Society 3 Journal de la Société Française de Statistique & Revue de Statistique Appliquée 2 Artificial Intelligence 2 Computers & Mathematics with Applications 2 Information Processing Letters 2 Journal of Mathematical Biology 2 Fuzzy Sets and Systems 2 Scandinavian Actuarial Journal 2 Synthese 2 Mathematical Social Sciences 2 Operations Research Letters 2 Stochastic Analysis and Applications 2 Journal of Symbolic Computation 2 Econometric Reviews 2 Machine Learning 2 Stochastic Processes and their Applications 2 Journal of Biopharmaceutical Statistics 2 Statistica Sinica 2 PAA. Pattern Analysis and Applications 2 The Econometrics Journal 2 Probability in the Engineering and Informational Sciences 2 Brazilian Journal of Probability and Statistics 2 Statistical Applications in Genetics and Molecular Biology 2 Statistical Analysis and Data Mining 2 Journal of the Italian Statistical Society 2 Statistics Surveys 2 Journal of Theoretical Biology 2 Bayesian Analysis 2 Dependence Modeling 1 International Journal of General Systems 1 International Journal of Mathematical Education in Science and Technology 1 Journal of Computational Physics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications ...and 68 more Serials
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Cited in 28 Fields
771 Statistics (62-XX) 97 Probability theory and stochastic processes (60-XX) 85 Numerical analysis (65-XX) 76 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 55 Biology and other natural sciences (92-XX) 53 Computer science (68-XX) 30 Operations research, mathematical programming (90-XX) 23 Combinatorics (05-XX) 10 History and biography (01-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Information and communication theory, circuits (94-XX) 5 Mathematical logic and foundations (03-XX) 5 Commutative algebra (13-XX) 5 Systems theory; control (93-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Integral equations (45-XX) 2 Fluid mechanics (76-XX) 2 Geophysics (86-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX)
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http://epg.modot.mo.gov/index.php?title=620.2_Pavement_and_Curb_Markings_(MUTCD_Chapter_3B)
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# 620.2 Pavement and Curb Markings (MUTCD Chapter 3B)
## 620.2.1 Yellow Centerline Pavement Markings and Warrants (MUTCD Section 3B.01)
Standard. Centerline pavement markings, when used, shall be the pavement markings used to delineate the separation of traffic lanes that have opposite directions of travel on a roadway and shall be yellow.
Option. Centerline pavement markings may be placed at a location that is not the geometric center of the roadway.
Standard. The centerline markings on two-lane, two-way roadways shall be one of the following as shown in Fig. 620.2.2.0.1, Examples of Two-Lane, Two-Way Marking Applications:
A. Two-direction passing zone markings consisting of a normal broken yellow line where crossing the centerline markings for passing with care is permitted for traffic traveling in either direction;
B. One-direction no-passing zone markings consisting of a double yellow yellow line, one of which is a normal broken yellow line and the other is a normal solid yellow line where crossing the centerline markings for passing with care is permitted for the traffic traveling adjacent to the broken line, but is prohibited for traffic traveling adjacent to the solid line; or
C. Two-direction no-passing zone markings consisting of two normal solid yellow lines where crossing the centerline markings for passing is prohibited for traffic traveling in either direction.
A single solid yellow line shall not be used as a centerline marking on a two-lane roadway.
The centerline markings on undivided two-way roadways with four or more lanes for moving motor vehicle traffic always available shall be the two-direction no-passing zone markings consisting of a solid double yellow line separated by 4 in. as shown in Fig. 620.2.2.0.2, Examples of Four-Lane Undivided, Two-Way Marking Applications.
See Widths and Patterns of Longitudinal Pavement Markings for line patterns.
Option. Centerline marking combinations may be accomplished using a 2 line or 3 line system.
Standard. Those routes that currently are marked using a 3 line system, for centerline markings shall be maintained using the same system until such time as the line is obliterated.
On those routes that are receiving a 2 line system on only part of the route, the break between the 2 line and 3 line systems shall be at an appropriate transition point.
Option. The transition point between a 2 line and 3 line system may be a controlled intersection, railroad crossing, or the leading edge of a bridge deck.
A striping vehicle from the 1930s. The extended front functioned like a long scope, helping the driver stay true so he could place paint accurately.
Guidance. After the centerline is obliterated from the entire route, or a significant portion of the route, it should be replaced using the 2 line systems.
On two-way roadways with three through lanes for moving motor vehicle traffic, two lanes should be designated for traffic in one direction by using one- or two-direction no-passing zone markings as shown in Fig. 620.2.2.0.4, Examples of Three-Lane, Two-Way Marking Applications.
Standard. Centerline markings shall be placed on all paved roads that have traveled ways 18 ft. or wider. Centerline markings shall also be placed on all paved two-way streets or highways that have three or more lanes for moving motor vehicle traffic.
Guidance. Engineering judgment should be used in determining whether to place centerline markings on traveled ways that are narrower than 18 ft. because of the potential for traffic encroaching on the pavement edges, traffic being affected by parked vehicles, and traffic encroaching into the opposing traffic lane. Engineering judgment should also be used to determine if the pavement can support centerline markings.
Standard. Diversion bubbles shall be marked using 2 solid yellow lines to form both sides of the bubble at the beginning of a left turn bay where the bubble separates travel in opposite directions, and each installation of these markings will require individual treatment; therefore, no set dimensions have been established for their placement. Additional markings, such as cross-hatching inside the bubble, if used, shall also be yellow in color (See Fig. 620.2.2.0.3, Marking for Median Islands for Left Turn Bays).
Guidance. The taper length of transition zones should not be less than taper length calculated using the equations L = S x W or L = WS2/60 as defined in Lane Reduction Transition Markings. Installation of these markings should conform to the established general patterns.
## 620.2.2 No-Passing Zone Pavement Markings and Warrants (MUTCD Section 3B.02)
Standard. No-passing zones shall be marked by either the one direction no-passing zone pavement markings or the two-direction no-passing zone pavement markings described previously and shown in Fig. 620.2.2.0.1, Examples of Two-Lane, Two-Way Marking Applications and Fig. 620.2.2.0.4, Examples of Three-Lane, Two-Way Marking Applications.
When centerline markings are used, no-passing zone markings shall be used on two-way roadways at lane reduction transitions (see Lane Reduction Transition Markings (MUTCD Section 3B.09)) and on approaches to obstructions that must be passed on the right (see Approach Markings for Obstructions (MUTCD Section 3B.10)).
On two-way, two- or three-lane roadways where centerline markings are installed, no-passing zones shall be established at vertical and horizontal curves and other locations where an engineering study indicates that passing must be prohibited because of inadequate sight distances or other special conditions.
On roadways with centerline markings, no-passing zone markings shall be used at horizontal or vertical curves where the passing sight distance is less than the minimum necessary for reasonably safe passing at the 85th-percentile speed or the posted or statutory speed limit, whichever is higher, as shown in Table 620.2.2.1 Minimum Passing Sight Distances. The passing sight distance on a vertical curve is the distance at which an object 3.5 ft. (above the pavement surface can be seen from a point 3.5 ft. above the pavement (see Figure 620.2.2.2.1 Method of Locating and Determining the Limit of No-Passing Zones at Curves). Similarly, the passing sight distance on a horizontal curve is the distance measured along the centerline (or right-hand lane line of a three-lane roadway) between two points 3.5 ft. above the pavement on a line tangent to the embankment or other obstruction that cuts off the view on the inside of the curve (see Figure 620.2.2.2.1 Method of Locating and Determining the Limit of No-Passing Zones at Curves).
Guidance. Where the distance between successive no-passing zones is less than 400 ft., no-passing markings should connect the zones.
No passing zones should also be provided for a distance of 120 ft. in advance of intersections requiring traffic to stop, including intersections controlled by either stop signs or signals.
Standard. Where the no passing zone crosses a speed limit boundary, such as at city limits, the no passing zone shall be logged using the criteria for that section of roadways based on the posted speed limit or 85th percentile speed, whichever is greater only if there is a sufficient length of roadway to warrant this change.
No-passing zone markings shall be used on approaches to highway-rail grade crossings in conformance with MUTCD Section 8B.27. The minimum length of a no-passing zone on a railroad crossing approach shall be 500 feet.
Option. In addition to pavement markings, no-passing zone signs (see DO NOT PASS Sign, PASS WITH CARE Sign, and NO PASSING ZONE Sign) may be used to emphasize the existence and extent of a no-passing zone. The approval of the State Traffic Engineer is required before signs are used to enhance no-passing zones.
Support. Section 11-307 of the “Uniform Vehicle Code (UVC) Revised” contains further information regarding no-passing zones. The “UVC” can be obtained from the [www.ncutlo.org National Committee on Uniform Traffic Laws and Ordinances].
Guidance. The centerline marking on multi-lane, undivided roadways with 4 or more lanes should be marked using 2 solid yellow lines, 4 in. wide and separated by a minimum of 4 inches.
Fig. 620.2.2.0.1, Examples of Two-Lane, Two-Way Marking Applications (MUTCD Fig. 3B-1)
Fig. 620.2.2.0.2, Examples of Four-or-more-Lane, Two-Way Marking Applications (MUTCD Fig. 3B-2)
Fig. 620.2.2.0.3, Marking for Median Islands for Left Turn Bays
Fig. 620.2.2.0.4, Examples of Three-Lane, Two-Way Marking Applications (MUTCD Fig. 3B-3)
Standard. In no case shall a no passing zone be less than 500 ft. long. If the calculated no passing zone is less than 500 ft., an additional length of marking shall be added to the leading end of the zone to lengthen it to the full 500 feet.
On three-lane roadways where the direction of travel in the center lane transitions from one direction to the other, a no-passing buffer zone shall be provided in the center lane as shown in Figure 903.17.24 Typical Signing for Passing Lanes. A lane transition shall be provided at each end of the buffer zone.
The buffer zone shall be a flush median island formed by two sets of double yellow centerline markings that is at least 50 ft. long.
Guidance. For three-lane roadways having a posted or statutory speed limit of 45 mph or greater, the lane transition taper length should be computed by the formula L = WS for speeds in mph. For roadways where the posted or statutory speed limit is less than 45 mph, the formula L = WS2/60 for speeds in mph should be used to compute taper length. Under both formulas, L equals the taper length in feet, W equals the width of the center lane or offset distance in feet, and S equals the 85th-percentile speed or the posted or statutory speed limit, whichever is higher.
Standard. The minimum lane transition taper length shall be 100 ft. in urban areas and 200 ft. in rural areas.
When used to delineate between climbing lanes on long grades, a no passing zone shall be provided on the taper as well as a distance of 1/2 the taper length in advance of and following the taper.
Guidance. The tangent line should not extend beyond the right-of-way line. Consideration should be given to vegetation or any other seasonal variations when determining the locations of no passing zones (see Fig. 620.2.2.2.1, Method of Locating and Determining the Limit of No-Passing Zones at Curves).
When performing a speed study, an attempt should be made to complete a minimum of 1 study per 10-mile section of roadway, each at a typical section of the roadway. This spacing may vary depending on the degree of uniformity, varying geometrics, cross sections and roadside development. Generally, the criteria determined for a route should be consistent throughout its entire length, without fluctuation due to short changes in terrain that could produce lower speeds. Substantial sections of roadway that have been reconstructed, and thereby provide an increased prevailing speed, should be considered independently of the overall route.
Support. The beginning of a no-passing zone at point “a” in Fig. 620.2.2.2.1, Method of Locating and Determining the Limit of No-Passing Zones at Curves is that point where the sight distance first becomes less than that specified in Table 620.2.2.1 Minimum Passing Sight Distances for No-Passing Zone Markings. The end of the no-passing zone at point “b” in Fig. 620.2.2.2.1 Method of Locating and Determining the Limit of No-Passing Zones at Curves is that point at which the sight distance again becomes greater than the minimum specified.
The values of the minimum passing sight distance that are shown in Table 620.2.2.1 are for operational use in marking no-passing zones and are less than the values that are suggested for geometric design by AASHTO's A Policy on Geometric Design of Highways and Streets.
Guidance. The lane delineation between the climbing lanes provided on long grades, and the descending lane, should be accomplished using centerline markings. In these cases, if the conditions are adequate, a passing zone should be provided for traffic traveling in the single, down grade, lane. A no passing zone should be provided for the length of the climbing lanes for traffic traveling up grade. The up grade climbing lanes should be delineated from each other using a white broken line (see Fig. 620.2.9.2 Standard Pavement Markings for Climbing Lanes).
### 620.2.2.1 Establishing and Recording No Passing Zones
Standard. The establishment of no passing zones shall be accomplished using two vehicles maintaining a predetermined distance. This distance will mark the beginning and end of the no passing zone section where a target, 3.5 ft. above the road surface on the lead vehicle is just out of sight of the driver of the trailing vehicle, who's eye level is 3.5 ft. above the road surface. The use of a highly visible target, such as a flashing amber light, is recommended.
Guidance. The distance between the vehicles should be maintained constant and equal to the minimum passing sight distance value being used. A printed log of the no passing zone should be kept by the district office and copies given to the regional maintenance superintendents so no passing zones can be relocated after maintenance operations.
Option. Once determined, the beginning and end of no passing zones may be marked on the pavement by using an aerosol spray paint or a paint brush.
Table 620.2.2.1 Minimum Passing Sight Distances for No-Passing Zone Markings (MUTCD Table 3B-1)
85th Percentile of Posted or Statutory Speed Limit (mph) Minimum Passing Sight Distance (ft.)
30 500
35 550
40 600
45 700
50 800
55 900
60 1,000
65 1,100
70 1,200
### 620.2.2.2 Centerline Markings On Bridges
Standard. The centerline markings on bridges, having a clear roadway width of 16 ft. or greater, shall be the same as that marked on the adjoining roadway.
Centerline markings shall not be placed on one lane bridges. When dealing with this type of bridge, the centerline markings shall stop a distance of five 500 ft. from each edge of the bridge deck. Therefore, the length of surface not receiving centerline marking shall be 1,000 ft. plus the length of the bridge deck. These bridges will, however, receive the appropriate one-lane bridge markings (see Edgeline Pavement Markings (MUTCD Section 3B.06)).
Fig. 620.2.2.2.1, Method of Locating and Determining the Limit of No-Passing Zones at Curves (MUTCD Fig. 3B-4)
Fig. 620.2.2.2.2, Example of Application of Three-Lane, Two-Way Marking for Changing Direction of the Center Lane (MUTCD 3B-5)
Fig. 620.2.2.2.3, Example of Reversible Lane Marking Application (MUTCD 3B-6)
Fig. 620.2.2.2.4, Example of Two-Way Left-Turn Lane Marking Application (MUTCD 3B-7)
## 620.2.3 Other Yellow Longitudinal Pavement Markings (MUTCD Section 3B.03)
Standard. If reversible lanes are used, the lane line pavement markings on each side of reversible lanes shall consist of a normal broken double yellow line to delineate the edge of a lane in which the direction of travel is reversed from time to time, such that each of these markings serve as the centerline markings of the roadway during some period (see Example of Reversible Lane Marking Application)).
Signs (see REVERSIBLE LANE CONTROL Signs)), lane-use control signals (see Chapter 4M of MUTCD), or both shall be used to supplement reversible lane pavement markings.
If a two-way left-turn lane that is never operated as a reversible lane is used, the lane line pavement markings on each side of the two-way left-turn lane shall consist of a normal broken yellow line and a normal solid yellow line to delineate the edges of a lane that can be used by traffic in either direction as part of a left-turn maneuver. These markings shall be placed with the broken line toward the two-way left-turn lane and the solid line toward the adjacent traffic lane as shown in Example of Two-Way, Left-Turn Marking Applications.
White two-way left-turn lane-use arrows shall be used to indicate the proper use of these lanes. The left turn arrows shall be installed in pairs, one arrow per direction.
Option. Additional signs may be installed after major intersections, or in situations that require additional emphasis of the proper use of this lane. Two way left turn lanes may be established by the district if the roadway meets all of the guidelines listed in Two-Way Left-Turn Lanes.
Guidance. The pairs of arrows should be installed a maximum of 500 ft. apart, with the two arrows in the pair being 8 to 16 ft. apart (See Fig. 620.2.2.2.4, Example of Two-Way, Left-Turn Marking Applications) on the route containing this type of lane.
Signs should be used in conjunction with the two-way left turn markings (see TWO-WAY LEFT TURN ONLY/CENTER LANE ONLY Signs).
Standard. If a continuous flush median island formed by pavement markings separating travel in opposite directions is used, two sets of double solid yellow lines shall be used to form the island as shown in Fig. 620.2.2.0.2, Examples of Four-Lane Undivided, Two-Way Marking Applications and Fig. 620.2.2.2.2, Examples of Three-Lane, Two-Way Marking for Changing Direction of the Center Lane. Other markings in the median island area shall also be yellow, except crosswalk markings which shall be white (see Crosswalk Markings).
Option. Markings may be used to form islands as shown in Fig. 620.2.2.0.3 Marking for Median Islands for Left Turn Bays.
## 620.2.4 White Lane Line Pavement Markings and Warrants (MUTCD Section 3B.04)
Standard. When used, lane line pavement markings delineating the separation of traffic lanes that have the same direction of travel shall be white.
Lane line markings shall be used on all freeways and interstate highways.
Lane line markings shall be used on all roadways that are intended to operate with two or more adjacent traffic lanes in the same direction of travel, except as required for reversible lanes.
Guidance. Lane line markings should also be used at congested locations where the roadway will accommodate more traffic lanes with lane line markings than without the markings.
The lane width delineated by lane line pavement markings should not be less than 10 ft., with 12 ft. as the standard dimension.
Standard. White lane line, intermittent pavement markings on new concrete pavements shall be enhanced by the use of contrast markings.
Support. Examples of lane line markings are shown in the following figures:
Fig. 620.2.2.0.2, Examples of Four-or-More Lane, Two-Way marking Applications (MUTCD 3B-2)
Fig. 620.2.2.0.3, Marking for Median Islands for Left Turn Bays
Fig. 620.2.2.0.4, Examples of Three-Lane, Two-Way Marking Applications (MUTCD 3B-3)
Fig. 620.2.2.2.3, Examples of Reversible Lane Marking Application (MUTCD 3B-6)
Fig. 620.2.2.2.4, Example of Two-Way Left-Turn Lane Marking Application (MUTCD 3B-7)
Fig. 620.2.5.1, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 1 of 2) (MUTCD 3B-8)
Fig. 620.2.5.2, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 2 of 2) (MUTCD 3B-8)
Fig. 620.2.5.3, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 1 of 2) (MUTCD 3B-9)
Fig. 620.2.5.4, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 2 of 2) (MUTCD 3B-9)
Fig. 620.2.5.5, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 1 of 5) (MUTCD 3B-10)
Fig. 620.2.5.6, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 2 of 5) (MUTCD 3B-10)
Fig. 620.2.5.7, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 3 of 5) (MUTCD 3B-10)
Fig. 620.2.5.8, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 4 of 5) (MUTCD 3B-10)
Fig. 620.2.5.9, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 5 of 5) (MUTCD 3B-10)
Fig. 620.2.7, Edgeline Striping for At Grade Intersections
Fig. 620.2.7.1.1, Examples of Applications for Lane-Reduction Transition marking (MUTCD 3B-14)
Fig. 620.2.9.2, Standard Pavement markings for climbing Lanes
Fig. 620.2.10.1, Examples of Applications of Markings for Obstructions in the Roadway (Sheet 1 of 2) (MUTCD 3B-15)
Fig. 620.2.10.2, Examples of Applications of Markings for Obstructions in the Roadway (Sheet 2 of 2) (MUTCD 3B-15)
Standard. Where crossing the lane line markings with care is permitted, the lane line markings shall consist of a normal broken white line (See EPG 620.1.6 Functions, Widths and Patterns of Longitudinal Pavement Markings (MUTCD Section 3A.06)).
A dotted white line marking shall be used as the lane line to separate a through lane that continues beyond the interchange or intersection from an adjacent lane for any of the following conditions:
A. A deceleration or acceleration lane,
B. A through lane that becomes a mandatory exit or turn lane,
C. An auxiliary lane 2 miles or less in length between an entrance ramp and an exit ramp, or
D. An auxiliary lane 1 mile or less in length between two adjacent intersections.
For exit ramps with a parallel deceleration lane, a normal width dotted white lane line shall be installed from the upstream end of the full-width deceleration lane to the theoretical gore or to the upstream end of a solid white lane line, if used, that extends upstream from the theoretical gore as shown in "A" of Fig. 620.2.5.1 and "C" of Fig. 620.2.5.2.
Option. For exit ramps with a parallel deceleration lane, a normal width dotted white line extension may be installed in the taper area upstream from the full-width deceleration lane as shown in "A" of Fig. 620.2.5.1 and "C" of Fig. 620.2.5.2.
For an exit ramp with a tapered deceleration lane, a normal width dotted white line extension may be installed from the theoretical gore through the taper area such that it meets the edgeline at the upstream end of the taper as shown in "A" of Fig. 620.2.5.1.
Standard. For entrance ramps with a parallel acceleration lane, a normal width dotted white lane line shall be installed from the theoretical gore or from the downstream end of a solid white lane line, if used, that extends downstream from the theoretical gore, to a point at least one-half the distance from the theoretical gore to the downstream end of the acceleration taper, as shown in "A" of Fig. 620.2.5.3.
Option. For entrance ramps with a parallel acceleration lane, a normal width dotted white line extension may be installed from the downstream end of the dotted white lane line to the upstream end of the acceleration taper, as shown in "A" of Fig. 620.2.5.3.
For entrance ramps with a tapered acceleration lane, a normal width dotted white line extension may be installed from the downstream end of the channelizing line adjacent to the through lane to the theoretical gore, as shown in "B" of Fig. 620.2.5.3 and Fig 620.2.5.4.
Standard. A wide dotted white lane line shall be used:
A. As a lane drop marking in advance of lane drops at exit ramps to distinguish a lane drop from a normal exit ramp (see Figs.620.2.5.5, 620.2.5.6 and 620.2.5.7).
B. In advance of freeway route splits with dedicated lanes (see Fig. 620.2.5.8),
C. To separate a through lane that continues beyond an interchange from an adjacent
auxiliary lane between an entrance ramp and an exit ramp (see Fig. 620.2.5.9),
D. As a lane drop marking in advance of lane drops at intersections to distinguish a lane drop from an intersection through lane (see Fig. 620.2.5.10.1) and
E. To separate a through lane that continues beyond an intersection from an adjacent auxiliary lane between two intersections (see Fig. 620.2.5.10.2).
Guidance. Lane drop markings used in advance of lane drops at freeway and expressway exit ramps should begin at least 1/2 mile in advance of the theoretical gore or where signing indicates the exit only condition.
On the approach to a multi-lane exit ramp having an optional exit lane that also carries through traffic, lane line markings should be used as illustrated in Fig. 620.2.5.6. In this case, if the right-most exit lane is an added lane such as a parallel deceleration lane, the lane drop marking should begin at the upstream end of the full-width deceleration lane, as shown in Fig. 620.2.5.2.
Lane drop markings used in advance of lane drops at intersections should begin a distance in advance of the intersection that is determined by engineering judgment as suitable to enable drivers who do not desire to make the mandatory turn to move out of the lane being dropped prior to reaching the queue of vehicles that are waiting to make the turn. The lane drop marking should begin no closer to the intersection than the most upstream regulatory or warning sign associated with the lane drop.
The dotted white lane lines that are used for lane drop marking and that are used as a lane line separating through lanes from auxiliary lanes should consist of line segments that are 3 ft. long separated by 9 ft. gaps.
Support. EPG 620.2.20 contains information regarding other markings that are associated with lane drops, such as lane-use arrow markings and ONLY word markings.
EPG 620.2.9 contains information about the lane line markings that are to be used for transition areas where the number of through lanes is reduced.
Standard. Where crossing the lane line markings is discouraged, the lane line markings shall consist of a normal or wide solid white line.
Option. Where it is intended to discourage lane changing on the approach to an exit ramp, a wide solid white lane line may extend upstream from the theoretical gore or, for multiple lane exits, as shown in Fig. 620.2.5.6, for a distance that is determined by engineering judgment.
A solid lane line may also be used in lieu of the broken lane line to accentuate the lane marking in critical areas, such as, to separate a turn lane from the main traffic lanes at an intersection or to discourage lane changing at the approaches to intersections.
Where lane changes might cause conflicts, a wide or normal solid white lane line may extend upstream from an intersection.
In the case of a lane drop at an exit ramp or intersection, such a solid white line may replace a portion, but not all of the length of the wide dotted white lane line.
Support. EPG 620.2.9 contains information about the lane line markings that are to be used for transition areas where the number of through lanes is reduced.
Guidance. On approaches to intersections, a solid white lane line marking should be used to separate a through lane from an added mandatory turn lane.
Option. On approaches to intersections, solid white lane line markings may be used to separate adjacent through lanes or adjacent mandatory turn lanes from each other.
Where the median width allows the left-turn lanes to be separated from the through lanes to give drivers on opposing approaches a less obstructed view of opposing through traffic, white pavement markings may be used to form channelizing islands as shown in Figure 2B-17 of the MUTCD.
Solid white lane line markings may be used to separate through traffic lanes from auxiliary lanes, such as an added uphill truck lane or a preferential lane.
Wide solid lane line markings may be used for greater emphasis.
Standard. Where crossing the lane line markings is prohibited, the lane line markings shall consist of a solid double white line (see Fig. 620.2.5.11).
Guidance. When considering the use of double solid white lines to prohibit crossing all of the following criteria should be considered:
1. There has to be an identifiable need, such as crash history that the use of double solid white lines would expect to correct.
2. There needs to be a local ordinance supporting the crossing restriction and enforcement.
3. There needs to be proper signing of the restriction in advance and at the restricted area along with sufficient distance for motorist who need to properly change lanes prior to the start of the restriction.
4. Approval of the State Traffic Engineer is required before implementation.
Standard. Lane lines shall be offset approximately 2 in. to the right of the longitudinal joint. These 2 in. shall be the space between the longitudinal joint and the left edge of the lane line.
## 620.2.5 Other White Longitudinal Pavement Markings (MUTCD Section 3B.05)
Standard. A channelizing line shall be a wide or double solid white line.
Option. Channelizing lines may be used to form channelizing islands where traffic traveling in the same direction is permitted on both sides of the island.
Standard. Channelizing lines used to mark gores shall be wide solid white lines.
Other pavement markings in the channelizing island area shall be white.
Support. Examples of channelizing line applications are shown in the following figures:
Fig. 620.2.5.1, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 1 of 2) (MUTCD 3B-8)
Fig. 620.2.5.2, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 2 of 2) (MUTCD 3B-8)
Fig. 620.2.5.3, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 1 of 2) (MUTCD 3B-9)
Fig. 620.2.5.4, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 2 of 2) (MUTCD 3B-9)
Fig. 620.2.5.5, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 1 of 5) (MUTCD 3B-10)
Fig. 620.2.5.6, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 2 of 5) (MUTCD 3B-10)
Fig. 620.2.5.7, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 3 of 5) (MUTCD 3B-10)
Fig. 620.2.5.8, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 4 of 5) (MUTCD 3B-10)
Fig. 620.2.5.9, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 5 of 5) (MUTCD 3B-10)
Channelizing lines at exit ramps as shown in Fig. 620.2.5.1, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 1 of 2) and Fig. 620.2.5.2, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 2 of 2) define the neutral area, direct exiting traffic at the proper angle for smooth divergence from the main lanes into the ramp, and reduce the probability of colliding with objects adjacent to the roadway.
Channelizing lines at entrance ramps as shown in Fig. 620.2.5.3, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 1 of 2) promote orderly and efficient merging with the through traffic.
Standard. For all exit ramps and for entrance ramps with parallel acceleration lanes, channelizing lines shall be placed on both sides of the neutral area (see Fig. 620.2.5.1, Fig. 620.2.5.2, Fig. 620.2.5.5, Fig. 620.2.5.6, Fig. 620.2.5.7, Fig. 620.2.5.8, Fig. 620.2.5.9 and "A" in Fig. 620.2.5.3.
For entrance ramps with tapered acceleration lanes, channelizing lines shall be placed along both sides of the neutral area to a point at least one-half of the distance to the theoretical gore (see Fig. 620.2.5.4).
Option. For entrance ramps with tapered acceleration lanes, the channelizing lines may extend to the theoretical gore as shown in Fig. 620.2.5.3.
Fig. 620.2.5.1, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 1 of 2 of MUTCD 3B-8)
Fig. 620.2.5.2, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings (Sheet 2 of 2 of MUTCD 3B-8)
Fig. 620.2.5.3, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 1 of 2 of MUTCD 3B-9)
Fig. 620.2.5.4, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings (Sheet 2 of 2 of MUTCD 3B-9)
Fig. 620.2.5.5, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 1 of 5 of MUTCD 3B-10)
Fig. 620.2.5.6, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 2 of 5 of MUTCD 3B-10)
Fig. 620.2.5.7, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 3 of 5 of MUTCD 3B-10)
Fig. 620.2.5.8, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 4 of 5 of MUTCD 3B-10)
Fig. 620.2.5.9, Examples of Applications of Freeway and Expressway Lane-Drop Markings (Sheet 5 of 5 of MUTCD 3B-10)
Fig. 620.2.5.10.1, Examples of Applications of Conventional Road Lane-Drop Marking (Sheet 1 of 2 of MUTCD 3B-11)
Fig. 620.2.5.10.2, Examples of Applications of Conventional Road Lane-Drop Marking (Sheet 2 of 2 of MUTCD 3B-11)
Option. White chevron crosshatch markings (see EPG 620.2.24) may be placed in the neutral area of exit and entrance ramp gores for special emphasis as shown in Figs. 620.2.5.1 and 620.2.5.2, Figs. 620.2.5.5 through 620.2.5.9 and "A" of Fig. 620.2.5.3. The channelizing lines and the optional chevron crosshatch markings at exit ramp and entrance ramp gores may be supplemented with white retroreflective or internally illuminated raised pavement markers (see EPG 620.2.11) for enhanced nighttime visibility.
Guidance. The right edge of the acceleration lane edgeline should be continuous with the right edge of the gore stripe to provide a smooth, uninterrupted edgeline.
Options. In areas of limited sight distance due to vertical and/or horizontal curves, an edgeline extension may be used to delineate acceleration and deceleration lanes.
Standard. When entrance and exit ramp pavements are adjacent to each other, a double normal 4 in. solid yellow line extending from the points of channelization shall be used.
Fig. 620.2.5.11, Example of Solid Double White Lines Used to Prohibit Lane Changing
## 620.2.6 Edgeline Pavement Markings (MUTCD Section 3B.06)
Standard. If used, edgeline pavement markings shall delineate the right or left edges of a roadway.
Except for dotted edgeline extensions (see EPG 620.2.8), edgeline markings shall not be continued through intersections or major driveways.
If used on the roadways of divided highways or one-way streets, or on any ramp in the direction of travel, left edgeline pavement markings shall consist of a normal solid yellow line to delineate the left-hand edge of a roadway or to indicate driving or passing restrictions left of these markings.
If used, right edgeline pavement markings shall consist of a normal solid white line to delineate the right-hand edge of the roadway.
Guidance. The edgeline at the intersection of an at-grade crossing on a divided highway should begin and end at the taper points points when the intersection has no deceleration lanes. Where deceleration lanes are present, the edgeline should continue along the outside of the deceleration lane to the beginning of the turn radius (see Fig. 620.2.7 Edgeline Striping for At-Grade Intersections).
Option. Edgeline extension lines may be used at the district's discretion.
Guidance. Edgeline markings should not be broken for driveways or minor intersecting roads (See Fig. 620.2.7).
Permanent marking material should be used for marking the edgeline extension.
Support. Edgeline markings have unique value as visual references to guide road users during adverse weather and visibility conditions.
Option. Wide solid edgeline markings may be used for greater emphasis.
## 620.2.7 Warrants for Use of Edge Lines (MUTCD Section 3B.07)
Standard. Edgeline markings shall be placed on all divided highways and all routes with a weighted AADT of 400 or greater and a minimum pavement width of 20 feet.
Support. Edgelines on routes with weighted AADT between 400 and 1,000 were added to the program by December 31, 2012.
Option. Edgeline markings may be excluded, based on engineering judgment, for reasons such as if the traveled way edges are delineated by curbs, parking or other markings or where the pavement edge is not in good condition.
If a bicycle lane is marked on the outside portion of the traveled way, the edgeline that would mark the outside edge of the bicycle lane may be omitted.
Edgeline markings may be used where edge delineation is desirable to minimize unnecessary driving on paved shoulders or on refuge areas that have lesser structural pavement strength than the adjacent roadway.
Fig. 620.2.7, Edgeline Striping for At Grade Intersection
### 620.2.7.1 Bridge Edgeline
Standard. Bridges that are located on routes authorized for edgeline shall be striped in accordance with the following classifications (see Fig. 620.2.7.1.1 and Fig. 620.2.7.1.2, Bridge Edgeline Striping):
A. Non-shoulder width bridges that have been constructed with a deck less than 2 ft. wider than the adjacent roadway on each side of the pavement shall not have the edgeline placed on the bridge deck. The edgeline shall end on the adjacent roadway 50 ft. from the bridge deck.
B. Bridges wider than the roadway pavement by more than 2 ft. on each side shall receive edgeline that will be continuous with that of the adjoining roadway.
C. Three lane bridges designed and constructed with an additional lane for future use shall be marked as a two lane bridge. The edgeline in these cases shall not be offset to provide for the usage of the third lane and will be continuous across the bridge.
D. One lane bridges, weight restricted, have a reduced driving surface due to an inability to carry the weight of two lanes of traffic. These bridges shall be marked using a wide white edgeline that forms a 12 ft. travel lane on the bridge deck. These edgelines shall then taper from the edge of the bridge deck 200 ft. to the edge of the roadway pavement. The centerline marking, if applicable, shall end 500 ft. from the end of the bridge deck.
E. One Lane Bridges, Width Restriction, having a clear traveling surface 16 ft. or less shall be marked using a wide white edgeline that forms a 12 ft. travel lane on the bridge deck. These edgelines shall then taper from the edge of the bridge deck 200 ft. to the edge of the roadway pavement. The centerline marking, if applicable, shall end 500 ft. prior to the bridge deck.
Guidance. Special attention should be given to all bridges whose shoulders are 2 ft. or wider than the shoulders of the adjacent roadway.
Standard. If bridges whose shoulders are 2 ft. or wider than the shoulders of the adjacent roadway are on routes authorized for centerline marking, but not edgeline marking they shall be edgelined to delineate the travel way of the bridge. The edgeline marking for these bridges shall begin 500 ft. ahead of, and end 500 ft. beyond, the bridge deck, and are intended to guide vehicles from the wider bridge deck to the narrower adjacent roadway. (See Fig. 620.2.7.1.1 and Fig. 620.2.7.1.2).
Fig. 620.2.7.1.1, Bridge Edgeline Striping
Fig. 620.2.7.1.2, Bridge Edgeline Striping
## 620.2.8 Extensions Through Intersections or Interchanges (MUTCD Section 3B.08)
Standard. Except as provided in the Option, below, pavement markings extended into or continued through an intersection or interchange area shall be the same color and at least the same width as the line markings they extend.
Intersections that provide dual left turn lanes shall have extension lines traffic can follow through the intersection except as provided in the Support, below. These lines shall be marked with normal white skips, 2 ft. long and separated by 4 ft. gaps, and shall follow the appropriate turning radius of the intersection. This line shall begin at the solid white lane line of the left turn bay and end at the lane line delineating the lanes the traffic is being channelized to.
Option. A normal lane line may be used to extend a wide line through an intersection.
Support. Exceptions will be allowed when an intersection lacks adequate space to place extension lines for dual left turn lanes when an intersection lacks adequate space to place these lines for opposing left turn movements.
Guidance. Long life pavement markings should be used for extensions.
An attempt should be made to keep the painted portion of this line out of the wheel tracks to promote longer life.
Where highway design or reduced visibility conditions make it desirable to provide control or to guide vehicles through an intersection or interchange, such as at offset, skewed, complex, or multi-legged intersections, on curved roadways, where multiple turn lanes are used, or where offset left turn lanes might cause driver confusion, dotted line extension markings consisting of 2 ft. line segments and 4 ft. gaps should be used to extend longitudinal line markings through an intersection or interchange area.
Option. Dotted edgeline extensions may be placed through intersections or major driveways.
Guidance. Where greater restriction is required, solid lane lines or channelizing lines should be extended into or continued through intersections or major driveways.
Standard. Solid lines shall not be used to extend edgelines into or through major intersections or major driveways.
Guidance. Where a double line is extended through an intersection, a single line of equal width to one of the lines of the double line should be used.
To the extent possible, pavement marking extensions through intersections should be designed in a manner that minimizes potential confusion for drivers in adjacent or opposing lanes.
Fig. 620.2.8.1, Examples of Line Extensions through Intersections (Sheet 1 of 2, MUTCD 3B-13)
Fig. 620.2.8.2, Examples of Line Extensions through Intersections (Sheet 1 of 2, MUTCD 3B-13)
## 620.2.9 Lane Reduction Transition Markings (MUTCD Section 3B.09)
Support. Lane-reduction transition markings are used where the number of through lanes is reduced because of narrowing of the roadway or because of a section of on-street parking in what would otherwise be a through lane. Lane-reduction transition markings are not used for lane drops.
Standard. Except as provided in the Option, below, where pavement markings are used, lane reduction transition markings shall be used to guide traffic through transition areas where the number of through lanes is reduced, as shown in Fig. 620.2.9.1, Examples of Applications of Lane-Reduction Transition Marking. On two-way roadways, no-passing zone markings shall be used to prohibit passing in the direction of the convergence, and shall continue through the transition area.
Option. On low-speed urban roadways where curbs clearly define the roadway edge in the lane-reduction transition, or where a through lane becomes a parking lane, the edgeline and/or delineators shown in Fig. 620.2.9.1 may be omitted as determined by engineering judgment.
Standard. For roadways having a posted or statutory speed limit of 45 mph or greater, the transition taper length for a lane reduction shall be greater or equal to the length computed by the formula L = WS.
Guidance. For roadways where the posted or statutory speed limit is less than 45 mph, the formula $L = \frac{WS^2}{ 60}$ should be used to compute taper length.
Support. Under both formulas, L equals the taper length in ft., W equals the width of the offset distance in ft., and S equals the 85th-percentile speed or the posted or statutory speed limit, whichever is higher.
Guidance. Where observed speeds exceed posted or statutory speed limits, longer tapers should be used.
Option. On new construction, where no posted or statutory speed limit is established, the design speed may be used in the transition taper length formula.
Guidance. Lane line markings should be discontinued one-quarter of the distance between the Lane Ends sign (see LANE END Signs) and the point where the transition taper begins.
Except as provided in the Option, above, for low-speed urban roadways, edgeline markings should be installed from the location of the warning sign to beyond the beginning of the narrower roadway.
Support. Pavement markings at lane reduction transitions supplement the standard signs or delineators. See EPG 620.2.20, Pavement Word and Symbol Markings for provisions regarding use of lane-reduction arrows.
Fig. 620.2.9.1, Examples of Applications of Lane-Reduction Transition Marking (MUTCD 3B-14)
Fig. 620.2.9.2, Standard Pavement Markings for Climbing Lanes
Note: Refer to Fig. 620.2.9.1 for "L" and "E".
Fig. 620.2.9.3, Markings for Pavement Transitions
Refer to EPG 620.5 Delineators for delineator spacing.
## 620.2.10 Approach Markings for Obstructions (MUTCD Section 3B.10)
Standard. Pavement markings shall be used to guide traffic away from fixed obstructions within a paved roadway. Approach markings for bridge supports, refuge islands, median islands, and raised channelization islands shall consist of a tapered line or lines extending from the centerline or the lane line to a point 1 to 2 ft. to the right-hand side, or to both sides, of the approach end of the obstruction (see Fig. 620.2.10.1 Examples of Applications of Markings for Obstructions in the Roadway).
All lines used as obstruction pavement markings shall be no less than 4 in. and no more than 24 in. wide.
For roadways having a posted or statutory speed limit of 45 mph or greater, the taper length of the tapered line markings shall be computed by the formula L = WS.
Guidance. For roadways where the posted or statutory speed limit is less than 45 mph, the formula $L = \frac{WS^2}{60}$ for speeds in mph shall be used to compute taper length.
Support. Under both formulas, L equals the taper length in ft., W equals the width of the offset distance in ft. and S equals the 85th-percentile speed or the posted or statutory speed limit, whichever is higher.
Standard. The minimum taper length shall be 100 ft. in urban areas and 200 ft. in rural areas.
Support. Examples of approach markings for obstructions in the roadway are shown in Fig. 620.2.10.1 Examples of Applications of Markings for Obstructions in the Roadway.
Option. Where observed speeds exceed posted or statutory speed limits, longer tapers may be used.
Unique situations may require special markings or warning devices.
Standard. If traffic is required to pass only to the right of the obstruction, the markings shall consist of a two-direction no-passing zone marking at least twice the length of the diagonal portion as determined by the appropriate taper formula (see Fig. 620.2.10.1 Examples of Applications of Markings for Obstructions in the Roadway.
Option. If traffic is required to pass only to the right of the obstruction, yellow diagonal crosshatch markings (see EPG 620.2.24 may be placed in the flush median area between the no-passing zone markings as shown in Fig. 620.2.10.1. Other markings, such as yellow delineators, yellow channelizing devices, yellow raised pavement markers, and white crosswalk pavement markings, may also be placed in the flush median area.
Standard. If traffic can pass either to the right or left of the obstruction, the markings shall consist of two normal channelizing lines diverging from the lane line, one to each side of the obstruction. In advance of the point of divergence, a wide solid white line or normal solid double white line shall be extended in place of the broken lane line for a distance equal to the length of the diverging lines (see Fig. 620.2.10.1).
If diagonal lines, yellow or white are used, these markings shall be a minimum of 24 in. wide and slope away from the direction traffic is traveling in (see Fig. 620.2.10.1).
When an obstruction lies in the direct line of traffic, it shall be marked.
Option. If traffic can pass either to the right or left of the obstruction, additional white markings may be placed in the flush median area between the channelizing lines as shown in Fig. 620.2.10.1. Other markings, such as white delineators, white channelizing devices, white raised pavement markers, and white crosswalk markings may also be placed in the flush median area.
Option. The obstruction and marking may, if possible, be illuminated by overhead lighting that will adequately light the object without throwing a glare in the face of traffic approaching from either direction.
Standard. Reflective object markers shall be used.
Fig. 620.2.10.1, Examples of Applications of Markings for Obstructions in the Roadway (Sheet 1 of 2, MUTCD 3B-15)
Fig. 620.2.10.2, Examples of Applications of Markings for Obstructions in the Roadway (Sheet 2 of 2, MUTCD 3B-15)
## 620.2.11 Raised Pavement Markers (MUTCD Section 3B.11)
Support. There are two types of raised pavement markers, temporary and snowplowable. There are also two types of temporary markers. The Type 1 temporary marker is used on surface treatment projects and is applied before the surface treatment is applied. Type 1 temporary markers are also used for temporary edgeline marking and may be used as part of the "cluster marking" for lane lines on divided highways. The Type 2 temporary marker may be used on final surfaces on paving projects. The Type 2 markers are also part of the "cluster marking" for lane lines on divided highways. Snowplowable raised pavement markers are considered to be long life marking application.
MoDOT is responsible for the maintenance of snowplowable raised pavement markers. This maintenance involves the replacement of the reflective lenses that are inlaid into the castings and checking that the castings are firmly in the pavement.
Standard. The color of raised pavement markers under both daylight and nighttime conditions shall conform to the color of the marking for which they serve as a positioning guide, or for which they supplement or substitute.
No new snowplowable raised pavement markers will be installed on MoDOT roads.
Snowplowable raised pavement markers that are found to be loose in the pavement shall be removed.
Option. The side of a raised pavement marker that is visible to traffic proceeding in the wrong direction may be red (see EPG 620.1.5 Colors).
Retroreflective or internally illuminated raised pavement markers may be used in the roadway immediately adjacent to curbed approach ends of raised medians and curbs of islands, or on top of such curbs (see EPG 620.2.23).
Support. Retroreflective and internally illuminated raised pavement markers are available in mono-directional and bidirectional configurations. The bidirectional marker is capable of displaying the applicable color for each direction of travel.
Standard. When used, internally illuminated raised pavement markers shall be steadily illuminated and shall not be flashed.
Support. Flashing raised pavement markers are considered to be In-Roadway Lights (see MUTCD Chapter 4N).
Guidance. The spacing of raised pavement markers used to supplement or substitute for other types of longitudinal markings should correspond with the pattern of broken lines for which the markers supplement or substitute.
A visual inspection should be performed in the spring of the year to determine the condition and the number of reflectors needed to maintain the markers. The replacement schedule should be determined by the district to best use available time and personnel. This survey should also include the condition of the castings in the pavement.
Standard. The value of N for the spacing of raised pavement markers shall equal the length of one line segment plus one gap of the broken lines used on the highway.
The spacing of temporary pavement markers shall be in accordance with Standard Plan 620.
Option. The replacement of defective reflectors may be accomplished under contract.
## 620.2.12 Raised Pavement Markers as Vehicle Positioning Guides with Other Longitudinal Markings (MUTCD Section 3B.12)
Not used in Missouri.
## 620.2.13 Raised Pavement Markers Supplementing Other Markings (MUTCD Section 3B.13)
Not used in Missouri.
## 620.2.14 Raised Pavement Markers Substituting for Pavement Markings (MUTCD Section 3B.14)
Not used in Missouri.
## 620.2.15 Transverse Markings (MUTCD Section 3B.15)
Standard. Transverse markings, which include shoulder markings, word and symbol markings, arrows, stop lines, yield lines, crosswalk lines, speed measurement markings, speed reduction markings, speed hump markings, parking space markings, and others, shall be white unless otherwise provided herein.
Guidance. Because of the low approach angle at which pavement markings are viewed, transverse lines should be proportioned to provide visibility at least equal to that of longitudinal lines.
Transverse markings should use durable materials for permanent installations.
Support. Particular attention must be given to the maintenance of transverse lines and markings. Due to their placement on the pavement, these markings are subject to constant wear.
## 620.2.16 Stop and Yield Lines (MUTCD Section 3B.16)
Guidance. Stop lines should be used to indicate the point behind which vehicles are required to stop, in compliance with a traffic control signal.
Option. Stop lines may be used to indicate the point behind which vehicles are required to stop in compliance with a STOP (R1-1) sign, a Stop Here For Pedestrians (R1-5b or R1-5c) sign, or some other traffic control device that requires vehicles to stop, except YIELD signs that are not associated with passive grade crossings.
Yield lines may be used to indicate the point behind which vehicles are required to yield in compliance with a YIELD (R1-2) sign or a Yield Here to Pedestrians (R1-5 or R1-5a) sign.
Standard. Except as provided in MUTCD Section 8B.28, stop lines shall not be used at locations where drivers are required to yield in compliance with a YIELD (R1-2) sign or a Yield Here To Pedestrians (R1-5 or R1-5a) sign or at locations on uncontrolled approaches where drivers are required by State law to yield to pedestrians.
Yield lines shall not be used at locations where drivers are required to stop in compliance with a STOP (R1-1) sign, a Stop Here For Pedestrians (R1-5b or R1-5c) sign, a traffic control signal, or some other traffic control device.
Stop lines shall consist of solid white lines extending across approach lanes to indicate the point at which the stop is intended or required.
Stop lines shall be used in advance of railroad crossings to indicate the appropriate location to stop.
When any crosswalk is installed where a permanent traffic control device is provided, such as a STOP sign or traffic signal, a stop line shall be installed in advance of the crosswalk.
Stop lines shall be 24 in. wide and shall extend across all lanes affected by the traffic control device.
Yield lines (see Fig. 620.2.16, Examples of Yield Line Layouts) shall consist of a row of solid white isosceles triangles pointing toward approaching vehicles extending across approach lanes to indicate the point at which the yield is intended or required. The spacing of triangles in a yield line shall be consistent for that marking.
Guidance. If used, the smaller size yield line should be 16 in. wide by 24 in. tall and should be used on right turn lanes. The larger size yield line should be 24 in. wide by 36 in. tall and should be used on ramps where there is no acceleration lane.
The space between the triangles should be 3 to 6 in. as shown on Standard Plan 620.00.
Yield lines may be considered for those locations where a free right turn lane is developed but there is not an acceleration lane on the intersecting road. Yield lines may also be considered at on ramps with tapered acceleration lanes as shown in Fig. 620.2.5.3, Examples of Dotted Lined and Channelizing Line Applications for Entrance Ramp Markings.
Yield lines may also be used where engineering judgment indicates a need.
Guidance. If used, stop and yield lines should be placed a minimum of 4 ft. in advance of the nearest crosswalk line at controlled intersections, except for yield lines at roundabouts as provided for in EPG 620.3.4 Yield Lines for Roundabouts and at midblock crosswalks. In the absence of a marked crosswalk, the stop line or yield line should be placed at the desired stopping or yielding point, but should not be placed more than 30 ft. nor less than 4 ft. from the nearest edge of the intersecting traveled way. Stop lines should be placed to allow sufficient sight distance to all other approaches to an intersection.
When a stop line is used in conjunction with the STOP sign it should be placed adjacent to, or in line with, the STOP sign.
When a yield line is used in conjunction with the YIELD sign it should be placed adjacent to, or in line with, the YIELD sign.
Stop lines at midblock signalized locations should be placed at least 40 ft. in advance of the nearest signal indication.
If yield or stop lines are used at a crosswalk that crosses an uncontrolled multilane approach, the yield lines or stop lines should be placed 20 to 50 ft. in advance of the nearest crosswalk line, and parking should be prohibited in the area between the yield or stop line and the crosswalk (see Figure 620.2.17.1 Examples of Yield Lines at Unsignalized Midblock Crosswalks).
Standard. If yield (stop) lines are used at a crosswalk that crosses an uncontrolled multi-lane approach, Yield Here To (Stop Here For) Pedestrians (R1-5 series) signs (see EPG 620.2.11 Raised Pavement Markers shall be used).
Guidance. Yield (stop) lines and Yield Here To (Stop Here For) Pedestrians signs should not be used in advance of crosswalks that cross an approach to or departure from a roundabout.
Support. Drivers yielding or stopping too close to crosswalks that cross uncontrolled multi-lane approaches place pedestrians at risk by blocking other drivers’ views of pedestrians and by blocking pedestrians’ view of vehicles approaching in the other lanes.
Option. Stop and yield lines may be staggered longitudinally on a lane-by-lane basis. Refer to "D" of Fig. 620.2.8.2.
Support. Staggered stop lines and staggered yield lines can improve the driver's view of pedestrians, provide better sight distance for turning vehicles and increase the turning radius for left-turning vehicles.
EPG 620.2.28 Stop and Yield Lines at Highway-Rail Grade Crossings contains information regarding the use of stop lines and yield lines at grade crossings.
Fig. 620.2.16, Examples of Yield Line Layouts (MUTCD Fig. 3B-16)
## 620.2.17 Do Not Block Intersection Markings (MUTCD Section 3B.17)
Option. Do Not Block Intersection markings may be used to mark the edges of an intersection area that is in close proximity to a signalized intersection, railroad crossing or other nearby traffic control that might cause vehicles to stop within the intersection and impede other traffic entering the intersection. If authorized by law, Do Not Block Intersection markings with appropriate signs may also be used at other locations.
Standard. If used, Do Not Block Intersection markings (see Figure 620.2.17.2) shall consist of wide solid white lines that outline the intersection area that vehicles must not block 8 in. to 12 in. wide and white cross-hatching within the intersection area 4 in. to 6 in. wide.
Do Not Block Intersection markings shall be accompanied by one or more DO NOT BLOCK INTERSECTION (DRIVEWAY) (CROSSING) (R10-7) signs (see EPG 903.5.30), one or more DO NOT STOP ON TRACKS (R8-8) signs (see EPG 903.20 Signing for Rail and Light Rail Transit Grade Crossings) or one or more similar signs.
Fig. 620.2.17.1, Examples of Yield Lines at Unsignalized Midblock Crosswalks (MUTCD Fig. 3B-17)
Fig. 620.2.17.2, Do Not Block Intersection Markings (MUTCD Fig. 3B-18)
## 620.2.18 Crosswalk Markings (MUTCD Section 3B.18)
Support. Crosswalk markings provide guidance for pedestrians who are crossing roadways by defining and delineating paths on approaches to and within signalized intersections, and on approaches to other intersections where traffic stops.
In conjunction with signs and other measures, crosswalk markings help to alert road users of a designated pedestrian crossing point across roadways at locations that are not controlled by traffic control signals or STOP or YIELD signs.
At non-intersection locations, crosswalk markings legally establish the crosswalk.
Standard. When crosswalk lines are used, they shall consist of solid white lines that mark the crosswalk. They shall be not less than 6 in. nor greater than 24 in. wide and 6 ft. apart.
If transverse lines are used to mark a crosswalk, the gap between the lines shall not be less than 6 feet. If longitudinal lines are used without transverse lines to mark a crosswalk, the crosswalk shall not be less than 6 ft. wide.
Guidance. Crosswalk lines, if used on both sides of the crosswalk, should extend across the full width of pavement or to the edge of the intersecting crosswalk to discourage diagonal walking between crosswalks (see Standard Plan 620.00).
At locations controlled by traffic control signals or on approaches controlled by STOP or YIELD signs, crosswalk lines should be installed where engineering judgment indicates they are needed to direct pedestrians to the proper crossing path(s).
Crosswalk lines should not be used indiscriminately. An engineering study should be performed before a marked crosswalk installed at a location away from a traffic control signal or STOP or YIELD signs. The engineering study should consider the number of lanes, the presence of a median, the distance from adjacent signalized intersections, the pedestrian volumes and delays, the average annual daily traffic (AADT), the posted or statutory speed limit or 85th-percentile speed, the geometry of the location, the possible consolidation of multiple crossing points, the availability of street lighting and other appropriate factors.
New marked crosswalks alone, without other measures designed to reduce traffic speeds, shorten crossing distances, enhance driver awareness of the crossing, and/or provide active warning of pedestrian presence, should not be installed across uncontrolled roadways where the speed limit exceeds 40 mph and either:
A. The roadway has four or more lanes of travel without a raised median or pedestrian refuge island and an ADT of 12,000 vehicles per day or greater; or
B. The roadway has four or more lanes of travel with a raised median or pedestrian refuge island and an ADT of 15,000 vehicles per day or greater.
Support. Chapter 4F of the MUTCD contains information on Pedestrian Hybrid Beacons. Section 4L.03 contains information regarding Warning Beacons to provide active warning of a pedestrian's presence. Section 4N.02 contains information regarding In-Roadway Warning Lights at crosswalks. Chapter 7D contains information regarding school crossing supervision.
Guidance. Because non-intersection pedestrian crossings are generally unexpected by the road user, warning signs (see Non-vehicular Sign (W11-2, W11-7)) should be installed and adequate visibility should be provided by parking prohibitions.
If used, the “Zebra” pedestrian crosswalk marking should consist of longitudinal lines 30 in. wide and spaced equally, centering one block in each lane, one block across each lane line or centerline, and placing one half block against each edgeline.'
When longitudinal lines are used to mark a crosswalk, the transverse crosswalk lines should be omitted. The marking design should avoid the wheel paths.
Option. Existing 33 in. and 36 in. crosswalk blocks may be maintained in place or replaced with 30 in. blocks.
Support. EPG 620.2.16 contains information regarding placement of stop line markings near crosswalk markings.
Option. Where permanent traffic control devices are not provided, speeds are greater than 35 mph or the crosswalk is located in rural locations where they are unexpected, the width of the crosswalk line may be increased up to 24 inches.
Crosswalks may be located mid-block if this placement offers greater safety to the pedestrian than the normal placement at an intersection. In these cases, the “Zebra” pedestrian crosswalk marking may be used for greater emphasis and visibility. This type of marking may also be used at locations where substantial numbers of pedestrians cross without any other traffic control device, at locations where physical conditions are such that added visibility of the crosswalk is desired, or at places where a pedestrian crosswalk might not be expected.
Standard. All school crosswalks authorized by an agreement between the Commission and the school and/or city shall be marked. Crosswalks for schools shall be maintained in a manner that will provide a clearly visible marking at all times.
All school crosswalks shall be marked using both the advance school crosswalk and the school crosswalk sign, refer to EPG 903.19.8 School Sign (S1-1) and Plaques.
Option. When school crosswalks are located mid-block, the “Zebra” pedestrian crosswalk marking may be used for greater emphasis and visibility.
Guidance. Crosswalk markings should be located so that the curb ramps are within the extension of the crosswalk markings.
Support. Detectable warning surfaces mark boundaries between pedestrian and vehicular ways where there is no raised curb. Detectable warning surfaces are required by 49 CFR, Part 37 and by the Americans with Disabilities Act (ADA) where curb ramps are constructed at the junction of sidewalks and the roadway, for marked and unmarked crosswalks. Detectable warning surfaces contrast visually with adjacent walking surfaces, either light-on-dark, or dark-on-light. The Americans with Disabilities Act Accessibility Guidelines for Buildings and Facilities (ADAAG) (see MUTCD Section 1A.11) contains specifications for design and placement of detectable warning surfaces.
Fig. 620.2.18, Examples of Crosswalk Markings (MUTCD Figs. 3B-19 and -20)
## 620.2.19 Parking Space Markings (MUTCD Section 3B.19)
Support. Marking of parking space boundaries encourages more orderly and efficient use of parking spaces where parking turnover is substantial. Parking space markings tend to prevent encroachment into fire hydrant zones, bus stops, loading zones, approaches to intersections, curb ramps, and clearance spaces for islands and other zones where parking is restricted. Examples of parking space markings are shown in Fig. 620.2.20.1, Examples of Parking Space Markings.
If the parking lot is not striped, it is not necessary to mark the disabled reserved stall.
Standard. Parking space markings shall be white.
The marking used for disabled parking areas shall be white, except for the curb painting, which shall be blue in color.
If the parking lot is striped, then the required number of disabled stalls shall be marked as follows:
Total Parking in Lot Required Minimum Number of Accessible Spaces
1 to 25 1
26 to 50 2
51 to 75 3
76 to 100 4
101 to 150 5
151 to 200 6
201 to 300 7
301 to 400 8
401 to 500 9
501 to 1000 (2 percent of total)
1001 and over (20 plus 1 for each 100 over 1000
If disabled parking stalls are marked, then at least one shall be marked as "Van Accessible". Additional van accessible parking stalls are required in the ratio of one van accessible per eight disabled stalls. The neutral zone adjacent to a van accessible stall shall be 8 ft. wide as opposed to the standard 5 ft. width.
Fig. 620.2.19, Typical Hash Bar Markings
Option. Spaces required by the above may not need be provided in the particular lot. These spaces may be provided in a different location if they provide equivalent or greater accessibility for the disabled person (see Disabled Parking Areas).
Guidance. For disabled parking, depending upon the number of linear feet of curb requiring blue paint, 1 or 2 gallons of our standard white traffic paint should be taken to a local paint store to have blue paint pigment added. 10 ounces of the blue pigment should be added to 1 gallon of our standard white traffic paint. The blue paint pigment that can be used is available through Sherman Williams paint stores and other businesses that handle the "Blenda Color blue - No. A6011". The mixed blue paint will be lighter in color than the blue background we provide on our disabled parking signs, however, it will be acceptable.
Option. Blue lines may supplement white parking space markings of each parking space designated for use only by persons with disabilities.
Support. Additional parking space markings for the purpose of designating spaces for use only by persons with disabilities are discussed in EPG 620.2.20 and illustrated in International Symbol of Accessibility Parking Space Marking with Blue Background and White Border Options. The design and layout of accessible parking spaces for persons with disabilities is provided in the Americans with Disabilities Act Accessibility Guidelines for Buildings and Facilities (ADAAG) (see MUTCD Section 1A.11).
## 620.2.20 Pavement Word, Symbol and Arrow Markings (MUTCD Section 3B.20)
Guidance. Word, symbol and arrow markings on the pavement are used for the purpose of guiding, warning, or regulating traffic. These pavement markings can be helpful to road users in some locations by supplementing signs and providing additional emphasis for important regulatory, warning, or guidance messages, because the markings do not require diversion of the road user's attention from the roadway surface. Symbol messages are preferable to word messages. Examples of standard word and arrow pavement markings are shown in Standard Plan 620.00 and Fig. 620.2.20.7, Examples of Lane Reduction Arrow.
Option. Word, symbol and arrow markings, including those contained in the Standard Highway Signs and Markings book (see MUTCD Section 1A.11), may be used as determined by engineering judgment to supplement signs and/or to provide additional emphasis for regulatory, warning or guidance messages. Among the word, symbol and arrow markings that may be used are the following:
A. Regulatory:
1. STOP
2. YIELD
3. RIGHT (LEFT) TURN ONLY
4. 25 MPH
5. Lane use and wrong way Arrow Symbols
6. Other preferential lane word markings
B. Warning:
3. YIELD AHEAD Triangle Symbol
4. SCHOOL XING
6. PED XING
7. SCHOOL
8. R X R
9. BUMP
10. HUMP
11. Lane reduction arrows
C. Guide:
1. Route numbers (route shield pavement marking symbols and/or words such as I-70,US 40, STATE 135 or ROUTE 10)
2. Cardinal directions (NORTH, SOUTH, EAST or WEST)
3. TO
Standard. Word, symbol and arrow markings shall be white and reflectorized, except as otherwise provided in this article.
Pavement marking letters, numerals, symbols and arrows shall be installed in accordance with the design details in the Pavement Markings chapter of the Standard Highway Signs and Markings book (see MUTCD Section 1A.11).
Fig. 620.2.20.1, Examples of Parking Space Markings (MUTCD Fig. 3B-21)
Fig. 620.2.20.2, International Symbols of Accessibility Parking Space Marking
Fig. 620.2.20.3, Disabled Symbol Detail
Fig. 620.2.20.4, Disabled Parking Area
Fig. 620.2.20.5, Disabled Parking Area Multiple
Fig. 620.2.20.6, Example of Elongated Letters for Word Pavment Markings (MUTCD 3B-23)
Fig. 620.2.20.7, Examples of Standard Arrows for Pavment Markings (MUTCD 3B-24)
Guidance. When conveying mandatory messages, these markings should only be used as supplementary devices to the standard signs.
The elongation of these markings is dependent upon the posted speed limit and should be as follows:
Posted Speed Limit Elongated Length Approximate Space Between Word and Symbol Table 620.2.20 Pavement Marking Lettering Heights and Spacings 35 mph or less 8 ft. 32 ft. Greater than 35 mph 10 ft. 40 ft.
The spacing between the word and symbol is approximate and should be adjusted as field conditions warrant.
Word and symbol markings should not exceed three lines of information.
If a pavement marking word message consists of more than one line of information, it should read in the direction of travel. The first word of the message should be nearest to the road user.
Except for the two opposing arrows of a two-way left-turn lane marking (see Fig. 620.2.2.2.4, Example of Two-Way, Left-Turn Marking Applications), the longitudinal space between word or symbol message markings, including arrow markings, should be at least four times the height of the characters for low-speed roads, but not more than ten times the height of the characters under any conditions.
The number of different word and symbol markings used should be minimized to provide effective guidance and avoid misunderstanding.
Except as noted below for the SCHOOL word marking (see MUTCD Section 7C.03) in the Option, pavement word, symbol and arrow markings should be no more than one lane in width.
Option. The SCHOOL word marking may extend to the width of two approach lanes (see Section 7C.03 in the MUTCD).
Guidance. When the SCHOOL word marking is extended to the width of two approach lanes, the characters should be 10 ft. or more tall (see Section 7C.03 in the MUTCD).
Pavement word, symbol and arrow markings should be proportionally scaled to fit within the width of the facility upon which they are applied.
Option. On narrow, low-speed shared-use paths, the pavement words, symbols nd arrows may be smaller than suggested, but to the relative scale.
Pavement markings simulating Interstate, U.S., State, and other official highway route shield signs (see MUTCD Figure 2D-3) with appropriate route numbers, but elongated for proper proportioning when viewed as a marking, may be used to guide road users to their destinations (see Figure 620.2.20.8, Examples of Elongated Route Shields for Pavement Markings).
Fig. 620.2.20.8, Examples of Elongated Route Shields for Pavement Markings (MUTCD 3B-25)
Standard. Except at the ends of aisles in parking lots, the word STOP shall not be used on the pavement unless accompanied by a stop line (see 620.2.16 Stop and Yield Lines (MUTCD Section 3B.16) and STOP (see MUTCD Section 2B.05) sign. At the ends of aisles in parking lots, the word STOP shall not be used on the pavement unless accompanied by a stop line.
The word STOP shall not be placed on the pavement in advance of a stop line, unless every vehicle is required to stop at all times.
Option. A yield-ahead triangle symbol (see Figure 620.2.20.10 Yield Ahead Triangle Symbols) or YIELD AHEAD word pavement marking may be used on approaches to intersections where the approaching traffic will encounter a YIELD sign at the intersection.
Standard. The yield-ahead triangle symbol or YIELD AHEAD word pavement marking shall not be used unless a YIELD sign is in place at the intersection. The yield-ahead symbol marking shall be as shown in Figure 620.2.20.10, Yield Ahead Triangle Symbols.
Guidance. The International Symbol of Accessibility parking space marking (see Fig. 620.2.20.2) should be placed in each parking space designated for use by persons with disabilities.
Option. A blue background with white border may supplement the wheelchair symbol as shown in Fig. 620.2.20.2 International Symbol of Accessibility Parking Space Marking with Blue Background and White Border Options.
Support. Lane-use arrow markings (see Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings) are used to indicate the mandatory or permissible movements in certain lanes (see Fig. 620.2.22.2, Examples of Lane-Use Control Word and Arrow Pavement Markings) and in two-way left-turn lanes (see Fig. 620.2.2.2.4, Example of Two-Way Left-Turn Lane Marking Application).
Guidance. Lane-use arrow markings (see Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings) should be used in lanes designated for the exclusive use of a turning movement, including turn bays, except where engineering judgment determines that physical conditions or other markings (such as a dotted extension of the lane line through the taper into the turn bay) clearly discourage unintentional use of a turn bay by through vehicles. Lane use arrows markings should also be used in lanes from which movements are allowed that are contrary to the normals rules of the road Figs. 620.2.8.1 and 620.3.8.2, Examples of Line Extensions through Intersections. When used in turn lanes, at least two arrows should be used, one at or near the upstream end of the full-width turn lane and one an appropriate distance upstream from the stop line or intersection Figs. 620.2.5.10.1 and 620.2.5.10.2, Examples of Applications of Conventional Road lane-Drop Marking and Fig. 620.2.20.9, Spacing of Arrows in Left Turn Lanes.
The placement of arrows in channelizing lanes should be determined by the length of the lane and the following criteria (see Fig. 620.2.20.9 Spacing of Arrows in Left Turn Lanes):
A. The first arrow should be placed 75 ft. in advance of the stop bar.
B. The second arrow should be placed 200 ft. in advance of the stop bar.
C. Any additional arrows should be placed 400 ft. behind the stop bar.
Option. The distances between arrows may be adjusted if there are special circumstances that warrant the change.
Guidance. Where opposing offset channelized left-turn lanes exist, lane-use arrow markings should be placed near the downstream terminus of the offset left-turn lanes to reduce wrong-way movements (see MUTCD Fig. 2B-17).
Support. An arrow at the downstream end of a turn lane can help to prevent wrong way movements.
Standard. Where through lanes approaching an intersection become mandatory turn lanes, lane-use arrow markings shall be used and shall be accompanied by standard signs and the word ONLY.
The ONLY shall be placed on the pavement in advance of each arrow.
Lane use, lane reduction, and wrong-way arrow markings shall be designed as shown in Standard Plan 620.00 and Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings.
Guidance. The use of straight arrows should be reserved for correcting special cases, such as, locations where accidents are occurring as a result of vehicles making turns from the through lanes.
Where through lanes become mandatory turn lanes, signs or markings should be repeated as necessary to prevent entrapment and to help the road user select the appropriate lane in advance of reaching a queue of waiting vehicles.
The word ONLY should be centered between all arrows used in the mandatory lane. Spacing between the arrow and the ONLY should be 4 to 10 times the height of the ONLY. In cases where the ONLY is set between two arrows it should be equally spaced between the arrows. The use of ONLY should not apply to exit ramps.
Option. On freeways or expressways where a through lane becomes a mandatory exit lane, lane-use arrow markings may be used on the approach to the exit in the dropped lane and in an adjacent optional through-or-exit lane if one exists.
Guidance. A two-way left-turn lane-use arrow pavement marking, with opposing arrows spaced as shown in Fig. 620.2.2.2.4 Example of Two-Way Left-Turn Lane Marking Application, should be used at or just downstream from the beginning of a two-way left-turn lane.
Option. Additional two-way left-turn lane-use arrow markings may be used at other locations along a two-way left-turn lane where engineering judgment determines that such additional markings are needed to emphasize the proper use of the lane.
Standard. A single-direction lane-use arrow shall not be used in a lane bordered on both sides by yellow two-way left-turn lane longitudinal markings.
Lane-use, lane-reduction, and wrong-way arrow markings shall be designed as shown in Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings and in Standard Highway Signs and Markings (see MUTCD Section 1A.11).
Option. The ONLY word marking may be used to supplement the lane-use arrow markings in lanes that are designated for the exclusive use of a single movement (see Fig. 620.2.22.2, Examples of Lane-Use Control Word and Arrow Pavement Markings or to supplement a preferential lane word or symbol marking (see MUTCD Section 3D.01).
Standard. The ONLY word marking shall not be used in a lane that is shared by more than one movement.
Guidance. Where a lane-reduction transition occurs on a roadway with a speed limit of 45 mph or more, the lane-reduction arrow markings shown in "F" in Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings should be used (see Fig. 620.2.9.1, Examples of Applications for Lane-Reduction Transition Marking). Except for acceleration lanes, where a lane-reduction transition occurs on a roadway with a speed limit of less than 45 mph, the lane-reduction arrow markings shown in "F" in Figure 620.2.20.7 should be used if determined to be appropriate based on engineering judgment. Examples of locations where they may be effective are at the terminus of hill climbing lanes, lane drops immediately after intersections, or other areas where the geometrics create a lane drop situation that is not obvious to the driver.
Option. Lane-reduction arrow markings may be used in long acceleration lanes based on engineering judgment.
Directional pavement arrows may be used as a substitute for the wrong-way arrows when wrong-way arrows are required.
A maximum of two wrong-way arrows may be provided on a ramp, the placement of the second arrow is dependent upon the design and length of the ramp. Exit ramps that do not contain islands at the intersection of the exit ramp and the crossroad may receive one wrong-way pavement arrow at the top of the ramp. Ramps constructed with islands at the intersection of the exit ramp and the crossroad may receive two wrong-way arrows at the top of the ramp, one arrow on each side of the island.
Wrong-way pavement arrows may be placed on one way outer roads to further indicate the proper direction to travel.
Standard. In the case of two lane ramps where wrong-way pavement arrows are used, one arrow shall be provided for each lane.
Guidance. If used, the point of the wrong-way arrow should be located a distance of 25 ft. from the end of the ramp and the intersecting crossroad. When wrong-way arrows are used on one-way outer roads, the arrows should be installed 25 ft. in advance of the point where the edge of the crossroad and the outer road meet. Where a stop bar has been provided, the arrow should be placed 25 ft. in advance of this marking.
On ramps where directional pavement arrows have been provided to aid the motorist in proper lane usage, the wrong-way pavement arrows should not be used.
Where crossroad channelization or ramp geometrics do not make wrong-way movements difficult, the appropriate lane-use arrow should be placed in each lane of an exit ramp near the crossroad terminal where it will be clearly visible to a potential wrong-way road user.
Option. The wrong-way arrow markings shown in "D" in Fig. 620.2.20.7, Examples of Standard Arrows for Pavement Markings may be placed near the downstream terminus of a ramp as shown in Examples of Arrow Markings at Exit Ramp Terminals (MUTCD Figs. 2B-18 and -19) or at other locations where lane-use arrows are not appropriate, to indicate the correct direction of traffic flow and to discourage drivers from traveling in the wrong direction.
A yield-ahead triangle symbol or YIELD AHEAD word pavement marking may be used on approaches to intersections where the approaching traffic will encounter a YIELD sign at the intersection (see Yield Ahead Triangle Symbols).
Support. Lane-use arrow markings are often used to provide guidance in turn bays, where turns may or may not be mandatory, and in two-way left-turn lanes.
Fig. 620.2.20.9, Spacing of Arrow in Left-Turn Lanes
Fig. 620.2.20.10, Yield Ahead Triangle Symbols (MUTCD Fig. 3B-26)
Fig. 620.2.20.11, Examples of Lane-Use Control Word and Arrow Pavement Markings (MUTCD 3B-27)
## 620.2.21 Aircraft Speed Measurement Markings (MUTCD Section 3B.21)
Support. An aircraft speed measurement marking is a transverse marking placed on the roadway to assist the enforcement of speed regulations.
Standard. Aircraft speed check markings shall only be installed after the District Engineer or his/her representative receives a request from the Missouri State Highway Patrol. A member of the Highway Patrol shall be present when these stations are placed to verify their location and spacing for legal purposes.
Speed measurement markings, if used, shall be white, and shall be 24 in. x 24 in. and he distance between the block shall be 660 ft., measured from the leading edge of the first block to the leading edge of the second block. This distance shall be measured on the actual pavement surface and is the same for all posted speeds (See Fig. 620.2.21, Pavement Marking for Aircraft Speed Check Stations).
The markings shall be reflective, and are to be placed on the center of each driving lane.
Those markings, which have been improperly installed shall be removed by one of the methods noted in Obliteration of Pavement Markings.
Option. A third block may be installed at the special request of the Highway Patrol.
If the Highway Patrol wishes to only check traffic flowing in one direction, these markings may be omitted from the opposing lanes.
Guidance. Aircraft speed check markings should receive periodic inspection to ensure they are maintained in an acceptable and functional manner. Existing aircraft speed check markings that are no longer in use should be allowed to deteriorate.
The application of any material should be done following the manufacturer’s recommendations for installation.
Option. On concrete surfaces, black may be used to provide contrast of the speed blocks.
Fig. 620.2.21, Pavement Marking for Aircraft Speed Check Stations
## 620.2.22 Speed Reduction Markings (MUTCD Section 3B.22)
Support. Speed reduction markings (see Fig. 620.2.22, Example of the Application of speed Reduction Markings) are transverse markings that are placed on the roadway within a lane (along both edges of the lane) in a pattern of progressively reduced spacing to give drivers the impression that their speed is increasing. These markings might be placed in advance of an unexpectedly severe horizontal or vertical curve or other roadway feature where drivers need to decelerate prior to reaching the feature and where the desired reduction in speeds has not been achieved by the installation of warning signs and/or other traffic control devices.
Guidance. If used, speed reduction markings should be reserved for unexpected curves and should not be used on long tangent sections of roadway or in areas frequented mainly by local or familiar drivers, (e.g., school zones). If used, speed reduction markings should supplement the appropriate warning signs and other traffic control devices and should not substitute for these devices.
Standard. If used, speed reduction markings shall be a series of white transverse lines on both sides of the lane that are perpendicular to the centerline, edgeline or lane line. The longitudinal spacing between the markings shall be progressively reduced from the upstream to the downstream end of the marked portion of the lane.
Guidance. Speed reduction markings should not be greater than 12 in. wide and should not extend more than 18 in. into the lane.
Standard. Speed reduction markings shall not be used in lanes that do not have a longitudinal line (centerline, edgeline or lane line) on both sides of the lane.
Fig. 620.2.22, Example of the Application of Speed Reduction Markings (MUTCD 3B-28)
## 620.2.23 Curb Markings (MUTCD Section 3B.23)
Support. Curb markings are most often used to indicate parking regulations or to delineate the curb.
Standard. Where curbs are marked to convey parking regulations in those areas where curb markings are frequently obscured by snow and ice accumulation signs shall be used with the curb markings except as provided below.
All barrier curbs, curbs a minimum of 6 in. tall with a vertical face shall be marked.
Guidance. Except as provided in the Option, when curb markings are used without signs to convey parking regulations, a legible word marking regarding the regulation (such as “No Parking” or “No Standing”) should be placed on the curb.
Option. Curb markings without word markings or signs may be used to convey a general prohibition by statute of parking within a specified distance of a STOP sign, YIELD sign, driveway, fire hydrant or crosswalk.
Local highway agencies may prescribe special colors for curb markings to supplement standard signs for parking regulation.
Support. Since yellow and white curb markings are frequently used for curb delineation and visibility, it is advisable to establish parking regulations through the installation of standard signs (see EPG 903.5.35 Parking, Standing and Stopping Signs (R7 and R8 Series) (MUTCD Section 2B.39) through EPG 903.5.37 RESERVED PARKING For Persons with Disabilities Sign (R7-8, R7-8b) (MUTCD Section 2B.41b)).
Standard. Where curbs are marked for delineation or visibility purposes, the colors shall comply with to the general principles of markings (see EPG 620.1.5 Colors (MUTCD Section 3A.05).
Guidance. Curbs should not be marked in the following cases:
A. Where the posted speed limit is 40 mph or less,
B. Curbs that diverge from the normal traffic flow for commercial and private entrances,
C. Curbs that are mountable (less than 6 in. tall).
Standard. Barrier curbs shall be marked in cases A to C if they are used to redirect the flow of traffic.
Fig. 620.2.23, Typcial Markings for Barrier Curb
Note: Paint used on curbs shall be of the same color as the edgeline they parallel. If no edgeline is present, the curb shall be marked the appropriate color as if there was an edgeline present.
Option. The first 200 ft. of a barrier curb may also be painted in the above cases to mark the beginning of these barriers (See Fig. 620.2.23, Typical Markings for Barrier Curb).
Guidance. Retroreflective solid yellow markings should be placed on approach ends of raised medians and curbs of islands that are located in the line of traffic flow where the curb serves to channel traffic to the right of the obstruction.
Retroreflective solid white markings should be used when traffic is permitted pass on either side of the island.
Support. Where the curbs of the islands become parallel to the direction of traffic flow, it is not necessary to mark the curbs unless an engineering study indicates the need for this type of delineation.
Curbs at openings in a continuous median island need not be marked unless an engineering study indicates the need for this type of marking.
Option. Retroreflective or internally illuminated raised pavement markers of the appropriate color may be placed on the pavement in front of the curb and/or on the top of curbed noses of raised medians and curbs of islands, as a supplement to or substitute for retroreflective curb markings used for delineation.
## 620.2.24 Chevrons and Diagonal Crosshatch (Hash Bar) markings (MUTCD Section 3B.24)
Guidance. Hash bars may be used to supplement other pavement marking which delineate locations not to be driven on. Examples of such markings are:
A. Left turn bubbles,
B. No Parking areas,
C. Gore Points,
D. Shoulders,
E. Pavement Transitions and
F. Painted Medians.
If there is insufficient space to place a minimum of 3 hash bars at 50 ft. intervals, the spacing should be reduced (See Fig. 620.2.19 Typical Hash Bar Markings).
Option. Chevron and diagonal crosshatch markings may be used to discourage travel on certain paved areas, such as shoulders, gore areas, flush median areas between solid double yellow centerline markings or between white channelizing lines approaching obstructions in the roadway (see EPG 620.2.10 Approach Markings for Obstructions (MUTCD Section 3B.10) and Figs. 620.2.10.1 and 620.2.10.2, Examples of Applications of Markings for Obstructions in the Roadway), between solid double yellow centerline markings forming flush medians or channelized travel paths at intersections (see Fig. 620.2.2.0.2, Examples of Four-or-More Lane, Two-Way marking Applications and Fig. 620.2.2.2.2, Example of Application of Three-lane, Two-Way Makings for Changing Direction of the Center Lane), buffer spaces between preferential lanes and general-purpose lanes (see Figs. 620.4.2.2 Markings for Buffer-Separated Preferential Lanes (MUTCD 3D-2) and Fig. 620.4.2.5 Markings for Counter-Flow Preferential Lanes on Divided Highways (MUTCD 3D-4)), and at grade crossings (see MUTCD Part 8).
Standard. Hash bars shall be marked using a 24 in. wide stripe set at a 45 degree angle to the driving lane.
The standard spacing between hash bars shall be 50 ft. with a minimum of 3 hash bars being used per application.
When crosshatch markings are used in paved areas that separate traffic flows in the same general direction, they shall be white and they shall be shaped as chevron markings, with the point of each chevron facing toward approaching traffic, as shown in Figs. 620.2.5.1 and 620.2.5.2, Examples of Dotted Line and Channelizing Line Application for Exit Ramp Markings, "A" of Fig. 620.2.5.3, Examples of Dotted Line and Channelizing Line Application for Entrance Ramp Markings, Figs. 620.2.5.5 through 620.2.5.9, Examples of Applications of Freeway and Expressway Lane-Drop Markings and Fig. 620.2.10.2, Examples of Applications of Markings for Obstructions in the Roadway.
When crosshatch markings are used in paved areas that separate opposing directions of traffic, they shall be yellow diagonal markings that slant away from traffic in the adjacent travel lanes, as shown in Fig. 620.2.2.0.2, Examples of Four-or-More Lane, Two-Way marking Applications and Fig. 620.2.2.2.2, Example of Application of Three-lane, Two-Way Makings for Changing Direction of the Center Lane and Both "A" and "B" of Fig. 620.2.10.1, Examples of Applications of Markings for Obstructions in the Roadway.
When crosshatch markings are used on paved shoulders, they shall be diagonal markings that slant away from traffic in the adjacent travel lane. The diagonal markings shall be yellow when used on the left-hand shoulders of the roadways of divided highways and on the left-hand shoulders of one-way streets or ramps. The diagonal markings shall be white when used on right-hand shoulders.
## 620.2.25 Speed Hump Markings (MUTCD Section 3B.25)
Standard. If speed hump markings are used, they shall be a series of white markings placed on a speed hump to identify its location. If markings are used for a speed hump that does not also function as a crosswalk or speed table, the markings shall comply with Option A, B or C shown in Fig. 620.2.26.1, Pavement Markings for Speed Humps without Crosswalks. If markings are used for a speed hump that also functions as a crosswalk or speed table, the markings shall comply with Option A or B shown in Figure 620.2.26.2, Pavement Markings for Speed Tables or Speed Humps with Crosswalks.
## 620.2.26 Advance Speed Hump Markings (MUTCD Section 3B.26)
Option. Advance speed hump markings (see Fig. 620.2.26.3, Advance Warning Markings for Speed Humps) may be used in advance of speed humps or other engineered vertical roadway deflections such as dips where added visibility is desired or where such deflection is not expected.
Advance pavement wording such as BUMP or HUMP (see EPG 620.2.20) may be used on the approach to a speed hump either alone or in conjunction with advance speed hump markings. Appropriate advance warning signs may be used in compliance with MUTCD Section 2C.29.
Standard. If advance speed hump markings are used, they shall be a series of eight white 12 in. transverse lines that become longer and are spaced closer together as the vehicle approaches the speed humps or other deflection. If advance markings are used, they shall comply with the detailed design shown in Fig. 620.2.26.3, Advance Warning Markings for Speed Humps.
Guidance. If used, advance speed hump markings should be installed in each approach lane.
Fig. 620.2.26.1, Pavement Markings for Speed Humps without Crosswalks (MUTCD 3B-29)
Fig. 620.2.26.2, Pavement Markings for Speed Talbes or Speed Humps with Crosswalks (MUTCD 3B-30)
Fig. 620.2.26.3, Advance Warning Markings for Speed Humps (MUTCD 3B-31)
## 620.2.27 Pavement Markings for Highway-Rail Grade Crossings (MUTCD Section 8B.27)
Standard. All grade crossing pavement markings shall be retroreflectorized white. All other markings shall be in accordance with EPG 620 Pavement Marking.
On paved roadways, pavement markings in advance of a grade crossing shall consist of an X, the letters RR, a no-passing zone marking (on two-lane, two-way highways with centerline markings in compliance with EPG 620.2.1), and certain transverse lines as shown in Fig. 620.2.28.1, Example of Placement of Warning Signs and Pavement Markings at Grade Crossings and Fig. 620.2.28.2, Grade Crossing Pavement Markings.
Identical markings shall be placed in each approach lane on all paved approaches to grade crossings where signals or automatic gates are located, and at all other grade crossings where the posted or statutory highway speed is 40 mph or greater.
Pavement markings shall not be required at grade crossings where the posted or statutory highway speed is less than 40 mph if an engineering study indicates that other installed devices provide suitable warning and control. Pavement markings shall not be required at grade crossings in urban areas if an engineering study indicates that other installed devices provide suitable warning and control.
Guidance. When pavement markings are used, a portion of the X symbol should be directly opposite the Grade Crossing Advance Warning sign. The X symbol and letters should be elongated to allow for the low angle at which they will be viewed.
Option. When justified by engineering judgment, supplemental pavement marking symbol(s) may be placed between the Grade Crossing Advance Warning sign and the grade crossing.
## 620.2.28 Stop and Yield Lines at Highway-Rail Grade Crossings (MUTCD section 8B.28)
Standard. On paved roadways at grade crossings that are equipped with active control devices such as flashing-light signals, gates, or traffic control signals, a stop line (see EPG 620.2.16) shall be installed to indicate the point behind which highway vehicles are or might be required to stop.
Guidance. On paved roadway approaches to passive grade crossings where a STOP sign is installed in conjunction with the Crossbuck sign, a stop line should be installed to indicate the point behind which highway vehicles are required to stop or as near to that point as practical.
If a stop line is used, it should be a transverse line at a right angle to the traveled way and should be placed approximately 8 ft. in advance of the gate (if present), but no closer than 15 ft. in advance of the nearest rail.
Option. On paved roadway approaches to passive grade crossings where a YIELD sign is installed in conjunction with the Crossbuck sign, a yield line (see EPG 620.2.16) or a stop line may be installed to indicate the point behind which highway vehicles are required to yield or stop or as near to that point as practical.
Guidance. If a yield line is used, it should be a transverse line (see Fig. 620.2.16, Examples of Yield Line Layouts) at a right angle to the traveled way and should be placed no closer than 15 ft. in advance of the nearest rail (see Fig. 620.2.28.2, Grade Crossing Pavement Markings).
Fig. 620.2.28.1, Example of Placement of Warning Signs and Pavement Markings at Grade Crossings (MUTCD 8B-6)
Fig. 620.2.28.2, Grade Crossing Pavement Markings (MUTCD 8B-7)
Note: Refer to Fig. 620.2.28.1 for placement.
## 620.2.29 Pavement Markings for Bicycle Facilities (MUTCD Section 9C)
### 620.2.29.1 Functions of Markings (MUTCD Section 9C.01)
Support. Markings indicate the separation of the lanes for road users, assist the bicyclist by indicating assigned travel paths, indicate correct position for traffic control signal actuation and provide advance information for turning and crossing maneuvers.
### 620.2.29.2 General Principles (MUTCD Section 9C.03)
Guidance. Bikeway design guides (see MUTCD Section 9A.05) should be used when designing markings for bicycle facilities.
Standard. Markings used on bikeways shall be retroreflectorized.
Guidance. Pavement marking word messages, symbols, and/or arrows should be used in bikeways where appropriate. Consideration should be given to selecting pavement marking materials that will minimize loss of traction for bicycles under wet conditions.
Standard. The colors, width of lines, patterns of lines, symbols, and arrows used for marking bicycle facilities shall be as defined in EPG 620.1.5, EPG 620.1.6 and EPG 620.2.20.
Support. All the figures in EPG 620.2.29 show examples of the application of lines, word messages, symbols and arrows on designated bikeways.
Option. A dotted line may be used to define a specific path for a bicyclist crossing an intersection (see Figure 620.2.29.4.1) as described in EPG 620.1.6 and EPG 620.2.8.
### 620.2.29.3 Marking Patterns and Colors on Shared-Use Paths (MUTCD Section 9C.03)
Option. Where shared-use paths are of sufficient width to designate two minimum width lanes, a solid yellow line may be used to separate the two directions of travel where passing is not permitted, and a broken yellow line may be used where passing is permitted (see Fig. 620.2.29.4.2).
Guidance. Broken lines used on shared-use paths should have the usual 1-to-3 segment-to-gap ratio. A nominal 3 ft. segment with a 9 ft. gap should be used.
If conditions make it desirable to separate two directions of travel on shared-use paths at particular locations, a solid yellow line should be used to indicate no passing and no traveling to the left of the line.
Markings as shown in Fig 620.2.29.4.2 should be used at the location of obstructions in the center of the path, including vertical elements intended to physically prevent unauthorized motor vehicles from entering the path.
Option. A solid white line may be used on shared-use paths to separate different types of users. The R9-7 sign (see MUTCD Section 9B.12) may be used to supplement the solid white line.
Smaller size letters and symbols may be used on shared-use paths. Where arrows are needed on shared-use paths, half-size layouts of the arrows may be used (see EPG 620.2.20).
### 620.2.29.4 Markings for Bicycle Lanes (MUTCD Section 9C.04)
Support. Pavement markings designate that portion of the roadway for preferential use by bicyclists. Markings inform all road users of the restricted nature of the bicycle lane.
Standard. Longitudinal pavement markings shall be used to define bicycle lanes.
Guidance. If used, bicycle lane word, symbol, and/or arrow markings (see Figure 620.2.29.4.3) should be placed at the beginning of a bicycle lane and at periodic intervals along the bicycle lane based on engineering judgment.
Standard. If the bicycle lane symbol marking is used in conjunction with word or arrow messages, it shall precede them.
Option. If the word, symbol, and/or arrow pavement markings shown in Figure 620.2.29.4.3 are used, Bike Lane signs (see MUTCD Section 9B.04) may also be used, but to avoid overuse of the signs not necessarily adjacent to every set of pavement markings.
Standard. A through bicycle lane shall not be positioned to the right of a right turn only lane or to the left of a left turn only lane.
Support. A bicyclist continuing straight through an intersection from the right of a right-turn lane or from the left of a left-turn lane would be inconsistent with normal traffic behavior and would violate the expectations of right- or left-turning motorists.
Guidance. When the right through lane is dropped to become a right turn only lane, the bicycle lane markings should stop at least 100 ft. before the beginning of the right-turn lane. Through bicycle lane markings should resume to the left of the right turn only lane.
An optional through-right turn lane next to a right turn only lane should not be used where there is a through bicycle lane. If a capacity analysis indicates the need for an optional through-right turn lane, the bicycle lane should be discontinued at the intersection approach.
Posts or raised pavement markers should not be used to separate bicycle lanes from adjacent travel lanes.
Fig. 620.2.29.4.1, Example of Intersection Pavement Markings – Designated Bicycle Lane with Left-Turn Area, Heavy Turning Volumes, Parking, One-Way Traffic or Divided Highway (MUTCD Fig. 9C-1)
Fig. 620.2.29.4.2, Examples of Centerline Markings for shared-Use Paths (MUTCD Fig. 9C-2)
Support. Using raised devices creates a collision potential for bicyclists by placing fixed objects immediately adjacent to the travel path of the bicyclist. In addition, raised devices can prevent vehicles turning right from merging with the bicycle lane, which is the preferred method for making the right turn. Raised devices used to define a bicycle lane can also cause problems in cleaning and maintaining the bicycle lane.
Standard. Bicycle lanes shall not be provided on the circular roadway of a roundabout.
Guidance. Bicycle lane markings should stop at least 100 ft. before the crosswalk, or if no crosswalk is provided, at least 100 ft. before the yield line, or if no yield line is provided, then at least 100 ft. before the edge of the circulatory roadway.
Support. Examples of bicycle lane markings at right-turn lanes are shown in Figures 620.2.29.4.1, 620.2.29.7.1 and 620.2.29.7.2. Examples of pavement markings for bicycle lanes on a two-way street are shown in Figure 620.2.29.7.3. Pavement word message, symbol and arrow markings for bicycle lanes are shown in Figure 620.2.29.4.3.
Fig. 620.2.29.4.3, Word, Symbol and Arrow Pavement Markings for Bicycle Lanes (MUTCD Fig. 9C-3)
### 620.2.29.5 Bicycle Detector Symbol (MUTCD Section 9C.05)
Option. A symbol (see Fig. 620.2.29.7.4) may be placed on the pavement indicating the optimum position for a bicyclist to actuate the signal.
An R10-22 sign (see MUTCD Section 9B.13 and MUTCD Figure 9B-2) may be installed to supplement the pavement marking.
### 620.2.29.6 Pavement Markings for Obstructions (MUTCD Section 9C.06)
Guidance. In roadway situations where it is not practical to eliminate a drain grate or other roadway obstruction that is inappropriate for bicycle travel, white markings applied as shown in Figure 620.2.29.7.5 should be used to guide bicyclists around the condition.
### 620.2.29.7 Shared Lane Marking (MUTCD Section 9C.07)
Option. The Shared Lane Marking shown in Fig. 620.2.29.7.6 may be used to:
A. Assist bicyclists with lateral positioning in a shared lane with on-street parallel parking in order to reduce the chance of a bicyclist’s impacting the open door of a parked vehicle,
B. Assist bicyclists with lateral positioning in lanes that are too narrow for a motor vehicle and a bicycle to travel side by side within the same traffic lane,
C. Alert road users of the lateral location bicyclists are likely to occupy within the traveled way,
D. Encourage safe passing of bicyclists by motorists, and
E. Reduce the incidence of wrong-way bicycling.
Guidance. The Shared Lane Marking should not be placed on roadways that have a speed limit above 35 mph.
Standard. Shared Lane Markings shall not be used on shoulders or in designated bicycle lanes.
Guidance. If used in a shared lane with on-street parallel parking, Shared Lane Markings should be placed so that the centers of the markings are at least 11 ft. from the face of the curb, or from the edge of the pavement where there is no curb.
If used on a street without on-street parking that has an outside travel lane that is narrower than 14 ft., the centers of the Shared Lane Markings should be at least 4 ft. from the face of the curb, or from the edge of the pavement where there is no curb.
If used, the Shared Lane Marking should be placed immediately after an intersection and spaced at intervals not greater than 250 ft. thereafter.
Option. MUTCD Section 9B.06 describes a Bicycles May Use Full Lane sign that may be used in addition to or instead of the Shared Lane Marking to inform road users that bicyclists might occupy the travel lane.
Fig. 620.2.29.7.1, Example of Bicycle Lane Treatment at a Right Turn Only Lane (MUTCD Fig. 9C-4)
Fig. 620.2.29.7.2, Example of Bicycle Lane Treatment at Parking Lane into a Right turn Only Lane (MUTCD Fig. 9C-5)
Fig. 620.2.29.7.3, Example of Pavement Markings for Bicycle Lanes on a Two-Way Street (MUTCD Fig. 9C-6)
Fig. 620.2.29.7.4, Bicycle Detector Pavement Marking (MUTCD Fig. 9C-7)
Fig. 620.2.29.7.5, Examples of Obstruction Pavement Markings (MUTCD Fig. 9C-8)
Fig. 620.2.29.7.6, Shared Lane Marking (MUTCD Fig. 9C-9)
| 2015-05-28T05:38:17 |
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https://digital.library.txstate.edu/handle/10877/12359?show=full
|
dc.contributor.author Wang, Wei-Cheng ( ) dc.date.accessioned 2020-08-11T21:40:52Z dc.date.available 2020-08-11T21:40:52Z dc.date.issued 2002-06-18 dc.identifier.citation Wang, W. C. (2002). Nonlinear stability of centered rarefaction waves of the Jin-Xin relaxation model for $2 \times 2$ conservation laws. Electronic Journal of Differential Equations, 2002(57), pp. 1-20. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/12359 dc.description.abstract We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear 2 x 2 conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer. en_US dc.format Text dc.format.extent 20 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Southwest Texas State University, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Jin-Xin relaxation model en_US dc.subject Conservation laws en_US dc.subject Centered rarefaction wave en_US dc.title Nonlinear Stability of Centered Rarefaction Waves of the Jin-Xin Relaxation Model for 2 x 2 Conservation Laws en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License. dc.description.department Mathematics
| 2022-12-06T03:05:47 |
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https://www.aimsciences.org/article/doi/10.3934/proc.2009.2009.359
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Article Contents
Article Contents
# On the non-integrability of the Popowicz peakon system
• We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlevé analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of $N$-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension $3N$.
Mathematics Subject Classification: Primary: 37K05, 37K10; Secondary: 37J99.
Citation:
Open Access Under a Creative Commons license
| 2023-03-29T19:31:56 |
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http://pdglive.lbl.gov/DataBlock.action?node=M178M
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# ${{\boldsymbol D}_{{0}}^{*}{(2300)}^{0}}$ MASS INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$\bf{ 2300 \pm19}$ OUR AVERAGE
$2297$ $\pm8$ $\pm20$ 3.4k
2009 AB
BABR ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}$
$2308$ $\pm17$ $\pm32$
2004 D
BELL ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2407$ $\pm21$ $\pm35$ 9.8k 1
2004 A
FOCS ${{\mathit \gamma}}$ A
1 Possibly the feed-down from another state.
References:
AUBERT 2009AB
PR D79 112004 Dalitz Plot Analysis of
ABE 2004D
PR D69 112002 Study of ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{**0}}{{\mathit \pi}^{-}}$ ( ${{\mathit D}^{**0}}$ $\rightarrow$ ${{\mathit D}}{}^{(*)+}$ ${{\mathit \pi}^{-}}$ ) Decays
PL B586 11 Measurement of Masses and Widths of Excited Charm Mesons ${{\mathit D}_{{2}}^{*}}$ and Evidence for Broad States
| 2020-05-28T21:57:00 |
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https://par.nsf.gov/biblio/10248868-new-constraints-line-ratio-across-nearby-disc-galaxies
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New constraints on the 12CO(2–1)/(1–0) line ratio across nearby disc galaxies
ABSTRACT Both the CO(2–1) and CO(1–0) lines are used to trace the mass of molecular gas in galaxies. Translating the molecular gas mass estimates between studies using different lines requires a good understanding of the behaviour of the CO(2–1)-to-CO(1–0) ratio, R21. We compare new, high-quality CO(1–0) data from the IRAM 30-m EMIR MultiLine Probe of the ISM Regulating Galaxy Evolution survey to the latest available CO(2–1) maps from HERA CO-Line Extragalactic Survey, Physics at High Angular resolution in Nearby Galaxies-ALMA, and a new IRAM 30-m M51 Large Program. This allows us to measure R21 across the full star-forming disc of nine nearby, massive, star-forming spiral galaxies at 27 arcsec (∼1–2 kpc) resolution. We find an average R21 = 0.64 ± 0.09 when we take the luminosity-weighted mean of all individual galaxies. This result is consistent with the mean ratio for disc galaxies that we derive from single-pointing measurements in the literature, $R_{\rm 21, lit}~=~0.59^{+0.18}_{-0.09}$. The ratio shows weak radial variations compared to the point-to-point scatter in the data. In six out of nine targets, the central enhancement in R21 with respect to the galaxy-wide mean is of order of ${\sim}10{-}20{{\ \rm per\ cent}}$. We estimate an azimuthal scatter of ∼20 per cent in R21 at fixed more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10248868
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
504
Issue:
3
Page Range or eLocation-ID:
3221 to 3245
ISSN:
0035-8711
1. ABSTRACT It remains a major challenge to derive a theory of cloud-scale ($\lesssim100$ pc) star formation and feedback, describing how galaxies convert gas into stars as a function of the galactic environment. Progress has been hampered by a lack of robust empirical constraints on the giant molecular cloud (GMC) lifecycle. We address this problem by systematically applying a new statistical method for measuring the evolutionary timeline of the GMC lifecycle, star formation, and feedback to a sample of nine nearby disc galaxies, observed as part of the PHANGS-ALMA survey. We measure the spatially resolved (∼100 pc) CO-to-H α flux ratio and find amore »
4. We studied the molecular gas properties of AzTEC/C159, a star-forming disk galaxy at $z=4.567$. We secured $^{12}$CO molecular line detections for the $J=2\to1$ and $J=5\to4$ transitions using the Karl G. Jansky VLA and the NOEMA interferometer. The broad (FWHM$\sim750\,{\rm km\,s}^{-1}$) and tentative double-peaked profiles of both $^{12}$CO lines are consistent with an extended molecular gas reservoir, which is distributed in a rotating disk as previously revealed from [CII] 158$\mu$m line observations. Based on the $^{12}$CO(2$\to$1) emission line we derived $L'_{\rm{CO}}=(3.4\pm0.6)\times10^{10}{\rm \,K\,km\,s}^{-1}{\rm \,pc}^{2}$, that yields a molecular gas mass of $M_{\rm H_2 }(\alpha_{\rm CO}/4.3)=(1.5\pm0.3)\times 10^{11}{\rm M}_\odot$ and unveils a gas-rich systemmore »
| 2022-05-22T11:33:14 |
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https://zbmath.org/authors/?q=ai%3Aabramsky.samson
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## Abramsky, Samson
Compute Distance To:
Author ID: abramsky.samson Published as: Abramsky, Samson; Abramsky, S. External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr
Documents Indexed: 103 Publications since 1983 19 Contributions as Editor Biographic References: 1 Publication Co-Authors: 68 Co-Authors with 79 Joint Publications 1,761 Co-Co-Authors
all top 5
### Co-Authors
40 single-authored 10 Jagadeesan, Radha 7 Maibaum, Thomas Stephen Edward 6 Soares Barbosa, Rui 5 Gabbay, Dov M. 5 McCusker, Guy Andrew 4 Lenisa, Marina 4 Mansfield, Shane 3 Brandenburger, Adam 3 Carù, Giovanni 3 Coecke, Bob 3 Gay, Simon J. 3 Kishida, Kohei 3 Mislove, Michael W. 3 Nagarajan, Rajagopal 3 Shah, Nihil 2 Burn, Geoffrey L. 2 Constantin, Carmen M. 2 Curien, Pierre-Louis 2 de Silva, Nadish 2 Gavoille, Cyril 2 Ghica, Dan R. 2 Hankin, Chris L. 2 Heunen, Chris 2 Kirchner, Claude 2 Lal, Raymond 2 Malacaria, Pasquale 2 Meyer auf der Heide, Friedhelm 2 Palamidessi, Catuscia 2 Pitt, David H. 2 Poigné, Axel 2 Rydeheard, David E. 2 Spirakis, Paul G. 2 Väänänen, Jouko Antero 2 Vákár, Matthijs 2 Zvesper, Jonathan Alexander 1 Bechmann, Matthias 1 Blute, Richard F. 1 Cooper, Stuart Barry 1 Dawar, Anuj 1 Duncan, Ross 1 Fuller, David A. 1 Gorecki, Jerzy 1 Haghverdi, Esfandiar 1 Horsman, Dominic 1 Kendon, Viv M. 1 Kontinen, Juha 1 Mackie, Ian 1 Murawski, Andrzej S. 1 Naughton, Thomas J. 1 Panangaden, Prakash 1 Perdrix, Simon 1 Pérez-Jiménez, Mario J. 1 Pitts, Andrew M. 1 Román, Leopoldo 1 Romero-Campero, Francisco José 1 Sadrzadeh, Mehrnoosh 1 Savochkin, Andrei 1 Scott, Philip J. 1 Sebald, Angelika 1 Stepney, Susan 1 Tzevelekos, Nikos 1 Vickers, Steven 1 Vollmer, Heribert 1 Wang, Pengming 1 Winschel, Viktor 1 Yamada, Norihiro 1 Ying, Shenggang 1 Zapata, Octavio
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### Serials
10 Theoretical Computer Science 7 Lecture Notes in Computer Science 6 Information and Computation 6 MSCS. Mathematical Structures in Computer Science 4 Annals of Pure and Applied Logic 2 Synthese 2 Journal of Logic and Computation 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Journal of Computer and System Sciences 1 Journal of Mathematical Psychology 1 Journal of Philosophical Logic 1 Journal of Pure and Applied Algebra 1 The Journal of Symbolic Logic 1 Studia Logica 1 Science of Computer Programming 1 New Generation Computing 1 Applied Categorical Structures 1 Theory and Applications of Categories 1 Bulletin of the European Association for Theoretical Computer Science EATCS 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 New Journal of Physics 1 Proceedings of Symposia in Applied Mathematics 1 Electronic Notes in Theoretical Computer Science
all top 5
### Fields
83 Computer science (68-XX) 57 Mathematical logic and foundations (03-XX) 32 Quantum theory (81-XX) 26 Category theory; homological algebra (18-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 General and overarching topics; collections (00-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 2 Algebraic topology (55-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
90 Publications have been cited 1,454 times in 1,011 Documents Cited by Year
Domain theory in logical form. Zbl 0737.03006
Abramsky, Samson
1991
Full abstraction for PCF. Zbl 1006.68028
2000
Games and full completeness for multiplicative linear logic. Zbl 0822.03007
1994
Quantales, observational logic and process semantics. Zbl 0823.06011
Abramsky, Samson; Vickers, Steven
1993
Computational interpretations of linear logic. Zbl 0791.03003
Abramsky, Samson
1993
Full abstraction in the lazy lambda calculus. Zbl 0779.03003
Abramsky, Samson; Ong, C.-H. Luke
1993
A domain equation for bisimulation. Zbl 0718.68057
Abramsky, Samson
1991
Categorical quantum mechanics. Zbl 1273.81014
Abramsky, Samson; Coecke, Bob
2009
Call-by-value games. Zbl 0908.03035
Abramsky, Samson; McCusker, Guy
1998
Observation equivalence as a testing equivalence. Zbl 0626.68016
Abramsky, Samson
1987
Linearity, sharing and state: A fully abstract games semantics for idealized Algol with active expressions. (Extended abstract). Zbl 0909.68029
Abramsky, Samson; McCusker, Guy
1996
Geometry of interaction and linear combinatory algebras. Zbl 1014.03056
Abramsky, Samson; Haghverdi, Esfandiar; Scott, Philip
2002
The sheaf-theoretic structure of non-locality and contextuality. Zbl 1448.81028
2011
From IF to BI. A tale of dependence and separation. Zbl 1175.03016
Abramsky, Samson; Väänänen, Jouko
2009
Game semantics. Zbl 0961.68080
Abramsky, Samson; McCusker, Guy
1999
Full abstraction for PCF. Zbl 0942.68615
1994
Contextuality, cohomology and paradox. Zbl 1373.03048
Abramsky, Samson; Barbosa, Rui Soares; Kishida, Kohei; Lal, Raymond; Mansfield, Shane
2015
Proofs as processes. Zbl 0850.68297
Abramsky, Samson
1994
$$H^\ast$$-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics. Zbl 1267.18007
Abramsky, Samson; Heunen, Chris
2012
New foundations for the geometry of interaction. Zbl 0803.03014
1994
Strictness analysis for higher-order functions. Zbl 0603.68013
Burn, Geoffrey L.; Hankin, Chris; Abramsky, Samson
1986
Nuclear and trace ideals in tensored $$^*$$-categories. Zbl 0946.18004
Abramsky, Samson; Blute, Richard; Panangaden, Prakash
1999
A Cook’s tour of the finitary non-well-founded sets. Zbl 1279.03073
Abramsky, Samson
2005
A structural approach to reversible computation. Zbl 1081.68019
Abramsky, Samson
2005
Interaction categories and the foundations of typed concurrent programming. Zbl 0934.18007
Abramsky, Samson; Gay, Simon; Nagarajan, Rajagopal
1996
Semantics of interaction: An introduction to game semantics. Zbl 0938.91500
Abramsky, Samson
1997
An internal language for autonomous categories. Zbl 0806.03044
Mackie, Ian; Román, Leopoldo; Abramsky, Samson
1993
Handbook of logic in computer science. Vol. 3: Semantic structures. Zbl 0829.68111
1994
Abstract physical traces. Zbl 1065.18005
Abramsky, Samson; Coecke, Bob
2005
On semantic foundations for applicative multiprogramming. Zbl 0538.68064
Abramsky, Samson
1983
Abstract scalars, loops, and free traced and strongly compact closed categories. Zbl 1151.81002
Abramsky, Samson
2005
Full abstraction for idealized Algol with passive expressions. Zbl 0954.68028
Abramsky, Samson; McCusker, Guy
1999
Sequentiality vs. concurrency in games and logic. Zbl 1129.03014
Abramsky, Samson
2003
Temperley-Lieb algebra: from knot theory to logic and computation via quantum mechanics. Zbl 1135.81006
Abramsky, Samson
2008
The theory of strictness analysis for higher order functions. Zbl 0596.68009
Burn, G. L.; Hankin, C. L.; Abramsky, S.
1986
Relational hidden variables and non-locality. Zbl 1278.81101
Abramsky, Samson
2013
Applying game semantics to compositional software modeling and verification. Zbl 1126.68343
Abramsky, Samson; Ghica, Dan R.; Murawski, Andrzej S.; Ong, C.-H. Luke
2004
Abstract interpretation, logical relations, and Kan extensions. Zbl 0727.03020
Abramsky, Samson
1990
A categorical quantum logic. Zbl 1099.03059
Abramsky, Samson; Duncan, Ross
2006
Introduction to categories and categorical logic. Zbl 1217.18001
Abramsky, S.; Tzevelekos, N.
2011
Handbook of logic in computer science. Vol. 2: Background: Computational structures. Zbl 0777.68001
1992
Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting. Zbl 1364.91026
Abramsky, Samson; Winschel, Viktor
2017
A compositional game semantics for multi-agent logics of partial information. Zbl 1196.68241
Abramsky, Samson
2007
An operational interpretation of negative probabilities and no-signalling models. Zbl 1415.81009
2014
Linear realizability and full completeness for typed lambda-calculi. Zbl 1064.03012
Abramsky, Samson; Lenisa, Marina
2005
Algorithmic game semantics. A tutorial introduction. Zbl 1097.68574
Abramsky, Samson
2002
Strictness analysis and polymorphic invariance. Zbl 0624.68034
Abramsky, Samson
1986
Games and full completeness for multiplicative linear logic. (Extended Abstract). Zbl 0925.03041
1992
Relational databases and Bell’s theorem. Zbl 1397.68041
Abramsky, Samson
2013
The quantum monad on relational structures. Zbl 1441.68055
Abramsky, Samson; Barbosa, Rui Soares; de Silva, Nadish; Zapata, Octavio
2017
A fully abstract denotational semantics for the calculus of higher-order communicating systems. Zbl 0974.68109
Thomsen, B.; Abramsky, S.
2001
A fully complete PER model for ML polymorphic types. Zbl 0973.03015
Abramsky, Samson; Lenisa, Marina
2000
Specifying interaction categories. Zbl 0884.18008
Pavlović, D.; Abramsky, S.
1997
A game semantics for generic polymorphism. Zbl 1066.68074
2005
Experiments, powerdomains and fully abstract models for applicative multiprogramming. Zbl 0586.68022
Abramsky, Samson
1983
Game semantics for access control. Zbl 1337.68157
2009
Semantic unification. A sheaf theoretic approach to natural language. Zbl 1285.03021
2014
No-cloning in categorical quantum mechanics. Zbl 1192.81013
Abramsky, Samson
2010
Big toy models. Representing physical systems as Chu spaces. Zbl 1275.81008
Abramsky, Samson
2012
Relating structure and power: comonadic semantics for computational resources (extended abstract). Zbl 06962928
Abramsky, Samson; Shah, Nihil
2018
The pebbling comonad in finite model theory. Zbl 1452.03083
Abramsky, Samson; Dawar, Anuj; Wang, Pengming
2017
The cohomology of non-locality and contextuality. Zbl 1464.81012
Abramsky, Samson; Mansfield, Shane; Soares Barbosa, Rui
2012
Dependence logic. Theory and applications. Selected papers based on the presentations at the Dagstuhl seminar on ‘Dependence logic: theory and applications’, Wadern, Germany, February 2013. Zbl 1348.03004
2016
Games for recursive types. Zbl 0840.03054
Abramsky, Samson; McCusker, Guy
1995
Mixed computation of Prolog programs. Zbl 0654.68021
Fuller, David A.; Abramsky, Samson
1988
Operational theories and categorical quantum mechanics. Zbl 1355.81028
Abramsky, Samson; Heunen, Chris
2016
What are the fundamental structures of concurrency? We still don’t know! Zbl 1315.68188
Abramsky, Samson
2006
Petri nets, discrete physics, and distributed quantum computation. Zbl 1143.68468
Abramsky, Samson
2008
Intensionality, definability and computation. Zbl 1344.03003
Abramsky, Samson
2014
Handbook of logic in computer science. Vol. 4: Semantic modelling. Zbl 0876.68001
1995
A type-theoretic approach to deadlock-freedom of asynchronous systems. Zbl 0882.18002
Abramsky, Samson; Gay, Simon; Nagarajan, Rajagopal
1997
Fully complete minimal PER models for the simply typed $$\lambda$$-calculus. Zbl 0999.03010
Abramsky, Samson; Lenisa, Marina
2001
Axiomatizing fully complete models for ML polymorphic types. Zbl 0996.03041
Abramsky, Samson; Lenisa, Marina
2000
A specification structure for deadlock-freedom of synchronous processes. Zbl 0932.68061
Abramsky, S.; Gay, S. J.; Nagarajan, R.
1999
Process realizability. Zbl 0995.68064
Abramsky, Samson
2000
A game semantics for generic polymorphism. Zbl 1029.68038
2003
Category theory and computer programming. Tutorial and Workshop, Guildford, U.K., September 16-20, 1985. Proceedings. Zbl 0607.00015
1986
Handbook of logic in computer science. Vol. 1: Background: Mathematical structures. Zbl 0806.68003
1992
Coalgebras, Chu spaces, and representations of physical systems. Zbl 1270.81040
Abramsky, Samson
2013
A complete characterization of all-versus-nothing arguments for stabilizer states. Zbl 1404.81022
Abramsky, Samson; Soares Barbosa, Rui; Carù, Giovanni; Perdrix, Simon
2017
Relating structure and power: comonadic semantics for computational resources. Zbl 07533327
Abramsky, Samson; Shah, Nihil
2018
Non-locality, contextuality and valuation algebras: a general theory of disagreement. Zbl 1462.81012
Abramsky, Samson; Carù, Giovanni
2019
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference. Zbl 1328.03012
Abramsky, Samson; Zvesper, Jonathan
2012
Heterotic computing examples with optics, bacteria, and chemicals. Zbl 1374.68223
Stepney, Susan; Abramsky, Samson; Bechmann, Matthias; Gorecki, Jerzy; Kendon, Viv; Naughton, Thomas J.; Pérez-Jiménez, Mario J.; Romero-Campero, Francisco J.; Sebald, Angelika
2012
Games for dependent types. Zbl 1395.68177
2015
Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states. Zbl 1353.81024
Abramsky, Samson; Constantin, Carmen M.; Ying, Shenggang
2016
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference. Zbl 1328.03013
Abramsky, Samson; Zvesper, Jonathan
2015
Physical traces: quantum vs. classical information processing. Zbl 1270.68182
Abramsky, Samson; Coecke, Bob
2003
Minimum quantum resources for strong non-locality. Zbl 1427.81006
Abramsky, Samson; Barbosa, Rui Soares; Carù, Giovanni; De Silva, Nadish; Kishida, Kohei; Mansfield, Shane
2018
Contextual semantics: from quantum mechanics to logic, databases, constraints, and complexity. Zbl 1416.81016
Abramsky, Samson
2014
Non-locality, contextuality and valuation algebras: a general theory of disagreement. Zbl 1462.81012
Abramsky, Samson; Carù, Giovanni
2019
Relating structure and power: comonadic semantics for computational resources (extended abstract). Zbl 06962928
Abramsky, Samson; Shah, Nihil
2018
Relating structure and power: comonadic semantics for computational resources. Zbl 07533327
Abramsky, Samson; Shah, Nihil
2018
Minimum quantum resources for strong non-locality. Zbl 1427.81006
Abramsky, Samson; Barbosa, Rui Soares; Carù, Giovanni; De Silva, Nadish; Kishida, Kohei; Mansfield, Shane
2018
Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting. Zbl 1364.91026
Abramsky, Samson; Winschel, Viktor
2017
The quantum monad on relational structures. Zbl 1441.68055
Abramsky, Samson; Barbosa, Rui Soares; de Silva, Nadish; Zapata, Octavio
2017
The pebbling comonad in finite model theory. Zbl 1452.03083
Abramsky, Samson; Dawar, Anuj; Wang, Pengming
2017
A complete characterization of all-versus-nothing arguments for stabilizer states. Zbl 1404.81022
Abramsky, Samson; Soares Barbosa, Rui; Carù, Giovanni; Perdrix, Simon
2017
Dependence logic. Theory and applications. Selected papers based on the presentations at the Dagstuhl seminar on ‘Dependence logic: theory and applications’, Wadern, Germany, February 2013. Zbl 1348.03004
2016
Operational theories and categorical quantum mechanics. Zbl 1355.81028
Abramsky, Samson; Heunen, Chris
2016
Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states. Zbl 1353.81024
Abramsky, Samson; Constantin, Carmen M.; Ying, Shenggang
2016
Contextuality, cohomology and paradox. Zbl 1373.03048
Abramsky, Samson; Barbosa, Rui Soares; Kishida, Kohei; Lal, Raymond; Mansfield, Shane
2015
Games for dependent types. Zbl 1395.68177
2015
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference. Zbl 1328.03013
Abramsky, Samson; Zvesper, Jonathan
2015
An operational interpretation of negative probabilities and no-signalling models. Zbl 1415.81009
2014
Semantic unification. A sheaf theoretic approach to natural language. Zbl 1285.03021
2014
Intensionality, definability and computation. Zbl 1344.03003
Abramsky, Samson
2014
Contextual semantics: from quantum mechanics to logic, databases, constraints, and complexity. Zbl 1416.81016
Abramsky, Samson
2014
Relational hidden variables and non-locality. Zbl 1278.81101
Abramsky, Samson
2013
Relational databases and Bell’s theorem. Zbl 1397.68041
Abramsky, Samson
2013
Coalgebras, Chu spaces, and representations of physical systems. Zbl 1270.81040
Abramsky, Samson
2013
$$H^\ast$$-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics. Zbl 1267.18007
Abramsky, Samson; Heunen, Chris
2012
Big toy models. Representing physical systems as Chu spaces. Zbl 1275.81008
Abramsky, Samson
2012
The cohomology of non-locality and contextuality. Zbl 1464.81012
Abramsky, Samson; Mansfield, Shane; Soares Barbosa, Rui
2012
From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference. Zbl 1328.03012
Abramsky, Samson; Zvesper, Jonathan
2012
Heterotic computing examples with optics, bacteria, and chemicals. Zbl 1374.68223
Stepney, Susan; Abramsky, Samson; Bechmann, Matthias; Gorecki, Jerzy; Kendon, Viv; Naughton, Thomas J.; Pérez-Jiménez, Mario J.; Romero-Campero, Francisco J.; Sebald, Angelika
2012
The sheaf-theoretic structure of non-locality and contextuality. Zbl 1448.81028
2011
Introduction to categories and categorical logic. Zbl 1217.18001
Abramsky, S.; Tzevelekos, N.
2011
No-cloning in categorical quantum mechanics. Zbl 1192.81013
Abramsky, Samson
2010
Categorical quantum mechanics. Zbl 1273.81014
Abramsky, Samson; Coecke, Bob
2009
From IF to BI. A tale of dependence and separation. Zbl 1175.03016
Abramsky, Samson; Väänänen, Jouko
2009
Game semantics for access control. Zbl 1337.68157
2009
Temperley-Lieb algebra: from knot theory to logic and computation via quantum mechanics. Zbl 1135.81006
Abramsky, Samson
2008
Petri nets, discrete physics, and distributed quantum computation. Zbl 1143.68468
Abramsky, Samson
2008
A compositional game semantics for multi-agent logics of partial information. Zbl 1196.68241
Abramsky, Samson
2007
A categorical quantum logic. Zbl 1099.03059
Abramsky, Samson; Duncan, Ross
2006
What are the fundamental structures of concurrency? We still don’t know! Zbl 1315.68188
Abramsky, Samson
2006
A Cook’s tour of the finitary non-well-founded sets. Zbl 1279.03073
Abramsky, Samson
2005
A structural approach to reversible computation. Zbl 1081.68019
Abramsky, Samson
2005
Abstract physical traces. Zbl 1065.18005
Abramsky, Samson; Coecke, Bob
2005
Abstract scalars, loops, and free traced and strongly compact closed categories. Zbl 1151.81002
Abramsky, Samson
2005
Linear realizability and full completeness for typed lambda-calculi. Zbl 1064.03012
Abramsky, Samson; Lenisa, Marina
2005
A game semantics for generic polymorphism. Zbl 1066.68074
2005
Applying game semantics to compositional software modeling and verification. Zbl 1126.68343
Abramsky, Samson; Ghica, Dan R.; Murawski, Andrzej S.; Ong, C.-H. Luke
2004
Sequentiality vs. concurrency in games and logic. Zbl 1129.03014
Abramsky, Samson
2003
A game semantics for generic polymorphism. Zbl 1029.68038
2003
Physical traces: quantum vs. classical information processing. Zbl 1270.68182
Abramsky, Samson; Coecke, Bob
2003
Geometry of interaction and linear combinatory algebras. Zbl 1014.03056
Abramsky, Samson; Haghverdi, Esfandiar; Scott, Philip
2002
Algorithmic game semantics. A tutorial introduction. Zbl 1097.68574
Abramsky, Samson
2002
A fully abstract denotational semantics for the calculus of higher-order communicating systems. Zbl 0974.68109
Thomsen, B.; Abramsky, S.
2001
Fully complete minimal PER models for the simply typed $$\lambda$$-calculus. Zbl 0999.03010
Abramsky, Samson; Lenisa, Marina
2001
Full abstraction for PCF. Zbl 1006.68028
2000
A fully complete PER model for ML polymorphic types. Zbl 0973.03015
Abramsky, Samson; Lenisa, Marina
2000
Axiomatizing fully complete models for ML polymorphic types. Zbl 0996.03041
Abramsky, Samson; Lenisa, Marina
2000
Process realizability. Zbl 0995.68064
Abramsky, Samson
2000
Game semantics. Zbl 0961.68080
Abramsky, Samson; McCusker, Guy
1999
Nuclear and trace ideals in tensored $$^*$$-categories. Zbl 0946.18004
Abramsky, Samson; Blute, Richard; Panangaden, Prakash
1999
Full abstraction for idealized Algol with passive expressions. Zbl 0954.68028
Abramsky, Samson; McCusker, Guy
1999
A specification structure for deadlock-freedom of synchronous processes. Zbl 0932.68061
Abramsky, S.; Gay, S. J.; Nagarajan, R.
1999
Call-by-value games. Zbl 0908.03035
Abramsky, Samson; McCusker, Guy
1998
Semantics of interaction: An introduction to game semantics. Zbl 0938.91500
Abramsky, Samson
1997
Specifying interaction categories. Zbl 0884.18008
Pavlović, D.; Abramsky, S.
1997
A type-theoretic approach to deadlock-freedom of asynchronous systems. Zbl 0882.18002
Abramsky, Samson; Gay, Simon; Nagarajan, Rajagopal
1997
Linearity, sharing and state: A fully abstract games semantics for idealized Algol with active expressions. (Extended abstract). Zbl 0909.68029
Abramsky, Samson; McCusker, Guy
1996
Interaction categories and the foundations of typed concurrent programming. Zbl 0934.18007
Abramsky, Samson; Gay, Simon; Nagarajan, Rajagopal
1996
Games for recursive types. Zbl 0840.03054
Abramsky, Samson; McCusker, Guy
1995
Handbook of logic in computer science. Vol. 4: Semantic modelling. Zbl 0876.68001
1995
Games and full completeness for multiplicative linear logic. Zbl 0822.03007
1994
Full abstraction for PCF. Zbl 0942.68615
1994
Proofs as processes. Zbl 0850.68297
Abramsky, Samson
1994
New foundations for the geometry of interaction. Zbl 0803.03014
1994
Handbook of logic in computer science. Vol. 3: Semantic structures. Zbl 0829.68111
1994
Quantales, observational logic and process semantics. Zbl 0823.06011
Abramsky, Samson; Vickers, Steven
1993
Computational interpretations of linear logic. Zbl 0791.03003
Abramsky, Samson
1993
Full abstraction in the lazy lambda calculus. Zbl 0779.03003
Abramsky, Samson; Ong, C.-H. Luke
1993
An internal language for autonomous categories. Zbl 0806.03044
Mackie, Ian; Román, Leopoldo; Abramsky, Samson
1993
Handbook of logic in computer science. Vol. 2: Background: Computational structures. Zbl 0777.68001
1992
Games and full completeness for multiplicative linear logic. (Extended Abstract). Zbl 0925.03041
1992
Handbook of logic in computer science. Vol. 1: Background: Mathematical structures. Zbl 0806.68003
1992
Domain theory in logical form. Zbl 0737.03006
Abramsky, Samson
1991
A domain equation for bisimulation. Zbl 0718.68057
Abramsky, Samson
1991
Abstract interpretation, logical relations, and Kan extensions. Zbl 0727.03020
Abramsky, Samson
1990
Mixed computation of Prolog programs. Zbl 0654.68021
Fuller, David A.; Abramsky, Samson
1988
Observation equivalence as a testing equivalence. Zbl 0626.68016
Abramsky, Samson
1987
Strictness analysis for higher-order functions. Zbl 0603.68013
Burn, Geoffrey L.; Hankin, Chris; Abramsky, Samson
1986
The theory of strictness analysis for higher order functions. Zbl 0596.68009
Burn, G. L.; Hankin, C. L.; Abramsky, S.
1986
Strictness analysis and polymorphic invariance. Zbl 0624.68034
Abramsky, Samson
1986
Category theory and computer programming. Tutorial and Workshop, Guildford, U.K., September 16-20, 1985. Proceedings. Zbl 0607.00015
1986
On semantic foundations for applicative multiprogramming. Zbl 0538.68064
Abramsky, Samson
1983
Experiments, powerdomains and fully abstract models for applicative multiprogramming. Zbl 0586.68022
Abramsky, Samson
1983
all top 5
### Cited by 1,003 Authors
36 Abramsky, Samson 19 Murawski, Andrzej S. 15 Dezani-Ciancaglini, Mariangiola 14 Coecke, Bob 14 Honsell, Furio 12 Heunen, Chris 11 Lenisa, Marina 10 Yoshida, Nobuko 9 Ghica, Dan R. 9 McCusker, Guy Andrew 9 Paolini, Luca 9 Scott, Philip J. 9 Solovyov, Sergey A. 9 Tzevelekos, Nikos 9 Winskel, Glynn 8 Bezhanishvili, Nick 8 Clairambault, Pierre 8 de’Liguoro, Ugo 8 Dzhafarov, Ehtibar N. 8 Galliani, Pietro 8 Gogioso, Stefano 8 Honda, Kohei 8 Jacobs, Bart 8 Jagadeesan, Radha 8 Mislove, Michael W. 8 Panangaden, Prakash 8 Vicary, Jamie 8 Vickers, Steven 7 Alessi, Fabio 7 Bezhanishvili, Guram 7 Ingólfsdóttir, Anna 7 Japaridze, Giorgi 7 Jung, Achim 7 Klop, Jan Willem 7 Laird, James D. 7 Plotkin, Gordon D. 7 Zhao, Bin 6 Aceto, Luca 6 Blute, Richard F. 6 Kurz, Alexander 6 Mackie, Ian 6 Melliès, Paul-André 6 Rosenthal, Kimmo I. 6 Ulidowski, Irek 6 Yang, Fan 5 Barbanera, Franco 5 Berger, Martin J. 5 Ciardelli, Ivano A. 5 Curien, Pierre-Louis 5 Doberkat, Ernst-Erich 5 Ehrhard, Thomas 5 Gehrke, Mai 5 Han, Shengwei 5 Hasegawa, Masahito 5 Kujala, Janne V. 5 Li, Qingguo 5 Moshier, M. Andrew 5 Nielson, Flemming 5 Paseka, Jan 5 Pavlović, Duško 5 Phillips, Iain W. 5 Piccolo, Mauro 5 Resende, Pedro 5 Ronchi Della Rocca, Simona 5 Sadrzadeh, Mehrnoosh 5 Scedrov, Andre 5 Soares Barbosa, Rui 5 van Benthem, Johan F. A. K. 4 Alves, Sandra 4 Carù, Giovanni 4 Cervesato, Iliano 4 de Paiva, Valeria 4 de Vries, Fer-Jan J. 4 Fiore, Marcelo P. 4 Florido, Mário 4 Fu, Yuxi 4 Genovese, Fabrizio 4 Haghverdi, Esfandiar 4 Hasuo, Ichiro 4 Hennessy, Matthew C. B. 4 Hoshino, Naohiko 4 Hötzel Escardó, Martín 4 Hyland, J. Martin E. 4 Kaarsgaard, Robin 4 Kissinger, Aleks 4 Kontinen, Juha 4 Levy, Paul Blain 4 Malacaria, Pasquale 4 Power, John 4 Pym, David J. 4 Santocanale, Luigi 4 Saurin, Alexis 4 Schmidt, David A. 4 Straßburger, Lutz 4 van Bakel, Steffen 4 Vollmer, Heribert 4 Wang, Longchun 4 Worrell, James B. 3 Axelsen, Holger Bock 3 Baltag, Alexandru ...and 903 more Authors
all top 5
### Cited in 118 Serials
188 Theoretical Computer Science 69 Information and Computation 66 Annals of Pure and Applied Logic 47 MSCS. Mathematical Structures in Computer Science 22 Logical Methods in Computer Science 15 Journal of Pure and Applied Algebra 14 Fuzzy Sets and Systems 13 Foundations of Physics 10 Acta Informatica 10 Studia Logica 10 Synthese 10 Formal Aspects of Computing 10 Applied Categorical Structures 10 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 9 Journal of Functional Programming 9 The Journal of Logic and Algebraic Programming 7 International Journal of Theoretical Physics 7 Journal of Mathematical Psychology 7 Topology and its Applications 7 Journal of Logic, Language and Information 7 Journal of Logical and Algebraic Methods in Programming 6 Information Processing Letters 6 Journal of Mathematical Physics 6 Journal of Computer and System Sciences 6 Journal of Philosophical Logic 6 The Journal of Symbolic Logic 6 The Bulletin of Symbolic Logic 6 Quantum Information Processing 5 Cahiers de Topologie et Géométrie Différentielle Catégoriques 4 Communications in Algebra 4 Communications in Mathematical Physics 4 Semigroup Forum 4 Soft Computing 4 Journal of Applied Logic 3 Notre Dame Journal of Formal Logic 3 RAIRO. Informatique Théorique et Applications 3 Journal of Applied Non-Classical Logics 3 Annals of Mathematics and Artificial Intelligence 3 RAIRO. Theoretical Informatics and Applications 2 Computers & Mathematics with Applications 2 Advances in Mathematics 2 Journal of Algebra 2 New Generation Computing 2 International Journal of Approximate Reasoning 2 International Journal of Algebra and Computation 2 International Journal of Foundations of Computer Science 2 Journal of Knot Theory and its Ramifications 2 Cybernetics and Systems Analysis 2 Formal Methods in System Design 2 Theory and Applications of Categories 2 Theory of Computing Systems 2 Higher-Order and Symbolic Computation 2 LMS Journal of Computation and Mathematics 2 Computer Languages, Systems & Structures 2 Logica Universalis 2 The Review of Symbolic Logic 2 RAIRO. Theoretical Informatics and Applications 1 Artificial Intelligence 1 Lithuanian Mathematical Journal 1 The Mathematical Gazette 1 Nuclear Physics. B 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Algebra Universalis 1 Information Sciences 1 Kybernetika 1 Mathematica Slovaca 1 Proceedings of the American Mathematical Society 1 Programming and Computer Software 1 Science of Computer Programming 1 Mathematical Social Sciences 1 History and Philosophy of Logic 1 Journal of Computer Science and Technology 1 International Journal of Parallel Programming 1 Journal of Automated Reasoning 1 International Journal of Mathematics 1 International Journal of Computer Mathematics 1 Distributed Computing 1 Archive for Mathematical Logic 1 Indagationes Mathematicae. New Series 1 Topology Proceedings 1 Turkish Journal of Mathematics 1 Selecta Mathematica. New Series 1 The Journal of Artificial Intelligence Research (JAIR) 1 Topoi 1 Journal of the ACM 1 Algebras and Representation Theory 1 Journal of Discrete Mathematical Sciences & Cryptography 1 New Journal of Physics 1 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Applied Mathematics and Computer Science 1 Fundamenta Informaticae 1 Journal of High Energy Physics 1 Annales Henri Poincaré 1 International Game Theory Review 1 Journal of the Australian Mathematical Society 1 Logic and Logical Philosophy 1 Journal of Applied Mathematics and Computing 1 Journal of Dynamical Systems and Geometric Theories 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques ...and 18 more Serials
all top 5
### Cited in 42 Fields
603 Computer science (68-XX) 444 Mathematical logic and foundations (03-XX) 185 Category theory; homological algebra (18-XX) 133 Quantum theory (81-XX) 111 Order, lattices, ordered algebraic structures (06-XX) 86 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 General topology (54-XX) 25 Functional analysis (46-XX) 16 General algebraic systems (08-XX) 15 Group theory and generalizations (20-XX) 15 Probability theory and stochastic processes (60-XX) 14 Associative rings and algebras (16-XX) 12 Information and communication theory, circuits (94-XX) 9 Statistics (62-XX) 8 General and overarching topics; collections (00-XX) 8 Combinatorics (05-XX) 7 Manifolds and cell complexes (57-XX) 6 History and biography (01-XX) 6 Algebraic topology (55-XX) 6 Relativity and gravitational theory (83-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Topological groups, Lie groups (22-XX) 5 Operator theory (47-XX) 4 Measure and integration (28-XX) 4 Partial differential equations (35-XX) 3 Number theory (11-XX) 3 Commutative algebra (13-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Biology and other natural sciences (92-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 2 $$K$$-theory (19-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 1 Real functions (26-XX) 1 Geometry (51-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2022-10-03T15:10:45 |
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https://phys.libretexts.org/TextMaps/General_Physics_TextMaps/Map%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_I_(OpenStax)/6%3A_Applications_of_Newton's_Laws
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$$\require{cancel}$$
# 6: Applications of Newton's Laws
Car racing has grown in popularity in recent years. As each car moves in a curved path around the turn, its wheels also spin rapidly. The wheels complete many revolutions while the car makes only part of one (a circular arc). How can we describe the velocities, accelerations, and forces involved? What force keeps a racecar from spinning out, hitting the wall bordering the track? What provides this force? Why is the track banked? We answer all of these questions in this chapter as we expand our consideration of Newton’s laws of motion.
Thumbnail Figure 6.1 - Stock cars racing in the Grand National Divisional race at Iowa Speedway in May, 2015. Cars often reach speeds of 200 mph (320 km/h).
### Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2017-12-14T08:26:54 |
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https://ftp.aimsciences.org/article/doi/10.3934/proc.2011.2011.589
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Article Contents
Article Contents
# Distributed mathematical models of undetermined "without preference" motion of traffic flow
• Present work proceeds non-deterministic motion of the two-dimensional (2D) vehicular traffic flow, where the traffic flow is assumed as flow of particles in the investigated environment with allowed motion in both forward and opposite directions. Besides, it is assumed that at any fixed time interval in the 2D flow, vehicles could change its positions on the road to any arbitrary placements at the de ned probabilities, even they might be not the neighbouring ones. Such a non-deterministic motion of 2D traffic flow will be named as motion "without preference". Under the pointed assumptions, first it is constructed the non-deterministic discrete mathimatical model, and later by means f using the principle of continuous system there are applied limiting transitions to the constructed discrete model. As a result nondeterministic continuous model in the form of initial-boundary value problem for the integro-di fferential equation is elaborated. In addition probabilistic interpretations of the constructed models and the received results are given.
Mathematics Subject Classification: Primary: 45K05, 60J28, 82B31; Secondary: 65M75, 65N75.
Citation:
Open Access Under a Creative Commons license
| 2023-03-20T22:28:53 |
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https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-docs/notebooks/Skymaps.html
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# GBM Localizations and Sky Maps¶
As part of mission operations, GBM produces localizations for GRBs and disseminates these to the community. GCN notices are sent to interested follow-up observers containing brief summary information, and HEALPix FITS files containing the localization are created and hosted at the Fermi Science Support Center. These localizations contain the best-modeled systematic uncertainty in the localization and contain a host of metadata such as the individual detector pointings and the geocenter location as observed by Fermi.
You can read one of these HEALPix files using the GbmHealPix class:
[1]:
from gbm import test_data_dir
from gbm.data import GbmHealPix
# open a GBM localization
loc = GbmHealPix.open(test_data_dir+'/glg_healpix_all_bn190915240_v00.fit')
print(loc)
glg_healpix_all_bn190915240_v00.fit
You can easily access the HEALPix-specific info:
[2]:
print('Healpix nside: {}'.format(loc.nside))
print('Healpix npix: {}'.format(loc.npix))
print('Pixel area (sq. deg.): {}'.format(loc.pixel_area))
Healpix nside: 128
Healpix npix: 196608
Pixel area (sq. deg.): 0.20982341130279172
As for the localization information, you can retrieve the sky position with the highest probability (centroid):
[3]:
loc.centroid
[3]:
(48.8671875, 4.181528273111476)
Or you can determine the probability of the localization at a particular point in the sky:
[4]:
loc.probability(49.0, 4.0)
[4]:
0.009200395297273567
And if you want to determine the confidence level a particular point on the sky is relative to the localization:
[5]:
loc.confidence(40.0, 4.0)
[5]:
0.865783539232832
Often for follow-up observations, it’s useful to know how much sky area the localization covers at a some confidence level:
[6]:
loc.area(0.9) # 90% confidence in units of sq. degrees
[6]:
281.1633711457409
And for plotting or other purposes, you can retrieve the RA and Dec “paths” for a given confidence region.
Note: A confidence region may have many disjoint pieces, so this will be a list of arrays
[7]:
%matplotlib agg
loc.confidence_region_path(0.5)
[7]:
[array([[ 4.61281337e+01, 2.59721728e-01],
[ 4.53138456e+01, 5.02793296e-01],
[ 4.51253482e+01, 6.21222158e-01],
[ 4.43160681e+01, 1.50837989e+00],
[ 4.41225627e+01, 2.36616357e+00],
[ 4.40920226e+01, 2.51396648e+00],
[ 4.38604592e+01, 3.51955307e+00],
[ 4.38130019e+01, 4.52513966e+00],
[ 4.41225627e+01, 5.23313031e+00],
[ 4.43770701e+01, 5.53072626e+00],
[ 4.50410901e+01, 6.53631285e+00],
[ 4.51253482e+01, 6.62602576e+00],
[ 4.61281337e+01, 7.28272773e+00],
[ 4.66920493e+01, 7.54189944e+00],
[ 4.71309192e+01, 7.65985811e+00],
[ 4.81337047e+01, 7.71980664e+00],
[ 4.91364903e+01, 8.00964739e+00],
[ 5.01392758e+01, 8.17249985e+00],
[ 5.11420613e+01, 7.90708927e+00],
[ 5.21448468e+01, 7.74393795e+00],
[ 5.25325056e+01, 7.54189944e+00],
[ 5.31476323e+01, 7.20106267e+00],
[ 5.41504178e+01, 6.99819453e+00],
[ 5.47633728e+01, 6.53631285e+00],
[ 5.51532033e+01, 6.06643188e+00],
[ 5.55700960e+01, 5.53072626e+00],
[ 5.59253530e+01, 4.52513966e+00],
[ 5.61559889e+01, 3.88048183e+00],
[ 5.62452032e+01, 3.51955307e+00],
[ 5.61559889e+01, 3.35981053e+00],
[ 5.52575186e+01, 2.51396648e+00],
[ 5.51532033e+01, 2.39467763e+00],
[ 5.41504178e+01, 1.61425423e+00],
[ 5.38532764e+01, 1.50837989e+00],
[ 5.31476323e+01, 1.16845749e+00],
[ 5.21448468e+01, 7.09923588e-01],
[ 5.16444830e+01, 5.02793296e-01],
[ 5.11420613e+01, 3.16344923e-01],
[ 5.01392758e+01, 1.89394367e-01],
[ 4.91364903e+01, 1.24551411e-01],
[ 4.81337047e+01, -2.69349612e-02],
[ 4.71309192e+01, 7.52677558e-02],
[ 4.61281337e+01, 2.59721728e-01]])]
You can even determine the probability that a point source at a given location is association with the skymap (as opposed to the null hypothesis of two spatially-unrelated sources):
[8]:
# find the probability that a point source on the sky is associated with our skymap
print(loc.source_probability(50.0, 10.0))
print(loc.source_probability(150.0, 10.0))
0.9873891225982346
4.406012354285324e-15
You can also use the GbmHealPix.region_probability() function with another HEALPix object to return the probability that the two maps are spatially associated.
You can retrieve, as attributes, various other interesting tidbits:
[9]:
# Info of other relevant things...
print('Sun location: {}'.format(loc.sun_location))
print('Geocenter location: {}'.format(loc.geo_location))
print('Detector n0 pointing: {}'.format(loc.n0_pointing))
print('Fraction of localization on Earth {}'.format(loc.geo_probability))
Sun location: (172.5011935415178, 3.23797213866954)
Geocenter location: (319.8312390218318, 17.40612934717674)
Detector n0 pointing: (146.5959532829778, 36.96759511828569)
Fraction of localization on Earth 8.442885759828031e-06
Of course, if you have a HEALPix file, you’ll want to make a pretty sky map!
[10]:
%matplotlib inline
from gbm.plot import SkyPlot
# initialize
skyplot = SkyPlot()
w00t! This is for default plotting options, but you can do a lot of customization on what is plotted (more on that in Visualizations). What if we want filled contours instead of a gradient, no Galactic Plane, and only some of the detectors? Also, by default we’re plotting the 1-, 2-, and 3-sigma contours, so we could plot the 50% and 90% instead:
[11]:
skyplot = SkyPlot()
Sometimes localizations will have probability that overlaps the Earth. For primarily historical and logistical reasons, the GBM HEALPix maps don’t remove any probability that falls on the Earth, but you can do that using the GbmHealPix.remove_earth() function, which will return you a new GbmHealPix object with the probability on the Earth removed.
In addition to reading existing GBM HEALPix maps, you can create your own! In fact, you can build more generic maps using the HealPix class. For example, let’s create a 10-degree radius Gaussian centered at RA, Dec = 180.0, 0.0:
[12]:
from gbm.data import HealPix
# 10 degree gaussian centered at RA,Dec = 180.0, 0.0
gauss_map = HealPix.from_gaussian(180.0, 0.0, 10.0)
skyplot = SkyPlot()
# set to False and empy because we have no info to plot
Or a 3-degree-width annulus on the sky centered at RA, Dec = 300.0, -30.0, with radius of 80 degrees:
[13]:
annulus_map = HealPix.from_annulus(300.0, -30, 80.0, 3.0)
skyplot = SkyPlot()
Or what if you only have a list of coordinates and you want to plot an equal-probability region on the sky:
[14]:
ra_pts = [270.0, 180.0, 90.0]
dec_pts = [15.0, 60.0, 15.0]
verts_map = HealPix.from_vertices(ra_pts, dec_pts, nside=128)
skyplot = SkyPlot()
You can even convolve your map with a Gaussian or a model that is built out of Gaussians:
[15]:
from numpy import deg2rad
# a single Gaussian of sigma_deg radius
def gauss_model(sigma_deg):
return ([sigma],[1.0])
# convolved with a 5-deg radius Gaussian
verts_convolved = verts_map.convolve(gauss_model, 5.0)
skyplot = SkyPlot()
And finally, you can multiply maps together to produce a combined sky map:
[16]:
# multiply the Gaussian map with the annulus map
multiplied = HealPix.multiply(gauss_map, annulus_map)
skyplot = SkyPlot()
| 2023-03-23T13:46:39 |
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|
https://zbmath.org/authors/?q=ai%3Arannacher.rolf
|
# zbMATH — the first resource for mathematics
## Rannacher, Rolf
Compute Distance To:
Author ID: rannacher.rolf Published as: Rannacher, Rolf; Rannacher, R. Homepage: https://ganymed.math.uni-heidelberg.de/~rannache/ External Links: MGP · Wikidata · ResearchGate · dblp · GND
Documents Indexed: 169 Publications since 1975, including 25 Books
all top 5
#### Co-Authors
42 single-authored 16 Becker, Roland 10 Heywood, John G. 8 Turek, Stefan 7 Galdi, Giovanni Paolo 7 Heuveline, Vincent 7 Vexler, Boris 6 Blum, Heribert 6 Braack, Malte 5 Bock, Hans Georg 5 Kanschat, Guido 4 Bangerth, Wolfgang 4 Carraro, Thomas 4 Richter, Thomas 4 Suttmeier, Franz-Theo 4 Wollner, Winnifried 3 Dunne, Thomas 3 Frehse, Jens 3 Führer, Christian 3 Geiger, Michael Ernst 3 Hebeker, Friedrich-Karl 3 Hoàng Xuân Phù 3 Johnson, Claes G. L. 3 Meidner, Dominik 3 Meinköhn, Erik 3 Süli, Endre E. 3 Vihharev, Jevgeni 3 Wehrse, Rainer 3 Zhou, Guohui 2 Bönisch, Sebastian 2 Engell, Sebastian 2 Frei, Stefan 2 Friedmann, Elfriede 2 Griewank, Andreas 2 Hinze, Michael 2 Hujeirat, Ahmad 2 Jäger, Willi 2 Kapp, Hartmut Ulrich 2 Kirkilionis, Markus A. 2 Körkel, Stefan 2 Kostina, Ekaterina A. 2 Krömker, Susanne 2 Leugering, Günter 2 Luskin, Mitchell 2 Maier, Matthias Sebastian 2 Schlöder, Johannes P. 2 Tomi, Friedrich 2 Ulbrich, Stefan 2 Wendland, Wolfgang L. 2 Wittum, Gabriel 1 Bader, Georg 1 Becker, Christian 1 Benner, Peter 1 Besier, Michael 1 Boman, Mats 1 Brezzi, Franco 1 Claus, Juliane 1 Dobrowolski, Manfred 1 Feistauer, Miloslav 1 Fursikov, Andreĭ Vladimirovich 1 Gerecht, Daniel 1 Glowinski, Roland 1 Hackbusch, Wolfgang 1 Harbrecht, Helmut 1 Hoppe, Ronald H. W. 1 Houston, Paul 1 Hu, Jun 1 Klingmüller, Ursula 1 Knabner, Peter 1 Knauf, Stefan 1 Kozel, Karel 1 Kunisch, Karl 1 Kunoth, Angela 1 Kuznetsov, Yurii Alekseevich 1 Lin, Qun 1 Lisky, S. 1 Müller, Steffen 1 Nabh, Guido 1 Périaux, Jacques F. 1 Peter, Malte Andreas 1 Prohl, Andreas 1 Robertson, Anne M. 1 Schäfer, Michael 1 Schulz, Volker H. 1 Scott, Larkin Ridgway 1 Sequeira, Adélia 1 Shi, Zhongci 1 Szekeres, T. 1 Ulbrich, Michael 1 Verführt, Rüdiger 1 Verfürth, Rüdiger 1 Waguet, Cyrille 1 Warnatz, Jürgen 1 Westenberger, A. 1 Xu, Xuejun
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#### Serials
8 SIAM Journal on Numerical Analysis 7 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 6 Journal of Numerical Mathematics 5 East-West Journal of Numerical Mathematics 4 International Journal for Numerical Methods in Fluids 4 Numerische Mathematik 4 SIAM Journal on Control and Optimization 4 Computational Mechanics 4 Oberwolfach Reports 3 Computer Methods in Applied Mechanics and Engineering 3 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Calcolo 2 Computing 2 Mathematische Zeitschrift 2 RAIRO. Analyse Numérique 2 Numerical Methods for Partial Differential Equations 2 Applications of Mathematics 2 SIAM Journal on Scientific Computing 2 Vietnam Journal of Mathematics 2 Journal of Mathematical Fluid Mechanics 2 Computational Methods in Applied Mathematics 2 ISNM. International Series of Numerical Mathematics 2 Contributions in Mathematical and Computational Sciences 1 Applicable Analysis 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Mathematics of Computation 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Journal of Computational and Applied Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Journal of Computational Mathematics 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Combustion Theory and Modelling 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 Journal of Computational Acoustics 1 GAMM-Mitteilungen 1 Bonner Mathematische Schriften 1 Quaderni di Matematica 1 Oberwolfach Seminars 1 Communications in Mathematical Analysis 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Mathematical Fluid Mechanics 1 Contemporary Challenges in Mathematical Fluid Dynamics and Its Applications
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#### Fields
117 Numerical analysis (65-XX) 72 Fluid mechanics (76-XX) 71 Partial differential equations (35-XX) 27 General and overarching topics; collections (00-XX) 25 Mechanics of deformable solids (74-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 9 Biology and other natural sciences (92-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Systems theory; control (93-XX) 5 Astronomy and astrophysics (85-XX) 5 Operations research, mathematical programming (90-XX) 3 Ordinary differential equations (34-XX) 3 Integral equations (45-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX)
#### Citations contained in zbMATH Open
129 Publications have been cited 3,817 times in 2,750 Documents Cited by Year
Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. Zbl 0487.76035
Heywood, John G.; Rannacher, Rolf
1982
An optimal control approach to a posteriori error estimation in finite element methods. Zbl 1105.65349
Becker, Roland; Rannacher, Rolf
2001
Finite-element approximation of the nonstationary Navier-Stokes problem. IV: Error analysis for second-order time discretization. Zbl 0694.76014
Heywood, John G.; Rannacher, Rolf
1990
Simple nonconforming quadrilateral Stokes element. Zbl 0742.76051
Rannacher, R.; Turek, S.
1992
Adaptive finite element methods for differential equations. Zbl 1020.65058
Bangerth, Wolfgang; Rannacher, Rolf
2003
Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Zbl 0863.76016
Heywood, John G.; Rannacher, Rolf; Turek, Stefan
1996
A feed-back approach to error control in finite element methods: Basic analysis and examples. Zbl 0868.65076
Becker, R.; Rannacher, R.
1996
Some optimal error estimates for piecewise linear finite element approximations. Zbl 0483.65007
Rannacher, Rolf; Scott, Ridgway
1982
On the boundary value problem of the biharmonic operator on domains with angular corners. Zbl 0445.35023
Blum, H.; Rannacher, R.
1980
Adaptive finite element methods for optimal control of partial differential equations: Basic concept. Zbl 0967.65080
Becker, Roland; Kapp, Hartmut; Rannacher, Rolf
2000
On Chorin’s projection method for the incompressible Navier-Stokes equations. Zbl 0769.76053
Rannacher, Rolf
1992
Finite element solution of diffusion problems with irregular data. Zbl 0512.65082
Rannacher, Rolf
1984
A posteriori error control for finite element approximations of elliptic eigenvalue problems. Zbl 0995.65111
Heuveline, Vincent; Rannacher, Rolf
2001
Finite element approximation of the nonstationary Navier-Stokes problem. II. Stability of solutions and error estimates uniform in time. Zbl 0611.76036
Heywood, John G.; Rannacher, Rolf
1986
Finite element approximation of the nonstationary Navier-Stokes problem. III: Smoothing property and higher order error estimates for spatial discretization. Zbl 0646.76036
Heywood, John G.; Rannacher, Rolf
1988
Asymptotic error expansion and Richardson extrapolation for linear finite elements. Zbl 0594.65082
Blum, H.; Lin, Q.; Rannacher, R.
1986
Weighted a posteriori error control in FE methods. Zbl 0968.65083
Becker, R.; Rannacher, R.
1998
On the smoothing property of the Galerkin method for parabolic equations. Zbl 0483.65064
Luskin, Mitchell; Rannacher, Rolf
1982
A feed-back approach to error control in finite element methods: Application to linear elasticity. Zbl 0894.73170
Rannacher, R.; Suttmeier, F.-T.
1997
Nonconforming finite element methods for eigenvalue problems in linear plate theory. Zbl 0394.65035
Rannacher, Rolf
1979
Adaptive error control for multigrid finite element methods. Zbl 0848.65074
Becker, R.; Johnson, C.; Rannacher, R.
1995
Asymptotic $$L^\infty$$-error estimates for linear finite element approximations of quasilinear boundary value problems. Zbl 0386.65049
Frehse, Jens; Rannacher, Rolf
1978
Error analysis for a finite element approximation of elliptic Dirichlet boundary control problems. Zbl 1273.65087
May, S.; Rannacher, R.; Vexler, B.
2013
Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. Zbl 0948.65098
Bangerth, W.; Rannacher, R.
1999
On the smoothing property of the Crank-Nicolson scheme. Zbl 0476.65062
Luskin, Mitchell; Rannacher, Rolf
1982
A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Zbl 0954.74070
Rannacher, Rolf; Suttmeier, Franz-Theo
1999
Numerics and hydrodynamic stability: Toward error control in computational fluid dynamics. Zbl 0833.76063
Johnson, Claes; Rannacher, Rolf; Boman, Mats
1995
A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Zbl 0910.73064
Rannacher, R.; Suttmeier, F.-T.
1998
Finite element methods for the incompressible Navier-Stokes equations. Zbl 1107.76353
Rannacher, Rolf
2000
A priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time. Zbl 1234.49029
Meidner, Dominik; Rannacher, Rolf; Vexler, Boris
2011
Adaptive Galerkin finite element methods for the wave equation. Zbl 1283.35053
Bangerth, W.; Geiger, Michael; Rannacher, R.
2010
Zur $$L^\infty$$-Konvergenz linearer finiter Elemente beim Dirichlet- Problem. Zbl 0321.65055
Rannacher, Rolf
1976
Eine $$L^1$$-Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente. Zbl 0359.65093
Frehse, J.; Rannacher, R.
1976
Duality-based adaptivity in the $$hp$$-finite element method. Zbl 1050.65111
Heuveline, V.; Rannacher, R.
2003
A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115
Houston, Paul; Rannacher, Rolf; Süli, Endre
2000
Adaptive Galerkin finite element methods for partial differential equations. Zbl 0976.65101
Rannacher, R.
2001
Goal-oriented error control of the iterative solution of finite element equations. Zbl 1169.65340
Meidner, D.; Rannacher, R.; Vihharev, J.
2009
Numerical simulation of laminar flames at low Mach number by adaptive finite elements. Zbl 0951.76035
Becker, R.; Braack, M.; Rannacher, R.
1999
On nonconforming and mixed finite element methods for plate bending problems. The linear case. Zbl 0425.35042
Rannacher, Rolf
1979
A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements. Zbl 1113.65102
Rannacher, R.; Vexler, B.
2006
On the question of turbulence modeling by approximate inertial manifolds and the nonlinear Galerkin method. Zbl 0791.76042
Heywood, John G.; Rannacher, Rolf
1993
Finite element methods for nonlinear elliptic systems of second order. Zbl 0444.65077
Dobrowolski, Manfred; Rannacher, Rolf
1980
Pointwise superconvergence of the streamline diffusion finite-element method. Zbl 0841.65092
Zhou, Guohui; Rannacher, Rolf
1996
Hemodynamical flows. Modeling, analysis and simulation. Papers based on the presentations at the Oberwolfach seminar ‘Hemodynamical flows: Aspects of modeling, analysis and simulation’, Oberwolfach, Germany, November 20–26, 2005. Zbl 1137.76005
Galdi, Giovanni P. (ed.); Rannacher, Rolf (ed.); Robertson, Anne M. (ed.); Turek, Stefan (ed.)
2008
Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error. Zbl 1222.65123
Rannacher, R.; Westenberger, A.; Wollner, W.
2010
Adaptive finite element techniques for the acoustic wave equation. Zbl 1360.76122
Bangerth, Wolfgang; Rannacher, Rolf
2001
A domain splitting algorithm for parabolic problems. Zbl 0767.65073
Blum, H.; Lisky, S.; Rannacher, R.
1992
Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems. Zbl 1022.65123
Kanschat, G.; Rannacher, R.
2002
A posteriori error estimation in least-squares stabilized finite element schemes. Zbl 0934.65118
Rannacher, Rolf
1998
Error control in finite element computations. An introduction to error estimation and mesh-size adaptation. Zbl 0943.65123
Rannacher, R.
1999
Discretization of the heat equation with singular initial data. Zbl 0503.65060
Rannacher, R.
1982
Goal-oriented space-time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow. Zbl 1412.76060
Besier, Michael; Rannacher, Rolf
2012
On the numerical solution of the incompressible Navier-Stokes equations. Zbl 0798.76069
Rannacher, R.
1993
Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation. Zbl 1323.74082
Dunne, Thomas; Rannacher, Rolf
2006
Extrapolation techniques for reducing the pollution effect of reentrant corners in the finite element method. Zbl 0649.65060
Blum, H.; Rannacher, R.
1988
Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors. Zbl 1267.65184
Rannacher, R.; Vihharev, J.
2013
Adaptive finite element methods for PDE-constrained optimal control problems. Zbl 1398.76196
Becker, R.; Braack, M.; Meidner, D.; Rannacher, R.; Vexler, B.
2007
Finite element eigenvalue computation on domains with reentrant corners using Richardson extrapolation. Zbl 0719.65077
Blum, H.; Rannacher, R.
1990
On mixed finite element methods in plate bending analysis. I: The first Herrmann scheme. Zbl 0736.73061
Blum, H.; Rannacher, R.
1990
Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes. Zbl 0880.76036
Becker, Roland; Rannacher, Rolf
1995
Adaptive FEM for eigenvalue problems. Zbl 1043.65122
Heuveline, V.; Rannacher, R.
2003
$$L^ \infty$$-stability estimates and asymptotic error expansion for parabolic finite element equations. Zbl 0748.65072
Rannacher, Rolf
1991
Numerical analysis of the Navier-Stokes equations. Zbl 0798.76041
Rannacher, Rolf
1993
An adaptive finite element method for unsteady convection-dominated flows with stiff source terms. Zbl 0959.76043
Hebeker, Friedrich K.; Rannacher, Rolf
1999
An adaptive streamline-diffusion finite element method for hyperbolic conservation laws. Zbl 0885.65107
Führer, C.; Rannacher, R.
1997
Optimal Neumann control for the two-dimensional steady-state Navier-Stokes equations. Zbl 1200.35214
Fursikov, A. V.; Rannacher, R.
2010
Fundamental trends in fluid-structure interaction. Zbl 1410.76010
Galdi, Giovanni P. (ed.); Rannacher, Rolf (ed.)
2010
An analysis of stability concepts for the Navier-Stokes equations. Zbl 0598.35091
Heywood, John G.; Rannacher, Rolf
1986
An optimal control approach to adaptivity in computational fluid mechanics. Zbl 1047.76016
Becker, R.; Heuveline, V.; Rannacher, R.
2002
Implicit time-discretization of the nonstationary incompressible Navier-Stokes equations. Zbl 0882.76056
Müller, S.; Prohl, A.; Rannacher, R.; Turek, S.
1995
Defect correction techniques in the finite element method. Zbl 0784.65081
Rannacher, R.
1991
Well-posedness of a linear spatio-temporal model of the JAK2/STAT5 signaling pathway. Zbl 1277.35210
Friedmann, E.; Neumann, R.; Rannacher, R.
2013
Constrained optimization and optimal control for partial differential equations. Zbl 1231.49001
Leugering, Günter (ed.); Engell, Sebastian (ed.); Griewank, Andreas (ed.); Hinze, Michael (ed.); Rannacher, Rolf (ed.); Schulz, Volker (ed.); Ulbrich, Michael (ed.); Ulbrich, Stefan (ed.)
2012
Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem. Zbl 0383.65061
Rannacher, Rolf
1976
Some asymptotic error estimates for finite element approximation of minimal surfaces. Zbl 0356.35034
Rannacher, Rolf
1977
Adaptive finite element methods for optimization problems. Zbl 0954.65048
Becker, R.; Kapp, H.; Rannacher, R.
2000
On the order of pointwise convergence of some boundary element methods. I: Operators of negative and zero order. Zbl 0579.65147
Rannacher, R.; Wendland, W. L.
1985
Indirect multiple shooting for nonlinear parabolic optimal control problems with control constraints. Zbl 1294.49017
Carraro, T.; Geiger, Michael; Rannacher, R.
2014
A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. Zbl 1273.65164
Frei, S.; Rannacher, R.; Wollner, W.
2013
On finite element approximation of general boundary value problems in nonlinear elasticity. Zbl 0468.73091
Rannacher, R.
1980
A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints. Zbl 1356.49052
Rannacher, Rolf; Vexler, Boris; Wollner, Winnifried
2012
Numerical methods in multidimensional radiative transfer. Zbl 1155.65004
Kanschat, Guido (ed.); Meinköhn, Erik (ed.); Rannacher, Rolf (ed.); Wehrse, Rainer (ed.)
2009
The dual-weighted-residual method for error control and mesh adaptation in finite element methods. Zbl 0959.65117
Rannacher, Rolf
2000
Pointwise convergence of some boundary element methods. II. Zbl 0648.65092
Rannacher, Rolf; Wendland, Wolfgang L.
1988
An adaptive finite element method for fluid-structure interaction problems based on a fully Eulerian formulation. Zbl 1214.76005
Rannacher, R.; Richter, T.
2010
A short course on numerical simulation of viscous flow: discretization, optimization and stability analysis. Zbl 1457.65132
Rannacher, Rolf
2012
Computational aspects of pseudospectra in hydrodynamic stability analysis. Zbl 1301.76048
Gerecht, D.; Rannacher, R.; Wollner, W.
2012
An adaptive finite element method for problems in perfect plasticity. Zbl 0944.74074
Rannacher, R.; Suttmeier, F. T.
1999
Fast and reliable solution of the Navier-Stokes equations including chemistry. Zbl 1067.76560
Becker, R.; Braack, M.; Rannacher, R.; Waguet, C.
1999
Adaptive finite element discretization in PDE-based optimization. Zbl 1207.49023
Rannacher, Rolf; Vexler, Boris
2010
Mesh orientation and anisotropic refinement in the streamline diffusion method. Zbl 0812.76047
Zhou, Guohui; Rannacher, Rolf
1994
Towards a complete numerical description of lubricant film dynamics in ball bearings. Zbl 1398.76111
Knauf, Stefan; Frei, Stefan; Richter, Thomas; Rannacher, Rolf
2014
Spatial aspects in the SMAD signaling pathway. Zbl 1277.92007
Claus, J.; Friedmann, E.; Klingmüller, U.; Rannacher, R.; Szekeres, T.
2013
Adaptive FE eigenvalue computation with applications to hydrodynamic stability. Zbl 1374.76103
Rannacher, Rolf
2010
Determination of kinetic parameters in laminar flow reactors. I: Theoretical aspects. Zbl 1398.76227
Carraro, T.; Heuveline, V.; Rannacher, R.
2007
Zur asymptotischen Störungstheorie für Eigenwertaufgaben mit diskreten Teilspektren. Zbl 0295.47019
Rannacher, Rolf
1975
Stable finite element solutions to nonlinear parabolic problems of Navier-Stokes type. Zbl 0505.76049
Rannacher, Rolf
1982
Adaptive finite elements for reactive flows. Zbl 1068.76528
Braack, M.; Becker, R.; Rannacher, R.
1998
Evaluation of a CFD benchmark for laminar flows. Zbl 1075.76641
Schäfer, M.; Rannacher, R.; Turek, S.
1998
A priori error analysis for the finite element approximation of elliptic Dirichlet boundary control problems. Zbl 1157.65405
May, S.; Rannacher, R.; Vexler, B.
2008
Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems. Zbl 1351.65090
Maier, Matthias; Rannacher, Rolf
2016
Indirect multiple shooting for nonlinear parabolic optimal control problems with control constraints. Zbl 1294.49017
Carraro, T.; Geiger, Michael; Rannacher, R.
2014
Towards a complete numerical description of lubricant film dynamics in ball bearings. Zbl 1398.76111
Knauf, Stefan; Frei, Stefan; Richter, Thomas; Rannacher, Rolf
2014
Trends in PDE constrained optimization. Zbl 1306.49001
Leugering, Günter; Benner, Peter; Engell, Sebastian; Griewank, Andreas; Harbrecht, Helmut; Hinze, Michael; Rannacher, Rolf; Ulbrich, Stefan
2014
Error analysis for a finite element approximation of elliptic Dirichlet boundary control problems. Zbl 1273.65087
May, S.; Rannacher, R.; Vexler, B.
2013
Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors. Zbl 1267.65184
Rannacher, R.; Vihharev, J.
2013
Well-posedness of a linear spatio-temporal model of the JAK2/STAT5 signaling pathway. Zbl 1277.35210
Friedmann, E.; Neumann, R.; Rannacher, R.
2013
A priori error estimates for the finite element discretization of optimal distributed control problems governed by the biharmonic operator. Zbl 1273.65164
Frei, S.; Rannacher, R.; Wollner, W.
2013
Spatial aspects in the SMAD signaling pathway. Zbl 1277.92007
Claus, J.; Friedmann, E.; Klingmüller, U.; Rannacher, R.; Szekeres, T.
2013
Model based parameter estimation. Theory and applications. Based on the workshop on parameter estimation, Heidelberg, Germany, 2009. Zbl 1261.65002
Bock, Hans Georg; Carraro, Thomas; Jäger, Willi; Körkel, Stefan; Rannacher, Rolf; Schlöder, Johannes P.
2013
Goal-oriented space-time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow. Zbl 1412.76060
Besier, Michael; Rannacher, Rolf
2012
Constrained optimization and optimal control for partial differential equations. Zbl 1231.49001
Leugering, Günter; Engell, Sebastian; Griewank, Andreas; Hinze, Michael; Rannacher, Rolf; Schulz, Volker; Ulbrich, Michael; Ulbrich, Stefan
2012
A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints. Zbl 1356.49052
Rannacher, Rolf; Vexler, Boris; Wollner, Winnifried
2012
A short course on numerical simulation of viscous flow: discretization, optimization and stability analysis. Zbl 1457.65132
Rannacher, Rolf
2012
Computational aspects of pseudospectra in hydrodynamic stability analysis. Zbl 1301.76048
Gerecht, D.; Rannacher, R.; Wollner, W.
2012
A priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time. Zbl 1234.49029
Meidner, Dominik; Rannacher, Rolf; Vexler, Boris
2011
Adaptive Galerkin finite element methods for the wave equation. Zbl 1283.35053
Bangerth, W.; Geiger, Michael; Rannacher, R.
2010
Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error. Zbl 1222.65123
Rannacher, R.; Westenberger, A.; Wollner, W.
2010
Optimal Neumann control for the two-dimensional steady-state Navier-Stokes equations. Zbl 1200.35214
Fursikov, A. V.; Rannacher, R.
2010
Fundamental trends in fluid-structure interaction. Zbl 1410.76010
Galdi, Giovanni P.; Rannacher, Rolf
2010
An adaptive finite element method for fluid-structure interaction problems based on a fully Eulerian formulation. Zbl 1214.76005
Rannacher, R.; Richter, T.
2010
Adaptive finite element discretization in PDE-based optimization. Zbl 1207.49023
Rannacher, Rolf; Vexler, Boris
2010
Adaptive FE eigenvalue computation with applications to hydrodynamic stability. Zbl 1374.76103
Rannacher, Rolf
2010
Numerical simulation of fluid-structure interaction based on monolithic variational formulations. Zbl 1423.76227
Dunne, Th.; Rannacher, R.; Richter, Th.
2010
Advances in mathematical fluid mechanics. Dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday. Selected papers of the international conference on mathematical fluid mechanics, Estoril, Portugal, May 21–25, 2007. Zbl 1185.76020
Rannacher, Rolf; Sequeira, Adélia
2010
Goal-oriented error control of the iterative solution of finite element equations. Zbl 1169.65340
Meidner, D.; Rannacher, R.; Vihharev, J.
2009
Numerical methods in multidimensional radiative transfer. Zbl 1155.65004
Kanschat, Guido; Meinköhn, Erik; Rannacher, Rolf; Wehrse, Rainer
2009
Hemodynamical flows. Modeling, analysis and simulation. Papers based on the presentations at the Oberwolfach seminar ‘Hemodynamical flows: Aspects of modeling, analysis and simulation’, Oberwolfach, Germany, November 20–26, 2005. Zbl 1137.76005
Galdi, Giovanni P.; Rannacher, Rolf; Robertson, Anne M.; Turek, Stefan
2008
A priori error analysis for the finite element approximation of elliptic Dirichlet boundary control problems. Zbl 1157.65405
May, S.; Rannacher, R.; Vexler, B.
2008
Adaptive finite element methods for PDE-constrained optimal control problems. Zbl 1398.76196
Becker, R.; Braack, M.; Meidner, D.; Rannacher, R.; Vexler, B.
2007
Determination of kinetic parameters in laminar flow reactors. I: Theoretical aspects. Zbl 1398.76227
Carraro, T.; Heuveline, V.; Rannacher, R.
2007
Numerics of fluid-structure interaction. Zbl 1145.76055
Bönisch, Sebastian; Dunne, Thomas; Rannacher, Rolf
2007
Mesh and model adaptivity for flow problems. Zbl 1398.76092
Becker, R.; Braack, M.; Rannacher, R.; Richter, T.
2007
Methods for numerical flow simulation. Zbl 1144.76034
Rannacher, Rolf
2007
A priori error estimates for the finite element discretization of elliptic parameter identification problems with pointwise measurements. Zbl 1113.65102
Rannacher, R.; Vexler, B.
2006
Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation. Zbl 1323.74082
Dunne, Thomas; Rannacher, Rolf
2006
Contributions to current challenges in mathematical fluid mechanics. Zbl 1047.76001
Galdi, Giovanni P.; Heywood, John G.; Rannacher, Rolf
2004
Adaptive finite element methods for differential equations. Zbl 1020.65058
Bangerth, Wolfgang; Rannacher, Rolf
2003
Duality-based adaptivity in the $$hp$$-finite element method. Zbl 1050.65111
Heuveline, V.; Rannacher, R.
2003
Adaptive FEM for eigenvalue problems. Zbl 1043.65122
Heuveline, V.; Rannacher, R.
2003
Trends in nonlinear analysis. On the occasion of the 60th birthday of Willi Jäger. Zbl 1001.00073
Kirkilionis, Markus; Krömker, Susanne; Rannacher, Rolf; Tomi, Friedrich
2003
A numerical tool for flow simulation in a Wankel motor. Zbl 1076.76572
Rannacher, Rolf; Heuveline, Vincent
2003
Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems. Zbl 1022.65123
Kanschat, G.; Rannacher, R.
2002
An optimal control approach to adaptivity in computational fluid mechanics. Zbl 1047.76016
Becker, R.; Heuveline, V.; Rannacher, R.
2002
Adaptive finite element methods for partial differential equations. Zbl 1003.65130
Rannacher, R.
2002
An optimal control approach to a posteriori error estimation in finite element methods. Zbl 1105.65349
Becker, Roland; Rannacher, Rolf
2001
A posteriori error control for finite element approximations of elliptic eigenvalue problems. Zbl 0995.65111
Heuveline, Vincent; Rannacher, Rolf
2001
Adaptive Galerkin finite element methods for partial differential equations. Zbl 0976.65101
Rannacher, R.
2001
Adaptive finite element techniques for the acoustic wave equation. Zbl 1360.76122
Bangerth, Wolfgang; Rannacher, Rolf
2001
Adaptive finite element methods for flow problems. Zbl 1008.76037
Becker, Roland; Braack, Malte; Rannacher, Rolf
2001
Adaptive finite element methods for optimal control of partial differential equations: Basic concept. Zbl 0967.65080
Becker, Roland; Kapp, Hartmut; Rannacher, Rolf
2000
Finite element methods for the incompressible Navier-Stokes equations. Zbl 1107.76353
Rannacher, Rolf
2000
A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115
Houston, Paul; Rannacher, Rolf; Süli, Endre
2000
Adaptive finite element methods for optimization problems. Zbl 0954.65048
Becker, R.; Kapp, H.; Rannacher, R.
2000
The dual-weighted-residual method for error control and mesh adaptation in finite element methods. Zbl 0959.65117
Rannacher, Rolf
2000
Fundamental directions in mathematical fluid mechanics. Zbl 0948.00020
Galdi, Giovanni P.; Heywood, John G.; Rannacher, Rolf
2000
Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. Zbl 0948.65098
Bangerth, W.; Rannacher, R.
1999
A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity. Zbl 0954.74070
Rannacher, Rolf; Suttmeier, Franz-Theo
1999
Numerical simulation of laminar flames at low Mach number by adaptive finite elements. Zbl 0951.76035
Becker, R.; Braack, M.; Rannacher, R.
1999
Error control in finite element computations. An introduction to error estimation and mesh-size adaptation. Zbl 0943.65123
Rannacher, R.
1999
An adaptive finite element method for unsteady convection-dominated flows with stiff source terms. Zbl 0959.76043
Hebeker, Friedrich K.; Rannacher, Rolf
1999
An adaptive finite element method for problems in perfect plasticity. Zbl 0944.74074
Rannacher, R.; Suttmeier, F. T.
1999
Fast and reliable solution of the Navier-Stokes equations including chemistry. Zbl 1067.76560
Becker, R.; Braack, M.; Rannacher, R.; Waguet, C.
1999
A general concept of adaptivity in finite element methods with applications to problems in fluid and structural mechanics. Zbl 0937.65122
Becker, Roland; Rannacher, Rolf
1999
Weighted a posteriori error control in FE methods. Zbl 0968.65083
Becker, R.; Rannacher, R.
1998
A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity. Zbl 0910.73064
Rannacher, R.; Suttmeier, F.-T.
1998
A posteriori error estimation in least-squares stabilized finite element schemes. Zbl 0934.65118
Rannacher, Rolf
1998
Adaptive finite elements for reactive flows. Zbl 1068.76528
Braack, M.; Becker, R.; Rannacher, R.
1998
Evaluation of a CFD benchmark for laminar flows. Zbl 1075.76641
Schäfer, M.; Rannacher, R.; Turek, S.
1998
An adaptive finite element method for unsteady convection-dominated flows with stiff source terms. Zbl 0913.76048
Hebeker, F.-K.; Führer, Ch.; Rannacher, R.
1998
A method for computing compressible, highly stratified flows in astrophysics based on operator splitting. Zbl 0927.76059
Hujeirat, A.; Rannacher, R.
1998
A feed-back approach to error control in finite element methods: Application to linear elasticity. Zbl 0894.73170
Rannacher, R.; Suttmeier, F.-T.
1997
An adaptive streamline-diffusion finite element method for hyperbolic conservation laws. Zbl 0885.65107
Führer, C.; Rannacher, R.
1997
A comparative study of nonlinear Galerkin finite element methods for one-dimensional dissipative evolution problems. Zbl 0909.65065
Nabh, G.; Rannacher, R.
1997
Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Zbl 0863.76016
Heywood, John G.; Rannacher, Rolf; Turek, Stefan
1996
A feed-back approach to error control in finite element methods: Basic analysis and examples. Zbl 0868.65076
Becker, R.; Rannacher, R.
1996
Pointwise superconvergence of the streamline diffusion finite-element method. Zbl 0841.65092
Zhou, Guohui; Rannacher, Rolf
1996
Error analysis for the finite element approximation of a radiative transfer model. Zbl 0866.65093
Führer, Christian; Rannacher, Rolf
1996
Adaptive error control for multigrid finite element methods. Zbl 0848.65074
Becker, R.; Johnson, C.; Rannacher, R.
1995
Numerics and hydrodynamic stability: Toward error control in computational fluid dynamics. Zbl 0833.76063
Johnson, Claes; Rannacher, Rolf; Boman, Mats
1995
Finite element solution of the incompressible Navier-Stokes equations on anisotropically refined meshes. Zbl 0880.76036
Becker, Roland; Rannacher, Rolf
1995
Implicit time-discretization of the nonstationary incompressible Navier-Stokes equations. Zbl 0882.76056
Müller, S.; Prohl, A.; Rannacher, R.; Turek, S.
1995
Parallel solution methods for the Navier-Stokes equations. Zbl 0867.76045
Rannacher, R.
1995
Mesh orientation and anisotropic refinement in the streamline diffusion method. Zbl 0812.76047
Zhou, Guohui; Rannacher, Rolf
1994
On errror control in CFD. Zbl 0874.76037
Johnson, Claes; Rannacher, Rolf
1994
Domain decomposition in the nonstationary streamline diffusion finite element method. Zbl 0813.76047
Rannacher, R.
1994
Mesh adaptation via a predictor-corrector strategy in the streamline diffusion method for nonstationary hyperbolic systems. Zbl 0808.65098
Rannacher, Rolf; Zhou, Guohui
1994
On the question of turbulence modeling by approximate inertial manifolds and the nonlinear Galerkin method. Zbl 0791.76042
Heywood, John G.; Rannacher, Rolf
1993
On the numerical solution of the incompressible Navier-Stokes equations. Zbl 0798.76069
Rannacher, R.
1993
Numerical analysis of the Navier-Stokes equations. Zbl 0798.76041
Rannacher, Rolf
1993
Local error expansions and Richardson extrapolation for the streamline diffusion finite element method. Zbl 0835.65122
Chen, H.; Rannacher, R.
1993
Simple nonconforming quadrilateral Stokes element. Zbl 0742.76051
Rannacher, R.; Turek, S.
1992
On Chorin’s projection method for the incompressible Navier-Stokes equations. Zbl 0769.76053
Rannacher, Rolf
1992
A domain splitting algorithm for parabolic problems. Zbl 0767.65073
Blum, H.; Lisky, S.; Rannacher, R.
1992
$$L^ \infty$$-stability estimates and asymptotic error expansion for parabolic finite element equations. Zbl 0748.65072
Rannacher, Rolf
1991
Defect correction techniques in the finite element method. Zbl 0784.65081
Rannacher, R.
1991
Finite-element approximation of the nonstationary Navier-Stokes problem. IV: Error analysis for second-order time discretization. Zbl 0694.76014
Heywood, John G.; Rannacher, Rolf
1990
Finite element eigenvalue computation on domains with reentrant corners using Richardson extrapolation. Zbl 0719.65077
Blum, H.; Rannacher, R.
1990
On mixed finite element methods in plate bending analysis. I: The first Herrmann scheme. Zbl 0736.73061
Blum, H.; Rannacher, R.
1990
On the numerical analysis of the nonstationary Navier-Stokes equations. Zbl 0850.76528
Rannacher, Rolf
1990
...and 29 more Documents
all top 5
#### Cited by 3,038 Authors
85 He, Yinnian 48 Shi, Dongyang 42 Rannacher, Rolf 32 Feng, Xinlong 29 Rebholz, Leo G. 28 Vexler, Boris 24 Yang, Yidu 22 Carstensen, Carsten 22 Li, Jian 21 Shang, Yueqiang 20 Chen, Zhangxin 20 Hou, Yanren 20 Novo, Julia 19 An, Rong 19 John, Volker 19 Wick, Thomas 19 Yan, Ningning 18 Chen, Yanping 18 Houston, Paul 18 Huang, Pengzhan 18 Li, Buyang 18 Lin, Qun 18 Tavener, Simon J. 17 Brenner, Susanne Cecelia 17 Li, Kaitai 17 Sheen, Dongwoo 17 Turek, Stefan 16 Becker, Roland 16 Estep, Donald J. 16 Gong, Wei 16 Nochetto, Ricardo Horacio 16 Wollner, Winnifried 16 Xie, Hehu 15 Codina, Ramon 15 Hu, Jun 15 Shi, Zhongci 15 Vohralík, Martin 15 Wang, Kun 14 Bi, Hai 14 de Frutos, Javier 14 García-Archilla, Bosco 14 Huang, Yunqing 14 Ladevèze, Pierre 14 Leykekhman, Dmitriy 13 Chamoin, Ludovic 13 Latché, Jean-Claude 13 Mao, Shipeng 12 Larson, Mats G. 12 Layton, William J. 12 Nicaise, Serge 12 Oden, John Tinsley 12 Prudhomme, Serge 12 Schieweck, Friedhelm 12 Shen, Jie 11 Apel, Thomas 11 Bause, Markus 11 Beneš, Michal 11 Braack, Malte 11 Guillén González, Francisco M. 11 Han, Jiayu 11 Hansbo, Peter 11 Larsson, Fredrik 11 Li, Yuan 11 Lin, Yanping 11 Nataraj, Neela 11 Patera, Anthony T. 11 Stenberg, Rolf 11 Veneziani, Alessandro 11 Zhang, Zhimin 11 Zhou, Aihui 10 Burman, Erik 10 Chaudhry, Jehanzeb Hameed 10 Guan, Hongbo 10 Herbin, Raphaèle 10 Heuveline, Vincent 10 Hinze, Michael 10 Hoffman, Johan 10 Hoppe, Ronald H. W. 10 Liu, Steve Wenbin 10 Mateos, Mariano 10 Olshanskii, Maxim A. 10 Picasso, Marco 10 Quarteroni, Alfio M. 10 Repin, Sergeĭ Igorevich 10 Rojas-Medar, Marko Antonio 10 Salgado, Abner J. 10 Süli, Endre E. 10 Yang, Danping 9 Chen, Jinru 9 Darmofal, David L. 9 Díez, Pedro 9 Fidkowski, Krzysztof J. 9 Giani, Stefano 9 Guermond, Jean-Luc 9 Hron, Jaroslav 9 Luo, Zhendong 9 Manica, Carolina Cardoso 9 Neitzel, Ira 9 Prohl, Andreas 9 Richter, Thomas ...and 2,938 more Authors
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#### Cited in 241 Serials
288 Computer Methods in Applied Mechanics and Engineering 138 Journal of Computational Physics 137 Journal of Computational and Applied Mathematics 128 Numerische Mathematik 127 Journal of Scientific Computing 121 Applied Numerical Mathematics 117 Computers & Mathematics with Applications 117 Mathematics of Computation 92 Applied Mathematics and Computation 89 Numerical Methods for Partial Differential Equations 59 SIAM Journal on Numerical Analysis 52 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 48 SIAM Journal on Scientific Computing 45 International Journal for Numerical Methods in Engineering 41 Computers and Fluids 39 Advances in Computational Mathematics 33 International Journal for Numerical Methods in Fluids 33 Computational Mechanics 31 Journal of Mathematical Analysis and Applications 27 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 27 International Journal of Computer Mathematics 25 Numerical Functional Analysis and Optimization 25 Numerical Algorithms 24 Applications of Mathematics 22 Applied Mathematical Modelling 22 Computational Optimization and Applications 21 Journal of Numerical Mathematics 21 Science China. Mathematics 18 BIT 16 SIAM Journal on Control and Optimization 15 Mathematical Methods in the Applied Sciences 15 Calcolo 15 RAIRO. Modélisation Mathématique et Analyse Numérique 15 Mathematical Problems in Engineering 14 Computing 14 Acta Mathematicae Applicatae Sinica. English Series 14 Journal of Mathematical Fluid Mechanics 14 Computational Methods in Applied Mathematics 12 Applicable Analysis 12 Communications in Numerical Methods in Engineering 12 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 10 Mathematics and Computers in Simulation 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Applied Mathematics Letters 9 Acta Applicandae Mathematicae 9 Optimization Methods & Software 9 Computational Geosciences 9 Archives of Computational Methods in Engineering 9 Discrete and Continuous Dynamical Systems. Series B 8 Mathematical and Computer Modelling 8 Computing and Visualization in Science 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 RAIRO. Analyse Numérique 7 Physics of Fluids 7 Journal of Mathematical Sciences (New York) 7 Computational and Applied Mathematics 7 Engineering Computations 6 Journal of Fluid Mechanics 6 Journal of Differential Equations 6 Chinese Annals of Mathematics. Series B 6 Science in China. Series A 6 Japan Journal of Industrial and Applied Mathematics 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Vietnam Journal of Mathematics 6 Combustion Theory and Modelling 6 SIAM/ASA Journal on Uncertainty Quantification 6 Nonlinear Analysis. Theory, Methods & Applications 5 Archive for Rational Mechanics and Analysis 5 Journal of Soviet Mathematics 5 Applied Mathematics and Mechanics. (English Edition) 5 Applied Mathematical Finance 5 Abstract and Applied Analysis 5 Lobachevskii Journal of Mathematics 5 Nonlinear Analysis. Real World Applications 5 Journal of Systems Science and Complexity 5 Journal of Applied Mathematics and Computing 5 Boundary Value Problems 5 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 5 Frontiers of Mathematics in China 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Journal of Optimization Theory and Applications 4 Mathematische Zeitschrift 4 Journal of Integral Equations and Applications 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 ETNA. Electronic Transactions on Numerical Analysis 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 European Journal of Mechanics. B. Fluids 4 Mathematical Modelling and Analysis 4 Journal of Applied Mathematics 4 Multiscale Modeling & Simulation 4 International Journal of Numerical Analysis and Modeling 4 Inverse Problems in Science and Engineering 4 GAMM-Mitteilungen 4 Advances in Numerical Analysis 4 International Journal for Numerical Methods in Biomedical Engineering 4 S$$\vec{\text{e}}$$MA Journal 4 AMM. Applied Mathematics and Mechanics. (English Edition) 3 International Journal of Engineering Science 3 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) ...and 141 more Serials
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#### Cited in 42 Fields
2,096 Numerical analysis (65-XX) 1,158 Partial differential equations (35-XX) 1,117 Fluid mechanics (76-XX) 382 Mechanics of deformable solids (74-XX) 279 Calculus of variations and optimal control; optimization (49-XX) 76 Biology and other natural sciences (92-XX) 59 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 55 Classical thermodynamics, heat transfer (80-XX) 44 Optics, electromagnetic theory (78-XX) 43 Ordinary differential equations (34-XX) 39 Statistical mechanics, structure of matter (82-XX) 37 Systems theory; control (93-XX) 36 Integral equations (45-XX) 34 Geophysics (86-XX) 32 Probability theory and stochastic processes (60-XX) 26 Operations research, mathematical programming (90-XX) 24 Operator theory (47-XX) 23 Dynamical systems and ergodic theory (37-XX) 21 Potential theory (31-XX) 13 Approximations and expansions (41-XX) 13 Statistics (62-XX) 12 Functional analysis (46-XX) 9 Computer science (68-XX) 8 Real functions (26-XX) 8 Mechanics of particles and systems (70-XX) 8 Information and communication theory, circuits (94-XX) 7 Astronomy and astrophysics (85-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Quantum theory (81-XX) 4 History and biography (01-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-09-26T16:34:42 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S029AXI
|
# Search for Relic Invisible Axions INSPIRE search
Limits are for [$\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}]{}^{2}\rho _{\mathit A}$ where $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ denotes the axion two-photon coupling, $\mathit L_{{\mathrm {int}}}$ = $−$ ${\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\over 4}{{\mathit \phi}_{{A}}}{{\mathit F}}_{ {{\mathit \mu}} {{\mathit \nu}} }{{\widetilde{\mathit F}}}{}^{ {{\mathit \mu}} {{\mathit \nu}} }$ = $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\phi _{\mathit A}\mathbf {E}\cdot{}\mathbf {B}$, and $\rho _{\mathit A}$ is the axion energy density near the earth.
VALUE CL% DOCUMENT ID TECN COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
1
2017
AURG ${\mathit m}_{{{\mathit S}^{0}}}$ = $3.5 - 3.9$ peV
$<3 \times 10^{-42}$ 90 2
2017
${\mathit m}_{{{\mathit A}^{0}}}$ = $23.55 - 24.0$ $\mu$eV
$<1.0 \times 10^{-29}$ 95 3
2017
${\mathit m}_{{{\mathit A}^{0}}}$ = $24.7 - 29.1$ $\mu$eV
$<8.6 \times 10^{-42}$ 90 4
2016
ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ =$3.36 - 3.52$ or $3.55 - 3.69$ $\mu$eV
5
2013
${\mathit m}_{{{\mathit A}^{0}}}$ = 0.11 meV
$<3.5 \times 10^{-43}$ 6
2011
ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.3 - 3.69 \times 10^{-6}$ eV
$<2.9 \times 10^{-43}$ 90 7
2010
ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.34 - 3.53$ eV
$<1.9 \times 10^{-43}$ 98 8
2006
ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.98 - 2.17$ eV
$<5.5 \times 10^{-43}$ 90 9
2004
ADMX ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.9 - 3.3$ eV
10
1998
THEO
$<2 \times 10^{-41}$ 11
1990
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($5.4 - 5.9){}10^{-6}$ eV
$<6.3 \times 10^{-42}$ 95 12
1989
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($4.5 - 10.2){}10^{-6}$ eV
$<5.4 \times 10^{-41}$ 95 12
1989
CNTR ${\mathit m}_{{{\mathit A}^{0}}}$ = ($11.3 - 16.3){}10^{-6}$ eV
1 BRANCA 2017 look for modulations of the fine-structure constant and the electron mass due to moduli dark matter by using the cryogenic resonant-mass AURIGA detector. The limit on the assumed dilatonic coupling implies $\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $1.5 \times 10^{-24}$ GeV${}^{-1}$ for the scalar to two-photon coupling. See Fig. 5 for the mass-dependent limits.
2 BRUBAKER 2017 used a microwave cavity detector at the Yale Wright Laboratory to search for dark matter axions. See Fig. 3 for the mass-dependent limits.
3 CHOI 2017 used a microwave cavity detector with toroidal geometry. See Fig. 4 for their mass-dependent limits.
4 HOSKINS 2016 is analogous to DUFFY 2006 . See Fig.$~$12 for mass-dependent limits in terms of the local dark matter density.
5 BECK 2013 argues that dark-matter axions passing through Earth may generate a small observable signal in resonant S/N/S Josephson junctions. A measurement by HOFFMANN 2004 [Physical Review B70 180503 (2004)] is interpreted in terms of subdominant dark matter axions with ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.11 meV.
6 HOSKINS 2011 is analogous to DUFFY 2006 . See Fig.$~$4 for the mass-dependent limit in terms of the local density.
7 ASZTALOS 2010 used the upgraded detector of ASZTALOS 2004 to search for halo axions. See their Fig.$~$5 for the ${\mathit m}_{{{\mathit A}^{0}}}$ dependence of the limit.
8 DUFFY 2006 used the upgraded detector of ASZTALOS 2004 , while assuming a smaller velocity dispersion than the isothermal model as in Eq. (8) of their paper. See Fig. 10 of their paper on the axion mass dependence of the limit.
9 ASZTALOS 2004 looked for a conversion of halo axions to microwave photons in magnetic field. At 90$\%$ CL, the KSVZ axion cannot have a local halo density more than 0.45~GeV/cm${}^{3}$ in the quoted mass range. See Fig.~7 of their paper on the axion mass dependence of the limit.
10 KIM 1998 calculated the axion-to-photon couplings for various axion models and compared them to the HAGMANN 1990 bounds. This analysis demonstrates a strong model dependence of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ and hence the bound from relic axion search.
11 HAGMANN 1990 experiment is based on the proposal of SIKIVIE 1983 .
12 WUENSCH 1989 looks for condensed axions near the earth that could be converted to photons in the presence of an intense electromagnetic field via the Primakoff effect, following the proposal of SIKIVIE 1983 . The theoretical prediction with [$\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}]{}^{2}$ = $2 \times 10^{-14}$ MeV${}^{-4}$ (the three generation DFSZ model) and $\rho _{\mathit A}$ = 300 MeV/cm${}^{3}$ that makes up galactic halos gives ($\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }/{\mathit m}_{{{\mathit A}^{0}}}){}^{2}$ $\rho _{\mathit A}$ = $4 \times 10^{-44}$. Note that our definition of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ is (1/4$\pi$) smaller than that of WUENSCH 1989 .
References:
BRANCA 2017
PRL 118 021302 Search for Light Scalar Dark Matter Candidate with AURIGA Detector
BRUBAKER 2017
PRL 118 061302 First Results from a Microwave Cavity Axion Search at 24 Micro-eV
CHOI 2017
PR D96 061102 First Axion Dark Matter Search with Toroidal Geometry
HOSKINS 2016
PR D94 082001 Modulation Sensitive Search for Nonvirialized Dark-Matter Axions
BECK 2013
PRL 111 231801 Possible Resonance Effect of Axionic Dark Matter in Josephson Junctions
HOSKINS 2011
PR D84 121302 Search for Nonvirialized Axionic Dark Matter
ASZTALOS 2010
PRL 104 041301 A SQUID-Based Microwave Cavity Search for Dark-Matter Axions
DUFFY 2006
PR D74 012006 High Resolution Search for Dark-Matter Axions
ASZTALOS 2004
PR D69 011101 An Improved RF Cavity Search for Halo Axions
KIM 1998
PR D58 055006 Constraints on Very Light Axions from Cavity Experiments
HAGMANN 1990
PR D42 1297 Results from a Search for Cosmic Axions
WUENSCH 1989
PR D40 3153 Results of a Laboratory Search for Cosmic Axions and Other Weakly-Coupled Light Particles
HOFFMANN 2004
PR B70 180503 Mesoscopic Transition in the Shot Noise of Diffusive S/N/S Junctions
SIKIVIE 1983
PRL 51 1415 Experimental Tests of the Invisible'' Axion
| 2018-09-21T20:02:02 |
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|
https://par.nsf.gov/biblio/10340273-sami-galaxy-survey-mass-environment-independent-drivers-galaxy-dynamics
|
The SAMI galaxy survey: Mass and environment as independent drivers of galaxy dynamics
ABSTRACT The kinematic morphology–density relation of galaxies is normally attributed to a changing distribution of galaxy stellar masses with the local environment. However, earlier studies were largely focused on slow rotators; the dynamical properties of the overall population in relation to environment have received less attention. We use the SAMI Galaxy Survey to investigate the dynamical properties of ∼1800 early and late-type galaxies with log (M⋆/M⊙) > 9.5 as a function of mean environmental overdensity (Σ5) and their rank within a group or cluster. By classifying galaxies into fast and slow rotators, at fixed stellar mass above log (M⋆/M⊙) > 10.5, we detect a higher fraction (∼3.4σ) of slow rotators for group and cluster centrals and satellites as compared to isolated-central galaxies. We find similar results when using Σ5 as a tracer for environment. Focusing on the fast-rotator population, we also detect a significant correlation between galaxy kinematics and their stellar mass as well as the environment they are in. Specifically, by using inclination-corrected or intrinsic $\lambda _{R_{\rm {e}}}$ values, we find that, at fixed mass, satellite galaxies on average have the lowest $\lambda _{\, R_{\rm {e}},\rm {intr}}$, isolated-central galaxies have the highest $\lambda _{\, R_{\rm {e}},\rm {intr}}$, and group and cluster more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10340273
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
508
Issue:
2
Page Range or eLocation-ID:
2307 to 2328
ISSN:
0035-8711
National Science Foundation
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Satellite galaxies in the cluster environment are more likely to be quenched than galaxies in the general field. Recently, it has been reported that satellite galaxy quenching depends on the orientation relative to their central galaxies: satellites along the major axis of centrals are more likely to be quenched than those along the minor axis. In this paper, we report a detection of such anisotropic quenching up to z ∼ 1 based on a large optically selected cluster catalogue constructed from the Hyper Suprime-Cam Subaru Strategic Program. We calculate the quiescent satellite galaxy fraction as a function of orientation angle measured from the major axis of central galaxies and find that the quiescent fractions at 0.25 < z < 1 are reasonably fitted by sinusoidal functions with amplitudes of a few per cent. Anisotropy is clearer in inner regions (<r200m) of clusters and not significant in cluster outskirts (>r200m). We also confirm that the observed anisotropy cannot be explained by differences in local galaxy density or stellar mass distribution along the two axes. Quiescent fraction excesses between the two axes suggest that the quenching efficiency contributing to the anisotropy is almost independent of stellar mass, at least down to our stellarmore »
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| 2023-03-22T13:12:29 |
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https://e-magnetica.pl/file/wireless_charging_coils_tdk_e-m_jpg
|
# Encyclopedia Magnetica
### Site Tools
file:wireless_charging_coils_tdk_e-m_jpg
Planar coils (top and bottom sides) for wireless charging, for low power application such as mobile phone.
The rectangular backing has dimensions 38 x 32 x 1 mm. The black backing is 0.5 mm thick (it is deposited on the white layer of a thin substrate) and is partially filled with magnetic particles to increase magnetic coupling. The coil is wound with a double 0.25 mm thick wire, wound in a bifilar way, but shorted together at the terminals. There are 17 effective turns. The weight of the assembly is around 4.2 g. Inductance at 100 kHz = 11.1 μH, DC resistance = 0.25 Ω.
Some of the data was available from the Digikey distributor, datasheet for TDK17M2-G: https://media.digikey.com/pdf/Data%20Sheets/TDK%20PDFs/WR-383250-17M2-G.pdf {accessed 2021-06-11}
wireless_charging_coils_tdk_e-m.jpg
You are permitted and indeed encouraged to use this image freely, for any legal purpose including commercial, and with any modifications (the permission is hereby given, so there is no need to ask for it explicitly again), but you MUST always give the following credits:
S. Zurek, Encyclopedia Magnetica, CC-BY-4.0
We would appreciate if you let us know of any use: [email protected]
| 2021-12-05T07:09:55 |
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https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Book%3A_Conceptual_Physics_(Crowell)/08%3A_Relativity/8.03%3A_Dynamics
|
Skip to main content
$$\require{cancel}$$
# 8.3: Dynamics
So far we have said nothing about how to predict motion in relativity. Do Newton's laws still work? Do conservation laws still apply? The answer is yes, but many of the definitions need to be modified, and certain entirely new phenomena occur, such as the equivalence of energy and mass, as described by the famous equation $$E=mc^2$$.
## Contributors and Attributions
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
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| 2021-07-28T16:51:03 |
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https://indico.bnl.gov/event/1800/contributions/3504/
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# 11th international workshop on High-pT Physics in the RHIC & LHC Era
12-15 April 2016
BNL Physics Building
US/Eastern timezone
## $J/\psi$ and $\Upsilon$ measurements via di-lepton decay channels with the STAR experiment
12 Apr 2016, 12:05
30m
Large Seminar Room (BNL Physics Building)
### Speaker
Prof. Rosi Reed (Lehigh University)
### Description
Suppression of quarkonia in heavy-ion collisions due to the Debye screening of the potential between the heavy quarks was one of the first hypothesized signatures of the Quark Gluon Plasma (QGP). However, other effects besides Debye screening, such as the statistical recombination of heavy quark anti-quark pairs, or co-mover absorption, can also affect quarkonium production in heavy-ion collisions. The STAR experiment has made many successful measurements of the $J/\psi$ and $\Upsilon$ families via the di-electron channel in p+p, d+Au, Au+Au and U+U collisions, which provide constraints for models of quarkonium production in these various systems. These constraints are necessary to fully understand the influence of the different physics processes on the quarkonium yields. The Muon Telescope Detector (MTD), designed to both trigger on and identify muons based on precise timing information, was fully installed in STAR in 2014. This allows quarkonia measurements via the di-muon channel. In particular, it allows a potential separation of the different $\Upsilon$ states, as muons are much less affected by bremsstrahlung than electrons. In this talk, we present an overview of the measurements of $J/\psi$ and $\Upsilon$ mesons measured by the STAR experiment in both di-electron and di-muon channels. We will highlight the recent measurements of $J/\psi$ suppression and elliptic flow at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV down to low transverse momenta. Additionally we will show an outlook towards measuring the $\Upsilon$ in the di-muon channel. We will also present measurements of $\Upsilon$ suppression from both Au+Au and U+U collisions.
### Primary author
Prof. Rosi Reed (Lehigh University)
Slides
| 2020-11-29T17:14:15 |
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https://pub.uni-bielefeld.de/record/2941883
|
On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe
Rehmeier M (2021)
Stochastics and Partial Differential Equations: Analysis and Computations 9: 33-70.
Zeitschriftenaufsatz | Veröffentlicht | Englisch
483.19 KB
Autor*in
Einrichtung
Abstract / Bemerkung
We prove that joint uniqueness in law and the existence of a strong solution imply pathwise uniqueness for variational solutions to stochastic partial differential equations of type dXt = b(t, X)dt + s(t, X)dWt, t = 0, and show that for such equations uniqueness in law is equivalent to joint uniqueness in law for deterministic initial conditions. Here W is a cylindrical Wiener process in a separable Hilbert space U and the equation is considered in a Gelfand triple V. H. E, where H is some separable (infinite-dimensional) Hilbert space. This generalizes the corresponding results of Cherny, who proved these statements for the case of finite-dimensional equations.
Stichworte
Stochastic partial differential equations; Yamada-Watanabe theorem; Pathwise uniqueness; Uniqueness in law; Joint uniqueness in law; Variational solutions
Erscheinungsjahr
2021
Zeitschriftentitel
Stochastics and Partial Differential Equations: Analysis and Computations
Band
9
Seite(n)
33-70
Urheberrecht / Lizenzen
ISSN
2194-0401
eISSN
2194-041X
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2941883
Zitieren
Rehmeier M. On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations . 2021;9:33-70.
Rehmeier, M. (2021). On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations , 9, 33-70. https://doi.org/10.1007/s40072-020-00167-6
Rehmeier, Marco. 2021. “On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe”. Stochastics and Partial Differential Equations: Analysis and Computations 9: 33-70.
Rehmeier, M. (2021). On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations 9, 33-70.
Rehmeier, M., 2021. On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations , 9, p 33-70.
M. Rehmeier, “On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe”, Stochastics and Partial Differential Equations: Analysis and Computations , vol. 9, 2021, pp. 33-70.
Rehmeier, M.: On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe. Stochastics and Partial Differential Equations: Analysis and Computations . 9, 33-70 (2021).
Rehmeier, Marco. “On Cherny's results in infinite dimensions: a theorem dual to Yamada-Watanabe”. Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021): 33-70.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0):
Volltext(e)
Name
Access Level
Open Access
| 2023-01-31T08:06:30 |
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https://www.legisquebec.gouv.qc.ca/en/version/cr/Q-2,%20r.%2035.5?code=se:22&history=20220809
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### Q-2, r. 35.5 - Regulation respecting landfill methane reclamation and destruction projects eligible for the issuance of offset credits
22. For the purposes of the quantification of the GHG emission reductions attributable to a project, the promoter must calculate the GHG emissions in the project scenario attributable to fossil fuel consumption using Equation 9:
Equation 9
Where:
PE = GHG emissions in the project scenario attributable to fossil fuel consumption, in metric tonnes CO2 equivalent;
f = Type of fossil fuel;
n = Number of types of fossil fuel;
FFf = Total quantity of fossil fuel f consumed, expressed
— in kilograms, in the case of fuels whose quantity is expressed as a mass;
— in cubic metres at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in litres, in the case of fuels whose quantity is expressed as a volume of liquid;
EFCO2,f = CO2 emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere (chapter Q-2, r. 15), expressed
— in kilograms of CO2 per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in kilograms of CO2 per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in kilograms of CO2 per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
10-3 = Conversion factor, kilograms to metric tonnes;
EFCH4,f = CH4 emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere, expressed
— in grams of CH4 per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in grams of CH4 per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in grams of CH4 per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
GWPCH4 = Global warming potential of CH4 taken from Schedule A.1 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere;
10-6 = Conversion factor, grams to metric tonnes;
EFN2O,f = N2O emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere, expressed
— in grams of N2O per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in grams of N2O per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in grams of N2O per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
GWPN2O = Global warming potential of N2O taken from Schedule A.1 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere.
M.O. 2021-06-11, s. 22.
In force: 2021-07-15
22. For the purposes of the quantification of the GHG emission reductions attributable to a project, the promoter must calculate the GHG emissions in the project scenario attributable to fossil fuel consumption using Equation 9:
Equation 9
Where:
PE = GHG emissions in the project scenario attributable to fossil fuel consumption, in metric tonnes CO2 equivalent;
f = Type of fossil fuel;
n = Number of types of fossil fuel;
FFf = Total quantity of fossil fuel f consumed, expressed
— in kilograms, in the case of fuels whose quantity is expressed as a mass;
— in cubic metres at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in litres, in the case of fuels whose quantity is expressed as a volume of liquid;
EFCO2,f = CO2 emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere (chapter Q-2, r. 15), expressed
— in kilograms of CO2 per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in kilograms of CO2 per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in kilograms of CO2 per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
10-3 = Conversion factor, kilograms to metric tonnes;
EFCH4,f = CH4 emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere, expressed
— in grams of CH4 per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in grams of CH4 per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in grams of CH4 per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
GWPCH4 = Global warming potential of CH4 taken from Schedule A.1 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere;
10-6 = Conversion factor, grams to metric tonnes;
EFN2O,f = N2O emission factor for fossil fuel f specified in Tables 1-3 to 1-8 of QC.1.7 in Schedule A.2 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere, expressed
— in grams of N2O per kilogram, in the case of fuels whose quantity is expressed as a mass;
— in grams of N2O per cubic metre at standard conditions, in the case of fuels whose quantity is expressed as a volume of gas;
— in grams of N2O per litre, in the case of fuels whose quantity is expressed as a volume of liquid;
GWPN2O = Global warming potential of N2O taken from Schedule A.1 to the Regulation respecting mandatory reporting of certain emissions of contaminants into the atmosphere.
M.O. 2021-06-11, s. 22.
| 2022-10-05T22:16:30 |
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|
https://itl.nist.gov/div898/software/dataplot/refman1/auxillar/tolelimi.htm
|
Dataplot Vol 1 Vol 2
TOLERANCE LIMITS
Name:
TOLERANCE LIMITS
Type:
Analysis Command
Purpose:
Generates normal and non-parameteric tolerance intervals.
Description:
Tolerance intervals calculate a confidence interval that contains a fixed percentage (or proportion) of the data. This is related to, but distinct from, the confidence interval for the mean.
There are two numbers for the tolerance interval:
1. The coverage probability is the fixed percentage of the data to be covered.
2. The confidence level.
Tolerance limits are given by
$$\bar{X} \pm ks$$
with $$\bar{X}$$ and s denoting the sample mean and the sample standard deviation, respectively, and where k is determined so that one can state with (1-$$\alpha$$)% confidence that at least $$\phi$$% of the data fall within the given limits. The values for k, assuming a normal distribution, have been numerically tabulated.
This is commonly stated as something like "a 95% confidence interval for 90% coverage".
Dataplot computes the tolerance interval for three confidence levels (90%, 95%, and 99%) and five coverage percentages (50.0, 75.0, 90.0, 95.0, 99.9).
In addition, Dataplot computes non-parametric tolerance intervals. These may be preferred if the data are not adequately approximated by a normal distribution. In this case, the tables have been developed based on the smallest and largest data values in the sample.
Syntax 1:
TOLERANCE LIMITS <y> <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax generates both the normal and the non-parametric tolerance limits.
Syntax 2:
<NORMAL/LOGNORMAL/BOXCOX> TOLERANCE LIMITS <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax generates only the normal tolerance limits.
If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal tolerance limits will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal tolerance limits.
Similarly, if the keyword BOXCOX is present, a Box-Cox transformation to normality will be applied to the data before computing the normal tolerance limits. The computed lower and upper limits will then be transformed back to the original scale.
Syntax 3:
NONPARAMETRIC TOLERANCE LIMITS <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable,
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax generates only the non-parametric tolerance limits.
Examples:
TOLERANCE LIMITS Y1
TOLERANCE LIMITS Y1 SUBSET TAG > 2
NORMAL TOLERANCE LIMITS Y1 SUBSET TAG > 2
NONPARAMETRIC TOLERANCE LIMITS Y1 SUBSET TAG > 2
Note:
Two-sided tolerance limits are used when symmetric coverage intervals from the mean are desired.
In reliability and lifetime applications, one-sided tolerance limits are more common. In these cases, we typically want coverage intervals that are greater than a given value (lower tolerance intervals) or smaller than a given value (upper tolerance intervals). These tolerance intervals are equivalent to one-sided confidence limits for percentiles of the specified distribution.
Dataplot can compute one-sided (or two-sided) confidence limits for percentiles for a number of distributions commonly used in reliability applications. For example, to compute lower one-sided tolerance limits for the 2-parameter Weibull distribution, you can do the following
set maximum likelihood percentiles default
set distributional percentile lower
weibull maximum likelihood y
set maximum likelihood percentiles default
set bootstrap distributional percentile lower
bootstrap weibull maximum likelihood plot y
Note:
The following statistics are also supported:
LET A = NORMAL TOLERANCE K FACTOR Y
LET A = NORMAL TOLERANCE ONE SIDED K FACTOR Y
LET A = NORMAL TOLERANCE LOWER LIMIT Y
LET A = NORMAL TOLERANCE UPPER LIMIT Y
LET A = NORMAL TOLERANCE ONE SIDED LOWER LIMIT Y
LET A = NORMAL TOLERANCE ONE SIDED UPPER LIMIT Y
The above commands are for the raw data case (i.e., a a single response variable).
LET A = SUMMARY NORMAL TOLERANCE K FACTOR MEAN SD N
LET A = SUMMARY NORMAL TOLERANCE ONE SIDED K FACTOR MEAN SD N
LET A = SUMMARY NORMAL TOLERANCE LOWER LIMIT MEAN SD N
LET A = SUMMARY NORMAL TOLERANCE UPPER LIMIT MEAN SD N
LET A = SUMMARY NORMAL TOLERANCE ONE SIDED LOWER LIMIT ...
MEAN SD N
LET A = SUMMARY NORMAL TOLERANCE ONE SIDED UPPER LIMIT ...
MEAN SD N
The above commands are for the summary data case. The three arguments can be either parameters or variables. If a variable rather than a parameter is given, the first element of the variable is extracted. The three values denote the mean, standard deviation, and sample size of the original data.
To specify the coverage and confidence, enter the commands
LET ALPHA = <value>
LET GAMMA = <value>
where ALPHA specifies the confidence level and GAMMA specifies the coverage level. The defaults values are 0.95 for both the confidence and the coverage.
In addition to the above LET command, built-in statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).
Note:
A number of approaches have been proposed for computing the k factor for tolerance limits.
For two-sided intervals, the Wald-Wolfowitz method provides the basic approach. However, this method is computationally expensive. Weisberg and Beatty (1960) published tables based on this method. Gardiner and Hull (1966) proposed an approximation that replaced an integration with algebraic formulas. Howe (1969) proposed a simpler approximation for the tolerance limits that is considered to be more accurate than the Weisberg and Beatty method. Guenther (1977) proposed a correction term for Howe's method.
Howe's approximation is
$$k_2 = z_{(1+\gamma)/2} \sqrt{\frac{\nu \left(1 + \frac{1}{N}\right) }{\chi^2_{1-\alpha,\nu}}}$$
where
$$z$$ = the normal percent point function $$\gamma$$ = the coverage factor $$\alpha$$ = the confidence factor $$\chi^2$$ = the chi-square percent point function $$\nu$$ = the degrees of freedom
The degrees of freedom parameter is N - 1 by default. However, if the standard deviation is based on historical data rather than the current data set, then an independent value for the degrees of freedom may be given. In Dataplot, you can specify the degrees of freedom by entering the command
SET TOLERANCE LIMITS DEGREES OF FREEDOM <value>
If this command is not given, N - 1 will be used.
The Guenther correction is
$$k_2^{*} = wk_2$$
where
$$w = \sqrt{ 1 + \frac{N -3 - \chi^2_{N-1,1 - \alpha} } {2(N+1)^2}}$$
The details for the Gardinar method can be found in the Gardiner paper.
Dataplot supports both the Gardiner method and the Howe method. The default for the 2018/05 version is the Howe method. Prior versions use the Gardiner method.
To specify the method in Dataplot, enter the command
SET TOLERANCE LIMIT METHOD <HOWE/GARDINER>
BEATTY and WALD AND WOLFOWITZ can be used as synonyms for GARDINER.
To specify whether the Guenther correction will be applied to Howe's method, enter the command
SET GUENTHER CORRECTION <ON/OFF>
The default is OFF.
Dataplot supports two methods for one-sided intervals.
The first method uses the formula
$$k_1 = \frac{ t_{\alpha, \, N-1, \, \delta} }{ \sqrt{N} }$$
where t is the non-central t distribution with non-centrality parameter
$$\delta = z_{\gamma} \sqrt{N}$$
The non-central t distribution can lose accuracy as N gets large. The second method only uses the percent point function for the normal distribution and has the formula
$$k_1 = \frac{ z_{\gamma} + \sqrt{z_{\gamma}^2 - ab}} {a}$$
where
$$a = 1 - \frac{z_{\alpha}^2}{2(N-1)}$$
$$b = z_{\gamma}^2 - \frac{ z_{\alpha}^2}{N}$$
To specify the one-sided method, enter
SET TOLERANCE LIMIT ONE SIDED METHOD ...
<NONCENTRAL T/NORMAL/DEFAULT>
The default is to use the non-central t based approximation for N ≤ 100 and to use the normal based approximation for N > 100.
Default:
None
Synonyms:
None
Related Commands:
CONFIDENCE LIMITS = Generate the confidence limits for the mean. PREDICTION LIMITS = Generate prediction limits for the mean. MAXIMUM LIKELIHOOD = Generate maximum likelihood estimates for a distributional fit. T-TEST = Perform a t-test.
Reference:
Wilks (1941), "Determination of Sample Sizes for Setting Tolerance Limits", Annals of Mathematical Statistics, Vol. 12, No. 1, pp. 91-96.
Weisberg and Beatty (1960), "Tables of Tolerance-Limit Factors for Normal Distributions", Technometrics, Vol. 2, pp. 483-500.
Gardiner and Hull (1966), "An Approximation to Two-Sided Tolerance Limits for Normal Populations", Technometrics, Vol. 8, No. 1, pp. 115-122.
Howe (1969), "Two-Sided Tolerance Limits for Normal Populations - Some Improvements", Journal of the American Statistical Association, Vol. 64, pp. 610-620.
Guenther (1977), "Sampling Inspection in Statistical Quality Control", Griffin's Statistical Monographs, Number 37, London.
Natrella (1966), "Experimental Statistics: NBS Handbook 91", National Institute of Standards and Technology (formerly National Bureau of Standards), pp. 2-13 - 2-15.
Hahn and Meeker (1991), "Statistical Intervals: A Guide for Practitioners", Wiley.
Applications:
Quality Control, Reliability
Implementation Date:
1998/12
2006/3: Allow only the normal or only the non-parametric limits to be generated
2014/06: Support for LOGNORMAL and BOXCOX tolerance limits
2018/05: Support for Howe method and Guenther correction for two-sided limits
2018/05: Support for normal based approximation for one-sided limits
2018/05: Some tweaks to the output format
Program:
SKIP 25
SET WRITE DECIMALS 4
TOLERANCE LIMITS Y
The following output is generated:
Two-Sided Normal Tolerance Limits:
(XBAR +/- K*S)
Howe Method
Response Variable: Y
Summary Statistics:
Number of Observations: 195
Degrees of Freedom: 194
Sample Mean: 9.2615
Sample Standard Deviation: 0.0228
Coverage = 90%
---------------------------------------------------------
Confidence k Lower Upper
Value (%) Factor Limit Limit
---------------------------------------------------------
50.0 1.6519 9.2238 9.2991
75.0 1.7102 9.2225 9.3004
90.0 1.7657 9.2212 9.3017
95.0 1.8003 9.2204 9.3025
99.0 1.8683 9.2189 9.3040
99.9 1.9498 9.2170 9.3059
Coverage = 95%
---------------------------------------------------------
Confidence k Lower Upper
Value (%) Factor Limit Limit
---------------------------------------------------------
50.0 1.9684 9.2166 9.3063
75.0 2.0378 9.2150 9.3079
90.0 2.1039 9.2135 9.3094
95.0 2.1452 9.2126 9.3103
99.0 2.2263 9.2107 9.3122
99.9 2.3233 9.2085 9.3144
Coverage = 99%
---------------------------------------------------------
Confidence k Lower Upper
Value (%) Factor Limit Limit
---------------------------------------------------------
50.0 2.5869 9.2025 9.3204
75.0 2.6782 9.2004 9.3225
90.0 2.7650 9.1984 9.3245
95.0 2.8192 9.1972 9.3257
99.0 2.9258 9.1948 9.3281
99.9 3.0533 9.1919 9.3310
Two-Sided Distribution-Free Tolerance Limits
Response Variable: Y
Summary Statistics:
Number of Observations: 195
Sample Mean: 9.2615
Sample Standard Deviation: 0.0228
Involving X(3) = 9.207325 Involving X(N-2) = 9.310506
---------------------------
Confidence Coverage
Value (%) Value (%)
---------------------------
100.00 50.00
100.00 75.00
99.99 90.00
92.80 95.00
36.18 97.50
1.43 99.00
0.05 99.50
0.00 99.90
0.00 99.95
0.00 99.99
Involving X(2) = 9.206343 Involving X(N-1) = 9.320067
---------------------------
Confidence Coverage
Value (%) Value (%)
---------------------------
100.00 50.00
100.00 75.00
100.00 90.00
98.91 95.00
72.05 97.50
13.30 99.00
1.72 99.50
0.01 99.90
0.00 99.95
0.00 99.99
Involving X(1) = 9.196848 Involving X(N) = 9.327973
---------------------------
Confidence Coverage
Value (%) Value (%)
---------------------------
100.00 50.00
100.00 75.00
100.00 90.00
99.95 95.00
95.69 97.50
58.16 99.00
25.50 99.50
1.66 99.90
0.44 99.95
0.02 99.99
NIST is an agency of the U.S. Commerce Department.
Date created: 06/05/2001
Last updated: 05/31/2018
| 2021-11-27T02:30:32 |
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https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/5756/4451
|
Development of Miniature Stirling Cryocooler Technology for Infrared Focal Plane Array
A reliable miniature cryocooler is one of the basic and foremost requirements for successful operation of high performance cooled infrared focal plane array (IRFPA) used for defence applications. Technological complexity and requirement of long duration fail-safe operation of the cryocooler demands robust design, fabrication and assembly with tolerances and, perfection of an array of sub-technologies. The paper presents the progress of the development activities in Stirling cryocooler technology at Solid State Physics Laboratory (SSPL), which evolved through essential milestones like the development of single and dual piston linear motor driven split coolers to the state-of-the-art integral Brushless DC (BLDC) motor crank-driven type highly miniaturized coolers of capacities ranging from 0.25 to 0.5W at 80K. The theoretical investigations in the design of Stirling cycle cryocooler have been reported and the issues related to the design aspects are discussed in sufficient details. Experimental results of cryocooler performance tests are also presented. The paper also focuses on regenerator design optimization. The results of optimizations have been shown at the end considering a sample data.
Af Mean sectional area of void space Ar Area of regenerator cross-section At Regenerator tube cross-sectional area Cm Specific heat of matrix material dm Mesh wire diameter dr Internal diameter of regenerator tube hm Mean heat transfer coefficient k Thermal conductivity l Length lm Mesh distance M Mass of matrix n No. of wire mesh screens NTOTAL Total of different mesh size considered r Compression ratio T Temperature t Blow time u Velocity of fluid in matrix ρ Density υ Kinematic viscosity
Subscripts
m of matrix f of fluid r Regenerator 0 Void space c Compression e Expansion
Currently a large number of infrared (IR) detectors for night vision devices and missile guidance systems are in use. The temperature needed for cooling these detectors are, for the most part, lower than those produced by conventional refrigeration, and lies in cryogenic range1,2,3. These systems need miniature cryocooler of 0.25 W to 1 W at 80 K capacity for their cooling requirements. To meet this requirement various types of cryocoolers such as Stirling, Joule-Thomson and others have been investigated in the past few decades4. Stirling cryocoolers have emerged as preferred systems in terms of efficiency, low mass, compactness and relatively low production cost in the capacity ranges of interest. Various forms of Stirling cryocoolers e.g. split linear motor driven, integral rotary crank driven etc. having capacities of less than a Watt are already being manufactured by various companies across the world. Pioneer work was done by Stolfi5 in the development of miniature free piston free displacer (FPFD) cryocooler with a capacity of 1 W at 77 K. This cooler utilizes linear electric drive, resulting in long life cryocooler as there was no wear and tear caused by side forces. A detailed theoretical analysis is also given by Dejong6 and Koh7. The basic thermodynamic analysis of stirling cycle was attempted by walker8, and later Tailor9 presented it considering the dead volume and imperfect regeneration effects. A lot of work has been reported on the loss analysis of cryocooler. Orlowska10 has reported measurement of all the significant losses, whereas Reed11 and Yang12 analyzed the system losses related to compressor and expander subsystems respectively.
The SSPL is working in the field of IRFPA detectors for quite some time. As a part of this activity for cooling needs of the detector array, development of stirling cryocoolers has assumed the main focus apart from Joule-Thomson (JT) coolers for certain night vision equipment applications. In the past SSPL has worked on development of linear motor driven integral13 and split FPFD cryocoolers in single and dual piston configurations. Over the period of time, the focus has shifted gradually towards developing integrated cooler of crank driven type owing to its advantages especially suited to night vision equipment over the split configurations.
In this paper, a brief of activities starting from the theoretical background to the prototype development, covering mostly the related theoretical as well as practical design aspects has been discussed. The losses which are the main governing element in deciding the configuration and design are discussed. An attempt has also been made in optimizing the design of regenerative heat exchanger, called regenerator.
Miniature split cryocoolers, in both single and dual piston FPFD configurations having capacities 0.25 W to 0.5 W at 80 K have been developed at SSPL for ground based applications. In earlier cooler design with single piston14, the gas was compressed by axial movement of piston generating an axial thrust due to inherent high inertia, which in turn generates high vibrations and EM noise in cold region. This necessitated a passive vibration absorber in which a floating mass acts as a damper. This arrangement too was not able to completely eliminate the vibrations due to less predictable behaviour of the movement of free piston. The absorber increased not only the weight and size of the system but also the complexity due to more running components, thereby rendering this a low reliability system. To overcome these shortcomings of the single piston system, dual piston system was introduced in which the compressor was provided with two linear motors driving two co-axial pistons positioned 180o out of phase against a common compression volume, thereby mutually balancing the axial thrust and eliminating the related vibrations. Prototype of the dual piston cryocooler is shown in Fig. 1(a).
Figure 1. (a) Linear motor driven dual piston split cryocooler prototype of capacity 0.5W@80K (b) Cold-tip temperature during long performance run with Input power of 32 W.
2.1 Results
The prototype was tested for its performance using dummy vacuum jacket around the cold tip with a vacuum of the order of 10-5 millibar. Heat load was externally applied using a resistive heater element and cold tip temperature was monitored using a PT-100 RTD. Experimental results are shown in Fig. 1(b). The cold-tip temperature well below the required 80 K mark achieved at no-load conditions is shown in Fig. 1(b) which was obtained during a typical 100 h test.
As the work on the development of 320 x 256 MW IRFPA progressed at SSPL, requirement changed to smaller, compact and high efficiency cryocoolers. Therefore, the focus was shifted to the development of rotary integral cryocoolers. Earlier the rotary coolers were using dry rubbing seals which were a limiting factor in terms of reliability and lifetime as compared to linear motor cryocoolers. Later, with the advancement in manufacturing technology, rubbing seals were replaced by dynamic clearance seals, making the rotary coolers comparable to the linear motor systems in terms of lifetime and reliability. The integrated detector/dewar cooler assembly (IDCA) configuration was chosen owing to a number of advantages offered by this over linear motor coolers. The relevant system description and developmental work is presented in the following sections.
3.1 System Description
The schematic of IDCA cryocooler assembly is shown in Fig. 2. The cryocooler system is complex assembly of mechanical parts in which the compressor and expander modules are connected by a small internal delivery duct which is drilled inside the body of the cryocooler. The cooler is charged with high purity Helium gas which is used as refrigerant. The compression is achieved inside the piston- cylinder assembly in which the piston moves at a frequency in the range of 50
Figure 2. Schematic assembly view of IDCA cryocooler.
to 75 Hz. The cold-finger cylinder in which the expansion takes place is attached to the crankcase and is placed at right angle to the compressor cylinder to ensure an optimum phase relationship. The drive mechanism used is of slider-crank type, in which there are two separate connecting rods attached to a single crank-shaft, called the eccentric shaft, and drive is provided by a BLDC motor16.
The displacer cum regenerator consists of a fiber glass epoxy tube stacked with a number of SS wire-mesh discs. A flywheel made of high density special sintered alloy has been used for regulating the motor torque. Dynamic balancing of unbalance rotary masses has been done using the flywheel itself as a balance mass because of space constraints. The ground link of mechanism i.e. the main body is made up of special Aluminum alloy for added strength apart from fulfilling the high thermal conductivity and machinability requirements.
Dynamic clearance seals with precisely controlled geometry and surface finishes have been used for guiding the displacer and piston in their respective pair for preventing the occurrence of wear by rubbing, and hence negates the need for lubrication. An experimentally optimized radial clearance value of 7 µm - 8 µm is found to be the perfect enough for piston-cylinder arrangement. To achieve this sort of clearances, manufacturing process was developed to fabricate the seals and bearings in close tolerances. The piston-cylinder pair is lapped and polished to the surface finishes of the order of 0.05 µm Ra, and the piston is coated with a very high hardness special ceramic material with a low coefficient of friction to reduce wear. Further, the motor winding has been kept out of Helium atmosphere with the use of thin cylinder, called the pressure membrane, for keeping the cooler operation cleaner and free from winding contamination. The metallic seals have been used for final sealing of the cooler for reducing the leak rates to minimum and more importantly for obviating the need for welding. The IDCA cryocooler prototype developed having a cooling capacity of 0.5W@80K with steady state power input of less than 10 W is shown in Fig. 3.
Figure 3. IDCA cryocooler prototype developed at SSPL.
3.1.1 Brushless DC Motor
One of the critical technologies in the development of cryocooler is the development of an efficient brushless DC (BLDC) motor. It is the crucial component of the cryocooler system and to a large extent the performance of the system depends on this esp. when it comes to high efficiency and power savings in the battlefield, where the later is limited. A specially designed BLDC motor with a compact on-board integrated electronics17 has been developed to suit the desired physical and other characteristics governing the system performance. The inbuilt demand control is able to regulate the target space temperature within ±1 K. The motor is equipped with advance features like standby, shut-down and cool-down indicator modes. The motor delivers a maximum power of 20 W with efficiency close to 75 per cent even at the highest of working speeds.
3.2 Thermodynamic Analysis
The Stirling cooler basically works on the principle of Stirling cycle. It conceptually works by employing a pump to cyclically press the working fluid and passing it back and forth between the hot and cold regions across a regenerative heat exchanger. The pressure-volume (PV) and temperature-entropy (TS) diagrams pertaining to ideal Stirling cycle are shown in Fig. 4 The compression (1-2) and expansion processes (3-4) occurs as most efficient isothermal processes at temperatures Tc and Te respectively, where as the regenerative cooling (2-3) and heating (4-1) of the working fluid is achieved as constant volume processes. The performance and cooling capacity of the Stirling cycle coolers depends on various parameters including the dead volume ratio, swept volume ratio, the phase angle and the temperature ratio, etc4
Figure 4. Ideal Stirling cycle: Pressure-volume diagram and Temperature-entropy diagram.
In the present text, the cooler has been subjected to first order thermodynamic analysis with sinusoidal motions without considering losses for performance approximations. The instantaneous volume, Ve, of expansion space can be expressed as a function of crank angle ϕ, and expansion space swept volume, VE , and is given by
${V}_{e}=\frac{1}{2}{V}_{E}\left(1+\mathrm{cos}\varphi \right)$ (1)
if the phase lag between the piston and displacer is α, then volume variations of compression space is defined as
${V}_{c}=\frac{1}{2}\kappa {V}_{E}\left(1+\mathrm{cos}\left(\varphi -\alpha \right)\right)$ (2)
where k is the ratio of swept volumes, and is given by VC/VE. where Vc is compression space ${Q}_{e}$ swept volume.
The cyclic cold production or the heat extracted from the expansion space is a function of${V}_{E}$ , mean charge pressure${p}_{mean}$ , intermediate parameters $\theta$ and , and $\delta$ is given as follows8:
${Q}_{e}=\frac{{V}_{E}.{p}_{mean}.\delta .\pi .\mathrm{sin}\theta }{\left[\sqrt{\left(1-{\delta }^{2}\right)}+1\right]}$ (3)
where the parameter$\delta$ and $\delta$ are functions of dead volume ratio X , $κ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqOUdSgaaa@3786@$ and α, and can be calculated as
$\theta ={\mathrm{tan}}^{-1}\frac{\kappa .\mathrm{sin}\alpha }{\tau +\kappa .\mathrm{cos}\alpha }$ (4)
Here the term $τ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqiXdqhaaa@3799@$ is the temperature ratio and is defined as Tc/Te and
$\delta =\frac{\sqrt{{\tau }^{2}+{\kappa }^{2}+2.\tau .\kappa +2S}}{\tau +\kappa +2S}$ (5)
In above equation the term S is the reduced dead volume which is defined as
$S=\frac{2X\tau }{\tau +1}$ (6)
where X is the dead volume ratio and can be defined as VD/VE; VD being the total of all the non-swept volumes. Further the instantaneous pressure, ${p}_{\mathrm{max}}$ p, is a function of maximum pressure, and is calculated as follows.
$p=\frac{{p}_{\mathrm{max}}\left(1-\delta \right)}{\left[1+\delta .\mathrm{cos}\left(\varphi -\theta \right)\right]}$ (7)
where the maximum charge pressure,${p}_{\mathrm{max}}$ , is given by
${p}_{\mathrm{max}}={p}_{mean}\sqrt{\frac{1+\delta }{1-\delta }}$ (8)
Moreover considering the combined swept volume VT and by using Eqns (3), (7), and (8), a term cyclic dimensionless heat extracted,, may be defined as follows
${Q}_{e}^{*}=\frac{\pi {\left(1-\delta \right)}^{1/2}.\delta .\mathrm{sin}\theta }{\left(1+\kappa \right).{\left(1+\delta \right)}^{1/2}.\left[1+{\left(1-{\delta }^{2}\right)}^{1/2}\right]}$ (9)
The work done on the system, W, may be evaluated from the following
$W={Q}_{c}-{Q}_{e}=\left(\tau -1\right).{Q}_{e}$ (10)
where the heat of compression or the heat rejected by the system, Qc, is given as
${Q}_{c}=\tau .{Q}_{e}$ (11)
Then the ideal Coefficient of Performance COPideal is give by
:
$CO{P}_{ideal}=\frac{{Q}_{e}}{W}=\frac{1}{\tau -1}=\frac{{T}_{c}}{{T}_{c}-{T}_{e}}$ (12)
Likewise Eqn. (9), a term dimensionless cyclic work input W* may be defined using Eqn. (10) and can be written as follows.
${W}^{*}=\left(\tau -1\right).{Q}_{e}^{*}$ (13)
Now from Eqns. (9) and (13) the effect of various governing parameters on cooler performance can be analyzed in dimensionless terms.
3.2.1 SAMPLE CALCULATIONS
Numerical computations have been performed for analyzing the effect of various design parameters on coolers performance, using the parameters and related material property data given in Appendix. The data pertains to the IDCA cryocooler prototype under development. Figures 5(a) and 5(b) shows the dimensionless heat extraction and work done per cycle based on variation of α and κ respectively for different dead volume ratios. The dead volume VD considered is the total of non-swept volumes excluding the regenerator dead volume. The optimum of the heat extraction exists where the phase angle α is near to the 100o mark, and interestingly as the dead volume ratio increases the cyclic heat extraction decreases with a shift of phase angle towards the 90o mark. As can also be observed, heat extraction varies by only ±10% when the phase angle is in the range of 60° to 110°. So the advantage of manufacturing ease of making the 90 o arrangement overweighs the sacrificing a minuscule of the cooling power esp. where the dead volume ratios may have larger values due to the inherent ducting arrangements. Further, it can be clearly observed from . 5(b) that this optimum exists when the swept volume ratio κ is near to 3 for the present case.
Figure 5. (a)Effect of design parameters on dimensionless heat extraction and/or work done for different dead volume ratios X: (a) Phase angle α (b) Swept volume ratio κ.
It is clear that the above results help a designer in choosing the optimized values of various pa-rameters for a preliminary design, but numerous other factors govern the actual attainable cold pro-duction that will become more evident in next section.
3.3 .LOSS EVALUATION OF SYSTEM
In the previous section, we did not consider the losses and it was assumed that the system is ideal. However, in real system there are losses due to the non-ideality that persists inherently
Figure 5. Effect of design parameters on dimensionless heat extraction and/or work done for different dead volume ratios X: (a) Phase angle α (b) Swept volume ratio κ.
in the system. The evaluation of losses is necessary for predicting the actual cooling capacity and also from the point of view of impact of these losses in deciding the configuration and materials of different components of the system. These losses have the detrimental effect of reducing the refrigeration produced. Now consider the actual Coefficient of Performance of the cryocooler, COPactual, which may be defined as follows.
$CO{P}_{actual}=\frac{Q}{P}$ (14)
Where Q is the actual cooling capacity of real system and P is the corresponding actual power input. The term Carnot efficiency gives the numerical value of the deviation from the most ideal behavior, and is defined as8
${\eta }_{Carnot}=\frac{CO{P}_{actual}}{CO{P}_{ideal}}$ (15)
Considering the most ideal behavior of the cooler and using Eq. (12), for cooler working in the tem-perature range of Tc=300K and Te=80K the $CO{P}_{ideal}$ comes out to be 0.36. Now, consider the actual typ-ical miniature cooler, as is our case, with cooling capacity of 0.5W and power input of 15W [refer Sec. 3.4],$CO{P}_{actual}$ value is around 0.033, and the Carnot efficiency as calculated from Eq. (15) is barely 0.092, and a large amount of the power is consumed in overcoming the losses. Hence, a system level loss assessment is necessary for producing efficient coolers. Broadly, the losses can be divided into the following two categories18.
1. Losses that consume the fraction of input power available for the refrigeration like joule heat-ing in coil windings and irreversible compression etc., and are mostly related to the compressor part.
2. Losses that consume a part of refrigeration directly, and are related to the expander side.
In the present study the second category of losses have been considered, since these have direct impact on the coolers performance and can be controlled with less effort as compared to the other losses.
The net refrigeration available at cold end for cooling the actual load can be calculated from the following.
(16)
Where Qnet is actual net refrigeration available for cooling the application load, i.e. the detector array , Qe is maximum refrigeration available in ideal Stirling cycle as given in Eq. (3), the bracketed values are the sum of all the losses in which Qief is the loss due to thermal ineffectiveness of regenerator, Qpf is the loss due to frictional pressure drop Qrt is conduction loss associated with regenerator tube, Qcmg is longitudinal conduction loss of regenerator matrix whereas Qshtl and Qcf are the shuttle heat transfer loss and dewar (conduction and radiation) losses respectively. The following sub-sections cover the analysis of these losses, with a special emphasis given to the regenerator design optimization as an outcome of this analysis.
3.3.1. REGENERATOR LOSSES AND DESIGN OPTIMIZATION
As can be seen in Eq. (16), a large part of the losses is solely attributed to the regenerator component. Hence the regenerator in Stirling cryocooler assumes great importance. As compared to the larger units it becomes even more crucial in case of small capacity coolers where most of the cooling effort of the machine goes in overcoming the losses arising out of regenerator. The major part of the actual refrigeration available to cool a thermal load is consumed by the thermal and flow losses associated with regenerator.
The main function of the regenerator is to store maximum energy with minimum of the losses. In this context, a term regenerator efficiency is defined which is a function of total energy losses and the maximum heat storage in regenerator19. It gives a fair estimate of regenerator performance by ac-counting for the penalty incurred in attempt to store energy. In the present study the attempt has been made to optimize the regenerator design by maximizing the regenerator efficiency. Here, the design problem is basically to select the geometry of regenerator, which includes the wire-mesh specifications and the length of regenerator matrix, to give maximum efficiency.
3.3.1.1. REGENERATOR INEFFECTIVENESS LOSS
Because of the ineffectiveness of the regenerator, the temperature of the gas leaving the cold end of the regenerator is somewhat higher than the matrix temperature or some of the cooling effect is lost in cooling the gas to source temperature. This loss is called the regenerator ineffectiveness loss which is given as:
${Q}_{ief}=\stackrel{˙}{m}.{C}_{p}.\left({T}_{c}-{T}_{e}\right).\left(1-\epsilon \right)$ (17)
Where being the mass flow rate and Cp is the specific heat of fluid. The regenerator effectiveness is a function of many parameters which includes mass and material of matrix, frequency, number of heat transfer units Ntu, and heat capacity ratios of material and gas. The effectiveness is given by the following equation15.
$\epsilon =\frac{Crs}{Ntu{\left(1+Crs\right)}^{2}}\left[\left(\mathrm{exp}\left(-Ntu\right)\underset{0}{\overset{\eta -Ntu/Crs}{\int }}\left[1+2Crs+\left(1+Crs\right)\left(\eta -\frac{Ntu}{Crs}-z\right)+...$
(18)
where
$Ntu=\frac{{h}_{m}.A}{\stackrel{˙}{m}.{C}_{p}}$ , $\eta =\frac{Ntu}{Cr}$ , $Crs=\frac{M.{C}_{m}}{{l}_{r}.{A}_{f}.{\rho }_{0}.{C}_{p}}$ ,$Cr=\frac{M.{C}_{m}}{\stackrel{˙}{m}.{C}_{p}.t}$
where Cr and Crs are the heat capacity ratios of matrix material to the fluid flowing through the ma-trix and matrix material to fluid in void volume respectively. Further, the function $\left(2.\sqrt{Ntu.z}\right)$ is mod-ified Bessel function of the first kind of the order zero. The heat transfer coefficient is calculated as
$h=\frac{{k}_{f}.{N}_{ud}}{{d}_{m}}$ (19)
where ${N}_{ud}=0.42{\mathrm{R}}_{ed}{}^{0.56}$ where ${N}_{ud}$ is Nusselt number for wire screen and Reynolds number is given as
${\mathrm{R}}_{ed}=\frac{{d}_{m}u}{\upsilon }$ (20)
3.3.1.2. PRESSURE DROP LOSS
The pressure drop loss caused by the frictional flow across the regenerator matrix which reduces the magnitude of the pressure available for expansion thereby reducing the area of expansion space p-v diagram and the gross refrigeration produced. The pressure drop is expressed as15
$\nabla {p}_{f}=f.\rho .{u}^{2}.n/2$ (21)
The flow friction factor f is defined as
$f=\frac{33.6}{{\mathrm{Re}}_{l}}+0.337$ $f=\frac{33.6}{{\mathrm{Re}}_{l}}+0.337$ (22)
where ${\mathrm{Re}}_{l}$ is Reynolds number can be evaluated as
${\mathrm{Re}}_{l}=\frac{{l}_{m}.u}{\upsilon }$ (23)
The pressure drop loss can be calculated from the following equation12:
${Q}_{\Delta {p}_{f}}=\frac{{Q}_{e}.\Delta {p}_{f}}{Pa}$ (24)
where $Pa$ is pressure amplitude of the cycle, which is given in terms of compression ratio as
$Pa={P}_{mean}\frac{r-1}{r+1}$ (25)
3.3.1.3. LONGITUDINAL CONDUCTION LOSS
Longitudinal conduction through regenerator tube is given as :
${Q}_{rt}=\frac{{k}_{m}.{A}_{t}.\left({T}_{c}-{T}_{e}\right)}{{l}_{r}}$ (26)
whereas the longitudinal conduction through matrix and gas can be calculated from19:
${Q}_{cmg}=\frac{{k}_{eff}.{A}_{eff}.\left({T}_{c}-{T}_{e}\right)}{{l}_{r}}$ (27)
where ${k}_{eff}$ is the void space effective thermal conductivity of matrix and gas and is given as
${k}_{eff}={k}_{f}.\frac{\left(1+{k}_{m}/{k}_{f}\right)-\left(1-\varphi \right).\left(1-{k}_{m}/{k}_{f}\right)}{\left(1+{k}_{m}/{k}_{f}\right)+\left(1-\varphi \right).\left(1-{k}_{m}/{k}_{f}\right)}$ (28)
And ${A}_{eff}$ is the effective conduction area which may be written as:
${A}_{eff}={A}_{r}\left(1-\varphi \right)$ ; where $\varphi$ is the porosity of wire-mesh.
3.3.1.4. REGENERATOR EFFICIENCY
The regenerator efficiency from its definition may be written as
$\Psi =1-\frac{{Q}_{t}}{{Q}_{st}}$ (29)
Where ${Q}_{t}$ is the total of regenerator losses as explained above and ${Q}_{st}$ is the total heat stored in matrix which is
${Q}_{st}=\stackrel{˙}{m}.{C}_{p}.\left({T}_{c}-{T}_{e}\right).\epsilon$ (30)
3.3.2. SHUTTLE HEAT TRANSFER AND DEWAR LOSSES
This loss is a form of motional convective heat transfer which occurs when the displacer with an axial temperature gradient reciprocates inside the cylinder of cold-finger with a similar axial temperature gradient and causes an extra heat transfer from the high to the low temperature region in addition to the wall conduction20. This loss is calculated using the following equation as suggested in ref.21
${Q}_{shtl}=\frac{{k}_{f}.\pi .{d}_{r}.{s}^{2}.\left({T}_{c}-{T}_{e}\right)}{\left(5.4\right).C.{l}_{r}}$ (31)
where s is the stroke length and C is the radial clearance.
Dewar losses constitute the conduction and radiation in dewar vessel including the cold-finger. The conduction losses are those occurring through the wall of the cold-finger due to the thermal gradient that prevails between the two ends The radiation loss comes from the radiation heat exchanged between the dewar vessel inner wall and the external surface of the cold-finger tube.
3.3.3. RESULTS
The computation of losses and regenerator design optimization has been done considering the IDCA cooler data given in appendix. For this purpose a code has been written in MATLAB. The flow chart of the methodology followed is shown in Fig. 6 Various wire-mesh sizes ranging from 100 to 500 mesh number have been selected for the analysis. Mesh-sizes below 100 are not considered due to very low
Figure 6. Regenerator design optimization procedure.
values of effectiveness. Stainless Steel wire-mesh is chosen due to its favorable heat capacity and thermal properties in the temperature range of cooler operation22,23. Regenerator losses and ef-ficiency is then calculated for each mesh-size by computing the regenerator effectiveness from Eq. (18), which also considers the heat capacities and void volume effects. Then the optimum mesh size and length is chosen based on maximum efficiency.
Various regenerator losses are plotted in Fig. 7(a) for a 400 size mesh as a function of regenerator length. It can be observed that regenerator ineffectiveness loss and other longitudinal conduction losses decreases with increasing length while the flow losses due to drop in pressure increases. Rege-nerator efficiency is plotted in Fig. 7(b), where the mesh sizes 300 and 400 are the best choices for a length zone of 35-45 mm. The heat balance for IDCA cryocooler has been presented in Table 1.
3.4. EXPERIMENTAL RESULTS
A total of three prototypes were fabricated, assembled and tested for performance. Test results are summarised in Table 2.
Cooler was said to be failure if it does not meet the following conditions.
• Maximum input power < 20 W
• Figure 7.(a)Regenerator losses for a 400 mesh size (b) Regenerator efficiency for different mesh sizes.
Table 1 Heat balance sheet for IDCA cryocooler
• Cold tip temperature < 80 K
• Cool down time < 8-9 minutes depending upon ambient temp.
All the above parameters were monitored through a Data Acquisition (DAQ) system developed 'in-house'. A typical thermal performance test results are shown in Fig. 8 as a screen-shot of DAQ system, depicting the cold-tip temperature and the power input with time. It is evident from the results that the prototypes met the above conditions. The prototype PS-I was integrated with the detector-dewar assembly, primarily to determine the heat load capacity and size compatibility whereas the prototypes PD-01 and PD-02 were tested in dummy vacuum jacket of known heat load. The prototype PD-02 has operated for 330 cumulative hrs intermittently, but when put on continuous run it failed after 59 hrs. Similarly PS-I has run for 120 cumulative hrs, but failed after a continuous run of 19 hrs. Cause of failure is attributed to the poor quality of main housing bearing. All out efforts are in progress to find good quality bearings to enhance the lifetime and reliability of the cryocooler.
Table 2. Experimental test results of IDCA cryocooler
In this paper a brief review of the activities related to the development of miniature Stirling cryocoolers especially suited to IR sensor cooling applications has been presented. The technology for linear split and rotary integral coolers have been explained in due details. Thermodynamic analysis including the loss analysis has been presented from design point of view with a special emphasis on regenerator design optimization. The theoretical as well as the relevant experimental results have been presented and discussed.
Prototypes of both split and integral types have been tested in laboratory and also integrated with the thermal sight successfully. Optimization efforts to enhance the reliability and life time are still in progress. We expect to achieve these goals by carrying out further design modifications and will be in a position to predict MTTF of the coolers once produced in sufficient numbers. The cryocooler will also be subjected to environmental testing to make it usable in field application in future.
Authors are grateful to Director, Solid State Physics Laboratory (SSPL) for his constant support and encouragement during the course of this work. We are grateful to Mr Saket Mital, Mr K. Upadhayay and Mr Ramesh Chandra for their help in conducting experiments and documentation work. Thanks are also due to the SSPL workshop staff for fabrication of components.
1. Richard, D. Hudson. Jr. Infrared system engineering. John Wiley & Sons, New York, 1969. pp.642
2. Breckenridge Jr, R.W. Cryogenic coolers for IR systems. Optical Engineering, 1975, 14(1), 140-157.
3. Walker, G.; Fauvel, R. & Reader, G. Miniature refrigerators for cryogenic sensors and cold electronics. Cryogenics,1989, 29(8), 841-845.
4. Walker, G. Miniature refrigerators for cryogenic sensors and cold electronics. Clarendon Press, Oxford New York, 1989. 204 p.
5. Stolfi, F. & De Jonge, A. K. Stirling cryogenerators with linear drive. Philips Tech. Rev. , 1985, 42(1) , 1-10.
6. De Jonge, A.K. & Sereny, A. Analysis and optimisation of linear motor for compressor of a cryogenic refrigerator. In Advances in cryogenic engineering, 1982, 27, pp. 631-640.
7. Koh, D.Y.; Hong, Y. J.; Park, S.J.; Kim, H.B. & Lee, K.S. A study on the linear compressor characteristics of the Stirling cryocooler. Cryogenics, 2002, 42(6), 427-432.
8. Walker, G. Cryocoolers Part 1: Fundamentals. Plenum Press, New York and London, 1983. 364 p.
9. Tailor, P.R. & Narayankhedkar, K.G. Thermodynamic analysis of the Stirling cycle. Cryogenics, 1988, 28(1), 36-45.
10. Orlowska, A.H. & Davey, G.. Measurement of losses in a Stirling cycle cooler. Cryogenics, 1987, 27(11), 645-651.
11. Reed, J.S.; Davey, G.; Dadd, M.W. & Bailey, P.B. Compression losses in cryocoolers. Cryocoolers, 2005, 13, 209-214.
12. Yang, X. & Chung, J. N. Size effects on miniature Stirling cycle cryocoolers. Cryogenics, 2005, 45(8), 537-545.
13. Chhatwal, H.L.; Goswami, T.R., & Dewakar, R.K. Miniature linear motor driven integral type Stirling cooler for laboratory use. Indian J. Pure Appl. phys., 1992, 30(12), 771-772.
14. Chhatwal, H.L.; Goswami, T.R. & Dewakar, R.K. Prototype miniature split Stirling cryo-cooler. Indian J. Pure Appl. phys., 1993, 31(11), 794-797.
15. Miyabe, H.; Hamaguchi, K. & Takahashi, K. An approach to the design of Stirling engine regenerator matrix using packs of wire gauzes. In Proceeding IEEE, IECEC, 1982, 17, pp. 1839-1844.
16. Hanselman, Duane C. Brushless permanent-magnet motor design. McGraw-Hill, New York, 1994, 392p.
17. Ruehlich, I.; Korf, H. & Schellenberger, G. Advanced control electronics for Stirling cryocoolers. In Proceedings of SPIE, 2002, 4820, pp. 15-25.
18. Thirumaleshwar, M. & Subramanyam, S. V. Heat balance analysis of single stage Gifford-McMahon cycle cryorefrigerator. Cryogenics, 1986, 26(3), 189-195.
19. Pande, G.V. & Narayanamurthy, H. Design studies for stirling cycle cooler regenerator. J. Spacecr. Techno., 1995, 5(1), 57-63.
20. Chang, H. M.; Park, D. J. & Jeong, S. Effect of gap flow on shuttle heat transfer. Cryogenics, 2000, 40(3), 159-166.
21. Zimmerman, F.J. & Longsworth, R.C. Shuttle heat transfer. In Advances in cryogenic engineering. 1970, 16, pp. 342-351.
22. Andeen, B.R. Heat capacity and geometry impacts on regenerator performance. In Advances in Cryogenic Engineering. 1982, 27, pp. 611-619
23. De Waele, A.T.A.M. Finite heat-capacity effects in regenerators. Cryogenics, 2012, 52(1), 1-7.
Mr Manmohan Singh obtained his M.E (Thermal Engineering) from Delhi college of Engg., Delhi University. Presently, he is working as Head, Cryogenics Group, SSPL Delhi. His research interest includes manufacturing technology and Stirling cryocoolers. Mr Sunil Suchdev received his AMIE degree in Mech. Engg. He is working as Scientist in Cryocooler Group and his current interests include the development of cryocooler systems for defence applications. Mr Mukesh Sadana received his Masters degree from IIT, Delhi in 2009. He is working as Scientist and his current interests include the development of cryocooler systems and dynamics of machines. Mr Gaurav Pratap received his BTech from K.N.I.T, Sultanpur in 2006. He is working as Scientist and his current interests include the development of cryocooler systems for defence applications.
| 2019-10-14T03:12:54 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Gaia_archive/chap_datamodel/sec_dm_crossmatches/ssec_dm_panstarrs1_best_neighbour.html
|
# 14.5.9 panstarrs1_best_neighbour
Pan-STARRS1 BestNeighbour table lists each matched Gaia object with its best neighbour in the external catalogue.
There are $1\,327\,157$ objects in the filtered version of Pan-STARRS1 used to compute this cross-match that have too early epoch_mean.
Columns description:
source_id : Unique Gaia source identifier (long)
Unique identifier of the Gaia source, the attribute corresponds to gaia_source.source_id
original_ext_source_id : Original External Catalogue source identifier (long)
The unique source identifier in the original External catalogue.
angular_distance : Angular Distance between the two sources (double, Angle[arcsec])
Angular distance between a Gaia source and its nearest neighbour in the External Catalogue
number_of_neighbours : Number of neighbours in External Catalogue (int)
Number of sources in the External Catalogue which match the Gaia source within position errors.
The identifiers of all the neighbours can be found in the Neighbourhood table.
number_of_mates : Number of mates in Gaia Catalogue (short)
Number of other Gaia sources that have as best-neighbour the same External Catalogue source.
In case there are no other Gaia sources with the same best-neighbour in the external catalogue, the number of mates is equal to zero.
Given the Gaia high angular resolution, it will happen that what appears as a single object in an external catalogue will be resolved by Gaia and as such will be the best-match of more than one Gaia object.
best_neighbour_multiplicity : Number of neighbours with same probability as best neighbour (short)
The best-match to a Gaia source in an external catalogue is the source in the external catalogue that has the highest probability to be the best-match.
As the probability is based on positional and density properties, it could happen that there is more than one source in the external catalogue with the same probability.
Even if a single best-match is always chosen, this field tells the user if there were more ”best” neighbours. Those neighbours can be found in the Neighbourhood table.
gaia_astrometric_params : Number of Gaia astrometric params used (short)
This field indicates the number of Gaia astrometric parameters which were available in Gaia.
The field is set to 2 when only RA and DEC where available, while is set to 5 when RA, DEC, PMRA, PMDEC and PARALLAX are available and thus used to propagate a Gaia source position to the External Catalogue source coordinates epoch.
| 2019-05-22T06:52:46 |
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|
https://www.legisquebec.gouv.qc.ca/en/version/cs/n-1.01?code=se:6&history=20220809
|
### N-1.01 - Act respecting energy efficiency and energy conservation standards for certain products
6. (Repealed).
2011, c. 16, Sch. II, s. 6; 2016, c. 35, s. 1.
6. The comprehensive plan must include
(1) a status report with regard to energy efficiency and innovation in Québec;
(2) policy directions, priorities and targets with regard to energy efficiency and innovation;
(3) a summary of energy efficiency and energy innovation programs;
(4) the list of energy efficiency projects submitted by the electric power distributor under the fourth paragraph of section 8; and
(5) a summary of measures conducive to energy efficiency or innovation.
2011, c. 16, Sch. II, s. 6.
| 2022-12-06T07:40:42 |
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|
https://mfix.netl.doe.gov/doc/vvuq-manual/main/html/fluid/fld-07.html
|
# 3.7. FLD07: Steady, 2D fully-developed, turbulent channel flow¶
## 3.7.1. Description¶
This case uses 2D, fully-developed turbulent channel flow between two horizontal, parallel plates separated by a width, $$W$$, to assess the single phase k-ϵ model in MFIX. Periodic boundaries with a specified pressure drop are imposed in the y-direction as shown in Fig. 3.18.
Fig. 3.18 Turbulent flow in a 2D channel
The pressure drop along the channel is equated to the shear stress at the walls, $$\tau_{w}$$.
(3.11)$W\frac{dP_{g}}{\text{dy}} = {2\tau}_{w}$
The shear stress is related to the gas density, $$\rho_{g}$$, and friction velocity, $$v_{*}$$,
(3.12)$\tau_{w} = \rho_{g}v_{*}^{2},$
where, the friction velocity, is given by the Reynolds number.
(3.13)$\text{Re}_{\tau} = \frac{\rho_{g}v_{*}(W/2)}{\mu_{g}}$
## 3.7.2. Setup¶
#########################################################################
# #
# Author: Avinash Vaidheeswaran Date: July 2016 #
# Turbulent flow in a pipe problem: #
# #
# Turbulent flow through a channel is simulated and the results are #
# compared with the data from DNS #
# #
#########################################################################
RUN_NAME = 'FLD07'
DESCRIPTION = 'Turbulent channel flow'
#_______________________________________________________________________
# RUN CONTROL SECTION
UNITS = 'SI'
RUN_TYPE = 'NEW'
TSTOP = 1.0d8
DT = 0.02
ENERGY_EQ = .F.
SPECIES_EQ(0) = .F.
GRAVITY = 0.0
CALL_USR = .T.
#_______________________________________________________________________
# NUMERICAL SECTION
DISCRETIZE(1:9) = 9*2
NORM_g = 0.0
#_______________________________________________________________________
# GEOMETRY SECTION
COORDINATES = 'CARTESIAN'
ZLENGTH = 1.00 NO_K = .T.
XLENGTH = 2.00 IMAX = 8
YLENGTH = 1.00 JMAX = 4
#_______________________________________________________________________
# GAS-PHASE SECTION
RO_g0 = 1.0 ! (kg/m3)
MU_g0 = 1.0d-04 ! (Pa.s)
TURBULENCE_MODEL = 'K_EPSILON'
MU_GMAX = 1.0d6 ! (Pa.s)
#_______________________________________________________________________
# SOLIDS-PHASE SECTION
MMAX = 0
#_______________________________________________________________________
# INITIAL CONDITIONS SECTION
IC_X_w(1) = 0.0 ! (m)
IC_X_e(1) = 2.0 ! (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_U_G(1) = 1.0d-6 ! (m/sec)
IC_V_G(1) = 1.0 ! (m/sec)
IC_K_TURB_G(1) = 0.010 ! (m2/s2)
IC_E_TURB_G(1) = 0.001 ! (m2/s3)
#_______________________________________________________________________
# BOUNDARY CONDITIONS SECTION
! Flow boundaries: Periodic with specified pressure drop
!---------------------------------------------------------------------//
CYCLIC_Y_PD = .T.
DELP_Y = @(0.0543496*0.0543496) ! (Pa)
! The east and west boundaries are no-slip walls (NSW)
!---------------------------------------------------------------------//
BC_X_w(1:2) = 0.0 2.0 ! (m)
BC_X_e(1:2) = 0.0 2.0 ! (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) = 2*'NSW'
#_______________________________________________________________________
# OUTPUT CONTROL SECTION
RES_DT = 1.0d6
SPX_DT(1:9) = 9*1.0
FULL_LOG = .F.
RESID_STRING = 'P0' 'U0' 'V0' 'K0'
#_______________________________________________________________________
# DMP SETUP
! NODESI = 1 NODESJ = 2 NODESK = 1
## 3.7.3. Results¶
The pressure drop in the y-axial direction, domain length and width, and gas density were chosen to reflect the conditions of Lee and Moser [14] for $$\text{Re}_{\tau} = 543$$. The DNS dataset was accessed on November 10, 2016 from http://turbulence.ices.utexas.edu/channel2015/data/LM_Channel_0550_mean_prof.dat.
Transient simulations were performed for better numerical stability. The solution was considered converged when the L2 norms for the gas velocity components, $$u_{g}$$ and $$v_{g}$$, turbulent kinetic energy, $$k_{g}$$, and rate of turbulent kinetic energy dissipation, $$\epsilon_{g}$$, were all less than 10-10.
Simulations were conducted for three mesh levels [6, 12, 18] in the x-axial direction. Mesh levels were selected to ensure that the stream-ways velocity components in computational cells adjacent to the wall were located outside the buffer layer. Specifically, the first stream-ways velocity component should be located at least 30 wall units from the wall to be consistent with the $$k - \epsilon$$ model wall function implementation.
(3.14)$\frac{\Delta x}{2}\frac{\ v_{*}\rho_{g}}{\mu_{g}} > 30$
The MFIX results are shown in Fig. 3.19 along with the direct numerical simulation (DNS) data of Lee and Moser [14] for $$\text{Re}_{\tau} = 543$$. The velocity profiles for the three mesh levels are shown on the left whereas the normalized velocity profiles with respect to wall units are shown on the right.
Fig. 3.19 2D, fully developed, turbulent channel flow with the DNS data of Lee and Moser [14] ; (Left) Velocity profile; (Right) Non-dimensionalized channel width and velocity profile.
| 2022-07-03T18:48:53 |
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|
https://mooseframework.inl.gov/modules/heat_conduction/index.html
|
Heat Conduction Module
under construction
Documentation for the heat conduction module needs some work...
BCs
• Moose App
• ConvectiveFluxBCDetermines boundary values via the initial and final values, flux, and exposure duration
• DGFunctionDiffusionDirichletBC
• DiffusionFluxBCComputes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector.
• DirichletBCImposes the essential boundary condition , where is a constant, controllable value.
• EigenDirichletBCDirichlet BC for eigenvalue solvers
• FunctionDirichletBCImposes the essential boundary condition , where is a (possibly) time and space-dependent MOOSE Function.
• FunctionNeumannBCImposes the integrated boundary condition , where is a (possibly) time and space-dependent MOOSE Function.
• FunctionPenaltyDirichletBC
• FunctionPresetBCThe same as FunctionDirichletBC except the value is applied before the solve begins
• LagrangeVecDirichletBCImposes the essential boundary condition , where are constant, controllable values.
• LagrangeVecFunctionDirichletBCImposes the essential boundary condition , where components are calculated with functions.
• MatchedValueBCImplements a NodalBC which equates two different Variables' values on a specified boundary.
• NeumannBCImposes the integrated boundary condition , where is a constant, controllable value.
• OneDEqualValueConstraintBC
• PenaltyDirichletBCEnforces a Dirichlet boundary condition in a weak sense by penalizing differences between the current solution and the Dirichlet data.
• PostprocessorDirichletBC
• PostprocessorNeumannBC
• PresetBCSimilar to DirichletBC except the value is applied before the solve begins
• SinDirichletBCImposes a time-varying essential boundary condition , where varies from an given initial value at time to a given final value over a specified duration.
• SinNeumannBCImposes a time-varying flux boundary condition , where varies from an given initial value at time to a given final value over a specified duration.
• VacuumBC
• VectorNeumannBCImposes the integrated boundary condition , where is a user-defined, constant vector.
• WeakGradientBCComputes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector.
• Periodic
• Rdg App
• AEFVBCA boundary condition kernel for the advection equation using a cell-centered finite volume method.
• Functional Expansion Tools App
• FXFluxBCSets a flux boundary condition, evaluated using a FunctionSeries instance. This does not fix the flux, but rather 'strongly encourages' flux agreement by penalizing the differences through contributions to the residual.
• FXValueBCImposes a fixed value boundary condition, evaluated using a FunctionSeries instance.
• FXValuePenaltyBCSets a value boundary condition, evaluated using a FunctionSeries instance. This does not fix the value, but rather 'strongly encourages' value agreement by penalizing the differences through contributions to the residual.
• XFEMApp
• CrackTipEnrichmentCutOffBCSimilar to DirichletBC except the value is applied before the solve begins
• Heat Conduction App
• ConvectiveFluxFunctionDetermines boundary value by fluid heat transfer coefficient and far-field temperature
• CoupledConvectiveFlux
• CoupledConvectiveHeatFluxBCConvective heat transfer boundary condition with temperature and heat transfer coefficent given by auxiliary variables.
• GapHeatTransferTransfers heat across a gap between two surfaces dependant on the gap geometry specified.
• HeatConductionBC
• Richards App
• Q2PPiecewiseLinearSinkSink of fluid, controlled by (pressure, bare_fluxes) interpolation. This is for use in Q2P models
• RichardsExcavAllows the user to set variable values at the face of an excavation. You must have defined the excavation start time, start position, etc, through the excav_geom_function
• RichardsHalfGaussianSink
• RichardsPiecewiseLinearSink
• Tensor Mechanics App
• CoupledPressureBCApplies a pressure from a variable on a given boundary in a given direction
• DashpotBC
• DisplacementAboutAxisImplements a boundary condition that enforces rotationaldisplacement around an axis on a boundary
• InteractionIntegralBenchmarkBC
• PresetAccelerationPrescribe acceleration on a given boundary in a given direction
• PresetDisplacementPrescribe the displacement on a given boundary in a given direction.
• PresetVelocity
• PressureApplies a pressure on a given boundary in a given direction
• StickyBCImposes the boundary condition if exceeds the bounds provided
• CavityPressure
• CoupledPressure
• Pressure
• Navier Stokes App
• EnergyFreeBC
• INSMomentumNoBCBCLaplaceFormThis class implements the 'No BC' boundary condition based on the 'Laplace' form of the viscous stress tensor.
• INSMomentumNoBCBCTractionFormThis class implements the 'No BC' boundary condition based on the 'traction' form of the viscous stress tensor.
• INSTemperatureNoBCBCThis class implements the 'No BC' boundary condition discussed by Griffiths, Papanastiou, and others.
• ImplicitNeumannBCThis class implements a form of the Neumann boundary condition in which the boundary term is treated 'implicitly'.
• MassFreeBC
• MomentumFreeBC
• MomentumFreeSlipBC
• NSEnergyInviscidSpecifiedBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation.
• NSEnergyInviscidSpecifiedDensityAndVelocityBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation.
• NSEnergyInviscidSpecifiedNormalFlowBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation.
• NSEnergyInviscidSpecifiedPressureBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation.
• NSEnergyInviscidUnspecifiedBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation.
• NSEnergyViscousBCThis class couples together all the variables for the compressible Navier-Stokes equations to allow them to be used in derived IntegratedBC classes.
• NSEnergyWeakStagnationBCThe inviscid energy BC term with specified normal flow.
• NSImposedVelocityBCImpose Velocity BC.
• NSImposedVelocityDirectionBCThis class imposes a velocity direction component as a Dirichlet condition on the appropriate momentum equation.
• NSInflowThermalBCThis class is used on a boundary where the incoming flow values (rho, u, v, T) are all completely specified.
• NSMassSpecifiedNormalFlowBCThis class implements the mass equation boundary term with a specified value of rho*(u.n) imposed weakly.
• NSMassUnspecifiedNormalFlowBCThis class implements the mass equation boundary term with the rho*(u.n) boundary integral computed implicitly.
• NSMassWeakStagnationBCThe inviscid energy BC term with specified normal flow.
• NSMomentumConvectiveWeakStagnationBCThe convective part (sans pressure term) of the momentum equation boundary integral evaluated at specified stagnation temperature, stagnation pressure, and flow direction values.
• NSMomentumInviscidNoPressureImplicitFlowBCMomentum equation boundary condition used when pressure is not integrated by parts.
• NSMomentumInviscidSpecifiedNormalFlowBCMomentum equation boundary condition in which pressure is specified (given) and the value of the convective part is allowed to vary (is computed implicitly).
• NSMomentumInviscidSpecifiedPressureBCMomentum equation boundary condition in which pressure is specified (given) and the value of the convective part is allowed to vary (is computed implicitly).
• NSMomentumPressureWeakStagnationBCThis class implements the pressure term of the momentum equation boundary integral for use in weak stagnation boundary conditions.
• NSMomentumViscousBCThis class corresponds to the viscous part of the 'natural' boundary condition for the momentum equations.
• NSPenalizedNormalFlowBCThis class penalizes the the value of u.n on the boundary so that it matches some desired value.
• NSPressureNeumannBCThis kernel is appropriate for use with a 'zero normal flow' boundary condition in the context of the Euler equations.
• NSStagnationPressureBCThis Dirichlet condition imposes the condition p_0 = p_0_desired.
• NSStagnationTemperatureBCThis Dirichlet condition imposes the condition T_0 = T_0_desired.
• NSThermalBCNS thermal BC.
• Chemical Reactions App
• ChemicalOutFlowBCChemical flux boundary condition
• Porous Flow App
• PorousFlowHalfCubicSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a cubic.
• PorousFlowHalfGaussianSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a Gaussian.
• PorousFlowPiecewiseLinearSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a piecewise linear function.
• PorousFlowSinkApplies a flux sink to a boundary.
DiracKernels
• Moose App
• ConstantPointSource
• FunctionDiracSource
• Heat Conduction App
• GapHeatPointSourceMaster
• Richards App
• Q2PBoreholeApproximates a borehole in the mesh with given bottomhole pressure, and radii using a number of point sinks whose positions are read from a file. This DiracKernel is for use by Q2P models
• RichardsBoreholeApproximates a borehole in the mesh with given bottomhole pressure, and radii using a number of point sinks whose positions are read from a file
• RichardsPolyLineSinkApproximates a polyline sink in the mesh by using a number of point sinks whose positions are read from a file
• XFEMApp
• XFEMPressure
• Porous Flow App
• PorousFlowPeacemanBoreholeApproximates a borehole in the mesh using the Peaceman approach, ie using a number of point sinks with given radii whose positions are read from a file
• PorousFlowPolyLineSinkApproximates a polyline sink by using a number of point sinks with given weighting whose positions are read from a file
• PorousFlowSquarePulsePointSourcePoint source (or sink) that adds (removes) fluid at a constant mass flux rate for times between the specified start and end times.
• Contact App
• ContactMaster
• SlaveConstraint
Kernels
• Moose App
• AnisotropicDiffusionAnisotropic diffusion kernel with weak form given by .
• BodyForceDemonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form .
• CoefTimeDerivativeThe time derivative operator with the weak form of .
• ConservativeAdvectionConservative form of which in its weak form is given by: .
• CoupledForceImplements a source term proportional to the value of a coupled variable. Weak form: .
• CoupledTimeDerivativeTime derivative Kernel that acts on a coupled variable. Weak form: .
• DiffusionThe Laplacian operator (), with the weak form of .
• MassEigenKernelAn eigenkernel with weak form where is the eigenvalue.
• MassLumpedTimeDerivativeLumped formulation of the time derivative . Its corresponding weak form is where denotes the time derivative of the solution coefficient associated with node .
• MatDiffusionDiffusion equation Kernel that takes an isotropic Diffusivity from a material property
• MaterialDerivativeRankFourTestKernelClass used for testing derivatives of a rank four tensor material property.
• MaterialDerivativeRankTwoTestKernelClass used for testing derivatives of a rank two tensor material property.
• MaterialDerivativeTestKernelClass used for testing derivatives of a scalar material property.
• NullKernelKernel that sets a zero residual.
• ReactionImplements a simple consuming reaction term with weak form .
• TimeDerivativeThe time derivative operator with the weak form of .
• UserForcingFunctionDemonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form .
• VectorBodyForceDemonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form .
• VectorDiffusionThe Laplacian operator (), with the weak form of .
• Phase Field Test App
• GaussContForcing
• Phase Field App
• ACBarrierFunctionAllen Cahn kernel used when 'mu' is a function of variables
• ACGBPolyGrain-Boundary model concentration dependent residual
• ACGrGrElasticDrivingForceAdds elastic energy contribution to the Allen-Cahn equation
• ACGrGrMultiMulti-phase poly-crystaline Allen-Cahn Kernel
• ACGrGrPolyGrain-Boundary model poly-crystaline interface Allen-Cahn Kernel
• ACInterfaceGradient energy Allen-Cahn Kernel
• ACInterface2DMultiPhase1Gradient energy Allen-Cahn Kernel where the derivative of interface parameter kappa wrt the gradient of order parameter is considered.
• ACInterface2DMultiPhase2Gradient energy Allen-Cahn Kernel where the interface parameter kappa is considered.
• ACInterfaceKobayashi1Anisotropic gradient energy Allen-Cahn Kernel Part 1
• ACInterfaceKobayashi2Anisotropic Gradient energy Allen-Cahn Kernel Part 2
• ACInterfaceStressInterface stress driving force Allen-Cahn Kernel
• ACKappaFunctionGradient energy term for when kappa as a function of the variable
• ACMultiInterfaceGradient energy Allen-Cahn Kernel with cross terms
• ACSEDGPolyStored Energy contribution to grain growth
• ACSwitchingKernel for Allen-Cahn equation that adds derivatives of switching functions and energies
• AllenCahnAllen-Cahn Kernel that uses a DerivativeMaterial Free Energy
• AllenCahnElasticEnergyOffDiagThis kernel calculates off-diagonal jacobian of elastic energy in AllenCahn with respect to displacements
• CHBulkPFCTradCahn-Hilliard kernel for a polynomial phase field crystal free energy.
• CHInterfaceGradient energy Cahn-Hilliard Kernel with a scalar (isotropic) mobility
• CHInterfaceAnisoGradient energy Cahn-Hilliard Kernel with a tensor (anisotropic) mobility
• CHMathSimple demonstration Cahn-Hilliard Kernel using an algebraic double-well potential
• CHPFCRFFCahn-Hilliard residual for the RFF form of the phase field crystal model
• CHSplitChemicalPotentialChemical potential kernel in Split Cahn-Hilliard that solves chemical potential in a weak form
• CHSplitConcentrationConcentration kernel in Split Cahn-Hilliard that solves chemical potential in a weak form
• CHSplitFluxComputes flux as nodal variable
• CahnHilliardCahn-Hilliard Kernel that uses a DerivativeMaterial Free Energy and a scalar (isotropic) mobility
• CahnHilliardAnisoCahn-Hilliard Kernel that uses a DerivativeMaterial Free Energy and a tensor (anisotropic) mobility
• CoefCoupledTimeDerivativeScaled time derivative Kernel that acts on a coupled variable
• CoefReactionImplements the residual term (p*u, test)
• ConservedLangevinNoiseSource term for noise from a ConservedNoise userobject
• CoupledAllenCahnCoupled Allen-Cahn Kernel that uses a DerivativeMaterial Free Energy
• CoupledMaterialDerivativeKernel that implements the first derivative of a function material property with respect to a coupled variable.
• CoupledSusceptibilityTimeDerivativeA modified coupled time derivative Kernel that multiplies the time derivative of a coupled variable by a generalized susceptibility
• CoupledSwitchingTimeDerivativeCoupled time derivative Kernel that multiplies the time derivative by $\frac{dh_\alpha}{d\eta_i} F_\alpha + \frac{dh_\beta}{d\eta_i} F_\beta + \dots) • DiscreteNucleationForceTerm for inserting grain nuclei or phases in non-conserved order parameter fields • GradientComponentSet the kernel variable to a specified component of the gradient of a coupled variable. • HHPFCRFFReaction type kernel for the RFF phase fit crystal model • KKSACBulkCKKS model kernel (part 2 of 2) for the Bulk Allen-Cahn. This includes all terms dependent on chemical potential. • KKSACBulkFKKS model kernel (part 1 of 2) for the Bulk Allen-Cahn. This includes all terms NOT dependent on chemical potential. • KKSCHBulkKKS model kernel for the Bulk Cahn-Hilliard term. This operates on the concentration 'c' as the non-linear variable • KKSMultiACBulkCMulti-phase KKS model kernel (part 2 of 2) for the Bulk Allen-Cahn. This includes all terms dependent on chemical potential. • KKSMultiACBulkFKKS model kernel (part 1 of 2) for the Bulk Allen-Cahn. This includes all terms NOT dependent on chemical potential. • KKSMultiPhaseConcentrationKKS multi-phase model kernel to enforce . The non-linear variable of this kernel is , the final phase concentration in the list. • KKSPhaseChemicalPotentialKKS model kernel to enforce the pointwise equality of phase chemical potentials dFa/dca = dFb/dcb. The non-linear variable of this kernel is ca. • KKSPhaseConcentrationKKS model kernel to enforce the decomposition of concentration into phase concentration (1-h(eta))ca + h(eta)cb - c = 0. The non-linear variable of this kernel is cb. • KKSSplitCHCResKKS model kernel for the split Bulk Cahn-Hilliard term. This operates on the chemical potential 'c' as the non-linear variable • LangevinNoiseSource term for non-conserved Langevin noise • LaplacianSplitSplit with a variable that holds the Laplacian of a phase field variable. • MaskedBodyForceKernel that defines a body force modified by a material mask • MatAnisoDiffusionDiffusion equation Kernel that takes an anisotropic Diffusivity from a material property • MatGradSquareCoupledGradient square of a coupled variable. • MatReactionKernel to add -L*v, where L=reaction rate, v=variable • MultiGrainRigidBodyMotionAdds rigid mody motion to grains • SimpleACInterfaceGradient energy for Allen-Cahn Kernel with constant Mobility and Interfacial parameter • SimpleCHInterfaceGradient energy for Cahn-Hilliard equation with constant Mobility and Interfacial parameter • SimpleCoupledACInterfaceGradient energy for Allen-Cahn Kernel with constant Mobility and Interfacial parameter for a coupled order parameter variable. • SimpleSplitCHWResGradient energy for split Cahn-Hilliard equation with constant Mobility for a coupled order parameter variable. • SingleGrainRigidBodyMotionAdds rigid mody motion to a single grain • SoretDiffusionAdd Soret effect to Split formulation Cahn-Hilliard Kernel • SplitCHMathSimple demonstration split formulation Cahn-Hilliard Kernel using an algebraic double-well potential • SplitCHParsedSplit formulation Cahn-Hilliard Kernel that uses a DerivativeMaterial Free Energy • SplitCHWResSplit formulation Cahn-Hilliard Kernel for the chemical potential variable with a scalar (isotropic) mobility • SplitCHWResAnisoSplit formulation Cahn-Hilliard Kernel for the chemical potential variable with a tensor (anisotropic) mobility • SusceptibilityTimeDerivativeA modified time derivative Kernel that multiplies the time derivative of a variable by a generalized susceptibility • SwitchingFunctionConstraintEtaLagrange multiplier kernel to constrain the sum of all switching functions in a multiphase system. This kernel acts on a non-conserved order parameter eta_i. • SwitchingFunctionConstraintLagrangeLagrange multiplier kernel to constrain the sum of all switching functions in a multiphase system. This kernel acts on the lagrange multiplier variable. • SwitchingFunctionPenaltyPenalty kernel to constrain the sum of all switching functions in a multiphase system. • CHPFCRFFSplitKernel • HHPFCRFFSplitKernel • PFCRFFKernel • PolycrystalElasticDrivingForce • PolycrystalKernel • PolycrystalStoredEnergy • RigidBodyMultiKernel • Misc App • CoefDiffusionKernel for diffusion with diffusivity = coef + function • ThermoDiffusionKernel for thermo-diffusion (Soret effect, thermophoresis, etc.) • Navier Stokes Test App • AdvectionThis class solves the scalar advection equation, with SUPG stabilization. • Level Set App • LevelSetAdvectionImplements the level set advection equation: , where the weak form is . • LevelSetAdvectionSUPGSUPG stablization term for the advection portion of the level set equation. • LevelSetForcingFunctionSUPGThe SUPG stablization term for a forcing function. • LevelSetOlssonReinitializationThe re-initialization equation defined by Olsson et. al. (2007). • LevelSetTimeDerivativeSUPGSUPG stablization terms for the time derivative of the level set equation. • Solid Mechanics App • HomogenizationKernel • OutOfPlaneStress • SolidMechImplicitEuler • StressDivergence • StressDivergenceRSpherical • StressDivergenceRZ • XFEMApp • CrackTipEnrichmentStressDivergenceTensorsEnrich stress divergence kernel for small-strain simulations • Heat Conduction App • AnisoHeatConduction • HeatCapacityConductionTimeDerivativeTime derivative term of the heat equation with the heat capacity as an argument. • HeatConductionComputes residual/Jacobian contribution for term. • HeatConductionTimeDerivativeTime derivative term of the heat equation for quasi-constant specific heat and the density . • HeatSourceDemonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form . • HomogenizedHeatConduction • JouleHeatingSourceDemonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form . • SpecificHeatConductionTimeDerivativeTime derivative term of the heat equation with the specific heat and the density as arguments. • Richards App • DarcyFluxDarcy flux. nabla_i (k_ij/mu (nabla_j P - w_j)), where k_ij is the permeability tensor, mu is the fluid viscosity, P is the fluid pressure, and w_j is the fluid weight • PoroFullSatTimeDerivativeKernel = biot_coefficient*d(volumetric_strain)/dt + (1/biot_modulus)*d(porepressure)/dt. This is the time-derivative for poromechanics for a single-phase, fully-saturated fluid with constant bulk modulus • Q2PNegativeNodalMassOld- fluid_mass • Q2PNodalMassFluid mass lumped to the nodes divided by dt • Q2PPorepressureFluxFlux according to Darcy-Richards flow. The Variable for this Kernel should be the porepressure. • Q2PSaturationDiffusionDiffusion part of the Flux according to Darcy-Richards flow. The Variable of this Kernel must be the saturation. • Q2PSaturationFluxFlux according to Darcy-Richards flow. The Variable of this Kernel must be the saturation • RichardsFlux • RichardsFullyUpwindFlux • RichardsLumpedMassChange • RichardsMassChangeThe time derivative operator with the weak form of . • RichardsPPenaltyThis adds a term to the residual that attempts to enforce variable > lower_var. The term is a*(lower - variable) for variable • Tensor Mechanics App • CosseratStressDivergenceTensorsStress divergence kernel for the Cartesian coordinate system • DynamicStressDivergenceTensorsResidual due to stress related Rayleigh damping and HHT time integration terms • GeneralizedPlaneStrainOffDiagGeneralized Plane Strain kernel to provide contribution of the out-of-plane strain to other kernels • GravityApply gravity. Value is in units of acceleration. • InertialForceCalculates the residual for the interial force () and the contribution of mass dependent Rayleigh damping and HHT time integration scheme ($\eta \cdot M \cdot ((1+\alpha)velq2-\alpha \cdot vel-old) \$)
• InertialForceBeamCalculates the residual for the interial force/moment and the contribution of mass dependent Rayleigh damping and HHT time integration scheme.
• InertialTorqueKernel for interial torque: density * displacement x acceleration
• MomentBalancing
• OutOfPlanePressureApply pressure in the out-of-plane direction in 2D plane stress or generalized plane strain models
• PhaseFieldFractureMechanicsOffDiagStress divergence kernel for phase-field fracture: Computes off diagonal damage dependent Jacobian components. To be used with StressDivergenceTensors or DynamicStressDivergenceTensors.
• PlasticHeatEnergyPlastic heat energy density = coeff * stress * plastic_strain_rate
• PoroMechanicsCouplingAdds , where the subscript is the component.
• StressDivergenceBeamQuasi-static and dynamic stress divergence kernel for Beam element
• StressDivergenceRSphericalTensorsCalculate stress divergence for an spherically symmetric 1D problem in polar coordinates.
• StressDivergenceRZTensorsCalculate stress divergence for an axisymmetric problem in cylinderical coordinates.
• StressDivergenceTensorsStress divergence kernel for the Cartesian coordinate system
• StressDivergenceTensorsTrussKernel for truss element
• WeakPlaneStressPlane stress kernel to provide out-of-plane strain contribution
• DynamicTensorMechanics
• PoroMechanics
• TensorMechanics
• Porous Flow App
• PorousFlowAdvectiveFluxFully-upwinded advective flux of the component given by fluid_component
• PorousFlowBasicAdvectionAdvective flux of a Variable using the Darcy velocity of the fluid phase
• PorousFlowDesorpedMassTimeDerivativeDesorped component mass derivative wrt time.
• PorousFlowDesorpedMassVolumetricExpansionDesorped_mass * rate_of_solid_volumetric_expansion
• PorousFlowDispersiveFluxDispersive and diffusive flux of the component given by fluid_component in all phases
• PorousFlowEffectiveStressCouplingAdds , where the subscript is the component.
• PorousFlowEnergyTimeDerivativeDerivative of heat-energy-density wrt time
• PorousFlowExponentialDecayResidual = rate * (variable - reference). Useful for modelling exponential decay of a variable
• PorousFlowFullySaturatedDarcyBaseDarcy flux suitable for models involving a fully-saturated, single phase, single component fluid. No upwinding is used
• PorousFlowFullySaturatedDarcyFlowDarcy flux suitable for models involving a fully-saturated single phase, multi-component fluid. No upwinding is used
• PorousFlowFullySaturatedHeatAdvectionHeat flux that arises from the advection of a fully-saturated single phase fluid. No upwinding is used
• PorousFlowFullySaturatedMassTimeDerivativeFully-saturated version of the single-component, single-phase fluid mass derivative wrt time
• PorousFlowHeatAdvectionFully-upwinded heat flux, advected by the fluid
• PorousFlowHeatConductionHeat conduction in the Porous Flow module
• PorousFlowHeatVolumetricExpansionEnergy-density*rate_of_solid_volumetric_expansion
• PorousFlowMassRadioactiveDecayRadioactive decay of a fluid component
• PorousFlowMassTimeDerivativeComponent mass derivative wrt time for component given by fluid_component
• PorousFlowMassVolumetricExpansionComponent_mass*rate_of_solid_volumetric_expansion
• PorousFlowPlasticHeatEnergyPlastic heat energy density source = (1 - porosity) * coeff * stress * plastic_strain_rate
• PorousFlowPreDisPrecipitation-dissolution of chemical species
• Navier Stokes App
• DistributedForce
• DistributedPower
• INSChorinCorrectorThis class computes the 'Chorin' Corrector equation in fully-discrete (both time and space) form.
• INSChorinPredictorThis class computes the 'Chorin' Predictor equation in fully-discrete (both time and space) form.
• INSChorinPressurePoissonThis class computes the pressure Poisson solve which is part of the 'split' scheme used for solving the incompressible Navier-Stokes equations.
• INSCompressibilityPenaltyThe penalty term may be used when Dirichlet boundary condition is applied to the entire boundary.
• INSMassThis class computes the mass equation residual and Jacobian contributions for the incompressible Navier-Stokes momentum equation.
• INSMassRZThis class computes the mass equation residual and Jacobian contributions for the incompressible Navier-Stokes momentum equation in RZ coordinates.
• INSMomentumLaplaceFormThis class computes momentum equation residual and Jacobian viscous contributions for the 'Laplacian' form of the governing equations.
• INSMomentumLaplaceFormRZThis class computes additional momentum equation residual and Jacobian contributions for the incompressible Navier-Stokes momentum equation in RZ (axisymmetric cylindrical) coordinates, using the 'Laplace' form of the governing equations.
• INSMomentumTimeDerivativeThis class computes the time derivative for the incompressible Navier-Stokes momentum equation.
• INSMomentumTractionFormThis class computes momentum equation residual and Jacobian viscous contributions for the 'traction' form of the governing equations.
• INSMomentumTractionFormRZThis class computes additional momentum equation residual and Jacobian contributions for the incompressible Navier-Stokes momentum equation in RZ (axisymmetric cylindrical) coordinates.
• INSPressurePoissonThis class computes the pressure Poisson solve which is part of the 'split' scheme used for solving the incompressible Navier-Stokes equations.
• INSProjectionThis class computes the 'projection' part of the 'split' method for solving incompressible Navier-Stokes.
• INSSplitMomentumThis class computes the 'split' momentum equation residual.
• INSTemperatureThis class computes the residual and Jacobian contributions for the incompressible Navier-Stokes temperature (energy) equation.
• INSTemperatureTimeDerivativeThis class computes the time derivative for the incompressible Navier-Stokes momentum equation.
• MassConvectiveFlux
• MomentumConvectiveFlux
• NSEnergyInviscidFluxThis class computes the inviscid part of the energy flux.
• NSEnergyThermalFluxThis class is responsible for computing residuals and Jacobian terms for the k * grad(T) * grad(phi) term in the Navier-Stokes energy equation.
• NSEnergyViscousFluxViscous flux terms in energy equation.
• NSGravityForceThis class computes the gravity force contribution.
• NSGravityPowerThis class computes the momentum contributed by gravity.
• NSMassInviscidFluxThis class computes the inviscid flux in the mass equation.
• NSMomentumInviscidFluxThe inviscid flux (convective + pressure terms) for the momentum conservation equations.
• NSMomentumInviscidFluxWithGradPThis class computes the inviscid flux with pressure gradient in the momentum equation.
• NSMomentumViscousFluxDerived instance of the NSViscousFluxBase class for the momentum equations.
• NSSUPGEnergyCompute residual and Jacobian terms form the SUPG terms in the energy equation.
• NSSUPGMassCompute residual and Jacobian terms form the SUPG terms in the mass equation.
• NSSUPGMomentumCompute residual and Jacobian terms form the SUPG terms in the momentum equation.
• NSTemperatureL2This class was originally used to solve for the temperature using an L2-projection.
• TotalEnergyConvectiveFlux
• Fluid Properties Test App
• NaNInterfaceTestKernelKernel to test NaNInterface using NaNInterfaceTestFluidProperties
• Chemical Reactions App
• CoupledBEEquilibriumSubDerivative of equilibrium species concentration wrt time
• CoupledBEKineticDerivative of kinetic species concentration wrt time
• CoupledConvectionReactionSubConvection of equilibrium species
• CoupledDiffusionReactionSubDiffusion of equilibrium species
• DarcyFluxPressure
• DesorptionFromMatrixMass flow rate from the matrix to the porespace. Add this to TimeDerivative kernel to get complete DE for the fluid adsorbed in the matrix
• DesorptionToPorespaceMass flow rate to the porespace from the matrix. Add this to the other kernels for the porepressure variable to form the complete DE
• PrimaryConvectionConvection of primary species
• PrimaryDiffusionDiffusion of primary species
• PrimaryTimeDerivativeDerivative of primary species concentration wrt time
• Misc Test App
• Convection
| 2018-12-13T06:28:51 |
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|
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/56cff5a181fccb446af45e70
|
### Perpendicular from center to chord:
Perpendicular bisector of a chord passes through the center of a circle. In a circle a radius is perpendicular to a chord then the radius bisects the chord. If in a circle a radius bisects a chord then the radius is perpendicular to the chord, if in a circle a radius bisects a chord then the radius bisects the corresponding arc too, if a straight line bisects a chord of a circle and is perpendicular to the chord then the straight line passes through the center of the circle, and
| 2020-08-14T23:49:05 |
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https://par.nsf.gov/biblio/10339425-simulation-sensitivities-phased-icecube-gen2-deployment
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This content will become publicly available on March 18, 2023
Simulation and sensitivities for a phased IceCube-Gen2 deployment
The IceCube Neutrino Observatory opened the window on high-energy neutrino astronomy by confirming the existence of PeV astrophysical neutrinos and identifying the first compelling astrophysical neutrino source in the blazar TXS0506+056. Planning is underway to build an enlarged detector, IceCube-Gen2, which will extend measurements to higher energies, increase the rate of observed cosmic neutrinos and provide improved prospects for detecting fainter sources. IceCube-Gen2 is planned to have an extended in-ice optical array, a radio array at shallower depths for detecting ultra-high-energy (>100 PeV) neutrinos, and a surface component studying cosmic rays. In this contribution, we will discuss the simulation of the in-ice optical component of the baseline design of the IceCube-Gen2 detector, which foresees the deployment of an additional ~120 new detection strings to the existing 86 in IceCube over ~7 Antarctic summer seasons. Motivated by the phased construction plan for IceCube-Gen2, we discuss how the reconstruction capabilities and sensitivities of the instrument are expected to progress throughout its deployment.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10339425
Journal Name:
37th International Cosmic Ray Conference (ICRC2021)
Volume:
395
Page Range or eLocation-ID:
1186
3. Abstract Since summer 2021, the Radio Neutrino Observatory in Greenland (RNO-G) is searching for astrophysical neutrinos at energies $${>10}$$ > 10 PeV by detecting the radio emission from particle showers in the ice around Summit Station, Greenland. We present an extensive simulation study that shows how RNO-G will be able to measure the energy of such particle cascades, which will in turn be used to estimate the energy of the incoming neutrino that caused them. The location of the neutrino interaction is determined using the differences in arrival times between channels and the electric field of the radio signal ismore »
| 2022-09-26T14:08:40 |
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|
http://trilinos.sandia.gov/packages/docs/dev/packages/ifpack/doc/html/classIfpack__BlockRelaxation.html
|
IFPACK Development
Ifpack_BlockRelaxation< T > Class Template Reference
Ifpack_BlockRelaxation: a class to define block relaxation preconditioners of Epetra_RowMatrix's. More...
#include <Ifpack_BlockRelaxation.h>
Inheritance diagram for Ifpack_BlockRelaxation< T >:
[legend]
Collaboration diagram for Ifpack_BlockRelaxation< T >:
[legend]
List of all members.
## Public Member Functions
int NumLocalBlocks () const
Returns the number local blocks.
virtual bool IsInitialized () const
Returns true if the preconditioner has been successfully computed.
virtual bool IsComputed () const
Returns true if the preconditioner has been successfully computed.
virtual int SetParameters (Teuchos::ParameterList &List)
Sets all the parameters for the preconditioner.
virtual int Initialize ()
Initializes the preconditioner.
virtual int Compute ()
Computes the preconditioner.
virtual const Epetra_RowMatrixMatrix () const
Returns a pointer to the matrix to be preconditioned.
virtual double Condest (const Ifpack_CondestType CT=Ifpack_Cheap, const int MaxIters=1550, const double Tol=1e-9, Epetra_RowMatrix *Matrix_in=0)
Computes the condition number estimate, returns its value.
virtual double Condest () const
Returns the computed condition number estimate, or -1.0 if not computed.
std::ostream & Print (std::ostream &os) const
Prints basic information on iostream. This function is used by operator<<.
virtual int NumInitialize () const
Returns the number of calls to Initialize().
virtual int NumCompute () const
Returns the number of calls to Compute().
virtual int NumApplyInverse () const
Returns the number of calls to ApplyInverse().
virtual double InitializeTime () const
Returns the time spent in Initialize().
virtual double ComputeTime () const
Returns the time spent in Compute().
virtual double ApplyInverseTime () const
Returns the time spent in ApplyInverse().
virtual double InitializeFlops () const
Returns the number of flops in the initialization phase.
virtual double ComputeFlops () const
Returns the number of flops in the computation phase.
virtual double ApplyInverseFlops () const
Returns the number of flops in the application of the preconditioner.
Ifpack_BlockRelaxation (const Epetra_RowMatrix *Matrix)
Ifpack_BlockRelaxation constructor with given Epetra_RowMatrix.
virtual int Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
Applies the matrix to an Epetra_MultiVector.
virtual int ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
Applies the block Jacobi preconditioner to X, returns the result in Y.
virtual double NormInf () const
Returns the infinity norm of the global matrix (not implemented)
virtual int SetUseTranspose (bool UseTranspose_in)
virtual const char * Label () const
virtual bool UseTranspose () const
Returns the current UseTranspose setting.
virtual bool HasNormInf () const
Returns true if the this object can provide an approximate Inf-norm, false otherwise.
virtual const Epetra_CommComm () const
Returns a pointer to the Epetra_Comm communicator associated with this operator.
virtual const Epetra_MapOperatorDomainMap () const
Returns the Epetra_Map object associated with the domain of this operator.
virtual const Epetra_MapOperatorRangeMap () const
Returns the Epetra_Map object associated with the range of this operator.
## Detailed Description
### template<typename T> class Ifpack_BlockRelaxation< T >
Ifpack_BlockRelaxation: a class to define block relaxation preconditioners of Epetra_RowMatrix's.
The Ifpack_BlockRelaxation class enables the construction of block relaxation preconditioners of an Epetra_RowMatrix. Ifpack_PointRelaxation is derived from the Ifpack_Preconditioner class, which is derived from Epetra_Operator. Therefore this object can be used as preconditioner everywhere an ApplyInverse() method is required in the preconditioning step.
The class currently support:
• block Jacobi;
• block Gauss-Seidel;
• symmetric block Gauss-Seidel.
The idea of block relaxation method is to extend their point relaxation counterpart (implemented in Ifpack_PointRelaxation), by working on a group of equation simulteneously. Generally, larger blocks result in better convergence and increased robusteness.
The user can decide:
• the number of blocks (say, NumBlocks). If NumBlocks is equal to the number of rows, then the resulting scheme is equivalent to a point relaxation scheme;
• how to apply the inverse of each diagonal block, by choosing a dense container or a sparse container. The implementation of block relaxation schemes requires the application of the inverse of each diagonal block. This can be done using LAPACK (dense container), or any Ifpack_Preconditioner derived class (sparse container);
• blocks can be defined using a linear decomposition, by a simple greedy algorithm, or by resorting to METIS.
The following is an example of usage of this preconditioner with dense containers. First, we include the header files:
#include "Ifpack_AdditiveSchwarz.h"
#include "Ifpack_BlockPreconditioner.h"
#include "Ifpack_DenseContainer.h"
Then, we declare the preconditioner. Note that this is done through the class Ifpack_AdditiveSchwarz (see note below in this section).
// A is an Epetra_RowMatrix
// List is a Teuchos::ParameterList
IFPACK_CHK_ERR(Prec.SetParameters(List));
IFPACK_CHK_ERR(Prec.Initialize());
IFPACK_CHK_ERR(Prec.Compute());
// action of the preconditioner is given by ApplyInverse()
// Now use it in AztecOO, solver is an AztecOO object
solver.SetPrecOperator(&Prec);
The complete list of supported parameters is reported in page List of Supported Parameters. For a presentation of basic relaxation schemes, please refer to page Ifpack_PointRelaxation.
Date:
Definition at line 137 of file Ifpack_BlockRelaxation.h.
## Constructor & Destructor Documentation
template<typename T >
Ifpack_BlockRelaxation< T >::Ifpack_BlockRelaxation ( const Epetra_RowMatrix * Matrix )
Ifpack_BlockRelaxation constructor with given Epetra_RowMatrix.
Creates an Ifpack_Preconditioner preconditioner.
Parameters:
In Matrix - Pointer to matrix to be preconditioned.
Definition at line 451 of file Ifpack_BlockRelaxation.h.
References Epetra_Operator::Comm(), and Epetra_Comm::NumProc().
## Member Function Documentation
template<typename T >
int Ifpack_BlockRelaxation< T >::Apply ( const Epetra_MultiVector & X, Epetra_MultiVector & Y ) const [virtual]
Applies the matrix to an Epetra_MultiVector.
Parameters:
In X - A Epetra_MultiVector of dimension NumVectors to multiply with matrix. Out Y -A Epetra_MultiVector of dimension NumVectors containing the result.
Returns:
Integer error code, set to 0 if successful.
Implements Epetra_Operator.
Definition at line 494 of file Ifpack_BlockRelaxation.h.
template<typename T >
int Ifpack_BlockRelaxation< T >::ApplyInverse ( const Epetra_MultiVector & X, Epetra_MultiVector & Y ) const [virtual]
Applies the block Jacobi preconditioner to X, returns the result in Y.
Parameters:
In X - A Epetra_MultiVector of dimension NumVectors to be preconditioned. Out Y -A Epetra_MultiVector of dimension NumVectors containing result.
Returns:
Integer error code, set to 0 if successful.
Implements Ifpack_Preconditioner.
Definition at line 599 of file Ifpack_BlockRelaxation.h.
References Epetra_MultiVector::NumVectors(), and Epetra_MultiVector::Pointers().
The documentation for this class was generated from the following file:
| 2014-04-25T05:19:05 |
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|
https://malegislature.gov/Laws/GeneralLaws/PartI/TitleXXII/Chapter156D/Section8.21
|
# General Laws
## Section 8.21 Action without meeting
Section 8.21. ACTION WITHOUT MEETING
(a) Unless the articles of organization or bylaws provide that action required or permitted by this chapter to be taken by the directors may be taken only at a meeting, the action may be taken without a meeting if the action is taken by the unanimous consent of the members of the board of directors. The action must be evidenced by 1 or more consents describing the action taken, in writing, signed by each director, or delivered to the corporation by electronic transmission, to the address specified by the corporation for the purpose or, if no address has been specified, to the principal office of the corporation, addressed to the secretary or other officer or agent having custody of the records of proceedings of directors, and included in the minutes or filed with the corporate records reflecting the action taken.
(b) Action taken under this section is effective when the last director signs or delivers the consent, unless the consent specifies a different effective date.
(c) A consent signed or delivered under this section has the effect of a meeting vote and may be described as such in any document.
| 2016-02-12T13:33:01 |
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https://diamondhuntonline.fandom.com/wiki/Vendor
|
## FANDOM
479 Pages
The Vendor quest is accessible from level 300. You have to complete his quest in order to get access to him and his trades.
To impress the Vendor, players need to show him 5 rare and/or high value items. Showing a Blood Diamond will impress him instantly without 4 other items.
After completing his quest, he allows to trade items with him. Below are tables of the 50 items that can be selected from to impress the Vendor. The first is a table of the 33 items tested not to work; the second is comprised of the 16 items that are confirmed to work; the third lists the items that have not yet been tested (as of this edit, only the Faradox Tomb Key hasn't been checked):
### UnimpressiveEdit
Ores Gems Logs Leaves Bones Fish Others
### ImpressiveEdit
Ores Gems Logs Leaves Bones Fish Others
### UntestedEdit
As of this page's latest edit, the five cheapest items from the Player Market that impress the Vendor are: Moonstone (~20,000), Promethium (~60,000), Strange Logs (~75,000), Stardust Logs (~90,000), and Mars Rocks (~175,000). If you can't get one of these moon bones might - MAYBE - be the next best.
## Mechanism Edit
The vendor will change his set of three items randomly every 12 hours. It's possible to have repetitive items in a set.
There are currently 37 possible sets of unique trades. The chance to get at least one desired trade in a set of three each time would be calculated via this formula:
$P = \frac{Pr_{(n,q)} - Pr_{(n-1,q)}}{Pr_{(n,q)}}$ where
$Pr_{(n,q)} = n^q$ and
$Pr_{(n-1,q)} = (n-1)^q$
n = 37, q = 3
P = 1 - (36/37)^3 = 0.079 or 7.9%
With this chance, one should have 38.96% chance to get at least one desired trade after 3 days. The formula is binomial probability with at least one.
$P_2 = 1 - P_{(n, q, k)}$ where
$P_{(n, q, k)} = C_{(n,q)}k^q(1-k)^{n-q}$ and
$C_{(n, q)} = \frac{n!}{q!(n-q)!}$
n = 6, q = 0, k = 0.079
C(6, 0) = 1
P(6, 0, 0.079) = 1 * 0.079^0 * 0.921^6 = 0.61
P2 = 1 - 0.61 = 0.389
Days Chance
3 38.96%
6 62.75%
10 80.71%
## List of all tradable items Edit
Vendor sells Players give Remarks 1 3 This is currently the only way to get this item 1 1 1 This is currently the only way to get this item 1 SmeltingSpeed 1,000 1,000 1,000 1,000 This is currently the only way to get this item 149 - 431 10 Assuming Bones sell for 60k at the Market, and Threads sell for 30k, this is only profitable at 400+ Webs; 315 Webs if 55k/35k, respectively 1 3 1 3 1 5 2 - 10 1 1 1,000 1 - 8 3 1 1 As weird as this trade may look, it's actually a nice way to get some free cooking exp by re-cooking sharks 1,328 - 5,000 500 5 - 20 15 Generally not worth it 6 - 20 2 Generally not worth it 1 - 5 20,000 50,000 1 - 10 5 1 200 - 800 1 500 - 1,500 50,000 Generally not worth it, as gold bars aren't needed a lot and can be smelted 1,000 - 2,487 400 - 500 Although sand is rare in early game, this trade is very worth it when you're in late game and don't know what to do with all of this sand 200 - 800 1 1 200 - 800 3 104 - 906 10 Definitely not worth it, based on current market prices 52 - 115 50 200-490 150 (workers are a better choice) 10 - 30 1,500,000 / 2,000,000 Generally not worth it (workers are a better choice) 12 - 20 5,000,000 Generally not worth it (workers are a better choice) 1 - 5 2 1 2 1 - 6 500 Not worth it in terms of wood income, but gives you some free farming XP 1 - 5 1 1 2 150,000 - 1,000,000 25 25 100,000 - 150,000 1 Assuming Raw Swordfish sell for 350k at the Market, and Stardust sells for 10, this trade is always worth doing 1 - 50 50 50 Unless he offers 30+ bait, it is generally not worth it 1 - 3 1 If he's offering 2+ pancakes, it's worth it in term of energy, but you lose the potential cooking exp 10 - 100 375,000 1 - 2 1 If he is offering 2 fish stews, it's worth it in term of energy. 502,000 - 2,000,000 250,000 250,000 If the Vendor is offering over 1,000,000 stone, it is worth it as you are making profit when reselling them at the NPC store. 2,600,000-5,000,000 1,400,000 Generally not worth it, unless one is desperate to get stone 467 - 950 3 378 - 591 8 27 20 38 20 5-26 20
## Trivia Edit
• Each of his item varies in amount, while player's items are usually a fixed amount.
• When players are offline, the vendor timer won't run after the 12 hours renewal rotation. Players need to log in to trigger it.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-04-03T08:21:08 |
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|
http://adriann.github.io/ballsBins.html
|
Suppose you are a poor orkish messenger and have $n$ rings to distribute to the $n$ elven-kings under the sky. Of course each is supposed to get their own, but you’re lazy and the nasty elves all look the same anyway.
Due to your extensive experience with chaos randomization you quickly see that throwing rings at elves randomly is in expectation just as good. The number of rings for each elf is distributed as $\mbox{Bin}(n,1/n)$, so the expectation is one. You might also know that binomial random variables are pretty strongly concentrated around their expectation and you don’t think the dependencies between the elves will change anything about that.
Your boss however would like some more arguments why your approach is good enough. Let’s try to compute the maximum number of rings any elf will get.
The knowledgeable reader probably recognizes this as a classical balls-into-bins settings with all the immediate applications to scheduling, hashing, and so forth. From here I will use the more standard nomenclature.
## Counting Bins
This seems like a difficult problem to tackle, but it turns out we can use the first moment method1 on appropriately defined random variables.
As it is so often the case, ‘appropriately’ defining things gets you half way to a solution. The first moment method allows us to show that a random variable will be zero asymptotically almost surely. In our application we want to show that there will be no bins with a large number of balls, so let’s define $X\_k$ to count the number of bins who have $k$ or more rings.
As we already observed the number of balls is binomially distributed, so it is not so difficult to bound the probability that a bin contains more than $k$. To make things easier, we will use the Poisson approximation2 and cheat a little with the constant factors involved. $\mbox{Pr}(\mbox{elf has }\geq k \mbox{ rings})= \mbox{Pr}(\mbox{Bin}(n,1/n)\geq k) \leq n \mbox{Pr}(\mbox{Pois}(1) = k) =n e^{-1} \cdot \frac{1}{k!}\approx ne^{-1} \cdot 2^{-k \log k} \approx e^{\log n - k \log k}$
We used Stirling to approximate $k! \approx 2^{k\log k}$. By defining an indicator for every bin we see that the expectation is just $\mathbb{E}(X_k) \leq e^{2\log n - k \log k}$. Clearly this expectation goes to zero for $k \geq \frac{c\log n}{\log \log n}$ for some suitable $c$, depending on the exact values of the constants in the exponent.
## Remarks
Our sloppy calculations show that the number of bins with more than $O(\log n/\log \log n)$ balls is zero a.a.s., and hence the maximum load is sublogarithmic with high probability. The interested reader might want to show, using a variance calculation, that this bound is tight. Not bad for such a simple algorithm! If you’re feeling adventurous, you can try the exercise at the end of this blog post to see how much a simple twist can improve the algorithm. Perhaps I’ll write a bit about that in a different post.
You might be a little disappointed at how slowly the expectation goes to zero, but rest assured that this is just a symptom of our weak tools. After all we used nothing more advanced than Markov’s inequality! It is entirely possible (and indeed a common textbook example) to derive much stronger bounds by applying Chernoff-type bounds on a series of appropriately conditioned Poisson random variables, see for example chapter 5 of the excellent book Probability and Computing by Mitzenmacher and Upfal.
## Exercise
Intuitively you could do a little better by distributing the rings in rounds. In each round you pick two elves and give a ring to the elf who currently has fewer. Can you still compute the maximum number of rings a single elf will get?
1. Recently discussed in relation to triangles in random graphs.
2. I told you the Poisson distribution is useful in this post
CC-BY-SA Adrian Neumann (PGP Key A0A8BC98)
| 2017-04-28T12:01:31 |
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|
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2010.28.649
|
Article Contents
Article Contents
Existence of solutions for a semilinear wave equation with non-monotone nonlinearity
• For double-periodic and Dirichlet-periodic boundary conditions, we prove the existence of solutions to a forced semilinear wave equation with asymptotically linear nonlinearity, no resonance, and non-monotone nonlinearity when the forcing term is not flat on characteristics. The solutions are in $L^{\infty}$ when the forcing term is in $L^{\infty}$ and continous when the forcing term is continuous. This is in contrast with the results in [4], where the non-enxistence of continuous solutions is established even when forcing term is of class $C^{\infty}$ but isflat on a characteristic.
Mathematics Subject Classification: Primary: 35L71; Secondary: 47H09, 47H10.
Citation:
Open Access Under a Creative Commons license
| 2022-11-27T19:03:35 |
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|
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/10%3A__Nuclear_Physics/10.A%3A_Nuclear_Physics_(Answers)
|
$$\require{cancel}$$
10.1. eight
10.2. harder
10.3. Half-life is inversely related to decay rate, so the half-life is short. Activity depends on both the number of decaying particles and the decay rate, so the activity can be great or small.
10.4. Neither; it stays the same.
10.5. the same
10.6. the conversion of mass to energy
10.7. power
Conceptual Questions
1. The nucleus of an atom is made of one or more nucleons. A nucleon refers to either a proton or neutron. A nuclide is a stable nucleus.
3. A bound system should have less mass than its components because of energy-mass equivalence $$\displaystyle (E=mc^2)$$. If the energy of a system is reduced, the total mass of the system is reduced. If two bricks are placed next to one another, the attraction between them is purely gravitational, assuming the bricks are electrically neutral. The gravitational force between the bricks is relatively small (compared to the strong nuclear force), so the mass defect is much too small to be observed. If the bricks are glued together with cement, the mass defect is likewise small because the electrical interactions between the electrons involved in the bonding are still relatively small.
5. Nucleons at the surface of a nucleus interact with fewer nucleons. This reduces the binding energy per nucleon, which is based on an average over all the nucleons in the nucleus.
7. That it is constant.
9. Gamma (γ) rays are produced by nuclear interactions and X-rays and light are produced by atomic interactions. Gamma rays are typically shorter wavelength than X-rays, and X-rays are shorter wavelength than light.
11. Assume a rectangular coordinate system with an xy-plane that corresponds to the plane of the paper. αα bends into the page (trajectory parabolic in the xz-plane); $$\displaystyle β^+$$ bends into the page (trajectory parabolic in the xz-plane); and $$\displaystyle γ$$ is unbent.
13. Yes. An atomic bomb is a fission bomb, and a fission bomb occurs by splitting the nucleus of atom.
15. Short-range forces between nucleons in a nucleus are analogous to the forces between water molecules in a water droplet. In particular, the forces between nucleons at the surface of the nucleus produce a surface tension similar to that of a water droplet.
17. The nuclei produced in the fusion process have a larger binding energy per nucleon than the nuclei that are fused. That is, nuclear fusion decreases average energy of the nucleons in the system. The energy difference is carried away as radiation.
19. Alpha particles do not penetrate materials such as skin and clothes easily. (Recall that alpha radiation is barely able to pass through a thin sheet of paper.) However, when produce inside the body, neighboring cells are vulnerable.
Problems
21. Use the rule $$\displaystyle A=Z+N$$.
Atomic Number (Z) Neutron Number (N) Mass Number (A) (a) 29 29 58 (b) 11 13 24 (c) 84 126 210 (d) 20 25 45 (e) 82 124 206
23. a. $$\displaystyle r=r_0A^{1/3},ρ=\frac{3u}{4πr_0^3}$$;
b. $$\displaystyle ρ=2.3×10^{17}kg/m^3$$
25. side length =$$\displaystyle 1.6μm$$
27. 92.4 MeV
29. $$\displaystyle 8.790MeV≈graph’s value$$
31. a. 7.570 MeV;
b. $$\displaystyle 7.591MeV≈$$graph’s value
33. The decay constant is equal to the negative value of the slope or $$\displaystyle 10^{−9}s^{−1}$$. The half-life of the nuclei, and thus the material, is $$\displaystyle T_{1/2}=693$$million years.
35. a. The decay constant is $$\displaystyle λ=1.99×10^{−5}s^{−1}$$
b. Since strontium-91 has an atomic mass of 90.90 g, the number of nuclei in a 1.00-g sample is initially
$$\displaystyle N_0=6.63×10^{21}nuclei$$.
The initial activity for strontium-91 is
$$\displaystyle A_0=λN_0=1.32×10^{17}decays/s$$
The activity at $$\displaystyle t=15.0$$ $$\displaystyle h=5.40×10^4s$$ is
$$\displaystyle A=4.51×10^{16}decays/s$$.
37. $$\displaystyle 1.20×10^{−2}mol; 6.00×10^{−3}mol; 3.75×10^{−4}mol$$
39. a. 0.988 Ci;
b. The half-life of $$\displaystyle ^{226}Ra$$ is more precisely known than it was when the Ci unit was established.
41. a. $$\displaystyle 2.73μg$$;
b. $$\displaystyle 9.76×10^4Bq$$
43. a. $$\displaystyle 7.46×10^5Bq$$;
b. $$\displaystyle 7.75×10^5Bq$$
45. a. 4.273 MeV;
b. $$\displaystyle 1.927×10^{−5}$$;
c. Since $$\displaystyle ^{238}U$$ is a slowly decaying substance, only a very small number of nuclei decay on human timescales; therefore, although those nuclei that decay lose a noticeable fraction of their mass, the change in the total mass of the sample is not detectable for a macroscopic sample.
47. a. $$\displaystyle ^{90}_{38}Sr_{52}→^{90}_{39}Y_{51}+β^{−1}+\bar{v_e}$$;
b. 0.546 MeV
49. $$\displaystyle ^{3}_1H_2→^3_2He_1+β^−+\bar{v_e}$$
51. a. $$\displaystyle ^7_4Be+3+e^−→^7_3Li_4+v_e$$;
b. 0.862 MeV
53. a. $$\displaystyle X=^{208}_{82}Pb_{126}$$;
b. 33.05 MeV
55. a. 177.1 MeV;
b. This value is approximately equal to the average BEN for heavy nuclei.
c. $$\displaystyle n+^{238}_{92}U_{146}→^{96}_{38}Sr_{58}+^{140}_{54}Xe_{86}+3n$$,
$$\displaystyle A_i=239=A_f$$,
$$\displaystyle Z_i=92=38+54=Z_f$$
57. a. $$\displaystyle 2.57×10^3MW$$;
b. $$\displaystyle 8.04×10^{19}$$ fissions/s;
c. 991 kg
59. i. $$\displaystyle ^1_1H+^1_1H→^2_1H+e^++v_e$$
$$\displaystyle A+i=1+1=2;A_f=2, Z_i=1+1=2;$$
$$\displaystyle Z_f=1+1=2$$
ii. $$\displaystyle ^1_1H+^2_1H→^3_2H+γ$$
$$\displaystyle A_i=1+2=3;A_f=3+0=3, Z_i=1+1=2$$
$$\displaystyle Z_E=1+1=2$$;
iii. $$\displaystyle ^3_2H+^3_2H→^4_2H+^1_1H+^1_1H$$
$$\displaystyle A_i=3+3=6;A_f=4+1+1=6, Z_i=2+2=4$$
$$\displaystyle Z_f=2+1+1=4$$
61. 26.73 MeV
63. a. $$\displaystyle 3×10^{38}protons/s$$;
b. $$\displaystyle 6×10^{14}neutrinos/m^2⋅s$$;
This huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.
65. a. The atomic mass of deuterium $$\displaystyle (^2H)$$ is 2.014102 u, while that of tritium $$\displaystyle (^3H)$$ is 3.016049 u, for a total of 5.032151 u per reaction. So a mole of reactants has a mass of 5.03 g, and in 1.00 kg, there are $$\displaystyle (1000g)/(5.03g/mol)=198.8mol$$ of reactants. The number of reactions that take place is therefore
$$\displaystyle (198.8mol)(6.02×10^{23}mol^{−1})=1.20×10^{26}reactions$$.
The total energy output is the number of reactions times the energy per reaction:
$$\displaystyle E=3.37×10^{14}J$$;
b. Power is energy per unit time. One year has $$\displaystyle 3.16×10^7s$$, so
$$\displaystyle P=10.7MW$$.
We expect nuclear processes to yield large amounts of energy, and this is certainly the case here. The energy output of $$\displaystyle 3.37×10^{14}J$$ from fusing 1.00 kg of deuterium and tritium is equivalent to 2.6 million gallons of gasoline and about eight times the energy output of the bomb that destroyed Hiroshima. Yet the average backyard swimming pool has about 6 kg of deuterium in it, so that fuel is plentiful if it can be utilized in a controlled manner.
67. $$\displaystyle G_y=\frac{Sv}{RBE}: a. 0.01 Gy; b. 0.0025 Gy; c. 0.16 Gy 69. 1.24 MeV 71. 1.69 mm 73. For cancer: \(\displaystyle (3rem)(\frac{10}{10^6rem⋅y})=\frac{30}{10^6y},$$ The risk each year of dying from induced cancer is 30 in a million. For genetic defect: $$\displaystyle (3rem)(\frac{3.3}{10^6rem⋅y})=\frac{9.9}{10^6y},$$ The chance each year of an induced genetic defect is 10 in a million.
75. atomic mass(Cl)=35.5g/mol
77. a. $$\displaystyle 1.71×10^{58}kg$$;
b. This mass is impossibly large; it is greater than the mass of the entire Milky Way galaxy.
c. $$\displaystyle ^{236}U$$ is not produced through natural processes operating over long times on Earth, but through artificial processes in a nuclear reactor.
79. If $$\displaystyle 10%$$ of rays are left after 2.00 cm, then only $$\displaystyle (0.100)^2=0.01=1%$$ are left after 4.00 cm. This is much smaller than your lab partner’s result ($$\displaystyle 5%$$).
81. a. $$\displaystyle 1.68×10^{−5}Ci$$;
(b) From Appendix B, the energy released per decay is 4.27 MeV, so $$\displaystyle 8.65×10^{10}J$$;
(c) The monetary value of the energy is $$\displaystyle 2.9×10^3$$
83. We know that $$\displaystyle λ=3.84×10^{−12}s^{−1}$$ and $$\displaystyle A_0=0.25decays/s⋅g=15decays/min⋅g$$.
Thus, the age of the tomb is
$$\displaystyle t=−\frac{1}{3.84×10^{−12}s^{−1}}ln\frac{10decays/min⋅g}{15decays/min⋅g}=1.06×10^{11}s≈3350y$$.
Challenge Problems
85. a. $$\displaystyle 6.97×10^{15}Bq$$;
b. 6.24 kW;
c. 5.67 kW
87. a. Due to the leak, the pressure in the turbine chamber has dropped significantly. The pressure difference between the turbine chamber and steam condenser is now very low.
b. A large pressure difference is required for steam to pass through the turbine chamber and turn the turbine.
89. The energies are
$$\displaystyle E_γ=20.6MeV$$
$$\displaystyle E_{4_{He}}=5.68×10^{−2}MeV$$.
Notice that most of the energy goes to the γγ ray.
Contributors
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
| 2019-07-21T11:22:14 |
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|
https://gea.esac.esa.int/archive/documentation/GDR2/Data_processing/chap_cu4sso/sec_cu4sso_QAV/ssec_cu4sso_phasemag.html
|
# 4.5.5 Analysis of the phase - magnitude relation
Author(s): Alberto Cellino
A key parameter to describe the illumination conditions at the epoch of the observation of an SSO is the so-called phase angle, defined as the angle between the directions to the Sun and to the observer, as measured from the centre of mass of the object. According to its definition, the phase angle is zero when the object is observed in conditions of ideal solar opposition (or in conjunction with the Sun, when it is not evidently observable), and it reaches an upper limit that depends upon the orbit of the object and of the observer. More distant solar system objects can be observed from the Earth, or from the Gaia orbit, only in a narrow interval of possible phase angles, whereas objects approaching or sweeping the inner solar system can be observed over a much wider interval of phase angles. Based on the sky scanning law of Gaia, only very distant Solar System objects can be seen not far from solar opposition whereas, in the case of main-belt asteroids, the interval of possible phase angles has a minimum value around 10 degrees.
It is known that asteroids tend to become fainter when observed at increasingly large phase angles. In the domain of phase angles covered by Gaia observations, the behaviour consists of a nearly-linear increase of magnitude (normalized to unit distance) for increasing phase angle. It is therefore useful, as a first preliminary check of the Gaia asteroid photometry, to analyze the phase-mag relation. This is shown in Figure 4.33, displaying the whole set of SSO transits, after removal of those not passing the colour-based filter described in Section 4.5.4. The magnitude data shown in Figure 4.33 were obtained after a preliminary conversion of apparent $G$ magnitudes into the values corresponding to unit distance from both the Sun and Gaia, using Equation 4.9. It is interesting to see in this plot the presence of a small number of transits of objects seen at small phase angles. These are distant objects, belonging to the Centaur population (Chiron) or to the even more distant population of Kuiper belt objects, including the dwarf-planets Pluto, Haumea and Makemake. Apart from these, the plot shows essentially the behaviour of the asteroid population (dominated by, but not limited to, main belt objects, as explained in Section 4.2.1). A general trend of decreasing brightness for increasing phase angle is seen as expected, but some apparently strange features and discontinuities are also present, and cannot be immediately interpreted in a straightforward way.
Some caveats are immediately important. First, one has to consider that asteroid magnitudes are subject to significant shape-dependent, cyclic variations due to rotation around the spin axis. In classical ground-based studies, one deals normally with full light-curves obtained at different phase angles, and the phase - mag relation is derived by considering only values of magnitude taken at the maximum (or minimum) or each light-curve, in order to avoid to mix together magnitude data corresponding to different cross-sections of the rotating body. Moreover, in ground-based studies data are generally collected during one single apparition of an object, namely during a relatively short interval of time (several weeks), during which the object is seen in a nearly constant geometric configuration, with only the illumination conditions, described by the phase angle, varying with time. In the case of available Gaia data, instead, we deal with sparse photometric measurements taken during a considerable interval of time. The phase - mag relation derived by such data is intrinsically noisy, because it includes measurements taken at epochs corresponding to different illuminated cross-sections, due both to differences of rotation around the spin axis, and to differences of the orientation of the body with respect to the line of sight, if data were taken at epochs sufficiently distant in time. In other words, the phase - mag curves obtained from Gaia transits are contaminated by magnitude variations that are not uniquely due to differences in phase angle.
Moreover, we also have to take into account that at this stage we still do not have in general many transits per object, and those that we have cover often intervals of phase angles that may be fairly small. In other words, an analysis of the phase - mag relation in Gaia DR2 is forcefully still tentative, and it is certain that the achievable results must be considered as very preliminary. However, this analysis has been attempted at this stage, just as an exercise aimed at checking that the currently available Gaia photometric data for asteroids do not exhibit macroscopic anomalies. The analysis considered the available transits for a sample of 8473 objects observed during the interval of interest. For each object, we first computed the conversion from the measured apparent magnitude to the value corresponding to unit distance from the Sun and from Gaia, based on the known values of heliocentric and Gaia-centric distances at each transit. For each object, among all the subsets of magnitudes measured during the same Julian day, generally corresponding to two or more consecutive detections in the two FOV of Gaia, only the brightest recorded magnitude was kept for the analysis, to limit the noise due to different angles of rotation of the object around its spin axis, so mimicking in part the procedures used to exploit full light-curves taken from the ground. At this stage, the rejection filter based on colour data described in Section 4.5.4 was also applied. Transits for which the measured G magnitude had a nominal error of 0.1 mag or larger, and/or the $G_{\rm BP}-G$ or $G-G_{\rm RP}$ had abnormal values were discarded a priori. The next step was to discard all objects for which the number of magnitude measurements (after removal of all but one measurement taken during the same Julian day) was less than 6, or the interval of phase angles covered by the observations was narrower than 5 degrees. For each accepted object, a further averaging was done of all the magnitudes obtained in bins of phase angles 1 degree in width (in a very few cases, the latter averaging could lead to accept objects for which the finally averaged transits could eventually cover an interval of phase angles a little smaller than 5 ${}^{\circ}$). Finally, a linear least-squares fit of magnitude versus phase was computed.
The number of objects satisfying the above criteria was 6797. Figure 4.34 shows the histograms of some parameters of fundamental importance for the analysis, namely the number of magnitude measurements per object and the width of the interval of phase angles covered by the observations of each object. It is easy to see that the number of available data per object is in the majority of cases no larger than 5, and only in a minority of cases the interval of phase angles covered by the observations reaches at least 10 ${}^{\circ}$. In these conditions, we cannot expect to obtain linear phase - magnitude relations of a good quality.
These expectations are confirmed by the results of our exercise. The distribution of the computed linear slopes, and the distribution of the corresponding formal errors, are shown in Figure 4.35. The existence of a non-negligible fraction of aberrant cases, including negative slopes (corresponding to objects for which the brightness seems to increase for increasing phase angle), is well visible. The distribution of slope errors shows that in many cases the resulting linear fits are far from being affected by small uncertainties.
The fact that in many cases the available data cannot be reliably fitted by a linear relation is also shown in Figure 4.36, in which the histogram of the obtained values for the correlation of linear fits are shown. It is easy to see that the distribution peaks at high correlation values, but a very large tail of poor correlation values is also well visible.
The results confirm therefore the existence of many cases in which it is not possible to produce good linear fits of available phase - magnitude data. This fact, however, should not be overemphasized, because in many cases reasonably good linear fits are obtained, with slopes which are perfectly compatible with those that are typically found from extensive ground-based measurements. In many cases, the aberrant results can be removed by simply imposing strict acceptance criteria in terms of input data quality and quality of the best-fit results. Figure 4.37 shows, as an example, that negative values of the phase - magnitude slope (plotted in red) are mostly found among faint asteroids for which only small numbers of transits are available for computation of a linear fit. In the same plot, it is also evident that negative slopes are preferentially obtained in cases of objects for which poor values of the linear correlation are found, and these are preferentially cases for which the interval of phase angle values covered by the observations is narrow.
The importance of removing linear fits of bad quality data is also shown in Figure 4.38, in which the computed linear slopes are plotted as a function of the width of the available interval of phase angles. By removing objects for which the number of observations is low, the correlation of the linear fit is bad and the resulting linear slope is affected by large uncertainties, the plot becomes much more acceptable, with a nearly total removal of the cases of aberrant slope values.
Summarizing, we can say that an analysis of the phase - magnitude relation using available SSO photometric data in Gaia DR2 indicates that in most circumstances the available data cover only small intervals of phase angle, and/or the number of observations is too small to produce the clean linear trends that are obtained by using full lightcurve data taken from the ground, and using only the lightcurve maxima to compute the fits. However, even with these limitations, it turns out that in the most favourable cases the objects observed in Gaia DR2 exhibit a phase - magnitude behaviour fully compatible with expectations, taking into account the unavoidable noise produced by using only limited numbers of sparse photometric data.
| 2018-09-24T17:28:22 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=M055A1&home=sumtabM
|
$\boldsymbol a_{2}$ = $\boldsymbol M2/\sqrt {\boldsymbol E1{}^{2}+\boldsymbol M2{}^{2} }$ Magnetic quadrupole fractional transition amplitude INSPIRE search
VALUE ($10^{-2}$) EVTS DOCUMENT ID TECN COMMENT
$\bf{ -6.7 \pm0.9}$ OUR AVERAGE Error includes scale factor of 2.6.
$-7.40$ $\pm0.33$ $\pm0.34$ 164k 1
2017 N
BES3 ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$
$-6.26$ $\pm0.63$ $\pm0.24$ 39k
2009
CLEO ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$
$0.2$ $\pm3.2$ $\pm0.4$ 2090
2002
E835 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \chi}_{{c1}}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \gamma}}$
$-0.2$ ${}^{+0.8}_{-2.0}$ 921
1982
CBAL ${{\mathit \psi}{(2S)}}$ $\rightarrow$ ${{\mathit \chi}_{{c1}}}{{\mathit \gamma}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \gamma}}{{\mathit \gamma}}$
1 Correlated with ${{\mathit b}_{{2}}}$ with correlation coefficient $\rho _{ {{\mathit a}_{{2}}} {{\mathit b}_{{2}}} }$ = 0.133.
$\mathit a_{2}$ = $\mathit M2/\sqrt {\mathit E1{}^{2}+\mathit M2{}^{2} }$
References:
ABLIKIM 2017N
PR D95 072004 Measurement of Higher-Order Multipole Amplitudes in ${{\mathit \psi}{(3686)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \chi}_{{c1,2}}}$ with ${{\mathit \chi}_{{c1,2}}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit J / \psi}}$ and Search for the Transition ${{\mathit \eta}_{{c}}{(2S)}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit J / \psi}}$
ARTUSO 2009
PR D80 112003 Higher-Order Multipole Amplitudes in Charmonium Radiative Transitions
AMBROGIANI 2002
PR D65 052002 Study of the Angular Distributions of the Reactions ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \chi}_{{c1}}}$ , ${{\mathit \chi}_{{c2}}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \gamma}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$
OREGLIA 1982
PR D25 2259 Study of the Reaction ${{\mathit \psi}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit J / \psi}}$
| 2020-02-27T06:07:53 |
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|
https://par.nsf.gov/biblio/10095221-arctic-mediterranean-exchanges-consistent-volume-budget-trends-transports-from-two-decades-observations
|
Arctic Mediterranean exchanges: a consistent volume budget and trends in transports from two decades of observations
Abstract. The Arctic Mediterranean (AM) is the collective name forthe Arctic Ocean, the Nordic Seas, and their adjacent shelf seas. Water enters into thisregion through the Bering Strait (Pacific inflow) and through the passages across theGreenland–Scotland Ridge (Atlantic inflow) and is modified within the AM. The modifiedwaters leave the AM in several flow branches which are grouped into two differentcategories: (1) overflow of dense water through the deep passages across theGreenland–Scotland Ridge, and (2) outflow of light water – here termed surface outflow– on both sides of Greenland. These exchanges transport heat and salt into and out ofthe AM and are important for conditions in the AM. They are also part of the global oceancirculation and climate system. Attempts to quantify the transports by various methodshave been made for many years, but only recently the observational coverage has becomesufficiently complete to allow an integrated assessment of the AM exchanges based solelyon observations. In this study, we focus on the transport of water and have collecteddata on volume transport for as many AM-exchange branches as possible between 1993 and2015. The total AM import (oceanic inflows plusfreshwater) is found to be 9.1 Sv (sverdrup,1 Sv =106 m3 s−1) with an estimated uncertainty of 0.7 Sv and hasthe amplitude more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10095221
Journal Name:
Ocean Science
Volume:
15
Issue:
2
Page Range or eLocation-ID:
379 to 399
ISSN:
1812-0792
2. Abstract. Triplet excited states of organic matter are formed when colored organicmatter (i.e., brown carbon) absorbs light. While these “triplets” can beimportant photooxidants in atmospheric drops and particles (e.g., theyrapidly oxidize phenols), very little is known about their reactivity towardmany classes of organic compounds in the atmosphere. Here we measure thebimolecular rate constants of the triplet excited state of benzophenone(3BP), a model species, with 17 water-solubleC3C6 alkenes that have either been found in theatmosphere or are reasonable surrogates for identified species. Measured rateconstants (${k}_{\mathrm{ALK}+\mathrm{3}{\mathrm{BP}}^{\ast }}$more ») vary by a factor of 30 and are in therange of (0.24–7.5) ×109 M−1 s−1. Biogenic alkenesfound in the atmosphere – e.g., cis-3-hexen-1-ol, cis-3-hexenyl acetate, andmethyl jasmonate – react rapidly, with rate constants above 1×109 M−1 s−1. Rate constants depend on alkene characteristicssuch as the location of the double bond, stereochemistry, and alkylsubstitution on the double bond. There is a reasonable correlation between${k}_{\mathrm{ALK}+\mathrm{3}{\mathrm{BP}}^{\ast }}$ and the calculated one-electron oxidation potential(OP) of the alkenes (R2=0.58); in contrast, rate constants are notcorrelated with bond dissociation enthalpies, bond dissociation freeenergies, or computed energy barriers for hydrogen abstraction. Using the OPrelationship, we estimate aqueous rate constants for a number of unsaturatedisoprene and limonene oxidation products with 3BP: values are inthe range of (0.080–1.7) ×109 M−1 s−1, withgenerally faster values for limonene products. Rate constants with lessreactive triplets, which are probably more environmentally relevant, arelikely roughly 25 times slower. Using our predicted rate constants, alongwith values for other reactions from the literature, we conclude thattriplets are probably minor oxidants for isoprene- and limonene-relatedcompounds in cloudy or foggy atmospheres, except in cases in which the tripletsare very reactive.
4. Abstract. Chemical ionization massspectrometry (CIMS) instruments routinely detect hundreds of oxidized organic compoundsin the atmosphere. A major limitation of these instruments is the uncertaintyin their sensitivity to many of the detected ions. We describe thedevelopment of a new high-resolution time-of-flight chemical ionization massspectrometer that operates in one of two ionization modes: using eitherammonium ion ligand-switching reactions such as for ${\mathrm{NH}}_{\mathrm{4}}^{+}$ CIMS orproton transfer reactions such as for proton-transfer-reaction massspectrometer (PTR-MS). Switching between the modes can be done within 2 min.The more » CIMS mode of the new instrument has sensitivities of upto 67 000 dcps ppbv−1 (duty-cycle-corrected ion counts per second perpart per billion by volume) and detection limits between 1 and 60 pptv at2σ for a 1 s integration time for numerous oxygenated volatileorganic compounds. We present a mass spectrometric voltage scanning procedurebased on collision-induced dissociation that allows us to determine thestability of ammonium-organic ions detected by the ${\mathrm{NH}}_{\mathrm{4}}^{+}$ CIMS instrument.Using this procedure, we can effectively constrain the sensitivity of theammonia chemical ionization mass spectrometer to a wide range of detectedoxidized volatile organic compounds for which no calibration standards exist.We demonstrate the application of this procedure by quantifying thecomposition of secondary organic aerosols in a series of laboratoryexperiments.
| 2022-07-02T06:12:14 |
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|
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2016.07.014
|
• 论文 •
### 基于自适应在线极限学习机模型的预测方法
• 出版日期:2016-07-15 发布日期:2016-07-06
### Study on Prediction Method Based on Adaptive Ensemble Online Sequential Extreme learning machine
Xu Yong et al.
• Online:2016-07-15 Published:2016-07-06
Abstract:
Since the single online sequential extreme learning machine's performance is unstable, it propose an adaptive and selective OSELM. Firstly，it initializes the multiple online sequential extreme learning machine model, then adjustes adaptively the integrated weight of every online sequential extreme learning machine according to their training error and variance for each batch of data, and deletes the model that its integrated weight is smaller than the threshold to improve the training speed dynamically. Finally, the high accuracy and good generalization's model will be selected for integrated prediction. Experimental results show that the ASE-OSELM has higher forecast accuracy and generalization ability than BPNN、LS-SVM and OSELM.
| 2022-07-05T06:15:00 |
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|
http://dergipark.gov.tr/hujms/issue/38121/440361
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Yıl 2018, Cilt 47, Sayı 3, Sayfalar 659 - 673 2018-06-01
| | | |
Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable
Muhammad Irfan [1] , Maria Javed [2] , Muhammad Abid [3] , Zhengyan Lin [4]
31 124
This paper deals with efficient ratio type estimators for estimating finite population mean under simple random sampling scheme by using the knowledge of known median of a study and an auxiliary variable. Expressions for the bias and mean squared error of the proposed ratio type estimators are derived up to first order of approximation. It is found that our proposed estimators perform better as compared to the traditional ratio estimator, regression estimator, Subramani and Kumarapandiyan [23], Subramani and Prabavathy [24] and Yadav et al. [28] estimators. In addition, theoretical findings are veried with the help of real data sets.
Auxiliary variables, Bias, E ciency, Median, Mean squared error, Ratio estimators, RRMSE
• Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. Enhancing the mean ratio estimators for es- timating population mean using non-conventional location parameters, Revista Colombiana de Estadistica 39 (1), 63-79, 2016(a).
• Abid, M., Abbas, N. and Riaz, M. Improved modi ed ratio estimators of population mean based on deciles, Chiang Mai Journal of Science 43 (1), 1311-1323, 2016(b).
• Abid, M., Abbas, N., Sherwani, R. A. K. and Nazir, H. Z. Improved ratio estimators for the population mean using non-conventional measures of dispersion, Pakistan Journal of Statistics and Operation Research 12 (2), 353-367, 2016(c).
• Alvarez, E., Moya-Fernandez, P. J., Blanco-Encomienda, F. J. and Munoz, J. F. Methodolog- ical insights for industrial quality control management: The impact of various estimators of the standard deviation on the process capability index, Journal of King Saud University Science 27, 271-277, 2015.
• Cochran, W. G. The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce, Journal of Agriculture Science 30, 262-275, 1940.
• Kadilar, C., and Cingi, H. Ratio estimators in simple random sampling, Applied Mathe- matics and Computation 151, 893-902, 2004.
• Kadilar, C., and Cingi, H. An improvement in estimating the population mean by using the correlation coe cient, Hacettepe Journal of Mathematics and Statistics 35 (1), 103-109, 2006.
• Koyuncu, N., and Kadilar, C. E cient estimators for the population mean, Hacettepe Jour- nal of Mathematics and Statistics 38 (2), 217-225, 2009.
• Koyuncu, N., and Kadilar, C. On improvement in estimating population mean in strati ed random sampling, Journal of Applied Statistics 37 (6), 999-1013, 2010.
• Kumar, S. An estimator of the median estimation of study variable using median of auxiliary variable, Sri Lankan Journal of Applied Statistics 16 (2), 107-115, 2015.
• Mukhopadhyay, P. Theory and methods of survey sampling, PHI Learning, 2nd edition, New Delhi 1988.
• Munoz, J. F., Alvarez, E. and Rueda, M. M. Optimum design-based ratio estimators of the distribution function, Journal of Applied Statistics 41 (7), 1395-1407, 2014.
• Murthy, M. N. Product method of estimation, Sankhya 26, 294-307, 1964.
• Prassad, B. Some improved ratio type estimators of population mean and ratio in nite population sample surveys, Communications in Statistics: Theory and Methods 18, 379- 392, 1989.
• Robson, D. S. Application of multivariate polykays to the theory of unbiased ratio type estimation, Journal of American Statistical Association 52, 411-422, 1957.
• Silva, P. N., and Skinner, C. J. Estimating distribution functions with auxiliary information using post strati cation, Journal of O cial Statistics 11 (3), 277-294, 1995.
• Singh, H. P., and Solanki, R. S. Generalized ratio and product methods of estimation in survey sampling, Pakistan Journal of Statistics and Operational Research 7 (2), 245-264, 2011.
• Singh, H. P., and Solanki, R. S. An e cient class of estimators for the population mean using auxiliary information in systematic sampling, Journal of Statistics Theory Practice 6, 274-285, 2012.
• Singh, H. P. and Tailor, R. Use of known correlation coe cient in estimating the nite population means, Statistics in Transition 6 (4), 555-560, 2003.
• Singh, H. P., Tailor, R., Tailor, R. and Kakran, M. S. An improved estimator of population mean using power transformation, Journal of the Indian Society of Agriculture Statistics 58 (2), 223-230, 2004.
• Singh, R., Kumar, M., Chaudhary, M. K., and Kadilar, C. Improved exponential estimator in strati ed random sampling, Pakistan Journal of Statistics and Operational Research 5 (2), 67-82, 2009.
• Sisodia, B. V. S. and Dwivedi, V. K. A modi ed ratio estimator using coe cient of variation of auxiliary variable, Journal of the Indian Society of Agriculture Statistics 33 (1), 13-18, 1981.
• Subramani, J. and Kumarapandiyan, G. New modi ed ratio estimator for estimation of pop- ulation mean when median of the auxiliary variable is known, Pakistan Journal of Statistics and Operational Research 9 (2), 137-145, 2013.
• Subramani, J. and Prabavathy, G. Median based modi ed ratio estimators with linear com- binations of population mean and median of an auxiliary variable, Journal of Reliability and Statistical Studies 7 (1), 1-10, 2014.
• Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the nite population mean, Biometrical Journal 41 (5), 627-636, 1999.
• Watson, D. J. The estimation of leaf area in eld crops, Journal of Agriculture Science 27, 474-483, 1937.
• Yadav, S. K., and Kadilar, C. E cient family of exponential estimators for the population mean, Hacettepe Journal of Mathematics and Statistics 42 (6), 671-677, 2013.
• Yadav, S. K., Mishra, S. S. and Shukla, A. K. Improved ratio estimators for population mean based on median using linear combination of population mean and median of an auxiliary variable, American Journal of Operational Research 4 (2), 21-27, 2014.
• Yan, Z. and Tian, B. Ratio method to the mean estimation using coe cient of skewness of auxiliary variable, ICICA. Part II, CCIS 106, 103-110, 2010.
Birincil Dil en Matematik İstatistik Yazar: Muhammad Irfan (Sorumlu Yazar) Yazar: Maria Javed Yazar: Muhammad Abid Yazar: Zhengyan Lin
Bibtex @araştırma makalesi { hujms440361, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {659 - 673}, doi = {}, title = {Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable}, key = {cite}, author = {Irfan, Muhammad and Javed, Maria and Abid, Muhammad and Lin, Zhengyan} } APA Irfan, M , Javed, M , Abid, M , Lin, Z . (2018). Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable. Hacettepe Journal of Mathematics and Statistics, 47 (3), 659-673. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/440361 MLA Irfan, M , Javed, M , Abid, M , Lin, Z . "Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable". Hacettepe Journal of Mathematics and Statistics 47 (2018): 659-673 Chicago Irfan, M , Javed, M , Abid, M , Lin, Z . "Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable". Hacettepe Journal of Mathematics and Statistics 47 (2018): 659-673 RIS TY - JOUR T1 - Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable AU - Muhammad Irfan , Maria Javed , Muhammad Abid , Zhengyan Lin Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 659 EP - 673 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable %A Muhammad Irfan , Maria Javed , Muhammad Abid , Zhengyan Lin %T Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U ISNAD Irfan, Muhammad , Javed, Maria , Abid, Muhammad , Lin, Zhengyan . "Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 659-673.
| 2019-03-26T02:01:06 |
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|
http://www-spires.fnal.gov/spires/find/books/www?keyword=Polytopes
|
Fermilab Core Computing Division
Library Home | Ask a Librarian [email protected] | Book Catalog | Library Journals | Requests | SPIRES | Fermilab Documents |
Fermilab Library
SPIRES-BOOKS: FIND KEYWORD POLYTOPES *END*INIT* use /tmp/qspiwww.webspi1/20492.132 QRY 131.225.70.96 . find keyword polytopes ( in books using www
Call number: SPRINGER-2003-9781461300199:ONLINE Show nearby items on shelf Title: Convex Polytopes Author(s): Branko Grünbaum Date: 2003 Edition: Second Edition Size: 1 online resource (471 p.) Note: 10.1007/978-1-4613-0019-9 Contents: 1 Notation and prerequisites -- 1.1 Algebra -- 1.2 Topology -- 1.3 Additional notes and comments -- 2 Convex sets -- 2.1 Definition and elementary properties -- 2.2 Support and separation -- 2.3 Convex hulls -- 2.4 Extreme and exposed points faces and poonems -- 2.5 Unbounded convex sets -- 2.6 Polyhedral sets -- 2.7 Remarks -- 2.8 Additional notes and comments -- 3 Polytopes -- 3.1 Definition and fundamental properties -- 3.2 Combinatorial types of polytopes complexes -- 3.3 Diagrams and Schlegel diagrams -- 3.4 Duality of polytopes -- 3.5 Remarks -- 3.6 Additional notes and comments -- 4 Examples -- 4.1 The d-simplex -- 4.2 Pyramids -- 4.3 Bipyramids -- 4.4 Prisms -- 4.5 Simplicial and simple polytopes -- 4.6 Cubical polytopes -- 4.7 Cyclic polytopes -- 4.8 Exercises -- 4.9 Additional notes and comments -- 5 Fundamental properties and constructions -- 5.1 Representations of polytopes as sections or projections -- 5.2 The inductive construction of polytopes -- 5.3 Lower semicontinuity of the functions fk(P) -- 5.4 Gale-transforms and Gale-diagrams -- 5.5 Existence of combinatorial types -- 5.6 Additional notes and comments -- 6 Polytopes with few vertices -- 6.1 d-Polytopes with d + 2 vertices -- 6.2 d-Polytopes with d + 3 vertices -- 6.3 Gale diagrams of polytopes with few vertices -- 6.4 Centrally symmetric polytopes -- 6.5 Exercises -- 6.6 Remarks -- 6.7 Additional notes and comments -- 7 Neighborly polytopes -- 7.1 Definition and general properties -- 7.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG % aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga % aiaawUfacaGLDbaaaaa!40CC! $$\left[ {\frac{1} {2}d} \right]$$-Neighborly d-polytopes -- 7.3 Exercises -- 7.4 Remarks -- 7.5 Additional notes and comments -- 8 Euler’s relation -- 8.1 Euler’s theorem -- 8.2 Proof of Euler’s theorem -- 8.3 A generalization of Euler’s relation -- 8.4 The Euler characteristic of complexes -- 8.5 Exercises -- 8.6 Remarks -- 8.7 Additional notes and comments -- 9 Analogues of Euler’s relation -- 9.1 The incidence equation -- 9.2 The Dehn-Sommerville equations -- 9.3 Quasi-simplicial polytopes -- 9.4 Cubical polytopes -- 9.5 Solutions of the Dehn-Sommerville equations -- 9.6 The f-vectors of neighborly d-polytopes -- 9.7 Exercises -- 9.8 Remarks -- 9.9 Additional notes and comments -- 10 Extremal problems concerning numbers of faces -- 10.1 Upper bounds for fi, i ? 1, in terms of fo -- 10.2 Lower bounds for fi, i ? 1, in terms of fo -- 10.3 The sets f(P3) and f(PS3) -- 10.4 The set fP4) -- 10.5 Exercises -- 10.6 Additional notes and comments -- 11 Properties of boundary complexes -- 11.1 Skeletons of simplices contained in ?(P) -- 11.2 A proof of the van Kampen-Flores theorem -- 11.3 d-Connectedness of the graphs of d-polytopes -- 11.4 Degree of total separability -- 11.5 d-Diagrams -- 11.6 Additional notes and comments -- 12 k-Equivalence of polytopes -- 12.1 k-Equivalence and ambiguity -- 12.2 Dimensional ambiguity -- 12.3 Strong and weak ambiguity -- 12.4 Additional notes and comments -- 13 3-Polytopes -- 13.1 Steinitz’s theorem -- 13.2 Consequences and analogues of Steinitz’s theorem -- 13.3 Eberhard’s theorem -- 13.4 Additional results on 3-realizable sequences -- 13.5 3-Polytopes with circumspheres and circumcircles -- 13.6 Remarks -- 13.7 Additional notes and comments -- 14 Angle-sums relations the Steiner point -- 14.1 Gram’s relation for angle-sums -- 14.2 Angle-sums relations for simplicial polytopes -- 14.3 The Steiner point of a polytope (by G. C. Shephard) -- 14.4 Remarks -- 14.5 Additional notes and comments -- 15 Addition and decomposition of polytopes -- 15.1 Vector addition -- 15.2 Approximation of polytopes by vector sums -- 15.3 Blaschke addition -- 15.4 Remarks -- 15.5 Additional notes and comments -- 16 Diameters of polytopes (by Victor Klee) -- 16.1 Extremal diameters of d-polytopes -- 16.2 The functions ? and ?b -- 16.3 Wv Paths -- 16.4 Additional notes and comments -- 17 Long paths and circuits on polytopes -- 17.1 Hamiltonian paths and circuits -- 17.2 Extremal path-lengths of polytopes -- 17.3 Heights of polytopes -- 17.4 Circuit codes -- 17.5 Additional notes and comments -- 18 Arrangements of hyperplanes -- 18.1 d-Arrangements -- 18.2 2-Arrangements -- 18.3 Generalizations -- 18.4 Additional notes and comments -- 19 Concluding remarks -- 19.1 Regular polytopes and related notions -- 19.2 k-Content of polytopes -- 19.3 Antipodality and related notions -- 19.4 Additional notes and comments -- Tables -- Addendum -- Errata for the 1967 edition -- Additional Bibliography -- Index of Terms -- Index of Symbols ISBN: 9781461300199 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Graduate Texts in Mathematics: 221 Keywords: Mathematics , Convex geometry , Discrete geometry , Mathematics , Convex and Discrete Geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
| 2019-04-26T16:01:58 |
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|
https://par.nsf.gov/biblio/10374925-radio-scattering-horizons-galactic-extragalactic-transients
|
Radio Scattering Horizons for Galactic and Extragalactic Transients
Abstract
Radio wave scattering can cause severe reductions in detection sensitivity for surveys of Galactic and extragalactic fast (∼ms duration) transients. While Galactic sources like pulsars undergo scattering in the Milky Way interstellar medium (ISM), extragalactic fast radio bursts (FRBs) can also experience scattering in their host galaxies and other galaxies intervening in their lines of sight. We assess Galactic and extragalactic scattering horizons for fast radio transients using a combination of NE2001 to model the dispersion measure and scattering time (τ) contributed by the Galactic disk, and independently constructed electron density models for the Galactic halo and other galaxies’ ISMs and halos that account for different galaxy morphologies, masses, densities, and strengths of turbulence. For source redshifts 0.5 ≤zs≤ 1, an all-sky, isotropic FRB population has simulated values ofτ(1 GHz) ranging from ∼1μs to ∼2 ms (90% confidence, observer frame) that are dominated by host galaxies, althoughτcan be ≫2 ms at low Galactic latitudes. A population atzs= 5 has 0.01 ≲τ≲ 300 ms at 1 GHz (90% confidence), dominated by intervening galaxies. About 20% of these high-redshift FRBs are predicted to haveτ> 5 ms at 1 GHz (observer frame), and ≳40% of FRBs betweenzs∼ 0.5–5 haveτ≳ 1 ms forνmore »
Authors:
; ; ;
Publication Date:
NSF-PAR ID:
10374925
Journal Name:
The Astrophysical Journal
Volume:
934
Issue:
1
Page Range or eLocation-ID:
Article No. 71
ISSN:
0004-637X
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. ABSTRACT
Fast radio bursts (FRBs) are millisecond-time-scale radio transients, the origins of which are predominantly extragalactic and likely involve highly magnetized compact objects. FRBs undergo multipath propagation, or scattering, from electron density fluctuations on sub-parsec scales in ionized gas along the line of sight. Scattering observations have located plasma structures within FRB host galaxies, probed Galactic and extragalactic turbulence, and constrained FRB redshifts. Scattering also inhibits FRB detection and biases the observed FRB population. We report the detection of scattering times from the repeating FRB 20190520B that vary by up to a factor of 2 or more on minutes to days-long time-scales. In one notable case, the scattering time varied from 7.9 ± 0.4 ms to less than 3.1 ms ($95{{\ \rm per\ cent}}$ confidence) over 2.9 min at 1.45 GHz. The scattering times appear to be uncorrelated between bursts or with dispersion and rotation measure variations. Scattering variations are attributable to dynamic, inhomogeneous plasma in the circumsource medium, and analogous variations have been observed from the Crab pulsar. Under such circumstances, the frequency dependence of scattering can deviate from the typical power law used to measure scattering. Similar variations may therefore be detectable from other FRBs, even those with inconspicuous scattering, providing a unique probemore »
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Fast Radio Bursts (FRBs) are extragalactic radio transients that exhibit a distance-dependent dispersion of their signal, and thus can be used as cosmological probes. In this article we, for the first time, apply a model-independent approach to measure reionization from synthetic FRB data assuming these signals are detected beyond redshift 5. This method allows us to constrain the full shape of the reionization history as well as the CMB optical depthτwhile avoiding the problems of commonly used model-based techniques. A total of 100 localized FRBs, originating from redshifts 5–15, could constrain (at 68% confidence level) the CMB optical depth to within 11%, and the midpoint of reionization to 4%, surpassing current state-of-the-art CMB bounds and quasar limits. Owing to the higher numbers of expected FRBs at lower redshifts, theτconstraints are asymmetric (+14%, −7%), providing a much stronger lower limit. Finally, we show that the independent constraints on reionization from FRBs will improve limits on other cosmological parameters, such as the amplitude of the power spectrum of primordial fluctuations.
3. Abstract
We use medium-resolution Keck/Echellette Spectrograph and Imager spectroscopy of bright quasars to study cool gas traced by Caiiλλ3934, 3969 and Naiλλ5891, 5897 absorption in the interstellar/circumgalactic media of 21 foreground star-forming galaxies at redshifts 0.03 <z< 0.20 with stellar masses 7.4 ≤ logM*/M≤ 10.6. The quasar–galaxy pairs were drawn from a unique sample of Sloan Digital Sky Survey quasar spectra with intervening nebular emission, and thus have exceptionally close impact parameters (R< 13 kpc). The strength of this line emission implies that the galaxies’ star formation rates (SFRs) span a broad range, with several lying well above the star-forming sequence. We use Voigt profile modeling to derive column densities and component velocities for each absorber, finding that column densitiesN(Caii) > 1012.5cm−2(N(Nai) > 1012.0cm−2) occur with an incidencefC(Caii) = 0.63+0.10−0.11(fC(Nai) = 0.57+0.10−0.11). We find no evidence for a dependence offCor the rest-frame equivalent widthsWr(CaiiK) orWr(Nai5891) onRorM*. Instead,Wr(CaiiK) is correlated with local SFR at >3σsignificance, suggesting that Caiitraces star formation-driven outflows. While most of the absorbers have velocities within ±50 km s−1of the host redshift, their velocity widths (characterized by Δv90) are universally 30–177 km s−1larger than that implied by tilted-ring modeling of the velocities of interstellar material. These kinematics mustmore »
4. Abstract The Murchison Widefield Array (MWA) is an electronically steered low-frequency (<300 MHz) radio interferometer, with a ‘slew’ time less than 8 s. Low-frequency (∼100 MHz) radio telescopes are ideally suited for rapid response follow-up of transients due to their large field of view, the inverted spectrum of coherent emission, and the fact that the dispersion delay between a 1 GHz and 100 MHz pulse is on the order of 1–10 min for dispersion measures of 100–2000 pc/cm 3 . The MWA has previously been used to provide fast follow-up for transient events including gamma-ray bursts (GRBs), fast radio bursts (FRBs), and gravitational waves, using systems that respond to gamma-ray coordinates network packet-based notifications. We describe a system for automatically triggering MWA observations of such events, based on Virtual Observatory Event standard triggers, which is more flexible, capable, and accurate than previous systems. The system can respond to external multi-messenger triggers, which makes it well-suited to searching for prompt coherent radio emission from GRBs, the study of FRBs and gravitational waves, single pulse studies of pulsars, and rapid follow-up of high-energy superflares from flare stars. The new triggering system has the capability to trigger observations in both the regular correlatormore »
5. Abstract
We report the discoveries of a nuclear ring of diameter 10″ (∼1.5 kpc) and a potential low-luminosity active galactic nucleus (LLAGN) in the radio continuum emission map of the edge-on barred spiral galaxy NGC 5792. These discoveries are based on the Continuum Halos in Nearby Galaxies—an Expanded Very Large Array (VLA) Survey, as well as subsequent VLA observations of subarcsecond resolution. Using a mixture of Hαand 24μm calibrations, we disentangle the thermal and nonthermal radio emission of the nuclear region and derive a star formation rate (SFR) of ∼0.4Myr−1. We find that the nuclear ring is dominated by nonthermal synchrotron emission. The synchrotron-based SFR is about three times the mixture-based SFR. This result indicates that the nuclear ring underwent more intense star-forming activity in the past, and now its star formation is in the low state. The subarcsecond VLA images resolve six individual knots on the nuclear ring. The equipartition magnetic field strengthBeqof the knots varies from 77 to 88μG. The radio ring surrounds a point-like faint radio core ofS6 GHz= (16 ± 4)μJy with polarized lobes at the center of NGC 5792, which suggests an LLAGN with an Eddington ratio of ∼10−5. This radio nuclear ring is reminiscentmore »
| 2023-02-08T12:54:45 |
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|
https://par.nsf.gov/biblio/10004974-search-standard-model-higgs-boson-associated-wh-production-pp-collisions-d0-detector
|
Search for the Standard Model Higgs Boson in Associated $WH$ Production in $9.7 fb−1$ of $pp¯$ Collisions with the D0 Detector
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10004974
Journal Name:
Physical Review Letters
Volume:
109
Issue:
12
ISSN:
0031-9007
Publisher:
American Physical Society
| 2022-11-30T04:39:21 |
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|
https://lammps.sandia.gov/doc/pair_atm.html
|
# pair_style atm command
## Syntax
pair_style atm cutoff cutoff_triple
• cutoff = cutoff for each pair in 3-body interaction (distance units)
• cutoff_triple = additional cutoff applied to product of 3 pairwise distances (distance units)
## Examples
pair_style atm 4.5 2.5
pair_coeff * * * 0.072
pair_style hybrid/overlay lj/cut 6.5 atm 4.5 2.5
pair_coeff * * lj/cut 1.0 1.0
pair_coeff 1 1 atm 1 0.064
pair_coeff 1 1 atm 2 0.080
pair_coeff 1 2 atm 2 0.100
pair_coeff 2 2 atm 2 0.125
## Description
The atm style computes a 3-body Axilrod-Teller-Muto potential for the energy E of a system of atoms as
where nu is the three-body interaction strength. The distances between pairs of atoms r12, r23, r31 and the angles gamma1, gamma2, gamma3 are as shown in this diagram:
Note that for the interaction between a triplet of atoms I,J,K, there is no “central” atom. The interaction is symmetric with respect to permutation of the three atoms. Thus the nu value is the same for all those permutations of the atom types of I,J,K and needs to be specified only once, as discussed below.
The atm potential is typically used in combination with a two-body potential using the pair_style hybrid/overlay command as in the example above.
The potential for a triplet of atom is calculated only if all 3 distances r12, r23, r31 between the 3 atoms satisfy rIJ < cutoff. In addition, the product of the 3 distances r12*r23*r31 < cutoff_triple^3 is required, which excludes from calculation the triplets with small contribution to the interaction.
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 restart files read by the read_restart commands:
• K = atom type of the third atom (1 to Ntypes)
• nu = prefactor (energy/distance^9 units)
K can be specified in one of two ways. An explicit numeric value can be used, as in the 2nd example above. J <= K is required. LAMMPS sets the coefficients for the other 5 symmetric interactions to the same values. E.g. if I = 1, J = 2, K = 3, then these 6 values are set to the specified nu: nu123, nu132, nu213, nu231, nu312, nu321. This enforces the symmetry discussed above.
A wildcard asterisk can be used for K to set the coefficients for multiple triplets of atom types. This takes the form “*” or “*n” or “n*” or “m*n”. If N = the number of atom types, then an asterisk with no numeric values means all types from 1 to N. A leading asterisk means all types from 1 to n (inclusive). A trailing asterisk means all types from n to N (inclusive). A middle asterisk means all types from m to n (inclusive). Note that only type triplets with J <= K are considered; if asterisks imply type triplets where K < J, they are ignored.
Note that a pair_coeff command can override a previous setting for the same I,J,K triplet. For example, these commands set nu for all I,J.K triplets, then overwrite nu for just the I,J,K = 2,3,4 triplet:
pair_coeff * * * 0.25
pair_coeff 2 3 4 0.1
Note that for a simulation with a single atom type, only a single entry is required, e.g.
pair_coeff 1 1 1 0.25
For a simulation with two atom types, four pair_coeff commands will specify all possible nu values:
pair_coeff 1 1 1 nu1
pair_coeff 1 1 2 nu2
pair_coeff 1 2 2 nu3
pair_coeff 2 2 2 nu4
For a simulation with three atom types, ten pair_coeff commands will specify all possible nu values:
pair_coeff 1 1 1 nu1
pair_coeff 1 1 2 nu2
pair_coeff 1 1 3 nu3
pair_coeff 1 2 2 nu4
pair_coeff 1 2 3 nu5
pair_coeff 1 3 3 nu6
pair_coeff 2 2 2 nu7
pair_coeff 2 2 3 nu8
pair_coeff 2 3 3 nu9
pair_coeff 3 3 3 nu10
By default the nu value for all triplets is set to 0.0. Thus it is not required to provide pair_coeff commands that enumerate triplet interactions for all K types. If some I,J,K combination is not specified, then there will be no 3-body ATM interactions for that combination and all its permutations. However, as with all pair styles, it is required to specify a pair_coeff command for all I,J combinations, else an error will result.
Mixing, shift, table, tail correction, restart, rRESPA info:
This pair styles do not support the pair_modify mix, shift, table, and tail options.
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. However, if the atm potential is used in combination with other potentials using the pair_style hybrid/overlay command then pair_coeff commands need to be re-specified in the restart input script.
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 MANYBODY package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
| 2018-12-15T09:03:54 |
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|
https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Skolemization.html
|
# Skolem normal form
In mathematical logic, reduction to Skolem normal form (SNF) is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover.
A formula of first-order logic is in Skolem normal form (named after Thoralf Skolem) if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization (sometimes spelled "Skolemnization"). The resulting formula is not necessarily equivalent to the original one, but is equisatisfiable with it: it is satisfiable if and only if the original one is satisfiable.[1]
The simplest form of Skolemization is for existentially quantified variables which are not inside the scope of a universal quantifier. These may be replaced simply by creating new constants. For example, may be changed to , where is a new constant (does not occur anywhere else in the formula).
More generally, Skolemization is performed by replacing every existentially quantified variable with a term whose function symbol is new. The variables of this term are as follows. If the formula is in prenex normal form, are the variables that are universally quantified and whose quantifiers precede that of . In general, they are the variables that are quantified universally and such that occurs in the scope of their quantifiers. The function introduced in this process is called a Skolem function (or Skolem constant if it is of zero arity) and the term is called a Skolem term.
As an example, the formula is not in Skolem normal form because it contains the existential quantifier . Skolemization replaces with , where is a new function symbol, and removes the quantification over . The resulting formula is . The Skolem term contains , but not , because the quantifier to be removed is in the scope of , but not in that of ; since this formula is in prenex normal form, this is equivalent to saying that, in the list of quantifiers, precedes while does not. The formula obtained by this transformation is satisfiable if and only if the original formula is.
## How Skolemization works
Skolemization works by applying a second-order equivalence in conjunction to the definition of first-order satisfiability. The equivalence provides a way for "moving" an existential quantifier before a universal one.
where
is a function that maps to .
Intuitively, the sentence "for every there exists a such that " is converted into the equivalent form "there exists a function mapping every into a such that, for every it holds ".
This equivalence is useful because the definition of first-order satisfiability implicitly existentially quantifies over the evaluation of function symbols. In particular, a first-order formula is satisfiable if there exists a model and an evaluation of the free variables of the formula that evaluate the formula to true. The model contains the evaluation of all function symbols; therefore, Skolem functions are implicitly, existentially quantified. In the example above, is satisfiable if and only if there exists a model , which contains an evaluation for , such that is true for some evaluation of its free variables (none in this case). This may be expressed in second order as . By the above equivalence, this is the same as the satisfiability of .
At the meta-level, first-order satisfiability of a formula may be written with a little abuse of notation as , where is a model, is an evaluation of the free variables, and means that is true in under . Since first-order models contain the evaluation of all function symbols, any Skolem function contains is implicitly, existentially quantified by . As a result, after replacing an existential quantifier over variables into an existential quantifiers over functions at the front of the formula, the formula still may be treated as a first-order one by removing these existential quantifiers. This final step of treating as may be completed because functions are implicitly existentially quantified by in the definition of first-order satisfiability.
Correctness of Skolemization may be shown on the example formula as follows. This formula is satisfied by a model if and only if, for each possible value for in the domain of the model, there exists a value for in the domain of the model that makes true. By the axiom of choice, there exists a function such that . As a result, the formula is satisfiable, because it has the model obtained by adding the evaluation of to . This shows that is satisfiable only if is satisfiable as well. In the other way around, if is satisfiable, then there exists a model that satisfies it; this model includes an evaluation for the function such that, for every value of , the formula holds. As a result, is satisfied by the same model because one may choose, for every value of , the value , where is evaluated according to .
## Uses of Skolemization
One of the uses of Skolemization is automated theorem proving. For example, in the method of analytic tableaux, whenever a formula whose leading quantifier is existential occurs, the formula obtained by removing that quantifier via Skolemization may be generated. For example, if occurs in a tableau, where are the free variables of , then may be added to the same branch of the tableau. This addition does not alter the satisfiability of the tableau: every model of the old formula may be extended, by adding a suitable evaluation of , to a model of the new formula.
This form of Skolemization is an improvement over "classical" Skolemization in that, only variables that are free in the formula are placed in the Skolem term. This is an improvement because the semantics of tableau may implicitly place the formula in the scope of some universally quantified variables that are not in the formula itself; these variables are not in the Skolem term, while they would be there according to the original definition of Skolemization. Another improvement that may be used is applying the same Skolem function symbol for formulae that are identical up to variable renaming.[2]
Another use is in the resolution method for first order logic, where formulas are represented as sets of clauses understood to be universally quantified. (For an example see drinker paradox.)
## Skolem theories
In general, if is a theory and for each formula with free variables there is a Skolem function, then is called a Skolem theory.[3] For example, by the above, arithmetic with the Axiom of Choice is a Skolem theory.
Every Skolem theory is model complete, i.e. every substructure of a model is an elementary substructure. Given a model M of a Skolem theory T, the smallest substructure containing a certain set A is called the Skolem hull of A. The Skolem hull of A is an atomic prime model over A.
## Notes
1. "Normal Forms and Skolemization" (PDF). max planck institut informatik. Retrieved 15 December 2012.
2. R. Hähnle. Tableaux and related methods. Handbook of Automated Reasoning.
## External links
This article is issued from Wikipedia - version of the 4/8/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.
| 2022-06-27T18:42:53 |
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|
https://zbmath.org/authors/?q=ai%3Awhitehead.george-w
|
# zbMATH — the first resource for mathematics
Compute Distance To:
Documents Indexed: 34 Publications since 1942, including 4 Books
all top 5
#### Co-Authors
29 single-authored 3 Kan, Daniel Marinus 1 Eckmann, Beno 1 James, Ioan Mackenzie 1 Samelson, Hans 1 Thomas, Paul Emery 1 Toda, Hirosi
all top 5
#### Serials
10 Annals of Mathematics. Second Series 4 Proceedings of the National Academy of Sciences of the United States of America 2 Topology 2 Transactions of the American Mathematical Society 1 Boletín de la Sociedad Matemática Mexicana. Segunda Serie 1 Commentarii Mathematici Helvetici 1 Proceedings of the American Mathematical Society 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin of the American Mathematical Society 1 Journal of Mathematics and Mechanics 1 Graduate Texts in Mathematics 1 Regional Conference Series in Mathematics
#### Fields
4 Algebraic topology (55-XX) 3 History and biography (01-XX) 2 Manifolds and cell complexes (57-XX) 1 Algebraic geometry (14-XX) 1 General topology (54-XX)
#### Citations contained in zbMATH
29 Publications have been cited 946 times in 782 Documents Cited by Year
Elements of homotopy theory. Zbl 0406.55001
1978
Some aspects of stable homotopy theory. Zbl 0151.31101
1962
Generalized homology theories. Zbl 0124.38302
1962
A generalization of the Hopf invariant. Zbl 0045.44202
1950
On products in homotopy groups. Zbl 0060.41106
1946
Recent advances in homotopy theory. Zbl 0217.48601
1970
On the Freudenthal theorems. Zbl 0050.17501
1953
The reduced join of two spectra. Zbl 0142.40501
Kan, D. M.; Whitehead, G. W.
1965
On the homotopy groups of spheres and rotation groups. Zbl 0060.41105
1942
Note on cross-sections in Stiefel manifolds. Zbl 0118.18702
1963
The $$(n+2)^{nd}$$ homotopy group of the $$n$$-sphere. Zbl 0037.39703
1950
Homotopy properties of the real orthogonal groups. Zbl 0060.41415
1942
On the homology suspension. Zbl 0067.41201
1955
Fiber spaces and the Eilenberg homology groups. Zbl 0048.41302
1952
Orientability and Poincaré duality in general homology theories. Zbl 0136.20005
Kan, D. M.; Whitehead, G. W.
1965
The homology suspension. Zbl 0079.39101
1957
Homotopy theory. Compiled by Robert J. Aumann. Zbl 0053.43402
1953
A generalization of the Hopf invariant. Zbl 0041.51903
1950
On the symmetric square of a sphere. Zbl 0136.20301
James, I. M.; Thomas, Emery; Toda, Hirosi; Whitehead, G. W.
1963
On the realizability of singular cohomology groups. Zbl 0109.15801
Kan, D. M.; Whitehead, G. W.
1961
Some aspects of stable homotopy theory. Zbl 0127.38901
1963
On spaces with vanishing low-dimensional homotopy groups. Zbl 0031.28601
1948
Homotopy groups of joins and unions. Zbl 0073.18301
1956
Homotopy properties of the real orthogonal groups. JFM 68.0506.01
1942
Note on a theorem of Sugawara. Zbl 0103.16101
1959
Fifty years of homotopy theory. Zbl 0524.55002
1983
On families of continuous vector fields over spheres. Zbl 0060.41414
1946
Homology theories and duality. Zbl 0117.40202
1960
On fibering spheres by toruses. Zbl 0033.02601
Eckmann, Beno; Samelson, H.; Whitehead, G. W.
1949
Fifty years of homotopy theory. Zbl 0524.55002
1983
Elements of homotopy theory. Zbl 0406.55001
1978
Recent advances in homotopy theory. Zbl 0217.48601
1970
The reduced join of two spectra. Zbl 0142.40501
Kan, D. M.; Whitehead, G. W.
1965
Orientability and Poincaré duality in general homology theories. Zbl 0136.20005
Kan, D. M.; Whitehead, G. W.
1965
Note on cross-sections in Stiefel manifolds. Zbl 0118.18702
1963
On the symmetric square of a sphere. Zbl 0136.20301
James, I. M.; Thomas, Emery; Toda, Hirosi; Whitehead, G. W.
1963
Some aspects of stable homotopy theory. Zbl 0127.38901
1963
Some aspects of stable homotopy theory. Zbl 0151.31101
1962
Generalized homology theories. Zbl 0124.38302
1962
On the realizability of singular cohomology groups. Zbl 0109.15801
Kan, D. M.; Whitehead, G. W.
1961
Homology theories and duality. Zbl 0117.40202
1960
Note on a theorem of Sugawara. Zbl 0103.16101
1959
The homology suspension. Zbl 0079.39101
1957
Homotopy groups of joins and unions. Zbl 0073.18301
1956
On the homology suspension. Zbl 0067.41201
1955
On the Freudenthal theorems. Zbl 0050.17501
1953
Homotopy theory. Compiled by Robert J. Aumann. Zbl 0053.43402
1953
Fiber spaces and the Eilenberg homology groups. Zbl 0048.41302
1952
A generalization of the Hopf invariant. Zbl 0045.44202
1950
The $$(n+2)^{nd}$$ homotopy group of the $$n$$-sphere. Zbl 0037.39703
1950
A generalization of the Hopf invariant. Zbl 0041.51903
1950
On fibering spheres by toruses. Zbl 0033.02601
Eckmann, Beno; Samelson, H.; Whitehead, G. W.
1949
On spaces with vanishing low-dimensional homotopy groups. Zbl 0031.28601
1948
On products in homotopy groups. Zbl 0060.41106
1946
On families of continuous vector fields over spheres. Zbl 0060.41414
1946
On the homotopy groups of spheres and rotation groups. Zbl 0060.41105
1942
Homotopy properties of the real orthogonal groups. Zbl 0060.41415
1942
Homotopy properties of the real orthogonal groups. JFM 68.0506.01
1942
all top 5
#### Cited by 795 Authors
16 Gonçalves, Daciberg Lima 10 Dydak, Jerzy 8 Arkowitz, Martin 8 Koschorke, Ulrich 8 Lupton, Gregory M. 7 Papadima, Ștefan 6 Dranishnikov, Alexander Nikolaevich 6 Félix, Yves 6 Golasiński, Marek 6 Lee, Dae-Woong 6 Møller, Jesper Michael 6 Oprea, John F. 6 Repovš, Dušan D. 6 Strom, Jeffrey A. 6 Thomas, Jean-Claude 6 Yang, Huajian 5 Blanc, David Abraham 5 Conner, Pierre E. 5 Dwyer, William G. 5 Guaschi, John 5 James, Ioan Mackenzie 5 Kultze, Rolf 5 Landweber, Peter S. 5 Oda, Nobuyuki 5 Siegmund Puppe, Dieter 5 Smith, Samuel Bruce 5 Wu, Jie 4 Arlettaz, Dominique 4 Baues, Hans-Joachim 4 Burghelea, Dan 4 Cochran, Thomas (Tim) Daniel 4 Cohen, Frederick Ronald 4 Crowley, Diarmuid John 4 Hardie, Keith A. 4 Iwase, Norio 4 Kishimoto, Daisuke 4 Kołodziejczyk, Danuta 4 Kono, Akira 4 Neisendorfer, Joseph A. 4 Richter, William 4 Schochet, Claude L. 4 Spiez, Stanislaw 4 Suciu, Alexander I. 4 Taheri, Ali 4 Thomas, Paul Emery 4 Vandembroucq, Lucile 4 Whitehead, George W. 4 Wong, Peter N.-S. 3 Bauer, Friedrich-Wilhelm 3 Cavicchioli, Alberto 3 Dadarlat, Marius 3 De Melo, Thiago 3 Deleanu, Aristide 3 Fang, Fuquan 3 Farber, Michael S. 3 Floyd, Edwin E. 3 Forstnerič, Franc 3 Friedman, Greg 3 Gong, Guihua 3 Gonzalez, Jesus 3 Goodwillie, Thomas Gehret 3 Grant, Mark 3 Habegger, Nathan 3 Hurder, Steven E. 3 Intermont, Michele 3 Kaminker, Jerome 3 Karimov, Umed H. 3 Katz, Mikhail G. 3 Lück, Wolfgang 3 McCarthy, Randy 3 Menichi, Luc 3 Mimura, Mamoru 3 Noakes, J. Lyle 3 Prieto, Carlos Tejero 3 Randall, Duane 3 Ray, Nigel 3 Robinson, Christopher Alan 3 Sasao, Seiya 3 Sati, Hisham 3 Schultz, Reinhard E. 3 Segal, Jack 3 Smith, Larry 3 Stanley, Donald A. 3 Toda, Hirosi 3 Witbooi, Peter Joseph 3 Yokoi, Katsuya 3 Zhao, Xu-An 2 Alexander, James Crew 2 Arlt, Dietmar 2 Asok, Aravind 2 Ayala, Rafael 2 Baum, Paul Frank 2 Becker, James Cyril 2 Belegradek, Igor 2 Benson, David John 2 Berarducci, Alessandro 2 Bökstedt, Marcel 2 Brazas, Jeremy 2 Brown, Edgar H. jun. 2 Bullejos, Manuel ...and 695 more Authors
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#### Cited in 146 Serials
96 Topology and its Applications 87 Transactions of the American Mathematical Society 45 Journal of Pure and Applied Algebra 44 Proceedings of the American Mathematical Society 30 Mathematische Zeitschrift 30 Algebraic & Geometric Topology 25 Mathematische Annalen 19 Inventiones Mathematicae 19 Bulletin of the American Mathematical Society 16 Geometry & Topology 14 Advances in Mathematics 12 Israel Journal of Mathematics 12 Mathematical Proceedings of the Cambridge Philosophical Society 11 Annales de l’Institut Fourier 11 Manuscripta Mathematica 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Geometriae Dedicata 8 Tohoku Mathematical Journal. Second Series 7 Communications in Mathematical Physics 7 Cahiers de Topologie et Géométrie Différentielle Catégoriques 7 $$K$$-Theory 7 Journal of Homotopy and Related Structures 6 Compositio Mathematica 6 Duke Mathematical Journal 6 Journal of Algebra 6 Kodai Mathematical Journal 6 Proceedings of the Japan Academy 5 Journal of Geometry and Physics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Archiv der Mathematik 5 Proceedings of the Edinburgh Mathematical Society. Series II 5 Differential Geometry and its Applications 5 Journal of Fixed Point Theory and Applications 4 Journal of Mathematical Physics 4 Bulletin de la Société Mathématique de France 4 Nagoya Mathematical Journal 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Annals of Mathematics. Second Series 3 Bulletin of the Australian Mathematical Society 3 Reports on Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Journal of Functional Analysis 3 Journal of the Mathematical Society of Japan 3 Journal of Symbolic Computation 3 Discrete & Computational Geometry 3 Forum Mathematicum 3 Science in China. Series A 3 Bulletin of the American Mathematical Society. New Series 3 Acta Mathematica Sinica. English Series 3 Cahiers de Topologie et Géométrie Différentielle Catégoriques 3 Journal of $$K$$-Theory 2 Archive for Rational Mechanics and Analysis 2 Communications in Algebra 2 Communications on Pure and Applied Mathematics 2 Mathematical Notes 2 Nuclear Physics. B 2 Acta Mathematica 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Czechoslovak Mathematical Journal 2 Publications Mathématiques 2 Journal of Differential Equations 2 Mathematika 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Chinese Annals of Mathematics. Series B 2 Journal of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Linear Algebra and its Applications 2 Expositiones Mathematicae 2 Indagationes Mathematicae. New Series 2 Topological Methods in Nonlinear Analysis 2 Journal of Mathematical Sciences (New York) 2 Selecta Mathematica. New Series 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of the Institute of Mathematics of Jussieu 2 Mediterranean Journal of Mathematics 2 Kodai Mathematical Seminar Reports 2 Journal of Topology and Analysis 2 Science China. Mathematics 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Archive for History of Exact Sciences 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Linear and Multilinear Algebra 1 Ukrainian Mathematical Journal 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica Vietnamica 1 Applied Mathematics and Computation 1 Collectanea Mathematica 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 International Journal of Computer & Information Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Combinatorial Theory. Series B ...and 46 more Serials
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#### Cited in 44 Fields
483 Algebraic topology (55-XX) 207 Manifolds and cell complexes (57-XX) 80 Category theory; homological algebra (18-XX) 54 Differential geometry (53-XX) 51 Group theory and generalizations (20-XX) 49 General topology (54-XX) 41 Algebraic geometry (14-XX) 40 Global analysis, analysis on manifolds (58-XX) 33 $$K$$-theory (19-XX) 22 Several complex variables and analytic spaces (32-XX) 18 Topological groups, Lie groups (22-XX) 18 Dynamical systems and ergodic theory (37-XX) 17 Functional analysis (46-XX) 16 Associative rings and algebras (16-XX) 15 Quantum theory (81-XX) 11 Operator theory (47-XX) 9 Mathematical logic and foundations (03-XX) 8 Number theory (11-XX) 8 Commutative algebra (13-XX) 8 Convex and discrete geometry (52-XX) 8 Computer science (68-XX) 8 Mechanics of particles and systems (70-XX) 7 Nonassociative rings and algebras (17-XX) 7 Partial differential equations (35-XX) 6 History and biography (01-XX) 5 Combinatorics (05-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Ordinary differential equations (34-XX) 3 Mechanics of deformable solids (74-XX) 3 Systems theory; control (93-XX) 2 Geometry (51-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General algebraic systems (08-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-03-02T18:01:15 |
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https://zbmath.org/authors/?q=ai%3Agoodwillie.thomas-g
|
# zbMATH — the first resource for mathematics
## Goodwillie, Thomas Gehret
Compute Distance To:
Author ID: goodwillie.thomas-g Published as: Goodwillie, T.; Goodwillie, T. G.; Goodwillie, Thomas; Goodwillie, Thomas G. Homepage: http://www.math.brown.edu/faculty/goodwillie.html External Links: MGP · Wikidata · MathOverflow · GND
Documents Indexed: 24 Publications since 1982, including 2 Books Biographic References: 1 Publication
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#### Co-Authors
12 single-authored 4 Klein, John Robert 3 Weiss, Michael S. 2 Carlsson, Gunnar E. 2 Cohen, Ralph L. 2 Hsiang, Wu-Chung 2 McCarthy, Randy 1 Bökstedt, Marcel 1 Dundas, Bjørn Ian 1 Igusa, Kiyoshi 1 Lichtenbaum, Stephen 1 Madsen, Ib Henning 1 Munson, Brian A. 1 Ohrt, Christopher
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#### Serials
3 $$K$$-Theory 3 Annals of Mathematics. Second Series 3 Journal of Topology 2 Topology 2 Geometry & Topology 1 American Journal of Mathematics 1 Duke Mathematical Journal 1 Journal of Pure and Applied Algebra 1 Memoirs of the American Mathematical Society 1 Algebraic & Geometric Topology 1 Oberwolfach Reports 1 Algebra and Applications
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#### Fields
13 Algebraic topology (55-XX) 10 Manifolds and cell complexes (57-XX) 6 Category theory; homological algebra (18-XX) 6 $$K$$-theory (19-XX) 4 Global analysis, analysis on manifolds (58-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX)
#### Citations contained in zbMATH
21 Publications have been cited 586 times in 363 Documents Cited by Year
Cyclic homology, derivations, and the free loopspace. Zbl 0569.16021
Goodwillie, Thomas G.
1985
Calculus. II: Analytic functors. Zbl 0776.55008
Goodwillie, Thomas G.
1992
Calculus. III: Taylor series. Zbl 1067.55006
Goodwillie, Thomas G.
2003
Relative algebraic K-theory and cyclic homology. Zbl 0627.18004
Goodwillie, Thomas G.
1986
Calculus. I: The first derivative of pseudoisotopy theory. Zbl 0741.57021
Goodwillie, Thomas G.
1990
Embeddings from the point of view of immersion theory. II. Zbl 0927.57028
Goodwillie, Thomas G.; Weiss, Michael
1999
The local structure of algebraic K-theory. Zbl 1272.55002
Dundas, Bjørn Ian; Goodwillie, Thomas G.; McCarthy, Randy
2013
Multiple disjunction for spaces of smooth embeddings. Zbl 1329.57029
Goodwillie, Thomas G.; Klein, John R.
2015
On the general linear group and Hochschild homology. Zbl 0566.20021
Goodwillie, Thomas G.
1985
Spaces of smooth embeddings, disjunction and surgery. Zbl 0966.57001
Goodwillie, Thomas G.; Klein, John R.; Weiss, Michael S.
2001
Multiple disjunction for spaces of Poincaré embeddings. Zbl 1168.57017
Goodwillie, Thomas G.; Klein, John R.
2008
A Haefliger style description of the embedding calculus tower. Zbl 1034.57027
Goodwillie, Thomas G.; Klein, John R.; Weiss, Michael S.
2003
On the algebraic $$K$$-theory of simply connected spaces. Zbl 0867.19003
Bökstedt, M.; Carlsson, G.; Cohen, R.; Goodwillie, T.; Hsiang, W. C.; Madsen, I.
1996
A stable range description of the space of link maps. Zbl 1204.57025
Goodwillie, Thomas G.; Munson, Brian A.
2010
A multiple disjunction lemma for smooth concordance embeddings. Zbl 0717.57011
Goodwillie, Thomas G.
1990
A cohomological bound for the $$h$$-topology. Zbl 1045.14010
Goodwillie, T. G.; Lichtenbaum, S.
2001
The differential calculus of homotopy functors. Zbl 0759.55011
Goodwillie, Thomas G.
1991
The free loop space and the algebraic K-theory of spaces. Zbl 0649.55001
Carlsson, G. E.; Cohen, R. L.; Goodwillie, T.; Hsiang, W. C.
1987
Scissors congruence with mixed dimensions. Zbl 1368.52009
Goodwillie, Thomas G.
2017
A remark on the homology of cosimplicial spaces. Zbl 0924.55016
Goodwillie, Thomas G.
1998
An equivariant version of Hatcher’s $$G/O$$ construction. Zbl 1332.19005
Goodwillie, Thomas; Igusa, Kiyoshi; Ohrt, Christopher
2015
Scissors congruence with mixed dimensions. Zbl 1368.52009
Goodwillie, Thomas G.
2017
Multiple disjunction for spaces of smooth embeddings. Zbl 1329.57029
Goodwillie, Thomas G.; Klein, John R.
2015
An equivariant version of Hatcher’s $$G/O$$ construction. Zbl 1332.19005
Goodwillie, Thomas; Igusa, Kiyoshi; Ohrt, Christopher
2015
The local structure of algebraic K-theory. Zbl 1272.55002
Dundas, Bjørn Ian; Goodwillie, Thomas G.; McCarthy, Randy
2013
A stable range description of the space of link maps. Zbl 1204.57025
Goodwillie, Thomas G.; Munson, Brian A.
2010
Multiple disjunction for spaces of Poincaré embeddings. Zbl 1168.57017
Goodwillie, Thomas G.; Klein, John R.
2008
Calculus. III: Taylor series. Zbl 1067.55006
Goodwillie, Thomas G.
2003
A Haefliger style description of the embedding calculus tower. Zbl 1034.57027
Goodwillie, Thomas G.; Klein, John R.; Weiss, Michael S.
2003
Spaces of smooth embeddings, disjunction and surgery. Zbl 0966.57001
Goodwillie, Thomas G.; Klein, John R.; Weiss, Michael S.
2001
A cohomological bound for the $$h$$-topology. Zbl 1045.14010
Goodwillie, T. G.; Lichtenbaum, S.
2001
Embeddings from the point of view of immersion theory. II. Zbl 0927.57028
Goodwillie, Thomas G.; Weiss, Michael
1999
A remark on the homology of cosimplicial spaces. Zbl 0924.55016
Goodwillie, Thomas G.
1998
On the algebraic $$K$$-theory of simply connected spaces. Zbl 0867.19003
Bökstedt, M.; Carlsson, G.; Cohen, R.; Goodwillie, T.; Hsiang, W. C.; Madsen, I.
1996
Calculus. II: Analytic functors. Zbl 0776.55008
Goodwillie, Thomas G.
1992
The differential calculus of homotopy functors. Zbl 0759.55011
Goodwillie, Thomas G.
1991
Calculus. I: The first derivative of pseudoisotopy theory. Zbl 0741.57021
Goodwillie, Thomas G.
1990
A multiple disjunction lemma for smooth concordance embeddings. Zbl 0717.57011
Goodwillie, Thomas G.
1990
The free loop space and the algebraic K-theory of spaces. Zbl 0649.55001
Carlsson, G. E.; Cohen, R. L.; Goodwillie, T.; Hsiang, W. C.
1987
Relative algebraic K-theory and cyclic homology. Zbl 0627.18004
Goodwillie, Thomas G.
1986
Cyclic homology, derivations, and the free loopspace. Zbl 0569.16021
Goodwillie, Thomas G.
1985
On the general linear group and Hochschild homology. Zbl 0566.20021
Goodwillie, Thomas G.
1985
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#### Cited by 326 Authors
13 Klein, John Robert 12 McCarthy, Randy 9 Goodwillie, Thomas Gehret 9 Johnson, Brenda Lynn 9 Volić, Ismar 8 Kuhn, Nicholas J. 8 Weibel, Charles A. 7 Arone, Gregory Z. 7 Blumberg, Andrew J. 7 Ching, Michael 6 Cortiñas, Guillermo H. 6 Kassel, Christian 6 Vigué-Poirrier, Micheline 6 Weiss, Michael S. 5 Chorny, Boris 5 Connes, Alain 5 Harper, John E. 5 Jones, John D. S. 5 Lodder, Gerald Matthew 5 Malkiewich, Cary 5 Munson, Brian A. 5 Solotar, Andrea Leonor 5 Tabuada, Gonçalo 5 Turchin, Victor Éduardovich 5 Williams, Bruce 4 Biedermann, Georg 4 Carlsson, Gunnar E. 4 Cohen, Ralph L. 4 Consani, Caterina 4 Dotto, Emanuele 4 Dundas, Bjørn Ian 4 Dwyer, William G. 4 Francis, John 4 Geller, Susan C. 4 Hasemeyer, Christian 4 Lambrechts, Pascal 4 Lindenstrauss, Ayelet 4 Sinha, Dev P. 4 Skopenkov, Arkadiĭ Borisovich 4 Zakharevich, Inna 3 Ayala, David 3 Barnes, David 3 Behrens, Mark Joseph 3 Bökstedt, Marcel 3 Budney, Ryan David 3 Eldred, Rosona 3 Frauenfelder, Urs Adrian 3 Groth, Moritz 3 Hsiang, Wu-Chung 3 Igusa, Kiyoshi 3 Kelly, Shane 3 Koytcheff, Robin 3 Krishna, Amalendu 3 Morrow, Matthew 3 Ogle, Crichton 3 Pirashvili, Teimuraz 3 Rognes, John 3 Röndigs, Oliver 3 Song, Yongjin 3 Songhafouo Tsopméné, Paul Arnaud 3 Stanley, Donald A. 3 Šťovíček, Jan 2 Albers, Peter 2 Angeltveit, Vigleik 2 Ausoni, Christian 2 Banerjee, Abhishek 2 Barwick, Clark 2 Bauer, Kristine 2 Baues, Hans-Joachim 2 Berger, Clemens 2 Betley, Stanislaw 2 Chachólski, Wojciech 2 Cho, Ilwoo 2 Cieliebak, Kai 2 Cohen, Frederick Ronald 2 Conant, James 2 Cuntz, Joachim 2 Ducoulombier, Julien 2 Emmanouil, Ioannis 2 Geisser, Thomas H. 2 Gepner, David 2 Gorchinskiĭ, Sergeĭ Olegovich 2 Herscovich, Estanislao 2 Hess, Kathryn P. 2 Hesselholt, Lars 2 Holland, Martin P. 2 Huber-Klawitter, Annette 2 Keller, Bernhard 2 Kerz, Moritz C. 2 Khalkhali, Masoud 2 Kupers, Alexander 2 Lambre, Thierry 2 Lawson, Tyler Douglas 2 Lind, John Alexander 2 Macko, Tibor 2 Madsen, Ib Henning 2 Mandell, Michael A. 2 Nicas, Andrew J. 2 Nistor, Victor 2 Oman, Peter J. ...and 226 more Authors
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#### Cited in 75 Serials
34 Algebraic & Geometric Topology 32 Journal of Pure and Applied Algebra 26 Transactions of the American Mathematical Society 26 $$K$$-Theory 24 Advances in Mathematics 19 Geometry & Topology 13 Inventiones Mathematicae 10 Journal of Homotopy and Related Structures 9 Journal of Topology 8 Proceedings of the American Mathematical Society 7 Journal of Algebra 7 Journal für die Reine und Angewandte Mathematik 6 Annales de l’Institut Fourier 6 Mathematische Annalen 6 Topology and its Applications 6 Journal of the American Mathematical Society 6 Journal of $$K$$-Theory 4 Communications in Algebra 4 Communications in Mathematical Physics 4 Israel Journal of Mathematics 4 Acta Mathematica 4 Compositio Mathematica 4 Mathematische Zeitschrift 3 Nagoya Mathematical Journal 3 Forum Mathematicum 3 Theory and Applications of Categories 3 Journal of Noncommutative Geometry 2 Journal of Geometry and Physics 2 Bulletin de la Société Mathématique de France 2 Colloquium Mathematicum 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Memoirs of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 International Journal of Mathematics 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Knot Theory and its Ramifications 2 Selecta Mathematica. New Series 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Izvestiya: Mathematics 2 Documenta Mathematica 2 Annals of Mathematics. Second Series 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Journal of Fixed Point Theory and Applications 2 Complex Analysis and Operator Theory 2 Annals of $$K$$-Theory 1 Bulletin of the Australian Mathematical Society 1 Nuclear Physics. B 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Bulletin of the London Mathematical Society 1 Czechoslovak Mathematical Journal 1 Fundamenta Mathematicae 1 Glasgow Mathematical Journal 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Osaka Journal of Mathematics 1 Annals of Global Analysis and Geometry 1 Science in China. Series A 1 MSCS. Mathematical Structures in Computer Science 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Applied Categorical Structures 1 Kyushu Journal of Mathematics 1 Advances in Applied Clifford Algebras 1 Journal of the Institute of Mathematics of Jussieu 1 Proceedings of the Steklov Institute of Mathematics 1 Algebra & Number Theory 1 Involve 1 Tbilisi Mathematical Journal 1 Forum of Mathematics, Sigma 1 EMS Surveys in Mathematical Sciences 1 Research in the Mathematical Sciences 1 Bollettino dell’Unione Matematica Italiana
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#### Cited in 30 Fields
210 Algebraic topology (55-XX) 138 Category theory; homological algebra (18-XX) 118 $$K$$-theory (19-XX) 79 Manifolds and cell complexes (57-XX) 59 Associative rings and algebras (16-XX) 42 Algebraic geometry (14-XX) 19 Commutative algebra (13-XX) 17 Nonassociative rings and algebras (17-XX) 15 Group theory and generalizations (20-XX) 15 Differential geometry (53-XX) 15 Global analysis, analysis on manifolds (58-XX) 11 Functional analysis (46-XX) 8 Number theory (11-XX) 6 Quantum theory (81-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Topological groups, Lie groups (22-XX) 3 Operator theory (47-XX) 2 Mathematical logic and foundations (03-XX) 2 Geometry (51-XX) 2 Convex and discrete geometry (52-XX) 2 Mechanics of particles and systems (70-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-03-03T11:39:33 |
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http://publications.jrc.ec.europa.eu/repository/handle/JRC56931
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Title: Dynamics of infectious disease transmission by inhalable respiratory droplets Authors: STILIANAKIS Nikolaos; DROSSINOS Ioannis Citation: JOURNAL OF THE ROYAL SOCIETY INTERFACE vol. 7 p. 1355-1366 Publisher: ROYAL SOC Publication Year: 2010 JRC N°: JRC56931 ISSN: 1742-5689 URI: http://publications.jrc.ec.europa.eu/repository/handle/JRC56931 DOI: 10.1098/rsif.2010.0026 Type: Articles in Journals Abstract: Transmission of respiratory infectious diseases in humans, for instance influenza, occurs by several modes. Respiratory droplets provide a vector of transmission of an infectious pathogen that may contribute to different transmission modes. An epidemiological model incorporating the dynamics of inhalable respiratory droplets is developed to assess their relevance in the infectious process. Inhalable respiratory droplets are divided into respirable droplets, diameter less than 10$\mu$m, and inspirable droplets, diameter in the range 10 to 100$\mu$m: both droplet classes may be inhaled or settle. Droplet dynamics is determined by their physical properties (size), whereas population dynamics by, among other parameters, the pathogen infectivity and the host contact rates. Three model influenza epidemic scenarios, mediated by different airborne or settled droplet classes, are analyzed. The scenarios are distinguished by the characteristic times associated with breathing at contact and with hand-to-face contact. The scenarios suggest that airborne transmission, mediated by respirable droplets, provides the dominant transmission mode in middle and long-term epidemics, whereas inspirable droplets, be they airborne or settled, characterise short-term epidemics with high attack rates. The model neglects close-contact transmission by droplet sprays (direct projection onto facial mucous membranes), retaining close-contact transmission by inspirable droplets. JRC Institute: Institute for the Protection and Security of the Citizen
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| 2015-01-29T22:26:51 |
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http://lanl.gov/science-innovation/science-programs/office-of-science-programs/high-energy-physics/theoretical-physics-q2.php
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# Los Alamos National Laboratory
Delivering science and technology to protect our nation and promote world stability
# Quarterly Progress Reports
Investigating the field of high energy physics through experiments that strengthen our fundamental understanding of matter, energy, space, and time.
## Los Alamos HEP Theory Quarterly Report 2014-02
Tanmoy Bhattacharya, Alexander Friedland, Michael L. Graesser, Rajan Gupta, Emil Mottola, Michael S. Warren
The theory group is active in a number of diverse areas of research. Their primary areas of interest are in physics beyond the Standard Model, cosmology, dark matter, lattice quantum chromodynamics, neutrinos, the fundamentals of quantum field theory and gravity, and particle astrophysics. Generally the questions pursued by this group relate to deep mysteries in our understanding of Nature at the boundaries of the Standard Model and the grammar we use to describe it–quantum field theory and General Relativity. The theory group continues to make advances at the forefront of research in these areas.
## Lattice QCD
The Los Alamos Lattice QCD team and their collaborators are carrying out four precision studies investigating signatures of new physics at the TeV scale, elucidating the structure of the nucleon, and understanding QCD at finite temperature. Progress on these four projects is described below.
### Nucleon charges and form-factors
Bhattacharya, Gupta, Yoon and their external collaborators (the PNDME collaboration) have reanalyzed the calculation of renormalization constants and the matrix elements of scalar and tensor operators to probe new physics at the TeV scale. They have revised the manuscript (arXiv:1306.5435 [hep-lat]) and submitted it for publication. They have submitted proposals for allocation of computer resources for FY15 to USQCD and XSEDE. The calculations on cluster and GPU computers at Los Alamos of the largest ${64}^{3}×144$ lattices at the weakest coupling are continuing.
Latest Reference: Physical Review D85:5, (2012) 054512.
### Matrix elements of novel CP violating operators and nEDM
Bhattacharya, Cirigliano, Gupta and Yoon are continuing to carry out the analysis of the mixing and renormalization of novel CP violating operators that contribute to the Neutron Electric Dipole Moment. They have determined an operator basis that allows for off-shell renormalization using external fixed momentum states, and a paper describing the one-loop matching between MSbar and a renormalization independent scheme is in progress. The numerical calculations of the relevant matrix elements are being done in collaboration with the RBC group using resources provided by the national USQCD initiative. Bhattacharya, Gupta, and Yoon have also started investigating the calculation of disconnected diagrams for the quark electric dipole matrix elements using clover fermions on HISQ lattices.
Latest References: Bhattacharya et al., arXiv:1212.4918 [hep-lat]; arXiv:1403.2445 [hep-lat].
### Behavior of QCD at finite temperature
Bhattacharya and Gupta carried out the statistical analysis of the entire data set generated by the full HotQCD collaboration to determine the equation of state. They are developing the final analysis tools using the free software package R to make simultaneous fits to data at different N_T to extrapolate to the continuum limit with full propagation of errors. These results will be presented by Bazavov at Quark Matter 2014 and by Bhattacharya at Lattice 2014 conferences. Bhattacharya and Gupta also contributed to the analysis and writing of the manuscript on the deconfinement transition and U(1) axial anomaly being prepared for publication in PRL using domain wall fermions.
### Disconnected diagrams and Transverse Momentum Distribution Functions
Bhattacharya, Gupta and Yoon, in collaboration with Michael Engelhardt, have started production runs for to investigate the signal in both connected and disconnected diagrams that will be needed to evaluate the Sivers function and other transverse momentum distribution functions using computing resources provided by USQCD at JLab.
## Improving searches for new particles at the LHC
Graesser and LANL post-doc Tuhin Roy began a collaboration to use Q-Jets to improve searches for new physics at the LHC. Tuhin is one of the originators of the Q-Jet idea. Previous Q-Jet studies have focused on improving the efficiency to tag a hadronically-decaying W boson through improving the mass resolution and cutting on the variance in the mass variable (called volatility by the Q-Jet authors). The new element here is to apply the Q-Jet idea to the whole event, that is, to consider multiple clustering interpretations of the whole event. They are specifically looking at improving the efficiency for identifying all-hadronic top quark pairs. Any significant improvements here will have implications for BSM searches. Computations for this project are being done on LANL's Institutional Computing cluster resources.
## Precision Cosmology Simulations
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute clustering amplitude of high-density regions mapped out by galaxy surveys, Warren and collaborators propose a relative measurement that compares those to the underdense regions, cosmic voids. On the basis of realistic mock catalogs they demonstrate that cross correlating galaxies and voids opens up the possibility to calibrate galaxy bias and to define a static ruler thanks to the observable geometric nature of voids.
Reference: N. Hamaus, B.D. Wandelt, P.M. Sutter, G. Lavaux, M. S. Warren, Cosmology with Void-Galaxy Correlations, Phys. Rev. Lett., 112(4):041304, 2014.
## Quantum Field Theory and Gravity
### Instability of Global de Sitter space
We (Paul R. Anderson of Wake Forest Univ. and E. M.) have shown that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The decay rate of de Sitter space into particles may be calculated in very much analogous manner as that of a uniform, constant electric field first found by Schwinger. For de Sitter space with ${H}^{2}=\Lambda /3$, the decay rate per unit volume to scalar particles of mass $M$ is
$\begin{array}{ccc}\phantom{\rule{6.0em}{0ex}}& \Gamma =\genfrac{}{}{0.1ex}{}{8{H}^{4}}{{\pi }^{2}}\mathrm{ln}\left[\mathrm{coth}\left(\pi \sqrt{\genfrac{}{}{0.1ex}{}{{M}^{2}}{{H}^{2}}-\genfrac{}{}{0.1ex}{}{9}{4}}\right)\right].\hfill & \hfill \text{(1)}\phantom{\rule{6.0em}{0ex}}\end{array}$
We studied the particle creation process in real time, computed their energy density in global ${𝕊}^{3}$ spatial sections, and showed that in the contracting phase they lead to an exponentially large energy density, necessitating an inclusion of their backreaction effects, which lead to large deviation of the spacetime from de Sitter space before the expanding phase can begin. These results are quite general and can be understood as also following from the effective action of the quantum conformal anomaly (2) for fields of any spin in de Sitter space, viz.
$\begin{array}{ccc}\phantom{\rule{6.0em}{0ex}}& {S}_{\mathrm{eff}}=\genfrac{}{}{0.1ex}{}{b\prime }{2}\int {d}^{4}x\sqrt{-g}\phantom{\rule{0.167em}{0ex}}\left\{-{\left(\square \varphi \right)}^{2}+2\left({R}^{ab}-\genfrac{}{}{0.1ex}{}{1}{3}R{g}^{ab}\right)\left({\nabla }_{a}\varphi \right)\left({\nabla }_{b}\varphi \right)+\left(\mathcal{E}-\genfrac{}{}{0.1ex}{}{2}{3}\square R\right)\varphi \right\}\hfill & \hfill \text{(2)}\phantom{\rule{6.0em}{0ex}}\end{array}$
where the curvature invariants $\mathcal{E}$ and $\mathcal{F}$ are given in terms of the Riemann curvature ${R}_{abcd}$ by
$\begin{array}{ccc}\phantom{\rule{6.0em}{0ex}}& \mathcal{E}\equiv {R}_{abcd}{R}^{abcd}-4{R}_{ab}{R}^{ab}+{R}^{2},\phantom{\rule{2.00em}{0ex}}\mathcal{F}\equiv {R}_{abcd}{R}^{abcd}-2{R}_{ab}{R}^{ab}+\genfrac{}{}{0.1ex}{}{1}{3}{R}^{2}.\hfill & \hfill \text{(3)}\phantom{\rule{6.0em}{0ex}}\end{array}$
The field $\varphi$ is an additional scalar degrees of freedom in the low energy effective theory of gravity, not present in the classical Einstein theory, which describes the long distance quantum correlations due to the trace anomaly.
The stress tensor derived from this effective action shows that states invariant under the $O\left(4\right)$ subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the $O\left(4,1\right)$ isometry group and its $O\left(4\right)$ subgroup are broken by quantum state fluctuations. In the expanding patch a small amplitude deviation of the state in sufficiently high $k$ modes also produces large deviations of the stress tensor at early times, emphasizing the extreme sensitivity of inflation to its initial conditions.
The main conclusion of our analysis is that the most symmetric state usually assumed in inflation is not the stable vacuum state. These results suggest that spatially inhomogeneous and/or dynamical models of cosmological dark energy within a Hubble horizon volume possessing only rotational $O\left(3\right)$ symmetry are relevant for determining the vacuum state and magnitude of cosmological dark energy in the universe.
These two papers have now been published in:
During this quarter the following invited talks were given:
• “New Horizons in Gravity: Dark Energy and Condensate Stars,” U. Miami, Physics Dept. seminar, Feb. 13, 2014.
• “Instability of de Sitter Space, the Schwinger Effect and Dynamical Dark Energy,” FAUST seminar, Florida Atlantic Univ., Boca Raton, FL, Feb. 24, 2014
• “What's the (Quantum) Matter with Black Holes?,” Barry Univ., Dept. of Physical Sciences, Miami Shores, FL, Feb. 26, 2014.
Contacts | Media | Calendar
| 2018-07-18T18:25:02 |
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|
https://indico.bnl.gov/event/8649/?print=1
|
High Energy / Nuclear Theory / RIKEN seminars
# [virtual NT/RIKEN seminar] QCD factorization and resummation in the small-x regime
## by Zhangbo Kang (UCLA)
US/Eastern
Bluejeans
#### Bluejeans
Description
The physics of gluon saturation or color glass condensate (CGC) has been one of the main driving forces for the future Electron Ion Collider. Significant progress has been made in the theory and phenomenology for computing physics observables measured at RHIC and LHC in the past decades. However, the higher-order perturbative calculations in the CGC formalism still remains a bit elusive, especially in comparison with the conventional QCD collinear factorization in the dilute regime. In this talk, using single hadron production in proton-nucleus collisions as an example, I point out some of the interesting difficulties and demonstrate how this can be solved. For example, in the standard collinear factorization, the natural hard scale will automatically arise from a higher-order calculation, while choosing the natural rapidity scale for small-x remains quite tricky even with explicit higher-order calculation. I further show how to perform threshold resummation and demonstrate how this would solve the well-known negative cross section problem for this process.
| 2022-01-26T17:56:35 |
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|
https://www.anl.gov/article/department-of-energy-supports-argonne-nuclear-technologies
|
# .argonne-logo-style0{fill:#231F20;} .argonne-logo-style1{fill:#FFFFFF;} .argonne-logo-style2{fill:#007836;} .argonne-logo-style3{fill:#0082CA;} .argonne-logo-style4{fill:#0B1F8F;} .argonne-logo-style5{fill:none;} .argonne-logo-style6{fill:#A12B2F;} .argonne-logo-style7{fill:#CD202C;} .argonne-logo-style8{fill:#77B300;} Argonne National Laboratory
Announcement | Argonne National Laboratory
# Department of Energy supports Argonne nuclear technologies
This fall, U.S. Department of Energy (DOE) Secretary Rick Perry announced nearly $4.7 million in funding for DOE’s Argonne National Laboratory across 16 projects in three divisions. The award is part of DOE’s Technology Commercialization Fund (TCF), designed to mature promising energy technologies with the potential for high impact.” This new funding shows the breadth and depth of Argonne’s Energy and Global Security directorate.” - Jeff Binder, Associate Laboratory Director for Energy and Global Security Four of those TCF awards, representing more than$1 million in funds, are slated for Argonne’s Nuclear Engineering division. The awards will support:
• Technology that diagnoses performance problems in nuclear power plants
• Technology to increase natural convection in advanced reactors
• An analytical capability to improve the safety of next-generation lead-cooled fast reactors (LFRs)
• Improvements in code acceptability to expedite the approval process for sodium-cooled fast reactors (SFRs)
This new funding shows the breadth and depth of Argonne’s Energy and Global Security directorate,” said Jeff Binder, Associate Laboratory Director for Energy and Global Security. The awards highlight the ingenuity of our world-class researchers and demonstrate the laboratory’s ability to help bring new nuclear energy technologies to market.”
The four projects include:
#### Advanced physics-based fluid system performance monitoring to support nuclear power plant operation
An Argonne team led by Rick Vilim, senior nuclear engineer, is seeking to speed commercialization of a technology that detects and diagnoses performance-related problems in the thermal-hydraulic systems of nuclear power plants. The technology eliminates the need for fault diagnosis by humans, which is time consuming and prone to errors, by using comparable automated sensors. Vilim and his team expects the technology - known as Parameter-Free Reasoning Operator for Automated, Identification and Diagnosis (PRO-AID) - to reduce costs and increase efficiency by spotting any faults early so they can be fixed.
To make PRO-AID commercially available, the team must first move from a simulation-level to a pilot-level environment. The team also needs to improve PRO-AID’s software and algorithms so Argonne’s partners in industry can understand and apply the code.
Argonne will work on this project with LPI, Inc., an engineering consulting company that offers extensive expertise in the area of fluid systems. LPI will provide a team of engineers familiar with power plant engineering to work with Argonne experts on the project.
#### Passive, high efficiency ventilation for the dracs and other natural circulation systems
Nuclear engineers view natural circulation as one of the more promising ways to remove decay heat from the reactor core in future advanced reactors. For these air-based cooling systems, engineers need an effective chimney design to ensure that air flows naturally and adequately in all weather conditions. An Argonne team led by Darius Lisowski, nuclear engineer, seeks to commercially develop a unique patent-pending invention that addresses this challenge. Argonne’s invention not only protects against wind and rain, but it also addresses several areas that existing chimney caps do not.
The technology has already passed laboratory tests. Now, the team plans to integrate the chimney cap design into the direct reactor auxiliary cooling system (DRACS), a passive decay-heat removal system developed by General Atomics for its Energy Multiplier Module (EM2) Small Modular Reactor concept. This project is poised to create significant market impacts due to the prevalence of chimney systems across industries and the nuclear industry’s recent focus on natural systems to remove passive decay heat.
The team will collaborate with General Atomics to test and evaluate the technology. The team will also examine its performance in real-world accident and abnormal operating scenarios.
During the proposed partnership, nuclear engineers will focus on experimental testing and will examine the chimney cap design to see how it will perform when installed along with the DRACS and within the EM2 reactor building.
#### Joint development of SAS4A code in application to oxide-fueled lfr severe accident analysis
Argonne is collaborating with Westinghouse Electric Company to expand the reach of its safety analysis software, known as SAS4A. It is part of Argonne’s suite of software that, through simulation, helps make sure these next-generation nuclear reactors are safe, sustainable and secure. SAS4A currently helps nuclear engineers analyze very rare, multiple-failure accidents in liquid-metal-cooled reactors.
The project will expand applicability of SAS4A to lead-cooled fast reactors, a next-generation nuclear technology with significant safety and economic potential. It is led by Tanju Sofu, the program manager for advanced modeling and simulation in Argonne’s Nuclear Engineering division. By expanding SAS4A’s use to LFRs, Sofu’s team expects to help overcome a significant licensing barrier to deployment of this promising technology.
To apply the code to lead-cooled fast reactors, the team will need to revise SAS4A to allow modeling of these reactors’ fuel and coolant system characteristics and unique phenomena involved in accidents with fuel failures. Westinghouse will work with the Argonne team to apply the code to the company’s specific LFR design. Sofu expects nuclear engineers to use the new SAS4A models to also analyze a broader spectrum of lead- or lead-bismuth-eutectic-cooled fast reactor design tracks.
#### NRC qualification of advanced reactor safety analysis software
When obtaining a commercial license for a nuclear reactor from the Nuclear Regulatory Commission, one must show that the codes and methods used for safety analyses are acceptable. To improve this process and facilitate the use of the U.S. Department of Energy’s resources, a team at Argonne, led by Nuclear Engineer Acacia Brunett, is addressing the need to qualify advanced reactor safety analysis software; and in particular, the systems-level liquid-metal analysis tool SAS4A/SASSYS-1.
While software qualification needs can vary with each vendor’s design, this project will address the critical characteristics common to most domestic sodium-cooled fast reactor designs. As part of this process, the Argonne team will identify and, more importantly, document relevant capabilities and features of SAS4A/SASSYS-1 to meet modern regulation’s state-of-the-art qualification requirements.
The team will work extensively with SFR industry members such as TerraPower and GE-Hitachi to obtain feedback and develop a pedigreed analysis tool that meets industry’s needs. The project’s ultimate goal is to reduce applicants’ typical licensing burden and to help SFR modeling and simulation capabilities mature and widen their acceptability within the nuclear industry.
The TCF awards are supported and managed by DOE’s Office of Technology Transition.
Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.
The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the Office of Science website.
| 2021-01-20T20:56:34 |
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http://www.malinc.se/math/geogebra/spreadsheeten.php
|
The spreadsheet in GeoGebra has most of the regular spreadsheet-features. When it comes to just doing numerical calculations, regular spreadsheet software is more advanced than the GeoGebra spreadsheet; the object-oriented way of doing things in GeoGebra however, makes it a much stronger tool than regular spreadsheets. Apart from manipulating numbers and formulas, you can also manipulate all GeoGebra-objects in the spreadsheet view.
Whenever you need many objects that follow some regular pattern, you can use the spreadsheet.
The basic features of the GeoGebra spreadsheet, features such as: how to make relative copies, how to plot points from the spreadsheet on the drawing pad, and how to use sliders when generating numbers in the spreadsheet, are explained on the pages Functions - Tables and Spreadsheet and Functions - Percentage Change.
## Geometrical objects and functions
The recording below demonstrates how to make a simple pattern of circles. It also shows a demonstration of how the Taylor expansion of $$f(x)=e^x$$ approximates the graph better and better as more terms are used. It is meant as a demonstration of how functions are handled in the spreadsheet, if you just want to demonstrate Taylor expansion, you can use the command:
TaylorPolynomial[<Function>, <x-Value>, <Order
Number>]
When inserting geometrical objects into the spreadsheet, you must write the command for the object needed. In most cases you can guess the name of the command, start writing and then the code-completion will help.
## Dynamic Colour
You can make a parabola using trace, as on this page Functions - The Parabola. These traces can instead be created as lines in a spreadsheet.
If you let the y-axis be the directrix and a free point A be the focus, then you must make a number of perpendicular bisectors between points on the y-axis and the point A.
In a similar way, you can make perpendicular bisectors between a point and points on a circle, this is shown in the topmost applet.
You specify a dynamic colour by specifying values for red, green and blue. Each value should be between 0 and 1. It is dynamic since you can use variables when specifying the values. In the example above, the following is entered under the Advanced-tab for the first line (in cell B1), these values are then relatively copied when dragging the small rectangle.
When very many objects are used in a worksheet, it may be slow. In such cases it is better to use lists. This is what the next page is about.
# further info:
Fourier Series - Square Wave from Wolfram MathWorld
RGB colour model
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License
www.malinc.se
| 2015-10-04T03:13:16 |
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|
http://www-spires.fnal.gov/spires/find/books/www?keyword=Printing
|
Fermilab Core Computing Division
Library Home | Ask a Librarian [email protected] | Book Catalog | Library Journals | Requests | SPIRES | Fermilab Documents |
Fermilab Library
SPIRES-BOOKS: FIND KEYWORD PRINTING *END*INIT* use /tmp/qspiwww.webspi1/31989.170 QRY 131.225.70.96 . find keyword printing ( in books using www
Call number: 3527337857:ONLINE Show nearby items on shelf Title: Fundamentals of Inkjet Printing The Science of Inkjet and Droplets Author(s): Hoath Date: 2016 Publisher: Wiley-VCH Size: 1 online resource (473 p.) ISBN: 9783527337859 Series: eBooks Series: Wiley Online Library Series: Wiley 2016 package purchase Keywords: Materials Science Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 10442120:ONLINE Show nearby items on shelf Title: Microsoft Office Excel 2010 QuickSteps [electronic resource] Author(s): John Cronan Date: 2010 Publisher: New York : McGraw-Hill Size: 1 online resource (278 p.) Note: An illustrated guide to Microsoft Excel 2010 Contents: Stepping into Excel -- Entering and editing data -- Formatting a worksheet -- Using formulas and functions -- Viewing and printing data -- Charting data -- Working with illustrations -- Managing data -- Analyzing and sharing data -- Extending Excel ISBN: 9780071634908 Series: ebrary eBook Series: eBooks Keywords: Microsoft Excel (Computer file) , Business Computer programs , Electronic spreadsheets Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 10442115:ONLINE Show nearby items on shelf Title: Microsoft Office Word 2010 QuickSteps [electronic resource] Author(s): Martin S. Matthews Date: 2010 Edition: 2nd ed. Publisher: New York : McGraw-Hill Size: 1 online resource (253 p.) Contents: 1 Stepping into Word -- 2 Working with Documents -- 3 Formatting a Document -- 4 Customizing a Document -- 5 Printing and Using a Mail Merge -- 6 Using Tables -- 7 Working with Illustrations -- 8 Using Special Features -- 9 Using Word with Other People ISBN: 0071634878 Series: ebrary eBook Series: eBooks Keywords: Microsoft Word Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Full Text: Click here Location: ONLINE
Call number: 10310727:ONLINE Show nearby items on shelf Title: A Guide to Microsoft Excel 2007 for scientists and engineers [electronic resource] Author(s): Bernard V. Liengme David J. Ellert Date: 2009 Size: 1 online resource (336 p.) Contents: 1. The Microsoft Excel Window 2. Basic Operations 3. Printing a Worksheet 4. Using Functions 5. Decision Functions 6. Charts 7. Curve Fitting 8. User-defined Functions 9. Modelling I 10. Solving Equations 11. Numerical Integration 12. Differential Equations 13. Modelling II 14. Statistics for Experimenters 15. Report Writing ISBN: 9780123746238 Series: ebrary eBook Series: eBooks Keywords: Engineering - Data processing , Microsoft Excel (Computer file) , Science - Data processing Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: Z246.W634::2004 Show nearby items on shelf Title: The non-designers design book Design and typographic principles for the visual novice Author(s): Robin Williams Date: 2004 Publisher: Peachpit Press ISBN: 9780321193858 Keywords: Layout (Printing) Handbooks, manuals, etc. , Graphic design (Typography) , Graphic arts. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: T385.F694737::2005 Show nearby items on shelf Title: AutoCAD 2006 and AutoCAD LT 2006 : no experience required Author(s): David Frey Date: 2005 Publisher: San Francisco : SYBEX Size: 667p Contents: 1. Getting to know AutoCAD -- 2. Basic commands to get started -- 3. Setting up a drawing -- 4. Gaining drawing strategies : part 1 -- 5. Gaining drawing strategies : part 2 -- 6. Using layers to organize your drawing -- 7. Grouping objects into blo cks -- 8. Generating elevations -- 9. Working with hatches and fills -- 10. Controlling text in a drawing -- 11. Dimensioning a drawing -- 12. Managing external references -- 13. Using layouts to set up a print -- 14. Printing an AutoCAD drawing. ISBN: 9780782144147 Keywords: AutoCAD 2006 , AutoCAD LT 2006 , Computer graphics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: T11.K55::2006 Show nearby items on shelf Title: Punctuation matters Advice on punctuation for scientific and technical writing Author(s): Alfred John Kirkman Date: 2006 Edition: 4th ed. Publisher: New York : Routledge Size: 145 p. Contents: Difficulties caused by lack of punctuation p. 3 The jobs done by punctuation marks p. 5 The relation of punctuation to intonation and stress p. 7 Is 'open' or 'light' punctuation enough? p. 9 How punctuation helps reading p. 9 Reducing uncertainty by punctuating carefully p. 13 Absence of punctuation may damage your credibility p. 14 Redundancy as helpful reinforcement p. 16 The lazy writer's evasion of responsibility p. 16 Guidelines p. 19 Apostrophe p. 21 Capital letters p. 24 Colon p. 27 Comma p. 34 Dash (em rule and en rule) p. 53 Ellipsis points p. 58 Exclamation mark p. 61 Full stop p. 62 Hyphen p. 66 Inverted commas (or quotation marks) p. 78 Parentheses (or brackets) p. 84 Question mark p. 89 Semi-colon p. 91 Slash p. 93 Underlining p. 96 Variations in printing: bold type and italic type p. 98 Appendices p. 103 Paragraphing p. 105 Word-division p. 115 Differences in punctuation in American English and British English p. 119 Bibliography p. 138 Index p. 140 ISBN: 0415399815 Keywords: Technical writing. , Punctuation. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: TA684.A47::2011 Show nearby items on shelf Title: Steel construction manual Author(s): Date: 2011 Edition: Fourteenth edition. Publisher: American Institute of Steel Construction Size: 1 volume (various pagings) Note: Fourth printing, 2015 Contents: Dimensions and properties -- General design considerations -- Design of flexural members -- Design of compression members -- Design of tension members -- Design of members subject to combined forces -- Design considerations for bolts -- Design consi derations for welds -- Design of connecting elements -- Design of simple shear connections -- Design of partially restrained moment connections -- Design of fully restrained moment connections -- Design of bracing connections and truss connections -- Desi gn of beam bearing plates, column base plates, anchor rods, and column splices -- Design of hanger connections, bracket plates, and crane-rail connections -- Specifications and codes -- Miscellaneous data and mathematical information -- Index and general nomenclature. ISBN: 9781564240606 Keywords: Building, Iron and steel, Tables. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: SPRINGER-2016-9781441980717:ONLINE Show nearby items on shelf Title: Encyclopedia of Color Science and Technology Author(s): Date: 2016 Publisher: New York, NY : Springer New York Size: 1 online resource (553 p.) Note: 10.1007/978-1-4419-8071-7 Contents: Introduction -- Accessibility and Color -- Art Conservation and Color -- Capturing Color -- The Chemistry of Color -- Color and Architecture -- Color and Computer Graphics -- Color and Culture -- Color and Education -- Color Appearance Correlates -- Color Crosscuts -- Color Design -- Color Differences -- Color Harmony -- Color Imaging -- Colorimetry and Color Spaces -- Color Management -- Color Palettes -- Data Visualization and Color -- The Description of Color -- Displaying Color -- Encoding Color -- History of Color -- Industrial Color -- The Measurement of Color -- Organizing Color -- The Perception of Color -- The Physics of Color -- Printing Color -- Processing Color -- Quality of Color ISBN: 9781441980717 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Physics , Printing , Publishers and publishing , Chemical engineering , Image processing , Optics , Optoelectronics , Plasmons (Physics) , Physics , Optics, Optoelectronics, Plasmonics and Optical Devices , Signal, Image and Speech Processing , Industrial Chemistry/Chemical Engineering , Image Processing and Computer Vision , Printing and Publishing Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642249860:ONLINE Show nearby items on shelf Title: VCSELs [electronic resource] : Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers Author(s): Rainer Michalzik Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The huge progress which has been achieved in the field is covered here, in the first comprehensive monograph on vertical-cavity surface-emitting lasers (VCSELs) since eight years. Apart from chapters reviewing the research fieldand the laser fundamen tals, there are comprehensive updates on red and blue emitting VCSELs, telecommunication VCSELs, optical transceivers, and parallel-optical links for computer interconnects. Entirely new contributions are made tothe fields of vectorial three-dimensional o ptical modeling, single-mode VCSELs, polarization control, polarization dynamics, very-high-speed design, high-power emission, use of high-contrast gratings, GaInNAsSb long-wavelength VCSELs,optical video links, VCSELs for optical mice and sensing, as wel l as VCSEL-based laser printing. The book appeals to researchers, optical engineers and graduate students Note: Springer eBooks Contents: Basic VCSEL Characteristics A Research Review Fundamentals Three Dimensional Modeling Single Mode VCSELs Device Technology and Performance Polarization Control Polarization Dynamics Design and Performance of High Speed VCSELs High Power VCSEL Arrays High Contrast Grating VCSELs From Infrared to Violet Emission Long Wavelength VCSELs with Buried Tunnel Junction GaInNAs(Sb) Long Wavelength VCSELs Red Emitting VCSELs GaN Based VCSELs Applications VCSEL Based Transceivers for Data Communications Low Cost Optical Video Links Progress in VCS ISBN: 9783642249860 Series: e-books Series: SpringerLink (Online service) Series: Springer Series in Optical Sciences, 0342-4111 : v166 Series: Physics and Astronomy (Springer-11651) Keywords: Microwaves , Optical materials Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461460060:ONLINE Show nearby items on shelf Title: Wavelets Made Easy [electronic resource] Author(s): Yves Nievergelt Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Originally published in 1999, Wavelets Made Easyoffers a lucid and concise explanation of mathematical wavelets.Written at the level of a first course in calculus and linear algebra, its accessible presentation is designedfor undergraduates in a vari ety of disciplinescomputer science, engineering, mathematics, mathematical sciencesas well as for practicing professionals in these areas. The presentsoftcover reprintretainsthecorrectionsfromthesecond printing (2001) andmakesthis uniquetext available to a wider audience. The first chapter startswith a description of the key features and applications of wavelets, focusing on Haar's wavelets but using onlyhigh-school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least-squaresapproximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates h ow to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particularattention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the cla ssroom as well as a valuable resource for self-study Note: Springer eBooks Contents: Preface Outline A. Algorithms for Wavelet Transforms Haar's Simple Wavelets Multidimensional Wavelets and Applications Algorithms for Daubechies Wavelets B. Basic Fourier Analysis Inner Products and Orthogonal Projections Discrete and Fast Fourier Transforms Fourier Series for Periodic Functions C. Computation and Design of Wavelets Fourier Transforms on the Line and in Space Daubechies Wavelets Design Signal Representations with Wavelets. D. Directories Acknowledgements Collection of Symbols Bibliography Index. ISBN: 9781461460060 Series: e-books Series: SpringerLink (Online service) Series: Modern Birkhuser Classics Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Harmonic analysis , Fourier analysis , Computer science Mathematics , Computer engineering Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461459729:ONLINE Show nearby items on shelf Title: Intersections of Random Walks [electronic resource] Author(s): Gregory F Lawler Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which hasapplications in many areas, par ticularly in statistical physics and statistical chemistry. Originally published in 1991,Intersections of Random Walks focuses on and explores a number of problems dealing primarily with thenonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusionlimited aggregation (DLA) the probability that independent random walks do not intersect and properties of walks without self-intersections. The presentsoftcover reprint includes corrections andaddenda fromthe1996 printing,and makesthis classic monographavailable to a wider audience. With a self-contained introduction to the properties of si mple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probabilityand statistical physics and to graduate students interested in basic properties of random walks Note: Springer eBooks Contents: Simple Random Walk Harmonic Measure Intersection Probabilities Four Dimensions Two and Three Dimensions Self Avoiding Walks Loop Erased walk Recent Results ISBN: 9781461459729 Series: e-books Series: SpringerLink (Online service) Series: Modern Birkhuser Classics Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Distribution (Probability theory) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2011-9781441974242:ONLINE Show nearby items on shelf Title: Interactive Quantum Mechanics [electronic resource] : Quantum Experiments on the Computer Author(s): S Brandt T Stroh H.D Dahmen Date: 2011 Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: harmonic waves and wave packets, f ree particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), two-particle systems, coupled harmonic oscillators, distinguishable and indistinguishable particles, coherent an d squeezed states in time-dependent motion, quantized angularmomentum, spin and magnetic resonance, hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies ofquant um-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on special functions of mathematical physics, coordinate systems and units, over 300 class-tested problems withhints for solutions, and a complete users guide to the INTERQUANTA program are also included. No programming or computer experience is needed to use INTERQUANTA. Its Java-based interface is as simple to use as surfing theInternet. Features of the INTERQUANTA program include: easy- to-use interface allowing fast change of physics parameters, demonstrations for each chapter illustrating new physical concepts andfeatures of INTERQUANTA, electronic help files guiding users through the program, simple printing of user-produced graphi cs. INTERQUANTA runs on: personal computers under Windowsand Linux, Macintosh computers under Mac OS X.(INTERQUANTA was tested on 32-bit systems under Windows 98, NT, 2000, ME, XP, Vista, and 7, under Linux Note: Springer eBooks Contents: Introduction Free Particle Motion in One Dimension Bound States in One Dimension Scattering in One Dimension A Two Particle System Free Particle Motion in Three Dimensions Bound States in Three Dimensions Scattering in Three Dimensions Spin and Magnetic Resonance Hybridization Special Functions of Mathematical Physics Additional Material and Hints for the Solution of Exercises A Systematic Guide to IQ How to Install IQ ISBN: 9781441974242 Series: e-books Series: SpringerLink (Online service) Series: Physics and Astronomy (Springer-11651) Keywords: Quantum theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2010-9783642033117:ONLINE Show nearby items on shelf Title: Large Deviations Techniques and Applications [electronic resource] Author(s): Amir Dembo Ofer Zeitouni Date: 2010 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter. Originallydeveloped in the context of s tatistical mechanics and of (random) dynamical systems, it proved to be a powerful tool in the analysis of systems where the combined effects of random perturbations lead to a behavior significantlydifferent from the noiseless case. The volume complements the central elements of this theory with selected applications in communication and control systems, bio-molecular sequence analysis, hypothesis testing problems in statistics,and the Gibbs conditioning principle in statistical mechanics. Starting with t he definition of the large deviation principle (LDP), the authors provide an overview of large deviation theorems in ${{\rm I\!R}}^d$ followed by theirapplication. In a more abstract setup where the underlying variables take values in a topological space, the authors provide a collection of methods aimed at establishing the LDP, such as transformations of the LDP, relations betweenthe LDP and Laplace's method for the evaluation for exponential integrals, properties of the LDP in topological vector spaces, and the behavior of the LDP under projective limits. They then turn to the study of the LDP for the samplepaths of certain stochastic processes and the application of such LDP's to the problem of the exit of randomly perturbed solutions of differential e quations from the domain of attraction of stable equilibria. They conclude with the LDPfor the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mix ing sequences and their application. The present soft cover editionis a corrected printing of the 1998 edition. Amir Dembo is a Professor of Mathematics and of Statistics at Stanford University. Ofer Ze Note: Springer eBooks Contents: LDP for Finite Dimensional Spaces Applications The Finite Dimensional Case General Principles Sample Path Large Deviations The LDP for Abstract Empirical Measures Applications of Empirical Measures LDP ISBN: 9783642033117 Series: e-books Series: SpringerLink (Online service) Series: Stochastic Modelling and Applied Probability, 0172-4568 : v38 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Systems theory , Distribution (Probability theory) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2008-9783540776956:ONLINE Show nearby items on shelf Title: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms [electronic resource] Author(s): Rufus Bowen Jean-Ren Chazottes Date: 2008 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: Rufus Bowen has left us a masterpiece ofmathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have beenproved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems. Note: Springer eBooks Contents: Preface to the 2nd edition by David Ruelle 0. Introduction 1.Gibbs measures A.Gibbs measures B.Ruelle's Perron Frobenius Theorem C.Construction of Gibbs measures D.Variational principle E.Further properties References 2.General thermodynamic formalism A.Entropy B.Pressure C.Variational principle D.Equilibrium states References 3.Axiom A diffeomorphisms A.Definition B. Spectral decomposition C.Markov partitions D.Symbolic dynamics References 4.Ergodic theory of Axiom A diffeomorphisms A.Equilibrium states for basic sets B.The ISBN: 9783540776956 Series: e-books Series: SpringerLink (Online service) Series: Lecture Notes in Mathematics, 0075-8434 : v470 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Differentiable dynamical systems , Distribution (Probability theory) , Cell aggregation Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2008-9783540378891:ONLINE Show nearby items on shelf Title: Cohomology of Number Fields [electronic resource] Author(s): Jrgen Neukirch Alexander Schmidt Kay Wingberg Date: 2008 Edition: Second Edition Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part providesalgebraic background: coho mology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galoisgroups of local and global fields: Tate duality , structure of absolute Galois groups of local fields, extensions with restricted ramification, Poitou-Tate duality, Hasse principles, theorem of Grunwald-Wang, Leopoldts conjecture,Riemanns existence theorem, the theorems of Iwasawa and of afarevic on so lvable groups as Galois groups, Iwasawa theory, and anabelian principles. New material is introduced here on duality theorems for unramified and tamelyramified extensions, a careful analysis of 2-extensions of real number fields and a complete proof of Ne ukirchs theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008edition Note: Springer eBooks Contents: Part I Algebraic Theory: Cohomology of Profinite Groups Some Homological Algebra Duality Properties of Profinite Groups Free Products of Profinite Groups Iwasawa Modules Part II Arithmetic Theory: Galois Cohomology Cohomology of Local Fields Cohomology of Global Fields The Absolute Galois Group of a Global Field Restricted Ramification Iwasawa Theory of Number Fields Anabelian Geometry Literature Index ISBN: 9783540378891 Series: e-books Series: SpringerLink (Online service) Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v323 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Group theory , Number theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2005-9783540266532:ONLINE Show nearby items on shelf Title: Martingale Methods in Financial Modelling [electronic resource] Author(s): Marek Musiela Marek Rutkowski Date: 2005 Edition: 2 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including theCox-Ross-Rubinstein binomia l model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendixcontaining all the necessary results is included. This m odel setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing ispresented. The second part of the text is devoted to the term structure modelling an d the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice. In the 2ndedition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devot ed to volatility risk. In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has beenextensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options arepresented in some detail. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with c onstant volatility. Part II of the book has been revisedfundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choic e of a model should be based on thereality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identif Note: Springer eBooks Contents: Spot and Futures Markets An Introduction to Financial Derivatives Discrete time Security Markets Benchmark Models in Continuous Time Foreign Market Derivatives American Options Exotic Options Volatility Risk Continuous time Security Markets Fixed income Markets Interest Rates and Related Contracts Short Term Rate Models Models of Instantaneous Forward Rates Market LIBOR Models Alternative Market Models Cross currency Derivatives ISBN: 9783540266532 Series: e-books Series: SpringerLink (Online service) Series: Stochastic Modelling and Applied Probability, 0172-4568 : v36 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Finance , Distribution (Probability theory) , Economics Statistics , Banks and banking Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2003-9780387216539:ONLINE Show nearby items on shelf Title: Interactive Quantum Mechanics Author(s): Siegmund Brandt Date: 2003 Size: 1 online resource (306 p.) Note: 10.1007/978-0-387-21653-9 Contents: 1 Introduction -- 2 Free Particle Motion in One Dimension -- 3 Bound States in One Dimension -- 4 Scattering in One Dimension -- 5 A Two-Particle System: Coupled Harmonic Oscillators -- 6 Free Particle Motion in Three Dimensions -- 7 Bound States in Three Dimensions -- 8 Scattering in Three Dimensions -- 9 Special Functions of Mathematical Physics -- 10 Additional Material and Hints for the Solution of Exercises -- A A Systematic Guide to IQ -- A.1 Overview -- A.1.1 Starting IQ -- A.1.2 Introductory Demonstration -- A.1.3 Selecting a Descriptor File -- A.1.4 Selecting a Descriptor and Producing a Plot -- A.1.5 Printing a Plot -- A.1.6 Changing Colors and Line Widths -- A.1.7 Changing Parameters -- A.1.8 Saving a Changed Descriptor -- A.1.9 Creating a Mother Descriptor -- A.1.10 Editing Descriptor Files -- A.1.11 Printing a Set of Plots -- A.1.12 Running a Demonstration -- A.1.13 Customizing -- A.1.14 Help and Context-Sensitive Help -- A.2 Coordinate Systems and Transformations -- A.2.1 The Different Coordinate Systems -- A.2.2 Defining the Transformations -- A.3 The Different Types of Plot -- A.3.1 Surface over Cartesian Grid in 3D -- A.3.2 Surface over Polar Grid in 3D -- A.3.3 2D Function Graph -- A.3.4 Contour-Line Plot in 2D -- A.3.5 Contour-Surface Plot in 3D -- A.3.6 Polar Diagram in 3D -- A.3.7 Probability-Ellipsoid Plot -- A.3.8 3D Column Plot -- A.4 Parameters — The Subpanel Physics -- A.4.1 The Subpanel Physics—Comp. Coord. -- A.4.2 The Subpanel Multiple Plot -- A.5 Parameters — The Subpanel Graphics -- A.5.1 The Subpanel Graphics—Geometry -- A.5.2 The Subpanel Graphics—Accuracy -- A.5.3 The Subpanel Graphics—Hidden Lines -- A.6 The Subpanel Background -- A.6.1 The Subpanel Background—Box -- A.6.2 The Subpanel Background—Scales -- A.6.3 The Subpanel Background—Arrows -- A.6.4 The Subpanel Background—Texts -- A.7 Parameters — The Subpanel Format -- A.8 Coding Mathematical Symbols and Formulae -- A.9 A Combined Plot and its Mother Descriptor -- A.9.1 The Subpanel Type and Format -- A.9.2 The Subpanel Table of Descriptors -- A.9.3 Special Cases -- A.10 Details of Printing -- A.10.1 Preview. Colors and Line Widths -- A.10.2 Using a System Printer -- A.10.3 Creating PostScript Files: IQ Export -- A.11 Preparing a Demonstration -- B How to Install IQ -- B.1 Contents of the CD-ROM -- B.2 Computer Systems on which INTERQUANTA Can Be Used -- B.3 Installation with Options. The File ReadMe.txt -- B.4 Quick Installation for the Impatient User ISBN: 9780387216539 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Physics , Quantum physics , Optics , Electrodynamics , Physics , Quantum Physics , Optics and Electrodynamics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2003-9780387216409:ONLINE Show nearby items on shelf Title: Nonlinear Dynamics in Physiology and Medicine Author(s): Date: 2003 Size: 1 online resource (436 p.) Note: 10.1007/978-0-387-21640-9 Contents: 1 Theoretical Approaches in Physiology -- 2 Introduction to Dynamics in Nonlinear Difference and Differential Equations -- 3 Bifurcations Involving Fixed Points and Limit Cycles in Biological Systems -- 4 Dynamics of Excitable Cells -- 5 Resetting and Entraining Biological Rhythms -- 6 Effects of Noise on Nonlinear Dynamics -- 7 Reentry in Excitable Media -- 8 Cell Replication and Control -- 9 Pupil Light Reflex: Delays and Oscillations -- 10 Data Analysis and Mathematical Modeling of Human Tremor -- A An Introduction to XPP -- Michael C. Mackey -- A.1 ODE Files -- A.2 Starting and Quitting XPP -- A.3 Time Series -- A.4 Numerics -- A.5 Graphic Tricks -- A.5.1 Axis -- A.5.2 Multiplotting -- A.5.3 Erasing -- A.5.4 Printing the Figures -- A.6 Examining the Numbers -- A.7 Changing the Initial Condition -- A.8 Finding the Fixed Points and Their Stability -- A.9 Drawing Nullclines and Direction Field -- A.10 Changing the Parameters -- A.11 Auto -- A.11.1 Bifurcation Diagram -- A.11.2 Scrolling Through the Points on the Bifurcation Diagram -- A.12 Saving Auto Diagrams -- B An Introduction to Matlab -- Michèle S. Titcombe and Caroline Haurie -- R.1 Starting and Quitting Matlab -- B.2 Vectors and Matrices -- B 2 1 Creating Matrices and Vectors -- .B.3 Suppressing Output to the Screen (the Semicolon!) -- B.4 Operations on Matrices -- B.5 Programs (M-Files) -- B.5.1 Script Files -- B.5.2 Function Files -- B.6 The Help Command -- B.7 Loops -- B.8 Plotting -- B.8.1 Examples -- B.8.2 Clearing Figures and Opening New Figures -- B.8.3 Symbols and Colors for Lines and Points -- B.9 Loading Data -- B.9.1 Examples -- B.10 Saving Your Work -- C Time Series Analysis -- Roderick Edwards and Michèle S. Titcombe -- C.1 The Distribution of Data Points -- C.2 Linear Processes -- C.3 Fourier Analysis ISBN: 9780387216409 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Interdisciplinary Applied Mathematics: 25 Keywords: Mathematics , Neurosciences , Neurobiology , Biomathematics , Biophysics , Biological physics , Mathematics , Mathematical and Computational Biology , Neurosciences , Neurobiology , Biophysics and Biological Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2002-9780387217062:ONLINE Show nearby items on shelf Title: Modern Applied Statistics with S Author(s): W. N Venables Date: 2002 Edition: Fourth Edition Size: 1 online resource (498 p.) Note: 10.1007/978-0-387-21706-2 Contents: 1 Introduction -- 1.1 A Quick Overview of S -- 1.2 Using S -- 1.3 An Introductory Session -- 1.4 What Next? -- 2 Data Manipulation -- 2.1 Objects -- 2.2 Connections -- 2.3 Data Manipulation -- 2.4 Tables and Cross-Classification -- 3 The S Language -- 3.1 Language Layout -- 3.2 More on S Objects -- 3.3 Arithmetical Expressions -- 3.4 Character Vector Operations -- 3.5 Formatting and Printing -- 3.6 Calling Conventions for Functions -- 3.7 Model Formulae -- 3.8 Control Structures -- 3.9 Array and Matrix Operations -- 3.10 Introduction to Classes and Methods -- 4 Graphics -- 4.1 Graphics Devices -- 4.2 Basic Plotting Functions -- 4.3 Enhancing Plots -- 4.4 Fine Control of Graphics -- 4.5 Trellis Graphics -- 5 Univariate Statistics -- 5.1 Probability Distributions -- 5.2 Generating Random Data -- 5.3 Data Summaries -- 5.4 Classical Univariate Statistics -- 5.5 Robust Summaries -- 5.6 Density Estimation -- 5.7 Bootstrap and Permutation Methods -- 6 Linear Statistical Models -- 6.1 An Analysis of Covariance Example -- 6.2 Model Formulae and Model Matrices -- 6.3 Regression Diagnostics -- 6.4 Safe Prediction -- 6.5 Robust and Resistant Regression -- 6.6 Bootstrapping Linear Models -- 6.7 Factorial Designs and Designed Experiments -- 6.8 An Unbalanced Four-Way Layout -- 6.9 Predicting Computer Performance -- 6.10 Multiple Comparisons -- 7 Generalized Linear Models -- 7.1 Functions for Generalized Linear Modelling -- 7.2 Binomial Data -- 7.3 Poisson and Multinomial Models -- 7.4 A Negative Binomial Family -- 7.5 Over-Dispersion in Binomial and Poisson GLMs -- 8 Non-Linear and Smooth Regression -- 8.1 An Introductory Example -- 8.2 Fitting Non-Linear Regression Models -- 8.3 Non-Linear Fitted Model Objects and Method Functions -- 8.4 Confidence Intervals for Parameters -- 8.5 Profiles -- 8.6 Constrained Non-Linear Regression -- 8.7 One-Dimensional Curve-Fitting -- 8.8 Additive Models -- 8.9 Projection-Pursuit Regression -- 8.10 Neural Networks -- 8.11 Conclusions -- 9 Tree-Based Methods -- 9.1 Partitioning Methods -- 9.2 Implementation in rpart -- 9.3 Implementation in tree -- 10 Random and Mixed Effects -- 10.1 Linear Models -- 10.2 Classic Nested Designs -- 10.3 Non-Linear Mixed Effects Models -- 10.4 Generalized Linear Mixed Models -- 10.5 GEE Models -- 11 Exploratory Multivariate Analysis -- 11.1 Visualization Methods -- 11.2 Cluster Analysis -- 11.3 Factor Analysis -- 11.4 Discrete Multivariate Analysis -- 12 Classification -- 12.1 Discriminant Analysis -- 12.2 Classification Theory -- 12.3 Non-Parametric Rules -- 12.4 Neural Networks -- 12.5 Support Vector Machines -- 12.6 Forensic Glass Example -- 12.7 Calibration Plots -- 13 Survival Analysis -- 13.1 Estimators of Survivor Curves -- 13.2 Parametric Models -- 13.3 Cox Proportional Hazards Model -- 13.4 Further Examples -- 14 Time Series Analysis -- 14.1 Second-Order Summaries -- 14.2 ARIMA Models -- 14.3 Seasonality -- 14.4 Nottingham Temperature Data -- 14.5 Regression with Autocorrelated Errors -- 14.6 Models for Financial Series -- 15 Spatial Statistics -- 15.1 Spatial Interpolation and Smoothing -- 15.2 Kriging -- 15.3 Point Process Analysis -- 16 Optimization -- 16.1 Univariate Functions -- 16.2 Special-Purpose Optimization Functions -- 16.3 General Optimization -- Appendices -- A Implementation-Specific Details -- A.1 Using S-PLUS under Unix / Linux -- A.2 Using S-PLUS under Windows -- A.3 Using R under Unix / Linux -- A.4 Using R under Windows -- A.5 For Emacs Users -- B The S-PLUS GUI -- C Datasets, Software and Libraries -- C.1 Our Software -- C.2 Using Libraries -- References ISBN: 9780387217062 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Computer mathematics , Computer software , Probabilities , Statistics , Mathematics , Probability Theory and Stochastic Processes , Computational Mathematics and Numerical Analysis , Mathematical Software , Statistics and Computing/Statistics Programs , Statistical Theory and Methods Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2000-9781461204930:ONLINE Show nearby items on shelf Title: Introduction to Graphical Modelling Author(s): David Edwards Date: 2000 Edition: Second Edition Size: 1 online resource (335 p.) Note: 10.1007/978-1-4612-0493-0 Contents: 1 Preliminaries -- 1.1 Independence and Conditional Independence -- 1.2 Undirected Graphs -- 1.3 Data, Models, and Graphs -- 1.4 Simpson’s Paradox -- 1.5 Overview of the Book -- 2 Discrete Models -- 2.1 Three-Way Tables -- 2.2 Multi-Way Tables -- 3 Continuous Models -- 3.1 Graphical Gaussian Models -- 3.2 Regression Models -- 4 Mixed Models -- 4.1 Hierarchical Interaction Models -- 4.2 Breaking Models into Smaller Ones -- 4.3 Mean Linearity -- 4.4 Decomposable Models -- 4.5 CG-Regression Models -- 4.6 Incomplete Data -- 4.7 Discriminant Analysis -- 5 Hypothesis Testing -- 5.1 An Overview -- 5.2 X2-Tests -- 5.3 F-Tests -- 5.4 Exact Conditional Tests -- 5.5 Deviance-Based Tests -- 5.6 Permutation F-Test -- 5.7 Pearson x2-Test -- 5.8 Fisher’s Exact Test -- 5.9 Rank Tests -- 5.10 Wilcoxon Test -- 5.11 Kruskal-Wallis Test -- 5.12 Jonckheere-Terpstra Test -- 5.13 Tests for Variance Homogeneity -- 5.14 Tests for Equality of Means Given Homogeneity -- 5.15 Hotelling’s T2 -- 6 Model Selection and Criticism -- 6.1 Stepwise Selection -- 6.2 The EH-Procedure -- 6.3 Selection Using Information Criteria -- 6.4 Comparison of the Methods -- 6.5 Box-Cox Transformations -- 6.6 Residual Analysis -- 6.7 Dichotomization -- 7 Directed Graphs and Their Models -- 7.1 Directed Acyclic Graphs -- 7.2 Chain Graphs -- 7.3 Local Independence Graphs -- 7.4 Covariance Graphs -- 7.5 Chain Graphs with Alternative Markov Properties -- 7.6 Reciprocal Graphs -- 8 Causal Inference -- 8.1 Philosophical Aspects -- 8.2 Rubin’s Causal Model -- 8.3 Pearl’s Causal Graphs -- 8.4 Discussion -- A The MINI Command Language -- A.1 Introduction -- A.2 Declaring Variables -- A.3 Undirected Models -- A.3.1 Deleting Edges -- A.3.2 Adding Edges -- A.3.3 Other Model-Changing Commands -- A.3.4 Model Properties -- A.4 Block-Recursive Models -- A.4.1 Defining the Block Structure -- A.4.2 Block Mode -- A.4.3 Defining Block-Recursive Models -- A.4.4 Working with Component Models -- A.5 Reading and Manipulating Data -- A.5.1 Reading Casewise Data -- A.5.2 Reading Counts, Means, and Covariances -- A.5.3 Transforming Data -- A.5.4 Restricting Observations -- A.5.5 Generating Raw Data -- A.5.6 Deleting Variables -- A.6 Estimation -- A.6.1 Undirected Models (Complete Data) -- A.6.2 Undirected Models (Missing Data) -- A.6.3 CG-Regression Models -- A.7 Hypothesis Testing -- A.7.1 x2-Tests -- A.7.2 Test of Homogeneity -- A.7.3 F-Tests -- A.7.4 Edge Deletion Tests -- A.7.5 Edge Deletion F-Tests -- A.7.6 Exact Tests -- A.7.7 Symmetry Tests -- A.7.8 Randomisation Tests -- A.8 Model Selection -- A.8.1 Stepwise Selection -- A.8.2 The EH-Procedure -- A.8.3 Selection Using Information Criteria -- A.9 The Box-Cox Transformation -- A.10 Residuals -- A.11 Discriminant Analysis -- A.12 Utilities -- A.12.1 File Input -- A.12.2 The Workspace -- A.12.3 Printing Information -- A.12.4 Displaying Parameter Estimates -- A.12.5 Displaying Summary Statistics -- A.12.6 Setting the Maximum Model -- A.12.7 Fixing Variables -- A.12.8 Macros -- B Implementation Specifics of MB’! -- B.1 Calling MIM -- B.2 The Main Menu -- B.3 Entering Commands and Navigating the Work Area -- B.4 The Built-In Editor -- B.5 Interactive Data Entry -- B.6 Independence Graphs -- B.7 Simple Data Graphics -- B.7.1 Scatter Plots -- B.7.2 Histograms -- B.7.3 Box Plots -- B.8 Graphics Export Formats -- B.9 Direct Database Access -- B.10 Program Intercommunication -- C On Multivariate Symmetry -- D On the Estimation Algorithms -- D.1 The MIPS Algorithm -- D.1.1 Notation -- D.1.2 The Likelihood Equations -- D.1.3 The General Algorithm -- D.1.4 The A-Collapsible Variant -- D.1.5 The Mean Linear Variant -- D.1.6 The Q-Equivalent Variant -- D.1.7 The Step-Halving Variant -- D.2 The EM-Algorithm -- D.3 The ME-Algorithm -- References ISBN: 9781461204930 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Mathematical models , Statistics , Mathematics , Mathematical Modeling and Industrial Mathematics , Statistical Theory and Methods Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1999-9781447105831:ONLINE Show nearby items on shelf Title: Astronomical Equipment for Amateurs Author(s): Martin Mobberley Date: 1999 Size: 1 online resource (266 p.) Note: 10.1007/978-1-4471-0583-1 Contents: 1 Fundamentals for Beginners -- Using Low Magnification -- Using High Magnification -- Eyepiece Sizes -- 2 Refractors and Reflectors -- Achromatic Refractors -- Apochromatic Refractors -- Semi-Apochromatic Refractors -- Refractors or Reflectors? -- Newtonian Reflectors -- Long-Focus Newtonians -- Collimation -- Dobsonians -- Buying a Telescope -- Beginners’ Telescopes -- Buyer Beware! -- High-Quality Refractors -- Apochromats for the Connoisseur -- Other Telescope Considerations -- 3 Catadioptrics, Cassegrains and Schmidt-Cassegrains -- Cassegrains -- Schmidt-Cassegrains -- Maksutovs -- Schiefspieglers -- 4 Binoculars -- Stands for Binoculars -- Image-Stabilised Binoculars -- 5 Eyepieces -- Magnification -- Practical Considerations -- Comet Seeking -- Focusing-Tube Diameter -- Real Field Limitations -- Popular Commercial Eyepieces -- High-Definition Eyepieces -- Barlow Lenses -- Eyepiece Projection -- Illuminated-Reticle Eyepieces -- Commercial Guiding Eyepieces -- 6 Telescope Mountings -- The Equatorial Mounting -- Commercial Telescope Mounting Systems -- Commercial Drive Systems -- Home-Made Drives and Unusual Mountings -- Electronic Drive Design -- Unusual Mountings -- Poncet Platforms -- Alt-azimuth Field De-Rotators -- 7 Accessories -- Finders -- Guide Telescopes -- Off-Axis Guiders -- Horses for Courses -- Photographic Equipment - Film versus CCD -- Undriven Astrophotography -- Simple Tracking -- Dew -- Film, Meteor-Photography Equipment and Wide-Field Camera Equipment -- Satellite Trails -- Medium-Format Cameras -- Fish-Eye Lenses -- Developing and Printing -- Developing Tanks -- Developing Colour Film -- Black-and-White Printing -- Cold Cameras and Film Hypersensitising -- Camera Interfaces -- Focusers -- Commercial Schmidt-Cassegrain Focusing -- Manual Guiding and Off-Axis Guiders -- Guiding for Comet Photography -- A Comet Marathon -- Coma Correctors -- A Final Word on Focusers -- Filters -- Planetary Filters -- Deep Sky Filters -- Comet Filters -- Photographic Filters -- Photometric Filters for CCDs -- Schmidt Cameras and Astrographs -- 8 Electronic Imaging and the Electronics Revolution -- CCDs -- Buying a CCD Camera -- Starlight Xpress -- SBIG and Meade -- Auto-Slewing with a Schmidt-Cassegrain and a CCD Camera -- SBIG Autoguiding -- Other Manufacturers -- Using a CCD Camera -- Understanding and Processing the Digital Image -- A Dark Frame -- Background Brightness -- Flat-Field -- Diffraction Focusers -- Useful Processing Routines -- Unsharp Masking -- Deconvolution -- Median Filters -- Non-Linear Contrast-Stretch -- Image Formats -- Astrometry -- Photometry -- 9 Image Processing, Planetarium and Telescope Control Software -- QMips 1.81 by Christian Buil -- MIRA AL by Axiom -- Hidden Image by Sehgal -- CCD Astrometry -- Paintshop Pro -- Adobe Photoshop -- Printers and Scanners -- Planetarium Software -- Planetarium Telescope Control -- 10 Video Astronomy -- Image Intensifiers -- 11 Observatories -- The Simplest Solution -- Simple Observatories -- If It Can Go Wrong -- Observatory Domes -- 12 Equipment for Observing the Sun -- Eyepiece Projection -- Direct Solar Observation -- Observing in White Light -- Seeing -- Hydrogen-Alpha Equipment -- Viewing Eclipses -- 13 Star Atlases and Deep Sky Atlases -- Appendix 1 Dealers, Bibliography and URLs -- Equipment Suppliers -- Quality Binocular Mounting Suppliers -- Societies Worth Joining -- Internet URLs -- Books -- Appendix 2 Photographic and Visual Magnitude Limits ISBN: 9781447105831 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Physics , Observations, Astronomical , Astronomy , Astrophysics , Physics , Astronomy, Observations and Techniques , Astrophysics and Astroparticles Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1998-9781461222125:ONLINE Show nearby items on shelf Title: Maple V Learning Guide Author(s): K. M Heal Date: 1998 Size: 1 online resource (8 p.) Note: 10.1007/978-1-4612-2212-5 Contents: 1. Interactive Use of Maple -- 1.1 The Worksheet Interface -- 1.2 Tutorial 1: Solving Problems -- 1.4 Tutorial 3: Documenting Your Work -- 1.5 Tutorial 4: Multiple Worksheets -- 1.6 Tutorial 5: Getting Help -- 1.7 Conclusion -- 2. Mathematics with Maple: the Basics -- 2.1 Introduction -- 2.2 Numerical Computations -- 2.3 Basic Symbolic Computations -- 2.4 Assigning Names to Expressions -- 2.5 More Basic Types of Maple Objects -- 2.6 Expression Manipulation -- 2.7 Conclusion -- 3. Finding Solutions -- 3.1 Simple solve -- 3.2 Solving Numerically: fsolve -- 3.3 Other Solvers -- 3.4 Polynomials -- 3.5 Calculus -- 3.6 Differential Equations: dsolve -- 3.7 The Organization of Maple -- 3.8 The Maple Packages -- 3.9 Conclusion -- 4. Graphics -- 4.1 Graphing in Two Dimensions -- 4.2 Graphing in Three Dimensions -- 4.3 Animation -- 4.4 Annotating Plots -- 4.5 Composite Plots -- 4.6 Special Types of Plots -- 4.7 Manipulating Graphical Objects -- 4.8 Conclusion -- 5. Evaluation and Simplification -- 5.1 Mathematical Manipulations -- 5.2 The Assume Facility -- 5.3 Structural Manipulations -- 5.4 Evaluation Rules -- 5.5 Conclusion -- 6. Examples from Calculus -- 6.1 Introductory Calculus -- 6.2 Ordinary Differential Equations -- 6.3 Partial Differential Equations -- 6.4 Conclusion -- 7. Input and Output -- 7.1 Reading Files -- 7.2 Writing Data to a File -- 7.3 Exporting Whole Worksheets -- 7.4 Printing Graphics -- 7.5 Conclusion ISBN: 9781461222125 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Chemometrics , Computer science , Algorithms , Physics , Computational intelligence , Mathematics , Algorithms , Symbolic and Algebraic Manipulation , Theoretical, Mathematical and Computational Physics , Math. Applications in Chemistry , Computational Intelligence Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1997-9781461218265:ONLINE Show nearby items on shelf Title: Discovering Curves and Surfaces with Maple® Author(s): Grażyna Klimek Date: 1997 Size: 1 online resource (217 p.) Note: 10.1007/978-1-4612-1826-5 Contents: 1. Maple Preliminaries -- 1.1 General Comments -- 1.2 Basic Plots -- 1.3 Accessing Plotting Structures -- 2. Two-Dimensional Plots -- 2.1 Basic Graphs -- 2.2 Additional Options -- 2.3 Maps of Surfaces -- 3. Geometric Manipulation -- 3.1 Affine Transformations in Two Dimensions -- 3.2 Affine Transformations in Three Dimensions -- 3.3 Coordinate Systems -- 3.4 Perspective -- 3.5 Shadow and Radial Projections -- 3.6 Matrix Notation -- 3.7 General Transformations of Plots -- 4. Three-Dimensional Plots -- 4.1 Basic Three-Dimensional Plots -- 4.2 Overview of Plotting Options -- 4.3 Color -- 4.4 Lighting -- 4.5 PLOT and PLOT3D Data Structures -- 4.6 Examples -- 5. Functions and Procedures -- 5.1 Elementary Functions -- 5.2 Graphics and Functions -- 5.3 Procedures -- 5.4 Interpolation -- 5.5 Iteration and Fractals -- 5.6 Mixing Curves and Surfaces -- 6. Animations -- 6.1 Overview of Animation Commands -- 6.2 Animations in Two-Dimensions -- 6.3 Animations in Three-Dimensions -- 7. The plottools Package -- 7.1 The plottools Objects -- 7.2 Plot Transformations -- 8. Specialized Graphics -- 8.1 Graphing Complex Functions -- 8.2 Differential Equations -- 8.3 Miscellaneous Commands -- 9. Saving and Exporting Maple Graphics -- 9.1 Saving, Editing, and Printing -- 9.2 External Rendering and Ray Tracing ISBN: 9781461218265 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1995-9781461384311:ONLINE Show nearby items on shelf Title: Lectures on Polytopes Updated Seventh Printing of the First Edition Author(s): Günter M Ziegler Date: 1995 Size: 1 online resource (300 p.) Note: 10.1007/978-1-4613-8431-1 Contents: and Examples -- Polytopes, Polyhedra, and Cones -- Faces of Polytopes -- Graphs of Polytopes -- Steinitz’ Theorem for 3-Polytopes -- Schlegel Diagrams for 4-Polytopes -- Duality, Gale Diagrams, and Applications -- Fans, Arrangements, Zonotopes, and Tilings -- Shellability and the Upper Bound Theorem -- Fiber Polytopes, and Beyond -- Fiber Polytopes, and Beyond ISBN: 9781461384311 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Graduate Texts in Mathematics: 152 Keywords: Mathematics , Geometry , Mathematics , Geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1994-9781461226765:ONLINE Show nearby items on shelf Title: ITSM for Windows A User’s Guide to Time Series Modelling and Forecasting Author(s): Peter J Brockwell Date: 1994 Size: 1 online resource (118 p.) Note: 10.1007/978-1-4612-2676-5 Contents: 1 Introduction -- 1.1 The Programs -- 1.2 System Requirements -- 1.3 Creating Data Files -- 2 PEST -- 2.1 Getting Started -- 2.2 Preparing Your Data for Modelling -- 2.3 Finding a Model for Your Data -- 2.4 Testing Your Model -- 2.5 Prediction -- 2.6 Model Properties -- 2.7 Nonparametric Spectral Estimation -- 3 SMOOTH -- 3.1 Introduction -- 3.2 Moving Average Smoothing -- 3.3 Exponential Smoothing -- 3.4 Removing High Frequency Components -- 4 SPEC -- 4.1 Introduction -- 4.2 Bivariate Spectral Analysis -- 5 TRANS -- 5.1 Introduction -- 5.2 Computing Cross Correlations -- 5.3 An Overview of Transfer Function Modelling -- 5.4 Fitting a Preliminary Transfer Function Model -- 5.5 Calculating Residuals from a Transfer Function Model -- 5.6 LS Estimation and Prediction with Transfer Function Models -- 6 ARVEC -- 6.1 Introduction -- 6.2 Model Selection with the AICC Criterion -- 6.3 Forecasting with the Fitted Model -- 7 BURG -- 7.1 Introduction -- 8 ARAR -- 8.1 Introduction -- 8.2 Running the Program -- 9 LONGMEM -- 9.1 Introduction -- 9.2 Parameter Estimation -- 9.3 Prediction -- 9.4 Simulation -- 9.5 Plotting the Model and Sample ACVF -- Appendix A: The Screen Editor WORD6 -- A.1 Basic Editing -- A.2 Alternate Keys -- A.3 Printing a File -- A.4 Merging Two or More Files -- A.5 Margins and Left and Centre Justification -- A.6 Tab Settings -- A.7 Block Commands -- A.8 Searching -- A.9 Special Characters -- A.10 Function Keys -- A. 11 Editing Information -- Appendix B: Data Sets ISBN: 9781461226765 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Statistics , Computer simulation , Statistics , Statistics and Computing/Statistics Programs , Simulation and Modeling Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1991-9781461231165:ONLINE Show nearby items on shelf Title: ITSM: An Interactive Time Series Modelling Package for the PC Author(s): Peter J Brockwell Date: 1991 Size: 1 online resource (104 p.) Note: 10.1007/978-1-4612-3116-5 Contents: 1 Introduction -- 1.1 The Programs -- 1.2 System Requirements -- 1.3 Creating Data Files -- 2 PEST -- 2.1 Getting Started -- 2.2 Preparing Your Data for Modelling -- 2.3 Finding a Model for Your Data -- 2.4 Testing Your Model -- 2.5 Prediction -- 2.6 Model Properties -- 2.7 Nonparametric Spectral Estimation -- 3 SMOOTH -- 3.1 Introduction -- 3.2 Moving Average Smoothing -- 3.3 Exponential Smoothing -- 4 SPEC -- 4.1 Introduction -- 4.2 Bivariate Spectral Analysis -- 5 TRANS -- 5.1 Introduction -- 5.2 Computing Cross Correlations -- 5.3 An Overview of Transfer Function Modelling -- 5.4 Fitting a Preliminary Transfer Function Model -- 5.5 Calculating Residuals from a Transfer Function Model -- 5.6 LS Estimation and Prediction with Transfer Function Models -- 6 ARVEC -- 6.1 Introduction -- 6.2 Model Selection with the AICC Criterion -- 6.3 Forecasting with the Fitted Model -- 7 ARAR -- 7.1 Introduction -- 7.2 Running the Program -- A Word6: A Screen Editor -- A.1 Basic Editing -- A.2 Alternate Keys -- A.3 Printing a File -- A.4 Merging Two or More Files -- A.5 Margins Left and Centre Justification -- A.6 Tab Settings -- A.7 Block Commands -- A.8 Searching -- A.9 Special Characters -- A.10 Function Keys -- A.11 Editing Information -- B Data Sets ISBN: 9781461231165 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Applied mathematics , Engineering mathematics , Mathematics , Applications of Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1986-9783642827181:ONLINE Show nearby items on shelf Title: Ion Formation from Organic Solids (IFOS III) Mass Spectrometry of Involatile Material Author(s): Date: 1986 Size: 1 online resource (222 p.) Note: 10.1007/978-3-642-82718-1 Contents: I 252Cf-Plasma Desorption -- Use of Polymer Surfaces for Molecular Ion Adsorption and Desorption -- Electronic Sputtering of Biomolecules -- On the Charge-State Dependence of Secondary Ion Emission from Phenylalanine -- Particle Desorption from Non-Metallic Surfaces by High Energy Heavy Ions -- 252Cf-PDMS: Multiplicity of Desorbed Ions and Correlation Effects -- II Secondary Ion Mass Spectrometry (SIMS) -- Surface Organic Reactions Induced by Ion Bombardment -- Ion Bombardment MS: A Sensitive Probe of Chemical Reactions Occurring at the Surface of Organic Solids -- Ion-Neutral Correlations Following Metastable Decay -- Metastable Ion Studies with a 252Cf Time-of-Flight Mass Spectrometer -- Increasing Secondary Ion Yields: Derivatization/SIMS -- Aspects and Applications of Derivatization/SIMS -- Influence of the Target Preparation on the SI-Emission of Organic Molecules -- Secondary Ion Formation Processes in Amino Acid-Metal Adsorption Systems -- Analytical Applications of High-Performance TOF-SIMS -- TOF-SIMS of Polymers in the High Mass Range -- The Application of Time-of-Flight Secondary Ion Mass Spectrometry in the Characterization of Apolipoprotein Mutants -- III Liquid SIMS Including FAB -- Sputtering Yields from Liquid Organic Matrices -- Sputtering from Liquid and Solid Organic Matrices -- Secondary Ion Emission from Glycerol and Silver Supported Organic Molecules -- Temperature Effects in Particle Bombardment Mass Spectrometry of Methanol -- Internal Energy Distribution of Ions Emitted in Secondary Ion Mass Spectrometry -- Fast Atom Bombardment of Peptides Above 5000 Daltons -- Amino Acid Sequencing of Peptide Mixture: Structural Analysis of Human Hemoglobin Variants (Digit Printing Method) -- Oligonucleotide Sputtering from Liquid Matrices -- Some Experiments on the Production of Ions in Soft Ionisation Mass Spectrometry -- Decompositions Occurring Remote from the Charge Site: A New Class of Fragmentation of FAB-Desorbed Ions -- IV Laser-Induced Ion Formation -- Laser and Plasma Desorption: Matrices and Metastables in Time-of-Flight Mass Spectrometry -- Evidence for Simultaneous Generation of Ion Pairs in Laser Mass Spectrometry -- The Influence of the Substrate on Ultraviolet Laser Desorption Mass Spectrometry of Biomolecules -- On Different Desorption Modes in LDMS -- V Other Ion Formation Processes -- “Spontaneous” Desorption of Negative Ions from Organic Solids and Films of Ice at Low Temperature -- Electric Pulse-Induced Desorption Compared to Other Techniques — Mechanism, Mass Spectra, and Applications -- VI Instrumentation -- A New Dual-MS Technique Combining Negative Ion Formation by Plasma Desorption with EI-like Positive Ion Formation by In-Beam Desorption -- The Chemical Ionization/Particle-Induced Ion Source -- Design of Modern Time-of-Flight Mass Spectrometers -- Design of an Organic SIMS Instrument with Separate Triple Stage Quadrupole (TSQ) and Time-of-Flight (TOF) Spectrometers -- High-Resolution TOF Secondary Ion Mass Spectrometer -- VII Fourier Transform Ion Cyclotron Resonance -- Laser Desorption Fourier Transform Mass Spectrometry: Mechanisms of Desorption and Analytical Applications -- Desorption Ionization and Fourier Transform Mass Spectrometry for the Analysis of Large Biomolecules -- Application of Secondary Ion Mass Spectrometry Combined with Fourier Transform Ion Cyclotron Resonance -- Index of Contributors ISBN: 9783642827181 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Springer Proceedings in Physics: 9 Keywords: Chemistry , Physical chemistry , Chemistry , Physical Chemistry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1983-9781461211402:ONLINE Show nearby items on shelf Title: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Author(s): John Guckenheimer Date: 1983 Size: 1 online resource (462 p.) Note: 10.1007/978-1-4612-1140-2 Contents: Contents: Introduction: Differential Equations and Dynamical Systems -- An Introduction to Chaos: Four Examples -- Local Bifurcations -- Averaging and Perturbation from a Geometric Viewpoint -- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors -- Global Bifurcations -- Local Codimension Two Bifurcations of Flows -- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index ISBN: 9781461211402 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Applied Mathematical Sciences: 42 Keywords: Mathematics , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1977-9781461299387:ONLINE Show nearby items on shelf Title: FORTRAN Programming A Supplement for Calculus Courses Author(s): William R Fuller Date: 1977 Size: 1 online resource (148 p.) Note: 10.1007/978-1-4612-9938-7 Contents: 1 A Little Vocabulary -- 2 Fortran Basics -- Arithmetic operations -- Arithmetic hierarchies -- Variable names -- Assignment statements -- Number types, type statements -- Simplified output -- Use of the data card -- 3 Branching statements -- Logical IF, Go to -- Logical connectives -- Stop -- 4 Supplied functions, Arithmetic statement functions -- Supplied functions -- Arithmetic statement functions -- 5 Algorithms and flow charts -- Symbols -- Compute through -- 6 Sequences -- Approximation by sequences, monotonic sequences -- Squeeze theorem -- Recursive definitions -- 7 Output formatting -- Print, format statements -- Specifying number types -- Skip symbol, pX -- Printing headings -- Vertical carriage control -- 8 Roundoff error -- Word length capability -- Accumulated error -- Differencing -- Double Precision -- Double Precision functions -- 9 Potpourri of Fortran statements -- Do, Continue -- Subscripts and dimension -- Read -- Subprograms -- Alphameric constants -- Arithmetic IF -- Computed Go to -- 10 Numerical evaluation of integrals -- Fundamental theorem -- Definition of integral -- Error terms -- 11 Applications to Functions of Two Variables, Infinite Series -- Maxima and Minima -- Gradient method -- Numerical evaluations of double integrals -- Surface Area (Triangularization) -- Infinite series -- 12 Differential equations -- Line elements -- Euler’s method -- Runge-Kutta method -- Solutions by power series -- Picard’s method -- Higher order equations and systems -- Solutions to selected exercises -- Computer problems by topics -- Typical course outline ISBN: 9781461299387 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Computer science , Computer Science , Computer Science, general Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1974-9781475708271:ONLINE Show nearby items on shelf Title: Acoustical Holography Volume 5 Author(s): Date: 1974 Size: 1 online resource (738 p.) Note: 10.1007/978-1-4757-0827-1 Contents: TRW Acousto-Optical Nonimmersion Flaw-Imaging System -- Recent Developments with the Scanning Laser Acoustic Microscope -- Bragg-Diffraction Imaging: A Potential Technique for Medical Diagnosis and Material Inspection, Part II -- Linearized Subfringe Interferometric Holography -- Acoustical Holography Using Temporally Modulated Optical Holography -- High-Resolution Acoustic Imaging by Contact Printing -- Acoustic Holographic Interferometry -- High Frequency Acoustic Holography in Solids -- Ultrasonic Holography Through Metal Barriers -- Experimental Results from an Underwater Acoustical Holographic System -- Acoustical Holographic Transverse Wave Scanning Technique for Imaging Flaws in Thick-Walled Pressure Vessels -- A Survey of Sound Propagation in Soils -- Applications of Acoustic Surface Wave Visualization to Nondestructive Testing -- Acoustical Holography — A Comparison with Phased Array Sonar -- Threshold Contrast for Three Real-Time Acoustic-Imaging Systems -- A New Ultrasound Imaging Technique Employing Two-Dimensional Electronic Beam Steering -- A Study of Near Field Ultrasonic Beam Patterns from a Pulsed Linear Array -- Acoustic Imaging with Thin Annular Apertures -- An Electronically Focused Acoustic Imaging Device -- Rigorous Analysis of the Liquid-Surface Acoustical Holography System -- Elimination of Spurious Detail in Acoustic Images -- Methods for Increasing the Lateral Resolution of B-Scan -- Medical Uses of Acoustical Holography -- A Medical Imaging Acoustical Holography System Using Linearized Subfringe Holographic Interferometry -- Digital Processing of Acoustical Holograms -- An Ultrasonic Holographic Imaging System for Medical Applications -- A New, High-Performance Ultrasonic Camera -- Potential Medical Applications for Ultrasonic Holography -- Complex On-Axis Holograms and Reconstruction without Conjugate Images -- A Computerized Acoustic Imaging Technique Incorporating Automatic Object Recognition -- Computer Enhancement of Acoustic Images -- Image Reconstruction by Computer in Acoustical Holography -- The Effects of Circuit Parameters on Image Quality in a Holographic Acoustic Imaging System -- Algebraic Reconstruction of Spatial Distributions of Acoustic Absorption within Tissue from Their Two-Dimensional Acoustic Projections -- Optical Processing of Anamorphic Holograms Constructed in an Ultrasonic Holography System with a Moving Source and an Electronic Reference -- An Acoustic Image Sensor Using a Transmit-Receive Array -- Advances in the Sokoloff Tube -- Linear Receiving Array for Acoustic Imaging and Holography -- A Progress Report on the Sokolov Tube Utilizing a Metal Fiber Faceplate -- Real Time Acoustical Imaging with a 256 × 256 Matrix of Electrostatic Transducers -- Modified Sokolov Camera Utilizing Condenser-Microphone Arrays of the Foil-Electret Type -- A Solid Plate Acoustical Viewer for Underwater Diving ISBN: 9781475708271 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Physics , Optics , Optoelectronics , Plasmons (Physics) , Physics , Optics, Optoelectronics, Plasmonics and Optical Devices Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: Q172.5.C45S767::1994B Show nearby items on shelf Title: Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering Author(s): Steven Henry Strogatz Date: 1994 Publisher: Cambridge, Mass. : Perseus Pub. Size: 498 p. Note: First paperback printing, 2000 Contents: 1. Overview -- Pt. I. One-Dimensional Flows. 2. Flows on the Line. 3. Bifurcations. 4. Flows on the Circle -- Pt. II. Two-Dimensional Flows. 5. Linear Systems. 6. Phase Plane. 7. Limit Cycles. 8. Bifurcations Revisited -- Pt. III. Chaos. 9. Lorenz Equations. 10. One-Dimensional Maps. 11. Fractals. 12. Strange Attractors ISBN: 0738204536 Series: Studies in nonlinearity Keywords: Chaotic behavior in systems , Dynamics , Nonlinear theories Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QC786.A1UN38::1968B Show nearby items on shelf Title: Design report : National Accelerator Laboratory Author(s): Fermi National Accelerator Laboratory Date: 1968 Publisher: Washington, D.C. : Universities Research Association under the auspices of the U.S. Atomic Energy Commission Size: 267 p Note: This 2nd printing, July 1968, has ... brought up to date the parameters of the accelerator given in tables throughout the report and collected in an appendix. Some of the text has been rewritten...--Pref. to the 2nd printing Corp. Author: Fermi National Accelerator Laboratory Keywords: Synchrotron , Proton-antiproton colliders--Illinois--Batavia Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Location: Fermilab collection on the cross-walk Report-number: FERMILAB-DESIGN-1968-01
Call number: QC571.M7813 Show nearby items on shelf Title: Electrostatics and its Applications Author(s): Arthur Dearth Moore 1895 -,(ed.) Date: 1973 Publisher: Wiley: New York Size: 481 pgs. Contents: 1. Introduction, 2. Introduction ot Electrostatics, 3. Mathematical Formulation of Electric Field Analysis, 4. Charging Macroscopic Particles, 5. Static Electrification of Dielectrics and at Materials' Interfaces, 6. Long-Lasting Electrization and Electrets, 7. Electrostatic Motors, 8. Electrostatic Generators, 9. Electrostatic Precipitation, 10. Electrostatic Separation, 11. Electrostatic Coating, 12. Electrostatic Imaging, 13. Nonimpact Printing, 14. Nonumiform Field Effects: Dielectrophoresis, 15. Dielectrophoresis of Biological Materials, 16. Electrostatics in the Power Industry, 17. Atmospheric Electrostatics, 18. Electrostaic Nuisances and Hazards, 19. Other Electrostatic Effects and Applications, 20. The Status Abroad ISBN: 0471614505 Keywords: Electrostatics. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QB476.5.W55::2000 Show nearby items on shelf Title: Tools of Radio Astronomy : Problems and Solutions Author(s): T. L. (Thomas L.) Wilson 1942- S. (Susanne) Huttemeister 1963- Date: 2000 Publisher: Springer, New York Note: 1st edition, corrected 2nd printing 2005 Contents: Radio Astronomical Fundamentals Electromagnetic Wave Propagation Wave Polarization Signal Processing and Receivers Antenna Fundamentals Filled Aperture Antennas Interferrometers and Aperture Synthesis Observational Methods Emission Mechanisms of Continuous Radiation Some Examples of Thermal and Non-Thermal Radio Sources Spectral Line Fundamentals Line Radiation of Neutral Hydrogen Recombination Lines Molecules in Interstellar space ISBN: 3540668020 Series: Astronomy and astrophysics library Keywords: Radio astronomy , Radio astronomy Problems, exercises, etc. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QB3.S52::1960 Show nearby items on shelf Title: Source book in astronomy, 1900-1950 Author(s): Harlow Shapley (ed.) Date: 1960 Publisher: Cambridge : Harvard University Press Size: 423 p Note: 3rd printing ISBN: 0674821858 Series: Source books in the history of the sciences Keywords: Astronomy Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: QA79.TK5105.8885.D74B78::2011 Show nearby items on shelf Title: Sams teach yourself Adobe Dreamweaver CS5 in 24 hours Author(s): Betsy Bruce John Ray Robyn Ness Date: 2011 Publisher: Indianapolis, Ind. : Sams Pub Size: 480 p Contents: A World Wide Web of Dreamweaver possibilities -- A tour of Dreamweaver -- Setting up a website -- Adding text and lists -- Making hyperlinks, anchors, and mailto links -- Displaying data in tables -- Looking under the hood : exploring HTML -- Displaying images -- Making web graphics in Fireworks CS5 -- Adding Flash and other multimedia to a web page -- Formatting web pages with cascading style sheets -- Using CS% for positioning -- Creating CS% for mobile devices and printing -- Using site assets, library items, and templates -- Designing for WordPress an content management systems -- Adding Spry menu bars for navigation -- Using dynamic HTML and AP Divs -- Adding interactivity with behaviors -- Using Spry, the widget browser and extensions -- Using the Dreamweaver HTML5 features -- Creating a form and collecting data -- Sending and reacting to form data -- Uploading, sharing, and managing web projects -- Maintaining a website ISBN: 9780672333309 Keywords: Dreamweaver (Computer file) , Web sites Authoring programs , Web sites Design Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.9.U83S89::2008 Show nearby items on shelf Title: Rapid GUI programming with Python and Qt: The definitive guide to PyQt programming Author(s): Mark Summerfield Date: 2008 Publisher: Upper Saddle River, NJ: Prentice Hall Size: 625 p. Contents: pt. I. Python programming -- Data types and data structures -- Control structures -- Classes and modules -- pt. II. Basic GUI programming -- Introduction to GUI programming -- Dialogs -- Main windows -- Using Qt designer -- Data handling and custom fi le formats -- pt. III. Intermediate GUI programming -- Layouts and multiple documents -- Events, the clipboard, and drag and drop -- Custom widgets -- Item-based graphics -- Rich text and printing -- Model/view programming -- Databases -- pt. IV. Advanced GUI programming -- Advanced model/view programming -- Online help and internationalization -- Networking -- Multithreading -- Appendix A. Installing -- Appendix B. Selected PyQt widgets -- Appendix C. Selected PyQt class hierarchies ISBN: 9780132354189 Series: Prentice Hall open source software development series Keywords: Qt (Electronic resource) , Graphical user interfaces (Computer systems) , Python (Computer program language) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.9.MW6P65::2015 Show nearby items on shelf Title: Windows 10: the missing manual Author(s): David Pogue Date: 2015 Publisher: O'Reilly Size: 673 p Contents: The Windows desktop. Desktop & start menu File explorer, taskbar & action center Organizing & finding your files Redesigning the desktop Cortana, your voice assistant -- The programs of Windows 10. Programs & documents Settings & control panel The windows starter apps -- Windows online. Getting online The Edge browser Mail Security & privacy -- Hardware and peripherals. Tablets, laptops & hybrids Printing, fonts & PDFs Hardware & drivers Maintenance, speed & troubleshooting Backups & fi le history The disk chapter -- The Windows network. Accounts (and logging on) Setting up a small network Sharing files on the network -- Appendixes. Appendix A. Installing & upgrading to Windows 10 Appendix B. Where'd it go? Appendix C. Master list o f keyboard shortcuts & gestures. ISBN: 9781491947173 Keywords: Microsoft Windows (Computer file) , Operating systems (Computers) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.9.ME9S95::2013 Show nearby items on shelf Title: Excel 2013: Absolute beginner's guide Author(s): Tracy Syrstad Date: 2013 Publisher: Indianapolis, IN: Que Size: 387 p. Contents: Understanding the Microsoft Excel interface -- Working wtih workbooks, sheets, rows, columns, and cells -- Getting data onto a sheet -- Formatting sheets and cells -- Using formulas -- Using functions -- Sorting data -- Filtering and consolidating dat a -- Distributing and printing a workbook -- Subtotals and grouping -- Creating charts and sparklines -- PivotTables and slicers -- Using power view to create reports -- Inserting SmartArt, WordArt, and pictures -- An introduction to using macros and UDFs -- Introducing the Excel web app ISBN: 9780789750570 Series: Absolute beginner's guide Keywords: Microsoft Excel (Computer file) , Electronic spreadsheets Computer programs. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.9.ME9F79::2013 Show nearby items on shelf Title: Microsoft Excel 2013 plain & simple Author(s): Curtis Frye Date: 2013 Publisher: Sebastopol, CA: O'Reilly Media Size: 351 p Contents: About this book -- What's new and improved in Excel 2013 -- Getting started with Excel 2013 -- Building a workbook -- Managing and viewing worksheets -- Using formulas and functions -- Formatting the cell -- Formatting the worksheet -- Printing work sheets -- Customizing Excel to the way you work -- Sorting and filtering worksheet data -- Summarizing data using charts -- Enhancing your worksheets with graphics -- Sharing Excel data with other programs -- Using Excel in a group environment. ISBN: 9780735672437 Series: Plain & simple Keywords: Microsoft Excel (Computer file) , Business, Computer programs , Electronic spreadsheets Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.9.F48A366::2013 Show nearby items on shelf Title: Adobe Acrobat XI The official training workbook from Adobe Systems. Author(s): Date: 2013 Publisher: San Jose, Calif. : AdobePress Size: 323 p Note: includes 1 CD-ROM Contents: Getting started -- Introducing Adobe Acrobat XI -- Creating Adobe PDF files -- Reading and working with PDF files -- Enhancing PDF documents -- Editing content in PDF files -- Using Acrobat with Microsoft Office files (Windows) -- Combining files -- Adding signatures and security -- Using Acrobat in a review cycle -- Working with forms in Acrobat -- Using formscentral (Acrobat Pro) -- Using actions (Acrobat Pro) -- Using Acrobat in professional printing ISBN: 9780321886798 Series: Classroom in a book. Keywords: Adobe Acrobat. , Portable document software. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.76.O63P63::2011 Show nearby items on shelf Title: MAC OS X Lion : the missing manual Author(s): David Pogue Date: 2011 Publisher: Sebastopol, CA : Pogue Press/O'Reilly Size: 909p. Contents: Chapter 0. The New Lion Landscape, Chapter 1. Folders and Windows, Chapter 2. Organizing Your Stuff, Chapter 3. Spotlight, Chapter 4. Dock, Desktop and Toolbars, Chapter 5. Documents, Programs, and Mission Control, Chapter 6. Entering Data, Moving Data and Time Machine, Chapter 7. Services, Automator and AppleScript, Chapter 8. Windows on Macintosh, Chapter 9. System Prefrences, Chapter 10. The Free Programs, Chapter 11. CDs, DVDs and iTunes Chapter 12. Accounts, Parental Controls and Security, Chapter 13. Networking, File Sharing and AirDrop, Chapter 14. Printing, Scanning, Fonts and Graphics, Chapter 15. Sound, Movies and Speech, Chapter 16. The Unix Crash Course, Chapter 17. Internet Setup and iCloud, Chapter 18. Mail and Contacts, Chapter 19. Safari, Chapter 20. iChat, Chapter 21. SSH, FTP, VPN and Web Sharing ISBN: 9781449397494 Series: Missing manual Keywords: Operating systems (Computers) , Macintosh (Computer) Programming Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA76.76.H94S3524::2010 Show nearby items on shelf Title: CSS cookbook Author(s): Christopher Schmitt Date: 2010 Edition: 3rd ed. Publisher: Sebastopol, CA : O'Reilly Size: 702 p Contents: Using HTML basics -- CSS basics -- Web typography -- Images -- Page elements -- Lists -- Links and navigation -- Forms -- Tables -- Designing web pages for printing -- Page layouts -- Hacks, workarounds, and troubleshooting -- Designing with CSS -- Interacting with Java Script. ISBN: 9780596155933 Keywords: Cascading style sheets. , Web sites Design. , Cascading Style Sheets 2.1 , Cascading Style Sheets Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Location: MAIN
Call number: QA459.H64::1954 Show nearby items on shelf Title: Plane Geometry Problems, with Solutions Author(s): Marcus Horblit Kaj L. Nielsen Date: 1954 Publisher: Barnes & Noble Note: Fourth Printing [c1947] Series: College Outline Series Keywords: Geometry, Plane Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. Location: MAIN
Call number: QA162.M39::1992 Show nearby items on shelf Title: Abstract algebra and solution by radicals Author(s): John Edward Maxfield Margaret W. Maxfield Date: 1992 Edition: Dover ed. Publisher: New York : Dover Publications Size: 209 p Note: This Dover edition, first published in 1992, is an unabridged, corrected republication of the second (corrected) printing of the work first published by the W.B. Saunders Company, Philadelphia, 1971 Contents: Groups, Other Abstract Algebras, More About Groups, Mappings That Preserve Relations, Groups of Prime Order, Two Alternating Groups, Historical Intermission, Polynomials, Algebraic Field Extensions, Galois theory, Radicals and Roots of Unity, Solution by Radicals ISBN: 0486671216 Keywords: Algebra, Abstract. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
Call number: NC997.G676::2005 Show nearby items on shelf Title: Basics of design: Layout and typography for beginners Author(s): Lisa Graham Date: 2005 Edition: 2nd ed. Publisher: Clifton Park, N.Y. : Thomson/Delmar Learning Size: 305 p Note: Study book for the IAAP CAP Exam (Certified Administrative Professional Exam) Contents: Pt. 1. Design & layout basics -- Before you begin to design -- Emphasis -- Contrast -- Balance -- Alignment -- Repetition -- Flow -- Images -- Color -- pt. 2. Typography basics -- Overview of technical terms -- A few simple type rules -- pt. 3. Projects & resources -- Focus on ... -- Tools and resources. ISBN: 1401879527 Keywords: Layout (Printing) , Graphic design (Typography) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com Location: MAIN
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# Step 9
Use efficient methods to add, subtract, multiply and divide fractions
### Examples of what pupils should know and be able to do
Add and subtract more complex fractions, e.g. $\frac{11}{18}+\frac{7}{24}$, including mixed numbers.
Solve problems involving fractions, e.g. In a survey of 24 pupils $\frac{1}{3}$ liked football best, $\frac{1}{4}$ liked basketball, $\frac{3}{8}$ liked athletics and the rest liked swimming. How many liked swimming?
### Probing questions
• Give pupils some examples of addition, subtraction, multiplication and division of fractions with common mistakes in them. e.g.$\frac{2}{8}+\frac{3}{6}=\frac{5}{14}$. Ask them to talk you through the mistakes and how they would correct them.
• The answer is:$\frac{3}{8}$. What is the question?
| 2013-06-18T05:14:23 |
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|
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.12%20001
|
• •
### 全球价值链要素收入与中国制造业竞争力研究
• 出版日期:2019-12-25 发布日期:2020-12-28
### Research on the Competitive Competence of China’s Manufacturing Industry Based on GVC Factor Income
Yang Yong
• Online:2019-12-25 Published:2020-12-28
Abstract: The domain of global value chain (GVC) competition has turned from “product“to “activity” and the domestic factor income other than gross export becomes a more intuitive trade benefit indicator. This paper constructs a method which can account GVC income at the sector and factor level respectively, and then applies it to the competitiveness evaluation for China′s manufacturing industry through the revealed comparative advantage index of GVC factor income. I use WIOT and SEA database to test the change in the RCA of China’s manufacturing GVC by sector and factor. The result is that factor income in China′s manufacturing GVC is growing rapidly, but the revealed comparative advantage of labor and tangible capital is disappearing and the RCA of intangible capital is still obvious comparatively. While GVC employment in China′s manufacturing industry is growing but nonfabricationoriented and serviceoriented trend is obvious. We should improve China’s GVC factor income and employment monitoring, matching mechanism of industrial chain at home and abroad, and promote specialization in high valueadded activities in the future. It is also a key point to build a matching and coordinating mechanism of value chain between home and abroad. Countries should strengthen evaluating the chain effect of accumulation along GVC of international trade policies and promote the competence of the GVC governance and coordination within the framework of multilateralism.
| 2022-12-03T13:42:26 |
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|
https://par.nsf.gov/biblio/10132223
|
Tight decomposition functions for mixed monotonicity
Mixed monotonicity is a property of a system’s vector field that says that the vector field admits a decomposition function, in a lifted space, that has some order preserving properties. It is recently shown that this property allows one to efficiently over-approximate the system’s onestep reachable set with a hyperinterval, which is obtained by evaluating the vector field’s decomposition function at two points. Such decomposition functions are usually not unique and some decompositions may not be tight in the sense that the resulting hyperintervals are not the smallest ones that contain the exact one-step reachable set, which leads to conservative over-approximation. In this paper, we show that for a general class of functions, there exists a tight decomposition, which can be implicitly constructed as the solution of certain optimization problems. This implies that any function from Rn to Rm (hence any forward complete system) is mixed-monotone. However, the usefulness of the constructed tight decomposition functions is limited by the fact that it might not be possible to evaluate them efficiently. We show that under certain conditions, the tight decompositions can reduce to a function with explicit expression, which can be directly evaluated. This result suggests that it is not mixed monotonicity itself, more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10132223
Journal Name:
58th IEEE Conference on Decision and Control (CDC)
2. Abstract The classical serendipity and mixed finite element spaces suffer from poor approximation on nondegenerate, convex quadrilaterals. In this paper, we develop families of direct serendipity and direct mixed finite element spaces, which achieve optimal approximation properties and have minimal local dimension. The set of local shape functions for either the serendipity or mixed elements contains the full set of scalar or vector polynomials of degree r , respectively, defined directly on each element (i.e., not mapped from a reference element). Because there are not enough degrees of freedom for global $$H^1$$ H 1 or $$H(\text {div})$$ H ( div ) conformity, exactly two supplemental shape functions must be added to each element when $$r\ge 2$$ r ≥ 2 , and only one when $$r=1$$ r = 1 . The specific choice of supplemental functions gives rise to different families of direct elements. These new spaces are related through a de Rham complex. For index $$r\ge 1$$ r ≥ 1 , the new families of serendipity spaces $${\mathscr {DS}}_{r+1}$$ DS r + 1 are the precursors under the curl operator of our direct mixed finite element spaces, which can be constructed to have reduced or full $$H(\text {div})$$ H (more »
5. A Boolean {\em $k$-monotone} function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of the classical {\em monotone} functions, which are the {\em $1$-monotone} functions. Motivated by the recent interest in $k$-monotone functions in the context of circuit complexity and learning theory, and by the central role that monotonicity testing plays in the context of property testing, we initiate a systematic study of $k$-monotone functions, in the property testing model. In this model, the goal is to distinguish functions that are $k$-monotone (or are close to being $k$-monotone) from functions that are far from being $k$-monotone. Our results include the following: \begin{enumerate} \item We demonstrate a separation between testing $k$-monotonicity and testing monotonicity, on the hypercube domain $\{0,1\}^d$, for $k\geq 3$; \item We demonstrate a separation between testing and learning on $\{0,1\}^d$, for $k=\omega(\log d)$: testing $k$-monotonicity can be performed with $2^{O(\sqrt d \cdot \log d\cdot \log{1/\eps})}$ queries, while learning $k$-monotone functions requires $2^{\Omega(k\cdot \sqrt d\cdot{1/\eps})}$ queries (Blais et al. (RANDOM 2015)). \item We present a tolerant test for functions $f\colon[n]^d\to \{0,1\}$ with complexity independent ofmore »
| 2023-02-03T00:39:48 |
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http://starcraft.wikia.com/wiki/Fossil_fuels
|
# Fossil fuels
6,854pages on
this wiki
Fossil fuels are hydrocarbons, formed from the remains of organisms such as phytoplankton and zooplankton that have settled in anoxic conditions and been subjected to heat and pressure. Since the beginning of their use en masse at the start of the Industrial Revolution, fossil fuels became humanity's primary fuel source.
Fossil fuels are non-renewable resources however, a fact that became most apparant in the 22nd century. A lack of affordable fuels bit deep into the world economy, causing many economic systems to collapse in on themselves. Although society continued to exist under the auspecies of the United Powers League in the 23rd century, the quest for alternative fuel sources was a pressing issue. It was in this period that a scientist, Doran Routhe, theorized that alternative fuel sources could be found beyond the Solar System. This, and other factors, led to the dispatch of the four supercarriers from Earth[1] in 2231,[2][3] heading for the outlying world of Gantris VI. Due to a computer malfunction, the ships missed their target and ended up in the Koprulu Sector.[1]
Although Routhe didn't know it, his belief that alternative fuels existed was vindicated by the existence of vespene gas.[1] However, both gasoline[4] and coal[5] are still used for small scale power generation and heat respectively and oil is compatible with at least one siege tank variant.[5]
## ReferencesEdit
1. 1.0 1.1 1.2 Underwood, Peter, Bill Roper, Chris Metzen and Jeffrey Vaughn. StarCraft (Manual). Irvine, Calif.: Blizzard Entertainment, 1998.
2. April 6, 2010. "Timeline". StarCraft II: Heaven's Devils. Simon & Schuster (Gallery Books). pp. 311 - 323. ISBN 978-1416-55084-6.
3. April 12, 2011. "Timeline." StarCraft II: Devils' Due. Simon & Schuster (Gallery Books). pp. 248-262. ISBN 978-1416-55085-3.
4. Grubb, Jeff (February 27, 2001). StarCraft: Liberty's Crusade. Simon & Schuster (Pocket Star). ISBN 0-671-04148-7.
5. 5.0 5.1 McNeill, Graham (December 30, 2008). StarCraft: I, Mengsk. Simon & Schuster (Pocket Star). ISBN 1416-55083-6.
This page uses content from the English Wikipedia. The original content was at Fossil fuels The list of authors can be seen in the page history of Fossil fuels. Wikipedia content was licensed under the GNU Free Documentation License prior to June 15, 2009 is. Wikipedia content from June 15, 2009, and StarCraft Wiki content, is licensed under the Creative Commons Attribution-Share Alike License 3.0 (Unported).
| 2017-05-25T23:56:05 |
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http://schneider.ncifcrf.gov/delila/normreg.html
|
Delila Program: normreg
# normreg program
## Pascal source code: normreg.p (wget instructions) Instructions on compiling Alphabetic List of Delila Programs Delila Programs by Most Recent Update Please report broken links Copyright Statement for Delila Programs
### Documentation for the normreg program is below, with links to related programs in the "see also" section.
{version = 1.11; (* of normreg.p 1995 October 24}
(* begin module describe.normreg *)
(*
name
normreg: normalize results from sequence/value linear regression
synopsis
normreg(normregp: in, fresep: out, output: out)
files
normregp: parameters to control the program.
First line: maxsequences (integer): the maximum number of sequences to
generate. This determines the precision of the result.
Remaining lines: values to normalize, 5 per line.
The first, an integer, is the position in the binding site.
The remainder are real, the 4 linear regression weights for A, C, G,
and T.
fresep: 5 integers per line, giving the number of sequences
(maxsequences) and the number of bases at each frequency.
output: messages to the user
description
We would like to view the results of a linear regression of sequences versus
measured values by a sequence logo. This program generates the 'frequencies'
and produces them in a form useful by the program frese.
examples
Using a value of 1000 for maxsequences and the normalized data in figure 3b
of Barrick.ribosomes1994 (see documentation) the normregp is:
1000
-11 -0.36 -0.70 0.70 -0.23
-10 -0.21 -0.59 0.52 -0.05
-9 -0.03 -0.60 0.56 -0.31
-8 0.12 -0.59 0.06 0.22
-7 0.37 -0.48 0.22 -0.38
-6 0.31 -0.51 0.07 -0.04
-5 0.18 0.08 -0.38 0.04
-4 0.04 -0.28 0.26 -0.10
-3 0.61 -0.16 -0.68 -0.23
-2 0.30 -0.02 -0.44 0.02
-1 -0.06 -0.07 -0.20 0.27
0 1.14 -2.28 -0.76 -1.18
Since normalizing data that are already normalized has no effect, these
can be used as input to this program. The results given to output are:
normreg 1.10
information Afrequency Cfrequency Gfrequency Tfrequency
0.2255 0.1743 0.1241 0.5031 0.1985
0.1197 0.2027 0.1386 0.4207 0.2379
SumInteger = 1001 maxsequences = 1000
at position -10, 1 was added to Ainteger to get them to sum properly
SumInteger = 1002 maxsequences = 1000
at position -10, -1 was added to Ainteger to get them to sum properly
0.1410 0.2424 0.1371 0.4373 0.1832
SumInteger = 999 maxsequences = 1000
at position -9, 1 was added to Ainteger to get them to sum properly
0.0565 0.2826 0.1389 0.2661 0.3123
0.0926 0.3623 0.1548 0.3118 0.1711
0.0562 0.3411 0.1502 0.2683 0.2404
SumInteger = 999 maxsequences = 1000
at position -6, 1 was added to Ainteger to get them to sum properly
0.0284 0.2989 0.2705 0.1707 0.2599
0.0283 0.2603 0.1890 0.3244 0.2263
SumInteger = 999 maxsequences = 1000
at position -4, 1 was added to Ainteger to get them to sum properly
0.1681 0.4608 0.2134 0.1269 0.1989
0.0463 0.3379 0.2454 0.1612 0.2554
SumInteger = 999 maxsequences = 1000
at position -2, 1 was added to Ainteger to get them to sum properly
0.0235 0.2353 0.2329 0.2045 0.3273
0.9402 0.7809 0.0255 0.1168 0.0767
SumInteger = 1001 maxsequences = 1000
at position 0, 1 was added to Ainteger to get them to sum properly
SumInteger = 1002 maxsequences = 1000
at position 0, -1 was added to Ainteger to get them to sum properly
When the fresep is then run through fresep, makebk, alist (to make sure all is
ok), encode, rseq, dalvec and makelogo, the result is figure 5b in
Barrick.ribosomes1994.
documentation
@article{Barrick.ribosomes1994,
author = "D. Barrick
and K. Villanueba
and J. Childs
and R. Kalil
and T. D. Schneider
and C. E. Lawrence
and L. Gold
and G. D. Stormo",
title = "Quantitative Analysis of Ribosome Binding Sites in
{{\em E. coli.}}",
journal = "Nucl. Acids Res.",
volume = "22",
pages = "1287-1295",
comment = "1994 April 11. 22(7)",
year = "1994"}
frese.p
author
Thomas Dana Schneider
bugs
technical notes
When rounding a set of real numbers to integers, they will not always add to
the exact required. Although this is a minor detail, the frese program
cannot work unless the numbers all add to the same value at every position.
So this program detects when the integers do not add to the maxsequences,
and then searches for a solution by adding or subracting from the A integer
value. The search is conducted in the series 1, -1, 2, -2, 3, -3 ... and
either +1 or -1 is given by the example shown above. Higher cases are NOT
expected. Since this only modifies the last decimal place (for maxsequences
a power of 10) it does not significantly alter the sequence logo.
*)
(* end module describe.normreg *)
{This manual page was created by makman 1.44}
| 2015-07-05T17:30:26 |
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|
https://googology.wikia.org/wiki/Buchholz%27s_function
|
## FANDOM
10,508 Pages
Buchholz's psi functions are ordinal collapsing functions created by German mathematician Wilfried Buchholz. Although there are many Buchholz's psi functions, we explain the most famous one in this community, which is a hierarchy of single-argument functions $$\psi_\nu(\alpha)$$ introduced in 1986,[1] because the other ones are not currently used in this community. These functions are a simplified version of Feferman's $$\theta$$ functions, but nevertheless have the same strength as those.
## Definition
Buchholz defined his functions as follows:
• $$C_\nu^0(\alpha) = \Omega_\nu$$,
• $$C_\nu^{n+1}(\alpha) = C_\nu^n(\alpha) \cup \{\gamma | P(\gamma) \subseteq C_\nu^n(\alpha)\} \cup \{\psi_\mu(\xi) | \xi \in \alpha \cap C_\nu^n(\alpha) \wedge \xi \in C_\mu(\xi) \wedge \mu \leq \omega\}$$,
• $$C_\nu(\alpha) = \bigcup_{n < \omega}C_\nu^n (\alpha)$$,
• $$\psi_\nu(\alpha) = \min\{\gamma | \gamma \not\in C_\nu(\alpha)\}$$,
where $$\omega$$ is the smallest infinite ordinal,
$$\Omega_\nu=\left\{\begin{array}{lcr}1\text{ if }\nu=0\\\aleph_\nu\text{ if }\nu>0\\\end{array}\right.$$
and $$P(\gamma)=\{\gamma_1,\cdots,\gamma_k\}$$ is the set of additive principal numbers in form $$\omega^\xi$$,
$$P=\{\alpha\in \textrm{On}: 0<\alpha \wedge \forall \xi, \eta < \alpha (\xi+\eta < \alpha)\}=\{\omega^\xi: \xi \in \textrm{On}\}$$,
the sum of which gives this ordinal $$\gamma$$:
$$\gamma=\alpha_1+\alpha_2+\cdots+\alpha_k$$ where $$\alpha_1\geq\alpha_2\geq\cdots\geq\alpha_k$$ and $$\alpha_1,\alpha_2,\cdots,\alpha_k \in P(\gamma)$$.
Note: Greek letters always denotes ordinals. $$\textrm{On}$$ denotes the class of all ordinals. The convention $$\Omega_0$$ depends on the context even if we are focussing on Buchholz's function. Actually, Buchholz himself uses $$\Omega_0$$ as both of shorthands of $$1$$ and $$\omega$$.[1][2]
The limit of this notation is Takeuti-Feferman-Buchholz ordinal.
## Properties
Buchholz showed following properties of those functions:
• $$\psi_\nu(0)=\Omega_\nu$$,
• $$\psi_\nu(\alpha)\in P$$,
• $$\psi_\nu(\alpha+1)=\text{min}\{\gamma\in P: \psi_\nu(\alpha)<\gamma\}\text{ if }\alpha\in C_\nu(\alpha)$$,
• $$\Omega_\nu\le\psi_\nu(\alpha)<\Omega_{\nu+1}$$,
• $$\alpha\le\beta\Rightarrow\psi_\nu(\alpha)\le\psi_\nu(\beta)$$,
• $$\psi_0(\alpha)=\omega^\alpha \text{ if }\alpha<\varepsilon_0$$,
• $$\psi_\nu(\alpha)=\omega^{\Omega_\nu+\alpha} \text{ if }\alpha<\varepsilon_{\Omega_\nu+1} \text{ and } \nu\neq 0$$,
• $$\theta(\varepsilon_{\Omega_\nu+1},0)=\psi_0(\varepsilon_{\Omega_\nu+1})$$ for $$0<\nu\le\omega$$.
## Explanation
Buchholz is working in Zermelo–Fraenkel set theory, that means every ordinal $$\alpha$$ is equal to set $$\{\beta|\beta<\alpha\}$$. Then condition $$C_\nu^0(\alpha)=\Omega_\nu$$ means that set $$C_\nu^0(\alpha)$$ includes all ordinals less than $$\Omega_\nu$$ in other words $$C_\nu^0(\alpha)=\{\beta|\beta<\Omega_\nu\}$$.
The condition $$C_\nu^{n+1}(\alpha) = C_\nu^n(\alpha) \cup \{\gamma | P(\gamma) \subseteq C_\nu^n(\alpha)\} \cup \{\psi_\mu(\xi) | \xi \in \alpha \cap C_\nu^n(\alpha) \wedge \mu \leq \omega\}$$ means that set $$C_\nu^{n+1}(\alpha)$$ includes:
1. all ordinals from previous set $$C_\nu^n(\alpha)$$,
2. all ordinals that can be obtained by summation the additively principal ordinals from previous set $$C_\nu^n(\alpha)$$,
3. all ordinals that can be obtained by applying ordinals less than $$\alpha$$ from the previous set $$C_\nu^n(\alpha)$$ as arguments of functions $$\psi_\mu$$, where $$\mu\le\omega$$.
That is why we can rewrite this condition as:
$$C_\nu^{n+1}(\alpha) = \{\beta+\gamma,\psi_\mu(\eta)|\beta, \gamma,\eta\in C_{\nu}^n(\alpha)\wedge\eta<\alpha \wedge \mu \leq \omega\}$$.
Thus union of all sets $$C_\nu^n (\alpha)$$ with $$n<\omega$$ i.e. $$C_\nu(\alpha) = \bigcup_{n < \omega} C_\nu^n (\alpha)$$ denotes the set of all ordinals which can be generated from ordinals $$<\aleph_\nu$$ by the functions + (addition) and $$\psi_{\mu}(\xi)$$, where $$\mu\le\omega$$ and $$\xi<\alpha$$.
Then $$\psi_\nu(\alpha) = \min\{\gamma | \gamma \not\in C_\nu(\alpha)\}$$ is the smallest ordinal that does not belong to this set.
### Examples
Consider the following examples:
$$C_0^0(\alpha)=\{0\} =\{\beta:\beta<1\}$$,
$$C_0(0)=\{0\}$$ (since no functions $$\psi(\eta<0)$$ and 0+0=0).
Then $$\psi_0(0)=1$$.
$$C_0(1)$$ includes $$\psi_0(0)=1$$ and all possible sums of natural numbers:
$$C_0(1)=\{0,1,2,...,\text{googol}, ...,\text{TREE(googol)},...\}$$.
Then $$\psi_0(1)=\omega$$ - first transfinite ordinal, which is greater than all natural numbers by its definition.
$$C_0(2)$$ includes $$\psi_0(0)=1, \psi_0(1)=\omega$$ and all possible sums of them.
Then $$\psi_0(2)=\omega^2$$.
For $$C_0(\omega)$$ we have set $$C_0(\omega)=\{0,\psi(0)=1,...,\psi(1)=\omega,...,\psi(2)=\omega^2,...,\psi(3)=\omega^3,...\}$$.
Then $$\psi_0(\omega)=\omega^\omega$$.
For $$C_0(\Omega)$$ we have set $$C_0(\Omega)=\{0,\psi(0)=1,...,\psi(1)=\omega,...,\psi(\omega)=\omega^\omega,...,\psi(\omega^\omega)=\omega^{\omega^\omega},...\}$$.
Then \begin{eqnarray*} & & \psi_0(\varepsilon_0)=\psi_0(\varepsilon_0+1) \\ & = & \cdots=\psi_0(\textrm{insert any countable ordinal above } \varepsilon_0 \textrm{which you like very much}) \\ & = & \cdots = \psi_0(\Omega)=\varepsilon_0. \end{eqnarray*} For $$C_0(\Omega+1)$$ we have set $$C_0(\Omega)=\{0,1,...,\psi_0(\Omega)=\varepsilon_0,...,\varepsilon_0+\varepsilon_0,...\psi_1(0)=\Omega,...\}$$.
Then $$\psi_0(\Omega+1)=\varepsilon_0\omega=\omega^{\varepsilon_0+1}$$.
$$\psi_0(\Omega2)=\varepsilon_1$$,
$$\psi_0(\Omega^2)=\zeta_0$$,
$$\psi_0(\Omega^\alpha(1+\beta)) = \varphi(\alpha,\beta)$$,
$$\psi_0(\Omega^\Omega)=\Gamma_0=\theta(\Omega,0)$$, using Feferman theta-function,
$$\psi_0(\Omega^{\Omega^\Omega})$$ is large Veblen ordinal,
$$\psi_0(\varepsilon_{\Omega+1})=\theta(\varepsilon_{\Omega+1},0)$$.
Now let's research how $$\psi_1$$ works:
$$C_1^0(\alpha)=\{\beta:\beta<\Omega_1\}=\{0,\psi(0)=1,2,...\text{googol},...,\psi_0(1)=\omega,...,\psi_0(\Omega)=\varepsilon_0,...$$
$$...,\psi_0(\Omega^\Omega)=\Gamma_0,...,\psi(\Omega^{\Omega^\Omega+\Omega^2}),...\}$$ i.e. includes all countable ordinals.
$$C_1(\alpha)$$ includes all possible sums of all countable ordinals. Then
$$\psi_1(0)=\Omega_1$$ first uncountable ordinal which is greater than all countable ordinal by its definition i.e. smallest number with cardinality $$\aleph_1$$.
$$C_1(1)=\{0,...,\psi_0(0)=\omega,...,\psi_1(0)=\Omega,...,\Omega+\omega,...,\Omega+\Omega,...\}$$
Then $$\psi_1(1)=\Omega\omega=\omega^{\Omega+1}$$.
Then $$\psi_1(2)=\Omega\omega^2=\omega^{\Omega+2}$$,
$$\psi_1(\psi_0(\Omega))=\Omega\varepsilon_0=\omega^{\Omega+\varepsilon_0}$$,
$$\psi_1(\psi_0(\Omega^\Omega))=\Omega\Gamma_0=\omega^{\Omega+\Gamma_0}$$,
$$\psi_1(\psi_1(0))=\psi_1(\Omega)=\Omega^2=\omega^{\Omega+\Omega}$$,
$$\psi_1(\psi_1(\psi_1(0)))=\omega^{\Omega+\omega^{\Omega+\Omega}}=\omega^{\Omega\cdot\Omega}=(\omega^{\Omega})^\Omega=\Omega^\Omega$$,
$$\psi_1^4(0)=\Omega^{\Omega^\Omega}$$,
$$\psi_1(\Omega_2)=\varepsilon_{\Omega+1}$$.
For case $$\psi(\Omega_2)$$ the set $$C_0(\Omega_2)$$ includes functions $$\psi_0$$ with all arguments less than $$\Omega_2$$ i.e. such arguments as $$0, \psi_1(0), \psi_1(\psi_1(0)), \psi_1^3(0),...$$
and then $$\psi_0(\Omega_2)=\psi_0(\psi_1(\Omega_2))=\psi_0(\varepsilon_{\Omega+1})$$.
In general case: $$\psi_0(\Omega_{\nu+1})=\psi_0(\psi_\nu(\Omega_{\nu+1}))=\psi_0(\varepsilon_{\Omega_\nu+1})=\theta(\varepsilon_{\Omega_\nu+1},0)$$.
We also can write:
$$\theta(\Omega_\nu,0)=\psi_0(\Omega_\nu^{\Omega_\nu})$$ ( for $$1\le\nu<\omega$$).
## Comparison between Buchholz’s and Veblen’s functions
### Up to Feferman–Schütte ordinal
Buchholz function Veblen function
a natural number $$n>0$$ is an abbriviation for $$\underbrace{\psi_0(0)+\cdots+\psi_0(0)}_{n\ \psi 's}$$ a natural number $$n>0$$ is an abbriviation for $$\underbrace{\varphi(0,0)+\cdots+\varphi(0,0)}_{n\ \varphi 's}$$
$$\psi_0(0)$$ $$\varphi(0,0)=1$$
$$\psi_0(0)+\psi_0(0)$$ $$\varphi(0,0) +\varphi(0,0)=2$$
$$\psi_0(1)$$ $$\varphi(0,1) =\omega$$
$$\psi_0(2)$$ $$\varphi(0,2) =\omega^2$$
$$\psi_0(\psi_0(1))$$ $$\varphi(0,\varphi(0,1)) =\omega^\omega$$
$$\psi_0(\psi_0(2))$$ $$\varphi(0,\varphi(0,2))=\omega^{\omega^2}$$
$$\psi_0(\psi_0(\psi_0(1)))$$ $$\varphi(0,\varphi(0,\varphi(0,1)))=\omega^{\omega^\omega}$$
$$\psi_0(\psi_1(0))$$ $$\varphi(1,0)=\varepsilon_0$$
$$\psi_0(\psi_1(0)+1)$$ $$\varphi(0,\varphi(1,0)+1)=\omega^{\varepsilon_0+1}=\varepsilon_0\omega$$
$$\psi_0(\psi_1(0)+2)$$ $$\varphi(0,\varphi(1,0)+2)=\omega^{\varepsilon_0+2}=\varepsilon_0\omega^2$$
$$\psi_0(\psi_1(0)+\psi_0(\psi_1(0)))$$ $$\varphi(0,\varphi(1,0)+\varphi(1,0))=\omega^{\varepsilon_0+\varepsilon_0}=\varepsilon_0^2$$
$$\psi_0(\psi_1(0)+\psi_0(\psi_1(0)+1))$$ $$\varphi(0,\varphi(0,\varphi(1,0)+1))=\omega^{\omega^{\varepsilon_0+1}}$$
$$\psi_0(\psi_1(0)+\psi_0(\psi_1(0)+\psi_0(\psi_1(0)+1)))$$ $$\varphi(0,\varphi(0,\varphi(0,\varphi(1,0)+1)))=\omega^{\omega^{\omega^{\varepsilon_0+1}}}$$
$$\psi_0(\psi_1(0)+\psi_1(0))$$ $$\varphi(1,1)=\varepsilon_1$$
$$\psi_0(\psi_1(0)+\psi_1(0)+\psi_1(0))$$ $$\varphi(1,2)=\varepsilon_2$$
$$\psi_0(\psi_1(1))$$ $$\varphi(1,\varphi(0,1))=\varepsilon_\omega$$
$$\psi_0(\psi_1(2))$$ $$\varphi(1,\varphi(0,2))=\varepsilon_{\omega^2}$$
$$\psi_0(\psi_1(\psi_0(\psi_1(0))))$$ $$\varphi(1,\varphi(1,0))=\varepsilon_{\varepsilon_0}$$
$$\psi_0(\psi_1(\psi_0(\psi_1(\psi_0(\psi_1(0))))))$$ $$\varphi(1,\varphi(1,\varphi(1,0)))=\varepsilon_{\varepsilon_{\varepsilon_0}}$$
$$\psi_0(\psi_1(\psi_1(0)))$$ $$\varphi(2,0)=\zeta_0$$
$$\psi_0(\psi_1(\psi_1(0))+1)$$ $$\varphi(0,\varphi(2,0)+1)=\omega^{\zeta_0+1}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_0(\psi_1(\psi_1(0))+1))$$ $$\varphi(0,\varphi(0,\varphi(2,0)+1))=\omega^{\omega^{\zeta_0+1}}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(0))$$ $$\varphi(1,\varphi(2,0)+1)=\varepsilon_{\zeta_0+1}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(0)+1)$$ $$\varphi(0,\varphi(1,\varphi(2,0)+1)+1)=\omega^{\varepsilon_{\zeta_0+1}+1}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(0)+\psi_1(0))$$ $$\varphi(1,\varphi(2,0)+2)=\varepsilon_{\zeta_0+2}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(1))$$ $$\varphi(1,\varphi(2,0)+\varphi(0,1))=\varepsilon_{\zeta_0+\omega}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(\psi_0(\psi_1(\psi_1(0))+\psi_1(1))))$$ $$\varphi(1,\varphi(1,\varphi(2,0)+\varphi(0,1))=\varepsilon_{\varepsilon_{\zeta_0+\omega}}$$
$$\psi_0(\psi_1(\psi_1(0))+\psi_1(\psi_1(0)))$$ $$\varphi(2,1)=\zeta_1$$
$$\psi_0(\psi_1(\psi_1(0)+1))$$ $$\varphi(2,\varphi(0,1))=\zeta_\omega$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_0(\psi_1(\psi_1(0)+1))))$$ $$\varphi(2,\varphi(2,\varphi(0,1)))=\zeta_{\zeta_\omega}$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_1(0)))$$ $$\varphi(3,0)=\eta_0$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_1(0))+\psi_1(\psi_1(0)+\psi_1(0)))$$ $$\varphi(3,1)=\eta_1$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_1(0)+1))$$ $$\varphi(3,\varphi(0,1))=\eta_{\omega}$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_1(0)+\psi_0(\psi_1(\psi_1(0)+\psi_1(0)+1)))$$ $$\varphi(3,\varphi(3,\varphi(0,1)))=\eta_{\eta_{\omega}}$$
$$\psi_0(\psi_1(\psi_1(0)+\psi_1(0)+\psi_1(0)))$$ $$\varphi(4,0)$$
$$\psi_0(\psi_1(\psi_1(1)))$$ $$\varphi(\varphi(0,1),0) = \varphi(\omega,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(1))))))$$ $$\varphi(\varphi(\varphi(0,1),0),0) = \varphi(\varphi(\omega,0),0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))))$$ $$\varphi(1,0,0)=\Gamma_0$$
### Up to Large Veblen ordinal
Buchholz function Veblen function
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+1)$$ $$\varphi(0,\varphi(1,0,0)+1)=\omega^{\Gamma_0+1}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0))$$ $$\varphi(1,\varphi(1,0,0)+1)=\varepsilon_{\Gamma_0+1}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(1))$$ $$\varphi(1,\varphi(1,0,0)+\varphi(0,1))=\varepsilon_{\Gamma_0+\omega}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)))$$ $$\varphi(2,\varphi(1,0,0)+1)=\zeta_{\Gamma_0+1}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)+1))$$ $$\varphi(2,\varphi(1,0,0)+\varphi(0,1))=\zeta_{\Gamma_0+\omega}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)+\psi_1(0)))$$ $$\varphi(3,\varphi(1,0,0)+1)=\eta_{\Gamma_0+1}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(1)))$$ $$\varphi(\varphi(0,1),\varphi(1,0,0)+1)=\varphi(\omega,\Gamma_0+1)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(1))))))$$ $$\varphi(\varphi(\varphi(0,1),0),\varphi(1,0,0)+1)=\varphi(\varphi(\omega,0),\Gamma_0+1)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))$$ $$\varphi(\varphi(1,0,0),1)=\varphi(\Gamma_0,1)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+1))$$ $$\varphi(\varphi(1,0,0),\varphi(0,1))=\varphi(\Gamma_0,\omega)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))$$
$$+\psi_0(\psi_1(\psi_1(\psi_1(0))))))$$
$$\varphi(\varphi(1,0,0),\varphi(1,0,0))=\varphi(\Gamma_0,\Gamma_0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))$$ $$\varphi(\varphi(1,0,0)+1,0)=\varphi(\Gamma_0+1,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))+1)))$$ $$\varphi(\varphi(0,\varphi(1,0,0)+1),0)=\varphi(\omega^{\Gamma_0+1},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+1))))$$ $$\varphi(\varphi(0,\varphi(0,\varphi(1,0,0)+1)),0)=\varphi(\omega^{\omega^{\Gamma_0+1}},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0)))))$$ $$\varphi(\varphi(1,\varphi(1,0,0)+1),0)=\varphi(\varepsilon_{\Gamma_0+1},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(1)))))$$ $$\varphi(\varphi(1,\varphi(1,0,0)+\varphi(0,1)),0)=\varphi(\varepsilon_{\Gamma_0+\omega},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0))))))$$ $$\varphi(\varphi(2,\varphi(1,0,0)+1),0)=\varphi(\zeta_{\Gamma_0+1},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)+1)))))$$ $$\varphi(\varphi(2,\varphi(1,0,0)+\varphi(0,1)),0)=\varphi(\zeta_{\Gamma_0+\omega},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)+\psi_1(0))))))$$ $$\varphi(\varphi(3,\varphi(1,0,0)+1),0)=\varphi(\eta_{\Gamma_0+1},0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(1))))))$$ $$\varphi(\varphi(\varphi(0,1),\varphi(1,0,0)+1),0)=\varphi(\varphi(\omega,\Gamma_0+1),0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))$$ $$\varphi(1,0,1)=\Gamma_1$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+1))$$ $$\varphi(1,0,\varphi(0,1))=\Gamma_{\omega}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(\psi_1(\psi_1(\psi_1(0))+1))))$$ $$\varphi(1,0,\varphi(1,0,\varphi(0,1)))=\Gamma_{\Gamma_{\omega}}$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0)))$$ $$\varphi(1,1,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0))+\psi_1(\psi_1(\psi_1(0))+\psi_1(0)))$$ $$\varphi(1,1,1)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0)+1))$$ $$\varphi(1,1,\varphi(0,1)) = \varphi(1,1,\omega)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0)+\psi_1(0)))$$ $$\varphi(1,2,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(1)))$$ $$\varphi(1,\varphi(0,1),0) = \varphi(1,\omega,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_1(0))))$$ $$\varphi(2,0,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)+1)))$$ $$\varphi(\varphi(0,1),0,0) = \varphi(\omega,0,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_0(\psi_1(\psi_1(\psi_1(0)+1))))))$$ $$\varphi(\varphi(\varphi(0,1),0,0),0,0) = \varphi(\varphi(\omega,0,0),0,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_1(0))))$$ $$\varphi(1,0,0,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_1(0)+\psi_1(0))))$$ $$\varphi(1,0,0,0,0)$$
$$\psi_0(\psi_1(\psi_1(\psi_1(1))))$$ Small Veblen ordinal
$$\psi(\psi_1(\psi_1(\psi_1(\psi_1(0)))))$$ Large Veblen ordinal
## Ordinal notation
Buchholz defined an ordinal notation $$(OT,<)$$ associated to $$\psi$$ as an array notation.[1] We explain the original definition of $$(OT,<)$$.
We simultaneously define the sets $$T$$ and $$PT$$ of formal strings consisting of $$0$$, $$D_v$$ indexed by an $$v \in \omega+1$$, braces, and commas in the following recursive way:
1. $$0 \in T$$ and $$0 \in PT$$.
2. For any $$(v,a) \in (\omega+1) \times T$$, $$D_va \in T$$ and $$D_va \in PT$$.
3. For any $$(a_i)_{i=0}^{k} \in PT^{k+1}$$ with $$k \in \mathbb{N} \setminus \{0\}$$, $$(a_0,\ldots,a_k) \in T$$. More precisely, this condition can be formulated without using ellipses in the following way:
1. For any $$(a_0,a_1) \in PT^2$$, $$(a_0,a_1) \in T$$.
2. For any $$(a_0,a_1) \in T \times PT$$, if there exists formal strings $$s$$ such that $$a_0 = (s)$$, then $$(s,a_1) \in T$$.
Namely, $$T$$ and $$PT$$ are the smallest sets satisfying the conditions above. An element of $$T$$ is called a term, and an element of $$PT$$ is called a principal term. By the definition, $$T$$ is a recursive set, $$PT$$ is a recursive subset of $$T$$, and every term is $$0$$, a principal term, or an array of principal terms of length $$\geq 2$$ in braces.
We also denote an $$a \in PT$$ by $$(a)$$. Since the clause 3 in the definition of $$T$$ and $$PT$$ is applicable only to arrays of length $$\geq 2$$, the additional convention does not cause serious ambiguity. By the convention, every term can be uniquely expressed as either $$0$$ or a non-empty array of principal terms in braces.
We define a binary relation $$a < b$$ on $$T$$ in the following recursive way:
1. If $$b = 0$$, then $$a < b$$ is false.
2. If $$a = 0$$, then $$a < b$$ is equivalent to $$b \neq 0$$.
3. Suppose $$a \neq 0$$ and $$b \neq 0$$.
1. If $$a = D_ua'$$ and $$b = D_vb'$$ for some $$((u,a'),(v,b')) \in ((\omega+1) \times T)^2$$, $$a < b$$ is equivalent to that either one of the following holds:
1. $$u < v$$.
2. $$u = v$$ and $$a' < b'$$.
2. If $$a = (a_0,\ldots,a_n)$$ and $$b = (b_0,\ldots,b_m)$$ for some $$(n,m) \in \mathbb{N}^2$$ with $$1 \leq n+m$$, $$a < b$$ is equivalent to that either one of the following holds:
1. $$n < m$$ and $$a_i = b_i$$ for any $$i \in \mathbb{N}$$ with $$i \leq n$$
2. There exists some $$k \in \mathbb{N}$$ such that $$k \leq \min\{n,m\}$$, $$a_k < b_k$$, and $$a_i = b_i$$ for any $$i \in \mathbb{N}$$ with $$i < k$$.
By the definition, $$<$$ is a recursive strict total ordering on $$T$$. We abbreviate $$(a < b) \lor (a = b)$$ to $$a \leq b$$. Although $$\leq$$ itself is not a well-ordering, its restriction to a recursive subset $$OT \subset T$$, which will be introduced later, forms a well-ordering.
In order to define $$OT$$, we define a subset $$G_ua \subset T$$ for each $$(u,a) \in (\omega+1) \times T$$ in the following recursive way:
1. If $$a = 0$$, then $$G_ua = \emptyset$$.
2. Suppose that $$a = D_va'$$ for some $$(v,a') \in (\omega+1) \times T$$.
1. If $$u \leq v$$, then $$G_ua = \{a'\} \cup G_ua'$$.
2. If $$u > v$$, then $$G_ua = \emptyset$$.
3. If $$a = (a_0,\ldots,a_k)$$ for some $$(a_i)_{i=0}^{k} \in PT^{k+1}$$ with $$k \in \mathbb{N} \setminus \{0\}$$,$$G_ua = \bigcup_{i=0}^{k} G_ua_i$$.
By the definition, $$b \in G_ua$$ is a recursive relation on $$(u,a,b) \in (\omega+1) \times T^2$$.
Finally, we define a subset $$OT \subset T$$ in the following recursive way:
1. $$0 \in OT$$.
2. For any $$(v,a) \in (\omega+1) \times T$$, $$D_va \in OT$$ is equivalent to $$a \in OT$$ and $$a' < a$$ for any $$a' \in G_va$$.
3. For any $$(a_i)_{i=0}^{k} \in PT^{k+1}$$, $$(a_0,\ldots,a_k) \in OT$$ is equivalent to $$(a_i)_{i=0}^{k} \in OT^{k+1}$$ and $$a_k \leq \cdots \leq a_0$$.
By the definition, $$OT$$ is a recursive subset of $$T$$. An element of $$OT$$ is called an ordinal term.
We define a map \begin{eqnarray*} o \colon OT & \to & C_0(\epsilon_{\Omega_{\omega}+1}) \\ a & \mapsto & o(a) \end{eqnarray*} in the following inductive way:
1. If $$a = 0$$, then $$o(a) = 0$$.
2. If $$a = D_va'$$ for some $$(v,a') \in (\omega+1) \times OT$$, then $$o(a) = \psi_v(o(a'))$$.
3. If $$a = (a_0,\ldots,a_k)$$ for some $$(a_i)_{i=0}^{k} \in (OT \cap PT)^{k+1}$$ with $$k \in \mathbb{N} \setminus \{0\}$$, then $$o(a) = o(a_0) \# \cdots \# o(a_k)$$, where $$\#$$ denotes the descending sum of ordinals, which coincides with the usual addition by the definition of $$OT$$.
Buchholz verified that the map $$o$$ satisfies the following:[1]
• The map $$o$$ is an order-preserving bijective map with respect to $$<$$ and $$\in$$. In particular, $$<$$ is a recursive strict well-ordering on $$OT$$.
• For any $$a \in OT$$ satisfying $$a < D_10$$, $$o(a)$$ coincides with the ordinal type of $$<$$ restricted to the countable subset $$\{x \in OT \mid x < a\}$$.
• The ordinal $$\psi_0(\varepsilon_{\Omega_{\omega}+1})$$ coincides with the ordinal type of $$<$$ restricted to the recursive subset $$\{x \in OT \mid x < D_10\}$$. In particular, $$(\{x \in OT \mid x < D_10\},<)$$ is an ordinal notation equivalent to $$\psi_0(\varepsilon_{\Omega_{\omega}+1})$$, and hence $$(OT,<)$$ is an ordinal notation whose ordinal type is strictly greater than the countable limit of $$\psi$$.
• For any $$v \in \mathbb{N} \setminus \{0\}$$, the well-foundedness of $$<$$ restricted to the recursive subset $$\{x \in OT \mid x < D_0D_{v+1}0\}$$ in the sense of the non-existence of a primitive recursive infinite descending sequence is not provable under $$\textrm{ID}_v$$.
• The well-foundedness of $$<$$ restricted to the recursive subset $$\{x \in OT \mid x < D_0D_{\omega}0\}$$ in the same sense above is not provable under $$\Pi_1^1-\textrm{CA}_0$$.
## Extension
We introduce the extension of Buchholz's definition by Googology WIki user Denis Maksudov as follows[3]:
• $$C_\nu^0(\alpha) = \{\beta|\beta<\Omega_\nu\}$$,
• $$C_\nu^{n+1}(\alpha) = \{\beta+\gamma,\psi_\mu(\eta)|\mu,\beta, \gamma,\eta\in C_{\nu}^n(\alpha)\wedge\eta<\alpha\}$$,
• $$C_\nu(\alpha) = \bigcup_{n < \omega} C_\nu^n (\alpha)$$,
• $$\psi_\nu(\alpha) = \min\{\gamma | \gamma \not\in C_\nu(\alpha)\}$$,
where
$$\Omega_\nu=\left\{\begin{array}{lcr} 1\text{ if }\nu=0 \\ \text{smallest ordinal with cardinality }\aleph_\nu \text{ if }\nu>0 \\ \end{array}\right.$$
There is only one little detail difference with original Buchholz definition: ordinal $$\mu$$ is not limited by $$\omega$$, now ordinal $$\mu$$ belongs to previous set $$C_n$$.
For example if $$C_0^0(1)=\{0\}$$ then $$C_0^1(1)=\{0,\psi_0(0)=1\}$$ and $$C_0^2(1)=\{0,...,\psi_1(0)=\Omega\}$$ and $$C_0^3(1)=\{0,...,\psi_\Omega(0)=\Omega_\Omega\}$$ and so on.
Limit of this notation must be omega fixed point $$\psi_0(\Omega_{\Omega_{\Omega_{\cdots}}})=\psi_0(\psi_{\psi_{\cdots}(0)}(0)) = \psi_0(\Lambda)$$ (see the next section).
## Normal form and fundamental sequences
### Normal form
The normal form for 0 is 0. If $$\alpha$$ is a nonzero ordinal number $$\alpha<\Lambda=\text{min}\{\beta|\psi_\beta(0)=\beta\}$$ then the normal form for $$\alpha$$ is $$\alpha=\psi_{\nu_1}(\beta_1)+\psi_{\nu_2}(\beta_2)+\cdots+\psi_{\nu_k}(\beta_k)$$ where $$k$$ is a positive integer and $$\psi_{\nu_1}(\beta_1)\geq\psi_{\nu_2}(\beta_2)\geq\cdots\geq\psi_{\nu_k}(\beta_k)$$ and each $$\nu_i$$, $$\beta_i$$ are ordinals satisfying $$\beta_i \in C_{\nu_i}(\beta_i)$$ also written in normal form. More precisely, the normality of an expression of an ordinal can be described in a recursive way with respect to the corresponding ordinal notation system extending the original ordinal notation system $$(OT,<)$$ explained above.
### Fundamental sequences
The fundamental sequence for an ordinal number $$\alpha$$ with cofinality $$\text{cof}(\alpha)=\beta$$ is a strictly increasing sequence $$(\alpha[\eta])_{\eta<\beta}$$ with length $$\beta$$ and with limit $$\alpha$$, where $$\alpha[\eta]$$ is the $$\eta$$-th element of this sequence. If $$\alpha$$ is a successor ordinal then $$\text{cof}(\alpha)=1$$ and the fundamental sequence has only one element $$\alpha[0]=\alpha-1$$. If $$\alpha$$ is a limit ordinal then $$\text{cof}(\alpha)\in\{\omega\}\cup\{\Omega_{\mu+1}|\mu\geq 0\}$$.
Although a system of fundamental sequences is not unique, there is a canonical choice of fundamental sequences in this community given by Denis. For nonzero ordinals $$\alpha<\Lambda$$, written in normal form, fundamental sequences are defined as follows:
1. If $$\alpha=\psi_{\nu_1}(\beta_1)+\psi_{\nu_2}(\beta_2)+\cdots+\psi_{\nu_k}(\beta_k)$$ where $$k\geq2$$ then $$\text{cof}(\alpha)=\text{cof}(\psi_{\nu_k}(\beta_k))$$ and $$\alpha[\eta]=\psi_{\nu_1}(\beta_1)+\cdots+\psi_{\nu_{k-1}}(\beta_{k-1})+(\psi_{\nu_k}(\beta_k)[\eta])$$,
2. If $$\alpha=\psi_{0}(0)=1$$, then $$\text{cof}(\alpha)=1$$ and $$\alpha[0]=0$$,
3. If $$\alpha=\psi_{\nu+1}(0)$$, then $$\text{cof}(\alpha)=\Omega_{\nu+1}$$ and $$\alpha[\eta]=\Omega_{\nu+1}[\eta]=\eta$$,
4. If $$\alpha=\psi_{\nu}(0)$$ and $$\text{cof}(\nu)\in\{\omega\}\cup\{\Omega_{\mu+1}|\mu\geq 0\}$$, then $$\text{cof}(\alpha)=\text{cof}(\nu)$$ and $$\alpha[\eta]=\psi_{\nu[\eta]}(0)=\Omega_{\nu[\eta]}$$,
5. If $$\alpha=\psi_{\nu}(\beta+1)$$ then $$\text{cof}(\alpha)=\omega$$ and $$\alpha[\eta]=\psi_{\nu}(\beta)\cdot \eta$$ (and note: $$\psi_\nu(0)=\Omega_\nu$$),
6. If $$\alpha=\psi_{\nu}(\beta)$$ and $$\text{cof}(\beta)\in\{\omega\}\cup\{\Omega_{\mu+1}|\mu<\nu\}$$ then $$\text{cof}(\alpha)=\text{cof}(\beta)$$ and $$\alpha[\eta]=\psi_{\nu}(\beta[\eta])$$,
7. If $$\alpha=\psi_{\nu}(\beta)$$ and $$\text{cof}(\beta) = \Omega_{\mu+1}$$ for a $$\mu\geq\nu$$ then $$\text{cof}(\alpha)=\omega$$ and $$\alpha[\eta]=\psi_{\nu}(\beta[\gamma[\eta]])$$ where $$\left\{\begin{array}{lcr} \gamma[0]=\Omega_\mu \\ \gamma[\eta+1]=\psi_\mu(\beta[\gamma[\eta]])\\ \end{array}\right.$$.
It is an extension of the system of fundamental sequences up to $$\psi_0(\varepsilon_{\Omega_{\omega}+1})$$ in Buchholz hierarchy given by modifying the rule ([].5) (ii) in recursive definition of the $$\textrm{dom}$$ function and $$[]$$ in Buchholz's original paper[1] by the rule 6 in the definition of $$[]$$ in p.6 in Buchholz's another paper[2] applied to the convention $$\Omega_0 = 1$$ except for the minor differences related to the difference $$\omega[n] = n+1$$ in the original definition and $$\omega[n] = n$$ in the definition here. (Please remember that $$\Omega_0$$ is defined as $$1$$ in the original paper, while it is defined as $$\omega$$ in the other paper.) More precisely, the fundamental sequence of $$\psi_0(2) = \omega \times \omega$$ is given as $$\omega \times \omega [n] = \omega \times (n+1)$$ in the original definition while we have $$\omega \times \omega[n] = \omega \times n$$ in the definition here, and the fundamental sequence of $$\psi_{\omega}(0) = \Omega_{\omega}$$ is given as $$\Omega_{\omega}[n] = \Omega_{n+1}$$ while we have $$\Omega_{\omega}[n] = \Omega_n$$ in the definition here.
If $$\alpha=\Lambda$$ then $$\text{cof}(\alpha)=\omega$$ and $$\alpha[0]=0$$ and $$\alpha[\eta+1]=\psi_{\alpha[\eta]}(0)=\Omega_{\alpha[\eta]}$$.
For comparison of ordinals written in normal form use the following property:
if $$\alpha<\beta$$ and $$1\le\eta<\omega$$ then $$\left\{\begin{array}{lcr} 0<\psi_\alpha(\gamma)\cdot\eta <\psi_\beta(\delta)\\ 0<\psi_\gamma(\alpha)\cdot\eta<\psi_\gamma(\beta)\\ \end{array}\right.$$
The comparison of expressions of ordinals can be described in a recursive way with respect to the corresponding ordinal notation system extending the original ordinal notation system $$OT$$.[1] In particular, the system of fundamental sequences above induce a recursive system of fundamental sequences on the corresponding ordinal notation, and hence the fast-growing hierarchy associated to it is recursive.
## Common Misconceptions
Here is a list of some common misconceptions regarding Buchholz's function, which appear in many introductory articles on Buchholz's function:
Common misconceptions Fact Reason
Buchholz's function is computable. Buchholz's function is not a computable function, despite the fact that the associated ordinal notation is computable. Turing machine defines a function whose domain and codomain are sets of tuple of natural numbers, neither of which includes transfinite ordinals.
$$\psi_0(\Omega_{\omega}+1)$$ is ill-defined. The ordinal $$\psi_{\nu}(\alpha)$$ is defined for all $$(\nu,\alpha) \in (\omega+1) \times \textrm{On}$$. Buchholz's original definition uses transfinite recursion on $$\alpha$$ and restricts $$v\le\omega$$.
$$\psi_0(\alpha)$$ with respect to Buchholz's function coincides with $$\psi_0(\alpha)$$ with respect to extended Buchholz's function. Buchholz's function is neither a restriction of extended Buchholz's function nor extended Buchholz's function itself. However, some values correspond, such as $$\psi_0(0)$$. Some ordinals don't correspond from extended Buchholz function to Buchholz function, such as $$\psi_0(\psi_{\psi_1(0)}(0))$$.
$$\psi_0(\varepsilon_0+1) = \varepsilon_0 \times \omega$$ $$\psi_0(\varepsilon_0+1) = \varepsilon_0$$. This is due to the fact that the $$\psi_0$$ function equals $$\varepsilon_0$$ for all inputs between $$\varepsilon_0$$ and $$\Omega$$ inclusive. This is because $$\varepsilon_0\notin C_0(\varepsilon_0+1)$$.
$$\psi_0(\psi_1(\psi_2(\psi_3(0)))) = \psi_0(\psi_3(0))$$ $$\psi_0(\psi_1(\psi_2(\psi_3(0)))) = \psi_0(\psi_2(0))$$. In fact, for any ordinal $$\alpha\geq\psi_2(0)$$, we have $$\psi_0(\psi_1(\alpha))=\psi_0(\psi_2(0))$$. This is because $$\psi_1(\psi_2(\psi_3(0)))\notin C_0(\psi_1(\psi_2(\psi_3(0))))$$.
The sequence $$\psi_0(0), \psi_0(\psi_1(0)), \psi_0(\psi_1(\psi_2(0))), \psi_0(\psi_1(\psi_2(\psi_3(0)))), \ldots$$ has a limit of $$\psi_0(\psi_{\omega}(0))$$. The sequence is an eventually constant sequence with limit $$\psi_0(\psi_2(0))$$. This is because for $$n\ge 3$$, $$\psi_1(\psi_2(\cdots\psi_n(0)\cdots))\notin C_0(\psi_1(\psi_2(\cdots\psi_n(0)\cdots)))$$.
It equals the least omega fixed point. See also $$\psi_0(\psi_I(0))$$. The ordinal $$\psi_I(0)$$ equals $$I$$. This is because $$C^0_I(0)$$ is defined as $$\Omega_I=I$$.
Community content is available under CC-BY-SA unless otherwise noted.
| 2020-08-11T01:05:24 |
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|
http://dergipark.gov.tr/cams
|
##### Communications in Advanced Mathematical Sciences
ISSN 2651-4001 | Periyot Yılda 4 Sayı | Başlangıç: 2018 | Yayıncı Emrah Evren Kara |
The main aim and scope of Communications in Advanced Mathematical Sciences (CAMS) (Commun. Adv. Math. Sci.) is publishing of refereed, high quality original research papers in all areas where mathematics plays an significant role. Communications in Advanced Mathematical Sciences publishes also refereed, high quality survey papers. The journal particularly emphasizes on research articles of common interest to a wide range of readers.
Communications in Advanced Mathematical Sciences has an Open Access policy: all content is freely available without charge to the users. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required.
The journal is published every three months and four issues per year (March, June, September and December).
The overall similarity index percentage must be below 39 %. If submitted paper has high similarity it means that it is of restricted originality and cannot be handled by CAMS. The content is in such a way to change that this rate will become less than 39 %. Otherwise we have to reject the paper.
Communications in Advanced Mathematical Sciences aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
Algebra Algebraic Geometry Category Theory Complex Analysis Control Theory and Optimization Differential Equations Differential Geometry Discrete Mathematics Dynamical Systems and Ergodic Theory Functional Analysis Geometry Mathematical Logic and Foundations Mathematical Physics Mathematical Finance Number Theory Numerical Analysis Operator Theory Probability Theory and Statistics Real Analysis Topology
## Communications in Advanced Mathematical Sciences
ISSN 2651-4001 | Periyot Yılda 4 Sayı | Başlangıç: 2018 | Yayıncı Emrah Evren Kara |
487
792
The main aim and scope of Communications in Advanced Mathematical Sciences (CAMS) (Commun. Adv. Math. Sci.) is publishing of refereed, high quality original research papers in all areas where mathematics plays an significant role. Communications in Advanced Mathematical Sciences publishes also refereed, high quality survey papers. The journal particularly emphasizes on research articles of common interest to a wide range of readers.
Communications in Advanced Mathematical Sciences has an Open Access policy: all content is freely available without charge to the users. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required.
The journal is published every three months and four issues per year (March, June, September and December).
The overall similarity index percentage must be below 39 %. If submitted paper has high similarity it means that it is of restricted originality and cannot be handled by CAMS. The content is in such a way to change that this rate will become less than 39 %. Otherwise we have to reject the paper.
Communications in Advanced Mathematical Sciences aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
Algebra Algebraic Geometry Category Theory Complex Analysis Control Theory and Optimization Differential Equations Differential Geometry Discrete Mathematics Dynamical Systems and Ergodic Theory Functional Analysis Geometry Mathematical Logic and Foundations Mathematical Physics Mathematical Finance Number Theory Numerical Analysis Operator Theory Probability Theory and Statistics Real Analysis Topology
Sayılar
Yazılar
Volume: 1 Issue: 2 Son Sayı
Cilt 1 - Sayı 2 - Ara 2018
1. Norm-Attainability and Range-Kernel Orthogonality of Elementary Operators
Sayfalar 91 - 98
Bernard Okelo
2. Modifications of Strongly Nodec Spaces
Sayfalar 99 - 112
3. Mixed-Type Functional Differential Equations: A $C_{0}$-Semigroup Approach
Sayfalar 113 - 125
Luis Gerardo Mármol, Carmen Judith Vanegas
4. On the Periodic Solutions of Some Systems of Difference Equations
Sayfalar 126 - 136
E. M. Elsayed, H. S. Gafel
5. L-Fuzzy Invariant Metric Space
Sayfalar 137 - 141
Servet Kütükçü
6. On Bicomplex Pell and Pell-Lucas Numbers
Sayfalar 142 - 155
Fügen Torunbalcı Aydın
7. On Growth and Approximation of Generalized Biaxially Symmetric Potentials on Parabolic-Convex Sets
Sayfalar 156 - 162
Devendra Kumar
8. Fixed Point Sets of Multivalued Contractions and Stability Analysis
Sayfalar 163 - 171
Nikhilesh Metiya, Binayak S. Choudhury, Sunirmal Kundu
Dizinler ve Platformlar
| 2019-02-22T16:12:52 |
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https://www.usgs.gov/center-news/volcano-watch-skylights-mark-current-k-lauea-lava-flows
|
# Volcano Watch — Skylights mark current Kīlauea lava flows
Release Date:
The 10-year-long eruption on Kīlauea's East Rift Zone continues with lava flowing from the vents on the south and west sides of Puu Oo to the sea in underground tubes.
The 10-year-long eruption on Kīlauea's East Rift Zone continues with lava flowing from the vents on the south and west sides of Puu Oo to the sea in underground tubes.
There are now two lava entries on the east and west sides of the Kamoamoa lava delta. The lava tube is characterized by a sequence of skylights from 2,350 feet to about 200 feet above sea level.
Skylights are openings in the top of the tube, where the roof has either collapsed or been pushed upwards by magma pressure within the tube, and can be identified from a distance by plumes of bluish fume.
Over the last week, a large aa flow was fed from a skylight located at about 1,820 feet elevation; this flow advanced down the pali, covered much of a heavily vegetated kipuka, and finally stopped at the 750-foot elevation. This was the largest aa flow to have occurred in many months.
On June 29, a large, fluid sheet flow leaked from the lava tube on the Kamoamoa delta. The point of origin was near the original coastline, which is now located about 0.4 miles inland from the present coastline. This sheet flow rapidly advanced to the sea and built a small lava delta before the flow stopped. A small flow has been intermittently active on the west side of the lava flow field above Paliuli near Laeapuki.
The Park Service has cut a trail to the area for viewing by visitors. However, due to the intermittent character of this flow, it is wise to check at the Visitor Center in Hawaii Volcanoes National Park or with rangers on duty near the end of Chain of Craters Road in the park.
During the last two weeks, there was a major and several minor collapses of the lava bench adjacent to the ocean where the lava enters the water. The largest occurred on Saturday, July 3, when most of the youngest bench of lava at the main Kamoamoa entry slid into the sea during the early morning. For much of that day, lava fountains and steam explosions built a new spatter cone at the point where lava entered the sea and scattered angular blocks over nearby lava flows. This bench collapse took place at about the same time that the aa flow started from the skylight at 1,820 feet elevation and coincided with a decrease in flow rates through the tube system.
The eruption rate, as determined by measuring the flow rate and cross-sectional area of the tube at several locations, has fluctuated significantly during the past several months, with maximum fluxes of about 420,000 cubic yards per day and minimum fluxes of about half that amount. This variable flux from day to day has led to instability in the tube and the many small flows emanating from the skylight.
On Thursday, there was little to see at the two ocean entries, because the lava pours directly into the sea, and the interaction is veiled in steam. In addition, steam explosions, collapse of the lava bench, and acidic fume all pose serious hazards in the area. For these reasons, the Park Service has closed this area to visitors. For your own safety, obey the area closure signs posted in the area.
The pond inside Puu O`o cinder cone has risen about 65 feet to about 243 feet below the rim in the last two weeks, but the surface is less active than when the pond was deeper.
There have been no earthquakes with magnitudes larger than 3.0 within the last two weeks anywhere in the Hawaiian Islands.
| 2020-01-21T23:53:51 |
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https://indico.fnal.gov/event/13106/contributions/17452/
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# 2017 JINA-CEE Frontiers in Nuclear Astrophysics
Feb 7 – 9, 2017
US/Eastern timezone
## Feasibility studies of $(d,{}^{2}\text{He})$ reactions at the AT-TPC
Feb 7, 2017, 4:45 PM
1h 15m
111 N Grand Ave, Lansing, MI 48933
Poster [Main Conference]
### Speaker
Dr Juan Carlos Zamora Cardona (NSCL)
### Description
Charge-exchange reactions at intermediary energies is a powerful tool to study spin-isospin excitations in nuclei. In particular, these type of reactions serve as a direct method for the extraction of the Gamow-Teller (GT) transition strengths which are of importance for a variety of applications where weak transition strengths play a role (e.g. electron capture and $\beta$-decay in stellar evolution, neutrino nucleosynthesis, etc.). GT transitions in the $\beta^+$ direction have been studied extensively through $(t,{}^{3}\text{He})$ charge-exchange reactions. The $(d,{}^{2}\text{He})$ reaction is another and potentially even more powerful probe for measurements of $B(\text{GT}^+)$ strengths, since the detection of ${}^{2}$He (two protons in the relative singlet ${}^{1}S_0$ state) ensures automatically that the reaction goes through spin-flip components. However, the major disadvantage lies in the detection and kinematic reconstruction of the ${}^{2}$He particle. The AT-TPC, a detector based on time projection chamber, provides a unique technique for achieving these type of experiments. Feasibility studies of $(d,{}^{2}\text{He})$ reactions using this technique have been done with GEANT4 simulations. In this contribution, the current status of the project will be presented.
### Primary author
Dr Juan Carlos Zamora Cardona (NSCL)
### Presentation materials
There are no materials yet.
| 2022-12-03T19:26:27 |
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|
https://portlandpress.com/bioscirep/article/36/3/e00341/91714/The-effects-of-maternal-and-post-weaning-diet
|
Substantial studies demonstrated that maternal nutrition can significantly determine the susceptibility to developing some metabolic diseases in offspring. However, investigations into the later-life effects of these diets on gut microbiota in the offspring are limited. Our objective was to explore the effects of maternal and post-weaning diet interaction on offspring's gut microbiota and glucose metabolism in later life. The male offspring of dams fed on either a high-fat (HF) diet or control (C) diet and then weaned to either a HF or C diet, generating four groups: C–C, HF–C, C–HF and HF–HF (n=8 in each group). The C–C offspring had lower body weight than C–HF group at 16 weeks of age (P<0.01) and both C–HF and HF–HF offspring had higher body weight than C–C group at 24 and 32 weeks of age (P<0.001 respectively). The blood glucose (BG) levels of the male offspring from the C and HF dams weaned HF diet were significantly higher at 30 min, 60 min and 120 min (P<0.001) after intraperitoneal glucose administration compared with those of the C–C group. The C–HF group had higher BG at 30 min than HF–HF group (P<0.01). Furthermore, area under the curve (AUC) in C–HF and HF–HF groups was also significantly larger than C–C group (P<0.001). Fasting BG and homoeostasis model assessment of insulin resistance (HOMA-IR) of the offspring were significantly higher in C–HF and HF–HF groups than C–C group at 32 weeks of age (P<0.05). Operational taxonomic unit (OTU), Chao and Shannon indexes showed a significantly lower diversity in C–HF offspring compared with HF–C and C–C groups (P<0.05). The dominant phyla of all the groups were Bacteroidetes, Firmicutes and Proteobacteria, which also showed significantly different percentages in the group (P<0.05). Furthermore, it is indicated that Lactobacillus and Bacteroides were significantly associated with glucose response to a glucose load (P<0.05). In conclusion, maternal and post-weaning diet interaction predisposes the offspring to aberrant glucose metabolism and alterations of gut microbiota in later life. Our study is novel in focusing on the effects of maternal and post-weaning diet interaction on offspring gut microbiota and glucose metabolism in later life.
The developmental origins of health and disease (DOHaD) hypothesis, firstly formulated in the early 1990s, proposes that imbalanced diet during early life plays a critical role in determining the risks of developing some metabolic diseases such as obesity, insulin resistance and diabetes mellitus in offspring [1]. Previous and recent studies have indicated that a maternal high-fat (HF) diet [2] and/or a postnatal weaning diet rich in fat [3] can increase susceptibility to obesity, glucose intolerance and insulin resistance in the adult offspring. However, the mechanisms underlying maternal imbalanced nutrition and such metabolic diseases in the offspring remain unclear.
Recently, gut microbiota, which can affect numerous biological functions throughout the body, has become a major and promising research area in biomedicine. The gut microbiota comprises 100 trillion bacteria generating a biomass of approximately 1–2 kg with 2000 distinct species, comprising a total genome of approximately 150 times as big as human genome [4]. Previous studies have suggested that gut microbiota is important in regulating metabolic pathways in healthy people and in patients with obesity, diabetes and cardiovascular diseases [5]. Numerous studies have demonstrated that the gut microbiota may play a key role in the development of obesity [6]. One study indicated that the gut microbiota derived from twins discordant for obesity could modulate metabolism in mice and it also revealed transmissible, rapid and modifiable effects of diet-by-microbiota interactions [7]. Another recent large human study provided further insights on the role of certain microbiotal members in obesity and insulin resistance [8]. It is indicated that obesity, insulin resistance and fatty liver were more prevalent in subjects of low bacterial richness [low gene count (LGC)], compared with those characterized by high gene count (HGC) [8]. The first metagenome-wide association study (MGWAS) showed that patients with Type 2 diabetes mellitus (T2DM) were characterized by a moderate degree of gut microbial dysbiosis, decreased butyrate-producing bacteria and increased various opportunistic pathogens, as well as an enrichment of other microbial whose functions are conferring sulfate reduction and oxidative stress resistance [9].
Most organs including liver, adipose tissue, pancreas, skeletal muscle and brain appear to be imprinted by these early disturbances [10]. However, little information is known about the gastrointestinal tract (GIT) in this programme and it is important given the central role of the GIT as a barrier between the outer environment such as diets and inner nutrient absorption and metabolism [11]. In the recent years, the gut microbiota is gradually known to be influenced by diet composition [12]. However, investigations into the later-life effects of these diets on gut microbiota in the offspring are limited. Our present objective was to explore the effect of maternal and post-weaning diet interaction on offspring's gut microbiota and glucose homoeostasis in later life.
Ethics statement
All procedures were approved by the Animal Care and Use Committee of the Peking Union Medical College Hospital (Beijing, China, MC-07-6004) and were conducted in compliance with the Guide for the Care and Use of Laboratory Animals, 8th ed., 2011.
Animal and diets
A total of ten male and 20 virgin female and male C57BL/6J mice (7 weeks old) that were specific pathogen free (SPF), were obtained from the Institute of Laboratory Animal Science, Chinese Academy of Medical Sciences and Peking Union Medical College (Beijing, China, SCXK-2013-0107). The animals were raised and kept under SPF conditions (room temperature at 22±2°C; 12 h light/dark cycle). Food and sterile water were provided ad libitum throughout the study period. Before mating, all the mice were randomly fed with the control (C) diet for 1 week for adaptation. Mating was performed by housing females with adult males fed with C diet for 3 days (male:female=1:2). Females were checked daily for postcopulatory plugs, and the presence of a plug in the morning after mating was taken as day 0.5 day of pregnancy.
Then, the pregnant mice were randomly assigned to two groups and were fed on either a C diet or C diet during pregnancy and lactation. The purified HF diet was composed of 58% of energy as fat, 25.5% carbohydrates and 16.4% protein. The purified C diet was composed of 11.4% of energy as fat, 62.8% carbohydrates and 25.8% protein. Both the C diet and HF diet were produced by Research Diets and the ingredient compositions were shown in Table 1. At day 1 after birth, the litter size of both the HF and C groups was standardized to six pups, to ensure no litter was nutritionally biased. All offspring were weaned at 3 weeks of age. At weaning, only one male offspring in each group was randomly selected from one litter. The male offspring of dams fed on either a HF diet or C diet and then weaned to either a HF or C diet for the following 29 weeks, generating four experimental groups: C–C (n=8), HF–C (n=8), C–HF (n=8) and HF–HF (n=8), which represents pregnancy and lactation compared with the post-weaning diet respectively. Male offspring were maintained until the end of the experimental period. The female offspring were not examined in our present study in order to prevent confounding factors related to their hormone profile and oestrus cycle.
Table 1
Nutritional composition of the C and HF diet fed to mice
C dietHF diet
Ingredientsgkcalgkcal
Casein 200 800 228 912
Amino acid 12
Corn starch 397 1590
Maltodextrin 132 528 170 680
Sucrose 100 400 175 700
Soya bean oil 70 630 25 225
Choline bitartrate 2.5
Mineral 35 40
Vitamin 10 40 10 40
Coconut oil 333.5 3001.5
kcal/g 3.9 5.56
C dietHF diet
Ingredientsgkcalgkcal
Casein 200 800 228 912
Amino acid 12
Corn starch 397 1590
Maltodextrin 132 528 170 680
Sucrose 100 400 175 700
Soya bean oil 70 630 25 225
Choline bitartrate 2.5
Mineral 35 40
Vitamin 10 40 10 40
Coconut oil 333.5 3001.5
kcal/g 3.9 5.56
Exsanguination and sampling
At the end of the experimental period (32 weeks of age), the male mice offspring were killed. Blood samples were collected from the intraorbital retrobulbar plexus after 10 h fasted anesthetized mice. Then, caecal and rectal content were quickly removed, snap frozen on top of dry ice, and stored at −80°C for further analysis, as previously described [13].
Food intake and body weight
The offspring had free access to food. Seventy-two hours food intake was measured biweekly from 3 to 32 weeks old and their average food intake (g) was calculated by carefully collecting and weighing the remaining food including the spillage in the cage, and then subtracting the total remaining food from the known amount given before. The total energy (kJ) consumed by the offspring was calculated by multiplying the food intake (g) by the energy information (kJ/g) according to the nutritional composition of the HF and C diet fed to mice. Body weight was measured at birth, at weaning and per week post-weaning for each mouse.
Glucose tolerance tests
After the mice had fasted for 10 h, glucose (2.0 g/kg body weight) was intraperitoneally administered. Blood glucose (BG) levels were measured before injection (time 0) and at 30, 60 and 120 min after injection from a tail bleed using a Contour TS glucometer (Bayer). The area under the curve (AUC) of intraperitoneal glucose tolerance test (IPGTT) was calculated by the trapezoid formula: AUC={0.5 × [(BG0 + BG30)/2]} + {0.5 × [(BG30 + BG60)/2]} + {1 × [(BG60 + BG120)/2]} [14].
Biochemical analyses
At 32 weeks of age of the mice offspring, blood samples were collected after killing. The blood samples were centrifuged at 4000 g for 10 min and serum was stored in aliquots at −80°C. Serum insulin concentration was measured using the Mouse Ultrasensitive Insulin ELISA kit from ALPCO Diagnostics (80-INSMSU-E01). The intra-assay coefficients of variation for insulin measurements were 4.2%. Insulin sensitivity was assessed using the homoeostasis model assessment of insulin resistance (HOMA-IR). The HOMA-IR was calculated as fasting insulin concentration (μ units/ml) × [fasting glucose concentration (mmol/l)/22.5] [15].
Microbial diversity analysis
DNA extraction and PCR amplification
Microbial diversity was analysed according to our recent publication [16]. Microbial DNA was extracted from caecal and rectal content samples using the E.Z.N.A.® Soil DNA Kit (Omega bio-tek), according to manufacturer's protocols. The V3–V4 region of the bacteria 16S rRNA gene were amplified by PCR (95°C for 2 min, followed by 27 cycles at 95°C for 30 s, 55°C for 30 s and 72°C for 45 s and a final extension at 72°C for 10 min) using primers 338F 5′-ACTCCTACGGGAGGCAGCA-3′ and 806R 5 ′-GGACTACHVGGGTWTCTAAT-3′, where barcode is an N-base sequence (N represent a unique 6–8 nt barcode) unique to each sample. PCR reactions were performed in 20 μl mixture containing 4 μl of 5× Fast Pfu Buffer, 2 μl of 2.5 mM dNTPs, 0.8 μl of each primer (5 μM), 0.4 μl of Fast Pfu Polymerase and 10 ng of template DNA. All reactions were carried out three biological replicates and each analysis consisted of three technical replicates.
Illumina MiSeq sequencing
Amplicons were extracted from 2% agarose gels and purified using the AxyPrep DNA Gel Extraction Kit (Axygen Biosciences) according to the manufacturer's instructions and quantified using QuantiFluor™-ST (Promega). Purified amplicons were pooled in equimolar and paired-end sequenced (2×300) on an Illumina MiSeq platform according to the standard protocols.
Bioinformatic analysis
Previous studies suggested that comparison of communities should be made using equal number of sequence reads in order to minimize the sequencing artefact as the number of spurious phylotypes increases with sequencing effort [17]. Therefore, we picked 14660 sequencing reads from each sample using a pseudorandom generator for comparison of community composition and structure among samples, due to that the lowest sequencing read of all the samples was 14660. Raw fastq files were demultiplexed, quality-filtered using QIIME (version 1.17) with the following three criteria: (1) The 300 bp reads were truncated at any site receiving an average quality score <20 over a 10 bp sliding window, discarding the truncated reads that were shorter than 50 bp. (2) Exact barcode matching, two nucleotides mismatch in primer matching, reads containing ambiguous characters were removed. (3) Only sequences that overlap longer than 10 bp were assembled according to their overlap sequence. Reads which could not be assembled were discarded. Operational taxonomic units (OTUs) were clustered with 97% similarity cut-off using UPARSE (version 7.1 http://drive5.com/uparse/) and chimaeric sequences were identified and removed using UCHIME. The phylogenetic affiliation of each 16S rRNA gene sequence was analysed by RDP Classifier (http://rdp.cme.msu.edu/) against the silva (SSU115) 16S rRNA database using confidence threshold of 70% [18].
Statistical analysis
Statistical differences of body weight and glucose metabolism parameters were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis. The Mann–Whitney test was used to evaluate the relative abundance (%) of gut microbiota between indicated groups. Correlation analyses between relative abundance of sequences belonging to different bacterial class and glucose response to a glucose load were performed by using Spearman's correlation analyses. P value <0.05 were considered to indicate statistical significance. All statistical analyses were calculated with SPSS 21.0 (SPSS).
Body weight and food intake
Body weight at birth and weaning were similar among the different diet groups. The offspring in C–C group had lower body weight throughout the study compared with C–HF and HF–HF groups. Specifically, the C–C offspring had body weight than C–HF group at 16 weeks of age (P<0.01) and both C–HF and HF–HF offspring had higher body weight than C–C group at 24 and 32 weeks of age (P<0.001 respectively). However, there is no significant difference between other groups (Figure 1). No difference in food and water consumption was observed among the groups throughout the experiment (results not shown).
Body weight for male offspring from 3 to 32 weeks
Figure 1
Body weight for male offspring from 3 to 32 weeks
Data represent as mean ± S.D. (n=8/in each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; **P<0.05 C–HF compared with the C–C group; ***P<0.001 C–HF compared with the C–C group; ###P<0.001 HF–HF compared with the C–C group. Dam and pup diets denoted before and after the dash line respectively.
Figure 1
Body weight for male offspring from 3 to 32 weeks
Data represent as mean ± S.D. (n=8/in each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; **P<0.05 C–HF compared with the C–C group; ***P<0.001 C–HF compared with the C–C group; ###P<0.001 HF–HF compared with the C–C group. Dam and pup diets denoted before and after the dash line respectively.
Close modal
Glucose response
The BG levels of the male offspring from the C and HF dams weaned HF diet were significantly higher at 30 min (P<0.001 and P<0.01 respectively), 60 min (P<0.001) and 120 min (P<0.001) after intraperitoneal glucose administration compared with those of the C–C group. The C–HF group had higher BG at 30 min than HF–HF group (P<0.01) (Figure 2a). Furthermore, AUC in C–HF and HF–HF groups was also significantly larger than C–C group (P<0.001). However, no difference in BG and AUC was observed between HF–C and C–C groups throughout the experiment (Figure 2b).
IPGTT (a) and AUC (b) for male offspring at 32 weeks
Figure 2
IPGTT (a) and AUC (b) for male offspring at 32 weeks
Data represent as mean ± S.D.(n=8/each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; ***P<0.001 C–HF compared with the C–C group; ##P<0.01, ###P<0.001 HF–HF compared with the C–C group; P<0.05 HF–HF compared with the C–HF group. Dam and pup diets denoted before and after the dash line respectively.
Figure 2
IPGTT (a) and AUC (b) for male offspring at 32 weeks
Data represent as mean ± S.D.(n=8/each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; ***P<0.001 C–HF compared with the C–C group; ##P<0.01, ###P<0.001 HF–HF compared with the C–C group; P<0.05 HF–HF compared with the C–HF group. Dam and pup diets denoted before and after the dash line respectively.
Close modal
Insulin resistance
To determine insulin sensitivity of the offspring, the levels of serum fasting BG and insulin were determined. There was no significant difference between the four groups (P<0.05, Figure 3b). However, fasting BG and HOMA-IR of the offspring were significantly higher in C–HF and HF–HF groups than C–C group at 32 weeks of age (P<0.05). However, there is no significant difference between HF–C and C–C groups (Figures 3a and 3c).
Fasting BG (a), serum insulin levels (b) and HOMA-IR (c) for male offspring at 32 weeks
Figure 3
Fasting BG (a), serum insulin levels (b) and HOMA-IR (c) for male offspring at 32 weeks
Data represent as mean ± S.D.(n=8/each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; *P<0.05 C–HF compared with the C–C group; #P<0.05 HF–HF compared with the C–C group. Dam and pup diets denoted before and after the dash line respectively.
Figure 3
Fasting BG (a), serum insulin levels (b) and HOMA-IR (c) for male offspring at 32 weeks
Data represent as mean ± S.D.(n=8/each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis; *P<0.05 C–HF compared with the C–C group; #P<0.05 HF–HF compared with the C–C group. Dam and pup diets denoted before and after the dash line respectively.
Close modal
Characteristics of sequencing results
The offspring in all the four groups (n=6, each group) of microbial diversity were investigated. A total of 351840 high-quality sequences were produced in the present study, with an average of 14660 sequences per sample (Table 2). The Good's coverage of each group was over 97%, indicating that the 16S rDNA sequences identified in these groups represent the majority of bacteria present in the samples of the present study. The OTU, the estimators of community richness (Chao) and diversity (Shannon) are also shown in Table 2. Lower OUT, Chao and Shannon indexes were observed in C–HF group and lower Chao was found in HF–HF group, compared with HF–C and C–C groups, demonstrating the significantly lower richness and diversity found in C–HF offspring compared with HF–C and C–C groups. And there were no significant differences of OUT, Chao and Shannon indexes between HF–C and C–C groups. Group HF–HF had a lower median OUT and Shannon indexes compared with the C group, but the difference was not significant (Table 2).
Table 2
Sequencing data summary
Data represent as mean ± S.D. (n=6, in each group). Statistical differences were determined using ANOVA followed by multiple-comparison testing using Bonferroni post hoc analysis. The number of OTUs, richness estimator Chao and diversity estimator Shannon were calculated at 3% distance. *P<0.05 C–HF compared with C–C group, P<0.05 C–HF compared with HF–C group, #P<0.05 HF–HF compared with C–C group, $P<0.05 HF–HF compared with HF–C group. Dam and pup diets denoted before and after the dash line respectively. C–CHF–CC–HFHF–HF Sequences 14660.00 14660.00 14660.00 14660.00 OTUs 239.3±6.1 262.7±9.6 108.7±68.4* 195.0±29.5 Chao 265.0±14.8 289.3±7.1 129.3±63.6* 220.7±19.7#$
Shannon 3.8±0.1 4.2±0.2 2.7±0.8* 3.3±1.2
C–CHF–CC–HFHF–HF
Sequences 14660.00 14660.00 14660.00 14660.00
OTUs 239.3±6.1 262.7±9.6 108.7±68.4* 195.0±29.5
Chao 265.0±14.8 289.3±7.1 129.3±63.6* 220.7±19.7#\$
Shannon 3.8±0.1 4.2±0.2 2.7±0.8* 3.3±1.2
Principal coordinates analysis among different groups
Closer analysis of bacterial differences induced by diet was determined by sequencing the 16S rRNA encoding genes present in the caecal and rectal content. Principal coordinates analysis (PCA) of Illumina MiSeq amplicon data demonstrated significantly separate clustering of the gut communities in the offspring among the four groups with PC1 percent variation explained=58.7% and PC2 percent variation explained=22.41%. It is indicated that there were significant difference of microbial composition offspring between post-weaning HF diet and C diet. However, no marked differences in the microbial composition were observed between HF–C and C–C groups (Figure 4).
PCA plots of gut communities in the offspring
Figure 4
PCA plots of gut communities in the offspring
n=6/each group; dam and pup diets denoted before and after the dash line respectively.
Figure 4
PCA plots of gut communities in the offspring
n=6/each group; dam and pup diets denoted before and after the dash line respectively.
Close modal
Microbial structures of the offspring differed significantly
The overall microbiota structure for each group at the phylum and genus level is shown in Figure 5. The dominant phyla of all the four groups were Bacteroidetes, Firmicutes and Proteobacteria. The Verrucomicrobias were significantly increased in C–HF and HF–HF groups, compared with C–C and HF–C groups and Bacteroidetes were significantly decreased in both C–HF and HF–HF groups. At the phylum and genus level, the relative abundance of microbiota sequences both revealed that C–HF microbiota exhibited a closer similarity to HF–HF group, and HF–C microbiota exhibited a closer similarity to C–C offspring. The heat map according to bacterial genus level also demonstrated the same phenomenon that the microbial structures of HF–C and C–C groups can be clustered together (Figure 6).
Relative abundance of bacterial phyla in microbiota in each group at the phylum (a) and genus (b) level
Figure 5
Relative abundance of bacterial phyla in microbiota in each group at the phylum (a) and genus (b) level
n=6/each group; dam and pup diets denoted before and after the dash line respectively.
Figure 5
Relative abundance of bacterial phyla in microbiota in each group at the phylum (a) and genus (b) level
n=6/each group; dam and pup diets denoted before and after the dash line respectively.
Close modal
Heat map analyses of abundant genera in each group
Figure 6
Heat map analyses of abundant genera in each group
n=6/each group; the y-axis is a neighbour-joining phylogenetic tree, each row is a different phylotype. The abundance plot shows the proportion of 16S rRNA gene sequences in each group. Dam and pup diets denoted before and after the dash line respectively.
Figure 6
Heat map analyses of abundant genera in each group
n=6/each group; the y-axis is a neighbour-joining phylogenetic tree, each row is a different phylotype. The abundance plot shows the proportion of 16S rRNA gene sequences in each group. Dam and pup diets denoted before and after the dash line respectively.
Close modal
Phylotypes significantly different in offspring mice
There were significant variations in the composition of the caecal and rectal content in the four groups at different bacterial levels. At the phylum level, Bacteroidetes, Firmicutes and Saccharibacteria were significantly decreased in C–HF group, compared with C–C group (P<0.05). Bacteroidetes and Saccharibacteria were significantly decreased, whereas Proteobacteria was significantly decreased in HF–HF offspring, compared with C–C offspring. At the genus level, with ten significantly different genera between C–HF and C–C groups, and five different genera between HF–HF and C–C groups. Specifically, total eight genera of Bacteroidales_S24-7_group_norank, Candidatus_Saccharimonas, Defluviitaleaceae_UCG-011, Lachnospiraceae_NK4A136_group, Lachnospiraceae_uncultured, Lactobacillus, Marvinbryantia and Ruminococcus_1 showed a significant lower percentage in C–HF group (P<0.05), whereas Bacteroides and Erysipelatoclostridium were increased in C–HF group, compared with C–C group (P<0.05). All five genera of Bacteroidales_S24-7_group_norank, Candidatus_Saccharimonas, Defluviitaleaceae_UCG-011, Lac-tobacillus and Ruminococcus_1 exhibited a statistically significant lower percentage in HF–HF group than C–C group. Furthermore, in order to determine the effects on microbial composition in the offspring exposed to different maternal diets during pregnancy and lactation, we compared the microbial composition between HF–C and C–C groups. It is indicated that there was no significant differences between HF–C and C–C groups at the phylum level. And only one genus of Bacteroides was lower in HF–C group, compared with C–C group (Table 3).
Table 3
Phylotypes significantly different in offspring groups
Statistical analysis was performed by Mann–Whitney test. Data of C–C, C–HF and HF–HF groups were relative abundance (percentage) of all sequences in each group. *P<0.05 C–HF compared with the C–C group, #P<0.05 HF–HF compared with the C–C group, &P<0.05 C–HF compared with the C–C group; n.s.: no significance. Dam and pup diets denoted before and after the dash line respectively.
Taxonomic rankC–C (%)HF–C (%)P valueC–HF (%)HF–HF (%)P valueP value
Phylum Actinobacteria 0.05 0.38 0.09 0.67 0.75 0.14 0.35
Phylum Bacteroidetes 57.10 45.59 0.22 38.85 31.18 0.04* 0.02#
Phylum Cyanobacteria 0.13 0.28 0.49 0.07 0.68 0.49 0.26
Phylum Deferribacteres 0.08 0.02 0.09 0.24 0.31 0.37 0.41
Phylum Firmicutes 41.09 47.82 0.48 20.00 33.46 0.04* 0.65
Phylum Proteobacteria 1.10 3.87 0.12 20.28 6.43 0.19 0.04#
Phylum Saccharibacteria 0.17 0.64 0.08 0.00 0.00 0.02* 0.02#
Phylum Verrucomicrobia 0.01 1.37 0.39 19.89 27.19 0.16 0.25
Genus Alloprevotella 11.50 5.49 0.31 0.70 1.47 0.05 0.07
Genus Bacteroidales_S24-7_group_norank 34.41 36.52 0.56 10.96 13.14 0.00* 0.00#
Genus Bacteroides 7.05 1.84 0.02& 24.30 6.44 0.03* 0.75
Genus Candidatus_Saccharimonas 0.17 0.64 0.08 0.00 0.00 0.02* 0.02#
Genus Christensenellaceae_uncultured 0.03 0.02 0.49 0.01 0.04 0.07 0.72
Genus Clostridiales_vadinBB60_group_norank 0.04 0.02 0.35 0.00 0.00 0.06 0.06
Genus Defluviitaleaceae_UCG-011 0.15 0.20 0.38 0.03 0.02 0.03* 0.01#
Genus Erysipelatoclostridium 0.46 0.06 0.12 4.27 0.46 0.04* 1.00
Genus Lachnospiraceae_NK4A136_group 15.93 13.85 0.58 1.07 7.68 0.00* 0.14
Genus Lachnospiraceae_unclassified 5.21 5.48 0.86 1.17 3.14 0.07 0.40
Genus Lachnospiraceae_uncultured 4.78 5.21 0.52 1.58 2.73 0.02* 0.15
Genus Lactobacillus 1.53 2.30 0.57 0.01 0.06 0.00* 0.00#
Genus Marvinbryantia 0.06 0.05 0.38 0.00 0.03 0.03* 0.35
Genus Parabacteroides 0.13 0.13 0.96 1.16 0.93 0.07 0.09
Genus Peptococcaceae_uncultured 0.17 0.48 0.10 0.04 0.23 0.05 0.22
Genus Ruminiclostridium_6 0.97 0.56 0.42 0.00 0.18 0.09 0.17
Genus Ruminococcus_1 0.21 0.46 0.36 0.00 0.01 0.03* 0.03#
Taxonomic rankC–C (%)HF–C (%)P valueC–HF (%)HF–HF (%)P valueP value
Phylum Actinobacteria 0.05 0.38 0.09 0.67 0.75 0.14 0.35
Phylum Bacteroidetes 57.10 45.59 0.22 38.85 31.18 0.04* 0.02#
Phylum Cyanobacteria 0.13 0.28 0.49 0.07 0.68 0.49 0.26
Phylum Deferribacteres 0.08 0.02 0.09 0.24 0.31 0.37 0.41
Phylum Firmicutes 41.09 47.82 0.48 20.00 33.46 0.04* 0.65
Phylum Proteobacteria 1.10 3.87 0.12 20.28 6.43 0.19 0.04#
Phylum Saccharibacteria 0.17 0.64 0.08 0.00 0.00 0.02* 0.02#
Phylum Verrucomicrobia 0.01 1.37 0.39 19.89 27.19 0.16 0.25
Genus Alloprevotella 11.50 5.49 0.31 0.70 1.47 0.05 0.07
Genus Bacteroidales_S24-7_group_norank 34.41 36.52 0.56 10.96 13.14 0.00* 0.00#
Genus Bacteroides 7.05 1.84 0.02& 24.30 6.44 0.03* 0.75
Genus Candidatus_Saccharimonas 0.17 0.64 0.08 0.00 0.00 0.02* 0.02#
Genus Christensenellaceae_uncultured 0.03 0.02 0.49 0.01 0.04 0.07 0.72
Genus Clostridiales_vadinBB60_group_norank 0.04 0.02 0.35 0.00 0.00 0.06 0.06
Genus Defluviitaleaceae_UCG-011 0.15 0.20 0.38 0.03 0.02 0.03* 0.01#
Genus Erysipelatoclostridium 0.46 0.06 0.12 4.27 0.46 0.04* 1.00
Genus Lachnospiraceae_NK4A136_group 15.93 13.85 0.58 1.07 7.68 0.00* 0.14
Genus Lachnospiraceae_unclassified 5.21 5.48 0.86 1.17 3.14 0.07 0.40
Genus Lachnospiraceae_uncultured 4.78 5.21 0.52 1.58 2.73 0.02* 0.15
Genus Lactobacillus 1.53 2.30 0.57 0.01 0.06 0.00* 0.00#
Genus Marvinbryantia 0.06 0.05 0.38 0.00 0.03 0.03* 0.35
Genus Parabacteroides 0.13 0.13 0.96 1.16 0.93 0.07 0.09
Genus Peptococcaceae_uncultured 0.17 0.48 0.10 0.04 0.23 0.05 0.22
Genus Ruminiclostridium_6 0.97 0.56 0.42 0.00 0.18 0.09 0.17
Genus Ruminococcus_1 0.21 0.46 0.36 0.00 0.01 0.03* 0.03#
Correlation analyses
Correlation analyses between relative abundance (percentage) of sequences belonging to a specific bacterial genus and glucose response to a glucose load were performed by using Spearman's correlation analyses. The glucose response to a glucose load was assessed by AUC of IPGTT. Interestingly, it is indicated that Lactobacillus percentage were negatively associated with AUC of IPGTT (r2=−0.43, P=0.01) and Bacteroides percentage were positively associated with AUC of IPGTT (r2=0.5, P=0.0006) (Figure 7).
Correlation analyses between relative abundance (%) of sequences belonging to Lactobacillus (a), Bacteroides (b) genus and glucose response to a glucose load
Figure 7
Correlation analyses between relative abundance (%) of sequences belonging to Lactobacillus (a), Bacteroides (b) genus and glucose response to a glucose load
n=6/each group.
Figure 7
Correlation analyses between relative abundance (%) of sequences belonging to Lactobacillus (a), Bacteroides (b) genus and glucose response to a glucose load
n=6/each group.
Close modal
Our study was designed to examine the effect of maternal and post-weaning HF diet interaction on offspring's gut microbiota and glucose homoeostasis in later life. This long-term HF diet mice model is particularly important in the light of the increasing consumption of refined foods with a high glycaemic index and fat content among men and women now consuming 30% more saturated fats than the recommended daily intake [19]. Similar to other studies [2022], we have shown that offspring from both HF and C dams fed on HF diet from weaning to adulthood had heavier body weight, severer impaired glucose tolerance and lower insulin sensitivity level at 32 weeks of age. It indicated that maternal and post-weaning HF diet interaction could contribute to abnormal glucose metabolism in the later life of offspring.
Our present study indicated that both HF–HF and C–HF offspring had lower bacterial richness. Similarly, one large human study also demonstrated that individuals with a low bacterial richness are characterized by more marked overall adiposity, insulin resistance and dyslipidaemia, which indicated that a low bacterial richness may be associated with abnormal glucose metabolism [8]. The dominant phyla of all the groups were Bacteroidetes, Firmicutes and Proteobacteria. These data were consistent with findings from Karlsson et al. [13] that assessed the long-term effects of a high-energy-dense diet, supplemented with Lactobacillus plantarum (Lp) or Escherichia coli (Ec) on weight gain, fattening and the gut microbiota in rats. More specifically, Tenericutes, Bacteroidete, Lactobacillus, Ruminococcus and Prevotella significantly decreased whereas Proteobacteria significantly increased in both C–HF and HF–HF groups. Jumpertz et al. [23] indicated that a corresponding decrease in Bacteroidetes was associated with an increased energy harvest of approximately 150 kcal/day in one inpatient study. Similar findings were found in a human study which showed the relative abundance of Bacteroides in the T2DM group (approximately 10%) was lower than that in the normal glucose tolerance and prediabetes groups [24]. Another study indicated that large alterations were associated with switching to the HF diet of wild-type mice, including a decrease in Bacteroidetes and an increase in Proteobacteria. These changes were seen for both genotypes (i.e. in the presence and absence of obesity), which indicated that it was the HF diet itself, and not the obese state, mainly accounting for the observed alterations in the gut microbiota. These findings demonstrated the importance of diet as a determinant of gut microbiome composition and suggest the need to C dietary variation when evaluating the composition of the human gut microbiome [25].
Of interest, our present study showed Lactobacillus percentage was negatively associated with glucose response to a glucose load and a corresponding positive correlation between Bacteroides and glucose response to a glucose load. It indicated gut microbiota such as Lactobacillus and Bacteroides might be important bacterial phyla in regulating glucose metabolism in the offspring and they can be the target of diabetes prevention and intervention. Recently, numerous studies have indicated that Lactic acid bacteria (LAB) are useful in preventing or delaying the onset of diabetes [26]. One study found that the BG levels were significantly lower in Type 2 diabetic mice which were administered Lactobacillus gasseri BNR17 than those in a C group [27]. The underlying mechanism may be that LAB can enhance pancreatic glutathione biosynthesis, thus reducing oxidative stress in the pancreas [28].
In conclusion, our data suggest that maternal and post-weaning HF diet interaction predisposes the offspring for obesity, glucose intolerance, insulin resistance and alters gut microbiota in later life. Our work is novel in showing the modulation of gut microbiota between maternal and post-weaning diet interaction and glucose homoeostasis. Therefore, as both ‘gut microbiota’ and ‘fetal programming’ become more evident and prevalent in obesity and T2DM, a better understanding of the role of the gut microbiota in ‘fetal programming’ might provide novel perspectives regarding its pathophysiological relevance and pave the way for new therapeutic principles of obesity and T2DM.
Xinhua Xiao and Qian Zhang conceived and designed experiments, Jia Zheng and Cuijuan Qi carried out experiments. Miao Yu and Jianping Xu analysed data. All authors were involved in writing the paper and had final approval of the submitted and published versions.
This work was supported by the National Natural Science Foundation of China [grant number 81570715]; the National Natural Science Foundation for Young Scholars of China [grant number 81300649]; and the National Key Program of Clinical Science and Peking Union Medical College Hospital.
• AUC
area under the curve
•
• BG
blood glucose
•
• C
control
•
• GIT
gastrointestinal tract
•
• HF
high-fat
•
• HOMA-IR
homoeostasis model assessment of insulin resistance
•
• IPGTT
intraperitoneal glucose tolerance test
•
• LAB
Lactic acid bacteria
•
• OTU
operational taxonomic unit
•
• PCA
principal coordinates analysis
•
• SPF
specific pathogen free
•
• T2DM
Type 2 diabetes mellitus
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This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution Licence 4.0 (CC BY).
| 2022-11-29T17:54:24 |
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https://pos.sissa.it/390/341/
|
Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Top Quark and Electroweak Physics
W boson measurements with the CMS experiment
R. Salvatico* on behalf of the CMS collaboration
*corresponding author
Full text: pdf
Pre-published on: January 20, 2021
Published on:
Abstract
The W boson, one of the two mediators of the weak interaction, has been broadly studied at both $\mathrm{e^+e^-}$ and hadron colliders since its discovery. Despite the increasing accuracy in the measurement of its properties, it still remains relatively poorly known if compared to the other mediator, the Z boson, due to the bigger experimental challenges in the reconstruction of the W boson decays. The CMS experiment at the CERN LHC covers a vast program in the electroweak physics sector, with numerous analyses aiming at measuring the W boson properties with high precision. Some of the latest results from the CMS Collaboration are presented in this report. These include measurements of the multi-differential W boson production cross sections, polarization and charge asymmetry, the first search for the rare decay of the W boson into a pion and a photon at the LHC, and the first evidence for WW production via double-parton scattering. Such measurements exploit, either partially or fully, the integrated luminosity collected by CMS during the LHC Run 2 (2016--2018), and allow us to further increase our knowledge of this fundamental piece of the standard model of particle physics.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2021-02-26T01:17:27 |
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|
http://pdglive.lbl.gov/DataBlock.action?node=S056ZOT
|
# Limits for other ${{\boldsymbol Z}^{\,'}}$ INSPIRE search
VALUE (GeV) CL% DOCUMENT ID TECN COMMENT
$> 1300$ 95 1
2018 B
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$
$\text{none 1200 - 2800}$ 95 2
2018 F
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$
$\bf{>2900}$ 95 3
2017 AK
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$
$\text{none 1100 - 2600}$ 95 4
2017 AO
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
$>2300$ 95 5
2017 AK
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$ , ${{\mathit h}}{{\mathit Z}}$
$\bf{> 2500}$ 95 6
2017 Q
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$>1190$ 95 7
2017 R
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
$\text{none 1210 - 2260}$ 95 7
2017 R
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
8
2018 G
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$
$> 1580$ 95 9
2017 B
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
10
2017 AX
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit \ell}}{{\mathit \ell}}$
11
2017 U
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
$> 1700$ 95 12
2017 A
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$
13
2017 AP
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit A}}$
14
2017 T
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$
15
2017 V
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit T}}{{\mathit t}}$
$\text{none 1100 - 1500}$ 95 16
2016
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$
17
2016 L
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit a}}{{\mathit \gamma}}$ , ${{\mathit a}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$
$\text{none 1500 - 2600}$ 95 18
2016 S
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$
$\text{none 1000 - 1100, none 1300 - 1500}$ 95 19
2016 AP
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
$> 2400$ 95 20
2016 E
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
21
2015 AO
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
22
2015 AT
ATLS monotop
23
2015 CD
ATLS ${{\mathit h}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{\,'}}$ , ${{\mathit Z}^{\,'}}{{\mathit Z}^{\,'}}$ ; ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$
24
2015 F
CMS monotop
25
2015 O
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit Z}}$
26
2014 AT
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}$
27
2014 A
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit V}}{{\mathit V}}$
28
2014
RVUE Electroweak
$\text{none 500 - 1740}$ 95 29
2013 AQ
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$\text{>1320 or 1000 - 1280}$ 95 30
2013 G
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$>915$ 95 30
2013 A
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$> 1300$ 95 31
2013 AP
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$> 2100$ 95 30
2013 BM
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
32
2012 BV
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
33
2012 K
ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
34
2012 AR
CDF Chromophilic
35
2012 N
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\overline{\mathit t}}}{{\mathit u}}$
$> 835$ 95 36
2012 R
D0 ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
37
2012 AI
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit u}}}$
38
2012 AQ
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
$> 1490$ 95 30
2012 BL
CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
39
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
40
2011 AE
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
41
2011 O
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit t}}{{\mathit t}}$
42
2008 D
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
42
2008 Y
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
42
2008 AA
D0 ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit t}}{{\overline{\mathit t}}}$
43
2004 A
D0 Repl. by ABAZOV 2008AA
44
2003 B
COSM Nucleosynthesis; light ${{\mathit \nu}_{{R}}}$
45
2000
RVUE $\mathit E_{6}$-motivated
46
1998
RVUE $\mathit E_{6}$-motivated
47
1997 G
CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\overline{\mathit q}}}{{\mathit q}}$
1 AABOUD 2018B search for resonances decaying to ${{\mathit W}}{{\mathit W}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 1. See their Fig.11 for limits on $\sigma \cdot{}{{\mathit B}}$.
2 AABOUD 2018F search for resonances decaying to ${{\mathit W}}{{\mathit W}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3. The limit becomes $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 2200 GeV for ${{\mathit g}_{{V}}}$ = 1. If we assume $\mathit M_{{{\mathit Z}^{\,'}}}$ = $\mathit M_{{{\mathit W}^{\,'}}}$, the limit increases $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 3500 GeV and $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 3100 GeV for ${{\mathit g}_{{V}}}$ = 3 and ${{\mathit g}_{{V}}}$ = 1, respectively. See their Fig.5 for limits on $\sigma \cdot{}{{\mathit B}}$.
3 AABOUD 2017AK search for a new resonance decaying to dijets in $pp$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above is for a leptophobic ${{\mathit Z}^{\,'}}$ boson having axial-vector coupling strength with quarks ${{\mathit g}_{{q}}}$ = 0.2. The limit is 2100 GeV if ${{\mathit g}_{{q}}}$ = 0.1.
4 AABOUD 2017AO search for resonances decaying to ${{\mathit h}}{{\mathit Z}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above is for a ${{\mathit Z}^{\,'}}$ in the heavy-vector-triplet model with ${{\mathit g}_{{V}}}$ = 3. See their Fig.4 for limits on $\sigma \cdot{}{{\mathit B}}$.
5 SIRUNYAN 2017AK search for resonances decaying to ${{\mathit W}}{{\mathit W}}$ or ${{\mathit h}}{{\mathit Z}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 and 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3. The limit becomes $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 2200 GeV for ${{\mathit g}_{{V}}}$ =1. If we assume $\mathit M_{{{\mathit Z}^{\,'}}}$ = $\mathit M_{{{\mathit W}^{\,'}}}$, the limit increases $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 2400 GeV for both ${{\mathit g}_{{V}}}$ = 3 and ${{\mathit g}_{{V}}}$ = 1. See their Fig.1 and 2 for limits on ${{\mathit \sigma}}\cdot{}{{\mathit B}}$.
6 SIRUNYAN 2017Q search for a resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above is for a resonance with relative width $\Gamma _{{{\mathit Z}^{\,'}}}$ $/$ $\mathit M_{{{\mathit Z}^{\,'}}}$ = 0.01. Limits for wider resonances are available. See their Fig.6 for limits on $\sigma \cdot{}\mathit B$.
7 SIRUNYAN 2017R search for resonances decaying to ${{\mathit h}}{{\mathit Z}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3. Mass regions $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 1150 GeV and 1250 GeV $<$ $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 1670 GeV are excluded for ${{\mathit g}_{{V}}}$ = 1. If we assume $\mathit M_{{{\mathit Z}^{\,'}}}$ = $\mathit M_{{{\mathit W}^{\,'}}}$, the excluded mass regions are 1000 $<$ $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 2500 GeV and 2760 $<$ $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 3300 GeV for ${{\mathit g}_{{V}}}$ = 3; 1000 $<$ $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 2430 GeV and 2810 $<$ $\mathit M_{{{\mathit Z}^{\,'}}}$ $<$ 3130 GeV for ${{\mathit g}_{{V}}}$ = 1. See their Fig.5 for limits on ${{\mathit \sigma}}\cdot{}{{\mathit B}}$.
8 SIRUNYAN 2018G search for a new resonance decaying to dijets in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV in the mass range $50 - 300$ GeV. See their Fig.7 for limits in the mass-coupling plane.
9 AABOUD 2017B search for resonances decaying to ${{\mathit h}}{{\mathit Z}}$ ( ${{\mathit h}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit c}}{{\overline{\mathit c}}}$ ; ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ , ${{\mathit \nu}}{{\overline{\mathit \nu}}}$ ) in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3. The limit becomes ${{\mathit M}}_{{{\mathit Z}^{\,'}}}>$ 1490 GeV for ${{\mathit g}_{{V}}}$ = 1. If we assume ${{\mathit M}}_{{{\mathit Z}^{\,'}}}$ = ${{\mathit M}}_{{{\mathit W}^{\,'}}}$, the limit increases ${{\mathit M}}_{{{\mathit Z}^{\,'}}}>$ 2310 GeV and ${{\mathit M}}_{{{\mathit Z}^{\,'}}}>$ 1730 GeV for ${{\mathit g}_{{V}}}$ = 3 and ${{\mathit g}_{{V}}}$ = 1, respectively. See their Fig.3 for limits on ${{\mathit \sigma}}\cdot{}{{\mathit B}}$.
10 KHACHATRYAN 2017AX search for lepto-phobic resonances decaying to four leptons in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV.
11 KHACHATRYAN 2017U search for resonances decaying to ${{\mathit h}}{{\mathit Z}}$ ( ${{\mathit h}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ ; ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ , ${{\mathit \nu}}{{\overline{\mathit \nu}}}$ ) in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit on the heavy-vector-triplet model is $\mathit M_{{{\mathit Z}^{\,'}}}$ = $\mathit M_{{{\mathit W}^{\,'}}}$ $>$ 2 TeV for ${{\mathit g}_{{V}}}$ = 3, in which constraints from the ${{\mathit W}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit W}}$ ( ${{\mathit h}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ ; ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}$ ) are combined. See their Fig.3 and Fig.4 for limits on $\sigma \cdot{}\mathit B$.
12 SIRUNYAN 2017A search for resonances decaying to ${{\mathit W}}{{\mathit W}}$ with ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit q}}{{\overline{\mathit q}}}$ , ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit q}}{{\overline{\mathit q}}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3. The limit becomes $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 1600 GeV for ${{\mathit g}_{{V}}}$ = 1. If we assume $\mathit M_{{{\mathit Z}^{\,'}}}$ = $\mathit M_{{{\mathit W}^{\,'}}}$, the limit increases $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 2400 GeV and $\mathit M_{{{\mathit Z}^{\,'}}}$ $>$ 2300 GeV for ${{\mathit g}_{{V}}}$ = 3 and ${{\mathit g}_{{V}}}$ = 1, respectively. See their Fig.6 for limits on $\sigma \cdot{}\mathit B$.
13 SIRUNYAN 2017AP search for resonances decaying into a SM-like Higgs scalar ${{\mathit h}}$ and a light pseudo scalar ${{\mathit A}}$. ${{\mathit A}}$ is assumed to decay invisibly. See their Fig.9 for limits on ${{\mathit \sigma}}\cdot{}{{\mathit B}}$.
14 SIRUNYAN 2017T search for a new resonance decaying to dijets in $pp$ collisions at $\sqrt {s }$ = 13 TeV in the mass range $100 - 300$ GeV. See their Fig.3 for limits in the mass-coupling plane.
15 SIRUNYAN 2017V search for a new resonance decaying to a top quark and a heavy vector-like top partner ${{\mathit T}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. See their table 5 for limits on the ${{\mathit Z}^{\,'}}$ production cross section for various values of $\mathit M_{{{\mathit Z}^{\,'}}}$ and $\mathit M_{T}$ in the range of $\mathit M_{{{\mathit Z}^{\,'}}}$ = $1500 - 2500$ GeV and $\mathit M_{T}$ = $700 - 1500$ GeV.
16 AABOUD 2016 search for a narrow resonance decaying into ${{\mathit b}}{{\overline{\mathit b}}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above is for a leptophobic ${{\mathit Z}^{\,'}}$ with SM-like couplings to quarks. See their Fig.6 for limits on $\sigma \cdot{}\mathit B$.
17 AAD 2016L search for ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit a}}{{\mathit \gamma}}$ , ${{\mathit a}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. See their Table 6 for limits on $\sigma \cdot{}\mathit B$.
18 AAD 2016S search for a new resonance decaying to dijets in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above is for a leptophobic ${{\mathit Z}^{\,'}}$ having coupling strength with quark ${{\mathit g}_{{q}}}$ = 0.3 and is taken from their Figure 3.
19 KHACHATRYAN 2016AP search for a resonance decaying to ${{\mathit h}}{{\mathit Z}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. Both ${{\mathit h}}$ and ${{\mathit Z}}$ are assumed to decay to fat jets. The quoted limit is for heavy-vector-triplet ${{\mathit Z}^{\,'}}$ with ${{\mathit g}_{{V}}}$ = 3.
20 KHACHATRYAN 2016E search for a leptophobic top-color ${{\mathit Z}^{\,'}}$ decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. The quoted limit assumes that ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$ = 0.012. Also ${\mathit m}_{{{\mathit Z}^{\,'}}}$ $<$ 2.9 TeV is excluded for wider topcolor ${{\mathit Z}^{\,'}}$ with ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$ = 0.1.
21 AAD 2015AO search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. See Fig. 11 for limit on $\sigma \mathit B$.
22 AAD 2015AT search for monotop production plus large missing $\mathit E_{T}$ events in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV and give constraints on a ${{\mathit Z}^{\,'}}$ model having ${{\mathit Z}^{\,'}}{{\mathit u}}{{\overline{\mathit t}}}$ coupling. ${{\mathit Z}^{\,'}}$ is assumed to decay invisibly. See their Fig. 6 for limits on $\sigma \cdot{}\mathit B$.
23 AAD 2015CD search for decays of Higgs bosons to 4 ${{\mathit \ell}}$ states via ${{\mathit Z}^{\,'}}$ bosons, ${{\mathit h}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{\,'}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ or ${{\mathit h}}$ $\rightarrow$ ${{\mathit Z}^{\,'}}{{\mathit Z}^{\,'}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ . See Fig. 5 for the limit on the signal strength of the ${{\mathit h}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{\,'}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ process and Fig. 16 for the limit on ${{\mathit h}}$ $\rightarrow$ ${{\mathit Z}^{\,'}}{{\mathit Z}^{\,'}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ .
24 KHACHATRYAN 2015F search for monotop production plus large missing $\mathit E_{T}$ events in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV and give constraints on a ${{\mathit Z}^{\,'}}$ model having ${{\mathit Z}^{\,'}}{{\mathit u}}{{\overline{\mathit t}}}$ coupling. ${{\mathit Z}^{\,'}}$ is assumed to decay invisibly. See Fig. 3 for limits on $\sigma \mathit B$.
25 KHACHATRYAN 2015O search for narrow ${{\mathit Z}^{\,'}}$ resonance decaying to ${{\mathit Z}}{{\mathit h}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. See their Fig. 6 for limit on $\sigma \mathit B$.
26 AAD 2014AT search for a narrow neutral vector boson decaying to ${{\mathit Z}}{{\mathit \gamma}}$ . See their Fig. 3b for the exclusion limit in ${\mathit m}_{{{\mathit Z}^{\,'}}}−\sigma \mathit B$ plane.
27 KHACHATRYAN 2014A search for new resonance in the ${{\mathit W}}{{\mathit W}}$ ( ${{\mathit \ell}}{{\mathit \nu}}{{\mathit q}}{{\overline{\mathit q}}}$ ) and the ${{\mathit Z}}{{\mathit Z}}$ ( ${{\mathit \ell}}{{\mathit \ell}}{{\mathit q}}{{\overline{\mathit q}}}$ ) channels using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$=8 TeV. See their Fig.13 for the exclusion limit on the number of events in the mass-width plane.
28 MARTINEZ 2014 use various electroweak data to constrain the ${{\mathit Z}^{\,'}}$ boson in the 3-3-1 models.
29 AAD 2013AQ search for a leptophobic top-color ${{\mathit Z}^{\,'}}$ decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . The quoted limit assumes that ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$ = 0.012.
30 CHATRCHYAN 2013BM search for top-color ${{\mathit Z}^{\,'}}$ decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$=8 TeV. The quoted limit is for ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$ = 0.012.
31 CHATRCHYAN 2013AP search for top-color leptophobic ${{\mathit Z}^{\,'}}$ decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$=7 TeV. The quoted limit is for ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$ = 0.012.
32 AAD 2012BV search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$=7 TeV. See their Fig. 7 for limit on $\sigma \cdot{}$B.
33 AAD 2012K search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ using ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$=7 TeV. See their Fig. 5 for limit on $\sigma \cdot{}$B.
34 AALTONEN 2012AR search for chromophilic ${{\mathit Z}^{\,'}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. See their Fig. 5 for limit on $\sigma \cdot{}$B.
35 AALTONEN 2012N search for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit t}}{{\mathit Z}^{\,'}}$ , ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\overline{\mathit t}}}{{\mathit u}}$ events in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions. See their Fig. 3 for the limit on $\sigma \cdot{}$B.
36 ABAZOV 2012R search for top-color ${{\mathit Z}^{\,'}}$ boson decaying exclusively to ${{\mathit t}}{{\overline{\mathit t}}}$ . The quoted limit is for ${\Gamma}_{{\mathit Z}^{\,'}}/{\mathit m}_{{{\mathit Z}^{\,'}}}$= 0.012.
37 CHATRCHYAN 2012AI search for ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit t}}{{\mathit t}}$ events and give constraints on a ${{\mathit Z}^{\,'}}$ model having ${{\mathit Z}^{\,'}}{{\overline{\mathit u}}}{{\mathit t}}$ coupling. See their Fig. 4 for the limit in mass-coupling plane.
38 Search for resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . See their Fig. 6 for limit on $\sigma \cdot{}$B.
39 Search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . See their Fig. 4 for limit on $\sigma \cdot{}$B.
40 Search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . See their Fig. 3 for limit on $\sigma \cdot{}$B.
41 CHATRCHYAN 2011O search for same-sign top production in ${{\mathit p}}{{\mathit p}}$ collisions induced by a hypothetical FCNC ${{\mathit Z}^{\,'}}$ at $\sqrt {s }$ = 7 TeV. See their Fig. 3 for limit in mass-coupling plane.
42 Search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . See their Fig.$~$3 for limit on $\sigma \cdot{}$B.
43 Search for narrow resonance decaying to ${{\mathit t}}{{\overline{\mathit t}}}$ . See their Fig.$~$2 for limit on $\sigma \cdot{}$B.
44 BARGER 2003B use the nucleosynthesis bound on the effective number of light neutrino $\delta \mathit N_{{{\mathit \nu}}}$. See their Figs.$~4 - 5$ for limits in general $\mathit E_{6}$ motivated models.
45 CHO 2000 use various electroweak data to constrain ${{\mathit Z}^{\,'}}$ models assuming ${\mathit m}_{{{\mathit H}}}$=100 GeV. See Fig.$~$2 for limits in general $\mathit E_{6}$-motivated models.
46 CHO 1998 study constraints on four-Fermi contact interactions obtained from low-energy electroweak experiments, assuming no ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing.
47 Search for ${{\mathit Z}^{\,'}}$ decaying to dijets at $\sqrt {\mathit s }=1.8$ TeV. For ${{\mathit Z}^{\,'}}$ with electromagnetic strength coupling, no bound is obtained.
References:
AABOUD 2018F
PL B777 91 Search for Diboson Resonances with Boson-Tagged Jets in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
AABOUD 2018B
EPJ C78 24 Search for Heavy Resonances Decaying into ${{\mathit W}}{{\mathit W}}$ in the ${{\mathit e}}{{\mathit \nu}}{{\mathit \mu}}{{\mathit \nu}}$ Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
SIRUNYAN 2018G
JHEP 1801 097 Search for Low Mass Vector Resonances Decaying into Quark-Antiquark Pairs in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
AABOUD 2017AO
PL B774 494 Search for Heavy Resonances Decaying to a ${{\mathit W}}$ or ${{\mathit Z}}$ Boson and a Higgs Boson in the ${\mathit {\mathit q}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
AABOUD 2017AK
PR D96 052004 Search for New Phenomena in Dijet Events using 37 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ Collision Data Collected at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
AABOUD 2017B
PL B765 32 Search for New Resonances Decaying to a ${{\mathit W}}$ or ${{\mathit Z}}$ Boson and a Higgs Boson in the ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$, ${{\mathit \ell}}{{\mathit \nu}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$, and ${{\mathit \nu}}{{\overline{\mathit \nu}}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ Channels with ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
KHACHATRYAN 2017AX
PL B773 563 Search for Leptophobic ${{\mathit Z}^{\,'}}$ Bosons Decaying into Four-Lepton Final States in Proton–Proton Collisions at $\sqrt {s }$ = 8 TeV
KHACHATRYAN 2017U
PL B768 137 Search for Heavy Resonances Decaying into a Vector Boson and a Higgs Boson in Final States with Charged Leptons, Neutrinos, and ${\mathit {\mathit b}}$ Quarks
SIRUNYAN 2017T
PRL 119 111802 Search for Low Mass Vector Resonances Decaying to Quark-Antiquark Pairs in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017AK
PL B774 533 Combination of Searches for Heavy Resonances Decaying to ${{\mathit W}}{{\mathit W}}$, ${{\mathit W}}{{\mathit Z}}$, ${{\mathit Z}}{{\mathit Z}}$, ${{\mathit W}}{{\mathit H}}$, and ${{\mathit Z}}{{\mathit H}}$ Boson Pairs in Proton-Proton Collisions at $\sqrt {s }$ = 8 and 13 TeV
SIRUNYAN 2017R
EPJ C77 636 Search for Heavy Resonances that Decay into a Vector Boson and a Higgs Boson in Hadronic Final States at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017Q
JHEP 1707 001 Search for ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances in Highly Boosted Lepton+Jets and Fully Hadronic Final States in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017V
JHEP 1709 053 Search for a Heavy Resonance Decaying to a Top Quark and a Vector-Like Top Quark at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017A
JHEP 1703 162 Search for Massive Resonances Decaying into ${{\mathit W}}{{\mathit W}}$, ${{\mathit W}}{{\mathit Z}}$ or ${{\mathit Z}}{{\mathit Z}}$ Bosons in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
SIRUNYAN 2017AP
JHEP 1710 180 Search for Associated Production of Dark Matter with a Higgs Boson Decaying to ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ or ${{\mathit \gamma}}{{\mathit \gamma}}$ at $\sqrt {s }$ = 13 TeV
AABOUD 2016
PL B759 229 Search for Resonances in the Mass Distribution of Jet Pairs with One or Two Jets Identified as ${\mathit {\mathit b}}$-Jets in Proton-proton Collisions at $\sqrt {s }$ =13 TeV with the ATLAS Detector
EPJ C76 210 Search for New Phenomena in Events with at Least Three Photons Collected in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
PL B754 302 Search for New Phenomena in Dijet Mass and Angular Distributions from ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector
KHACHATRYAN 2016E
PR D93 012001 Search for Resonant ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
KHACHATRYAN 2016AP
JHEP 1602 145 Search for a Massive Resonance Decaying into a Higgs Boson and a ${{\mathit W}}$ or ${{\mathit Z}}$ Boson in Hadronic Final States in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
PR D92 092001 Search for New Light Gauge Bosons in Higgs Boson Decays to Four-Lepton Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector at the LHC
EPJ C75 79 Search for Invisible Particles Produced in Association with Single-Top-Quarks in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
JHEP 1508 148 A Search for ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances using Lepton-plus-Jets Events in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
KHACHATRYAN 2015F
PRL 114 101801 Search for Monotop Signatures in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV
KHACHATRYAN 2015O
PL B748 255 Search for Narrow High-Mass Resonances in Proton$−$Proton Collisions at$\sqrt {s }$ = 8 TeV Decaying to a ${{\mathit Z}}$ and a Higgs Boson
PL B738 428 Search for New Resonances in ${{\mathit W}}{{\mathit \gamma}}$ and ${{\mathit Z}}{{\mathit \gamma}}$ Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
KHACHATRYAN 2014A
JHEP 1408 174 Search for Massive Resonances Decaying into Pairs of Boosted Bosons in Semi-Leptonic Final States at $\sqrt {s }$ = 8 TeV
MARTINEZ 2014
PR D90 015028 Constraints on 3-3-1 Models with Electroweak ${{\mathit Z}}$ Pole Observables and ${{\mathit Z}^{\,'}}$ Search at the LHC
JHEP 1301 116 Search for Resonances Decaying into Top-Quark Pairs using Fully Hadronic Decays in ${{\mathit p}}{{\mathit p}}$ Collisions with ATLAS at $\sqrt {s }$ = 7 TeV
PR D88 012004 A Search for ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances in the Lepton Plus Jets Final State with ATLAS using 4.7 ${\mathrm {fb}}{}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
AALTONEN 2013A
PRL 110 121802 Search for Resonant Top-Antitop Production in the Lepton Plus Jets Decay Mode Using the Full CDF Data Set
CHATRCHYAN 2013AP
PR D87 072002 Search for ${{\mathit Z}^{\,'}}$ Resonances Decaying to ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ in dilepton+jets Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
CHATRCHYAN 2013BM
PRL 111 211804 Searches for New Physics using the ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Invariant Mass Distribution in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV
EPJ C72 2083 A Search for ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances with the ATLAS Detector in 2.05 ${\mathrm {fb}}{}^{-1}$ of proton-proton Collisions at $\sqrt {s }$ = 7 TeV
JHEP 1209 041 A Search for ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances in Lepton+Jets Events with Highly Boosted Top Quarks Collected in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
AALTONEN 2012N
PRL 108 211805 Search for a Heavy Particle Decaying to a Top Quark and a Light Quark in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
AALTONEN 2012AR
PR D86 112002 Search for a Heavy Vector Boson Decaying to Two Gluons in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
ABAZOV 2012R
PR D85 051101 Search for a Narrow ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonance in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
CHATRCHYAN 2012AI
JHEP 1208 110 Search for New Physics in events with Same-Sign Dileptons and ${\mathit {\mathit b}}$-Tagged Jets in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
CHATRCHYAN 2012AQ
JHEP 1209 029 Search for Anomalous ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production in the Highly-Boosted All-Hadronic Final State
CHATRCHYAN 2012BL
JHEP 1212 015 Search for Resonant ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production in Lepton+Jets Events in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV
PR D84 072003 Search for Resonant Production of ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Decaying to Jets in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
AALTONEN 2011AE
PR D84 072004 Search for Resonant Production of ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ pairs in 4.8 fb${}^{-1}$ of Integrated Luminosity of ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
CHATRCHYAN 2011O
JHEP 1108 005 Search for Same-Sign Top-Quark Pair Production at $\sqrt {s }$ = 7 TeV and Limits on Flavour Changing Neutral Currents in the Top Sector
AALTONEN 2008D
PR D77 051102 Limits on the Production of Narrow ${{\mathit t}}{{\overline{\mathit t}}}$ Resonances in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
AALTONEN 2008Y
PRL 100 231801 Search for Resonant ${{\mathit t}}{{\overline{\mathit t}}}$ Production in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
ABAZOV 2008AA
PL B668 98 Search for ${{\mathit t}}{{\overline{\mathit t}}}$ Resonances in the Lepton Plus Jets Final State in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
ABAZOV 2004A
PRL 92 221801 Search for Narrow ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Resonances in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at = 1.8 TeV
BARGER 2003B
PR D67 075009 Primordial Nucleosynthesis Constraints on ${{\mathit Z}^{\,'}}$ Properties
CHO 2000
MPL A15 311 Looking for ${{\mathit Z}^{\,'}}$ Bosons in Supersymmetric E(6) Models Through Electroweak Precision Data
CHO 1998
EPJ C5 155 Constraints on Four Fermi Contact Interactions from Low-Energy Electroweak Experiments
ABE 1997G
PR D55 5263 Search for New Particles Decaying to Dijets at CDF
AABOUD 2016AG
EPJ C76 670 Measurement of the ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ Dijet Cross Section in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
| 2019-03-25T09:54:21 |
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|
https://www.usgs.gov/media/images/k-lauea-volcano-halemaumau-crater-cracks
|
# Kīlauea Volcano — Halemaumau Crater Cracks
Due to a lapse in appropriations, the majority of USGS websites may not be up to date and may not reflect current conditions. Websites displaying real-time data, such as Earthquake and Water and information needed for public health and safety will be updated with limited support. Additionally, USGS will not be able to respond to inquiries until appropriations are enacted. For more information, please see www.doi.gov/shutdown
## Detailed Description
A closer view of the cracks cutting across the parking lot for the former Halema‘uma‘u visitor overlook (closed since 2008, when an active vent opened within the crater). Additional photos—ground views—of the parking lot cracks were posted on June 7 and 11.
## Details
Image Dimensions: 5184 x 3888
Date Taken:
Location Taken: Kīlauea Volcano, HI, US
| 2019-01-23T19:32:02 |
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|
https://par.nsf.gov/biblio/10206909-regularized-momentum-iterative-hessian-sketch-large-scale-linear-system-equations
|
Regularized Momentum Iterative Hessian Sketch for Large Scale Linear System of Equations
In this article, Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale linear Least Squares (LS) problems, are proposed and analyzed in detail. The proposed techniques are obtained by incorporating the Heavy Ball Acceleration into the Iterative Hessian Sketch algorithm and they provide significant improvements over the randomized preconditioning techniques. Through the error analyses of the M-IHS variants, lower bounds on the sketch size for various randomized distributions to converge at a pre-determined rate with a constant probability are established. The bounds present the best results in the current literature for obtaining a solution approximation and they suggest that the sketch size can be chosen proportional to the statistical dimension of the regularized problem regardless of the size of the coefficient matrix. The statistical dimension is always smaller than the rank and it gets smaller as the regularization parameter increases. By using approximate solvers along with the iterations, the M-IHS variants are capable of avoiding all matrix decompositions and inversions, which is one of the main advantages over the alternative solvers such as the Blendenpik and the LSRN. Similar to the Chebyshev Semi-iterations, the M-IHS variants do not use any inner products and eliminate the corresponding more »
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10206909
Journal Name:
International Conferene on Acoustics, Speech and Signal Processing
| 2023-03-20T18:48:02 |
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https://pdglive.lbl.gov/DataBlock.action?node=B098W&home=BXXX025
|
# ${{\boldsymbol \Sigma}{(1910)}}$ WIDTH INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 150\text{ to }300\text{ }(\approx220) }$ OUR ESTIMATE
$224$ $\pm25$
2019
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$170$ $\pm25$
1978 B
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit N}}{{\overline{\mathit K}}^{*}}$
$300$ $\pm80$
1977
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
$150$ $\pm75$
1975
IPWA ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}}$
$160$ ${}^{+70}_{-40}$
1975
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$
$330$ $\pm80$
1974
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Sigma}}{{\mathit \pi}}$
$60$ $\pm20$
1974 B
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}^{0}}$
$70$ ${}^{+30}_{-20}$
1974 C
DPWA ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Delta}{(1232)}}{{\overline{\mathit K}}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$157$ or $159$ 1
1977
DPWA ${{\overline{\mathit K}}}{{\mathit N}}$ multichannel
1 The two MARTIN 1977 values are from a T-matrix pole and from a Breit-Wigner fit.
References:
SARANTSEV 2019
EPJ A55 180 Hyperon II: Properties of excited hyperons
CAMERON 1978B
NP B146 327 Partial Wave Analysis of ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\overline{\mathit K}}^{*}}{{\mathit N}}$ between 1830 and 2170 MeV $\mathit E_{{\mathrm {cm}}}$ Including New Data below 1960 MeV
GOPAL 1977
NP B119 362 Partial Wave Analyses of ${{\overline{\mathit K}}}{{\mathit N}}$ Two Body Reactions between 1480 and 2170 MeV
MARTIN 1977
NP B127 349 ${{\overline{\mathit K}}}{{\mathit N}}$ Interactions in the Resonance Region. 3. Resonance Spectra
BAILLON 1975
NP B94 39 Energy Independent Partial Wave Analysis of ${{\overline{\mathit K}}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}}$ between 1540 and 2150 MeV
VANHORN 1975
NP B87 145 Energy Dependent Partial Wave Analysis of ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \pi}^{0}}$ between 1540 and 2215 MeV
KANE 1974
LBL-2452 LBL-2452
LITCHFIELD 1974B
NP B74 19 Partial Wave Analysis of the Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}{(1520)}}{{\mathit \pi}}$ in the Energy Region $1915 - 2170$ MeV
LITCHFIELD 1974C
NP B74 39 Partial Wave Analysis of the Reaction ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\overline{\mathit K}}}{{\mathit \Delta}{(1232)}}$ in the Energy Region $1915 - 2170$ MeV
| 2020-10-25T10:47:50 |
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https://par.nsf.gov/biblio/10336781-mosdef-survey-dependence-uv-sfr-ratios-sfr-size
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The MOSDEF survey: the dependence of H α-to-UV SFR ratios on SFR and size at z ∼ 2
ABSTRACT We perform an aperture-matched analysis of dust-corrected H α and UV star formation rates (SFRs) using 303 star-forming galaxies with spectroscopic redshifts 1.36 < zspec < 2.66 from the MOSFIRE Deep Evolution Field survey. By combining H α and H β emission line measurements with multiwaveband resolved Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey/3D-HST imaging, we directly compare dust-corrected H α and UV SFRs, inferred assuming a fixed attenuation curve shape and constant SFHs, within the spectroscopic aperture. Previous studies have found that H α and UV SFRs inferred with these assumptions generally agree for typical star-forming galaxies, but become increasingly discrepant for galaxies with higher SFRs (≳100 M⊙ yr−1), with H α-to-UV SFR ratios being larger for these galaxies. Our analysis shows that this trend persists even after carefully accounting for the apertures over which H α and UV-based SFRs (and the nebular and stellar continuum reddening) are derived. Furthermore, our results imply that H α SFRs may be higher in the centres of large galaxies (i.e. where there is coverage by the spectroscopic aperture) compared to their outskirts, which could be indicative of inside-out galaxy growth. Overall, we suggest that the persistent difference between nebular and stellar continuum reddening and high H α-to-UV SFR ratios at the centres more »
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NSF-PAR ID:
10336781
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Monthly Notices of the Royal Astronomical Society
Volume:
508
Issue:
1
Page Range or eLocation-ID:
1431 to 1445
ISSN:
0035-8711
National Science Foundation
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| 2023-02-06T16:01:57 |
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https://www.usgs.gov/center-news/volcano-watch-pu-u-extinct-or-waiting
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Volcano Watch — Pu‘u ‘Ō‘ō: extinct or waiting?
Release Date:
Puu Oo was alive and well on Wednesday, January 29, with acrid fumes drifting across the landscape and an active pond glowing red at night. The next morning, it seemed to be a dead, gutted hulk. So goes the cinder-and-spatter cone whose name has become synonymous with 14 years of eruption at Kīlauea Volcano. What happened?
Puu Oo was alive and well on Wednesday, January 29, with acrid fumes drifting across the landscape and an active pond glowing red at night. The next morning, it seemed to be a dead, gutted hulk. So goes the cinder-and-spatter cone whose name has become synonymous with 14 years of eruption at Kīlauea Volcano. What happened?
On Wednesday, January 29, at 6:41 p.m., the east rift zone eruption changed its style. Magma from Kīlauea Volcano's main conduit was cut off from Puu Oo. As a consequence, over the next 24 hours the flow of lavathrough shallow tubes dwindled to a dribble and the coastal steam plume dissipated.
These changes resulted from the opening of new cracks underground along the east zift zone near Napau Crater, 6 km (4 mi) closer to Kīlauea's summit. As the cracks opened, magma rapidly drained from the magma reservoir that lies deep beneath the summit caldera and upper east rift zone. The lava pond at Puu Oo also drained, apparently into subterranean cracks nearby. The force that drove the drainback was gravity, but gravity needed an opportunity. Its chance came when a part of the Earth's crust became so weakened that it could fracture and open with only the slightest change in magmatic pressure.
With its lava pond and plumbing system drained, Puu Oo lost much of its underlying support. First the crater floor collapsed. Then large slices of crater wall slid downward, filling the empty pipe with debris. The collapses generated clouds of red rock dust that roiled upward 300 m (1,000 ft) or so and drifted downwind to be deposited as a thin blanket across an area reaching 5 km (3 mi) southwestward from the cone.
In the aftermath, the cone gained a new shape. Its crater walls are nearly vertical, and the crater floor, once only 60 m (200 ft) below the rim, is now about 250 m deep (820 ft). Collapse wasn't limited to the crater, however. The "Great Pit," a once-circular crater on the cone's northwest flank, has widened into a great gash. The gash enlarged abruptly as magma drained away from Puu Oo. Before dawn on Thursday, January 30, the gash had consumed blocks from the summit and lowered the cone by as much as 45 m (150 ft).
Today, Puu Oo steams slightly as rain and fog dissipate the heat that remains. The crater is deeply notched where it connects to the gash. The cone is notably lower when seen from many viewpoints in the Puna district. The glow is extinguished.
Is Puu Oo extinct or merely waiting? Only time will tell. Magma supplied from deep in the Earth is slowly refilling the summit magma chamber that lies beneath Kīlauea caldera, 16 km distant (10 mi). Once that space has been reoccupied, magma is likely to seek other pathways to the surface. Scientists at HVO are uncertain what to expect. But given the lengthy eruptive history from the Puu Oo vent area, we wouldn't be surprised by a reappearance of lava in the crater pond or from a new vent nearby. Puu Oo is one site where money might be made by those who bet on future eruptions.
| 2019-12-15T13:52:14 |
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https://iopscience.iop.org/article/10.1088/1361-6463/ab0ab7
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Paper The following article is Open access
# Full-wave modelling of terahertz frequency plasmons in two-dimensional electron systems
, , , , , , and
Published 14 March 2019 © 2019 IOP Publishing Ltd
, , Citation A Dawood et al 2019 J. Phys. D: Appl. Phys. 52 215101
0022-3727/52/21/215101
## Abstract
While models of terahertz frequency plasmons in 2D electron systems are usually developed by reducing the number of spatial dimensions, fully 3D models may be needed for the design and analysis of realistic structures. Using full-wave electromagnetic simulations, we have analysed the plasmons and magnetoplasmons observed in two recent experiments. Here, we demonstrate agreement between the theoretical and the experimental results, and discuss further device characteristics such as plasmon transmission, reflection, absorption, and field distributions. We then compare the 3D full-wave simulations with a 2D model. Finally, we discuss approaches for increasing signal transmission and reducing reflection, with direct relevance for improving future experiments.
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## 1. Introduction
Two-dimensional electron systems (2DESs) are capable of supporting plasmons, which are slow electromagnetic waves caused by collective electron motion. In 2DESs formed in III-V semiconductor heterostructures, plasmon frequencies typically lie in the microwave to terahertz frequency ranges. Terahertz plasmons are particularly attractive as they could be exploited in a range of practical devices, and notably, emitters and detectors.
Ever since the pioneering works of Dyakonov and Shur [1, 2], one of the most commonly studied geometry for terahertz plasmon emitters and detectors is that based on the field-effect transistor (figure 1(a)). A 2DES is terminated by two ohmic contacts, which allows application and detection of a dc voltage as well as the coupling-in and -out of terahertz waves [37]. Above the 2DES is a gate, which controls the electron density in the 2DES, and is frequently used for coupling into the free-space radiation. Variations of this basic structure have also been made, such double-grating-gate, meander-gate, and comb-gate devices [812].
Theoretical studies of such devices have been made predominantly with two-dimensional (2D) models [1, 1424], in which the devices are assumed to be infinitely long in the y -direction (figure 1(a)). Three-dimensional (3D) models, however, may be needed to describe realistic devices, especially when agreement with experiment is sought. As an example, figures 1(b) and (c) show, respectively, a micrograph and a sketch of the experimental device used by Wu et al [7, 13]. Several features that cannot be taken into account by a 2D model stand out. First, the width of the 2DES (25 $\mu$m in the y -direction) is smaller than its length (73 $\mu$m in the x-direction). Second, the 2DES is connected at both ends to a coplanar waveguide. Third, the 2DES has a non-rectangular shape with four short stubs.
Full-wave numerical simulations are a natural choice for analysis of such structures. In this paper, we will:
• 1.
compare a full-wave 3D electromagnetic model with the experiments by Wu et al [7] on plasmon- (section 3) and magneto-plasmon transmission (section 4);
• 2.
analyse the experimental devices beyond the available experimental data (section 3);
• 3.
compare the 3D model with a 2D model based on mode-matching (sections 3 and 4);
• 4.
design and model a device geometry with improved characteristics (section 5).
## 2. Device structure and modelling considerations
Wu et al [7] formed a 2DES in a GaAs/AlGaAs heterostructure grown by molecular beam epitaxy. The depth of the 2DES was h = 75 nm. We have found that slight variations of the permittivity due to the detailed layer structure had little effect on the simulation results, and we assumed that the substrate material was GaAs, with a relative permittivity of 12.4, see figure 1. The dc electron density in the 2DES was $n_{2D}=6.5\times10^{11}$ cm−2. The electron scattering time was determined from dc conductivity measurements to be $\tau=33$ ps. The device was formed by etching a rectangular mesa (see table 1 for dimensions). The mesa had four stubs connected to four metal lines, two of which were shorted to form a gate above the 2DES. We have found that including these features into simulations was needed for full agreement with experiments. Two ohmic contacts were formed at both ends of the mesa. A metallic gate was then deposited. An LT-GaAs layer grown on the same substrate allowed Wu et al to form two photoconductive switches, one at each side of the device (not shown in figure 1), which were used for excitation and detection of picosecond-duration current pulses. The pulses were both delivered to and extracted from the 2DES using two coplanar waveguides, the centre conductors of which were connected to the ohmic contacts (see figure 1). A negative voltage applied to the gate relative to an ohmic contact depleted the 2DES underneath the gate, and the relationship between the gate voltage and the electron density was found to be
where $V_g$ is in volts, n2D is in cm−2, $\alpha_1=5.3813\times10^{15}$ cm−2, $\alpha_2=2.601$, and $\gamma=0.2295$. In the experiments, the voltage typically varied between −0.4 and −2.4 V. Further details about the devices, experimental arrangement, and measurements can be found in [7, 13].
Table 1. Dimensions used in simulations (see figure 1).
2DES length, l 73 $\mu$m
2DES width/width of centre conductor, w 73 $\mu$m
2DES depth/mesa height, h 75 nm
Length of first ungated 2DES section, ls1 48.9 $\mu$m
Length of second ungated 2DES section, ls2 19.7 $\mu$m
Gate width/length of gated 2DES section, lg 4.4 $\mu$m
Stub width, ws 24 $\mu$m
Stub length, ls 11 $\mu$m
Width of 2DES side extension, we 14 $\mu$m
Separation between left contact and stub, lt1 16 $\mu$m
Separation between stubs, lt2 21.9 $\mu$m
Separation between right contact and stub, lt3 13.1 $\mu$m
Coplanar waveguide gap, wg 20 $\mu$m
Width of waveguide ground plane, wcw 15 $\mu$m
Substrate thickness, t 50 $\mu$m
Depth of ohmic contact, tc 1250 nm
Length of ohmic contact, lc 12.5 $\mu$m
When describing semiconductor plasmons theoretically, one has to choose how to model electron dynamics (both in the 2DES and at the junctions) and the electromagnetic fields. This paper uses the standard model based on Euler's hydrodynamic equation of motion [1] that, in the absence of static magnetic fields, leads to an isotropic ac 2D Drude conductivity of the form
where e is the electron charge, m* is the effective electron mass and $\omega$ is the angular frequency. The paper also uses the full system of Maxwell's equations, which then dictate the boundary conditions.
We solved the equations using the rf module of the COMSOL Multiphysics® numerical package. The 2DES was modelled using a surface current density defined by (2). The ohmic contacts, the coplanar waveguides, and the gate were modelled as perfect conductors. The whole structure was enclosed in a bounding box with dimensions 223 $\mu$m $\times\,100$ $\mu$m $\times\,60$ $\mu$m. Two sides of the bounding box were used as excitation and detection ports, while the other sides were perfect electric conductors. The two outer (ground) conductors of the coplanar waveguides were connected to a perfectly conducting box along the length of the structure. This ensured that the even coplanar mode was excited, which was found to couple well to plasmons in the experiments (rather than the slot-line mode, which did not) [7]. The waveguide sections to the both sides of the 2DES were 75 $\mu$m long.
## 3. Comparison with experiments: gate-modulation signals
In the experiments, picosecond current pulses from a photoconductive switch were injected into one of the coplanar waveguides. Figure 2 shows the time-domain profile and the power spectrum of the input pulses. They then passed through the 2DES and coupled into the waveguide at the other side of the 2DES. This waveguide was connected to a second switch, where the transmitted pulses were detected. To increase the signal-to-noise ratio of the detected signals, a gate-modulation technique was used. The gate voltage was periodically modulated by a weak signal around a stationary value, which allowed Wu et al to employ lock-in detection. As a result, the detected signals were proportional to the absolute value of the derivative of the transmission coefficient with respect to the gate voltage. Figure 3(a) shows, as a colour plot, the experimentally measured signals in the frequency range 100–400 GHz and for a range of gate voltages. The lines superimposed on the plot show the positions of the resonances calculated by a 2D mode-matching technique [24] as reported previously in [25].
In the simulations, we excite the even mode in the left coplanar waveguide at a single frequency, calculate its transmission to the waveguide on the opposite side, and then repeat the calculation for a range of frequencies and electron densities. The simulations are performed in the frequency domains with the same excitation power at every frequency. The experiments, however, excitation power effectively varied with frequency owing to the limited bandwidth of the photoconductive switch used for signal excitation (see figure 2). To allow direct comparison between the simulations and the experiments, we therefore scale the simulation results assuming an exponential decay of the excitation power with the frequency. We then calculate, using (1), the derivative of the transmission with the gate voltage.
Figure 3(b) shows the simulated gate-modulation signals for $\tau=33$ ps, the value obtained from dc conductivity measurements. The simulated resonances are clearly narrower than the experimentally observed ones, indicating higher losses in the experiment than predicted from the dc value of the scattering time. Such reduction of the quality factors of the experimental terahertz resonances was observed in a number of other experiments that used different 2DES geometries and excitation and detection techniques. For example, Popov et al [26] found that the value of $\tau$ required to fit the absorption measurements in a grid-gated field-effect transistor was lower than the value predicted from the dc conductivity by roughly an order of magnitude. El Fatimy et al [27] reported that a plasmon resonance in a high-electron-mobility transistors measured experimentally had a quality factor of three, lower than the value of 13 expected from the measurements of the dc mobility. A number of explanations of the apparent reduction of the value of $\tau$ were proposed, such as different relaxation mechanisms involved at dc and the THz frequencies [28], ballistic transport and viscosity [27], leakage of gated plasmons into ungated regions, and oblique modes [29]. No explanation appears so far to have gained wide acceptance. We note, however, that our 3D model directly takes into account the interaction of plasmons in the gated and ungated regions as well as the plasmon field distribution both along and across the device, and so it is unlikely that plasmon leakage and oblique modes are responsible for the difference between figures 3(a) and (b). Following other authors, we have, therefore, decided to treat τ as a phenomenological parameter, and have repeated the calculations for a number of lower values of $\tau$. We found the best agreement between the experiments and the simulations for $\tau = 7$ ps, as shown in figure 3(c).
Three strong features can be seen both in the theoretical and experimental plots. The first one starts at around 100 GHz for the lowest value of the gate voltage. The second starts at 200 GHz. The third lies around 300 GHz, and is strong only for low values of the gate voltage. The experimental features are shifted to the higher frequencies compared to the theoretical ones. A possible reason for the shift is the approximate nature of (1) that was used to estimate the gate voltage from the theoretical values of the concentration. In the experiments, the gate voltage was measured directly. The maximum amplitudes of the experimental and modelled signals decrease with increasing frequency and with decreasing gate voltage. There are, however, differences in the relationships between the amplitudes of the peaks between the experiment and the simulations. It may be due to the complex shape of the excitation spectrum, which was not fully reproduced in the simulations.
## 4. Beyond experiment: transmission, reflection, absorption and field profiles
The use of the gate-modulation technique in the experiments was dictated by the need to increase the signal-to-noise ratio and eliminate direct cross-talk between the components on either side of the 2DES. In addition, the picosecond pulses used in the experiments delivered less power at higher frequencies, leading to weaker plasmon excitation.
On the other hand, numerical simulations are free from these constraints, allowing us to analyse the device across a wide parameter space. The colour plot in figure 4(a) shows the simulated transmission (S21) coefficient for $\tau=7$ ps (as before, the dashed lines are the resonances calculated by the 2D model). More resonances can now be seen than in the gate-modulation plot of figure 3(c). This is because the resonances that depend weakly on the gated electron density are no longer suppressed, and the excitation amplitude is kept constant at all frequencies.
Figure 4(b) shows the transmission (S21, black line) at a single value of the gate voltage, $V_g=-2$ V. It also shows the reflection (S11) and the absorption coefficients (blue and red lines), the later calculated as $1-|S_{21}|^2-|S_{11}|^2$. The reflection and absorption of the signal dominate, and the transmitted signal does not exceed −25 dB. The transmission plot shows five resonances at 126, 192, 249, 300, and 358 GHz. To explain their nature, figure 5 shows the longitudinal (x-) component of the electric field, first, as contour plots in the plane of the 2DES (left column) and, second, across the middle of the 2DES (right column).
At the lowest-frequency resonance, only the gated section of the 2DES is excited strongly and evenly across the width of the 2DES (y -direction). It has a single peak along the length (x-direction) of the gated section, which fits roughly a half of a plasmon wavelength. This is, therefore, the first longitudinal gated-section resonance, and its position agrees well with the 2D calculation shown by dashed lines in figure 4(a).
At the next resonance, the longer (left-hand side) ungated section of the 2DES is excited in addition to the gated section. In the ungated section, the field maximum and minimum are reached at the opposite ends, and the field has a distorted half-wavelength pattern. The excitation amplitudes are higher at the 2DES edges, suggesting excitation of edge plasmons. The field in the gated portion of the 2DES is non-uniform across the width of the 2DES, showing both longitudinal and transverse plasmon excitation. The resonance position agrees well with the 2D calculation (see dashed line in figure 4(a)) which suggests that this resonance corresponds to the first-order longitudinal resonance of the long section of the 2DES.
The third resonance, at 249 GHz, shows strong excitation of both the gated and the long ungated sections, each fitting around one plasmon wavelength. Even though the edges of the ungated section are also excited, it appears to be a predominantly a longitudinal resonance that is a result of an interaction between the gated and the long ungated sections. The nature of the resonance is confirmed, again, by the good agreement with the 2D model seen from figure 4(a).
The fields of the final two resonances are strongly non-uniform across the width of the different 2DES sections. The gated 2DES shows both longitudinal and transverse plasmon excitation, with multiple field minima and maxima along the x- and y -directions. The long and short ungated 2DESs are excited strongly at the edges. As can be expected, the 2D calculations fail to predict the position of these two resonances.
## 5. Comparison with experiments: magnetoplasmons
Using the same device and technique, Wu et al detected magnetoplasmon resonances in a magnetic field applied perpendicular to the plane of the 2DES [13]. The colour plot in figure 6(a) shows the measured gate-modulation signals. The gate voltage was −2 V, and the magnetic field varied between 0 and 0.4 T. The dashed black lines show the position of 2D resonances found by the mode-matching technique. The red line is the cyclotron resonance.
In the presence of a static magnetic field B0 pointing in the positive z-direction, the 2D Drude conductivity becomes anisotropic. The current density, J, can then be expressed as
where
and $\omega_{\rm c} = eB_0/m^*$ is the cyclotron frequency.
Figure 6(b) shows the gate-modulation signals simulated using (3)–(5). The qualitative agreement with the experiment is good for the features lying below 300 GHz. As before, the difference in the relative strength of the measured and simulated resonances can be attributed to the spectrum of the excitation pulses. Some of the resonances modelled above 300 GHz do not show in the measurements, possibly because the excitation signals were weak. To the right of the cyclotron line, the simulations predict a strong signal but only a faint feature can be seen in the measurements.
While figures 6(a) and (b) show the gate-modulation signals, figure 7 shows the simulated true transmission coefficient. The maximum transmission does not exceed −25 dB for all values of the magnetic field. The behaviour of the lowest resonance with the magnetic field agrees well with the prediction of the 2D model. The next two resonances agree well with the 2D model at low magnetic field. They do not follow, however, the parabolic behaviour of the 2D curves, and it leads to a discrepancy between the 3D simulation and the 2D model at higher fields. As can be expected from the results for zero magnetic field discussed above, the full-wave 3D simulations and the 2D model disagree in their predictions of the resonance positions. We attribute this disagreement to the excitation of edge plasmons and of transverse plasmons (with non-trivial component of the wavenumber in the y -direction), both of which are not taken into account by the 2D model.
## 6. Improving device performance
The simulated transmission for the experimental device did not exceed 25 dB, as shown in figures 4 and 7. Such a low value is due to two factors: high plasmon absorption in the 2DES, and high signal reflection between the 2DES and the coplanar waveguides (figure 4(b)). The plasmon loss could be reduced by shortening the length of the 2DES. The high reflection can be attributed to the dissimilar field distributions in the 2DES and the coplanar waveguides. The even mode supported by the coplanar waveguide is a quasi-TEM mode whose field is concentrated in the gaps between the centre and the ground conductors [30]. On the other hand, plasmons are TM modes whose field is concentrated around the 2DES. Rearranging the waveguide electrodes to create high electric field along the 2DES is, therefore, likely to improve the coupling. It can be done by connecting the gate and the ground electrodes via a capacitor (which will decouple the gate and the ground at dc allowing voltages to be applied to the gate).
A possible device is shown schematically in figure 8. The length of the gated section here is 4 $\mu$m, and the ungated sections have been both reduced to 2 $\mu$m. The device width remains 30 $\mu$m. Figure 9(a) shows the simulated transmission for a range of voltages, and figure 9(b) shows the transmission, reflection and absorption for the gate voltage of −2 V. Improvements can be seen upon comparing figure 9 for the new device to figure 4 for the original experimental device. The maximum transmission has increased by over 20 dB for the peak at 165 GHz. The reflection has also decreased by a similar amount. The observed three resonances correspond to the excitation of the longitudinal gated plasmons, as can be seen from the field distributions shown in figure 10 for $V_g = -2$ V at 164, 272 and 393 GHz. The peak frequencies are close to the three lowest resonant frequencies of longitudinal gated plasmons (144, 279, and 407 GHz) assuming an integer number of plasmon wavelengths in the gated section.
## 7. Conclusions
A full-wave 3D model of the experimental devices showed agreement with the experimental results obtained by gate-modulation, both for plasmons and magnetoplasmons. We used this model to analyse device characteristics that could not be directly measured in experiments, such as the true transmission, reflection, and absorption, as well as to study the field distributions at the transmission maxima. We also compared the predictions of the fully 3D model with a 2D model based on modal expansions. While the frequencies of some plasmon resonances could be explained equally well by both approaches, the full-wave simulations showed additional resonances that we attribute to plasmon excitation across and at the edges of the device. Our calculations predict the transmission in the experimental devices to be below −25 dB, in part due to the high plasmon absorption, and in part due to high reflection. By reducing the length of the ungated sections and modifying the coupling geometry between the 2DES and the coplanar waveguides, we presented a device in which the maximum transmission increased by 20 dB.
## Acknowledgments
The authors are grateful to Dr S Zonetti and Mr S Siaber for helpful discussions. C D W, E H L, L L, A G D, J E C, and OS acknowledge the financial support by the EPSRC (Grant Nos. EP/R004994/1, EP/R00501X, and EP/P021859/1). E H L acknowledges support of the Royal Society and Wolfson Foundation. Data underlying this article can be accessed at https://doi.org/10.5281/zenodo.2586740, and used under the Creative Commons Attribution licence.
| 2021-07-27T12:12:34 |
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|
https://par.nsf.gov/biblio/10093502-multitribe-evolutionary-search-stable-cupdag-nanoparticles-using-neural-network-models
|
Multitribe evolutionary search for stable Cu–Pd–Ag nanoparticles using neural network models
We present an approach based on two bio-inspired algorithms to accelerate the identification of nanoparticle ground states. We show that a symbiotic co-evolution of nanoclusters across a range of sizes improves the search efficiency considerably, while a neural network constructed with a recently introduced stratified training scheme delivers an accurate description of interactions in multielement systems. The method's performance has been examined in extensive searches for stable elemental (30–80 atoms), binary (50, 55, and 80 atoms), and ternary (50, 55, and 80 atoms) Cu–Pd–Ag clusters. The best candidate structures identified with the neural network model have consistently lower energy at the density functional theory level compared with those found with traditional interatomic potentials.
Authors:
; ; ;
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Publication Date:
NSF-PAR ID:
10093502
Journal Name:
Physical Chemistry Chemical Physics
Volume:
21
Issue:
17
Page Range or eLocation-ID:
8729 to 8742
ISSN:
1463-9076
3. ABSTRACT We present the results of a proof-of-concept experiment that demonstrates that deep learning can successfully be used for production-scale classification of compact star clusters detected in Hubble Space Telescope(HST) ultraviolet-optical imaging of nearby spiral galaxies ($D\lesssim 20\, \textrm{Mpc}$) in the Physics at High Angular Resolution in Nearby GalaxieS (PHANGS)–HST survey. Given the relatively small nature of existing, human-labelled star cluster samples, we transfer the knowledge of state-of-the-art neural network models for real-object recognition to classify star clusters candidates into four morphological classes. We perform a series of experiments to determine the dependence of classification performance on neural network architecture (ResNet18 and VGG19-BN), training data sets curated by either a single expert or three astronomers, and the size of the images used for training. We find that the overall classification accuracies are not significantly affected by these choices. The networks are used to classify star cluster candidates in the PHANGS–HST galaxy NGC 1559, which was not included in the training samples. The resulting prediction accuracies are 70 per cent, 40 per cent, 40–50 per cent, and 50–70 per cent for class 1, 2, 3 star clusters, and class 4 non-clusters, respectively. This performance is competitive with consistency achieved in previously published human and automated quantitative classification of starmore »
| 2023-03-31T14:06:53 |
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|
https://par.nsf.gov/biblio/10336841-chemical-abundance-scaling-relations-multiple-elements-star-forming-galaxies
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Chemical Abundance Scaling Relations for Multiple Elements in z ≃ 2–3 Star-forming Galaxies
Abstract The chemical abundance patterns of gas and stars in galaxies are powerful probes of galaxies’ star formation histories and the astrophysics of galaxy assembly but are challenging to measure with confidence in distant galaxies. In this paper, we report the first measurements of the correlation between stellar mass ( M * ) and multiple tracers of chemical enrichment (including O, N, and Fe) in individual z ∼ 2–3 galaxies, using a sample of 195 star-forming galaxies from the Keck Baryonic Structure Survey. The galaxies’ chemical abundances are inferred using photoionization models capable of reconciling high-redshift galaxies’ observed extreme rest-UV and rest-optical spectroscopic properties. We find that the M * –O/H relation for our sample is relatively shallow, with moderately large scatter, and is offset ∼0.35 dex higher than the corresponding M * –Fe/H relation. The two relations have very similar slopes, indicating a high level of α -enhancement—O/Fe ≈ 2.2 × (O/Fe) ⊙ —across two decades in M * . The M * –N/H relation has the steepest slope and largest intrinsic scatter, which likely results from the fact that many z ∼ 2 galaxies are observed near or past the transition from “primary” to “secondary” N production, and more »
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; ; ;
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NSF-PAR ID:
10336841
Journal Name:
The Astrophysical Journal
Volume:
925
Issue:
2
Page Range or eLocation-ID:
116
ISSN:
0004-637X
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 »
3. ABSTRACT We analyse the rest-optical emission-line ratios of z ∼ 1.5 galaxies drawn from the Multi-Object Spectrometer for Infra-Red Exploration Deep Evolution Field (MOSDEF) survey. Using composite spectra, we investigate the mass–metallicity relation (MZR) at z ∼ 1.5 and measure its evolution to z = 0. When using gas-phase metallicities based on the N2 line ratio, we find that the MZR evolution from z ∼ 1.5 to z = 0 depends on stellar mass, evolving by $\Delta \rm log(\rm O/H) \sim 0.25$ dex at M*< $10^{9.75}\, \mathrm{M}_{\odot }$ down to $\Delta \rm log(\rm O/H) \sim 0.05$ at M* ≳ $10^{10.5}\, \mathrm{M}_{\odot }$. In contrast, the O3N2-based MZR shows a constant offset of $\Delta \rm log(\rm O/H) \sim 0.30$ across all masses, consistent with previous MOSDEF results based on independent metallicity indicators, and suggesting that O3N2 provides a more robust metallicity calibration for our z ∼ 1.5 sample. We investigated the secondary dependence of the MZR on star formation rate (SFR) by measuring correlated scatter about the mean M*-specific SFR and M*−$\log (\rm O3N2)$ relations. We find an anticorrelation between $\log (\rm O/H)$ and sSFR offsets, indicating the presence of a M*−SFR−Z relation, though with limited significance. Additionally, we find that our z ∼ 1.5more »
5. Abstract We present a joint analysis of rest-UV and rest-optical spectra obtained using Keck/LRIS and Keck/MOSFIRE for a sample of 62 star-forming galaxies at z ∼ 2.3. We divide our sample into two bins based on their location in the [OIII]5007/Hβ vs. [NII]6584/Hα BPT diagram, and perform the first differential study of the rest-UV properties of massive ionizing stars as a function of rest-optical emission-line ratios. Fitting BPASS stellar population synthesis models, including nebular continuum emission, to our rest-UV composite spectra, we find that high-redshift galaxies offset towards higher [OIII]λ5007/Hβ and [NII]λ6584/Hα have younger ages ($\log (\textrm {~Age/yr})=7.20^{+0.57}_{-0.20}$) and lower stellar metallicities ($Z_*=0.0010^{+0.0011}_{-0.0003}$) resulting in a harder ionizing spectrum, compared to the galaxies in our sample that lie on the local BPT star-forming sequence ($\log (\textrm {Age/yr})=8.57^{+0.88}_{-0.84}$, $Z_*=0.0019^{+0.0006}_{-0.0006}$). Additionally, we find that the offset galaxies have an ionization parameter of $\log (U)=-3.04^{+0.06}_{-0.11}$ and nebular metallicity of ($12+\log (\textrm {~O/H})=8.40^{+0.06}_{-0.07}$), and the non-offset galaxies have an ionization parameter of $\log (U)=-3.11^{+0.08}_{-0.08}$ and nebular metallicity of $12+\log (\textrm {~O/H})=8.30^{+0.05}_{-0.06}$. The stellar and nebular metallicities derived for our sample imply that the galaxies offset from the local BPT relation are more α-enhanced ($7.28^{+2.52}_{-2.82}\textrm {~O/Fe}_{\odot }$) compared to those consistent with the local sequencemore »
| 2023-02-08T11:55:51 |
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|
https://par.nsf.gov/biblio/10366717-characterising-orbit-circumstellar-environment-high-mass-binary-mwc
|
This content will become publicly available on September 1, 2023
Characterising the orbit and circumstellar environment of the high-mass binary MWC 166 A
Context. Stellar evolution models are highly dependent on accurate mass estimates, especially for highly massive stars in the early stages of stellar evolution. The most direct method for obtaining model-independent stellar masses is derivation from the orbit of close binaries. Aims. Our aim was to derive the first astrometric plus radial velocity orbit solution for the single-lined spectroscopic binary star MWC 166 A, based on near-infrared interferometry over multiple epochs and ∼100 archival radial velocity measurements, and to derive fundamental stellar parameters from this orbit. A supplementary aim was to model the circumstellar activity in the system from K band spectral lines. Methods. The data used include interferometric observations from the VLTI instruments GRAVITY and PIONIER, as well as the MIRC-X instrument at the CHARA Array. We geometrically modelled the dust continuum to derive relative astrometry at 13 epochs, determine the orbital elements, and constrain individual stellar parameters at five different age estimates. We used the continuum models as a base to examine differential phases, visibilities, and closure phases over the Br γ and He I emission lines in order to characterise the nature of the circumstellar emission. Results. Our orbit solution suggests a period of P = 367.7 ± 0.1 d, approximately more »
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10366717
Journal Name:
Astronomy & Astrophysics
Volume:
665
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A146
ISSN:
0004-6361
Accretion signatures from bound brown dwarf and protoplanetary companions provide evidence for ongoing planet formation, and accreting substellar objects have enabled new avenues to study the astrophysical mechanisms controlling the formation and accretion processes. Delorme 1 (AB)b, a ∼30–45 Myr circumbinary planetary-mass companion, was recently discovered to exhibit strong Hαemission. This suggests ongoing accretion from a circumplanetary disk, somewhat surprising given canonical gas disk dispersal timescales of 5–10 Myr. Here, we present the first NIR detection of accretion from the companion in Paβ, Paγ, and Brγemission lines from SOAR/TripleSpec 4.1, confirming and further informing its accreting nature. The companion shows strong line emission, withLline≈ 1–6 × 10−8Lacross lines and epochs, while the binary host system shows no NIR hydrogen line emission (Lline< 0.32–11 × 10−7L). Observed NIR hydrogen line ratios are more consistent with a planetary accretion shock than with local line excitation models commonly used to interpret stellar magnetospheric accretion. Using planetary accretion shock models, we derive mass accretion rate estimates of$Ṁpla∼3$–4 × 10−8MJyr−1, somewhat higher than expected under the standard star formation paradigm. Delorme 1 (AB)b’s high accretion rate is perhaps more consistent with formation via disk fragmentation. Delorme 1 (AB)b is themore »
| 2023-02-03T03:47:54 |
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https://pbn.nauka.gov.pl/pbn-report-web/pages/publication/id/58b4ddacd5de30c391042337
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Monte Carlo Simulation of the Torsional Strength due to Concrete Compression of Reinforced Concrete Element
PBN-AR
Instytucja
Wydział Budownictwa, Mechaniki i Petrochemii (Politechnika Warszawska)
##### Informacje podstawowe
Główny język publikacji
en
Czasopismo
Applied Mechanics and Materials
ISSN
1662-7482
EISSN
Wydawca
Scientific.Net
DOI
Rok publikacji
2015
Numer zeszytu
Strony od-do
27-34
Numer tomu
797
Identyfikator DOI
Liczba arkuszy
0.5
##### Autorzy
(liczba autorów: 2)
##### Słowa kluczowe
pl
-
en
Concrete Compression, Monte Carlo Simulation, Reinforced Concrete, Reliability, Torsion
##### Streszczenia
Język
pl
Treść
-
Język
en
Treść
The aim of the work was to assess the safety margin of reinforced concrete element of rectangular cross-sections subjected to torsion. In the performed analyses two models of torsional resistance based on concrete compressive strength was taken into account. Assessment was performed with use of Monte Carlo method. Utilized models of shear resistance were taken from formerly used Polish standards: PN-84/B-03264, PN-B-03264:2002 and the actual Polish standard EN-1992-1-1:2004. From the same standards necessary assumptions related with the models were taken. The safety margin and influence of the differences in assumptions on the obtained results were analyzed. The selected models was also evaluated in terms of their “sensitivity” to changes of basic parameters of distribution functions of selected random variables. Results showed that average torsional resistance differs of about 50% times depending of assumed model. The reliability level, measured with the partial reliability exponent ΔR, differs of 10% if different models are concerned but the differences are much higher (up to 5 times, when the standard deviation of concrete compressive strength distribution changes).
##### Inne
System-identifier
| 2020-04-08T12:43:33 |
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https://par.nsf.gov/biblio/10313103-laminar-flame-speeds-degenerate-oxygenneon-mixtures
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Laminar Flame Speeds in Degenerate Oxygen–Neon Mixtures
Abstract The collapse of degenerate oxygen–neon cores (i.e., electron-capture supernovae or accretion-induced collapse) proceeds through a phase in which a deflagration wave (“flame”) forms at or near the center and propagates through the star. In models, the assumed speed of this flame influences whether this process leads to an explosion or to the formation of a neutron star. We calculate the laminar flame speeds in degenerate oxygen–neon mixtures with compositions motivated by detailed stellar evolution models. These mixtures include trace amounts of carbon and have a lower electron fraction than those considered in previous work. We find that trace carbon has little effect on the flame speeds, but that material with electron fraction has laminar flame speeds that are times faster than those at . We provide tabulated flame speeds and a corresponding fitting function so that the impact of this difference can be assessed via full star hydrodynamical simulations of the collapse process.
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; ;
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NSF-PAR ID:
10313103
Journal Name:
The Astrophysical Journal
Volume:
891
Issue:
1
ISSN:
0004-637X
Many core-collapse supernovae (SNe) with hydrogen-poor and low-mass ejecta, such as ultra-stripped SNe and type Ibn SNe, are observed to interact with dense circumstellar material (CSM). These events likely arise from the core collapse of helium stars that have been heavily stripped by a binary companion and have ejected significant mass during the last weeks to years of their lives. In helium star models run to days before core collapse we identify a range of helium core masses ≈2.5–3Mwhose envelopes expand substantially due to the helium shell burning while the core undergoes neon and oxygen burning. When modeled in binary systems, the rapid expansion of these helium stars induces extremely high rates of late-stage mass transfer ($Ṁ≳10−2M⊙yr−1$) beginning weeks to decades before core collapse. We consider two scenarios for producing CSM in these systems: either mass transfer remains stable and mass loss is driven from the system in the vicinity of the accreting companion, or mass transfer becomes unstable and causes a common envelope event (CEE) through which the helium envelope is unbound. The ensuing CSM properties are consistent with the CSM masses (∼10−2–1M) and radii (∼1013–1016cm) inferred for ultra-stripped SNe and severalmore »
Most neutron stars (NSs) and black holes (BHs) are believed to be the final remnants in the evolution of massive stars. In this study, we propose a new formation channel for the formation of BHs and peculiar NSs [specifically, magnetars and Thorne–Żytkow objects (T$\dot{\rm Z}$Os)], which we refer to as the core-merger-induced collapse (CMIC) model. This model involves the merger during a common-envelope phase of an oxygen/neon/magnesium composition white dwarf and the core of a hydrogen-rich or helium-rich non-degenerate star, leading to the creation of peculiar new types of objects. The results of binary population synthesis simulations show that the CMIC channel could make important contributions to the populations of (millisecond) pulsars, T$\dot{\rm Z}$Os, magnetars, and BHs. The possibility of superluminous supernovae powered by T$\dot{\rm Z}$Os, magnetars, and BHs formed through the CMIC model is also being investigated. Magnetars with immediate matter surroundings formed after the CMIC might be good sources for fast radio bursts.
| 2022-12-02T17:00:45 |
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http://pdglive.lbl.gov/Particle.action?node=M129&home=sumtabM
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STRANGE MESONS($\boldsymbol S$ = $\pm1$, $\boldsymbol C$ = $\boldsymbol B$ = 0) ${{\mathit K}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit K}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit s}}}$, ${{\overline{\mathit K}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit s}}$, ${{\mathit K}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit K}^{*}}$'s INSPIRE search
# ${{\boldsymbol K}{(3100)}}$ $I^G(J^{PC})$ = $?^?(?^{? ?})$
Narrow peak observed in several ( ${{\mathit \Lambda}}{{\overline{\mathit p}}}$ + pions) and ( ${{\overline{\mathit \Lambda}}}{{\mathit p}}$ + pions) states in ${{\mathit \Sigma}^{-}}{}^{}\mathrm {Be}$ reactions by BOURQUIN 1986 and in ${{\mathit n}}{{\mathit p}}$ and ${{\mathit n}}$ A reactions by ALEEV 1993 . Not seen by BOEHNLEIN 1991 . If due to strong decays, this state has exotic quantum numbers ($\mathit B=0,\mathit Q=+1,\mathit S=-1$ for ${{\mathit \Lambda}}{{\overline{\mathit p}}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ and $\mathit I$ ${}\geq{}$ 3$/$2 for ${{\mathit \Lambda}}{{\overline{\mathit p}}}{{\mathit \pi}^{-}}$ ). Needs confirmation.
${{\boldsymbol K}{(3100)}}$ MASS
Mass $\mathit m$ $\approx3100$ MeV
3-BODY DECAYS $3054 \pm11$ MeV
4-BODY DECAYS $3059 \pm11$ MeV
5-BODY DECAYS
${{\boldsymbol K}{(3100)}}$ WIDTH
3-BODY DECAYS
4-BODY DECAYS
5-BODY DECAYS
| 2019-08-24T16:09:31 |
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|
http://dergipark.gov.tr/beuscitech/issue/32937/357531
|
Yıl 2017, Cilt 7, Sayı 2, Sayfalar 145 - 153 2017-12-26
| | | |
Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks
Davut ARI [1] , Musa ÇIBUK [2] , Fikri AĞGÜN [3]
116 143
In multi-hop Wireless Sensor Networks (WSN), sensor nodes which cannot communicate directly with the Coordinator Node(CN) can communicate with CN thanks to the other joined sensor nodes. The multi-hop WSN structure is preferred for large-scale WSNs and that consist of multiple sensor and CN.As in the networks sensor node count increase, hop count increase as well. Because of this, end-to-end delay increases. Unless it is taken prevention, end-to-end delays reach a level that negatively effects on network performance in multi-hop WSN.
In this study, for multi-hop WSNs, it is aimed to design a new a relay-priority mechanism which will reduce the end-to-end delay. This is a method that will reach the CN with a minimum hop count while joining the node. Thanks to the minimum hop, end-to-end delay is reduced. Performance analysis of this study was done in Riverbed (OPNET) Modeler simulation environment.
Wireless Sensor Networks, Relay-Priority Mechanism, MAC Protocol, End-to-End Delay
• Li, L. E., And Sinha, P., 2003. Throughput and energy efficiency in topology-controlled multi-hop wireless sensor networks. In Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications (pp. 132-140). ACM.
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• Vergados, D. D., Vergados, D. J., Sgora, A., Vouyioukas, D., And Anagnostopoulos, I., 2007. Enhancing fairness in wireless multi-hop networks. In Proceedings of the 3rd international conference on Mobile multimedia communications (p. 37). ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering).
• Duan, C., Shi, F., Ding, X., Xiao, X., And Duan, P., 2011. A novel TDMA and multi-hop MAC protocol in cluster-based wireless sensor networks. In Industrial Electronics and Applications (ICIEA), 2011 6th IEEE Conference on (pp. 805-808). IEEE.
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• Zhao, J. J., And Sun, X., 2008. MAC protocol based on T-MAC multi-hop reservation for short-latency wireless sensor network. In Communication Technology, 2008. ICCT 2008. 11th IEEE International Conference on (pp. 114-117). IEEE.
• Nguyen, K., And Ji, Y., 2010. AM-MAC: an energy efficient, Adaptive Multi-hop MAC protocol for sensor networks. In Proceedings of the 6th International Wireless Communications and Mobile Computing Conference (pp. 432-436). ACM.
• Lee, J. W., And Cho, H. S., 2014. Cascading multi-hop reservation and transmission in underwater acoustic sensor networks. Sensors, 14(10), 18390-18409.
• Furuta, T., Sasaki, M., Ishizaki, F., Ukai, T., Miyazawa, H., And Koo, W., 2010. New formulation for scheduling problem in multi-hop wireless sensor networks. In Proceedings of the 6th International Wireless Communications and Mobile Computing Conference (pp. 73-78). ACM.
• Dou, F., And Peng, Z., 2015. On-demand Pipelined MAC for Multi-hop Underwater Wireless Sensor Networks. In Proceedings of the 10th International Conference on Underwater Networks & Systems (p. 26). ACM.
• Chang, X., 1999. Network simulations with OPNET. In Simulation Conference Proceedings, 1999 Winter (Vol. 1, pp. 307-314). IEEE
Konular Fen Articles Yazar: Davut ARI (Sorumlu Yazar)Ülke: Turkey Yazar: Musa ÇIBUK (Sorumlu Yazar)Ülke: Turkey Yazar: Fikri AĞGÜNÜlke: Turkey
Bibtex @araştırma makalesi { beuscitech357531, journal = {Bitlis Eren University Journal of Science and Technology}, issn = {}, eissn = {2146-7706}, address = {Bitlis Eren Üniversitesi}, year = {2017}, volume = {7}, pages = {145 - 153}, doi = {10.17678/beuscitech.357531}, title = {Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks}, key = {cite}, author = {ÇIBUK, Musa and AĞGÜN, Fikri and ARI, Davut} } APA ARI, D , ÇIBUK, M , AĞGÜN, F . (2017). Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks. Bitlis Eren University Journal of Science and Technology, 7 (2), 145-153. DOI: 10.17678/beuscitech.357531 MLA ARI, D , ÇIBUK, M , AĞGÜN, F . "Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks". Bitlis Eren University Journal of Science and Technology 7 (2017): 145-153 Chicago ARI, D , ÇIBUK, M , AĞGÜN, F . "Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks". Bitlis Eren University Journal of Science and Technology 7 (2017): 145-153 RIS TY - JOUR T1 - Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks AU - Davut ARI , Musa ÇIBUK , Fikri AĞGÜN Y1 - 2017 PY - 2017 N1 - doi: 10.17678/beuscitech.357531 DO - 10.17678/beuscitech.357531 T2 - Bitlis Eren University Journal of Science and Technology JF - Journal JO - JOR SP - 145 EP - 153 VL - 7 IS - 2 SN - -2146-7706 M3 - doi: 10.17678/beuscitech.357531 UR - http://dx.doi.org/10.17678/beuscitech.357531 Y2 - 2017 ER - EndNote %0 Bitlis Eren University Journal of Science and Technology Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks %A Davut ARI , Musa ÇIBUK , Fikri AĞGÜN %T Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks %D 2017 %J Bitlis Eren University Journal of Science and Technology %P -2146-7706 %V 7 %N 2 %R doi: 10.17678/beuscitech.357531 %U 10.17678/beuscitech.357531 ISNAD ARI, Davut , ÇIBUK, Musa , AĞGÜN, Fikri . "Effect of Relay-Priority Mechanism on Multi-hop Wireless Sensor Networks". Bitlis Eren University Journal of Science and Technology 7 / 2 (Aralık 2017): 145-153. http://dx.doi.org/10.17678/beuscitech.357531
| 2019-01-20T16:51:32 |
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|
https://par.nsf.gov/biblio/10364290-jcmt-bistro-survey-multiwavelength-polarimetry-bright-regions-ngc-far-infrared-submillimetre-range-pol-hawc+
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The JCMT BISTRO Survey: multiwavelength polarimetry of bright regions in NGC 2071 in the far-infrared/submillimetre range, with POL-2 and HAWC+
ABSTRACT
Polarized dust emission is a key tracer in the study of interstellar medium and of star formation. The observed polarization, however, is a product of magnetic field structure, dust grain properties, and grain alignment efficiency, as well as their variations in the line of sight, making it difficult to interpret polarization unambiguously. The comparison of polarimetry at multiple wavelengths is a possible way of mitigating this problem. We use data from HAWC+ /SOFIA and from SCUBA-2/POL-2 (from the BISTRO survey) to analyse the NGC 2071 molecular cloud at 154, 214, and 850 $\mu$m. The polarization angle changes significantly with wavelength over part of NGC 2071, suggesting a change in magnetic field morphology on the line of sight as each wavelength best traces different dust populations. Other possible explanations are the existence of more than one polarization mechanism in the cloud or scattering from very large grains. The observed change of polarization fraction with wavelength, and the 214-to-154 $\mu$m polarization ratio in particular, are difficult to reproduce with current dust models under the assumption of uniform alignment efficiency. We also show that the standard procedure of using monochromatic intensity as a proxy for column density may produce spurious results at HAWC+wavelengths. more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Publication Date:
NSF-PAR ID:
10364290
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
512
Issue:
2
Page Range or eLocation-ID:
p. 1985-2002
ISSN:
0035-8711
Publisher:
Oxford University Press
Continuum polarization over the UV-to-microwave range is due to dichroic extinction (or emission) by asymmetric, aligned dust grains. Scattering can also be an important source of polarization, especially at short wavelengths. Because of both grain alignment and scattering physics, the wavelength dependence of the polarization, generally, traces the size of the aligned grains. Similarly because of the differing wavelength dependencies of dichroic extinction and scattering polarization, the two can generally be reliably separated. Ultraviolet (UV) polarimetry therefore provides a unique probe of the smallest dust grains (diameter$< 0.09~\upmu \text{m}$$<0.09\phantom{\rule{0ex}{0ex}}\text{μm}$), their mineralogy and interaction with the environment. However, the current observational status of interstellar UV polarization is very poor with less than 30 lines of sight probed. With the modern, quantitative and well-tested, theory of interstellar grain alignment now available, we have the opportunity to advance the understanding of the interstellar medium (ISM) by executing a systematic study of the UV polarization in the ISM of the Milky Way and near-by galaxies. The Polstar mission will provide the sensitivity and observing time needed to carry out such a program (probing hundreds of stars in the Milky Way and dozens of stars in the LMC/SMC), addressing questions of dust composition asmore »
We present the stability analysis of two regions, OMC-3 and OMC-4, in the massive and long molecular cloud complex of Orion A. We obtained 214 $\mu$m HAWC + /SOFIA polarization data, and we make use of archival data for the column density and C18O (1–0) emission line. We find clear depolarization in both observed regions and that the polarization fraction is anticorrelated with the column density and the polarization-angle dispersion function. We find that the filamentary cloud and dense clumps in OMC-3 are magnetically supercritical and strongly subvirial. This region should be in the gravitational collapse phase and is consistent with many young stellar objects (YSOs) forming in the region. Our histogram of relative orientation (HRO) analysis shows that the magnetic field is dynamically sub-dominant in the dense gas structures of OMC-3. We present the first polarization map of OMC-4. We find that the observed region is generally magnetically subcritical except for an elongated dense core, which could be a result of projection effect of a filamentary structure aligned close to the line of sight. The relative large velocity dispersion and the unusual positive shape parameters at high column densities in the HROs analysis suggest that our viewing angle may be closemore »
| 2023-02-06T12:22:29 |
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https://tjyj.stats.gov.cn/CN/Y2018/V35/I10/28
|
• •
### 基于半参数混频误差修正模型的中国CPI预测研究
• 出版日期:2018-10-25 发布日期:2018-10-22
### Research on China CPI forecast Based on Semi-parametric ECM-MIDAS Model
Lu Wanbo & Yang Dong
• Online:2018-10-25 Published:2018-10-22
Abstract: Considering that the macroeconomic variables have obvious nonlinear characteristics, a semi-parametric ECM-MIDAS model is constructed for the data which exist cointegration relation in the MIDAS model. By using the GLR test, the problem of the consistency test of the functional form of the parametric regression model is solved. The simulation result shows that SEMI-ECM-MIDAS has better forecast performance when the error term is nonlinear. In application part, China's stock market weekly data, China’s monetary market and crude oil market international data are used to make short-term forecast of China's CPI. A comprehensive comparison was made among the models. The results show that the error correction term has obvious nonlinear characteristics. The semi-parametric ECM-MIDAS model proposed in this paper always has the best prediction accuracy. In addition, the prediction results are not affected by the choice of dynamic mixed frequency cointegration relationship.
| 2023-03-25T14:20:06 |
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|
http://gams.cam.nist.gov/12.20
|
# §12.20 Approximations
Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions $U\left(a,b,x\right)$ and $M\left(a,b,x\right)$13.2(i)) whose regions of validity include intervals with endpoints $x=\infty$ and $x=0$, respectively. As special cases of these results a Chebyshev-series expansion for $U\left(a,x\right)$ valid when $\lambda\leq x<\infty$ follows from (12.7.14), and Chebyshev-series expansions for $U\left(a,x\right)$ and $V\left(a,x\right)$ valid when $0\leq x\leq\lambda$ follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). Here $\lambda$ denotes an arbitrary positive constant.
| 2017-11-23T01:58:30 |
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|
https://atap.gov.au/tools-techniques/cost-benefit-analysis/appendix-a-benefit-where-the-related-market-is-a-congested-road-technical-proof.aspx
|
# Appendix A Benefit where the related market is a congested road - technical proof
This appendix provides a technical proof of the alternative measure of benefit on related infrastructure referred to in footnote in section 7.2.
The exact benefit area is negative the gap between the marginal social cost (MSC) and average perceived cost (APC) curves between Q1 and Q2,
$\text{Benefit}={\int }_{{Q}_{1}}^{{Q}_{2}}\left(\text{APC}-\text{MSC}\right)dQ$ ,
which is consistent with the formula in the text of section 7.2 except for replacing average social cost (assumed constant in the formula in section 7.2) with marginal social cost. (See Harberger 1972, pp. 262-3)
$\text{Benefit}={\int }_{{Q}_{1}}^{{Q}_{2}}\left(\text{APC}–\text{ASC}\right)dQ+{\int }_{{Q}_{1}}^{{Q}_{2}}\text{ASC}dQ-{\int }_{{Q}_{1}}^{{Q}_{2}}\frac{d\text{TSC}}{dQ}dQ$
where TSC is total social cost.
Since $\text{TSC}=\text{ASC}×Q$ , the total cost terms, can be written as ${-\text{ASC}}_{2}{Q}_{2}+{\text{ASC}}_{1}{Q}_{1}$ .
The term ${\int }_{{Q}_{1}}^{{Q}_{2}}\text{ASC}dQ$ is the area under the average cost curve between Q1 and Q2. It can be approximated by $\left({\text{ASC}}_{2}+{\text{ASC}}_{1}\right)\left({Q}_{2}-{Q}_{1}\right)/2$ .
The last term, the resource correction, can be approximated as $\left(\text{APC}–\text{ASC}\right)\left({Q}_{2}-{Q}_{1}\right)$ where $\text{APC}=\left({\text{APC}}_{1}+{\text{APC}}_{2}\right)/2$ and $\text{ASC}=\left({\text{ASC}}_{1}+{\text{ASC}}_{2}\right)/2$ .
Combining the terms:
$\text{Benefit}=\left({\text{ASC}}_{2}+{\text{ASC}}_{1}\right)\left({Q}_{2}-{Q}_{1}\right)/2+{-\text{ASC}}_{2}{Q}_{2}+{\text{ASC}}_{1}{Q}_{1}+\left(\text{APC}–\text{ASC}\right)\left({Q}_{2}-{Q}_{1}\right)$
which simplifies to .
Assuming ${\text{ASC}}_{1}-{\text{ASC}}_{2}={\text{APC}}_{1}-{\text{APC}}_{2}$ , the benefit can be expressed as:
(Neuberger 1971, p. 56 has this formula without the resource correction.)
Note that if the cost change is positive, as would occur on an upstream or downstream road where the demand curve shifts rightward, ${\text{APC}}_{1}-{\text{APC}}_{2}<0$, the formula will give a negative result, reflecting the increase in net social cost due to greater congestion.
| 2019-03-25T10:46:42 |
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|
https://www.itl.nist.gov/div898/handbook/pmd/section3/pmd32.htm
|
4. Process Modeling
4.3. Data Collection for Process Modeling
## Why is experimental design important for process modeling?
Output from Process Model is Fitted Mathematical Function The output from process modeling is a fitted mathematical function with estimated coefficients. For example, in modeling resistivity, $$y$$, as a function of dopant density, $$x$$, an analyst may suggest the function $$y = \beta_{0} + \beta_{1}x + \beta_{11}x^{2} + \varepsilon$$ in which the coefficients to be estimated are $$\beta_0$$, $$\beta_1$$, and $$\beta_{11}$$. Even for a given functional form, there is an infinite number of potential coefficient values that potentially may be used. Each of these coefficient values will in turn yield predicted values.
What are Good Coefficient Values? Poor values of the coefficients are those for which the resulting predicted values are considerably different from the observed raw data $$y$$. Good values of the coefficients are those for which the resulting predicted values are close to the observed raw data $$y$$. The best values of the coefficients are those for which the resulting predicted values are close to the observed raw data $$y$$, and the statistical uncertainty connected with each coefficient is small.
There are two considerations that are useful for the generation of "best" coefficients:
1. Least squares criterion
2. Design of experiment principles
Least Squares Criterion For a given data set (e.g., 10 $$(x,y)$$ pairs), the most common procedure for obtaining the coefficients for $$y = f(x;\vec{\beta} + \varepsilon)$$ is the least squares estimation criterion. This criterion yields coefficients with predicted values that are closest to the raw data $$y$$ in the sense that the sum of the squared differences between the raw data and the predicted values is as small as possible.
The overwhelming majority of regression programs today use the least squares criterion for estimating the model coefficients. Least squares estimates are popular because
1. the estimators are statistically optimal (BLUEs: Best Linear Unbiased Estimators);
2. the estimation algorithm is mathematically tractable, in closed form, and therefore easily programmable.
How then can this be improved? For a given set of $$x$$ values it cannot be; but frequently the choice of the $$x$$ values is under our control. If we can select the $$x$$ values, the coefficients will have less variability than if the $$x$$ are not controlled.
Design of Experiment Principles As to what values should be used for the $$x$$'s, we look to established experimental design principles for guidance.
Principle 1: Minimize Coefficient Estimation Variation The first principle of experimental design is to control the values within the $$x$$ vector such that after the $$y$$ data are collected, the subsequent model coefficients are as good, in the sense of having the smallest variation, as possible.
The key underlying point with respect to design of experiments and process modeling is that even though (for simple $$(x,y)$$ fitting, for example) the least squares criterion may yield optimal (minimal variation) estimators for a given distribution of $$x$$ values, some distributions of data in the $$x$$ vector may yield better (smaller variation) coefficient estimates than other $$x$$ vectors. If the analyst can specify the values in the $$x$$ vector, then he or she may be able to drastically change and reduce the noisiness of the subsequent least squares coefficient estimates.
Five Designs To see the effect of experimental design on process modeling, consider the following simplest case of fitting a line: $$y = \beta_{0} + \beta_{1}x + \varepsilon$$ Suppose the analyst can afford 10 observations (that is, 10 $$(x,y)$$ pairs) for the purpose of determining optimal (that is, minimal variation) estimators of $$\beta_0$$ and $$\beta_1$$. What 10 $$x$$ values should be used for the purpose of collecting the corresponding 10 $$y$$ values? Colloquially, where should the 10 $$x$$ values be sprinkled along the horizontal axis so as to minimize the variation of the least squares estimated coefficients for $$\beta_0$$ and $$\beta_1$$? Should the 10 $$x$$ values be:
1. ten equi-spaced values across the range of interest?
2. five replicated equi-spaced values across the range of interest?
3. five values at the minimum of the $$x$$ range and five values at the maximum of the $$x$$ range?
4. one value at the minimum, eight values at the mid-range, and one value at the maximum?
5. four values at the minimum, two values at mid-range, and four values at the maximum?
or (in terms of "quality" of the resulting estimates for $$\beta_0$$ and $$\beta_1$$) perhaps it doesn't make any difference?
For each of the above five experimental designs, there will of course be $$y$$ data collected, followed by the generation of least squares estimates for $$\beta_0$$ and $$\beta_1$$, and so each design will in turn yield a fitted line.
Are the Fitted Lines Better for Some Designs? But are the fitted lines, i.e., the fitted process models, better for some designs than for others? Are the coefficient estimator variances smaller for some designs than for others? For given estimates, are the resulting predicted values better (that is, closer to the observed $$y$$ values) than for other designs? The answer to all of the above is YES. It DOES make a difference.
The most popular answer to the above question about which design to use for linear modeling is design #1 with ten equi-spaced points. It can be shown, however, that the variance of the estimated slope parameter depends on the design according to the relationship $$\mbox{Var}(\hat{\beta}_1) \propto \frac{1}{\sum_{i=1}^{n}(x_i-\bar{x})}$$ Therefore to obtain minimum variance estimators, one maximizes the denominator on the right. To maximize the denominator, it is (for an arbitrarily fixed $$\bar{x}$$), best to position the $$x$$'s as far away from $$\bar{x}$$ as possible. This is done by positioning half of the $$x$$'s at the lower extreme and the other half at the upper extreme. This is design #3 above, and this "dumbbell" design (half low and half high) is in fact the best possible design for fitting a line. Upon reflection, this is intuitively arrived at by the adage that "2 points define a line", and so it makes the most sense to determine those 2 points as far apart as possible (at the extremes) and as well as possible (having half the data at each extreme). Hence the design of experiment solution to model processing when the model is a line is the "dumbbell" design--half the $$x$$'s at each extreme.
What is the Worst Design? What is the worst design in the above case? Of the five designs, the worst design is the one that has maximum variation. In the mathematical expression above, it is the one that minimizes the denominator, and so this is design #4 above, for which almost all of the data are located at the mid-range. Clearly the estimated line in this case is going to chase the solitary point at each end and so the resulting linear fit is intuitively inferior.
Designs 1, 2, and 5 What about the other 3 designs? Designs 1, 2, and 5 are useful only for the case when we think the model may be linear, but we are not sure, and so we allow additional points that permit fitting a line if appropriate, but build into the design the "capacity" to fit beyond a line (e.g., quadratic, cubic, etc.) if necessary. In this regard, the ordering of the designs would be
• design 5 (if our worst-case model is quadratic),
• design 2 (if our worst-case model is quartic)
• design 1 (if our worst-case model is quintic and beyond)
| 2018-05-27T09:37:38 |
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|
https://pumas.nasa.gov/examples/dollar-or-cent
|
Sorry, you need to enable JavaScript to visit this website.
# Dollar$or Cent$?
It is common in the real world to see mathematical examples where the cents sign was used when the dollar sign was supposed to be used. Converting and comparing decimals and fractions can help clear up this misconception. Two real coupons clipped from the Sunday paper coupon section are included in this activity.
Author(s):
Jackie Vogel
Date Accepted: 2006-07-14 Grade Group: Upper Elementary (3-5) Benchmarks: Keywords: dollars cents shopping coupons pricing units Microsoft Word: PDF Document:
| 2021-09-18T20:08:46 |
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|
https://pos.sissa.it/398/249/
|
Volume 398 - The European Physical Society Conference on High Energy Physics (EPS-HEP2021) - T04: Neutrino Physics
Testing the neutrino mass generation mechanism at the future colliders
A. Das
Full text: pdf
Pre-published on: March 07, 2022
Published on: May 12, 2022
Abstract
The generation of the neutrino mass is an essential observation from the neutrino oscillation experiments. This indicates a major revision of the Standard Model which initiated with the massless neutrinos. A possible interesting scenario is the seesaw mechanism where SM gauge singlet Right Handed Neutrinos are introduced. Another interesting aspect is the extension of the SM with SU$(2)_{\rm L}$ triplet fermions. Alternatively a general U$(1)$ extension of the SM is also an interesting idea which involves three generations of the SM singlet RHNs to generate the tiny neutrino mass through the seesaw mechanism. Additionally such models can contain a $Z^\prime$ boson which could be tested at the colliders through the pair production of the RHNs.
DOI: https://doi.org/10.22323/1.398.0249
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
| 2022-08-15T07:14:55 |
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|
https://lammps.sandia.gov/doc/fix_orient.html
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# fix orient/bcc command
fix ID group-ID orient/fcc nstats dir alat dE cutlo cuthi file0 file1
fix ID group-ID orient/bcc nstats dir alat dE cutlo cuthi file0 file1
• ID, group-ID are documented in fix command
• nstats = print stats every this many steps, 0 = never
• dir = 0/1 for which crystal is used as reference
• alat = fcc/bcc cubic lattice constant (distance units)
• dE = energy added to each atom (energy units)
• cutlo,cuthi = values between 0.0 and 1.0, cutlo < cuthi
• file0,file1 = files that specify orientation of each grain
## Examples
fix gb all orient/fcc 0 1 4.032008 0.001 0.25 0.75 xi.vec chi.vec
fix gb all orient/bcc 0 1 2.882 0.001 0.25 0.75 ngb.left ngb.right
## Description
The fix applies an orientation-dependent force to atoms near a planar grain boundary which can be used to induce grain boundary migration (in the direction perpendicular to the grain boundary plane). The motivation and explanation of this force and its application are described in (Janssens). The adaptation to bcc crystals is described in (Wicaksono1). The computed force is only applied to atoms in the fix group.
The basic idea is that atoms in one grain (on one side of the boundary) have a potential energy dE added to them. Atoms in the other grain have 0.0 potential energy added. Atoms near the boundary (whose neighbor environment is intermediate between the two grain orientations) have an energy between 0.0 and dE added. This creates an effective driving force to reduce the potential energy of atoms near the boundary by pushing them towards one of the grain orientations. For dir = 1 and dE > 0, the boundary will thus move so that the grain described by file0 grows and the grain described by file1 shrinks. Thus this fix is designed for simulations of two-grain systems, either with one grain boundary and free surfaces parallel to the boundary, or a system with periodic boundary conditions and two equal and opposite grain boundaries. In either case, the entire system can displace during the simulation, and such motion should be accounted for in measuring the grain boundary velocity.
The potential energy added to atom I is given by these formulas
which are fully explained in (Janssens). For fcc crystals this order parameter Xi for atom I in equation (1) is a sum over the 12 nearest neighbors of atom I. For bcc crystals it is the corresponding sum of the 8 nearest neighbors. Rj is the vector from atom I to its neighbor J, and RIj is a vector in the reference (perfect) crystal. That is, if dir = 0/1, then RIj is a vector to an atom coord from file 0/1. Equation (2) gives the expected value of the order parameter XiIJ in the other grain. Hi and lo cutoffs are defined in equations (3) and (4), using the input parameters cutlo and cuthi as thresholds to avoid adding grain boundary energy when the deviation in the order parameter from 0 or 1 is small (e.g. due to thermal fluctuations in a perfect crystal). The added potential energy Ui for atom I is given in equation (6) where it is interpolated between 0 and dE using the two threshold Xi values and the Wi value of equation (5).
The derivative of this energy expression gives the force on each atom which thus depends on the orientation of its neighbors relative to the 2 grain orientations. Only atoms near the grain boundary feel a net force which tends to drive them to one of the two grain orientations.
In equation (1), the reference vector used for each neighbor is the reference vector closest to the actual neighbor position. This means it is possible two different neighbors will use the same reference vector. In such cases, the atom in question is far from a perfect orientation and will likely receive the full dE addition, so the effect of duplicate reference vector usage is small.
The dir parameter determines which grain wants to grow at the expense of the other. A value of 0 means the first grain will shrink; a value of 1 means it will grow. This assumes that dE is positive. The reverse will be true if dE is negative.
The alat parameter is the cubic lattice constant for the fcc or bcc material and is only used to compute a cutoff distance of 1.57 * alat / sqrt(2) for finding the 12 or 8 nearest neighbors of each atom (which should be valid for an fcc or bcc crystal). A longer/shorter cutoff can be imposed by adjusting alat. If a particular atom has less than 12 or 8 neighbors within the cutoff, the order parameter of equation (1) is effectively multiplied by 12 or 8 divided by the actual number of neighbors within the cutoff.
The dE parameter is the maximum amount of additional energy added to each atom in the grain which wants to shrink.
The cutlo and cuthi parameters are used to reduce the force added to bulk atoms in each grain far away from the boundary. An atom in the bulk surrounded by neighbors at the ideal grain orientation would compute an order parameter of 0 or 1 and have no force added. However, thermal vibrations in the solid will cause the order parameters to be greater than 0 or less than 1. The cutoff parameters mask this effect, allowing forces to only be added to atoms with order-parameters between the cutoff values.
File0 and file1 are filenames for the two grains which each contain 6 vectors (6 lines with 3 values per line) which specify the grain orientations. Each vector is a displacement from a central atom (0,0,0) to a nearest neighbor atom in an fcc lattice at the proper orientation. The vector lengths should all be identical since an fcc lattice has a coordination number of 12. Only 6 are listed due to symmetry, so the list must include one from each pair of equal-and-opposite neighbors. A pair of orientation files for a Sigma=5 tilt boundary are shown below. A tutorial that can help for writing the orientation files is given in (Wicaksono2)
Restart, fix_modify, output, run start/stop, minimize info:
The fix_modify energy option is supported by this fix to add the potential energy of atom interactions with the grain boundary driving force to the system’s potential energy as part of thermodynamic output.
The fix_modify respa option is supported by these fixes. This allows to set at which level of the r-RESPA integrator a fix is adding its forces. Default is the outermost level.
This fix calculates a global scalar which can be accessed by various output commands. The scalar is the potential energy change due to this fix. The scalar value calculated by this fix is “extensive”.
This fix also calculates a per-atom array which can be accessed by various output commands. The array stores the order parameter Xi and normalized order parameter (0 to 1) for each atom. The per-atom values can be accessed on any timestep.
No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.
## Restrictions
This fix is part of the MISC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
This fix should only be used with fcc or bcc lattices.
| 2019-09-17T16:29:03 |
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|
https://par.nsf.gov/biblio/10373619-effects-local-stellar-radiation-dust-depletion-non-equilibrium-interstellar-chemistry
|
The effects of local stellar radiation and dust depletion on non-equilibrium interstellar chemistry
ABSTRACT
Interstellar chemistry is important for galaxy formation, as it determines the rate at which gas can cool, and enables us to make predictions for observable spectroscopic lines from ions and molecules. We explore two central aspects of modelling the chemistry of the interstellar medium (ISM): (1) the effects of local stellar radiation, which ionizes and heats the gas, and (2) the depletion of metals on to dust grains, which reduces the abundance of metals in the gas phase. We run high-resolution (400 M⊙ per baryonic particle) simulations of isolated disc galaxies, from dwarfs to Milky Way-mass, using the fire galaxy formation models together with the chimes non-equilibrium chemistry and cooling module. In our fiducial model, we couple the chemistry to the stellar fluxes calculated from star particles using an approximate radiative transfer scheme; and we implement an empirical density-dependent prescription for metal depletion. For comparison, we also run simulations with a spatially uniform radiation field, and without metal depletion. Our fiducial model broadly reproduces observed trends in H i and H2 mass with stellar mass, and in line luminosity versus star formation rate for [C ii]$_{158 \rm {\mu m}}$, [O i]$_{63 \rm {\mu m}}$, [O iii]$_{88 \rm {\mu m}}$, [N ii]$_{122 \rm {\mu m}}$, and more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10373619
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
517
Issue:
2
Page Range or eLocation-ID:
p. 1557-1583
ISSN:
0035-8711
Publisher:
Oxford University Press
1. Abstract We present self-consistent radiation hydrodynamic simulations of hydrogen reionization performed with arepo-rt complemented by a state-of-the-art galaxy formation model. We examine how photoheating feedback, due to reionization, shapes the galaxies properties. Our fiducial model completes reionization by z ≈ 6 and matches observations of the Ly α forest, the cosmic microwave background electron scattering optical depth, the high-redshift ultraviolet (UV) luminosity function, and stellar mass function. Contrary to previous works, photoheating suppresses star formation rates by more than $50{{\ \rm per\ cent}}$ only in haloes less massive than ∼108.4 M⊙ (∼108.8 M⊙) at z = 6 (z = 5), suggesting inefficient photoheating feedback from photons within galaxies. The use of a uniform UV background that heats up the gas at z ≈ 10.7 generates an earlier onset of suppression of star formation compared to our fiducial model. This discrepancy can be mitigated by adopting a UV background model with a more realistic reionization history. In the absence of stellar feedback, photoheating alone is only able to quench haloes less massive than ∼109 M⊙ at z ≳ 5, implying that photoheating feedback is sub-dominant in regulating star formation. In addition, stellar feedback, implemented as a non-local galactic wind scheme in the simulations, weakens the strength of photoheating feedback by reducing the amountmore »
We present new [${\rm O\, {\small III}}$] 88-$\mu \mathrm{{m}}$ observations of five bright z ∼ 7 Lyman-break galaxies spectroscopically confirmed by ALMA through [${\rm C\, {\small II}}$] 158 $\mu \mathrm{{m}}$, unlike recent [${\rm O\, {\small III}}$] detections where Lyman α was used. This nearly doubles the sample of Epoch of Reionization galaxies with robust (5σ) [${\rm C\, {\small II}}$] and [${\rm O\, {\small III}}$] detections. We perform a multiwavelength comparison with new deep HST images of the rest-frame UV, whose compact morphology aligns well with [${\rm O\, {\small III}}$] tracing ionized gas. In contrast, we find more spatially extended [${\rm C\, {\small II}}$] emission likely produced in neutral gas, as indicated by an [${\rm N\, {\small II}}$] 205-$\mu \mathrm{{m}}$ non-detection in one source. We find a correlation between the optical ${[{\rm O\, {\small III}}]}+ {\mathrm{H\,\beta }}$ equivalent width and [${\rm O\, {\small III}}$]/[${\rm C\, {\small II}}$], as seen in local metal-poor dwarf galaxies. cloudy models of a nebula of typical density harbouring a young stellar population with a high-ionization parameter adequately reproduce the observed lines. Surprisingly, however, our models fail to reproduce the strength of [${\rm O\, {\small III}}$] 88-$\mu \mathrm{{m}}$, unless we assume an α/Fe enhancement and near-solar nebular oxygenmore »
3. ABSTRACT We report the detection of the far-infrared (FIR) fine-structure line of singly ionized nitrogen, [N ii] 205 $\mu$m , within the peak epoch of galaxy assembly, from a strongly lensed galaxy, hereafter ‘The Red Radio Ring’; the RRR, at z = 2.55. We combine new observations of the ground-state and mid-J transitions of CO (Jup = 1, 5, 8), and the FIR spectral energy distribution (SED), to explore the multiphase interstellar medium (ISM) properties of the RRR. All line profiles suggest that the H ii regions, traced by [N ii] 205 $\mu$m , and the (diffuse and dense) molecular gas, traced by CO, are cospatial when averaged over kpc-sized regions. Using its mid-IR-to-millimetre (mm) SED, we derive a non-negligible dust attenuation of the [N ii] 205 $\mu$m line emission. Assuming a uniform dust screen approximation results a mean molecular gas column density >1024 cm−2, with a molecular gas-to-dust mass ratio of 100. It is clear that dust attenuation corrections should be accounted for when studying FIR fine-structure lines in such systems. The attenuation corrected ratio of $L_{\rm N\,{\small II}205} / L_{\rm IR(8\!-\!1000\, \mu m)} = 2.7 \times 10^{-4}$ is consistent with the dispersion of local and z > 4 SFGs. We find that the lower limit, [N ii] 205 $\mu$m -based star formation rate (SFR) is less thanmore »
5. ABSTRACT Observations of emission lines in active galactic nuclei (AGNs) often find fast (∼1000 km s−1) outflows extending to kiloparsec scales, seen in ionized, neutral atomic and molecular gas. In this work we present radiative transfer calculations of emission lines in hydrodynamic simulations of AGN outflows driven by a hot wind bubble, including non-equilibrium chemistry, to explore how these lines trace the physical properties of the multiphase outflow. We find that the hot bubble compresses the line-emitting gas, resulting in higher pressures than in the ambient interstellar medium or that would be produced by the AGN radiation pressure. This implies that observed emission line ratios such as [O iv]$_{25 \, \rm {\mu m}}$ / [Ne ii]$_{12 \, \rm {\mu m}}$, [Ne v]$_{14 \, \rm {\mu m}}$ / [Ne ii]$_{12 \, \rm {\mu m}}$, and [N iii]$_{57 \, \rm {\mu m}}$ / [N ii]$_{122 \, \rm {\mu m}}$ constrain the presence of the bubble and hence the outflow driving mechanism. However, the line-emitting gas is under-pressurized compared to the hot bubble itself, and much of the line emission arises from gas that is out of pressure, thermal and/or chemical equilibrium. Our results thus suggest that assuming equilibrium conditions, as commonly done in AGN line emission models, is not justifiedmore »
| 2023-02-08T14:52:48 |
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|
https://www.detailedpedia.com/wiki-1907_Kingston_earthquake
|
# 1907 Kingston earthquake
UTC time 1907-01-14 20:36:00 n/a n/a January 14, 1907 15:30 6.5 Mw 18°12′N 76°42′W / 18.2°N 76.7°W[1] Jamaica yes ~1,000
The 1907 Kingston earthquake which shook the capital of the island of Jamaica with a magnitude of 6.5 on the moment magnitude scale on Monday January 14, at about 3:30 p.m. local time (20:36 UTC), is described by the United States Geological Survey as one of the world's deadliest earthquakes recorded in history.[2] Every building in Kingston was damaged by the earthquake and subsequent fires, which lasted for three hours before any efforts could be made to check them, culminated in the death of about 1,000 people, and caused approximately $30 million in material damage ($823.18 million in 2019).[1] Shortly after, a tsunami was reported on the north coast of Jamaica, with a maximum wave height of about 2 m (6–8 ft).[2]
## Tectonic setting
Jamaica lies within a complex zone of faulting that forms the boundary between the Gonâve Microplate and the Caribbean Plate. To the east of the island the main fault is the Enriquillo–Plantain Garden fault zone while to the west the main structure is the Walton fault zone, both major sinistral (left lateral) strike-slip faults. The transfer of plate boundary displacement between these major fault zones takes place on a series of NW-SE trending faults, such as the Wagwater Belt. The overall tectonic setting is one of transpression at this restraining bend in the plate boundary.[3]
## Damage
The narrow harbour street of the burned district
The greatest damage occurred at Kingston and at Buff Bay and Annotto Bay on the northern coast. Eighty-five percent of buildings in Kingston were destroyed by the shaking, which was followed by a fire that destroyed parts of the business and warehouse districts.[4] The Elder-Dempster passenger steamer Port Kingston, which was under repair in Kingston Harbour at the time, was threatened by fire on the nearby wharf. A rapid temporary repair allowed her to be moved to the safety of an unaffected railway wharf.[5] A suspension bridge was destroyed at Port Maria.[1]
## Characteristics
View of Kingston in 1907 showing damage caused by the earthquake.
### Earthquake
The main shock lasted for about 35 seconds after some minor initial tremors and was accompanied by a roaring sound. The intensity of the shaking grew quickly to a first and strongest climax. The intensity then lessened before again reaching a second weaker climax. There were eighty aftershocks recorded up to 5 February, while the strongest of all was recorded on 23 February.[4]
The epicenter of the earthquake is not well constrained. The only seismograph in Jamaica at the time was put out of action by the earthquake.[1] The rupture may have been on an eastward continuation of the South Coast Fault Zone, within the Wagwater Belt or in the Blue Mountains.[3] The greatest felt intensity was noted for areas built on unconsolidated sands and gravels. To the east of Kingston, along the Palisadoes, there were sandblows and surface faulting associated with areas of subsidence and flooding.[4]
### Tsunami
Northward view of the street in the business section
After the earthquake, tsunami were observed along much of the north coast of Jamaica at Hope Bay, Port Antonio, Orange Bay, Sheerness Bay, Saint Ann's Bay, Buff Bay, Port Maria and Annotto Bay; there were also some reports of waves along the south coast. Seiches were reported in Kingston Harbour. The level of the sea at Annotto Bay was reported to have initially dropped by more than 3 metres (9.8 ft), as the sea withdrew a distance of about 80 m (260 ft), before returning at a height of about 2 metres (6 ft 7 in) above normal, flooding the lower parts of the town.[6]
## Aftermath
The Port Kingston, the only passenger ship in Kingston Harbour, was used as a makeshift hospital, with improvised operating theatres in three parts of the ship and on the adjoining wharf. Kingston Public Hospital, despite loss of its water supply, continued to function throughout the following night.[7] Three United States Navy warships, the battleships USS Indiana and USS Missouri and the destroyer USS Whipple, landed men and supplies on 17 January, although an offer of eight surgeons was rejected by Governor of Jamaica Alexander Swettenham.[5]
## References
1. ^ a b c d NGDC. "Comments for the Significant Earthquake". Retrieved 27 August 2010.
2. ^ a b "Today in Earthquake History". USGS. 14 January 2010. Retrieved 15 January 2010.
3. ^ a b Mann, P.; Demets C. & Wiggins-Grandison M. (2007). "Toward a better understanding of the Late Neogene strike-slip restraining bend in Jamaica: geodetic, geological, and seismic constraints" (PDF). In Cunningham W.D. & Mann P. (ed.). Restraining bends, transpressional deformation and basement controls on development. Geological Society, London, Special Publications. 290. Geological Society, London. pp. 239–253. Retrieved 29 October 2010.
4. ^ a b c Brown, C.W. (May 1907). "The Jamaica earthquake". Popular Science: 385–403. Retrieved 2 November 2010.
5. ^ a b Caine, R.H. (18 January 1907). "Saw Kingston's day of terror" (PDF). The New York Times. Retrieved 3 November 2010.
6. ^ Maul, G.A. (2006). "The Case for an Atlantic tsunami warning system". In Mercado-Irizarry A. & Liu P.L.F. (ed.). Caribbean tsunami hazard. World Scientific. p. 35. ISBN 978-981-256-535-8.
7. ^ Evans, A.J. (9 February 1907). "Experiences during the recent earthquake in Jamaica". British Medical Journal. 1 (2406): 348. doi:10.1136/bmj.1.2406.348. PMC 2356668. PMID 20763070.
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| 2022-01-19T02:36:23 |
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https://www.zbmath.org/authors/?q=ai%3Aluczak.malwina-j
|
zbMATH — the first resource for mathematics
Luczak, Malwina J.
Compute Distance To:
Author ID: luczak.malwina-j Published as: Luczak, M. J.; Luczak, Malwina; Luczak, Malwina J.; Łuczak, Malwina External Links: MGP · Wikidata · ORCID
Documents Indexed: 38 Publications since 2001
all top 5
Co-Authors
3 single-authored 8 Janson, Svante 7 Brightwell, Graham R. 7 McDiarmid, Colin J. H. 6 Barbour, Andrew D. 3 van der Hofstad, Remco W. 2 House, Thomas 2 Norris, James R. 2 Windridge, Peter 2 Xia, Aihua 1 Fairthorne, Marianne 1 Levin, David A. 1 Łuczak, Tomasz 1 Noble, Steven Derek 1 Peres, Yuval 1 Spencer, Joel H. 1 Upfal, Eli 1 Winkler, Peter M.
all top 5
Serials
9 Random Structures & Algorithms 7 The Annals of Applied Probability 4 Probability Theory and Related Fields 3 Journal of Mathematical Biology 3 The Annals of Probability 3 Electronic Journal of Probability 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Journal of the American Statistical Association 1 Combinatorics, Probability and Computing
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Fields
26 Probability theory and stochastic processes (60-XX) 17 Combinatorics (05-XX) 6 Operations research, mathematical programming (90-XX) 6 Biology and other natural sciences (92-XX) 5 Computer science (68-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX)
Citations contained in zbMATH
34 Publications have been cited 272 times in 207 Documents Cited by Year
Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. Zbl 1187.82076
Levin, David A.; Luczak, Malwina J.; Peres, Yuval
2010
A new approach to the giant component problem. Zbl 1177.05110
Janson, Svante; Luczak, Malwina J.
2009
A simple solution to the $$k$$-core problem. Zbl 1113.05091
Janson, Svante; Luczak, Malwina J.
2007
On the maximum queue length in the supermarket model. Zbl 1102.60083
Luczak, Malwina J.; McDiarmid, Colin
2006
Law of large numbers for the SIR epidemic on a random graph with given degrees. Zbl 1328.05170
Janson, Svante; Luczak, Malwina; Windridge, Peter
2014
Asymptotic normality of the $$k$$-core in random graphs. Zbl 1157.05047
Janson, Svante; Luczak, Malwina J.
2008
Building uniformly random subtrees. Zbl 1050.60007
Luczak, Malwina; Winkler, Peter
2004
Random subgraphs of the 2D Hamming graph: The supercritical phase. Zbl 1188.05141
van der Hofstad, Remco; Luczak, Malwina J.
2010
On the power of two choices: balls and bins in continuous time. Zbl 1079.60016
Luczak, Malwina J.; McDiarmid, Colin
2005
Susceptibility in subcritical random graphs. Zbl 1159.81324
Janson, Svante; Luczak, Malwina J.
2008
Asymptotic distributions and chaos for the supermarket model. Zbl 1131.60005
Luczak, Malwina J.; McDiarmid, Colin
2007
Strong approximation for the supermarket model. Zbl 1080.60086
Luczak, Malwina J.; Norris, James
2005
Bisecting sparse random graphs. Zbl 0968.05071
Luczak, Malwina J.; McDiarmid, Colin
2001
Multivariate approximation in total variation. II: Discrete normal approximation. Zbl 1393.62008
Barbour, A. D.; Luczak, M. J.; Xia, A.
2018
Concentration of measure and mixing for Markov chains. Zbl 1357.60075
Luczak, Malwina J.
2008
Laws of large numbers for epidemic models with countably many types. Zbl 1197.92039
Barbour, A. D.; Luczak, M. J.
2008
The phase transition in the cluster-scaled model of a random graph. Zbl 1089.05066
Łuczak, Malwina; Łuczak, Tomasz
2006
On-line routing of random calls in networks. Zbl 1028.90009
Luczak, Malwina J.; McDiarmid, Colin; Upfal, Eli
2003
Concentration for locally acting permutations. Zbl 1025.60003
Luczak, Malwina J.; McDiarmid, Colin
2003
Multivariate approximation in total variation. I: Equilibrium distributions of Markov jump processes. Zbl 1393.62007
Barbour, A. D.; Luczak, M. J.; Xia, A.
2018
The greedy independent set in a random graph with given degrees. Zbl 1386.05175
Brightwell, Graham; Janson, Svante; Luczak, Malwina
2017
Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory. Zbl 1274.60244
Luczak, M. J.; Norris, J. R.
2013
Central limit approximations for Markov population processes with countably many types. Zbl 1284.92079
Barbour, Andrew; Luczak, Malwina
2012
A law of large numbers approximation for Markov population processes with countably many types. Zbl 1395.60083
Barbour, A. D.; Luczak, M. J.
2012
Order-invariant measures on fixed causal sets. Zbl 1260.06003
Brightwell, Graham; Luczak, Malwina
2012
Order-invariant measures on causal sets. Zbl 1274.60026
Brightwell, Graham; Luczak, Malwina
2011
Individual and patch behaviour in structured metapopulation models. Zbl 1334.92327
Barbour, A. D.; Luczak, M. J.
2015
Vertices of high degree in the preferential attachment tree. Zbl 1244.05197
Brightwell, Graham; Luczak, Malwina
2012
The second largest component in the supercritical 2D Hamming graph. Zbl 1208.05139
van der Hofstad, Remco; Luczak, Malwina J.; Spencer, Joel
2010
A quantiative law of large numbers via exponential martingales. Zbl 1038.60068
Luczak, Malwina J.
2003
Component structure of the configuration model: barely supercritical case. Zbl 1425.05145
van der Hofstad, Remco; Janson, Svante; Luczak, Malwina
2019
The supermarket model with bounded queue lengths in equilibrium. Zbl 1403.60075
Brightwell, Graham; Fairthorne, Marianne; Luczak, Malwina J.
2018
Extinction times in the subcritical stochastic SIS logistic epidemic. Zbl 1394.60080
Brightwell, Graham; House, Thomas; Luczak, Malwina
2018
Near-critical SIR epidemic on a random graph with given degrees. Zbl 1358.05259
Janson, Svante; Luczak, Malwina; Windridge, Peter; House, Thomas
2017
Component structure of the configuration model: barely supercritical case. Zbl 1425.05145
van der Hofstad, Remco; Janson, Svante; Luczak, Malwina
2019
Multivariate approximation in total variation. II: Discrete normal approximation. Zbl 1393.62008
Barbour, A. D.; Luczak, M. J.; Xia, A.
2018
Multivariate approximation in total variation. I: Equilibrium distributions of Markov jump processes. Zbl 1393.62007
Barbour, A. D.; Luczak, M. J.; Xia, A.
2018
The supermarket model with bounded queue lengths in equilibrium. Zbl 1403.60075
Brightwell, Graham; Fairthorne, Marianne; Luczak, Malwina J.
2018
Extinction times in the subcritical stochastic SIS logistic epidemic. Zbl 1394.60080
Brightwell, Graham; House, Thomas; Luczak, Malwina
2018
The greedy independent set in a random graph with given degrees. Zbl 1386.05175
Brightwell, Graham; Janson, Svante; Luczak, Malwina
2017
Near-critical SIR epidemic on a random graph with given degrees. Zbl 1358.05259
Janson, Svante; Luczak, Malwina; Windridge, Peter; House, Thomas
2017
Individual and patch behaviour in structured metapopulation models. Zbl 1334.92327
Barbour, A. D.; Luczak, M. J.
2015
Law of large numbers for the SIR epidemic on a random graph with given degrees. Zbl 1328.05170
Janson, Svante; Luczak, Malwina; Windridge, Peter
2014
Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory. Zbl 1274.60244
Luczak, M. J.; Norris, J. R.
2013
Central limit approximations for Markov population processes with countably many types. Zbl 1284.92079
Barbour, Andrew; Luczak, Malwina
2012
A law of large numbers approximation for Markov population processes with countably many types. Zbl 1395.60083
Barbour, A. D.; Luczak, M. J.
2012
Order-invariant measures on fixed causal sets. Zbl 1260.06003
Brightwell, Graham; Luczak, Malwina
2012
Vertices of high degree in the preferential attachment tree. Zbl 1244.05197
Brightwell, Graham; Luczak, Malwina
2012
Order-invariant measures on causal sets. Zbl 1274.60026
Brightwell, Graham; Luczak, Malwina
2011
Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. Zbl 1187.82076
Levin, David A.; Luczak, Malwina J.; Peres, Yuval
2010
Random subgraphs of the 2D Hamming graph: The supercritical phase. Zbl 1188.05141
van der Hofstad, Remco; Luczak, Malwina J.
2010
The second largest component in the supercritical 2D Hamming graph. Zbl 1208.05139
van der Hofstad, Remco; Luczak, Malwina J.; Spencer, Joel
2010
A new approach to the giant component problem. Zbl 1177.05110
Janson, Svante; Luczak, Malwina J.
2009
Asymptotic normality of the $$k$$-core in random graphs. Zbl 1157.05047
Janson, Svante; Luczak, Malwina J.
2008
Susceptibility in subcritical random graphs. Zbl 1159.81324
Janson, Svante; Luczak, Malwina J.
2008
Concentration of measure and mixing for Markov chains. Zbl 1357.60075
Luczak, Malwina J.
2008
Laws of large numbers for epidemic models with countably many types. Zbl 1197.92039
Barbour, A. D.; Luczak, M. J.
2008
A simple solution to the $$k$$-core problem. Zbl 1113.05091
Janson, Svante; Luczak, Malwina J.
2007
Asymptotic distributions and chaos for the supermarket model. Zbl 1131.60005
Luczak, Malwina J.; McDiarmid, Colin
2007
On the maximum queue length in the supermarket model. Zbl 1102.60083
Luczak, Malwina J.; McDiarmid, Colin
2006
The phase transition in the cluster-scaled model of a random graph. Zbl 1089.05066
Łuczak, Malwina; Łuczak, Tomasz
2006
On the power of two choices: balls and bins in continuous time. Zbl 1079.60016
Luczak, Malwina J.; McDiarmid, Colin
2005
Strong approximation for the supermarket model. Zbl 1080.60086
Luczak, Malwina J.; Norris, James
2005
Building uniformly random subtrees. Zbl 1050.60007
Luczak, Malwina; Winkler, Peter
2004
On-line routing of random calls in networks. Zbl 1028.90009
Luczak, Malwina J.; McDiarmid, Colin; Upfal, Eli
2003
Concentration for locally acting permutations. Zbl 1025.60003
Luczak, Malwina J.; McDiarmid, Colin
2003
A quantiative law of large numbers via exponential martingales. Zbl 1038.60068
Luczak, Malwina J.
2003
Bisecting sparse random graphs. Zbl 0968.05071
Luczak, Malwina J.; McDiarmid, Colin
2001
all top 5
Cited by 298 Authors
19 Luczak, Malwina J. 15 Janson, Svante 13 van der Hofstad, Remco W. 10 Lubetzky, Eyal 10 Peres, Yuval 7 Barbour, Andrew D. 7 Riordan, Oliver Maxim 6 Bollobás, Béla 6 Ding, Jian 5 Bhamidi, Shankar 5 McDiarmid, Colin J. H. 5 Nachmias, Asaf 5 Sly, Allan 4 Komjáthy, Júlia 4 Li, Quanlin 4 van Leeuwaarden, Johan S. H. 4 Xia, Aihua 3 Auletta, Vincenzo 3 Bramson, Maury D. 3 Brightwell, Graham R. 3 Dhara, Souvik 3 Ferraioli, Diodato 3 Gheissari, Reza 3 House, Thomas 3 Kang, Mihyun 3 Kovchegov, Yevgeniy V. 3 Lelarge, Marc 3 Leung, Ka Yin 3 Molloy, Michael S. O. 3 Mukherjee, Debankur 3 Otto, Peter Tak-Hun 3 Pasquale, Francesco 3 Persiano, Giuseppe 3 Reed, Bruce Alan 3 Reinert, Gesine D. 3 Scoppola, Benedetto 3 Spencer, Joel H. 3 Windridge, Peter 2 Addario-Berry, Louigi 2 Ball, Frank G. 2 Bianchi, Alessandra 2 Britton, Tom 2 Budhiraja, Amarjit S. 2 Burch, Mark G. 2 Chatterjee, Sourav 2 Coja-Oghlan, Amin 2 Cooley, Oliver 2 Dai, Guirong 2 Deijfen, Maria 2 Diekmann, Odo 2 Federico, Lorenzo 2 Goldschmidt, Christina 2 Jacobsen, Karly A. 2 Kaur, Gursharn 2 Kiss, István Z. 2 Lu, Yi 2 Lui, John C. S. 2 Lyons, Russell 2 Martinelli, Fabio 2 Mcvinish, Ross S. 2 Menshikov, Mikhail V. 2 Norris, James R. 2 Paulin, Daniel 2 Pittel, Boris G. 2 Pollett, Philip K. 2 Poole, Daniel J. 2 Prabhakar, Balaji 2 Rempała, Grzegorz A. 2 Röllin, Adrian 2 Schlichting, André 2 Sen, Sanchayan 2 Simon, Peter L. 2 Skubch, Kathrin 2 Tien, Joseph H. 2 Trapman, Pieter 2 Vachkovskaia, Marina 1 Achlioptas, Dimitris 1 Adamczak, Radosław 1 Adriaans, Erwin 1 Aghajani, Reza 1 Amini, Hamed 1 Angel, Omer 1 Anselmi, Jonatha 1 Athreya, Siva R. 1 Backhausz, Ágnes M. 1 Bandyopadhyay, Antar 1 Barlow, Martin T. 1 Barnard, Rosanna C. 1 Baroni, Enrico 1 Barrera, Javiera 1 Barroso, Manuel A. 1 Batagelj, Vladimir 1 Bauerschmidt, Roland 1 Becker, Simon 1 Bermolen, Paola 1 Berthouze, Luc 1 Bertoin, Jean 1 Bertoncini, Olivier 1 Boden, Brigitte 1 Bodineau, Thierry ...and 198 more Authors
all top 5
Cited in 70 Serials
20 The Annals of Applied Probability 18 Journal of Statistical Physics 16 Random Structures & Algorithms 16 Combinatorics, Probability and Computing 8 Journal of Mathematical Biology 7 The Annals of Probability 7 Stochastic Processes and their Applications 6 Journal of Applied Probability 6 Probability Theory and Related Fields 5 Communications in Mathematical Physics 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Electronic Journal of Probability 5 Bernoulli 3 Journal of Mathematical Physics 3 Journal of Combinatorial Theory. Series B 3 Journal of Functional Analysis 3 Algorithmica 3 Stochastic Systems 2 Mathematical Biosciences 2 Advances in Applied Mathematics 2 Statistics & Probability Letters 2 Journal of Theoretical Probability 2 SIAM Journal on Discrete Mathematics 2 Discrete Event Dynamic Systems 2 Electronic Communications in Probability 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Stochastic Models 1 Advances in Applied Probability 1 Communications on Pure and Applied Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Physica A 1 Arkiv för Matematik 1 Bulletin of Mathematical Biology 1 Theory of Probability and its Applications 1 Dissertationes Mathematicae 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Kybernetika 1 Mathematics of Operations Research 1 Memoirs of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Combinatorica 1 Acta Mathematica Hungarica 1 Computers & Operations Research 1 Asia-Pacific Journal of Operational Research 1 Journal of the American Mathematical Society 1 Queueing Systems 1 Journal of the Ramanujan Mathematical Society 1 Geometric and Functional Analysis. GAFA 1 Games and Economic Behavior 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Discrete and Continuous Dynamical Systems 1 Data Mining and Knowledge Discovery 1 Journal of the European Mathematical Society (JEMS) 1 Methodology and Computing in Applied Probability 1 Living Reviews in Relativity 1 Advances in Difference Equations 1 Journal of Statistical Mechanics: Theory and Experiment 1 Mathematical Biosciences and Engineering 1 Journal of Biological Dynamics 1 Advances in Data Analysis and Classification. ADAC 1 Probability Surveys 1 Computer Science Review 1 Special Matrices 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
all top 5
Cited in 28 Fields
137 Probability theory and stochastic processes (60-XX) 98 Combinatorics (05-XX) 49 Statistical mechanics, structure of matter (82-XX) 31 Operations research, mathematical programming (90-XX) 26 Biology and other natural sciences (92-XX) 21 Computer science (68-XX) 9 Statistics (62-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Ordinary differential equations (34-XX) 4 Numerical analysis (65-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Systems theory; control (93-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-19T16:08:40 |
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|
https://par.nsf.gov/biblio/10206903
|
Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-Layer Networks
We develop exact representations of training twolayer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden neurons. Our theory utilizes semi-infinite duality and minimum norm regularization. We show that ReLU networks trained with standard weight decay are equivalent to block 1 penalized convex models. Moreover, we show that certain standard convolutional linear networks are equivalent semidefinite programs which can be simplified to 1 regularized linear models in a polynomial sized discrete Fourier feature space.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10206903
Journal Name:
International Conference on Machine Learning
1. Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In this paper, we develop a novel unified framework to reveal a hidden regularization mechanism through the lens of convex optimization. We first show that the training of multiple threelayer ReLU sub-networks with weight decay regularization can be equivalently cast as a convex optimization problem in a higher dimensional space, where sparsity is enforced via a group 1- norm regularization. Consequently, ReLU networks can be interpreted as high dimensional feature selection methods. More importantly, we then prove that the equivalent convex problem can be globally optimized by a standard convex optimization solver with a polynomial-time complexity with respect to the number of samples and data dimension when the width of the network is fixed. Finally, we numerically validate our theoretical results via experiments involving both synthetic and real datasets.
2. We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons, and data dimension. More specifically, we develop a convex analytic framework utilizing semi-infinite duality to obtain equivalent convex optimization problems for several two- and three-layer CNN architectures. We first prove that two-layer CNNs can be globally optimized via an 2 norm regularized convex program. We then show that multi-layer circular CNN training problems with a single ReLU layer are equivalent to an 1 regularized convex program that encourages sparsity in the spectral domain. We also extend these results to three-layer CNNs with two ReLU layers. Furthermore, we present extensions of our approach to different pooling methods, which elucidates the implicit architectural bias as convex regularizers.
| 2023-03-31T22:06:38 |
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|
https://www.usgs.gov/center-news/volcano-watch-large-rocks-strange-places
|
# Volcano Watch — Large rocks in strange places
Release Date:
Sometimes in science you find something that theory says you shouldn't. Then your pulse starts racing. Are your observations or calculations wrong? Is the theory wrong? Or is there a middle ground, in which observations can be fit to theory if both are tweaked a little?
Sometimes in science you find something that theory says you shouldn't. Then your pulse starts racing. Are your observations or calculations wrong? Is the theory wrong? Or is there a middle ground, in which observations can be fit to theory if both are tweaked a little?
In late August two volcanologists from the USGS (one from HVO) and one from the Smithsonian Institution were faced with this dilemma. We don't yet know what the final outcome will be, but we're pretty excited.
As this column has previously noted, Kīlauea has exploded more often than many people think. Ongoing research at HVO is trying to learn as much as possible about these explosions, for flying rocks are clearly hazardous events that will impact the public.
We went looking for rocks that were thrown out of the volcano about 1,000 years ago. Work in past months had shown that a wide variety of material was exploded from Kīlauea then, mostly cherry-sized scoria and other fine-grained material. However, several times explosions were apparently more violent or powerful. They ejected large, heavy rocks, much like those from the 1924 explosions that litter the surface around Halemaumau today. The question we asked was how far out were such rocks thrown?
Using a hand-held GPS unit, we established a grid between the Hilina Pali Road and the Ainahou Ranch Road. The grid is about 700 m (2,300 feet) on a side. At each node of the grid, we spent a total of 18 minutes looking for rocks on the surface-6 minutes per person with a full crew, and 9 minutes with only two of us. We selected the largest 10 rocks we could find during the search. It was like an Easter egg hunt, except the rocks can't be eaten and Nature put them there.
We were searching for the largest rocks we could find. We were not interested in those that broke off the surface of the lava flow beneath our feet, but in those that were clearly foreign-that reached their resting place by flying through the air ballistically. After a little practice, recognizing the ballistics became a simple matter. Some of the rocks are even coarse-grained gabbro, which cooled and crystallized underground before being blasted out.
What we found surprised, even shocked, us. Rather than seeing few, if any, large rocks so far from the caldera, we found lots. And some were very large.
At a distance of 10 km (6 miles) from the summit, we found one rock (a gabbro) weighing 1292 g (2 lbs 13 oz.). At 7.9 km (4.7 miles) from the summit, we found another weighing 1998 g (4 lbs 5 oz.). Many others weigh 100 g (3.5 oz.) or more.
When we compared our findings with theoretical models of how far such large rocks could have been thrown from a volcanic vent, we found that we were observing the impossible. The models simply say no dice, it can't be done. Even if we assume that the source for the rocks was on the east rift zone, say near Pauahi Crater or Mauna Ulu, the distance of more than 5.25 km (3.2 miles) is still too great for the models to accept. But, models or no models, the rocks traveled through the air to get where we found them-and that has to be explained.
We think we are on to something. Kīlauea has likely had explosions that were either more powerful, or of a different type, than existing theoretical models can explain.
Before you toss out theory, all steps in the observation and interpretation process must be checked and double checked. We are doing that now. Explosions of such unusual power or type are significant; we can leave no stone unturned (pun intended) in trying to determine their nature and cause.
### Volcano Activity Update
Eruptive activity of Kīlauea Volcano continued unabated during the past week, following a brief pause two weeks ago. Lava is erupting from Puu Oo and flowing through the old tube system for 1.5 km (0.9 mi) to the southeast. Breakouts from the old tube system at the 2,300-ft elevation feed two diverging flows. One flow is to the southwest and extends down to the 1900-ft elevation. The second flow is to the southeast and extends 3.6 km (2.2 mi) down to the 1700-ft elevation.
Residents of Pahala felt an earthquake at 7:06 p.m. on September 3. The magnitude-3.4 earthquake was located 4 km (2.4 mi) south of Pahala at a depth of 11 km (6.6 mi).
| 2020-12-04T01:53:43 |
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|
https://www.bnl.gov/event.php?q=6143
|
# Nuclear Physics & RIKEN Theory Seminar
## "Thermal photons from heavy ion collisions: A spectral function approach"
#### Presented by Ismail Zahed, SUNY Stony brook
Friday, February 5, 2010, 2:00 pm — Small Seminar Room, Bldg. 510
We analyze the photon rates from a hadronic gas in equilibrium using chiral reduction formulas and a density expansion. The chiral reduction is carried to second order in the pion density which in principal includes all kinetic processes of the type $X\to \pi\gamma$ and $X\to \pi\pi\gamma$. The resulting rates are encoded in the form of vacuum correlation functions which are amenable to experiment. The hadronic rates computed in this work along with the known perturbative QGP rates are integrated over the space-time evolution of a hydrodynamic model tuned to hadronic observables. The resulting yields are compared to the recent photon and low mass dilepton measurements at the SPS and RHIC. Predictions for the LHC are made.
Hosted by: Kevin Dusling
6143 | INT/EXT | Events Calendar
| 2019-09-16T14:28:35 |
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https://www.bnl.gov/event.php?q=12089
|
# Nuclear Theory Seminar
## "Helicity Evolution at Small x and the Proton Spin"
#### Presented by Yuri Kovchegov, Ohio State University
Friday, January 20, 2017, 2:00 pm — Small Seminar Room, Bldg. 510
We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g_1 structure function. These evolution equations resum powers of alpha_s ln^2 (1/x) in the polarization-dependent evolution along with the powers of alpha_s ln (1/x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N_c and large-N_c & N_f limits. After solving the large-N_c equations numerically we obtain the following small-x asymptotics for the flavor-singlet
g_1 structure function along with quarks helicity PDFs and TMDs (in absence of saturation effects):
g_1^S (x, Q^2) ~ \Delta q^S (x, Q^2) ~ g_{1L}^S (x, k_T^2) ~ ( 1/x )^{alpha_h} \approx t( 1/x )^{2.31 \sqrt{\alpha_s N_c/(2pi}}
This result is valid for all flavors. We also give an estimate of how much of the proton's spin may reside at small x and what impact this has on the so-called spin crisis.'' This work would help one better understand longitudinal polarization data to be obtained at the proposed Electron-Ion Collider (EIC).
Hosted by: Heikki Mantysaari
12089 | INT/EXT | Events Calendar
| 2021-12-01T19:04:40 |
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|
https://ftp.aimsciences.org/article/doi/10.3934/jimo.2021049
|
Article Contents
Article Contents
# Free boundary problem for an optimal investment problem with a borrowing constraint
• * Corresponding author: Rui Zhou
The work is supported by NNSF of China (No.11901244 and No.11901093), Universities and Colleges Special Innovation Project of Guangdong Province (No.2019KTSCX166), and Research Grants Council of Hong kong under grant 15213218 and 15215319
• This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small.
Mathematics Subject Classification: Primary: 91B70, 91G10; Secondary: 35R35, 35B65.
Citation:
• Figure 1. Free boundaries with various $k$ and $b$
• [1] S. Asmussen and M. Taksar, Controlled diffusion models for optimal dividend pay-out, Insurance: Mathematics and Economics, 20 (1997), 1-15. doi: 10.1016/S0167-6687(96)00017-0. [2] T. R. Bielecki, H. Jin, S. R. Pliska and X. Y. Zhou, Continuous-time mean-variance portfolio selection with bankruptcy prohibition, Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 15 (2005), 213-244. doi: 10.1111/j.0960-1627.2005.00218.x. [3] M. Dai, Z. Q. Xu and X. Y. Zhou, Continuous-time Markowitz's model with transaction costs, SIAM Journal on Financial Mathematics, 1 (2010), 96-125. doi: 10.1137/080742889. [4] M. Dai and F. Yi, Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem, Journal of Differential Equations, 246 (2009), 1445-1469. doi: 10.1016/j.jde.2008.11.003. [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. [6] A. Friedman, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, Journal of Functional Analysis, 18 (1975), 151-176. doi: 10.1016/0022-1236(75)90022-1. [7] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2$^nd$ edition, Springer-Verlag, Berlin, 1983. doi: 10.1007/978-3-642-61798-0. [8] C. Guan, On a free boundary problem for an optimal investment problem with different interest rates, Communications in Mathematical Sciences, 18 (2020), 31-54. doi: 10.4310/CMS.2020.v18.n1.a2. [9] C. Guan, X. Li, Z. Q. Xu and F. Yi, A stochastic control problem and related free boundaries in finance, Mathematical Control & Related Fields, 7 (2017), 563-584. doi: 10.3934/mcrf.2017021. [10] C. Guan, F. Yi and J. Chen, Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain, Journal of Differential Equations, 266 (2019), 1245-1284. doi: 10.1016/j.jde.2018.07.070. [11] B. Hu, J. Liang and Y. Wu, A free boundary problem for corporate bond with credit rating migration, Journal of Mathematical Analysis and Applications, 428 (2015), 896-909. doi: 10.1016/j.jmaa.2015.03.040. [12] O. A. Ladyzhenskaia, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasi-Linear Equations of Parabolic Type, American Mathematical Society, 1968. doi: 10.1090/mmono/023. [13] X. Li and Z. Q. Xu, Continuous-time Markowitz's model with constraints on wealth and portfolio, Operations Research Letters, 44 (2016), 729-736. doi: 10.1016/j.orl.2016.09.004. [14] X. Li, X. Y. Zhou and A. E. B. Lim, Dynamic mean-variance portfolio selection with no-shorting constraints, SIAM Journal on Control and Optimization, 40 (2002), 1540-1555. doi: 10.1137/S0363012900378504. [15] G. M. Lieberman, Second Order Parabolic Differential Equations, World scientific, 1996. doi: 10.1142/3302. [16] R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The review of Economics and Statistics, 51 (1969), 247-257. doi: 10.2307/1926560. [17] R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413. doi: 10.1016/0022-0531(71)90038-X. [18] A. O. Olejnik and E. V. Radkevic, Second Order Equations with Nonnegative Characteristic Form, AMS, New York-London, 1973. doi: 10.1007/978-1-4684-8965-1. [19] P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, The Review of Economics and Statistics, 51 (1969), 239-246. doi: 10.2307/1926559. [20] M. I. Taksar, Optimal risk and dividend distribution control models for an insurance company, Mathematical Methods of Operations Research, 51 (2000), 1-42. doi: 10.1007/s001860050001. [21] Z. Yang, F. Yi and M. Dai, A parabolic variational inequality arising from the valuation of strike reset options, Journal of Differential Equations, 230 (2006), 481-501. doi: 10.1016/j.jde.2006.07.026. [22] T. Zariphopoulou, Consumption-investment models with constraints, SIAM Journal on Control and Optimization, 32 (1994), 59-85. doi: 10.1137/S0363012991218827.
Open Access Under a Creative Commons license
Figures(1)
| 2022-12-08T16:00:40 |
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|
https://par.nsf.gov/biblio/10367347-close-puffy-neptune-hidden-friends-enigma-toi
|
A Close-in Puffy Neptune with Hidden Friends: The Enigma of TOI 620
Abstract
We present the validation of a transiting low-density exoplanet orbiting the M2.5 dwarf TOI 620 discovered by the NASA Transiting Exoplanet Survey Satellite (TESS) mission. We utilize photometric data from both TESS and ground-based follow-up observations to validate the ephemerides of the 5.09 day transiting signal and vet false-positive scenarios. High-contrast imaging data are used to resolve the stellar host and exclude stellar companions at separations ≳0.″2. We obtain follow-up spectroscopy and corresponding precise radial velocities (RVs) with multiple precision radial velocity (PRV) spectrographs to confirm the planetary nature of the transiting exoplanet. We calculate a 5σupper limit ofMP< 7.1MandρP< 0.74 g cm−3, and we identify a nontransiting 17.7 day candidate. We also find evidence for a substellar (1–20MJ) companion with a projected separation ≲20 au from a combined analysis of Gaia, adaptive optics imaging, and RVs. With the discovery of this outer companion, we carry out a detailed exploration of the possibilities that TOI 620 b might instead be a circum-secondary planet or a pair of eclipsing binary stars orbiting the host in a hierarchical triple system. We find, under scrutiny, that we can exclude both of these scenarios from the multiwavelength transit photometry, thus validating TOI 620 more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10367347
Journal Name:
The Astronomical Journal
Volume:
163
Issue:
6
Page Range or eLocation-ID:
Article No. 269
ISSN:
0004-6256
Publisher:
DOI PREFIX: 10.3847
National Science Foundation
##### More Like this
1. Abstract We present the Transiting Exoplanet Survey Satellite (TESS) discovery of the LHS 1678 (TOI-696) exoplanet system, comprised of two approximately Earth-sized transiting planets and a likely astrometric brown dwarf orbiting a bright ( V J = 12.5, K s = 8.3) M2 dwarf at 19.9 pc. The two TESS-detected planets are of radius 0.70 ± 0.04 R ⊕ and 0.98 ± 0.06 R ⊕ in 0.86 day and 3.69 day orbits, respectively. Both planets are validated and characterized via ground-based follow-up observations. High Accuracy Radial Velocity Planet Searcher RV monitoring yields 97.7 percentile mass upper limits of 0.35 M ⊕ and 1.4 M ⊕ for planets b and c, respectively. The astrometric companion detected by the Cerro Tololo Inter-American Observatory/Small and Moderate Aperture Telescope System 0.9 m has an orbital period on the order of decades and is undetected by other means. Additional ground-based observations constrain the companion to being a high-mass brown dwarf or smaller. Each planet is of unique interest; the inner planet has an ultra-short period, and the outer planet is in the Venus zone. Both are promising targets for atmospheric characterization with the James Webb Space Telescope and mass measurements via extreme-precision radial velocity. Amore »
2. ABSTRACT
We present a precise characterization of the TOI-561 planetary system obtained by combining previously published data with TESS and CHEOPS photometry, and a new set of 62 HARPS-N radial velocities (RVs). Our joint analysis confirms the presence of four transiting planets, namely TOI-561 b (P = 0.45 d, R = 1.42 R⊕, M = 2.0 M⊕), c (P = 10.78 d, R = 2.91 R⊕, M = 5.4 M⊕), d (P = 25.7 d, R = 2.82 R⊕, M = 13.2 M⊕), and e (P = 77 d, R = 2.55 R⊕, M = 12.6 R⊕). Moreover, we identify an additional, long-period signal (>450 d) in the RVs, which could be due to either an external planetary companion or to stellar magnetic activity. The precise masses and radii obtained for the four planets allowed us to conduct interior structure and atmospheric escape modelling. TOI-561 b is confirmed to be the lowest density (ρb = 3.8 ± 0.5 g cm−3) ultra-short period (USP) planet known to date, and the low metallicity of the host star makes it consistent with the general bulk density-stellar metallicity trend. According to our interior structure modelling, planet b has basically no gas envelope, and it could host a certain amount of water. In contrast, TOI-561 c, d, and e likely retainedmore »
3. Abstract We report the discovery of TOI-2180 b, a 2.8 M J giant planet orbiting a slightly evolved G5 host star. This planet transited only once in Cycle 2 of the primary Transiting Exoplanet Survey Satellite (TESS) mission. Citizen scientists identified the 24 hr single-transit event shortly after the data were released, allowing a Doppler monitoring campaign with the Automated Planet Finder telescope at Lick Observatory to begin promptly. The radial velocity observations refined the orbital period of TOI-2180 b to be 260.8 ± 0.6 days, revealed an orbital eccentricity of 0.368 ± 0.007, and discovered long-term acceleration from a more distant massive companion. We conducted ground-based photometry from 14 sites spread around the globe in an attempt to detect another transit. Although we did not make a clear transit detection, the nondetections improved the precision of the orbital period. We predict that TESS will likely detect another transit of TOI-2180 b in Sector 48 of its extended mission. We use giant planet structure models to retrieve the bulk heavy-element content of TOI-2180 b. When considered alongside other giant planets with orbital periods over 100 days, we find tentative evidence that the correlation between planet mass and metal enrichment relativemore »
4. Abstract
Exoplanet systems with multiple transiting planets are natural laboratories for testing planetary astrophysics. One such system is HD 191939 (TOI 1339), a bright (V= 9) and Sun-like (G9V) star, which TESS found to host three transiting planets (b, c, and d). The planets have periods of 9, 29, and 38 days each with similar sizes from 3 to 3.4R. To further characterize the system, we measured the radial velocity (RV) of HD 191939 over 415 days with Keck/HIRES and APF/Levy. We find thatMb= 10.4 ± 0.9MandMc= 7.2 ± 1.4M, which are low compared to most known planets of comparable radii. The RVs yield only an upper limit onMd(<5.8Mat 2σ). The RVs further reveal a fourth planet (e) with a minimum mass of 0.34 ± 0.01MJupand an orbital period of 101.4 ± 0.4 days. Despite its nontransiting geometry, secular interactions between planet e and the inner transiting planets indicate that planet e is coplanar with the transiting planets (Δi< 10°). We identify a second high-mass planet (f) with 95% confidence intervals on mass between 2 and 11MJupand period between 1700 and 7200 days, based on a joint analysis of RVs and astrometry from Gaia and Hipparcos. As a bright starmore »
5. Abstract
Populating the exoplanet mass–radius diagram in order to identify the underlying relationship that governs planet composition is driving an interdisciplinary effort within the exoplanet community. The discovery of hot super-Earths—a high-temperature, short-period subset of the super-Earth planet population—has presented many unresolved questions concerning the formation, evolution, and composition of rocky planets. We report the discovery of a transiting, ultra-short-period hot super-Earth orbitingTOI-1075(TIC351601843), a nearby (d= 61.4 pc) late-K/early-M-dwarf star, using data from the Transiting Exoplanet Survey Satellite. The newly discovered planet has a radius of 1.791$−0.081+0.116$Rand an orbital period of 0.605 day (14.5 hr). We precisely measure the planet mass to be 9.95$−1.30+1.36$Musing radial velocity measurements obtained with the Planet Finder Spectrograph mounted on the Magellan II telescope. Our radial velocity data also show a long-term trend, suggesting an additional planet in the system. While TOI-1075 b is expected to have a substantial H/He atmosphere given its size relative to the radius gap, its high density ($9.32−1.85+2.05$g cm−3) is likely inconsistent with this possibility. We explore TOI-1075 b’s location relative to the M-dwarf radius valley, evaluate the planet’s prospects for atmospheric characterization, andmore »
| 2023-02-02T21:59:36 |
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http://dergipark.gov.tr/hujms/issue/38121/439928
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Yıl 2018, Cilt 47, Sayı 3, Sayfalar 521 - 538 2018-06-01
| | | |
## Existence of periodic solutions for a mechanical system with piecewise constant forces
#### Duygu Aruğaslan [1] , Nur Cengiz [2]
##### 39 61
In this study, we consider spring-mass systems subjected to piecewise constant forces. We investigate sufficient conditions for the existence of periodic solutions of homogeneous and nonhomogeneous damped spring-mass systems with the help of the Floquet theory. In addition to determining conditions for the existence of periodic solutions, stability analysis is performed for the solutions of the homogeneous system. The
Floquet multipliers are taken into account for the stability analysis [3]. The results are stated in terms of the parameters of the systems. These results are illustrated and supported by simulations for different values of the parameters.
Generalized piecewise constant forces, spring-mass system, stability and periodic solutions
• Aftabizadeh, A.R., Wiener, J. and Xu, J.-M. Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. Amer. Math. Soc. 99, 673 679, 1987.
• Akhmet, M.U. Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. 66, 367383, 2007.
• Akhmet, M.U. Nonlinear Hybrid Continuous/Discrete Time Models, Amsterdam, Paris, Atlantis Press, 2011.
• Akhmet, M.U. On the integral manifolds of the differential equations with piecewise constant argument of generalized type, Proceedings of the Conference on Dierential and Dierence Equations at the Florida Institute of Technology, August 1-5, 2005, Melbourne, Florida, Editors: R.P. Agarval and K. Perera, Hindawi Publishing Corporation, 1120, 2006.
• Akhmet, M.U. Quasilinear retarded differential equations with functional dependence on piecewise constant argument, Communications On Pure And Applied Analysis 13 (2), 929 947, 2014.
• Akhmet, M.U. Stability of differential equations with piecewise constant arguments of gen- eralized type, Nonlinear Anal. 68, 794803, 2008.
• Akhmet, M.U. and Aru§aslan, D. Lyapunov-Razumikhin method for differential equations with piecewise constant argument, Discrete and Continuous Dynamical Systems, Series A 25 (2), 457466, 2009.
• Akhmet, M.U., Aru§aslan, D. and Liu, X. Permanence of nonautonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type, Dynamics of Continuous Discrete and Impulsive Systems Series A. Mathematical Analysis 15 (1), 3751, 2008.
• Akhmet, M.U., Aru§aslan, D. and Ylmaz, E. Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Networks 23, 805811, 2010.
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Birincil Dil en Matematik Matematik Yazar: Duygu Aruğaslan (Sorumlu Yazar) Yazar: Nur Cengiz
Bibtex @araştırma makalesi { hujms439928, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {521 - 538}, doi = {}, title = {Existence of periodic solutions for a mechanical system with piecewise constant forces}, key = {cite}, author = {Aruğaslan, Duygu and Cengiz, Nur} } APA Aruğaslan, D , Cengiz, N . (2018). Existence of periodic solutions for a mechanical system with piecewise constant forces. Hacettepe Journal of Mathematics and Statistics, 47 (3), 521-538. Retrieved from http://dergipark.gov.tr/hujms/issue/38121/439928 MLA Aruğaslan, D , Cengiz, N . "Existence of periodic solutions for a mechanical system with piecewise constant forces". Hacettepe Journal of Mathematics and Statistics 47 (2018): 521-538 Chicago Aruğaslan, D , Cengiz, N . "Existence of periodic solutions for a mechanical system with piecewise constant forces". Hacettepe Journal of Mathematics and Statistics 47 (2018): 521-538 RIS TY - JOUR T1 - Existence of periodic solutions for a mechanical system with piecewise constant forces AU - Duygu Aruğaslan , Nur Cengiz Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 521 EP - 538 VL - 47 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Existence of periodic solutions for a mechanical system with piecewise constant forces %A Duygu Aruğaslan , Nur Cengiz %T Existence of periodic solutions for a mechanical system with piecewise constant forces %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 3 %R %U ISNAD Aruğaslan, Duygu , Cengiz, Nur . "Existence of periodic solutions for a mechanical system with piecewise constant forces". Hacettepe Journal of Mathematics and Statistics 47 / 3 (Haziran 2018): 521-538.
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https://large-numbers.fandom.com/wiki/Latin_square
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A Latin square is an n × n matrix of n distinct symbols, where each row and column contains exactly one of each symbol.[1]
The number of size-n Latin squares is a rapidly growing function, although not terribly impressive from a googologist's point of view:
\begin{eqnarray*} L(1) &=& 1 \\ L(2) &=& 2 \\ L(3) &=& 12 \\ L(4) &=& 576 \\ L(5) &=& 161,280 \\ L(6) &=& 812,851,200 \\ L(7) &=& 61,479,419,904,000 \end{eqnarray*}
No simple formula is yet known for the function $$L(n)$$. It is upper-bounded by the function $$n \mapsto (n!)^n$$, since each of the $$n$$ rows has an arrangement of $$n$$ distinct symbols.
Sources Edit
1. [1]
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# 3.4E: Exercises for Section 3.4
In exercises 1 - 3, the given functions represent the position of a particle traveling along a horizontal line.
a. Find the velocity and acceleration functions.
b. Determine the time intervals when the object is slowing down or speeding up.
1) $$s(t)=2t^3−3t^2−12t+8$$
2) $$s(t)=2t^3−15t^2+36t−10$$
Answer
a. $$v(t)=6t^2−30t+36,\quad a(t)=12t−30$$;
b. speeds up for $$(2,2.5)∪(3,∞)$$, slows down for $$(0,2)∪(2.5,3)$$
3) $$s(t)=\dfrac{t}{1+t^2}$$
4) A rocket is fired vertically upward from the ground. The distance $$s$$ in feet that the rocket travels from the ground after $$t$$ seconds is given by $$s(t)=−16t^2+560t$$.
a. Find the velocity of the rocket 3 seconds after being fired.
b. Find the acceleration of the rocket 3 seconds after being fired.
Answer
a. $$464\; \text{ft/s}^2$$
b. $$−32\;\text{ft/s}^2$$
5) A ball is thrown downward with a speed of 8 ft/s from the top of a 64-foot-tall building. After $$t$$ seconds, its height above the ground is given by $$s(t)=−16t^2−8t+64.$$
a. Determine how long it takes for the ball to hit the ground.
b. Determine the velocity of the ball when it hits the ground.
6) The position function $$s(t)=t^2−3t−4$$ represents the position of the back of a car backing out of a driveway and then driving in a straight line, where $$s$$ is in feet and $$t$$ is in seconds. In this case, $$s(t)=0$$ represents the time at which the back of the car is at the garage door, so $$s(0)=−4$$ is the starting position of the car, 4 feet inside the garage.
a. Determine the velocity of the car when $$s(t)=0$$.
b. Determine the velocity of the car when $$s(t)=14$$.
Answer
a. $$5$$ ft/s
b. $$9$$ ft/s
7) The position of a hummingbird flying along a straight line in $$t$$ seconds is given by $$s(t)=3t^3−7t$$ meters.
a. Determine the velocity of the bird at $$t=1$$ sec.
b. Determine the acceleration of the bird at $$t=1$$ sec.
c. Determine the acceleration of the bird when the velocity equals 0.
8) A potato is launched vertically upward with an initial velocity of 100 ft/s from a potato gun at the top of an 85-foot-tall building. The distance in feet that the potato travels from the ground after $$t$$ seconds is given by $$s(t)=−16t^2+100t+85$$.
a. Find the velocity of the potato after $$0.5$$ s and $$5.75$$ s.
b. Find the speed of the potato at $$0.5$$ s and $$5.75$$ s.
c. Determine when the potato reaches its maximum height.
d. Find the acceleration of the potato at $$0.5$$ s and $$1.5$$ s.
e. Determine how long the potato is in the air.
f. Determine the velocity of the potato upon hitting the ground.
Answer
a. 84 ft/s, −84 ft/s
b. 84 ft/s
c. $$\frac{25}{8}$$ s
d. $$−32 \; \text{ft/s}^2$$ in both cases
e. $$\frac{1}{8}(25+\sqrt{965})$$ s
f. $$−4\sqrt{965}$$ ft/s
9) The position function $$s(t)=t^3−8t$$ gives the position in miles of a freight train where east is the positive direction and $$t$$ is measured in hours.
a. Determine the direction the train is traveling when $$s(t)=0$$.
b. Determine the direction the train is traveling when $$a(t)=0$$.
c. Determine the time intervals when the train is slowing down or speeding up.
10) The following graph shows the position $$y=s(t)$$ of an object moving along a straight line.
a. Use the graph of the position function to determine the time intervals when the velocity is positive, negative, or zero.
b. Sketch the graph of the velocity function.
c. Use the graph of the velocity function to determine the time intervals when the acceleration is positive, negative, or zero.
d. Determine the time intervals when the object is speeding up or slowing down.
Answer
a. Velocity is positive on $$(0,1.5)∪(6,7)$$, negative on $$(1.5,2)∪(5,6)$$, and zero on $$(2,5)$$.
b.
c. Acceleration is positive on $$(5,7)$$, negative on $$(0,2)$$, and zero on $$(2,5)$$.
d. The object is speeding up on $$(6,7)∪(1.5,2)$$ and slowing down on $$(0,1.5)∪(5,6)$$.
11) The cost function, in dollars, of a company that manufactures food processors is given by $$C(x)=200+\dfrac{7}{x}+\dfrac{x}{27}$$, where $$x$$ is the number of food processors manufactured.
a. Find the marginal cost function.
b. Find the marginal cost of manufacturing 12 food processors.
c. Find the actual cost of manufacturing the thirteenth food processor.
12) The price p (in dollars) and the demand $$x$$ for a certain digital clock radio is given by the price–demand function $$p=10−0.001x$$.
a. Find the revenue function $$R(x)$$
b. Find the marginal revenue function.
c. Find the marginal revenue at $$x=2000$$ and $$5000$$.
Answer
a. $$R(x)=10x−0.001x^2$$
b.$$R′(x)=10−0.002x$$
c. $6 per item,$0 per item
13) [T] A profit is earned when revenue exceeds cost. Suppose the profit function for a skateboard manufacturer is given by $$P(x)=30x−0.3x^2−250$$, where $$x$$ is the number of skateboards sold.
a. Find the exact profit from the sale of the thirtieth skateboard.
b. Find the marginal profit function and use it to estimate the profit from the sale of the thirtieth skateboard.
14) [T] In general, the profit function is the difference between the revenue and cost functions: $$P(x)=R(x)−C(x)$$.
Suppose the price-demand and cost functions for the production of cordless drills is given respectively by $$p=143−0.03x$$ and $$C(x)=75,000+65x$$, where $$x$$ is the number of cordless drills that are sold at a price of $$p$$ dollars per drill and $$C(x)$$ is the cost of producing $$x$$ cordless drills.
a. Find the marginal cost function.
b. Find the revenue and marginal revenue functions.
c. Find $$R′(1000)$$ and $$R′(4000)$$. Interpret the results.
d. Find the profit and marginal profit functions.
e. Find $$P′(1000)$$ and $$P′(4000)$$. Interpret the results.
Answer
a. $$C′(x)=65$$
b. $$R(x)=143x−0.03x^2$$,$$R′(x)=143−0.06x$$
c. $$R′(1000)=83, \quad R′(4000) = −97$$. At a production level of 1000 cordless drills, revenue is increasing at a rate of $83 per drill; at a production level of 4000 cordless drills, revenue is decreasing at a rate of$97 per drill.
d. $$P(x)=−0.03x^2+78x−75000, \quad P′(x)=−0.06x+78$$
e. $$P′(1000)=18, \quad P′(4000) =−162$$. At a production level of 1000 cordless drills, profit is increasing at a rate of $18 per drill; at a production level of 4000 cordless drills, profit is decreasing at a rate of$162 per drill.
15) A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of change of the town’s population. The study found that the town’s population (measured in thousands of people) can be modeled by the function $$P(t)=−\frac{1}{3}t^3+64t+3000$$, where $$t$$ is measured in years.
a. Find the rate of change function $$P′(t)$$ of the population function.
b. Find $$P′(1),\; P′(2),\; P′(3)$$, and $$P′(4)$$. Interpret what the results mean for the town.
c. Find $$P''(1),\; P''(2),\; P''(3)$$, and $$P''(4)$$. Interpret what the results mean for the town’s population.
16) [T] A culture of bacteria grows in number according to the function $$N(t)=3000(1+\dfrac{4t}{t^2+100})$$, where $$t$$ is measured in hours.
a. Find the rate of change of the number of bacteria.
b. Find $$N′(0),\; N′(10),\; N′(20)$$, and $$N′(30)$$.
c. Interpret the results in (b).
d. Find $$N''(0),\; N''(10),\; N''(20),$$ and $$N''(30)$$. Interpret what the answers imply about the bacteria population growth.
Answer
a. $$N′(t)=3000\left(\dfrac{−4t^2+400}{(t^2+100)^2}\right)$$
b. $$120,0,−14.4,−9.6$$
c. The bacteria population increases from time 0 to 10 hours; afterwards, the bacteria population decreases.
d. $$0,−6,0.384,0.432$$. The rate at which the bacteria is increasing is decreasing during the first 10 hours. Afterwards, the bacteria population is decreasing at a decreasing rate.
17) The centripetal force of an object of mass m is given by $$F(r)=\dfrac{mv^2}{r}$$, where $$v$$ is the speed of rotation and $$r$$ is the distance from the center of rotation.
a. Find the rate of change of centripetal force with respect to the distance from the center of rotation.
b. Find the rate of change of centripetal force of an object with mass 1000 kilograms, velocity of 13.89 m/s, and a distance from the center of rotation of 200 meters.
The following questions concern the population (in millions) of London by decade in the 19th century, which is listed in the following table.
Year Since 1800 Population (millions) 1 0.8975 11 1.040 21 1.264 31 1.516 41 1.661 51 2.000 61 2.634 71 3.272 81 3.911 91 4.422
Population of LondonSource: http://en.Wikipedia.org/wiki/Demographics_of_London
18) [T]
a. Using a calculator or a computer program, find the best-fit linear function to measure the population.
b. Find the derivative of the equation in a. and explain its physical meaning.
c. Find the second derivative of the equation and explain its physical meaning.
Answer
a. $$P(t)=0.03983+0.4280$$
b. $$P′(t)=0.03983$$. The population is increasing.
c. $$P''(t)=0$$. The rate at which the population is increasing is constant.
19) [T]
a. Using a calculator or a computer program, find the best-fit quadratic curve through the data.
b. Find the derivative of the equation and explain its physical meaning.
c. Find the second derivative of the equation and explain its physical meaning.
For the following exercises, consider an astronaut on a large planet in another galaxy. To learn more about the composition of this planet, the astronaut drops an electronic sensor into a deep trench. The sensor transmits its vertical position every second in relation to the astronaut’s position. The summary of the falling sensor data is displayed in the following table.
Time after dropping (s) Position (m) 0 0 1 −1 2 −2 3 −5 4 −7 5 −14
20) [T]
a. Using a calculator or computer program, find the best-fit quadratic curve to the data.
b. Find the derivative of the position function and explain its physical meaning.
c. Find the second derivative of the position function and explain its physical meaning.
Answer
a. $$p(t)=−0.6071x^2+0.4357x−0.3571$$
b. $$p′(t)=−1.214x+0.4357$$. This is the velocity of the sensor.
c. $$p''(t)=−1.214$$. This is the acceleration of the sensor; it is a constant acceleration downward.
21) [T]
a. Using a calculator or computer program, find the best-fit cubic curve to the data.
b. Find the derivative of the position function and explain its physical meaning.
c. Find the second derivative of the position function and explain its physical meaning.
d. Using the result from c. explain why a cubic function is not a good choice for this problem.
The following problems deal with the Holling type I, II, and III equations. These equations describe the ecological event of growth of a predator population given the amount of prey available for consumption.
22) [T] The Holling type I equation is described by $$f(x)=ax$$, where $$x$$ is the amount of prey available and $$a>0$$ is the rate at which the predator meets the prey for consumption.
a. Graph the Holling type I equation, given $$a=0.5$$.
b. Determine the first derivative of the Holling type I equation and explain physically what the derivative implies.
c. Determine the second derivative of the Holling type I equation and explain physically what the derivative implies.
d. Using the interpretations from b. and c. explain why the Holling type I equation may not be realistic.
Answer
a.
b. $$f′(x)=a$$. The more increase in prey, the more growth for predators.
c. $$f''(x)=0$$. As the amount of prey increases, the rate at which the predator population growth increases is constant.
d. This equation assumes that if there is more prey, the predator is able to increase consumption linearly. This assumption is unphysical because we would expect there to be some saturation point at which there is too much prey for the predator to consume adequately.
23) [T] The Holling type II equation is described by $$f(x)=\dfrac{ax}{n+x}$$, where $$x$$ is the amount of prey available and $$a>0$$ is the maximum consumption rate of the predator.
a. Graph the Holling type II equation given $$a=0.5$$ and $$n=5$$. What are the differences between the Holling type I and II equations?
b. Take the first derivative of the Holling type II equation and interpret the physical meaning of the derivative.
c. Show that $$f(n)=\frac{1}{2}a$$ and interpret the meaning of the parameter n.
d. Find and interpret the meaning of the second derivative. What makes the Holling type II function more realistic than the Holling type I function?
24) [T] The Holling type III equation is described by $$f(x)=\dfrac{ax^2}{n^2+x^2}$$, where x is the amount of prey available and $$a>0$$ is the maximum consumption rate of the predator.
a. Graph the Holling type III equation given $$a=0.5$$ and $$n=5.$$ What are the differences between the Holling type II and III equations?
b. Take the first derivative of the Holling type III equation and interpret the physical meaning of the derivative.
c. Find and interpret the meaning of the second derivative (it may help to graph the second derivative).
d. What additional ecological phenomena does the Holling type III function describe compared with the Holling type II function?
Answer
a.
b. $$f′(x)=\dfrac{2axn^2}{(n^2+x^2)^2}$$. When the amount of prey increases, the predator growth increases.
c. $$f''(x)=\dfrac{2an^2(n^2−3x^2)}{(n^2+x^2)^3}$$. When the amount of prey is extremely small, the rate at which predator growth is increasing is increasing, but when the amount of prey reaches above a certain threshold, the rate at which predator growth is increasing begins to decrease.
d. At lower levels of prey, the prey is more easily able to avoid detection by the predator, so fewer prey individuals are consumed, resulting in less predator growth.
25) [T] The populations of the snowshoe hare (in thousands) and the lynx (in hundreds) collected over 7 years from 1937 to 1943 are shown in the following table. The snowshoe hare is the primary prey of the lynx.
Population of snowshoe hare (thousands) Population of lynx (hundreds) 20 10 5 15 65 55 95 60
Snowshoe Hare and Lynx PopulationsSource: http://www.biotopics.co.uk/newgcse/predatorprey.html.
a. Graph the data points and determine which Holling-type function fits the data best.
b. Using the meanings of the parameters $$a$$ and $$n$$, determine values for those parameters by examining a graph of the data. Recall that $$n$$ measures what prey value results in the half-maximum of the predator value.
c. Plot the resulting Holling-type I, II, and III functions on top of the data. Was the result from part a. correct?
## Contributors and Attributions
• Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
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https://gea.esac.esa.int/archive/documentation/GEDR3/Catalogue_consolidation/chap_cu9val/sec_cu9val_943/ssec_cu9val_943_parallax.html
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# 8.3.2 Parallax distribution
The median of the parallax is computed in each healpix bin and presented in Figure 8.11 in three magnitude bins. The median parallaxes are generally in very good agreement between Gaia EDR3 and GOG20. There are however a few places where the difference is significant, close to the Galactic centre or the Galactic plane (in particular at intermediate magnitudes). The Magellanic Clouds also appear since they are not generated by the model and what we see is the difference between the median parallax in the Magellanic Clouds (of the order of 0.02 mas) and the median parallax of field stars in the same region (which depends on magnitude, see Figure 8.12).
Figure 8.12 shows the parallax averaged over the whole sky per magnitude bin, for Gaia EDR3, Gaia DR2, and GOG20. There is a systematic difference which, in absolute value, depends on magnitude, and is quite high at bright magnitudes, more than 1 mas. This systematic is a bit reduced compared to Gaia DR2. At $G>10$ the difference goes below 0.1 mas.
Summary of the results:
• The median parallaxes are generally in very good agreement between Gaia EDR3 and the model.
• There is a systematic difference which is quite high at bright magnitudes, but is reduced compared to Gaia DR2.
| 2021-08-01T17:37:39 |
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https://www.zbmath.org/authors/?q=ai%3Aspeh.birgit
|
# zbMATH — the first resource for mathematics
## Speh, Birgit
Compute Distance To:
Author ID: speh.birgit Published as: Speh, B.; Speh, Birgit External Links: MGP · Wikidata · GND
Documents Indexed: 46 Publications since 1977, including 2 Books Reviewing Activity: 30 Reviews
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#### Co-Authors
13 single-authored 13 Rohlfs, Jürgen 4 Kobayashi, Toshiyuki 4 Venkataramana, Tyakal Nanjundiah 3 Knapp, Anthony William 2 Müller, Werner 2 Ørsted, Bent 2 Vogan, David Alexander jun. 1 Barbasch, Dan M. 1 Gomez, Raul 1 Lapid, Erez Moshe 1 Sahi, Siddhartha 1 Shin, Sug Woo 1 Templier, Nicolas 1 Zhang, Guanghao
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#### Serials
3 Journal of Functional Analysis 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Mathematische Annalen 1 Indian Journal of Pure & Applied Mathematics 1 Acta Mathematica 1 Inventiones Mathematicae 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Forum Mathematicum 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the National Academy of Sciences of the United States of America 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Oberwolfach Reports 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Pure and Applied Mathematics Quarterly 1 Lecture Notes in Mathematics
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#### Fields
40 Topological groups, Lie groups (22-XX) 18 Number theory (11-XX) 6 Abstract harmonic analysis (43-XX) 4 Manifolds and cell complexes (57-XX) 2 Algebraic geometry (14-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX)
#### Citations contained in zbMATH
34 Publications have been cited 311 times in 245 Documents Cited by Year
Reducibility of generalized principal series representations. Zbl 0457.22011
Speh, Birgit; Vogan, David A. jun.
1980
Unitary representations of Gl(n,R) with non-trivial (g,K)-cohomology. Zbl 0505.22015
Speh, Birgit
1983
The unitary dual of $$Gl(3,R)$$ and $$Gl(4,R)$$. Zbl 0483.22005
Speh, Birgit
1981
Symmetry breaking for representations of rank one orthogonal groups. Zbl 1334.22015
Kobayashi, Toshiyuki; Speh, Birgit
2015
Absolute convergence of the spectral side of the Arthur trace formula for $$\text{GL}_n$$. Zbl 1083.11031
Müller, W.; Speh, B.; Lapid, E. M.
2004
On limit multiplicities of representations with cohomology in the cuspidal spectrum. Zbl 0626.22008
Rohlfs, Jürgen; Speh, Birgit
1987
Irreducible unitary representations of SU(2,2). Zbl 0543.22011
Knapp, A. W.; Speh, B.
1982
Degenerate series representations of the universal covering group of SU(2,2). Zbl 0415.22012
Speh, Birgit
1979
Automorphic representations and Lefschetz numbers. Zbl 0689.22005
Rohlfs, Jürgen; Speh, Birgit
1989
Status of classification of irreducible unitary representations. Zbl 0496.22018
Knapp, A. W.; Speh, B.
1982
A reducibility criterion for generalized principal series. Zbl 0367.22015
Speh, Birgit; Vogan, David
1977
Intertwining operators and the restriction of representations of rank-one orthogonal groups. Zbl 1283.22005
Kobayashi, Toshiyuki; Speh, Birgit
2014
Discrete components of some complementary series representations. Zbl 1197.22008
Speh, B.; Venkataramana, T. N.
2010
Lefschetz numbers and twisted stabilized orbital integrals. Zbl 0808.11039
Rohlfs, J.; Speh, B.
1993
Repesentations with cohomology in the discrete spectrum of subgroups of SO(n,1)($${\mathbb{Z}})$$ and Lefschetz numbers. Zbl 0626.22010
Rohlfs, Jürgen; Speh, Birgit
1987
Symmetry breaking for representations of rank one orthogonal groups. II. Zbl 1421.81003
Kobayashi, Toshiyuki; Speh, Birgit
2018
Discrete components of some complementary series. Zbl 1282.11054
Speh, Birgit; Venkataramana, T. N.
2011
On cuspidal cohomology of arithmetic groups and cyclic base change. Zbl 0780.11030
Rohlfs, Jürgen; Speh, Birgit
1992
Branching laws for some unitary representations of $$\mathrm{SL}(4,\mathbb C)$$. Zbl 1135.22014
Ørsted, Bent; Speh, Birgit
2008
Degenerate series representations for GL(2n,$${\mathbb{R}})$$ and Fourier analysis. Zbl 0715.22009
Barbasch, Dan; Sahi, Siddhartha; Speh, Birgit
1989
A cohomological method for the determination of limit multiplicities. Zbl 0631.22011
Rohlfs, Jürgen; Speh, Birgit
1987
The role of basic cases in classification: Theorems about unitary representations applicable to SU(N,2). Zbl 0524.22013
Knapp, A. W.; Speh, B.
1983
Unitary representations of SL(n,R) and the cohomology of congruence subgroups. Zbl 0516.22008
Speh, Birgit
1981
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups. Zbl 1341.22012
Speh, B.; Zhang, G.
2016
Pseudo Eisenstein forms and the cohomology of arithmetic groups. III: Residual cohomology classes. Zbl 1326.11025
Rohlfs, Jürgen; Speh, Birgit
2011
Construction of some generalised modular symbols. Zbl 1177.11041
Speh, B.; Venkataramana, T. N.
2005
Derived functors and intertwining operators for principal series representations of $$\mathrm{SL}_2(\mathbb R)$$. Zbl 1370.22012
Gomez, Raul; Speh, Birgit
2016
On the restriction of representations of $$SL(2, \mathbb C)$$ to $$SL(2, \mathbb R)$$. Zbl 1252.22001
Speh, B.; Venkataramana, T. N.
2012
Restriction of some representations of $$U(p,q)$$ to a symmetric subgroup. Zbl 1242.22021
Speh, Birgit
2011
Representation theory and the cohomology of arithmetic groups. Zbl 1130.11026
Speh, Birgit
2006
Analytic torsion and automorphic forms. Zbl 0845.57028
Speh, Birgit
1994
Lefschetz numbers and cyclic base change for purely imaginary extensions. Zbl 0787.11021
Rohlfs, Jürgen; Speh, Birgit
1992
Boundary contributions to Lefschetz numbers for arithmetic groups. I. Zbl 0853.22014
Rohlfs, Jürgen; Speh, Birgit
1990
Induced representations and the cohomology of discrete subgroups. Zbl 0505.22014
Speh, Birgit
1982
Symmetry breaking for representations of rank one orthogonal groups. II. Zbl 1421.81003
Kobayashi, Toshiyuki; Speh, Birgit
2018
Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups. Zbl 1341.22012
Speh, B.; Zhang, G.
2016
Derived functors and intertwining operators for principal series representations of $$\mathrm{SL}_2(\mathbb R)$$. Zbl 1370.22012
Gomez, Raul; Speh, Birgit
2016
Symmetry breaking for representations of rank one orthogonal groups. Zbl 1334.22015
Kobayashi, Toshiyuki; Speh, Birgit
2015
Intertwining operators and the restriction of representations of rank-one orthogonal groups. Zbl 1283.22005
Kobayashi, Toshiyuki; Speh, Birgit
2014
On the restriction of representations of $$SL(2, \mathbb C)$$ to $$SL(2, \mathbb R)$$. Zbl 1252.22001
Speh, B.; Venkataramana, T. N.
2012
Discrete components of some complementary series. Zbl 1282.11054
Speh, Birgit; Venkataramana, T. N.
2011
Pseudo Eisenstein forms and the cohomology of arithmetic groups. III: Residual cohomology classes. Zbl 1326.11025
Rohlfs, Jürgen; Speh, Birgit
2011
Restriction of some representations of $$U(p,q)$$ to a symmetric subgroup. Zbl 1242.22021
Speh, Birgit
2011
Discrete components of some complementary series representations. Zbl 1197.22008
Speh, B.; Venkataramana, T. N.
2010
Branching laws for some unitary representations of $$\mathrm{SL}(4,\mathbb C)$$. Zbl 1135.22014
Ørsted, Bent; Speh, Birgit
2008
Representation theory and the cohomology of arithmetic groups. Zbl 1130.11026
Speh, Birgit
2006
Construction of some generalised modular symbols. Zbl 1177.11041
Speh, B.; Venkataramana, T. N.
2005
Absolute convergence of the spectral side of the Arthur trace formula for $$\text{GL}_n$$. Zbl 1083.11031
Müller, W.; Speh, B.; Lapid, E. M.
2004
Analytic torsion and automorphic forms. Zbl 0845.57028
Speh, Birgit
1994
Lefschetz numbers and twisted stabilized orbital integrals. Zbl 0808.11039
Rohlfs, J.; Speh, B.
1993
On cuspidal cohomology of arithmetic groups and cyclic base change. Zbl 0780.11030
Rohlfs, Jürgen; Speh, Birgit
1992
Lefschetz numbers and cyclic base change for purely imaginary extensions. Zbl 0787.11021
Rohlfs, Jürgen; Speh, Birgit
1992
Boundary contributions to Lefschetz numbers for arithmetic groups. I. Zbl 0853.22014
Rohlfs, Jürgen; Speh, Birgit
1990
Automorphic representations and Lefschetz numbers. Zbl 0689.22005
Rohlfs, Jürgen; Speh, Birgit
1989
Degenerate series representations for GL(2n,$${\mathbb{R}})$$ and Fourier analysis. Zbl 0715.22009
Barbasch, Dan; Sahi, Siddhartha; Speh, Birgit
1989
On limit multiplicities of representations with cohomology in the cuspidal spectrum. Zbl 0626.22008
Rohlfs, Jürgen; Speh, Birgit
1987
Repesentations with cohomology in the discrete spectrum of subgroups of SO(n,1)($${\mathbb{Z}})$$ and Lefschetz numbers. Zbl 0626.22010
Rohlfs, Jürgen; Speh, Birgit
1987
A cohomological method for the determination of limit multiplicities. Zbl 0631.22011
Rohlfs, Jürgen; Speh, Birgit
1987
Unitary representations of Gl(n,R) with non-trivial (g,K)-cohomology. Zbl 0505.22015
Speh, Birgit
1983
The role of basic cases in classification: Theorems about unitary representations applicable to SU(N,2). Zbl 0524.22013
Knapp, A. W.; Speh, B.
1983
Irreducible unitary representations of SU(2,2). Zbl 0543.22011
Knapp, A. W.; Speh, B.
1982
Status of classification of irreducible unitary representations. Zbl 0496.22018
Knapp, A. W.; Speh, B.
1982
Induced representations and the cohomology of discrete subgroups. Zbl 0505.22014
Speh, Birgit
1982
The unitary dual of $$Gl(3,R)$$ and $$Gl(4,R)$$. Zbl 0483.22005
Speh, Birgit
1981
Unitary representations of SL(n,R) and the cohomology of congruence subgroups. Zbl 0516.22008
Speh, Birgit
1981
Reducibility of generalized principal series representations. Zbl 0457.22011
Speh, Birgit; Vogan, David A. jun.
1980
Degenerate series representations of the universal covering group of SU(2,2). Zbl 0415.22012
Speh, Birgit
1979
A reducibility criterion for generalized principal series. Zbl 0367.22015
Speh, Birgit; Vogan, David
1977
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#### Cited by 216 Authors
14 Speh, Birgit 11 Vogan, David Alexander jun. 10 Ørsted, Bent 9 Kobayashi, Toshiyuki 8 Dobrev, Vladimir K. 8 Rohlfs, Jürgen 7 Barbasch, Dan M. 7 Frahm, Jan 6 Zhang, Genkai 5 Collingwood, David H. 5 Deitmar, Anton 5 Li, Jian-Shu 5 Schwermer, Joachim 4 Baldoni-Silva, Maria Welleda 4 Clerc, Jean-Louis 4 Grobner, Harald 4 Kionke, Steffen 4 Lapid, Erez Moshe 4 Moeglin, Colette 4 Paul, Annegret 4 Sahi, Siddhartha 4 Schlichtkrull, Henrik 4 Shin, Sug Woo 3 Gourevitch, Dmitry 3 Grbac, Neven 3 Günaydin, Murat 3 Hanzer, Marcela 3 Knapp, Anthony William 3 Matumoto, Hisayosi 3 Muić, Goran 3 Müller, Werner 3 Pevzner, Michael 3 Salamanca-Riba, Susana A. 3 Sayag, Eitan 3 Shelstad, Diana 3 Sun, Binyong 3 Tadić, Marko 3 Templier, Nicolas 2 Andler, Martin 2 Ash, Avner 2 Bang-Jensen, Jesper 2 Bergeron, Nicolas 2 Blomer, Valentin 2 Boe, Brian Douglas 2 Bouaziz, Abderrazak 2 Brumley, Farrell 2 Clozel, Laurent 2 Delorme, Patrick 2 Finis, Tobias 2 Gan, Wee Teck 2 Gotsbacher, Gerald 2 Howe, Roger Evans 2 Huang, Jing-Song 2 Ichino, Atsushi 2 Januszewski, Fabian 2 Koufany, Khalid 2 Matz, Jasmin 2 Mezo, Paul 2 Müller, Werner G. 2 Ne’eman, Yuval 2 Paneitz, Stephen M. 2 Pavey, Mark 2 Raghuram, Anantharam 2 Renard, David A. 2 Savin, Gordan 2 Šijački, Djordje 2 Somberg, Petr 2 Su, Feng 2 Tan, Eng-Chye 2 Tauchi, Taito 2 Venkatesh, Akshay 2 Wilson, Raj 2 Wolf, Joseph Albert 2 Xiang, Zhengyu 2 Zhu, Chen-Bo 1 Al-Dweik, Ahmad Y. 1 Arancibia, Nicolás 1 Azad, Hassan 1 Bao, Yixin 1 Bars, Itzhak 1 Ben Saïd, Salem 1 Bhagwat, Chandrasheel 1 Blasius, Don 1 Borel, Armand 1 Branson, Thomas Patrick 1 Brega, Alfredo O. 1 Bushnell, Colin J. 1 Calegari, Frank 1 Cant, A. 1 Casian, Luis G. 1 Casselman, William A. 1 Chang, Jen-Tseh 1 Ciubotaru, Dan 1 Clare, Pierre 1 Dickson, Martin J. 1 Dong, Chao-Ping 1 Elstrodt, Jürgen 1 Emerton, Matthew 1 Enright, Thomas J. 1 Fermigier, Stéfane ...and 116 more Authors
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#### Cited in 64 Serials
25 Journal of Functional Analysis 16 Compositio Mathematica 16 Inventiones Mathematicae 14 Mathematische Annalen 13 Duke Mathematical Journal 12 Journal of Mathematical Physics 10 Advances in Mathematics 10 Transactions of the American Mathematical Society 6 Annals of Mathematics. Second Series 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Mathematische Zeitschrift 5 Bulletin of the American Mathematical Society. New Series 5 Transformation Groups 4 Journal of Algebra 4 Manuscripta Mathematica 4 Memoirs of the American Mathematical Society 4 International Journal of Mathematics 4 Selecta Mathematica. New Series 4 Representation Theory 4 Journal of the Institute of Mathematics of Jussieu 3 Communications in Mathematical Physics 3 Israel Journal of Mathematics 3 Acta Mathematica 3 Proceedings of the Japan Academy. Series A 3 Forum Mathematicum 3 Geometric and Functional Analysis. GAFA 2 Letters in Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 Annales de l’Institut Fourier 2 Journal of Number Theory 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Journal of the American Mathematical Society 2 Differential Geometry and its Applications 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 International Journal of Number Theory 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Journal d’Analyse Mathématique 1 Physics Letters. B 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Journal of Soviet Mathematics 1 Mathematische Nachrichten 1 Proceedings of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 The Journal of Geometric Analysis 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal de Théorie des Nombres de Bordeaux 1 Journal of Lie Theory 1 Journal of High Energy Physics 1 Science China. Mathematics 1 Kyoto Journal of Mathematics 1 Forum of Mathematics, Sigma 1 Annales Mathématiques du Québec 1 Journal de l’École Polytechnique – Mathématiques 1 Tunisian Journal of Mathematics
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#### Cited in 26 Fields
187 Topological groups, Lie groups (22-XX) 85 Number theory (11-XX) 27 Group theory and generalizations (20-XX) 26 Differential geometry (53-XX) 24 Nonassociative rings and algebras (17-XX) 22 Abstract harmonic analysis (43-XX) 17 Quantum theory (81-XX) 13 Algebraic geometry (14-XX) 13 Global analysis, analysis on manifolds (58-XX) 10 Manifolds and cell complexes (57-XX) 6 Special functions (33-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Operator theory (47-XX) 5 Algebraic topology (55-XX) 3 Associative rings and algebras (16-XX) 3 Partial differential equations (35-XX) 3 Relativity and gravitational theory (83-XX) 2 Combinatorics (05-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.
| 2021-01-24T03:16:55 |
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|
https://www.usgs.gov/center-news/volcano-watch-loihi-seamount-swarms-earthquake-activity
|
# Volcano Watch — Loihi seamount swarms with earthquake activity
Release Date:
Kīlauea Volcano continues to erupt from the episode 52 and 53 vents on the flank of the Puu Oo cone on the East Rift Zone. For the past several weeks, the lava flow has been confined within a tube system that extends from the vent area to the coast at Kamoamoa.
Loihi seamount swarms with earthquake activity
(Public domain.)
Kīlauea Volcano continues to erupt from the episode 52 and 53 vents on the flank of the Puu Oo cone on the East Rift Zone. For the past several weeks, the lava flow has been confined within a tube system that extends from the vent area to the coast at Kamoamoa. The lava continues to extend the coastline and has built the youngest bench of lava up to the level of the main lava delta. Explosive periods occasionally produce lava spatter at the ocean entry. These explosive episodes are strong enough to be recorded on a nearby seismometer. Several small slivers of the coastal bench have slid into the ocean, and the hazard at the coast remains high. The National Park Service has closed dangerous areas, and their signs and warning should be observed.
During a typical week, 300-400 located earthquakes occur beneath the Big Island as recorded on the U.S. Geological Survey's seismic network. However, only a few have magnitudes greater than 3.0, roughly the threshold for felt earthquakes. During the past two weeks, however, we recorded six such earthquakes, all of which occurred in a swarm beneath Loihi Seamount that began about 10:00 a.m. Tuesday, October 12. The largest of these earthquakes had a magnitude of about 3.6. In the first 24 hours, more than 120 earthquakes were recorded at Loihi Seamount. The next 24 hours saw only 15 more events, and the following 24 hours saw only about 12. Scattered earthquakes continued to occur beneath Loihi until early afternoon on October 17.
We have shown the region in which the earthquakes at Loihi Seamount occurred on the map, rather than plotting each earthquake. The earthquake swarm beneath Loihi Seamount is the eleventh such swarm since 1970. Earlier swarms occurred in 1971, 1972, 1975, 1984, 1985, 1986, 1988, 1989, 1990, and 1991. The previous Loihi swarm took place on December 19, 1991. It included about 22 earthquakes having magnitudes greater than 3.0, and several with magnitudes greater than 4.0, but the swarm did not last as long as this one. Those earthquakes were centered beneath the east flank and the 3,210-feet deep summit of the volcano.
These earthquake swarms are the primary evidence that Loihi Seamount is an active Hawaiian volcano and the youngest in the Hawaiian-Emperor volcanic chain, a string of over 125 volcanoes stretching across almost 3,700 miles of the north Pacific Ocean. The oldest volcanoes, those at the northwest end of the chain, formed about 80 million years ago, whereas the three youngest volcanoes, Mauna Loa, Kīlauea, and Loihi, are still active. Fresh, glassy lavas recovered from the summit and from the north and south rift zones, and active low-temperature hydrothermal vents near the summit and along the south rift zone, also attest to the youthfulness of Loihi Seamount. The earthquake data suggests that Loihi has become much more active in the last 10 years than in the previous decade. There is no seismic evidence of any Loihi activity between 1962 and 1971, when the first large swarm was recorded.
The locations and depths of earthquakes beneath Loihi are not well constrained, because all our seismic stations are located on the Island of Hawaii, more than 20 miles to the east and to the north. However, most of the earthquakes in this swarm appear to be about 6-9 miles deep and are located beneath the south rift zone and southwest flank of the volcano. For the first time during a swarm on Loihi, an ocean-bottom seismometer was operating on the summit of Loihi Seamount. The University of Hawaii at Manoa had a self-contained instrument package deployed on Loihi that included a seismometer and a pressure sensor. The data from these instruments, when combined with the seismic data recorded on our land-based network, will provide greatly improved information on the locations and depth of the Loihi earthquakes.
The moderate depths determined for these earthquakes suggest that they are caused by upward migration of magma to Loihi. Earthquakes such as these do not necessarily indicate that Loihi Seamount erupted. Ocean-bottom seismometers or pressure sensors, such as those in the University of Hawaii instrument package, or ocean bottom tilt meters, which have been tested on Loihi in the past, would help determine whether the earthquakes indicate an eruption or an intrusion within the volcano.
In the future, such instruments should be available on Loihi Seamount all the time because the University of Hawaii planned to install a fiber-optic cable from an area near Whittington Beach to Loihi Seamount in early 1995. The first permanent instruments will be installed on the end of the cable using the deep-diving sumbersible Pisces V, operated by the Hawaii Undersea Research Laboratory at the University of Hawaii. This installation has been named HUGO, which stands for Hawaii Undersea Geo-Observatory, and will be operated by the University with the data flowing through the Hawaiian Volcano Observatory. Once HUGO is installed, we will certainly develop a better understanding of the structure and activity of this youngest of Hawaiian volcanoes. In the meantime, the temporary self-contained instrument package just recovered will provide important data that will improve our understanding of Lo`ihi Seamount.
| 2019-12-10T16:16:47 |
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|
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2018.09.010
|
• •
### 缺失数据下的逆概率多重加权分位回归估计及其应用
• 出版日期:2018-09-25 发布日期:2018-09-25
### Inverse Probability Multiple Weighted Quantile Regression Estimation and Its Application with Missing Data
Tai Lingnan et al.
• Online:2018-09-25 Published:2018-09-25
Abstract: In the practical research, there is always an issue of missing data. This paper proposes a new effective estimation, inverse probability multiple weighted (IPMW) estimator, which is under MAR to deal with the problem of missing data in the linear quantile regression (QR) from the perspective of model inference. This method is based on the traditional inverse probability weighted (IPW) estimator, combined with the propensity score matching and the idea of model average. This method applies to situations where the response variable is independent and identically distributed (IID) or independent and identically distributed (INID) and also applicable to most missing scenarios. Based on the theoretical and simulation study, it is found that IPMW estimator is more robust than the traditional IPW estimator. Finally, by applying the IPMW to missing survey data, this paper analyzes the influence factors of consumption in middle income group and the different features of consumption among middle income group, and finds the SD of IPMW estimator is smaller than IPW estimator, and the estimation results are more robust.
| 2022-11-28T16:03:36 |
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