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31 results for “Symmetry”
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Research ArticleOpen accessEvery word in the titleMeasure of Departure from Partial Symmetry for Square Contingency TablesYusuke Saigusa, Kouji Tahata, Sadao TomizawaFor square contingency tables, the present paper newly considers the partial symmetry model which indicates that there is a symmetric structure of probabilities for at least one of pairs of symmetric cells. It also proposes the measure to express the degree of departure from the partial symmetry model. Examples are given. …Journal of Mathematics and Statistics, Vol. 12, Issue 3 · 9 Aug 2016 · 7,416 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAnalysis of Unaided Vision Data using New Decomposition of SymmetryKouji Yamamoto, Sadao TomizawaProblem statement: First, this study considers how the structure of symmetry for probabilities is decomposed into two structures. Secondly, this study infers the structure of unknown probabilities which indicates how the right eye is better (or worse) than the left eye for three kinds of data on unaided distance vision of (1) women in Britain, (2) students in an university … …Current Research in Medicine, Vol. 3, Issue 1 · 25 Feb 2012 · 7,449 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleDecompositions for Ordinal Quasi-Symmetry Model in Square Contingency Tables with Ordered CategoriesKouji Yamamoto, Satoru Shinoda, Sadao TomizawaProblem statement: For square contingency tables with ordered categories, this study considers four kinds of extensions of the marginal homogeneity model and gives decompositions for the ordinal quasi-symmetry model. The decompositions are extensions of some existing decompositions. Approach: This study gives a decomposition theorem that the ordinal quasi-symmetry model holds if and only if the quasi-symmetry model and the proposed … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 28 Oct 2011 · 7,152 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleSymmetry of Nonparametric Statistical Tests on Three SamplesAnna E. Bargagliotti, Donald G. SaariProblem statement: Many different nonparametric statistical procedures can be used to analyze ranked data. Inconsistencies among the outcomes of such procedures can occur when analyzing the same ranked data set. Understanding why these peculiarities can occur is imperative to providing an accurate analysis of the ranking data. In this context, this study addressed why inconsistent outcomes can occur and which … …Journal of Mathematics and Statistics, Vol. 6, Issue 4 · 4 Nov 2010 · 7,071 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleMeasure of Departure from Average Cumulative Symmetry for Square Contingency Tables with Ordered CategoriesKouta Miyazawa, Sadao Tomizawa, Kouji TahataProblem statement: For square contingency tables with ordered categories, we are interested in considering a structure of weak symmetry when Bowker's symmetry model does not hold and in measuring the degree of departure from weak symmetry. Approach: The present study considered the average cumulative symmetry model that has a weaker restriction than the structure of symmetry. It also gave a … …Current Research in Biostatistics, Vol. 1, Issue 1 · 30 Jun 2010 · 7,621 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleMeasure of Departure from Conditional Partial Symmetry for Square Contingency TablesYusuke Saigusa, Nobuki Fukumoto, Tomoyuki Nakagawa, Sadao TomizawaFor square contingency tables, asymmetry of conditional probability in part of the off-diagonal cells isconsidered with respect to the main diagonal. A measure is proposed torepresent the degree of departure from the symmetric structure and gives theapproximate confidence interval. Some numerical experiments are performed toillustrate the validity and usefulness of the proposed measure. Japaneseoccupational data are analyzed using the measure. …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 4 Oct 2022 · 5,561 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleCircular Rydberg States of Lithium Atoms or Lithium-Like Ions in a High-Frequency Laser Field: The Break of the Algebraic SymmetryNikolay Kryukov, Eugene OksBeletsky, V. V. (2001). Essays on the Motion of Celestial Bodies (1st ed.). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8360-3 Bethe, H. A., & Salpeter, E. E. (1957). Quantum Mechanics of One- and Two-Electron Atoms (1st ed.). Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12869-5 Kapitza, P. L. (1951a). A pendulum with oscillating suspension. Uspekhi Fizicheskikh Nauk, 44(1), 7–20. Kapitza, P. L. (1951b). Dynamic stability of a pendulum … …Physics International, Vol. 13, Issue 1 · 5 Mar 2022 · 7,161 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleREFLECTION OF A WEAK DISCONTINUITY OF THE AXIS AND THE PLANE OF SYMMETRYBulat Pavel ViktorovichIn this article we consider the problem of discontinuous characteristic (weak discontinuity) reflection from the axis and the plane of symmetry of the supersonic flow. There is a known problem of perturbations radial focusing when during numerical calculations reflection of a weak perturbation wave from the axis of symmetry leads to an abrupt change in the distribution of dynamics variables … …American Journal of Applied Sciences, Vol. 11, Issue 6 · 17 Apr 2014 · 6,529 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Variational Symmetries of P.D.E's Incorporating Boundary Value ConstraintsUchechukwu Michael Opara, Festus Irimisose Arunaye et al.A crucial interface between Optimization theory, Trace theory, and Lie Symmetry theory is brought to the fore in this paper, as an enhancement of standard known results established in Partial Differential Equation (P.D.E) analysis. In particular, the incorporation of compatible Boundary Value constraints in the re-assessment of admitted variational symmetries is a key process in the development of the discussions … …Journal of Mathematics and Statistics, Vol. 21, Issue 1 · 22 Jan 2025 · 8,433 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Bacterial Chromosomal Sequence and Related IssuesThi Huyen Phan, Duc Luong NguyenThere has been a rapid increasing in the number of bacterial genomes that are completely sequenced recently. However, nucleotide arrangement in bacterial chromosome is still not clear, though it is known that the chromosomal strand is symmetric as a whole but asymmetric locally. The unequal distribution of adenine and thymine as well as cytosine and guanine in the local genomic … …Current Research in Virology, Vol. 2, Issue 1 · 29 Jul 2013 · 13,208 accessesView PDFCite