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On the compatibility of Dyson’s conditions

Statistics & Probability Letters, 2008
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Berenhaut, Kenneth S.   +2 more
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Compatible Conditional Distributions

Journal of the American Statistical Association, 1989
Abstract Consider two families of candidate conditional densities (or probability mass functions), {f(x | y);y ∈ S y} and {f(y | x): x ∈ S x}. This article investigates necessary and sufficient conditions for the existence of a joint density (or joint probability mass function) f(x, y) with the given families as its associated conditional densities ...
Barry C. Arnold, S. James Press
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On kinematic conditions of compatibility

Journal of Elasticity, 1991
Let \(C\) and \(\overline C\) denote two symmetric positive definite constant matrices. It follows from linear algebra that there are matrices \(F\) and \(\overline F\) such that: (*) \(F^ T F=C\), \(\text{det} F>0\); \(\overline{F}^ T\overline{F}=\overline C\), \(\text{det} \overline F>0\).
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A Note on the Compatibility Conditions of Finite Deformations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1987
In this short note the author studies the compatibiity conditions of finite deformations from a different point of view. In continuum mechanics, in order to obtain a single valued and continuous displacement field u from a given Cauchy-Green strain tensor \({\mathbb{C}}\), which has six independent components, certain differential relations which are ...
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A Necessary Condition and a Sufficient Condition for Pairwise Compatibility Graphs

2016
In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let \(G^c\) be the complement of G. We show that if \(G^c\) has two disjoint chordless cycles then G is not a PCG. On the other hand, if \(G^c\) has no cycle then G is a PCG.
Md. Iqbal Hossain 0001   +2 more
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