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Matrix-Variate Statistical Distributions and Fractional Calculus

Mathai, A., Haubold, H. (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...

Maximal column rank preservers of fuzzy matrices

Seok-Zun Song, Soo-Roh Park (2001)

Discussiones Mathematicae - General Algebra and Applications

This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.

Maximal solutions of two–sided linear systems in max–min algebra

Pavel Krbálek, Alena Pozdílková (2010)

Kybernetika

Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations A x = B x , with given coefficient matrices A and B . We present a polynomial method for...

Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges

Yi-Zheng Fan, Ying-Ying Tan, Xi-Xi Peng, An-Hong Liu (2016)

Discussiones Mathematicae Graph Theory

In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.

Max-min interval systems of linear equations with bounded solution

Helena Myšková (2012)

Kybernetika

Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where a b = max { a , b } , a b = min { a , b } . The notation 𝐀 𝐱 = 𝐛 represents an interval system of linear equations, where 𝐀 = [ A ̲ , A ¯ ] , 𝐛 = [ b ̲ , b ¯ ] are given interval matrix and interval vector, respectively, and a solution is from a given interval vector 𝐱 = [ x ̲ , x ¯ ] . We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.

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