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Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem

Sedighe Khaleghzade, Mostafa Zangiabadi, Aljoša Peperko, Masoud Hajarian (2022)

Kybernetika

In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability...

Interval solutions of linear interval equations

Jiří Rohn (1990)

Aplikace matematiky

It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

Invariants of four subspaces

Gerry W. Schwarz, David L. Wehlau (1998)

Annales de l'institut Fourier

We consider problems in invariant theory related to the classification of four vector subspaces of an n -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.

Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.

Chu Wenchang (1997)

Collectanea Mathematica

A pair of simple bivariate inverse series relations are used by embedding machinery to produce several double summation formulae on shifted factorials (or binomial coefficients), including the evaluation due to Blodgett-Gessel. Their q-analogues are established in the second section. Some generalized convolutions are presented through formal power series manipulation.

Inversion des matrices de Toeplitz dont le symbole admet un zéro d’ordre rationnel positif, valeur propre minimale

Philippe Rambour, Abdellatif Seghier (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Cet article présente trois résultats distincts. Dans une première partie nous donnons l’asymptotique quand N tend vers l’infini des coefficients des polynômes orthogonaux de degré N associés au poids ϕ α ( θ ) = | 1 - e i θ | 2 α f 1 ( e i θ ) , où f 1 est une fonction strictement positive suffisamment régulière et α > 1 2 , α ∈ ℝ ∖ ℕ . Nous en déduisons l’asymptotique des éléments de l’inverse de la matrice de Toeplitz T N ( ϕ α ) au moyen d’un noyau intégral G α . Nous prolongeons ensuite un résultat de A. Böttcher et H. Windom relatif à l’asymptotique de la valeur propre...

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