On Brauer–Ostrowski and Brualdi sets

Ela on the Brualdi-li Matrix and Its Perron Eigenspace

The n × n Brualdi-Li matrix Bn has recently been shown to have maximal Perron value (spectral radius) ρ among all tournament matrices of even order n, thus settling the conjecture by the same name. This renews our interest in estimating ρ and motivates us to study the Perron eigenvector x of Bn, which is normalized to have 1-norm equal to one. It follows that x minimizes the 2-norm among all Pe...

Gershgorin-Brualdi Perturbations and Riccati Equations

For uncertain linear systems with complex parameter perturbations of static output feedback type a quadratic Liapunov function of maximal robustness was constructed in [5]. Such Liapunov functions can be used to ensure the stability of uncertain systems under arbitrary nonlinear and time-varying perturbations which are smaller than the stability radius. In this paper we establish analogous resu...

On bD-Sets and Associated Separation Axioms

On a Generalization of the Ryser-Brualdi-Stein Conjecture

A rainbow matching for (not necessarily distinct) sets F1, . . . , Fk of hypergraph edges is a matching consisting of k edges, one from each Fi. The aim of the paper is twofold to put order in the multitude of conjectures that relate to this concept (some of them first presented here), and to present some partial results on one of these conjectures, that seems central among them.

on semihypergroups and hypergroups

in this thesis, first the notion of weak mutual associativity (w.m.a.) and the necessary and sufficient condition for a $(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some family of $lesssim$-preordered semigroups to be a hypergroup, are given. second, by proving the fact that the concrete categories, semihypergroups and hypergroups have not free objects we will introduce t...