As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices (a proper subset of H -matrices); that is, we show that the Schur complement of a generalized doubly diagonally dominant matrix is a generaliz...

A stronger version of the van der Waerden permanent conjecture asserts that if J„ denotes the n X n matrix all of whose entries are \/n and A is any fixed matrix on the boundary of the set ofnxn doubly stochastic matrices, then per(A/4 + (1 — \)Jn) as a function of X is nondecreasing in the interval [0, 1]. In this paper, we elucidate the relation of this assertion to some other conjectures kno...

We introduce a constructive method, by using a doubly stochastic measure, to describe all the copulas that, in view of Sklar’s Theorem, are able to connect a bivariate distribution to its marginals. We use this to give the lower and upper optimal bounds for all the copulas that extend a given subcopula.

In this paper, we use the Yoshida approximation to prove the existence and uniqueness of a solution for the backward doubly stochastic differential equation when the generator is monotone and continuous. Before that we present the results for existence and uniqueness of an adapted solution of the backward doubly stochastic differential equation under some generals conditions.

The algebraic structure of the set of doubly stochastic circulants is that of a semi-ring. The concept of a prime in the doubly stochastic circulants is introduced in this paper and examples are given. The classiication of a prime in the doubly stochastic circulants is equivalent to the solvability of a linear equation over a doubly stochastic circulant. A representation of doubly stochastic ci...

In this paper, we consider the relationships between the second order linear recurrences, and the generalized doubly stochastic permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n 1 Ln+1 = Ln + Ln 1 (1.2) where ...

The distributed averaging problem is to devise a protocol which will enable the members of a group of n > 1 agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar agreement variables. A typical averaging protocol can be modeled by a linear iterative equation whose update matrices are doubly stochastic. Building on the ideas proposed in [1...

To a unitary matrix U we associate a doubly stochastic matrix M by taking the modulus squared of each element of U. To study the connection between onset of quantum chaos on graphs and ergodicity of the underlying Markov chain, specified by M, we study the limiting distribution of the spectral gap of M when U is taken from the Circular Unitary Ensemble and the dimension N of U is taken to infin...

We study the calculation of the volume of the polytope Bn of n × n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices. The second involves the enumeration of “magic squares”, i.e., n×n non-negative integer matrices whose rows and columns a...

In the present we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms convex polytope. Finally, we study analogue of Birkhoff’s theorem for the class of doubly stochastic operators. Mathematics Subject Classification: 15A51, 15A63, 4...