We analyze properties of a map f sending a unitary matrix U of size N into a doubly stochastic matrix B = f (U) defined by Bi,j = |Ui,j| 2. For any U we define its defect, determined by the dimension of the image Df (TU U) of the space TU U tangent to the manifold of unitary matrices U at U under the tangent map Df corresponding to f. The defect, equal to zero for a generic unitary matrix, give...

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...

Given an n-vertex graph G, the matrix Ω(G) = (In + L(G))−1 = (ωij) is called the doubly stochastic graph matrix of G, where In is the n × n identity matrix and L(G) is the Laplacian matrix of G. Let ω(G) be the smallest element of Ω(G). Zhang and Wu [X.D. Zhang and J.X. Wu. Doubly stochastic matrices of trees. Appl. Math. Lett., 18:339–343, 2005.] determined the tree T with the minimum ω(T ) am...

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...

In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are d...