let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

In this talk, we presented the Birkhoff-von Neumann type theorem for a multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multi-stochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly-stochastic matrices are just permutation matrices. However, we find that extreme poin...