In the single source unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given digraph. The demand of each commodity must be routed along a single path. In a groundbreaking paper Dinitz, Garg, and Goemans [4] prove that any given (splittable) flow satisfying certain demands can be turned into an unsplittable flow ...

We continue our recent efforts to exploit the notion of a unitary isotope to study convex combinations of unitaries in an arbitrary JB∗-algebra. Exact analogues of C∗-algebraic results, due to R. V. Kadison, C. L. Olsen and G. K. Pedersen, are proved for general JB∗-algebras. We show that if a contraction in a JB∗-algebra is a convex combination of n unitaries, then it is also a mean of n unita...

It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general ...

where T and S are diagonal m.by.m and n-by-n real matrices, respectively with diagonal entries from [0, 1]. Our goal is to characterize the above sets with respect to the inheri tance of rank r , which is meant that each matr ix f rom these sets is of rank r . It should b e noted that, for square and nonsingular A and B, nonsingulari ty o f our sets has been studied in [2]. We shall dose this s...