We study the semialgebraic structure of Dr, the set of nonnegative tensors of nonnegative rank not more than r, and use the results to infer various properties of nonnegative tensor rank. We determine all nonnegative typical ranks for cubical nonnegative tensors and show that the direct sum conjecture is true for nonnegative tensor rank. Under some mild condition (non-defectivity), we show that...

in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

is known to be stable if and only if ρ(A) < 1. Models of real world dynamical phenomena often involve positive quantities. A dynamical system (1) is called positive if any trajectory of the system starting in the positive orthant R+ remains in R+. In this case, the matrix A has only real positive entries. In many cases, it may be useful to consider systems with a known “nominal” part A and a un...

In this paper, the nonnegative Q-matrix completion problem is studied. A real n × n matrix is a Q-matrix if for k ∈ {1, . . . , n}, the sum of all k × k principal minors is positive. A digraph D is said to have nonnegative Q-completion if every partial nonnegative Q-matrix specifying D can be completed to a nonnegative Q-matrix. For nonnegative Q-completion problem, necessary conditions and suf...