This paper defines Structured Markovian Arrival Processes (SMAPs). An SMAP consists of several blocks each being represented by a random variable specifying the duration of staying in that block. Leaving a block indicates an arrival event of the SMAP. The routing between blocks is governed by a stochastic matrix Q. It is shown that the joint moments of the SMAP can be directly determined from t...

Design matrices are sparse matrices in which the supports of different columns intersect in a few positions. Such matrices come up naturally when studying problems involving point sets with many collinear triples. In this work we consider design matrices with block (or matrix) entries. Our main result is a lower bound on the rank of such matrices, extending the bounds proven in [BDWY12, DSW14] ...

We generalize in various directions a result of Friedland and Karlin on a lower bound for the spectral radius of a matrix that is positively diagonally equivalent to a • The research of these authors was supported by their joint grant No. 90-00434 from the United States-Israel Binational Science Foundation, Jerusalem, Israel. t The research of this author was supported in part by NSF Grant DMS-...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

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 ...