This contribution proposes a decompositional iterative method for the steadystate analysis of Kronecker structured Markov chains [1]. The Markovian system, which is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions, is assumed to have irreducible subsystem matrices associated with local tr...

let x1;x2;...;xn have a jointly multivariate exchangeable normal distribution. in this work we investigate another proof of the independence of x and s2 using order statistics. we also assume that (xi ; yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

The paper presents a system theoretic analysis of network-of-networks which are formed from smaller factor networks via graph Kronecker products. We provide a compositional framework for extending trajectories, stabilizability, controllability and observability of the factor networks to that of the composite network-of-networks. We proceed to delve into the effectiveness of applying these compo...

We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n− 1, 1) which sp...

The Heisenberg product is an associative defined on symmetric functions which interpolates between the usual and Kronecker product. In 1938, Murnaghan discovered that of two Schur stabilizes. We prove analogous result for functions.

The group $SL(2,\mathbb{C})$ of all complex $2\times 2$ matrices with determinant one is closely related to the $\boldsymbol{\mathcal{L}}_{+}^\uparrow$ real $4\times 4$ representing restricted Lorentz transformations. This relation, sometimes called spinor map, fundamental importance in relativistic quantum mechanics and has applications also general relativity. In this paper we show how map ma...