where detξ denotes the determinant of ξ, and (C4) W (PξQ) = W (ξ) for all ξ ∈ M and all P,Q ∈ SO(3) for N = 3, with SO(3) := {Q ∈ M : QQ = QQ = I3 and detQ = 1}, where I3 denotes the identity matrix in M 3×3 and Q is the transposed matrix of Q. (In fact, (C4) is an additional condition which is not related to (2). However, it means that W is frame-indifferent, i.e., W (Pξ) = W (ξ) for all ξ ∈ M...

Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integer powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P. Slightly generalizing [H-H], we define a multiparameter deformation Lλ/μVP of the classical skew Schur module. In case R is a field and q is not a root of 1, arguments like t...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

We construct a Q-matrix for the eight-vertex model at roots of unity for crossing parameter η = 2mK/L with odd L, a case for which the existing constructions do not work. The new Q-matrix Q̂ depends on the spectral parameter v and also on a free parameter t. For t = 0 Q̂ has the standard properties. For t 6= 0, however, it does not commute with the operator S and not with itself for different val...

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

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...

Example 1B. Here we extend the analysis of Example 1B to censored regression models with random coefficients. Let us assume for simplicity that B (x, θ) has full-column rank q, for all θ, almost surely in x. Let V be a T × q matrix such that Q = V V ′ and V ′V = Iq. Let also U be a T × (T − q) matrix such that W = UU ′, and U ′U = IT−q. Lastly, let (μ, ν) = ( V ′Σ− 1 2 y, U ′Σ− 1 2 y ) . Then, ...