We obtain some oscillation criteria for the Hamiltonian difference system (AY{t) = B{t)Y{t+\) + C{t)Z{t), I AZ{t) = -A{t)Y{t + 1) B*{t)Z{t), where A, B, C, Y, Z are dxd matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.

For matrix power series with coefficients over a field, the notion of a matrix power series remainder sequence and its corresponding cofactor sequence are introduced and developed. An algorithm for constructing these sequences is presented. It is shown that the cofactor sequence yields directly a sequence of Pad6 fractions for a matrix power series represented as a quotient B(z)-lA(z). When B(z...

Extended Abstract 1 Preliminaries. Following the spectral graph theory, a graph coloring technique and algebraic methods in graph theory (see [5], [13]), we continue a Coxeter spectral study the category Bigrn of connected non-negative loop-free edge-bipartite (signed) graphs ∆, with n ≥ 1 vertices (bigraphs, in short), and their morsifications introduced by the second named author in [22]-[25]...

We show that for k ≥ 3, given any matrix in GL(k,Z), there is a hyperbolic fully irreducible automorphism of the free group of rank k whose induced action on Z is the given matrix.

In this paper, a so-called auxiliary matrix polynomial Xn(z) and a true right formal orthogonal matrix polynomial (FOMP) A 1 n (z) is connected to each well-conditioned leading principal block submatrix of a given block Toeplitz matrix. From these two matrix polynomi-als, all other right FOMPs of block n of a system of block biorthogonal matrix polynomials with respect to the block Toeplitz mom...

We define the principal matrix solution Z(t, s) of the linear Volterra vector integro-differential equation x (t) = A(t)x(t) + t s B(t, u)x(u) du in the same way that it is defined for x = A(t)x and prove that it is the unique matrix solution of ∂ ∂t Z(t, s) = A(t)Z(t, s) + t s B(t, u)Z(u, s) du, Z(s, s) = I. Furthermore, we prove that the solution of x (t) = A(t)x(t) + t τ B(t, u)x(u) du + f (...

A 2-variable matrix B ∈ GLn(Z[u±1, v±1]) is defined for any n-string link, generalizing the Burau matrix of an nbraid. The specialization u = 1, v = t−1 recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t−1, v = 1 results in a matrix with a natural algebraic interpretation, and one that yields homological...

ABSTRACT. A 2-variable matrix B ∈ GLn(Z[u±1, v±1]) is defined for any n-string link, generalizing the Burau matrix of an n-braid. The specialization u = 1, v = t−1 recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t−1, v = 1 results in a matrix with a natural algebraic interpretation, and one that yields ...

In this paper, we provide a new approach for computing regular solutions of first-order linear difference systems. We use the setting of factorial series known to be very well suited for dealing with difference equations and we introduce a sequence of functions which play the same role as the powers of the logarithm in the differential case. This allows us to adapt the approach of [5] where we ...

The IR absorption spectrum of salicylhydroxamic acid (sha) isolated in an argon matrix at 12-21 K has been recorded. Calculations of all the possible entgegen and zusammen keto conformers of sha have been performed at the B3LYP/6-311++G(d,p) level of theory. The computed energies, optimized structures, and relative abundances show that sha exists in the matrix as the z,z,z,z-conformer [relative...