We present an upper bound O(n 2) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant, and nd tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion process on a circle indeed mixes more rapidly than the corresponding symmetric process.

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decisionmaking, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to c...

For a non-autonomous dynamics with discrete time defined by tempered sequence of upper-triangular matrices, we obtain lower and upper bounds for the Grobman regularity coefficients. We also give two applications these results: an bound coefficients exterior powers sequence, simple proof Oseledets' multiplicative ergodic theorem cocycles over measure-preserving transformation without using Kingm...

We prove a lower bound of 52n2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

We consider decidability questions for the emptiness problem of intersections of matrix semigroups. This problem was studied by A. Markov [7] and more recently by V. Halava and T. Harju [5]. We give slightly strengthened results of their theorems by using a different matrix encoding. In particular, we show that given two finitely generated semigroups of non-singular upper triangular 3× 3 matric...

We show that it is undecidable for finite sets S of upper triangular 4 × 4matrices over Z[x, x−1] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of the Laurent polynomials of the first row. This result follows from a representations of the integer weighted finite automata by matrices over Laurent polynomials.

We compute all the relations in cohomology satisfied by the elements of degree two of H∗(Un(Fp), Z) where p ≥ n and Un(Fp) is the group of of upper triangular matrices of GLn(Fp) with 1 on the main diagonal. e-mail: [email protected]

We consider positive entropy G-systems for certain countable, discrete, infinite left-orderable amenable groups G. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the stable sets. Examples are given for the case of integer lattice groups, the Heizenberg group, and the groups of integral unipotent upper triangular matrices.