Let QBn be the set of n x n (n > 8) non-symmetric primitive matrices with at least one pair of nonzero symmetric entries. For each positive integer 2 ::; k ::; n 2, we give the kth upper generalized exponent set for Q Bn by using a graph theoretical method.

We construct, for every even n, a set of n points in the plane that generates Ω ne √ ln 4· √ ln n/ √ ln n halving edges. This improves Tóth’s previous bound by a constant factor in the exponent. Our construction is significantly simpler than Tóth’s.

We examine the stability of a 1D electrical transmission line in simultaneous presence PT-symmetry and fractionality. The array contains binary gain/loss distribution $\gamma_{n}$ fractional Laplacian characterized by exponent $\alpha$. For an infinite periodic chain, spectrum is computed closed form, its imaginary sector examined to determine stable/unstable regions as function strength expone...

Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree n, and 2) by all but one conjugates of algebraic integers of degree n + 1.

Let us denote by Fn the n-th Fibonacci number. In this paper we show that for a fixed integer y there exists at most one exponent > 0 such Diophantine equation + Fm = ya has solution (n; m; a) in positive integers satisfying n m 0, unless 2; 3; 4; 6 or 10.

We give a new bound on the exponent for nonexistence of stable solutions to the biharmonic problem ∆u = u, u > 0 in R where p > 1, n ≥ 20.

A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear flow. We derive a generalized Boltzmann equation for an extended one-particle distribution that includes deviations from the reference phase space point. Th...

Let G be a finite additive abelian group with exponent exp(G) = n > 1 and let A be a nonempty subset of {1, . . . , n − 1}. In this paper, we investigate the smallest positive integer m, denoted by sA(G), such that any sequence {ci}i=1 with terms from G has a length n = exp(G) subsequence {cij}nj=1 for which there are a1, . . . , an ∈ A such that ∑n j=1 aicij = 0. When G is a p-group, A contain...