and Applied Analysis 3 The coefficients {ci ki (z)}, {di ti (z)} are meromorphic functions and small functions, S (r) = ∑T (r, a (i) ) +∑T(r, b (j) )

1 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Laboratory of Network Control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China 3 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 4 School of Communication and I...

Given a non-degenerate interval of real numbers D, and a continuous function f : Dk → D with k ≥ 2, we consider a kth-order difference equation of the form yn+1 = f (yn, . . . , yn−k+1); n = 0, 1, 2, . . .. We develop an easy-to-apply necessary condition so that all solutions of the above-mentioned equation are periodic of the same period. c © 2005 Elsevier Ltd. All rights reserved.

In this paper we consider the random difference equations S =d (X + S)Y and T =d X+TY , where =d denotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right-hand side are independent of (X,Y ). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at...

The purpose of this article is to prove several evaluations of determinants of matrices, the entries of which are given by the recurrence ai,j = ai−1,j−1+ai−1,j , i, j ≥ 2, with various choices for the first row a1,j and first column ai,1.

In this paper we present a uni1ed distributional study of the classical discrete q-polynomials (in the Hahn’s sense). From the distributional q-Pearson equation we will deduce many of their properties such as the three-term recurrence relations, structure relations, etc. Also several characterizations of such q-polynomials are presented. c © 2001 Elsevier Science B.V. All rights reserved.

The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction which was proposed by V. Kolmanovskii and L. Shaikhet and successfully used already for functional differential equations, for difference equations with discrete time, for difference equations with continuous time, is used he...

1 We investigate the zeros of polynomial solutions to the differential-difference equation P n+1 (x) = A n (x)P ′ n (x) + B n (x)P n (x), n = 0, 1,. .. where A n and B n are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent degree are interlac-ing. Our result holds for general classe...

will contain infinitely many prime terms — known as Mersenne primes. The Mersenne prime conjecture is related to a classical problem in number theory concerning perfect numbers. A whole number is said to be perfect if, like 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14, it is equal to the sum of all its divisors apart from itself. Euclid pointed out that 2k−1(2k − 1) is perfect whenever 2 − 1 is pr...

where a . 21, p . 0 and k [ N is fixed, has positive non-oscillatory solutions which converge to the positive equilibrium x 1⁄4 aþ 1: This result solves Open Problem 1 in Stević, 2005, On the recursive sequence xnþ1 1⁄4 aþ ðxpn21=xnÞ; Journal of Applied Mathematics and Computing 18(1–2), 229–234, as well as, Open Problem 1 in DeVault, Kent and Kosmala, 2003, On the recursive sequence xnþ1 1⁄4 p...