We show that the first-order system of difference equations zn+1 = αz a nw b n, wn+1 = βz c nw d n, n ∈ N0, where a, b, c, d ∈ Z, α, β ∈ C \ {0}, z0, w0 ∈ C \ {0}, is solvable in closed form, by finding closed form formulas of its solutions.

In this work, oscillatory behavior of solutions of a class of fourth order neutral functional difference equations of the form ∆ ( r(n)∆(y(n) + p(n)y(n−m)) ) + q(n)G(y(n− k)) = 0 is studied under the assumption ∞ ∑

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...

Change your habit to hang or waste the time to only chat with your friends. It is done by your everyday, don't you feel bored? Now, we will show you the new habit that, actually it's a very old habit to do that can make your life more qualified. When feeling bored of always chatting with your friends all free time, you can find the book enPDF the nested universal relation database model and the...

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.

The idea of contrast plays an important role in the analysis of information structure and discourse structure. In the literature on information structure, we encounter the concept of contrastive focus and of contrastive topic, and there is also the opinion that focus in general establishes a contrast. In the literature on discourse structure, it is commonly held that there is a discourse relati...

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.