The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...

In this paper some new sufficient conditions for the oscillation of solutions of the third order half-linear difference equations ∆ ( an(∆ (xn + bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 and ∆ ( an(∆ (xn − bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 are established. Some examples are presented to illustrate the main results.

This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it. Previous work is available at http://eprint.iacr.org/2016/212 In this work we provide low rank estimations for sequences generated by two different designs based on coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP...

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...

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.