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.

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...