In this paper, some sufficient conditions for oscillation of the second-order nonlinear neutral delay dynamic equation (r(t)([y(t)+ p(t)y(t − )] ) ) + f (t, y(t − ))= 0, on a time scale T are established; here 1 is an odd positive integer with r(t) and p(t) are rd-continuous functions defined on T. Our results as a special case when T = R and T = N, involve and improve some well-known oscillati...

It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form xn+1 = a + bxn−1en , yn+1 = c + dyn−1en , where a, b, c, d are positive constants, and the initial values x−1, x0, y−1, y0 are positive real values. © 2011 Elsevier Ltd. All rights reserved.

The scalar difference equation xn+1 = fn(xn, xn−1, · · · , xn−k) may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally using the semiconjugate relation on a group which yields a reduction of order through the semiconjugate factorization of the difference equation of order k + 1 into equat...

In this paper, we define a new kind of the hypergeometric function, say, Hermite-Tricomi functions. An explicit representation, recurrence relations for the Hermite-Tricomi functions are given and differential equations satisfied them is presented. A new expansions of the exponential for a wide class of functions, whose properties, including recurrences, addition theorems, generating functions ...

A new, non-statistical method is presented for analysis of the past history and current evolution of economic and financial processes. The method is based on the sliding model approach using linear differential or difference equations applied to discrete information in the form of known chronological data (time series) about the process. An algorithm is proposed that allows one to project the c...

Deene transportation polytope Tn;m to be a polytope of nonnegative n m matrices with row sums equal to m and column sums equal to n. We present an eecient algorithm for computing the numbers f k of the k-dimensional faces for the transportation polytope T n;n+1. The construction relies on the new recurrence relation for the numbers f i , which is of independent interest.

Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N , there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, andwithEN+1=E( N+1) if and only if contiguous eigenvalues a...

In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of...

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations r t xΔ t γ Δ p t f x τ t 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r and p real-valued positive rdcontinuous functions defined on T. Our results not only extend some results established by Hassan in 2008 but also unify ...

A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover’s enumerative scheme, recurrence relations for calculating the number of these sequences are derived. Implementation of encoding and decoding procedures is also shown.