The theory of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects. Moreover, such equations may exhibit several real world phenomena in physics, biology, engineering, etc. (see [3, 4, 20]). At the same time, the boundary value problems for impulsive differenti...

We characterize, up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positivity condit...

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...

Suppose rate of change of coefficients of a linear time-variant system modeled via a difference equation is restricted. The work presented herein is an attempt at developing an algorithm that determines regions in coefficient-space where such a system is guaranteed to be globally asymptotically stable. Such information can be extremely useful in many applications. Some previously published rela...

This article concerns the existence of non-oscillatory solutions for non-linear, nonhomogeneous differential equations. In these equations, the unknown function depends on distributed arguments that can be retarded or advanced and have variable delays. Using contraction mappings, we show the existence of solutions, and estimate their norms. Then our results are extended to dynamic equations on ...

We present an oscillation criterion for first order delay dynamic equations on time scales, which contains well-known criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.

Evaluation routines are essential for any application that uses triangular B-spline surfaces. This paper describes an algorithm to efficiently evaluate triangular B-spline surfaces with arbitrary many variables. The novelty of the algorithm is its generality: there is no restriction on the degree of the B-spline surfaces or on the dimension of the domain. Constructing an evaluation graph allows...

We consider orthogonal polynomials {pn,N(x)}n=0 on the real line with respect to a weight w(x) = e (x) and in particular the asymptotic behaviour of the coefficients an,N and bn,N in the three term recurrence xπn,N (x) = πn+1,N (x)+bn,Nπn,N (x)+an,Nπn−1,N (x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrenc...

In this paper, by defining a class of functions, we establish some oscillation criteria for the second order nonlinear dynamic equations with forced term x (t) + a(t)f(x(q(t))) = e(t) on a time scale T. Our results unify the oscillation of the second order forced differential equation and the second order forced difference equation. An example is considered to illustrate the main results.

A class of representations of the canonical commutation relations is investigated. These representations, which are called exponential representations, are given by explicit formulas. Exponential representations are thus comparable to tensor product representations in the sense that they provide the possibility of computing useful criteria concerning various properties. In particular, they are ...