We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 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 positive conditions ([9]). Th...

In a wide subclass of generalized order statistics, representations of marginal density and distribution functions are developed. The results are applied to obtain several relations, such as recurrence relations, and explicit expressions for the moments of generalized order statistics from Pareto, power function and Weibull distributions. Moreover, characterizations of exponential distributions...

Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall’s inequality we determine function bounds for the solutions of the integro dynamic equation.

This note provides new quantitative bounds for the recursive equation yn+1 = A + yn yn−k , n = 0, 1, . . . , where y−k , y−k+1, . . . , y−1, y0, A ∈ (0,∞) and k ∈ {2, 3, 4, . . .}. Issues regarding exponential convergence of solutions are also considered. In particular, it is shown that exponential convergence holds for all (A, k) for which global asymptotic stability was proven in [R.M. Abu-Sa...

A nonlinear integro-differential equation of convolution type with order of nonlinearity more than one and a stable trivial solution is considered. The integral in this equation has an exponential kernel and polynomial integrand. The difference analogue of the equation considered is constructed in the form of a difference equation with continuous time and it is shown that this difference analog...

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...

An analysis of the long-term light curve of the intermediate polar DO Dra is presented. The courses of the outbursts were resolved and their light curves are analyzed. The decays of the respective outbursts are faster than exponential. The decay rate τ D = 0.92 days mag −1 vis in comparison with 1.68 days mag −1 vis for non-magnetic systems and suggests that the magnetosphere is not fully compr...

We give sufficient conditions for the exponential stabilizability of a class of perturbed time-varying difference equations with multiple delays and slowly varying coefficients. Under appropiate growth conditions on the perturbations, combined with the “freezing” technique, we establish explicit conditions for global feedback exponential stabilizability. Copyright q 2009 Medina Rigoberto. This ...

It is investigated the behaviour of the “constants” G, c and Λ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a c−variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving to the conclusion that if q < 0 (deceleration parameter) then G, c are growing functions on time t while Λ is a negati...