Assume that Nm(x) denotes the density of the population at a point x at the beginning of the reproductive season in the mth year. We study the following impulsive reaction-diffusion model for any m ∈ Z+  u (m) t = div(A∇u(m) − au(m)) + f(u(m)) for (x, t) ∈ Ω× (0, 1] u(m)(x, 0) = g(Nm(x)) for x ∈ Ω Nm+1(x) := u(m)(x, 1) for x ∈ Ω for functions f, g, a drift a and a diffusion matrix A and Ω ⊂...

Abstract. In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Hölder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are i...

We derive explicit stability conditions for time-dependent difference equations with several delays in C n (the set of n complex vectors) and estimates for the size of the solutions. The growth rates obtained here are not necessarily decay rates. 1. Introduction. Stability of systems of difference equations with delays has been discussed by many authors, for example, see Gil' and Cheng [6], Zha...

In this paper, a class of impulsive difference equations with time-varying delays is considered. By establishing an impulsive delay difference inequality, some sufficient conditions ensuring all solutions either oscillate or tend to zero are obtained. An example is given to illustrate the feasibility of the obtained result. AMS Subject Classifications: 34K15, 34K10.

Social network analysis has drawn the attention of many researchers recently. As the advance of communication technologies, the scale of social networks grows rapidly. To capture the characteristics of very large social networks, graph sampling is an important approach that does not require visiting the entire network. Prior studies on graph sampling focused on preserving the properties such as...

The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums of monomials). We give recurrence formulae w.r.t. arbitrary affine frames. As a corollary, it is amusing that we can also give closed-form expressions in the case of the frame (r, s) for curves, and t...

This technical note deals with a modified algebraic Riccati equation (MARE) and its corresponding inequality and difference equation, which arise in modified optimal control and filtering problems and are introduced into the cooperative control problems recently. The stabilizing property of the solution to MARE is presented. Then, the uniqueness is proved for the almost stabilizing and positive...

In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a funct...

In 1964 A. Garsia gave a stunningly brief proof of a useful maximal inequality of E. Hopf. The proof has become a textbook standard, but the inequality and its proof are widely regarded as mysterious. Here we suggest a straightforward first step analysis that may dispel some of the mystery. The development requires little more than the notion of a random variable, and, the inequality may be int...

This paper contributes to the literature on obtaining unbiased estimates of neighborhood effects, explored in the context of a centralized social welfare state. We employ a longitudinal database comprised of all working age adults in metropolitan Sweden 1991–1999 to investigate the degree to which neighborhood income mix relates to subsequent labor incomes of adults and how this relationship va...