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Abstract: Applying a fixed-point theorem of strict-set-contractions, some new criteria are established for the existence of positive periodic solutions of the following neutral differential system with feedback control. [Copyright &y& Elsevier]

Abstract: New oscillation criteria are established for second-order differential equations containing both delay and advanced arguments of the form, where α ≥ 1 and β ≥1; k, p, q, e, τ, σ are continuous real-valued functions; k(t) > 0 is nondecreasing; τ and o are nondecreasing, τ(t) ≥ t, σ(t) ≥ t, and lim t → ∞ τ(t) = ∞ The potentials p, q, and e are allowed to change sign and the information on the whole half-line is not required as opposed to the usual case in most articles. Among others, as an application of the results we are able to deduce that every solution of is oscillatory provided that either m 1 orm 2 is sufficiently large. [Copyright &y& Elsevier]

Abstract: By using averaging functions, new interval oscillation criteria are established for the second-order functional differential equation,that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [t 0, ∞], rather than on the whole half-line. Our results can be applied to three cases: ordinary, delay, and advance differential equations. In the case of half-linear functional differential equations, our criteria implies that the τ(t) ≤ t delay and Gt(t) ≥ t advance cases do not affect the oscillation. In particular, several examples are given to illustrate the importance of our results. [Copyright &y& Elsevier]

Abstract: In this paper, harmonic wavelets, which are analytically defined and band limited, are studied, together with their differentiable properties. Harmonic wavelets were recently applied to the solution of evolution problems and, more generally, to describe evolution operators. In order to consider the evolution of a solitary profile (and to focus on the localization property of wavelets), it seems to be more expedient to make use of functions with limited compact support (either in space or in frequency). The connection coefficients of harmonic wavelets are explicitly computed (in the following) at any order, and characterized by some recursive formulas. In particular, they are functionally and finitely defined by a simple formula for any order of the basis derivatives. [Copyright &y& Elsevier]

Abstract: In this paper, the author investigates two-species nonautonomous delay diffusive preypredator models with Michaelis-Menten functional response. Sufficient conditions are derived for permanence of the species. Further, the author also establishs the sufficient conditions that guarantee the arbitrary positive periodic solution of the systems is global attractive. [Copyright &y& Elsevier]

Abstract: In this paper, nutrient-phytoplankton-zooplankton interaction with general uptake functions in which nutrient recycling is either instantaneous or delayed is considered. To account for higher predation, zooplankton''s death rate is modeled by a quadratic term instead of the usual linear function. Persistence conditions for each of the delayed and nondelayed models are derived. Numerical simulations with data from the existing literature are explored to compare the two models. It is demonstrated numerically that increasing zooplankton death rate can eliminate periodic solutions of the system in both the instantaneous and the delayed nutrient recycling models. However, the delayed nutrient recycling can actually stabilize the nutrient-plankton interaction. [Copyright &y& Elsevier]

Abstract: We consider the ratio T(x, y) = г(x)г(y) / г2((x + y)/2) and its properties related to convexity, logarithmic convexity, Schur-convexity, and complete monotonicity. Several new bounds and asymptotic expansions for T are derived. Sharp bounds for the function x → x/(1 - e −x ) are presented, as well as bounds for the trigamma function. The results are applied to a problem related to the volume of the unit ball in R n and also to the problem of finding the inverse of the function x → T(1/x, 3/x), which is of importance in applied statistics. [Copyright &y& Elsevier]

In this paper, the lower bounds of Bloch constants Bn, for functions with multiplicity at least n, are improved by showing [Copyright &y& Elsevier]

After recalling the most important properties and applications of the Bell polynomials, we introduce an extension of this special class of functions. More precisely, we consider the case of multicomposite functions, and we show connections with the ordinary Bell polynomials. [Copyright &y& Elsevier]