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Abstract: A multiplicative calculus dealing with real valued functions is extended to a multiplicative type complex calculus (MCC) dealing with complex valued functions. Some fundamental theorems and concepts of the classical calculus are interpreted from the view point of the MCC and the analogies between them are given. Also new notations for the MCC are defined. The MCC is distinguished from the classical calculus by calling the classical calculus as the additive type complex calculus (ACC). [ABSTRACT FROM AUTHOR]

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: We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They arise considering the derivatives of functions f in several variables φ(i), (i = 1, 2, …, m), where φ(i) are composite functions of different orders, i.e. φ(i) (t) = (i,1) ((i,2) (… ((i,ri ) (t))), (i = 1, 2, …, m). We show that these new polynomials are always expressible in terms of the ordinary Bell polynomials, by means of suitable recurrence relations or formal multinomial expansions. Moreover, we give a recurrence relation for their computation. [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 concept of strong homomorphism of fuzzy group in the sense of [] is given. The fundamental homomorphism theorem of fuzzy group, in the sense of strong homomorphism, is also obtained. We built a category FGrp of fuzzy groups and strong homomorphism and show that category FGrp and the category Grp of group and homomorphism are not equivalent. These discussions show that fuzzy group is different from classical group. [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]

This paper is concerned with the limit circle and limit point criteria of second-order linear difference equations. A sufficient and necessary condition, a sufficient and necessary condition subject to a certain restriction, and several sufficient conditions are established. These results improve and extend some previous results. [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]

For the second-order delay differential equation y″(t)+a(t)y′(t)+∑lower limit i=1, upper limit n pi(t)y(gi(t))=0, t>0, t≠tk with impulsive conditions y(tκ+)-y(tκ−)=bκy(tκ−), y′(tκ+)-y′(tκ−)=bκy′(tκ−), an explicit necessary and sufficient condition for all bounded solutions to be oscillatory is obtained by the comparison theorem on bounded oscillation of the impulsive differential equation with the corresponding nonimpulsive differential equation. [Copyright &y& Elsevier]

Suppose E is a uniformly smooth Banach space and T : E → 2E is a multivalued φ-hemicontractive operator with bounded range. Suppose {an}, {bn}, {cn} and {an′}, {bn′} {cn′} are real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = a′n + b′n + c′n = 1, for all n ∊N; (ii) limn→∞ bn = limn→∞b′n = limn→∞ cn = 0; (iii) ∑∞n=1 bn = ∞; (iv) cn = o(bn). For arbitrary xi, u1, v1 ∊ E, define the sequence {xn}n=1∞ by xn+1 = anxn+bnηn+cnun, ∃ ηn ∊ Tyn, n ∊ N; yn = a′nxn + b′nξn + c′nvn ∃ξn ∊ Txn, n ∊ N, where {un}n=1∞ {vn}n=1∞ are arbitrary bounded sequences in E. Then {xn}n=1∞ converges strongly to the unique fixed point of T. Related results deal with the iterative solutions of nonlinear multivalued φ-accretive operator equation f ∊ Tx. [Copyright &y& Elsevier]

In this paper, we consider the approximate solution of the following problem. Given ω⊂RN (1 ⪯ N ⪯ 3), find u(x, t) such that ∂tb(u)−Δu+Pe▽u=0, in Q&z.tbnd;ω×(0,T), u=0, on ∑&z.tbnd;∂ω×(0,T), u(x,0)=u0(x), ∀x∈ω, where the function b(s) is a monotonically increasing function satisfying 0 ⪯ b′ ⪯ ∞ To solve this problem, we introduce a new nonstandard time discretization scheme. We prove stability and convergence results. [Copyright &y& Elsevier]

In this paper, we study a class of difference systems modelling a two-neuron network with feedback and McCulloch-Pitts type activation, which includes the discrete version of the two-neuron model with piecewise constant argument as its special case. We obtain some interesting sufficient conditions insuring the convergence of solutions, as well as the existence of periodic solutions. [Copyright &y& Elsevier]

In this paper, the existence of at least three positive solutions for the boundary value problem (BVP) of second-order functional differential equation with the form y″(t) + f(t, yt) = 0, for t ∊ [0,1], αy(t) -βy′(t) =η(t), for t ∊ [−τ,0], −γy(t) + Δy′(t) = ζ(t), for t ∊ [1, 1 + a], is studied. Moreover, we investigate the existence of at least three partially symmetric positive solutions for the above BVP with αΔ = βγ. [Copyright &y& Elsevier]