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In this paper, a novel weak form quadrature element method (QEM) is proposed for accurate free transverse vibration analysis of thin isotropic skew plates with general boundary conditions. In the formulation of the stiffness matrix, the first and second order derivatives of the shape functions at integration points are computed explicitly by using the differential quadrature rule. This leads to a great simplicity in formulating an N × N -node quadrature plate element and a large reduction of programming effort. Different from the existing weak form quadrature element method or differential quadrature finite element method, the element nodes can be either the same or different from the integration points. Convergence studies are performed. Free vibration of skew thin plates with various skew angles and different combinations of boundary conditions is analyzed. It is shown that although the assumed displacement field does not explicitly consider the bending moment singularities at the obtuse angles, the proposed QEM can yield accurate frequencies even for the thin isotropic skew plate with large skew angles. [ABSTRACT FROM AUTHOR]

Abstract: We study higher order eTCR (enhanced target collision resistance) hash functions, where th-order eTCR is denoted by eTCR . We prove that a few rounds of the MD (Merkle–Damgård) scheme and a few levels of the TR (tree) scheme can be eTCR under the compression function is eTCR for some positive integer . Additionally, we prove that the TH (tree hash) scheme also preserves eTCR. [Copyright &y& Elsevier]

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: The singular boundary value problem is studied in this paper.The singularity may appear at and the function may be superlinear at and change sign. The existence of solutions is obtained via an upper and lower solutions method. [Copyright &y& Elsevier]

Abstract: Determination of an unknown time-dependent function in parabolic partial differential equations, plays a very important role in many branches of science and engineering. In the current investigation, the Adomian decomposition method is used for finding a control parameter in the quasilinear parabolic equation , in with known initial and boundary conditions and subject to an additional condition in the form of which is called the boundary integral overspecification. The main approach is to change this inverse problem to a direct problem and then solve the resulting equation using the well known Adomian decomposition method. The decomposition procedure of Adomian provides the solution in a rapidly convergent series where the series may lead to the solution in a closed form. Furthermore due to the rapid convergence of Adomian’s method, a truncation of the series solution with sufficiently large number of implemented components can be considered as an accurate approximation of the exact solution. This method provides a reliable algorithm that requires less work if compared with the traditional techniques. Some illustrative examples are presented to show the efficiency of the presented method. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain, where is continuous and a nonnegative function that is allowed to vanish on some subintervals of of the measure chain. The method involves applications of a new fixed-point theorem due to Bai and Ge [Z.B. Bai, W.G. Ge, Existence of three positive solutions for some second order boundary-value problems, Comput. Math. Appl. 48 (2004) 699–707]. The emphasis is put on the nonlinear term involved with the first order delta derivative . [Copyright &y& Elsevier]

Abstract: In this paper, some necessary and sufficient conditions for the oscillation of a differential equation with fractional delay and piecewise constant argument are obtained. [Copyright &y& Elsevier]

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: The principle of this paper is to deal with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments. Easily verifiable sufficient criteria are established. The approach is based on the fixed-point theorem in cones. The paper extends some previous results and obtains some new results. [Copyright &y& Elsevier]

Abstract: By a new approach, we present a new existence result of positive solutions to the following Dirichlet boundary value problem, It is remarkable that the result of this paper is not obtained by employing the fixed-point theorems in cone and the method of the lower and upper functions. Our nonlinearity may change sign and be singular at t = 0, 1, χ = 0. [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: We find conditions for the solution to a first-order differential equations to be: bounded by an exponential function, uniformly stable, and uniformly asymptotically stable. Estimates are obtained using Liapunov functionals (energy functionals). Our assumptions are weaker than those in the references, and results are extended to systems of equations and to nonlinear equations. [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: Singularly perturbed self-adjoint boundary-value problems are considered in this article. A difference scheme based on quintic spline is proposed. This scheme is applied to the subproblems obtained from the given problem by dividing the whole domain into nonoverlapping subdomains. The proposed scheme is of fourth-order convergent and more suitable for parallel computers. Stability and convergence of the method are discussed. Numerical examples are provided to show the efficiency and accuracy. [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: This paper considers the existence of extreme solutions of the periodic boundary value problems for the second order functional differential equations. The novelty is that we introduce a new concept for lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid. Meanwhile, we extend previous results. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of positive solution for two classes of nonlinear second-order three-point boundary value problems using some monotone iterative schemes. In both cases, such schemes start off with known constant functions and, therefore, are useful to computation purpose. [Copyright &y& Elsevier]

Abstract: This paper introduces radial basis functions (RBF) into the collocation methods and the combined methods for elliptic boundary value problems. First, the Ritz-Galerkin method (RGM) is chosen using the RBF, and the integration approximation leads to the collocation method of RBF for Poisson''s equation. Next, the combinations of RBF with finite-element method (FEM), finite-difference method (FDM), etc., can be easily formulated by following Li [1] and Hu and Li [2,3], but more analysis of inverse estimates is explored in this paper. Since the RBFs have the exponential convergence rates, and since the collocation nodes may be scattered in rather arbitrary fashions in various applications, the RBF may be competitive to orthogonal polynomials for smooth solutions. Moreover, for singular solutions, we may use some singular functions and RBFs together. Numerical examples for smooth and singularity problems are provided to display effectiveness of the methods proposed and to support the analysis made. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some sufficient conditions for the asymptotic behavior of all nonoscillatory solutions of the differential equation, , under suitable condition on , and . [Copyright &y& Elsevier]

Abstract: We establish the Kuhn-Tucker type sufficient optimality conditions for complex minimax programming under generalized Type-I and related functions. Subsequently, we apply these optimality criteria to formulate two dual models. We also establish weak, strong, and strict converse duality theorems. [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: By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works. [Copyright &y& Elsevier]

Abstract: This paper deals with the stability analysis of numerical methods for the solution of advanced differential equations with piecewise continuous arguments. We focus on the behaviour of the one-leg θ-method and the linear θ-method in the solution of the equation x′(t) = ax(t + a 0 x([t]) + a 1 x([t+1]), with real a, a 0, a 1 and [·] designates the greatest-integer function. The stability regions of two θ-methods are determined. The conditions under which the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given. [Copyright &y& Elsevier]

Abstract: In this paper, we define B-smooth discontinuous dynamical systems which can be used as models of various processes in mechanics, electronics, biology, and medicine. We find sufficient conditions to guarantee the existence of such systems. These conditions are easy to verify. Appropriate examples are constructed. [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]

Abstract: This paper discusses the antiperiodic boundary value problem for first-order impulsive ordinary differential equations. We establish several existence results by using the Leray-Schauder alternative, the lower and upper solution method and the monotone iterative technique. [Copyright &y& Elsevier]

Abstract: High order differential functions of several variables are approximated by multivariate shift-invariant convolution type operators and their generalizations. The high order of this approximation is determined by giving some multivariate Jackson-type inequalities, engaging the first multivariate usual modulus of continuity of the N th-order partial derivatives of the multivariate function under approximation. [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]

This paper is devoted to the construction of an approximate solution of the stochastic differential equation of the Ito type, defined on a partition of the time-interval. The coefficients of the equation by their Taylor series up to arbitrary derivatives are approximated. The closeness of the original and approximate solutions is measured in the sense of the LP-norm and with probability one. [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]

Of concern is the Cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions. Under general and natural hypotheses, we establish some new theorems about the existence and uniqueness of solutions for the Cauchy problem. As a consequence, we unify and extend the corresponding theorems given previously for the Cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions. Moreover, we present two examples, one of which comes from heat conduction in materials with memory, to show that the existing results are not applicable to them, in contrast with ours. [Copyright &y& Elsevier]

In this article, we prove that the omega limit set of a uniformly asymptotically Zhukovskij stable orbit of a differential system in Rn is a closed orbit or a fixed point and also it is a uniform attractor. Further, if the system is defined on a compact subset of Rn and each orbit is uniformly asymptotically Zhukovskij stable, then the set of fixed points and closed orbits is finite. [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]

In recent years, many authors demonstrated the usefulness of fractional calculus operators in the derivation of (explicit) particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. In particular, by making use of the operators of fractional calculus based upon the Cauchy-Goursat integral formula, a certain family of nearly-simple harmonic vibration equations was considered systematically in a series of papers which appeared quite recently. The main object of the present sequel to all these earlier works is to investigate some relationships between such families of fractional differential equations and certain classes of ordinary differential equations. A preliminary interpretation of this family of nearly-simple harmonic vibration equations by means of an example involving linear electric circuits is also provided. [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]

The periodical boundary value problem for linear second-order ordinary differential equation with small parameter by the first and second derivatives is considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form, an exponentially fitted difference scheme is constructed in a uniform mesh which gives first-order uniform convergence in the discrete maximum norm. Numerical experiments support these theoretical results. [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]