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Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]

Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]

Abstract: Discrete models and continuous control systems are considered in regard to optimality of their trajectories. Some aspects of the principle of optimality [1, p. 83] are analyzed, and it is shown to imply total optimality, that is, the optimality of every part of an optimal trajectory. Certain autonomous systems with free admissible variations possess this property. Nonautonomous optimal systems are not, in general, totally optimal, in which case the principle of optimality is not valid. A modification is proposed for the derivation of the main functional equation to demonstrate that dynamic programming and its functional equations are valid also in the case of nonoptimal remaining trajectories under a certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown in an example of a widely used engineering system for which an optimal trajectory has all its remaining parts nonoptimal and noncontiguous to the optimal trajectory. The paper presents theoretical justification of dynamic programming for contiguous systems that do not conform to the principle of optimality. Examples are presented to illustrate the results which open new avenues in modeling and optimization of general (not totally optimal) control systems. [Copyright &y& Elsevier]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In this paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given. [Copyright &y& Elsevier]

Abstract: In this paper, we define generalized -Horadam sequence . After that, we study the properties of the generalized -Horadam sequence and prove some of these properties by means of determinant. Also, we obtain a generating function for the generalized -Horadam sequence. [Copyright &y& Elsevier]

Abstract: This paper aims at showing how the so-called mathematical kinetic theory for active particles can be properly developed to propose a new system biology approach. The investigation begins with an analysis of complexity in biological systems, continues with reviewing a general methodology to reduce complexity and furnishes the mathematical tools to describe the time evolution of such systems by capturing all their features. [Copyright &y& Elsevier]

Abstract: In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]

Abstract: In this paper we give some sufficient conditions in terms of regularly generated sequences for a sequence to be subsequentially convergent. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some new generalizations and refinements of Hölder’s inequality and some related inequalities. We also show that many existing inequalities related to the Hölder inequality are special cases of the inequalities presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the fourth-order nonlinear differential equations with a deviating argument. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established, which are new and complement previously known results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some new generalizations of Aczél’s inequality and of Bellman’s inequality; we will conclude by presenting some refinements of these inequalities. [Copyright &y& Elsevier]

Abstract: Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft -ideals and -idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) -ideals in BCI-algebras. We provide relations between fuzzy -ideals and -idealistic soft BCI-algebras. [Copyright &y& Elsevier]

Abstract: In this paper we study necessary and sufficient optimality conditions for a set-valued optimization problem. Convexity of the multifunction and the domain is not required. A definition of -approximating multifunction is introduced. This multifunction is the differentiability notion applied to the problem. A characterization of weak minimizers is obtained for invex and generalized -convexlike multifunctions using the Lagrange multiplier rule. [Copyright &y& Elsevier]

Abstract: In this paper, we obtained rich solutions for the discrete complex cubic Ginzburg–Landau equation by means of the extended tanh-function approach. These solutions include chirpless bright soliton, chirpless dark soliton, triangular function solutions and some solutions with alternating phases, and so on. Meanwhile, the range of parameters where some exact solution exists is given. [Copyright &y& Elsevier]

In this paper, we obtain some new sufficient conditions for the existence of nontrivial m-periodic solutions of the following nonlinear difference equationby using the critical point method, where f: Z × R → R is continuous in the second variable, m ≥2 is a given positive integer, p n+m = p n for any n ∈ Z and f(t + m, z)= f(t, z) for any (t, z)∈ Z × R, (−1)δ =−1 and δ >0. [Copyright &y& Elsevier]

Abstract: The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convex. The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. All these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, commodity markets, markets related to weather, inflation-linked or insurance-linked derivatives, etc.). [Copyright &y& Elsevier]

Abstract: In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions. [Copyright &y& Elsevier]

Abstract: This paper studies maximality and totality of stable functions in the category of stable bifinite domains. We present three main results as follows, [o] [(1)] every maximum-preserving function is a maximal element in the stable function spaces; [(2)] a maximal stable function f : D → E is maximum-preserving if D is maximum-separable and E is completely separable; and [(3)] a stable bifinite domain D is maximum-separable if and only if for any locally distributive stable bifinite domain E, each maximal stable function f : D → E is maximum-preserving. [Copyright &y& Elsevier]

Abstract: The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic honeycomb torus, which extends a known result about rhombic honeycomb torus. [Copyright &y& Elsevier]

Abstract: We consider the numerical approximations of the two-dimensional steady potential flow around a body moving in a liquid of finite-constant depth at constant speed and distance below a free surface. One vertical segment is introduced as the upstream artificial boundary and two vertical segments are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then, the original problem is reduced to a problem defined on a finite-computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite-element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective. [Copyright &y& Elsevier]

Abstract: Recently, circulant graphs have received a lot of attention; and a new method was proposed for designing fault-tolerant solutions for any given circulant graph. This method works by partitioning the offsets of the graph in many ways; each leads to one or more solutions. By comparing all these solutions, we can find the one with the least node-degree. In this paper, we shall first review this method; and then re-examine its applications to the design of k-fault-tolerant meshes (for all possible values of k). Our results demonstrate that the solutions obtained (for both two and three-dimensional meshes) are efficient. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of nontrivial nonnegative periodic solutions for the quasilinear parabolic equation with nonlocal terms based on the theory of Leray-Schauder''s degree. [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 we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra . Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systems to have bisymmetric solutions, and the system to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over are also mentioned. [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: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [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, we establish several sufficient conditions for the oscillation of solutionsof second-order neutral functional differential equations with distributed deviating arguments, which generalize and improve some known results. [Copyright &y& Elsevier]

Abstract: In this paper, some new oscillation criteria are obtained for the first-order delay difference equation , where k,l1,l2,, ls are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the partial difference equation , where k and l are two positive integers, {pm,n} is a real double sequence. Some new oscillation criteria for this equation are obtained. [Copyright &y& Elsevier]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [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]

In this paper, nonlinear dispersive variants of the generalized KdV equation are investigated. The compact and the noncompact physical structures are studied. Two general formulas for the focusing branch and the defocusing branch, that are of substantial interest, are formally derived. [Copyright &y& Elsevier]

In this paper, we investigate the following discrete periodic Lotka-Volterra system with delays: The sufficient and realistic conditions are obtained for the existence of positive periodic solutions and the permanence for the above system. [Copyright &y& Elsevier]

A partial word of length n over a finite alphabet A is a partial map from {0,…, n − 1} into A. Elements of {0,…, n − 1} without image are called holes (a word is just a partial word without holes). A fundamental periodicity result on words due to Fine and Wilf [1] intuitively determines how far two periodic events have to match in order to guarantee a common period. This result was extended to partial words with one hole by Berstel and Boasson [2] and to partial words with two or three holes by Blanchet-Sadri and Hegstrom [3]. In this paper, we give an extension to partial words with an arbitrary number of holes. [Copyright &y& Elsevier]

Some new oscillation criteria are established in this paper for the second-order nonlinear neutral delay differential equation [r(t)(x(t) + p(t)x(t−τ))′]′ + q(t)f(x(t−)δ)) = 0, where τ and δ are nonnegative constants, r, p, q ∊ C([t0, ∞), R), and f ∊ C(R, R). These results are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results are sharper than some previous results about neutral and delay differential equations. In particular, several examples that dwell upon the sharp conditions of our results are also included. [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. The main object of the present paper is to show how readily some recent contributions on this subject by several workers, involving various interesting classes of non-Fuchsian differential equations (including, for example, the Fukuhara and Tricomi equations and the celebrated Bessel and Whittaker equations), can be obtained (in a unified manner) by suitably applying some general theorems on (explicit) particular solutions of a certain family of linear ordinary fractional differintegral equations. [Copyright &y& Elsevier]

In this paper, without assuming the boundedness, monotonicity, and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural network models with fixed time delays. The results are applicable to both symmetric and nonsymmetric interconnection matrices, and all continuous nonmonotonic neuron activation functions. [Copyright &y& Elsevier]

In this paper, we improve the Brauer-type inclusion interval and present a modified Brauer-type theorem for singular values. Numerical examples show that our estimation for singular values is more precise than those corresponding results in recent literature. Moreover, we also consider the marginal singular value on the Brauer-type inclusion interval. Some applications of our results are presented. [Copyright &y& Elsevier]

In this paper, we present numerous sets of nonparametric sufficient optimality conditions and duality results under various generalized (F ϱ, θ)-convexity assumptions for a minmax fractional subset programming problem. [Copyright &y& Elsevier]

In this paper, the analysis of the dynamic system for iterative improvement of a solution is discussed, and the new iterative improvement of a solution is proposed based on the dynamic system. We have proved that the new iterative improvement of the solution is convergent unconditionally. The numerical experiments illustrate that the new iterative improvement of the solution is more effective for an ill-conditional system of linear equations. [Copyright &y& Elsevier]