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Abstract: In this paper we complete a distributional Fourier analysis developed by Howell in a serie of papers. We investigate convolution operators in the corresponding distribution spaces. [Copyright &y& Elsevier]

Abstract: In this paper and in a forthcoming one, we study difference equations in of the types which are linked to families of conics, cubics and quartics, respectively. These equations generalize Lyness'' one studied in several papers, whose behavior was completely elucidated in [G. Bastien, M. Rogalski, in press] through methods which are transposed in the present paper for the study of (1) and (2), and in the forthcoming one for (3). In particular we prove in the present paper a form of chaotic behavior for solutions of difference equations (1) and (2), and find all the possible periods for these solutions. [Copyright &y& Elsevier]

The paper presents a formula for the γ-interior of a set under special conditions for γ :expX→expX, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89–93]. There are also some applications. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra attains sufficiently many -continuous ⁎-representations in , to separate its points. Having achieved this, a usual notion of bounded elements on rises. On the other hand, a natural order exists on related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras. [Copyright &y& Elsevier]

Abstract: Let and be polynomials of degree respectively n and less than n such that A result due to Q.I. Rahman states that In this paper, we slightly improve the above inequality and discuss several sharpness aspects, including all cases of equality. [Copyright &y& Elsevier]

Abstract: The self-affine measure associated with an iterated function system and a weight is uniquely determined. The problem of determining whether a self-affine measure is absolutely continuous or singular has been studied extensively in recent years. In the present paper we consider the singularity of certain self-affine measures. We obtain a sufficient condition for such measures being singular. Two applications of this result are given, which extend several known results in a simple manner. [Copyright &y& Elsevier]

Abstract: In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer''s type and Hermite–Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to provide a new approach concerning the characterization of exponential dichotomy of difference equations by means of admissible pair of sequence spaces. We classify the classes of input and output spaces, respectively, and deduce necessary and sufficient conditions for exponential dichotomy applicable for a large variety of systems. By an example we show that the obtained results are the most general in this topic. As an application we deduce a general lower bound for the dichotomy radius of difference equations in terms of input–output operators acting on sequence spaces which are invariant under translations. [Copyright &y& Elsevier]

Abstract: In this paper we discuss a certain class of sets of generators for a full Hilbert -module which characterize Hilbert -modules over the -algebra of compact operators. An example of such sets of generators are orthonormal bases. [Copyright &y& Elsevier]

Abstract: In this paper, we study the free boundary problem for 1D compressible Navier–Stokes equations with density-dependent viscosity. We focus on the case where the viscosity coefficient vanishes on vacuum. We prove the global existence and uniqueness for discontinuous solutions to the Navier–Stokes equations when the initial density is a bounded variation function, and give a decay result for the density as . [Copyright &y& Elsevier]

Abstract: In this paper, we prove an important inequality and investigate some new calculating problems of random fixed point index, and generalize famous theorem by means of the theory of random fixed point index. [Copyright &y& Elsevier]

Abstract: In this paper, we consider dynamical behavior of non-autonomous plate-type evolutionary equations with critical nonlinearity. We prove the existence of a uniform attractor in the space . [Copyright &y& Elsevier]

Abstract: In this paper we study the global asymptotic stability for a class of delay logistic equations. A sufficient and necessary condition is derived. As a result, we obtain a full affirmative answer to the Gopalsamy and Liu'' conjecture. [Copyright &y& Elsevier]

Abstract: This paper investigates the regularity of solutions of convolution equations in the frame of classes of ultradifferentiable functions and ultradistributions. We improve previous work by Bonet, Chou, Fernández, Galbis, Meise and others. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to derive two transformation formulae which imply relations between basic and bilateral basic hypergeometric series. Some special cases of them are also discussed. [Copyright &y& Elsevier]

Abstract: The present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in . Upper and lower bounds are derived for the decay rates of higher order derivatives of solutions to the micropolar fluid flows. The findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized Gronwall type argument. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a food-limited population model with impulsive effect. Several explicit sufficient conditions are established for oscillation and nonoscillation of solutions of the equations. [Copyright &y& Elsevier]

Abstract: In this paper, we study the weak convergence of “Leray-type” solutions of a magneto-hydro-dynamic systems. The proofs are based on weak compactness arguments and linear algebra methods. [Copyright &y& Elsevier]

Abstract: We are interested in spatially extended pattern forming systems close to the threshold of the first instability in case when the so-called degenerated Ginzburg–Landau equation takes the role of the classical Ginzburg–Landau equation as the amplitude equation of the system. This is the case when the relevant nonlinear terms vanish at the bifurcation point. Here we prove that in this situation every small solution of the pattern forming system develops in such a way that after a certain time it can be approximated by the solutions of the degenerated Ginzburg–Landau equation. In this paper we restrict ourselves to a Swift–Hohenberg–Kuramoto–Shivashinsky equation as a model for such a pattern forming system. [Copyright &y& Elsevier]

Abstract: This paper presents a systematic investigation of the integrability conditions for nonautonomous quad-graph maps, using the Lax pair approach, the ultra-local singularity confinement criterion and direct construction of conservation laws. We show that the integrability conditions derived from each of the methods are the one and the same, suggesting that there exists a deep connection between these techniques for partial difference equations. [Copyright &y& Elsevier]

Abstract: This paper deals with the global attraction and global weak attraction of the origin for the generalized Liénard equation. The problem proposed by Jiang is solved by a negative answer and some new criteria for the globally asymptotically stability are obtained by the ways different from the usual Filippov''s conditions. [Copyright &y& Elsevier]

Abstract: In this paper we establish the exact blow-up rate of the large solutions of a porous media logistic equation. We consider the carrying capacity function with a general decay rate at the boundary instead of the usual cases when it can be approximated by a distant function. Obtaining the accurate blow-up rate allows us to establish the uniqueness result. Our result covers all previous results on the ball domain and can be further adapted in a more general domain. [Copyright &y& Elsevier]

Abstract: In this paper we consider the existence of nontrivial solutions for an elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones and computing the fixed point index in , and , we obtain that the elliptic system has three nontrivial solutions , and . It is remarkable that the third nontrivial solution is established on the Cartesian product of two cones, in which the feature of two equations can be exploited better. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions for the oscillation of the linear non-autonomous systems of difference equations with continuous arguments where , , , , ; τ, γ and , , are non-negative constants. Furthermore, assume , where , , , are continuous, bounded and do not change signs on . [Copyright &y& Elsevier]

Abstract: The classical criterion of asymptotic stability of the zero solution of equations is that there exists a function , for some , such that for some . In this paper we prove that if is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , , where , uniformly for . [Copyright &y& Elsevier]

Abstract: This paper discusses a class of second-order derivative nonlinear Schrödinger equations which are used to describe the upper-hybrid oscillation propagation. By establishing a variational problem, applying the potential well argument and the concavity method, we prove that there exists a sharp condition for global existence and blow-up of the solutions to the nonlinear Schrödinger equation. In addition, we also answer the question: how small are the initial data, the global solutions exist? [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the problem of framing 2-variable 2-parameter Bessel functions (2V2PBF) into the context of the representation of the 3-dimensional Lie algebra . Further, we derive generating relations and identities involving 2V2PBF. Furthermore, we deduce some new and known relations involving various other forms of generalized Bessel functions (GBF) and Bessel functions (BF) as applications of these results. [Copyright &y& Elsevier]

Abstract: In the paper we examine Pexiderized ϕ-homogeneity equation almost everywhere. Assume that G and H are groups with zero, and are a G- and an H-space, respectively. We prove, under some assumption on , that if functions and satisfy Pexiderized ϕ-homogeneity equation almost everywhere in then either almost everywhere in G or almost everywhere in X or there exists a homomorphism such that almost everywhere in G and there exists a function such that and where is a constant. From this result we derive solution of the classical Pexider equation almost everywhere. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new concept, namely that of a quasi-orthomorphism, on a vector lattice, which generalizes the notion of an orthomorphism. We consider quasi-multipliers on ℓ-algebras and establish the relationship between quasi-orthomorphisms and quasi-multipliers. We prove that, for certain Banach algebras, the quasi-orthomorphisms form a Dedekind complete Banach f-algebra with a multiplicative identity. We conclude with a Kakutani type representation theorem for . [Copyright &y& Elsevier]

Abstract: In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation: where and the initial values . The successive lengths of positive and negative semicycles of nontrivial solutions of the above equation is found to periodically occur, that is, , or, . By using the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable. [Copyright &y& Elsevier]

Abstract: In this paper, we establish certain new Ramanujan''s Schläfli-type mixed modular equations. [Copyright &y& Elsevier]

Abstract: In this paper we study a class of inequality problems for the stationary Navier–Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier–Stokes ones for the velocity and pressure with nonstandard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps. We also establish a result on the dependence of the solution set with respect to a locally Lipschitz superpotential appearing in the boundary condition. [Copyright &y& Elsevier]

Abstract: This paper studies the controllability and observability of a class of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of geometric type, they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria. [Copyright &y& Elsevier]

Abstract: In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. [Copyright &y& Elsevier]

Abstract: Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371–389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov–Svaiter''s APPA. Building the direction from current iterate to the new iterate obtained by Solodov–Svaiter''s APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method. [Copyright &y& Elsevier]

We establish in this paper some inequalities for vertex distances of two simplices, and give some applications thereof. [Copyright &y& Elsevier]

In this paper, the unbounded solutions for the following nonlinear planar system: is discussed, where a±,b± are positive constants satisfying x±=max{±x,0}, y±=max{±y,0}, ω∈R+&z.drule;Q, f(t),g(t)∈L∞[0,2π] are 2π-periodic functions. [Copyright &y& Elsevier]

In this paper the approach via time-map is used to investigate the existence of periodic solutions for second order equation with time-dependent potential. Our theorem generalized the results obtained by Ding, Habets, Omari and Zanolin which are for time-independent potential and relate the behavior of the primitive of the nonlinearity with respect to the Fučik spectrum of the periodic problem. [Copyright &y& Elsevier]

In the paper we shall present a survey of recent results on substochastic semigroups and provide new methods for determining their honesty. These methods are applied to the fragmentation equation with mass loss, yielding sufficient conditions for the existence of conservative and shattering solutions. Our results provide a mathematical framework that clarifies the discussion of [Phys. Rev. A 43 (1991) 656, Phys. Rev. A 41 (1990) 5755, J. Phys. A 24 (1991) 3967] on shattering fragmentation in such models showing, among others, that there occurs an unexpected mass loss associated with shattering which is not accounted for by the discrete and continuous mass loss, contrary to the conjecture of [Phys. Rev. A 43 (1991) 656, Phys. Rev A 41 (1990) 5755]. [Copyright &y& Elsevier]

The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence x=[xjk] into one whose core is a subset of the M-core of x. [Copyright &y& Elsevier]

The idea of almost convergence for double sequences was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283–294] and they also characterized the four dimensional strong regular matrices. In this paper we define and characterize the almost strongly regular matrices for double sequences and apply these matrices to establish a core theorem. [Copyright &y& Elsevier]

The purpose of this paper is to investigate when a weight ϕ on a partial O&ast;-algebra M is a trace weighted by a positive self-adjoint operator Ω, that is, ϕ(X†□X)=tr(X†&ast;Ω)&ast;(X†&ast;Ω) whenever X∈M s.t. X†∈L(X) and ϕ(X†□X)<∞. It is shown that if M contains the inverse N of a positive compact operator such that the weak multiplication N□N is defined, then every weight ϕ on M+ satisfying ϕ(N□N)<∞ is a trace weighted by some positive trace operator. [Copyright &y& Elsevier]

In the present paper, we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi-nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex Banach space, requiring one member T in the family to be semi-compact. Our results extend and improve some recent results. [Copyright &y& Elsevier]