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Abstract: In this paper we obtain a bilinear analogue of Fefferman–Steinʼs vector valued inequality for classical Hardy–Littlewood maximal function. Also, we prove the boundedness of bilinear Hardy–Littlewood maximal operator from , where , by applying the method of rotations. [Copyright &y& Elsevier]

Abstract: In this paper, we study -canal surfaces in terms of biharmonic -slant helices according to Bishop frame in the Heisenberg group Heis3. We give necessary and sufficient conditions for -slant helices to be biharmonic. We characterize -canal surfaces in the Heisenberg group Heis3. Additionally, we illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. [Copyright &y& Elsevier]

Abstract: In this paper we give a constructive method for rational finite element method in for quadrilateral. For , the usual polynomials splines require some supersmoothness at the vertices of the quadrilateral, even when dealing with macro-elements. This is no more a requirement for our rational approach. The process of the construction is illustrated with the help of two examples namely the case and the case. [Copyright &y& Elsevier]

Abstract: In this paper, we mainly discuss the infinite loss of regularity and μ-loss for a σ-evolution type model with oscillating in time coefficients. On the one hand, an explicit counter-example has been constructed in the frequency space to show the precise infinite loss of regularity. On the other hand, due to the finite propagation speed property for , we construct the counter-example of a sequence of solutions in by applying state of art techniques. [Copyright &y& Elsevier]

Abstract: By now the -spectra of self-conformal measures satisfying the so-called open set condition are well understood. However, if the open set condition is not satisfied, then almost nothing is known. In this paper we compute the mixed -spectra for self-conformal measures, which have bound distortion property and satisfy the weak separation condition. [Copyright &y& Elsevier]

Abstract: In this paper viability results for nonlinear fractional differential equations with the Caputo derivative are proved. We give the sufficient condition that guarantees fractional viability of a locally closed set with respect to nonlinear function. As an example we discuss positivity of solutions, particularly in linear case. [Copyright &y& Elsevier]

Abstract: In this paper second order quasilinear ordinary differential equations are considered, and a necessary and sufficient condition for the existence of a slowly growing positive solution is established. Moreover, the precise asymptotic forms as of slowly growing positive solutions and slowly decaying positive solutions are obtained. [Copyright &y& Elsevier]

Abstract: This paper concerns the threshold of global existence and finite time blow up of solutions to the time-dependent focusing Gross–Pitaevskii equation describing the Bose–Einstein condensation of trapped dipolar quantum gases. Via a construction of new cross-constrained invariant sets, it is shown that either the corresponding solution globally exists or blows up in finite time according to some appropriate assumptions about the initial datum. [Copyright &y& Elsevier]

Abstract: In this paper, by using the atomic decomposition and molecular characterization of the homogeneous and non-homogeneous weighted Herz-type Hardy spaces , we obtain some weighted boundedness properties of the Bochner–Riesz operator and the maximal Bochner–Riesz operator on these spaces for , and . [Copyright &y& Elsevier]

Abstract: In this paper we investigate and Sobolev boundedness of a certain class of pseudodifferential operators with non-regular symbols. We employ regularisation methods, namely convolution with a net of mollifiers , and we study the corresponding net of pseudodifferential operators providing and Sobolev estimates which relate the parameter ε with the non-regularity of the symbol. [Copyright &y& Elsevier]

Abstract: Let be the symmetrical Cantor set generated by and , where . Let s be the Hausdorff dimension of and μ the Cantor measure. In this paper, under the hypothesis that a is slightly greater than 1/3, we obtain the explicit formulas of the upper and lower s-densities , for every point . Moreover, we describe the range of a key quantity in these formulas. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Wang et al. [Nonlinear Anal. 71 (2009) 2134–2140] and Li et al. [J. Math. Anal. Appl. 340 (2008) 876–883] to more general equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the invertibility of nonnegative Hamiltonian operator with unbounded entries is studied, and the sufficient conditions for the everywhere defined bounded invertibility of nonnegative Hamiltonian operator are obtained. [ABSTRACT FROM AUTHOR]

Abstract: The Keller–Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less 8π, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar variables. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations. By introducing an auxiliary integrodifference system, the spreading speed is established for the integrodifference equation. It is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts. Furthermore, we prove that the traveling wavefronts are stable by applying the squeezing technique. Finally, we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology. [Copyright &y& Elsevier]

Abstract: Let be a fixed number. A function is said to be a-shift-generating (a-SG) if for every , is a totally positive sequence and it does not coincide with a sequence of the form , where and . In this paper, we describe all a-SG functions and obtain a new characterization of totally positive functions in the terms of a-SG functions. In addition, using characteristic properties of a-SG functions, we generalize the famous Jacobian identity in theory of elliptic functions. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the Borel points and shared-values of meromorphic functions in an angular domain. [Copyright &y& Elsevier]

Abstract: In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue. [Copyright &y& Elsevier]

Abstract: In this paper, essentially strongly order-preserving and conditionally set-condensing semiflows are considered. Obtained is a new type of generic quasi-convergence principles implying the existence of an open and dense set of stable quasi-convergent points when the state space is order bounded. The generic quasi-convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations, giving some results of theoretical and practical significance. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations , , . We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy . The asymptotic behavior of solutions is also described. [Copyright &y& Elsevier]

Abstract: In this paper, we will study the isometric extension problem for -spaces and prove that every surjective isometry from the unit sphere of onto that of a Banach space E can be extended to a linear surjective isometry from onto E. Moreover, we introduce the approximate isometric extension problem and show that, if E and F are Banach spaces and E satisfies the property (m) (special cases are , and ), then every bijective ϵ-isometry between the unit spheres of E and F can be extended to a bijective 5ϵ-isometry between their closed unit balls. At last, we will give an example to show that the surjectivity assumption cannot be omitted. Using this, we solve the non-surjective isometric extension problem in the negative. [Copyright &y& Elsevier]

Abstract: In this paper, we show that minimization problems involving sublinear regularizing terms are ill-posed, in general, although numerical experiments in image processing give very good results. The energies studied here are inspired by image restoration and image decomposition. Rewriting the nonconvex sublinear regularizing terms as weighted total variations, we give a new approach to perform minimization via the well-known Chambolle''s algorithm. The approach developed here provides an alternative to the well-known half-quadratic minimization one. [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: In this paper, we study the regularity of solutions to two microscopic–macroscopic models: Hookean spring model and FENE dumbbell model. By making use of the structure of Fokker–Planck operator and establishing the general Hardy–Littlewood''s inequality, we show that the classical solutions near the equilibrium obtained in [F. Lin, C. Liu, Ping Zhang, On a micro–macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math. 60 (6) (2007) 838–866] and [F. Lin, Ping Zhang, The FENE dumbbell model near equilibrium, Acta Math. Sinica (Chin. Ser.) 24 (2008) 529–538] become smooth with respect to the end-to-end vector variable q for any positive time. [Copyright &y& Elsevier]

Abstract: In the present paper we show some results concerning the orbital stability of dnoidal standing wave solutions and orbital instability of cnoidal standing wave solutions to the following Klein–Gordon equation: We also present a result of orbital instability of snoidal standing wave solutions to the Klein–Gordon equation The main tool to obtain these results is the classical Grillakis, Shatah and Strauss'' theory in the periodic context. [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: The goal of the paper is to study the loss of regularity for special p-evolution type models with bounded coefficients in the principal part. The obtained loss of regularity is related in an optimal way to some unboundedness conditions for the derivatives of coefficients up to the second-order with respect to t. [Copyright &y& Elsevier]

Abstract: In this paper, we improve contractivity conditions of solutions for the positive equilibrium of the following differential equation with piecewise constant arguments: where is a nonnegative continuous function on , , , , , and . In particular, for the case and , we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75–83]). For the other case and , under the condition , the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602–635] and others. [Copyright &y& Elsevier]

Abstract: In this paper we prove a new version of Cowling–Price''s theorem for the Dunkl transform on . [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: In this paper we study the existence of a positive periodic solutions for nested models of respiratory syncytial virus RSV, by using a continuation theorem based on coincidence degree theory. Conditions for the existence of periodic solutions in the model are given. Numerical simulations related to the transmission of respiratory syncytial virus in Madrid and Rio Janeiro are included. [Copyright &y& Elsevier]

Abstract: This paper extends the Hille–Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein–Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform. [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 uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44–48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395–406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828–831]. [Copyright &y& Elsevier]

Abstract: This paper focuses on a nonlinear equation from thin plate theory of the form . We obtain maximum principles for certain functions defined on the solution of this equation using P-functions or auxiliary functions of the types used by Payne [L.E. Payne, Some remarks on maximum principles, J. Anal. Math. 30 (1976) 421–433] and Schaefer [P.W. Schaefer, Solution, gradient, and laplacian bounds in some nonlinear fourth order elliptic equations, SIAM J. Math. Anal. 18 (1987) 430–434]. [Copyright &y& Elsevier]

Abstract: In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality. [Copyright &y& Elsevier]

Abstract: In this paper, we first give several operator identities involving the bivariate Rogers–Szegö polynomials. By applying the technique of parameter augmentation to the multiple q-binomial theorems given by Milne [S.C. Milne, Balanced summation theorems for basic hypergeometric series, Adv. Math. 131 (1997) 93–187], we obtain several new multiple q-series identities involving the bivariate Rogers–Szegö polynomials. These include multiple extensions of Mehler''s formula and Rogers''s formula. Our generalizations are quite natural as they are also a direct and immediate consequence of their (often classical) known one-variable cases and Milne''s fundamental theorem for or basic hypergeometric series in Theorem 1.49 of [S.C. Milne, An elementary proof of the Macdonald identities for , Adv. Math. 57 (1985) 34–70], as rewritten in Lemma 7.3 on p. 163 of [S.C. Milne, Balanced summation theorems for basic hypergeometric series, Adv. Math. 131 (1997) 93–187] or Corollary 4.4 on pp. 768–769 of [S.C. Milne, M. Schlosser, A new extension of Ramanujan''s summation with applications to multilateral series, Rocky Mountain J. Math. 32 (2002) 759–792]. [Copyright &y& Elsevier]

Abstract: In this paper, it is shown that some necessary characteristic conditions for unique extremality obtained by Zhu and Chen are also sufficient and some sufficient ones by them actually imply that the uniquely extremal Beltrami differentials have a constant modulus. In addition, some local properties of uniquely extremal Beltrami differentials are given. [Copyright &y& Elsevier]

Abstract: In this paper we consider the stability for a class of jump-diffusions with Markovian switching. We first construct them successively and show that they can be associated with some appropriate generators and they are non-explosive. We then prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity by making use of the relation between the transition probabilities of jump-diffusions and the corresponding diffusions. Finally, we also investigate their exponential ergodicity. [Copyright &y& Elsevier]

Abstract: Drewnowski and Paúl proved in [L. Drewnowski, P.J. Paúl, The Nikodým property for ideals of sets defined by matrix summability methods, Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000) 485–503] that for any strongly nonatomic submeasure η on the power set of the ideal has the Nikodym property (NP); in particular, this result applies to densities defined by strongly regular matrices A. Grahame Bennett and the authors stated in [G. Bennett, J. Boos, T. Leiger, Sequences of 0''s and 1''s, Studia Math. 149 (2002) 75–99] that the strong null domain of any strongly regular matrix A has the Hahn property (HP). Moreover, Stuart and Abraham [C.E. Stuart, P. Abraham, Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems, J. Math. Anal. Appl. 300 (2) (2004) 351–361] pointed out that the said results are in some sense dual and that the last one follows from the first one by considering the density (defined by A) as submeasure on and the ideal as well by identifying with the set χ of sequences of 0''s and 1''s. In this paper we aim at a better understanding of the intimated duality and at a characterization of those members of special classes of matrices A such that has NP (equivalently, has HP). [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature. [Copyright &y& Elsevier]

Abstract: In this paper we prove new identities in the Catalan triangle whose entry is defined by In fact, we show some new identities involving the well-known Catalan numbers, and specially the identity that appears in a problem related with the dynamical behavior of a family of iterative methods applied to quadratic polynomials. [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: This paper is concerned with chaos induced by regular snap-back repellers. One new criterion of chaos induced by strictly coupled-expanding maps in compact sets of metric spaces is established. By employing this criterion, the nondegenerateness assumption in the Marotto theorem established in 1978 is weakened. In addition, it is proved that a regular snap-back repeller and a regular homoclinic orbit to a regular expanding fixed point in finite-dimensional spaces imply chaos in the sense of Li–Yorke. An illustrative example is provided with computer simulations. [Copyright &y& Elsevier]