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As outlined below, this paper is devoted to a Carleson-type-measure-based study of the holomorphic Campanato 2-space on the open unit ball Bn of Cn, comprising all Hardy 2-functions whose oscillations in non-isotropic metric balls on the compact unit sphere Sn are proportional to some power of the radius other than the dimension n≥1.

It is known that, in many cases, the field (known as the Hecke field) generated by all Hecke eigenvalues of an elliptic modular newform f is in fact generated by the pth Hecke eigenvalue ap of f for a single prime number p. In this paper, we study the density of such primes in a more general situation in terms of Galois representations. This is applied to the study of the fields of rationality of certain automorphic representations.

In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D0+αu(t)+ft,u(t),D0+α−1u(t)=0,t∈(0,+∞), with the integral boundary conditions u(0)=0,D0+α−1u(∞)=∫0τg1(s)u(s)ds+a,D0+α−2u(0)=∫0τg2(s)u(s)ds+b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions for the boundary value problem in three cases τ=0,τ∈(0,+∞) and τ=+∞, are obtained, respectively. We also give out two corollaries as applications of the existence theorems and some examples to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.

The contribution of this paper is two-fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing vector field, by considering the Busemann–Hausdorff measure and Holmes–Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH-minimal surfaces in a Randers domain of constant flag curvature K=−1, which are the first examples of BH-minimal surfaces in the hyperbolic Randers space.

In this paper, we introduce the Schatten class and the Berezin transform of quaternionic operators. The first topic is of great importance in operator theory, but it is also necessary to study the second one, which requires the notion of trace class operators, a particular case of the Schatten class. Regarding the Berezin transform, we give the general definition and properties. Then we concentrate on the setting of weighted Bergman spaces of slice hyperholomorphic functions. Our results are based on the S-spectrum of quaternionic operators, which is the notion of spectrum that appears in the quaternionic version of the spectral theorem and in the quaternionic S-functional calculus. Copyright © 2016 John Wiley & Sons, Ltd.

This paper addresses the problem of well-posedness of non-autonomous linear evolution equations x=A(t)x in uniformly convex Banach spaces. We assume that A(t):D⊂X→X for each t is the generator of a quasi-contractive, strongly continuous group, where the domain D and the growth exponent are independent of t. Well-posedness holds provided that t↦A(t)y is Lipschitz for all y∈D. Holder continuity of degree α

In this paper, we introduce an algorithmic procedure that computes abelian subalgebras and ideals of a given finite-dimensional Malcev algebra. All the computations are performed by using the non-zero brackets in the law of the algebra as input. Additionally, the algorithm also computes the α and β invariants of these algebras, and as a supporting output, a list of abelian ideals and subalgebras of maximal dimension is returned too. To implement this algorithm, we have used the symbolic computation package MAPLE 12, performing a brief computational and statistical study for it and its implementation. Copyright © 2016 John Wiley & Sons, Ltd.

In the present paper, our aim is to establish several formulas involving integral transforms, fractional derivatives, and a certain family of extended generalized hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results. A probability density function involving the extended generalized hypergeometric function is introduced, and its properties are studied. The corresponding properties of some of the classical probability distributions and their associated probability density functions are easily derivable as special cases of our general results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we first prove the metric approximation property for weighted mixed-norm L (p1,...,pn) w spaces. Using Gabor frame representation, this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck’s theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these spaces as well as derive the corresponding trace formulae. Finally, we apply the notion of nuclearity to functions of the harmonic oscillator on modulation spaces.

The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya-type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in [1]. Copyright © 2016 John Wiley & Sons, Ltd.

The main objective of this paper was to study the global stability of the positive solutions and the periodic character of the difference equation xn+1=axn−l+bxn−k+cxn−sdxn−s−e,n=0,1,..., where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x−t,x−t + 1,...,x−1, x0 are positive real numbers where t = max{l,k,s}. Some numerical examples will be given to explicate our results. Copyright © 2016 John Wiley & Sons, Ltd.

Hermitian monogenic functions are the null solutions of two complex Dirac type operators. The system of these complex Dirac operators is overdetermined and may be reduced to constraints for the Cauchy datum together with what we called the Hermitian submonogenic system (see [8], [9]). This last system is no longer overdetermined and it has properties that are similar to those of the standard Dirac operator in Euclidean space, such as a Cauchy–Kowalevski extension theorem and Vekua type solutions. In this paper, we investigate plane wave solutions of the Hermitian submonogenic system, leading to the construction of a Cauchy kernel. We also establish a Stokes type formula that, when applied to the Cauchy kernel provides an integral representation formula for Hermitian submonogenic functions.

In this paper, we apply Borcea–Voisin's construction and give new examples of fourfolds containing a del Pezzo surface of degree six, which admit an elliptic fibration on a smooth threefold. Some of these fourfolds are Calabi–Yau varieties, which are relevant for the compactification of Type IIB string theory known as F-theory. As a by-product, we provide a new example of a Calabi–Yau threefold with Hodge numbers .

We give a sharp estimate for the codimension of the poly-Bergman space in the poly-Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for and the j-polyanalytic Bergman space over the domain U is trivial precisely when the complement of U has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non-analytic poly-Bergman space are trivial.

The main object of this paper is to extend some known approximation results for the complex beta operators of the first kind attached to analytic functions in strips of compact disks. The extensions of these approximation properties, which are presented here, involve bicomplex beta operators in compact -disk. Several other related results are also considered. Copyright © 2016 John Wiley & Sons, Ltd.

We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere., 20 pages, 17 figures, v2: minor corrections throughout the paper

In this paper we prove that a dynamically convex starshaped hypersurface in $\mathbb{C}^2$ which is invariant under complex conjugation admits a global surface of section which is invariant under conjugation as well. We obtain this invariant global surface by embedding $\mathbb{C}^2$ into $\mathbb{CP}^2$ and applying a stretching argument to real holomorphic curves in $\mathbb{CP}^2$. The motivation for this result arises from recent progress in applying holomorphic curve techniques to gain a deeper understanding on the dynamics of the restricted three body problem., 36 pages

In this paper, we introduce the notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from -operators on Lie algebroids. We study phase spaces of Lie algebroids in terms of left-symmetric algebroids. Representations of left-symmetric algebroids are studied in detail. At last, we study deformations of left-symmetric algebroids, which could be controlled by the second cohomology class in the deformation cohomology.

We start recalling the characterizing property of the ‘partial symmetries’ of a differential problem, that is, the property of transforming solutions into solutions only in a proper subset of the full solution set. This paper is devoted to analyze the role of partial symmetries in the special context of dynamical systems and also to compare this notion with other notions of ‘weak’ symmetries, namely, the λ-symmetries and the orbital symmetries. Particular attention is addressed to discuss the relevance of partial symmetries in dynamical systems admitting homoclinic (or heteroclinic) manifolds, which can be ‘broken’ by periodic perturbations, thus giving rise, according to the (suitably rewritten) Mel'nikov theorem, to the appearance of a chaotic behavior of Smale-horseshoes type. Many examples illustrate all the various aspects and situations. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we introduce the concept of Berinde's cyclic contraction that is a generalized cyclic contraction mapping by using the idea of weak contraction mapping which is defined by Berinde and prove best proximity point theorems for such a mapping in metric space with proximally complete property, Our results improve and extend the recent results of Eldred and Veeramani and some authors. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we give the sufficient and necessary conditions for the boundedness of fractional integral operators on the α-modulation spaces. The main theorem substantially extends and improves some known results.

We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric characterization. (Less)

In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag–Leffler expansions for Bessel functions of the first kind.

In the first part of this paper we provide a self-contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these determinants to derive new bounds on the discrete eigenvalues of compactly perturbed operators, broadly extending some recent results by Demuth et al. In addition, we also establish new bounds on the discrete eigenvalues of generators of C0-semigroups.

We prove that a double covering of P^3 branched along a very general sextic surface is not stably rational., A reference to the paper of Iliev-Katzarkov-Przyjalkowski added, and a small inaccuracy corrected

The present paper is dedicated to the study of various aspects of attraction and stability for semigroup actions on topological spaces. The main purpose is to present the connections among the distinct notions of attractors and stable sets. The concept of Conley attractor is also investigated and related to the other notions of attractors. All the results are applied to the theory of control systems.

In this paper, we show that a higher order Borel–Pompeiu (Cauchy–Pompeiu) formula, associated with an arbitrary orthogonal basis (called structural set) of a Euclidean space, can be extended to the framework of generalized Clifford analysis. Furthermore, in lower dimensional cases, as well as for combinations of standard structural sets, explicit expressions of the kernel functions are derived.

In this paper we present new results on two-weight Hardy, Hardy–Poincare and Rellich type inequalities with remainder terms on a complete noncompact Riemannian Manifold M. The method we use is flexible enough to obtain more weighted Hardy type inequalities. Our results improve and include many previously known results as special cases.

In this paper, we study the class of Banach spaces with James constant . It is shown that, for a Banach space of three or more dimensions, the James constant becomes if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on with James constant are completely characterized in terms of convex functions on the unit interval, which provides many new examples of such norms other than the Euclidean or regular octagonal norms. However, it is also shown that there exist two-dimensional normed spaces with James constant outside of the family of symmetric absolute norms.

We study the class of univalent analytic functions f in the unit disk of the form satisfying where Ω will be a proper subdomain of which is starlike with respect to . Let be the unique conformal mapping of onto Ω with and and . Let denote the arclength of the image of the circle , . The first result in this paper is an inequality for , which solves the general extremal problem , and contains many other well-known results of the previous authors as special cases. Other results of this article cover another set of related problems about integral means in the general setting of the class .

The goal of this paper is to prove the existence of indecomposable rank vector bundles on the Grassmannian variety . We will call them Tango bundles since in the particular case of they correspond to the celebrated vector bundle discovered by H. Tango in 1974. We will give a geometrical description of Tango bundles and we will prove that they are μ-stable.

In this paper, we obtain the existence of infinitely solutions for a class of nonlocal elliptic systems of (p1(x),⋯,pn(x))-Kirchhoff type. Our main results are new. Our approach are based on general variational principle because of B. Ricceri and the theory of the variable exponent Sobolev spaces. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we investigate the initial value problem (IVP henceforth) associated with the generalized Ostrovsky equation as follows: with initial data in the modified Sobolev space Hs~(R). Using Fourier restriction norm method, Tao's [k,Z]−multiplier method and the contraction mapping principle, we show that the local well-posedness is established for the initial data u0∈Hs~(R) with s≥−74(k = 2) and is established for the initial data u0∈Hs~(R) with s≥−14(k = 3). Using these results and conservation laws, we also prove that the IVP is globally well-posed for the initial data u0∈Hs~(R) with s = 0(k = 2,3). Finally, using complex variables technique and Paley–Wiener theorem, we prove the unique continuation property for the IVP benefited from the ideas of Zhang ZY. et al., On the unique continuation property for the modified Kawahara equation, Advances in Mathematics (China), http://advmath.pku.edu.cn/CN/10.11845/sxjz.2014078b. Copyright © 2015 John Wiley & Sons, Ltd.

A famous theorem due to Weyl and von Neumann asserts that two bounded self-adjoint operators are unitarily equivalent modulo the compacts, if and only if their essential spectrum agree. The above theorem does not hold for unbounded operators. Nevertheless, there exist closed subsets $M$ of $\mathbb{R}$ on which the Weyl--von Neumann Theorem hold: all (not necessarily bounded) self-adjoint operators with essential spectrum $M$ are unitarily equivalent modulo the compacts. In this paper, we determine exactly which $M$ satisfies this property.

In this paper, we investigate the generalized Stieltjes-Wigert and q-Laguerre polynomials. We derive the second- and the third-order nonlinear difference equations for the subleading coefficients of these polynomials and use them to find a few terms of the formal expansions in powers of q(n/2). We also show how the recurrence coefficients in the three-term recurrence relation for these polynomials can be computed efficiently by using the nonlinear difference equations for the subleading coefficient. Moreover, we obtain systems of difference equations with one of the equations being q-discrete Painleve III or V equations and analyze them by a singularity confinement. We also discuss certain generalized weights.

The purpose of the paper is to introduce Stancu-type linear positive operators generated by Dunkl generalization of exponential function. We present approximation properties with the help of well-known Korovkin-type theorem and weighted Korovkin-type theorem and also acquire the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and second-order modulus of continuity by Dunkl analogue of Szasz operators. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we discretize techniques for the construction of axially monogenic functions to the setting of discrete Clifford analysis. Wherefore, we work in the discrete Hermitian Clifford setting, where each basis vector ej is split into a forward and backward basis vector: . We prove a discrete version of Fueter's theorem in odd dimension by showing that for a discrete monogenic function f(ξ0,ξ1) left-monogenic in two variables ξ0 and ξ1 and for a left-monogenic Pk(ξ), the m-dimensional function is in itself left monogenic, that is, a discrete function in the kernel of the discrete Dirac operator. Closely related, we consider a Vekua-type system for the construction of axially monogenic functions. We consider some explicit examples: the discrete axial-exponential functions and the discrete Clifford–Hermite polynomials. Copyright © 2015 John Wiley & Sons, Ltd.

T. Qian As it will turn out in this paper, the recent hype about most of the Clifford–Fourier transforms is not thoroughly worth the pain. Almost everyone that has a real application is separable, and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study the homoclinic solutions of the following second-order Hamiltonian system where , and . Applying the symmetric Mountain Pass Theorem, we establish a couple of sufficient conditions on the existence of infinitely many homoclinic solutions. Our results significantly generalize and improve related ones in the literature. For example, is not necessary to be uniformly positive definite or coercive; through is still assumed to be superquadratic near , it is not assumed to be superquadratic near .

In this paper, we study the existence of infinitely many solutions to p-Kirchhoff-type equation (0.1) where f(x,u) = λh1(x)|u|m − 2u + h2(x)|u|q − 2u,a≥0,μ > 0,τ > 0,λ≥0 and . The potential function verifies , and h1(x),h2(x) satisfy suitable conditions. Using variational methods and some special techniques, we prove that there exists λ0>0 such that problem (0.1) admits infinitely many nonnegative high-energy solutions provided that λ∈[0,λ0) and . Also, we prove that problem (0.1) has at least a nontrivial solution under the assumption f(x,u) = h2|u|q − 2u,p < q< min{p*,p(τ + 1)} and has infinitely many nonnegative solutions for f(x,u) = h1|u|m − 2u,1 < m < p. Copyright © 2015 John Wiley & Sons, Ltd.

T. Qian In this paper, we prove two theorems on normal families of meromorphic functions, which improve a few of results from several authors. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the quasilinear Keller–Segel system with rotation where is a bounded domain with smooth boundary, D(u) is supposed to be sufficiently smooth and satisfies D(u)≥D0um − 1(m≥1) and D(u)≤D1(u + 1)K − mum − 1(K≥1) for all u≥0 with some positive constants D0 and D1, and f(u) is assumed to be smooth enough and non-negative for all u≥0 and f(0) = 0, while S(u,v,x) = (sij)n × n is a matrix with and with l≥2, where is nondecreasing on [0,∞). It is proved that when , the system possesses at least one global and bounded weak solution for any sufficiently smooth non-negative initial data. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness of the local mild solution to the Cauchy problem of the n-dimensional (n≥3) Wigner–Poisson–BGK equation in the space of some integrable functions whose inverse Fourier transform are integrable. The main difficulties in establishing mild solution are to derive the boundedness and locally Lipschitz properties of the appropriate nonlinear terms in the Wiener algebra. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Dirichlet boundary data as follows: −M∫Ω1p(x)|∇u|p(x)dxdiv(|∇u|p(x)−2∇u)=f(x,u)inΩ,u=0on∂Ω. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish some conditions on the existence of solutions. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny defined over its two-division field. We prove that at least half of all the quadratic twists of such an elliptic curve have arbitrarily large 2-Selmer rank, showing that the distribution of 2-Selmer ranks in the quadratic twist family of such an elliptic curve differs from the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve having either no rational two-torsion or full rational two-torsion., Comment: arXiv admin note: text overlap with arXiv:1203.1030

This paper proves nontrivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess method., 20 pages

This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving This paper deals with the model proposed for nonsimple materials with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.

In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is expressed uniformly in terms of natural parameters of the group. In the case of factorizations of minimal length, we recover a formula due to P. Deligne, J. Tits and D. Zagier in the real case and to D. Bessis in the complex case. For the symmetric group, our formula specializes to a formula of D. M. Jackson., Comment: 38 pages, including 18 pages appendix. To appear in Journal of the London Mathematical Society. v3: minor changes and corrected references; v2: added extended discussion on the definition of Coxeter elements

In this paper, we study the nonexistence result for the weighted Lane–Emden equation: −Δu=f(|x|)|u|p−1u,x∈RN(0.1) and the weighted Lane–Emden equation with nonlinear Neumann boundary condition: −Δu=f(|x|)|u|p−1u,x∈R+N,∂u∂ν=g(|x|)|u|−1u,x∈∂R+N,(0.2) where f(|x|) and g(|x|) are the radial and continuously differential functions, R+N={x=(x′,xN)∈RN−1×R+} is an upper half space in RN, and ∂R+N={x=(x′,0),x′∈RN−1}. Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems (0.1) and (0.2) under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd.