Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. Spectral algorithms form a general framework that unifies many regularization schemes in learning theory. In this paper, we propose and analyze a class of thresholded spectral algorithms that are designed based on empirical features. Soft thresholding is adopted to achieve sparse approximations. Our analysis shows that without sparsity assumption of the regression function, the output functions of thresholded spectral algorithms are represented by empirical features with satisfactory sparsity, and the convergence rates are comparable to those of the classical spectral algorithms in the literature. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500026

Pages: 1 - 25 Abstract: Analysis and Applications, Ahead of Print. The paper studies optimal strategies for a borrower who needs to repay his debt, in an infinite time horizon. An instantaneous bankruptcy risk is present, which increases with the size of the debt. This induces a pool of risk-neutral lenders to charge a higher interest rate, to compensate for the possible loss of part of their investment. Solutions are interpreted as Stackelberg equilibria, where the borrower announces his repayment strategy [math] at all future times, and lenders adjust the interest rate accordingly. This yields a highly non-standard problem of optimal control, where the instantaneous dynamics depend on the entire future evolution of the system. Our analysis shows the existence of optimal open-loop controls, deriving necessary conditions for optimality and characterizing possible asymptotic limits as [math]. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500038

Pages: 1 - 43 Abstract: Analysis and Applications, Ahead of Print. In this paper, we investigate the Cauchy problem for the 3D viscous nonhomogeneous incompressible magnetohydrodynamic equations in critical Besov spaces. We aim at proving the local and global well-posedness for respectively large and small initial data having critical Besov regularity, without assumptions of small density variation. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S0219530517500014

Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. We study a family of coherent states, called Schrödingerlets, both in the continuous and discrete setting. They are defined in terms of the Schrödinger equation of a free quantum particle and some of its invariant transformations. Citation: Analysis and Applications PubDate: 2017-01-23T07:19:36Z DOI: 10.1142/S021953051750004X

Authors:D. P. Hewett, A. Moiola Pages: 1 - 40 Abstract: Analysis and Applications, Ahead of Print. This paper concerns the following question: given a subset [math] of [math] with empty interior and an integrability parameter [math], what is the maximal regularity [math] for which there exists a non-zero distribution in the Bessel potential Sobolev space [math] that is supported in [math]? For sets of zero Lebesgue measure, we apply well-known results on set capacities from potential theory to characterize the maximal regularity in terms of the Hausdorff dimension of [math], sharpening previous results. Furthermore, we provide a full classification of all possible maximal regularities, as functions of [math], together with the sets of values of [math] for which the maximal regularity is attained, and construct concrete examples for each case. Regarding sets with positive measure, for which the maximal regularity is non-negative, we present new lower bounds on the maximal Sobolev regularity supported by certain fat Cantor sets, which we obtain both by capacity-theoretic arguments, and by direct estimation of the Sobolev norms of characteristic functions. We collect several results characterizing the regularity that can be achieved on certain special classes of sets, such as [math]-sets, boundaries of open sets, and Cartesian products, of relevance for applications in differential and integral equations. Citation: Analysis and Applications PubDate: 2016-12-09T07:50:46Z DOI: 10.1142/S021953051650024X

Authors:Feng Xie, Christian Klingenberg Pages: 1 - 18 Abstract: Analysis and Applications, Ahead of Print. General radiation magnetic hydrodynamics models include two main parts that are coupled: one part is the macroscopic magnetic fluid part, which is governed by the ideal compressible magnetohydrodynamic (MHD) equations with additional radiation terms; another part is the radiation field, which is described by a transfer equation. It is well known that in radiation hydrodynamics without a magnetic field there are two physical approximations: one is the so-called P1 approximation and the other is the so-called gray approximation. Starting out with a general radiation MHD model one can derive the so-called MHD-P1 approximation model. In this paper, we study the non-relativistic type limit for this MHD-P1 approximation model since the speed of light is much larger than the speed of the macroscopic fluid. This way we achieve a rigorous derivation of a widely used macroscopic model in radiation magnetohydrodynamics. Citation: Analysis and Applications PubDate: 2016-12-08T08:38:44Z DOI: 10.1142/S0219530516500238

Authors:Francesco De Anna Pages: 1 - 51 Abstract: Analysis and Applications, Ahead of Print. The most established theory for modeling the dynamics of nematic liquid crystals is the celebrated Ericksen–Leslie system, which presents some major analytical challenges. We study a simplified version of the system, which still exhibits the major difficulties. We consider the density-dependent case and study the Cauchy problem in the whole space. We establish the global existence of solutions for small initial data by assuming only that the initial density is bounded and kept away far from vacuum, while the initial velocity and the gradient of the initial director field belong to certain critical Besov spaces. Under slightly more assumptions on the initial velocity and the director field, we also prove that the solutions are unique. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:25Z DOI: 10.1142/S0219530516500172

Authors:Peter Greiner, Yutian Li Pages: 1 - 27 Abstract: Analysis and Applications, Ahead of Print. Let [math] denote the holomorphic tangential vector field to the generalized upper-half plane [math]. In our terminology, [math]. Consider the [math] operator on the boundary of [math], [math]; note that [math] is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution [math] to [math]. Our approach is based on special functions and their properties. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:24Z DOI: 10.1142/S0219530516500196

Authors:Patrick L. Combettes, Saverio Salzo, Silvia Villa Pages: 1 - 54 Abstract: Analysis and Applications, Ahead of Print. This paper proposes a unified framework for the investigation of constrained learning theory in reflexive Banach spaces of features via regularized empirical risk minimization. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a flexible model for various priors on the features, including, in particular, hard constraints and powers of Banach norms. In such context, the main results establish a new general form of the representer theorem and the consistency of the corresponding learning schemes under general conditions on the loss function, the geometry of the feature space, and the modulus of total convexity of the regularizer. In addition, the proposed analysis gives new insight into basic tools such as reproducing Banach spaces, feature maps, and universality. Even when specialized to Hilbert spaces, this framework yields new results that extend the state of the art. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:17Z DOI: 10.1142/S0219530516500202

Authors:Chunxia Guan, Kai Yan, Xuemei Wei Pages: 1 - 24 Abstract: Analysis and Applications, Ahead of Print. This paper is devoted to the existence and Lipschitz continuity of global conservative weak solutions in time for the modified two-component Camassa–Holm system on the real line. We obtain the global weak solutions via a coordinate transformation into the Lagrangian coordinates. The key ingredients in our analysis are the energy density given by the positive Radon measure and the proposed new distance functions as well. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:15Z DOI: 10.1142/S0219530516500226

Authors:Zhong Tan, Yong Wang, Leilei Tong Pages: 1 - 24 Abstract: Analysis and Applications, Ahead of Print. The asymptotic stability of the steady state with the strictly positive constant density and the vanishing velocity and magnetic field to the Cauchy problem of the three-dimensional compressible viscous, heat-conducting magnetohydrodynamic equations with Coulomb force is established under small initial perturbations. Using a general energy method, we obtain the optimal time decay rates of the solution and its higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces. As a corollary, the [math]–[math] [math] type of the decay rates follows without requiring that the [math] norm of initial data is small. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:13Z DOI: 10.1142/S0219530516500160

Authors:Brice Franke, Nejib Yaakoubi Pages: 1 - 14 Abstract: Analysis and Applications, Ahead of Print. We construct divergence free vector-fields on compact Riemannian surfaces which push the spectral gap of some diffusion generator above some prescribed value. The resulting diffusion describes some Brownian particle in a stationary incompressible fluid. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution. In other terms, we describe efficient fluid motion, to accelerate the convergence to equilibrium of some Brownian particle in a two-dimensional liquid. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:12Z DOI: 10.1142/S0219530516500184

Authors:Yunyun Zhai, Xianguo Geng Pages: 1 - 31 Abstract: Analysis and Applications, Ahead of Print. Based on the Lenard recursion equations and the stationary zero-curvature equation, we derive the coupled Sasa–Satsuma hierarchy, in which a typical number is the coupled Sasa–Satsuma equation. The properties of the associated trigonal curve and the meromorphic functions are studied, which naturally give the essential singularities and divisors of the meromorphic functions. By comparing the asymptotic expansions for the Baker–Akhiezer function and its Riemann theta function representation, we arrive at the finite genus solutions of the whole coupled Sasa–Satsuma hierarchy in terms of the Riemann theta function. Citation: Analysis and Applications PubDate: 2016-10-19T10:07:11Z DOI: 10.1142/S0219530516500214

Authors:A. Krivoshein, M. Skopina Pages: 1 - 22 Abstract: Analysis and Applications, Ahead of Print. Approximation properties of the expansions [math], where [math] is a linear differential operator and [math] is a matrix dilation, are studied. The sampling expansions are a special case of such differential expansions. Error estimations in [math]-norm, [math], are given in terms of the Fourier transform of [math]. The approximation order depends on the smoothness of [math], the order of [math], the order of Strang–Fix condition for [math] and [math]. A wide class of [math] including both band-limited and compactly supported functions is considered, but a special condition of compatibility [math] with [math] is required. Such differential expansions may be useful for engineers. Citation: Analysis and Applications PubDate: 2016-07-07T11:03:18Z DOI: 10.1142/S0219530516500147

Authors:Xiaoyi Chen, Zilong Song, Hui-Hui Dai Pages: 1 - 30 Abstract: Analysis and Applications, Ahead of Print. This paper studies the planar deformations of a beam composed of a linearly elastic material. Starting from the field equations for the plane-stress problem and adopting a series expansion for the displacement vector about the bottom surface, we deduce the beam equations with two unknowns in a consistent manner. The success relies on using the field equations together with the bottom traction conditions to establish the exact recursion relations, such that all quantities can be represented in terms of the two leading expansion coefficients of the displacements. Another feature is that the remainders of the series can be carried over to the beam equations. Then, based on the general solutions and the error terms of the beam equations, pointwise error estimates for displacement and stress fields are rigorously established. Three benchmark problems are considered, for which the two-dimensional exact solutions are available. It is shown that this new beam theory recovers the exact solutions for these problems. Two cases with boundary layer effects are also discussed in the appendix. Citation: Analysis and Applications PubDate: 2016-07-07T11:03:17Z DOI: 10.1142/S0219530516500135

Authors:Joachim Toft Pages: 1 - 37 Abstract: Analysis and Applications, Ahead of Print. We deduce continuity and Schatten–von Neumann properties for operators with matrices satisfying mixed quasi-norm estimates with Lebesgue and Schatten parameters in [math]. We use these results to deduce continuity and Schatten–von Neumann properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces, or in appropriate Hörmander classes. Citation: Analysis and Applications PubDate: 2016-07-07T11:03:16Z DOI: 10.1142/S0219530516500159

Authors:Mourad E. H. Ismail Pages: 1 - 11 Abstract: Analysis and Applications, Ahead of Print. We prove that the function [math] and its [math]-analogue are of the form [math] and [math] is completely monotonic in [math]. In particular both [math] and [math] are Laplace transforms of infinitely divisible distributions. We also extend Lerch’s inequality to the [math]-gamma function. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:18Z DOI: 10.1142/S0219530516500093

Authors:Yu Xia, Song Li Pages: 1 - 20 Abstract: Analysis and Applications, Ahead of Print. This paper considers the non-uniform sparse recovery of block signals in a fusion frame, which is a collection of subspaces that provide redundant representation of signal spaces. Combined with specific fusion frame, the sensing mechanism selects block-vector-valued measurements independently at random from a probability distribution [math]. If the probability distribution [math] obeys a simple incoherence property and an isotropy property, we can faithfully recover approximately block sparse signals via mixed [math]-minimization in ways similar to Compressed Sensing. The number of measurements is significantly reduced by a priori knowledge of a certain incoherence parameter [math] associated with the angles between the fusion frame subspaces. As an example, the paper shows that an [math]-sparse block signal can be exactly recovered from about [math] Fourier coefficients combined with fusion frame [math], where [math]. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:16Z DOI: 10.1142/S0219530516500032

Authors:Yonggeun Cho, Mouhamed M. Fall, Hichem Hajaiej, Peter A. Markowich, Saber Trabelsi Pages: 1 - 31 Abstract: Analysis and Applications, Ahead of Print. This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:14Z DOI: 10.1142/S0219530516500056

Authors:Daniel Alpay, Fabrizio Colombo, Jonathan Gantner, David P. Kimsey Pages: 1 - 33 Abstract: Analysis and Applications, Ahead of Print. The quaternionic analogue of the Riesz–Dunford functional calculus and the theory of semigroups and groups of linear quaternionic operators have recently been introduced and studied. In this paper, we suppose that [math] is the quaternionic infinitesimal generator of a strongly continuous group of operators [math] and we show how we can define bounded operators [math], where [math] belongs to a class of functions that is larger than the one to which the quaternionic functional calculus applies, using the quaternionic Laplace–Stieltjes transform. This class includes functions that are slice regular on the [math]-spectrum of [math] but not necessarily at infinity. Moreover, we establish the relation between [math] and the quaternionic functional calculus and we study the problem of finding the inverse of [math]. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:13Z DOI: 10.1142/S021953051650007X

Authors:Seung-Yeal Ha, Se Eun Noh, Jinyeong Park Pages: 1 - 25 Abstract: Analysis and Applications, Ahead of Print. We study the dynamic interplay between inertia and heterogeneous dynamics in an ensemble of Kuramoto oscillators. When external fields and internal forces are exerted on a system of Kuramoto oscillators, each oscillator has its own distinct dynamics, so that there is no notion of collective dynamics in the ensemble, and complete synchronization is not observed in such systems. In this paper, we study a relaxed version of synchronization, namely the “practical synchronization”, of Kuramoto oscillators, emerging from the dynamic interplay between inertia and heterogeneous decoupled dynamics. We will show that for some class of initial configurations and parameters, the fluctuation of phases and frequencies around the average values will be proportional to the inverse of the coupling strength. We provide several numerical examples, and compare these with our analytical results. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:12Z DOI: 10.1142/S0219530516500111

Authors:Xiaofeng Hou, Hongyun Peng, Changjiang Zhu Pages: 1 - 30 Abstract: Analysis and Applications, Ahead of Print. In this paper, we investigate the global well-posedness of classical solutions to three-dimensional Cauchy problem of the compressible Navier–Stokes type system with a Korteweg stess tensor under the condition that the initial energy is small. This result improves previous results obtained by Hattori–Li in [H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type, SIAM J. Math. Anal. 25 (1994) 85–98; H. Hattori and D. Li. Global solutions of a high-dimensional system for Korteweg materials. J. Math. Anal. Appl. 198 (1996) 84–97.], where the existence of the classical solution is established for initial data close to an equilibrium in some Sobolev space [math]. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:10Z DOI: 10.1142/S0219530516500123

Authors:Dekai Liu, Song Li Pages: 1 - 16 Abstract: Analysis and Applications, Ahead of Print. In this paper, we consider to recover a signal which is sparse in terms of a tight frame from undersampled measurements via [math]-minimization problem for [math]. In [Compressed sensing with coherent tight frames via [math]-minimization for [math], Inverse Probl. Imaging 8 (2014) 761–777], Li and Lin proved that when [math] there exists a [math], depending on [math] such that for any [math], each solution of the [math]-minimization problem can approximate the true signal well. The constant [math] is referred to as the [math]-RIP constant of order [math] which was first introduced by Candès et al. in [Compressed sensing with coherent and redundant dictionaries, Appl. Comput. Harmon. Anal. 31 (2011) 59–73]. The main aim of this paper is to give the closed-form expression of [math]. We show that for every [math]-RIP constant [math], if [math] where p̄ = min 1, 50 31(1 − δ2s) ,δ2s ∈ (0, 0.7183),0.4542, δ2s ∈ [0.7183, 0.7729),2(1 − δ2s), δ2s ∈ [0.7729, 1), then the [math]-minimization problem can reconstruct the true signal approximately well. Our main results also hold for the complex case, i.e. the measurement matrix, the tight frame and the signal are all in the complex domain. It should be noted that the[math]-RIP condition is independent of the coherence of the tight frame (see [Compressed sensing with coherent and redundant dictionaries, Appl. Comput. Harmon. Anal. 31 (2011) 59–73]). In particular, when the tight frame reduces to an identity matrix or an orthonormal matrix, the conclusions in our paper coincide with the results appeared in [Stable recovery of sparse signals via [math]-minimization, Appl. Comput. Harmon. Anal. 38 (2015) 161–176]. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:07Z DOI: 10.1142/S021953051650010X

Authors:Paolo Piersanti, Patrizia Pucci Pages: 1 - 34 Abstract: Analysis and Applications, Ahead of Print. The paper focuses on the existence of nontrivial solutions of a nonlinear eigenvalue perturbed problem depending on a real parameter [math] under homogeneous boundary conditions in bounded domains with Lipschitz boundary. The problem involves a weighted fractional [math]-Laplacian operator. Denoting by [math] a sequence of eigenvalues obtained via mini–max methods and linking structures we prove the existence of (weak) solutions both when there exists [math] such that [math] and when [math]. The paper is divided into two parts: in the first part existence results are determined when the perturbation is the derivative of a globally positive function whereas, in the second part, the case when the perturbation is the derivative of a function that could be either locally positive or locally negative at [math] is taken into account. In the latter case, it is necessary to extend the main results reported in [A. Iannizzotto, S. Liu, K. Perera and M. Squassina, Existence results for fractional [math]-Laplacian problems via Morse theory, Adv. Calc. Var. 9(2) (2016) 101–125]. In both cases, the existence of solutions is achieved via linking methods. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:06Z DOI: 10.1142/S0219530516500020

Authors:Xinglong Wu, Boling Guo Pages: 1 - 28 Abstract: Analysis and Applications, Ahead of Print. The present paper is devoted to the study of the global solution and nonlinear stability to the coupled complex Ginzburg–Landau and Burgers (CGL–Burgers) equations for sequential flames which describe the interaction of the excited oscillatory and the damped monotonic mode governing a sequential chemical reaction. If the solution blows up in finite time, we derive the lower bound of blow-up rate of blow-up solution. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:05Z DOI: 10.1142/S0219530516500044

Authors:Alaaeddine Hammoudi, Oana Iosifescu, Martial Bernoux Pages: 1 - 23 Abstract: Analysis and Applications, Ahead of Print. The aim of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction–diffusion–advection system with a quadratic reaction term. This is a spatial version of Modeling Organic changes by Micro-Organisms of Soil model, recently introduced by M. Pansu and his group. We show here that for any nonnegative initial condition, there exists a unique nonnegative weak solution. Moreover, if we assume time periodicity of model entries, taking into account seasonal effects, we prove existence of a minimal and a maximal periodic weak solution. In a particular case, these two solutions coincide and they become a global attractor of any bounded solution of the periodic system. Citation: Analysis and Applications PubDate: 2016-05-04T01:15:03Z DOI: 10.1142/S0219530516500081

Authors:Lan Luo, Hongjun Yu Abstract: Analysis and Applications, Ahead of Print. In this work, we show the spectrum structure of the linear Fokker–Planck equation by using the semigroup theory and the linear operator perturbation theory. As an application, we show the large time behavior of the solutions to the linear Fokker–Planck equation. Citation: Analysis and Applications PubDate: 2015-08-17T01:20:02Z DOI: 10.1142/S0219530515500219

Authors:Jun Cao, Svitlana Mayboroda, Dachun Yang Pages: 1 - 88 Abstract: Analysis and Applications, Ahead of Print. Let L be a divergence form inhomogeneous higher order elliptic operator with complex bounded measurable coefficients. In this paper, for all p ∈ (0, ∞) and L satisfying a weak ellipticity condition, the authors introduce the local Hardy spaces [math] associated with L, which coincide with Goldberg's local Hardy spaces hp(ℝn) for all p ∈ (0, ∞) when L ≡ -Δ (the Laplace operator). The authors also establish a real-variable theory of [math], which includes their characterizations in terms of the local molecules, the square functions or the maximal functions, the complex interpolation and dual spaces. These real-variable characterizations on the local Hardy spaces are new even when L ≡ -div(A∇) (the divergence form homogeneous second-order elliptic operator). Moreover, the authors show that [math] coincides with the Hardy space [math] associated with the operator L + δ for all p ∈ (0, ∞), where δ is some positive constant depending on the ellipticity and the off-diagonal estimates of L. As an application, the authors establish some mapping properties for the local Riesz transforms [math] on [math], where k ∈ {0,…,m} and p ∈ (0, 2]. Citation: Analysis and Applications PubDate: 2015-08-17T01:20:03Z DOI: 10.1142/S0219530515500189

Authors:Jin Liang, James H. Liu, Ti-Jun Xiao, Hong-Kun Xu Pages: 1 - 19 Abstract: Analysis and Applications, Ahead of Print. In this paper, we are concerned with the periodicity of solutions to the Cauchy problem for nonautonomous impulsive delay evolution equations with periodic inhomogenous terms in Banach spaces, where the operators in the linear part (possibly unbounded) depend on the time t and generate an evolution family of linear operators. We first establish two new Gronwall–Bellman-type inequalities, and then prove a new and general existence theorem for periodic mild solutions to the nonautonomous impulsive delay evolution equations, which extends essentially some existing results even for the autonomous case as well as for the case when impulsive perturbations or delays are absent. Citation: Analysis and Applications PubDate: 2015-08-17T01:20:02Z DOI: 10.1142/S0219530515500281

Authors:Filippo De Mari, Ernesto De Vito, Stefano Vigogna Pages: 1 - 19 Abstract: Analysis and Applications, Ahead of Print. We classify up to conjugation by GL(2, ℝ) (more precisely, block diagonal symplectic matrices) all the semidirect products inside the maximal parabolic of Sp(2, ℝ) by means of an essentially geometric argument. This classification has already been established in [G. S. Alberti, L. Balletti, F. De Mari and E. De Vito, Reproducing subgroups of Sp(2, ℝ). Part I: Algebraic classification, J. Fourier Anal. Appl.9(4) (2013) 651–682] without geometry, under a stricter notion of equivalence, namely, conjugation by arbitrary symplectic matrices. The present approach might be useful in higher dimensions and provides some insight. Citation: Analysis and Applications PubDate: 2015-08-17T01:20:00Z DOI: 10.1142/S0219530515500256

Authors:George A. Anastassiou Pages: 1 - 20 Abstract: Analysis and Applications, Ahead of Print. This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function. Citation: Analysis and Applications PubDate: 2015-08-17T01:19:59Z DOI: 10.1142/S0219530515500293

Authors:Lior Falach, Roberto Paroni, Paolo Podio-Guidugli Pages: 1 - 17 Abstract: Analysis and Applications, Ahead of Print. We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of Γ-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence Γ-converges to a functional representing the energy of a Timoshenko beam. Citation: Analysis and Applications PubDate: 2015-08-17T01:19:56Z DOI: 10.1142/S0219530515500207

Authors:M. Chipot, K. Kaulakytė, K. Pileckas, W. Xue Pages: 1 - 27 Abstract: Analysis and Applications, Ahead of Print. We study the stationary nonhomogeneous Navier–Stokes problem in a two-dimensional symmetric domain with a semi-infinite outlet (for instance, either paraboloidal or channel-like). Under the symmetry assumptions on the domain, boundary value and external force, we prove the existence of at least one weak symmetric solution without any restriction on the size of the fluxes, i.e. the fluxes of the boundary value a over the inner and the outer boundaries may be arbitrarily large. Only the necessary compatibility condition (the total flux is equal to zero) has to be satisfied. Moreover, the Dirichlet integral of the solution can be finite or infinite depending on the geometry of the domain. Citation: Analysis and Applications PubDate: 2015-08-17T01:19:54Z DOI: 10.1142/S0219530515500268

Authors:Yoshinori Morimoto, Shuaikun Wang, Tong Yang Pages: 1 - 21 Abstract: Analysis and Applications, Ahead of Print. In this paper, we will introduce a precise classification of characteristic functions in the Fourier space according to the moment constraint in the physical space of any order. Based on this, we construct measure-valued solutions to the homogeneous Boltzmann equation with the exact moment condition as the initial data. Citation: Analysis and Applications PubDate: 2015-08-17T01:19:54Z DOI: 10.1142/S0219530515500232

Authors:Yong Ding, Yaoming Niu Pages: 1 - 16 Abstract: Analysis and Applications, Ahead of Print. In the present paper, we give the local and global weighted Lq maximal estimate for the operator [math], which is defined by $$e^{it\phi(\sqrt{-\Delta})} f(\gamma(x,t)) = (2\pi)^{-1} \int_{{\mathbb R}} e^{i\gamma(x,t)\,{\cdot}\,\xi\,{+}\,it\phi( \xi )}\hat{f}(\xi)d\xi,$$ where ϕ satisfies some growth conditions, [math] is a pseudo-differential operator with symbol ϕ( ξ ) and γ : ℝ × ℝ → ℝ satisfies Hölder's condition of order α and bilipschitz conditions. As a corollary of the above conclusions, we show that if f ∈ Hs(ℝ) for s ≥ ¼ and ½ ≤ α ≤ 1, then $$\mathop{\rm lim}\limits_{t\rightarrow 0}e^{it\phi(\sqrt{-\Delta})}f(\gamma(x,t)) = f(x),\quad {\rm a.e.} x \in {\mathbb R}. \qquad\qquad\qquad (*)$$ In particular, if taking ϕ(r) = r2, then this improves a result in [C. Cho, S. Lee and A. Vargas, Problems on pointwise convergence of solutions to the Schrödinger equation, J. Fourier Anal. Appl.18 (2012) 972–994], where (*) holds for s > ¼ only. Citation: Analysis and Applications PubDate: 2015-08-17T01:19:53Z DOI: 10.1142/S021953051550027X