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2017年, 第37卷, 第2期　刊出日期：2017-04-25 上一期    下一期

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ON THE FOURIER-VILENKIN COEFFICIENTS Martin G. GRIGORYAN, Stepan SARGSYAN 数学物理学报(英文版). 2017 (2):  293-300.  DOI: 10.1016/S0252-9602(17)30002-4 摘要 ( 42 )   RICH HTML PDF   收藏 In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems:for any ε ∈(0,1), there exists a measurable set E ∈[0,1) of measure bigger than 1-ε such that for any function f ∈ L1[0,1), it is possible to find a function g ∈ L1[0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing. 参考文献 | 相关文章 | 计量指标

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UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR BEACTION-DIFFUSION EQUATIONS WITH SUPERCRITICAL EXPONENT 钟延生, 孙春友 数学物理学报(英文版). 2017 (2):  301-315.  DOI: 10.1016/S0252-9602(17)30003-6 摘要 ( 48 )   RICH HTML PDF   收藏 A new approach is established to show that the semigroup {S (t)}t ≥ 0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in Lq(Ω) (2 ≤ q < ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space. 参考文献 | 相关文章 | 计量指标

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ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNATEIN-UHLENBECK PROCESSES 郭精军, 李楚进 数学物理学报(英文版). 2017 (2):  316-328.  DOI: 10.1016/S0252-9602(17)30004-8 摘要 ( 74 )   RICH HTML PDF   收藏 In this article, we study the existence of collision local time of two independent d-dimensional fractional Ornstein-Uhlenbeck processes XtH1 and XtH2, with different parameters Hi ∈ (0,1), i=1,2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its' chaos expansion. 参考文献 | 相关文章 | 计量指标

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PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, 陈阳舟 数学物理学报(英文版). 2017 (2):  329-341.  DOI: 10.1016/S0252-9602(17)30005-X 摘要 ( 61 )   RICH HTML PDF   收藏 A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results. 参考文献 | 相关文章 | 计量指标

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IMPROVED GRAOIENT METHOD FOR MONOTONE AND LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES Kazuhide NAKAJO 数学物理学报(英文版). 2017 (2):  342-354.  DOI: 10.1016/S0252-9602(17)30006-1 摘要 ( 52 )   RICH HTML PDF   收藏 Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space C and {An}n∈N be a family of monotone and Lipschitz continuos mappings of C into E*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming[10] for solving the variational inequality problem for {An} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space. 参考文献 | 相关文章 | 计量指标

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APPLICATION OF HOLOMORPHIC INVARIANTS IN REPRODUCING KERNEL 潘利双, 王安 数学物理学报(英文版). 2017 (2):  355-367.  DOI: 10.1016/S0252-9602(17)30007-3 摘要 ( 43 )   RICH HTML PDF   收藏 We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains. 参考文献 | 相关文章 | 计量指标

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SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL M. Syed ALI, J. YOGAMBIGAI, 曹进德 数学物理学报(英文版). 2017 (2):  368-384.  DOI: 10.1016/S0252-9602(17)30008-5 摘要 ( 71 )   RICH HTML PDF   收藏 In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results. 参考文献 | 相关文章 | 计量指标

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ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R2 张再云, 黄建华, 孙明保 数学物理学报(英文版). 2017 (2):  385-394.  DOI: 10.1016/S0252-9602(17)30009-7 摘要 ( 65 )   RICH HTML PDF   收藏 In this article, we investigate the initial value problem(IVP) associated with the defocusing nonlinear wave equation on R2 as follows: where the initial data (u0, u1) ∈ Hs(R2)×Hs-1(R2). It is shown that the IVP is global well-posedness in Hs(R2)×Hs-1(R2) for any 1 > s > 2/5. The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy[1]. 参考文献 | 相关文章 | 计量指标

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GLOBAL REGULARITY TO THE 2D INCOMPRESSIBLE MHD WITH MIXED PARTIAL DISSIPATION AND MAGNETIC DIFFUSION IN A BOUNDED DOMAIN 于海波 数学物理学报(英文版). 2017 (2):  395-404.  DOI: 10.1016/S0252-9602(17)30010-3 摘要 ( 38 )   RICH HTML PDF   收藏 This article considers the global regularity to the initial——boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for ux and by, which are estimated by ▽×ux and ▽×by, respectively. Then, we establish the global estimates for ▽×u and ▽×b. 参考文献 | 相关文章 | 计量指标

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BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS 巴娜, 代晋军 数学物理学报(英文版). 2017 (2):  405-424.  DOI: 10.1016/S0252-9602(17)30011-5 摘要 ( 41 )   RICH HTML PDF   收藏 We study the bound states to nonlinear Schrödinger equations with electromagnetic fields ih (∂ψ/∂t)=(h/i▽-A(x))2ψ + V(x)ψ-K(x)|ψ|p-1ψ=0, on R+×RN. Let G (x)=[V (x)](p+1)/(p-1)-N/2[K(x)]-2/(p-1) and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states ψh(x, t)=e-iEt/h uh(x) with uh concentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V (x) and K(x) are allowed to be either compactly supported or unbounded at infinity. 参考文献 | 相关文章 | 计量指标

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THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL 黎深莲, 张学军, 徐思 数学物理学报(英文版). 2017 (2):  425-438.  DOI: 10.1016/S0252-9602(17)30012-7 摘要 ( 69 )   RICH HTML PDF   收藏 Let p > 0 and μ be a normal function on[0,1), ν(r)=(1-r2)1+(n/p) μ(r) for r ∈[0,1). In this article, the bounded or compact weighted composition operator Tφ,ψ from the μ-Bergman space Ap(μ) to the normal weight Bloch type space βν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator Cφ is compact from Ap(μ) to βν is given. At the same time, the authors give the briefly sufficient and necessary condition that Cφ is compact on βu for a > 1. 参考文献 | 相关文章 | 计量指标

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THE LARGEST EIGENVALUE DISTRIBUTION OF THE LAGUERRE UNITARY ENSEMALE Shulin LYU, Yang CHEN 数学物理学报(英文版). 2017 (2):  439-462.  DOI: 10.1016/S0252-9602(17)30013-9 摘要 ( 41 )   RICH HTML PDF   收藏 We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are in (0,t), that is, the largest eigenvalue distribution. Associated with this probability, in the ladder operator approach for orthogonal polynomials, there are recurrence coefficients, namely, αn(t) and βn(t), as well as three auxiliary quantities, denoted by rn(t), Rn(t), and σn(t). We establish the second order differential equations for both βn(t) and rn(t). By investigating the soft edge scaling limit when α=O(n) as n or→∞ or α is finite, we derive a PⅡ, the σ-form, and the asymptotic solution of the probability. In addition, we develop differential equations for orthogonal polynomials Pn(z) corresponding to the largest eigenvalue distribution of LUE and GUE with n finite or large. For large n, asymptotic formulas are given near the singular points of the ODE. Moreover, we are able to deduce a particular case of Chazy's equation for ρ(t)=Ξ'(t) with Ξ(t) satisfying the σ-form of PIV or PV. 参考文献 | 相关文章 | 计量指标

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EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE Adela CAPǍTǍ 数学物理学报(英文版). 2017 (2):  463-476.  DOI: 10.1016/S0252-9602(17)30014-0 摘要 ( 50 )   RICH HTML PDF   收藏 The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle,and to establish the connectedness of the solutions set. 参考文献 | 相关文章 | 计量指标

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SOME PROPERTIES OF DOUBLE DESIGNS IN TERMS OF LEE DISCREPANCY 邹娜, 覃红 数学物理学报(英文版). 2017 (2):  477-487.  DOI: 10.1016/S0252-9602(17)30015-2 摘要 ( 53 )   RICH HTML PDF   收藏 Doubling is a simple but powerful method of constructing two-level fractional factorial designs with high resolution. This article studies uniformity in terms of Lee discrepancy of double designs. We give some linkages between the uniformity of double design and the aberration case of the original one under different criteria. Furthermore, some analytic linkages between the generalized wordlength pattern of double design and that of the original one are firstly provided here, which extend the existing findings. The lower bound of Lee discrepancy for double designs is also given. 参考文献 | 相关文章 | 计量指标

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CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES 秦小龙, Sun Young CHO 数学物理学报(英文版). 2017 (2):  488-502.  DOI: 10.1016/S0252-9602(17)30016-4 摘要 ( 97 )   RICH HTML PDF   收藏 In this article, fixed points of generalized asymptotically quasi-φ-nonexpansive mappings and equilibrium problems are investigated based on a monotone projection algorithm. Strong convergence theorems are established without the aid of compactness in the framework of reflexive Banach spaces. 参考文献 | 相关文章 | 计量指标

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HYPERCYCLICITY, SUPERCYCLICITY AND GENERALIZED RAKO?EVI?'S PROPERTY Mohamed AMOUCH, Youness FAOUZI 数学物理学报(英文版). 2017 (2):  503-510.  DOI: 10.1016/S0252-9602(17)30017-6 摘要 ( 75 )   RICH HTML PDF   收藏 A Banach space operator satisfies generalized Rako?evi?'s property (gw) if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property (gw). 参考文献 | 相关文章 | 计量指标

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NONLINEAR ANALYSIS ON THE VIBRATION OF ELASTIC PLATES 丁敏, 龚胜波 数学物理学报(英文版). 2017 (2):  511-526.  DOI: 10.1016/S0252-9602(17)30018-8 摘要 ( 69 )   RICH HTML PDF   收藏 We consider the vibration of elastic thin plates under certain reasonable assump-tions. We derive the nonlinear equations for this model by the Hamilton Principle. Under the conditions on the hyperbolicity for the initial data, we establish the local time well-posedness for the initial and boundary value problem by Picard iteration scheme, and obtain the estimates for the solutions. 参考文献 | 相关文章 | 计量指标

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LOCAL ESTIMATE ABOUT SCHRÖDINGER MAXIMAL OPERATOR ON H-TYPE GROUPS 刘和平, 曾宏波 数学物理学报(英文版). 2017 (2):  527-538.  DOI: 10.1016/S0252-9602(17)30019-X 摘要 ( 65 )   RICH HTML PDF   收藏 Let △ be full Laplacian on H-type group G.Then for every compact set D ⊆ G, a local estimate of the Schrödinger maximal operator holds,that is, We also show that the above inequality fails when s < 1/4. 参考文献 | 相关文章 | 计量指标

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A VARIATIONAL PROBLEM ARISING IN REGISTRATION OF DIFFUSION TENSOR IMAGES 韩欢, 周焕松 数学物理学报(英文版). 2017 (2):  539-554.  DOI: 10.1016/S0252-9602(17)30020-6 摘要 ( 121 )   RICH HTML PDF   收藏 The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images. 参考文献 | 相关文章 | 计量指标

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MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITHÖSIGN-CHANGING POTENTIAL 王丽霞, 马世旺, 许娜 数学物理学报(英文版). 2017 (2):  555-572.  DOI: 10.1016/S0252-9602(17)30021-8 摘要 ( 48 )   RICH HTML PDF   收藏 In this article,we study the following nonhomogeneous Schrödinger-Poisson equations where λ > 0 is a parameter.Under some suitable assumptions on V,K,f and g,the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.In particular,the potential V is allowed to be signchanging. 参考文献 | 相关文章 | 计量指标