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2017年, 第37卷, 第1期　刊出日期：2017-02-25 上一期    下一期

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A TWO-DIMENSIONAL GLIMM TYPE SCHEME ON CAUCHY PROBLEM OF TWO-DIMENSIONAL SCALAR CONSERVATION LAW 阚辉, 杨小舟 数学物理学报(英文版). 2017 (1):  1-25.  DOI: 10.1016/S0252-9602(16)30111-4 摘要 ( 123 )   RICH HTML PDF   收藏 In this paper, we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law ∂tu+∂xf(u)+∂yg(u)=0, u(x, y, 0)=u0(x, y). In which initial data can be unbounded. Although the existence and uniqueness of the weak entropy solution are obtained, little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation. So we construct such scheme in our paper and get some new results. 参考文献 | 相关文章 | 计量指标

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DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES 刘振海, 曾生达 数学物理学报(英文版). 2017 (1):  26-32.  DOI: 10.1016/S0252-9602(16)30112-6 摘要 ( 104 )   RICH HTML PDF   收藏 In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem. 参考文献 | 相关文章 | 计量指标

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PERIODICITY OF THE UNIVOQUE β-EXPANSIONS 戈跃华, 谭波 数学物理学报(英文版). 2017 (1):  33-46.  DOI: 10.1016/S0252-9602(16)30113-8 摘要 ( 71 )   RICH HTML PDF   收藏 Let m≥1 be an integer, 1 < β < m+1. A sequence ε1ε2ε3… with εi∈{0, 1, …,m} is called a β-expansion of a real number x if x=∑i(εi)/(βi). It is known that when the base β is smaller than the generalized golden ration, any number has uncountably many expansions, while when β is larger, there are numbers which has unique expansion. In this paper, we consider the bases such that there is some number whose unique expansion is purely periodic with the given smallest period. We prove that such bases form an open interval, moreover, any two such open intervals have inclusion relationship according to the Sharkovskiǐ ordering between the given minimal periods. We remark that our result answers an open question posed by Baker, and the proof for the case m=1 is due to Allouche, Clarke and Sidorov. 参考文献 | 相关文章 | 计量指标

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A NECESSARY AND A SUFFICIENT CONDITION FOR THE EXISTENCE OF THE POSITIVE RADIAL SOLUTIONS TO HESSIAN EQUATIONS AND SYSTEMS WITH WEIGHTS Dragos-Patru COVEI 数学物理学报(英文版). 2017 (1):  47-57.  DOI: 10.1016/S0252-9602(16)30114-X 摘要 ( 118 )   RICH HTML PDF   收藏 In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou (existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters, Volume 50, December 2015, Pages 48-55). 参考文献 | 相关文章 | 计量指标

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GRADIENT ESTIMATES FOR SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV GROWTH AND HARDY POTENTIAL 向长林 数学物理学报(英文版). 2017 (1):  58-68.  DOI: 10.1016/S0252-9602(16)30115-1 摘要 ( 108 )   RICH HTML PDF   收藏 This note is a continuation of the work[17]. We study the following quasilinear elliptic equations -△pu-(μ)/(|x|p)|u|p-2u=Q(x)|u|(Np)/(N-p)-2u, x∈RN, where 1 < p < N, 0≤μ < ((N-p)/p)p and Q∈L∞(RN). Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity. 参考文献 | 相关文章 | 计量指标

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SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES 彭志刚, 钟广祯 数学物理学报(英文版). 2017 (1):  69-78.  DOI: 10.1016/S0252-9602(16)30116-3 摘要 ( 175 )   RICH HTML PDF   收藏 Let A be the space of functions analytic in the unit disk D={z:|z|<1}. Let U denote the set of all functions f∈A satisfying the conditions f(0)=f'(0) 1=0 and |f'(z)((z)/(f(z)))2-1|<1 (|z|< 1). Also, let denote the set of all functions f∈A satisfying the conditions f(0)=f'(0)-1=0 and |zf'(z)-f(z)|<(1)/(2) (|z|<1). In this article, we discuss the properties of U and Ω. 参考文献 | 相关文章 | 计量指标

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THE POINTWISE ESTIMATES OF SOLUTIONS FOR A NONLINEAR CONVECTION DIFFUSION REACTION EQUATION 刘国威 数学物理学报(英文版). 2017 (1):  79-96.  DOI: 10.1016/S0252-9602(16)30117-5 摘要 ( 94 )   RICH HTML PDF   收藏 This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension. First, the pointwise estimates of solutions are obtained, furthermore, we obtain the optimal Lp, 1≤p≤+∞, convergence rate of solutions for small initial data. Then we establish the local existence of solutions, the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data. Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates. 参考文献 | 相关文章 | 计量指标

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LIMITING DIRECTIONS OF JULIA SETS OF ENTIRE SOLUTIONS TO COMPLEX DIFFERENTIAL EQUATIONS 王珺, 陈宗煊 数学物理学报(英文版). 2017 (1):  97-107.  DOI: 10.1016/S0252-9602(16)30118-7 摘要 ( 62 )   RICH HTML PDF   收藏 In this paper, we mainly investigate the dynamical properties of entire solutions of complex differential equations. With some conditions on coefficients, we prove that the set of common limiting directions of Julia sets of solutions, their derivatives and their primitives must have a definite range of measure. 参考文献 | 相关文章 | 计量指标

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CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION 崔静, 闫理坦 数学物理学报(英文版). 2017 (1):  108-118.  DOI: 10.1016/S0252-9602(16)30119-9 摘要 ( 99 )   RICH HTML PDF   收藏 In this paper, we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H∈((1)/(2), 1) in a Hilbert space. We employ the α-norm in order to reflect the relationship between H and the fractional power α. Sufficient conditions are established by using stochastic analysis theory and operator theory. An example is provided to illustrate the effectiveness of the proposed result. 参考文献 | 相关文章 | 计量指标

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NON-EXISTENCE FOR FRACTIONALLY DAMPED FRACTIONAL DIFFERENTIAL PROBLEMS Mohammed D. KASSIM, Khaled M. FURATI, Nasser-eddine TATAR 数学物理学报(英文版). 2017 (1):  119-130.  DOI: 10.1016/S0252-9602(16)30120-5 摘要 ( 108 )   RICH HTML PDF   收藏 In this paper, we are concerned with a fractional differential inequality containing a lower order fractional derivative and a polynomial source term in the right hand side. A non-existence of non-trivial global solutions result is proved in an appropriate space by means of the test-function method. The range of blow up is found to depend only on the lower order derivative. This is in line with the well-known fact for an internally weakly damped wave equation that solutions will converge to solutions of the parabolic part. 参考文献 | 相关文章 | 计量指标

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THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES 梁美丽, 霍颖莹 数学物理学报(英文版). 2017 (1):  131-138.  DOI: 10.1016/S0252-9602(16)30121-7 摘要 ( 82 )   RICH HTML PDF   收藏 The article investigates the growth of multiple Dirichlet series. The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained. 参考文献 | 相关文章 | 计量指标

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SCALAR CURVATURE TYPE PROBLEM ON THE THREE DIMENSIONAL BOUNDED DOMAIN Mohamed BEN AYED, Habib FOURTI 数学物理学报(英文版). 2017 (1):  139-173.  DOI: 10.1016/S0252-9602(16)30122-9 摘要 ( 91 )   RICH HTML PDF   收藏 In this paper we prove an existence result for the nonlinear elliptic problem:-△u=Ku5, u>0 in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain of R3 and K is a positive function in Ω. Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument. 参考文献 | 相关文章 | 计量指标

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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE COMPRESSIBLE NEMATIC LIQUID CRYSTAL SYSTEM IN R3 李银, 位瑞英, 姚正安 数学物理学报(英文版). 2017 (1):  174-186.  DOI: 10.1016/S0252-9602(16)30123-0 摘要 ( 52 )   RICH HTML PDF   收藏 In this paper, we study a nematic liquid crystals system in three-dimensional whole space R3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1(R3) additionally. 参考文献 | 相关文章 | 计量指标

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ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS 高凌云 数学物理学报(英文版). 2017 (1):  187-194.  DOI: 10.1016/S0252-9602(16)30124-2 摘要 ( 72 )   RICH HTML PDF   收藏 In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations. 参考文献 | 相关文章 | 计量指标

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SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT Juan J. NIETO, Bessem SAMET 数学物理学报(英文版). 2017 (1):  195-204.  DOI: 10.1016/S0252-9602(16)30125-4 摘要 ( 103 )   RICH HTML PDF   收藏 In this paper, we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function, which generalizes the Riemann-Liouville fractional integral and the Hadamard fractional integral. We establish an existence result to such kind of equations using a generalized version of Darbo's theorem associated to a certain measure of noncompactness. Some examples are presented. 参考文献 | 相关文章 | 计量指标

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WAVELET-BASED ESTIMATOR FOR THE HURST PARAMETERS OF FRACTIONAL BROWNIAN SHEET 吴量, 丁义明 数学物理学报(英文版). 2017 (1):  205-222.  DOI: 10.1016/S0252-9602(16)30126-6 摘要 ( 58 )   RICH HTML PDF   收藏 It is proposed a class of statistical estimators ?=(?1, …, ?d) for the Hurst parameters H=(H1,…,Hd) of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging (DTI) of nuclear magnetic resonance (NMR). Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when Hi≥1/2, the estimators are accurate, and when Hi<1/2, there are some bias. 参考文献 | 相关文章 | 计量指标

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MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES 杨青, 朱家砚, 李正帮 数学物理学报(英文版). 2017 (1):  223-234.  DOI: 10.1016/S0252-9602(16)30127-8 摘要 ( 70 )   RICH HTML PDF   收藏 We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters. 参考文献 | 相关文章 | 计量指标

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EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY 马和平, 刘斌 数学物理学报(英文版). 2017 (1):  235-258.  DOI: 10.1016/S0252-9602(16)30128-X 摘要 ( 131 )   RICH HTML PDF   收藏 In the present paper, with the help of the resolvent operator and some analytic methods, the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay. As an application, we also give one example to demonstrate our results. 参考文献 | 相关文章 | 计量指标

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NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS 袁益让, 杨青, 李长峰, 孙同军 数学物理学报(英文版). 2017 (1):  259-279.  DOI: 10.1016/S0252-9602(16)30129-1 摘要 ( 120 )   RICH HTML PDF   收藏 Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device. 参考文献 | 相关文章 | 计量指标

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POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN Adam NOWAK, Krzysztof STEMPAK 数学物理学报(英文版). 2017 (1):  280-292.  DOI: 10.1016/S0252-9602(16)30130-8 摘要 ( 79 )   RICH HTML PDF   收藏 We study potential operators and, more generally, Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian. We characterize those 1≤p, q≤∞, for which the potential operators are Lp-Lq bounded. This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions. We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers. 参考文献 | 相关文章 | 计量指标