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2017年, 第37卷, 第6期　刊出日期：2017-12-25 上一期    下一期

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STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY 刘俊峰, Ciprian A. TUDOR 数学物理学报(英文版). 2017 (6):  1545-1566.  DOI: 10.1016/S0252-9602(17)30091-7 摘要 ( 115 )   RICH HTML PDF   收藏 In this paper we study a fractional stochastic heat equation on Rd (d ≥ 1) with additive noise (∂/∂t)u(t, x)=D(α/δ)u(t, x) +b(u(t, x)) +?H(t, x) where D(α/δ) is a nonlocal fractional differential operator and ?H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus. 参考文献 | 相关文章 | 计量指标

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DUALITY OF GENERALIZED DUNKL-LIPSCHITZ SPACES Samir KALLEL 数学物理学报(英文版). 2017 (6):  1567-1593.  DOI: 10.1016/S0252-9602(17)30092-9 摘要 ( 67 )   RICH HTML PDF   收藏 The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧α,p,qk (R), α ∈ R and 1 ≤ p, q ≤ ∞, in the context of Dunkl harmonic analysis. 参考文献 | 相关文章 | 计量指标

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DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS 韩艳丽, 高岩 数学物理学报(英文版). 2017 (6):  1594-1606.  DOI: 10.1016/S0252-9602(17)30093-0 摘要 ( 75 )   RICH HTML PDF   收藏 This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron. 参考文献 | 相关文章 | 计量指标

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DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES 高翔, 马际华 数学物理学报(英文版). 2017 (6):  1607-1618.  DOI: 10.1016/S0252-9602(17)30094-2 摘要 ( 83 )   RICH HTML PDF   收藏 This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ ξ < θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ=θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ almost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem. 参考文献 | 相关文章 | 计量指标

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A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES 王紫, 王玉文 数学物理学报(英文版). 2017 (6):  1619-1631.  DOI: 10.1016/S0252-9602(17)30095-4 摘要 ( 115 )   RICH HTML PDF   收藏 In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in[12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces. 参考文献 | 相关文章 | 计量指标

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BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS 高真圣, 谭忠 数学物理学报(英文版). 2017 (6):  1632-1638.  DOI: 10.1016/S0252-9602(17)30096-6 摘要 ( 77 )   RICH HTML PDF   收藏 In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d) is smooth up to time T provided that ∫0T║∇×u(t,·)║BMO(R3) + ║∇d(t,·)║L4(R3)8dt < ∞. 参考文献 | 相关文章 | 计量指标

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A VARIATIONAL-HEMIVARIATIONAL INEQUALITY IN CONTACT PROBLEM FOR LOCKING MATERIALS AND NONMONOTONE SLIP DEPENDENT FRICTION Stanis ław MIGÓRSKI, Justyna OGORZA LY 数学物理学报(英文版). 2017 (6):  1639-1652.  DOI: 10.1016/S0252-9602(17)30097-8 摘要 ( 80 )   RICH HTML PDF   收藏 We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle. 参考文献 | 相关文章 | 计量指标

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LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS 陈化, 陈洪葛, 段忆苪, 胡鑫 数学物理学报(英文版). 2017 (6):  1653-1664.  DOI: 10.1016/S0252-9602(17)30098-X 摘要 ( 77 )   RICH HTML PDF   收藏 Let Ω be a bounded open domain in Rn with smooth boundary ∂Ω, X=(X1, X2, …, Xm) be a system of real smooth vector fields defined on Ω and the boundary ∂Ω is non-characteristic for X. If X satisfies the Hörmander's condition, then the vector field is finitely degenerate and the sum of square operator △X=???20170608???Xj2 is a finitely degenerate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △X on Ω. 参考文献 | 相关文章 | 计量指标

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MULTIPLE SYMMETRIC RESULTS FOR A CLASS OF BIHARMONIC ELLIPTIC SYSTEMS WITH CRITICAL HOMOGENEOUS NONLINEARITY IN RN 邓志颖, 黄毅生 数学物理学报(英文版). 2017 (6):  1665-1684.  DOI: 10.1016/S0252-9602(17)30099-1 摘要 ( 54 )   RICH HTML PDF   收藏 This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in RN. By virtue of variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions. 参考文献 | 相关文章 | 计量指标

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RICCATI-TYPE RESULT FOR MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPOSITE FUNCTIONAL EQUATIONS 高凌云, 刘曼莉 数学物理学报(英文版). 2017 (6):  1685-1694.  DOI: 10.1016/S0252-9602(17)30100-5 摘要 ( 80 )   RICH HTML PDF   收藏 By use of Nevanlinna value distribution theory, we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation, the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth. 参考文献 | 相关文章 | 计量指标

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HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES Jongrak LEE 数学物理学报(英文版). 2017 (6):  1695-1704.  DOI: 10.1016/S0252-9602(17)30101-7 摘要 ( 85 )   RICH HTML PDF   收藏 In this paper we consider the block Toeplitz operators TΦ on the weighted Bergman space Aα2(D, Cn) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ=F + G* with matrix-valued polynomial functions F and G with degree 2. 参考文献 | 相关文章 | 计量指标

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FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY 尚随明, 田玉, 张雅静 数学物理学报(英文版). 2017 (6):  1705-1726.  DOI: 10.1016/S0252-9602(17)30102-9 摘要 ( 94 )   RICH HTML PDF   收藏 In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given. 参考文献 | 相关文章 | 计量指标

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ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ 数学物理学报(英文版). 2017 (6):  1727-1739.  DOI: 10.1016/S0252-9602(17)30103-0 摘要 ( 116 )   RICH HTML PDF   收藏 We present results on approximate solutions to the biadditive equation f(x + y, z-w) + f(x-y, z + w)=2f(x, z)-2f(y, w) on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability. 参考文献 | 相关文章 | 计量指标

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DISCONTINUOUS TRAVELING WAVE ENTROPY SOLUTIONS OF A MODIFIED ALLEN-CAHN MODEL 徐田媛, 金春花, 季善明 数学物理学报(英文版). 2017 (6):  1740-1760.  DOI: 10.1016/S0252-9602(17)30104-2 摘要 ( 66 )   RICH HTML PDF   收藏 This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena. 参考文献 | 相关文章 | 计量指标

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ANOTHER CHARACTERIZATIONS OF MUCKENHOUPT Ap CLASS 王定怀, 周疆, 陈文艺 数学物理学报(英文版). 2017 (6):  1761-1774.  DOI: 10.1016/S0252-9602(17)30105-4 摘要 ( 104 )   RICH HTML PDF   收藏 This manuscript addresses Muckenhoupt Ap weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces Lp(ω) to weighted Morrey spaces Mqp(ω) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on Mqp (ω), then ω ∈ Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators T∈ on weighted Morrey spaces. Finally, we show that ω ∈ Ap if and only if ω ∈ BMOp'(ω) for 1 ≤ p < ∞ and 1/p + 1/p'=1. 参考文献 | 相关文章 | 计量指标

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LARGE TIME BEHAVIOR OF SOLUTIONS TO THE PERTURBED HASEGAWA-MIMA EQUATION 王利娟 数学物理学报(英文版). 2017 (6):  1775-1790.  DOI: 10.1016/S0252-9602(17)30106-6 摘要 ( 55 )   RICH HTML PDF   收藏 The large time behavior of solutions to the two-dimensional perturbed HasegawaMima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions. 参考文献 | 相关文章 | 计量指标

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THE EQUIVALENT CHARACTERIZATION OF F(p, q, s) SPACE ON BOUNDED SYMMETRIC DOMAINS OF Cn 黎深莲, 张学军, 徐思 数学物理学报(英文版). 2017 (6):  1791-1802.  DOI: 10.1016/S0252-9602(17)30107-8 摘要 ( 62 )   RICH HTML PDF   收藏 Let Ω be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p,q,s) on Ω. Characterizing functions in the F(p,q,s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p,q,s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p,q,s) space and Bloch type space on Ω too. 参考文献 | 相关文章 | 计量指标

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SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY 孔凡超, 罗治国 数学物理学报(英文版). 2017 (6):  1803-1816.  DOI: 10.1016/S0252-9602(17)30108-X 摘要 ( 57 )   RICH HTML PDF   收藏 This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results. 参考文献 | 相关文章 | 计量指标

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THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES 崔艳艳, 王朝君, 刘浩 数学物理学报(英文版). 2017 (6):  1817-1829.  DOI: 10.1016/S0252-9602(17)30109-1 摘要 ( 64 )   RICH HTML PDF   收藏 In this paper, we extend the Roper-Suffridge extension operator in complex Banach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables. 参考文献 | 相关文章 | 计量指标

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PROPERTIES OF DIFFERENCE PAINLEVÉ IV EQUATIONS 兰双婷, 陈宗煊 数学物理学报(英文版). 2017 (6):  1830-1840.  DOI: 10.1016/S0252-9602(17)30110-8 摘要 ( 67 )   RICH HTML PDF   收藏 In this paper, we investigate difference Painlevé IV equations, and obtain some results on Nevanlinna exceptional values of transcendental meromorphic solutions w(z) with finite order, their differences △w(z)=w(z + 1)-w(z) and divided differences ((△w(z))/(w(z))). 参考文献 | 相关文章 | 计量指标

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UNIFORM HÖLDER ESTIMATES FOR A TYPE OF NONLINEAR ELLIPTIC EQUATIONS WITH RAPIDLY OSCILLATORY COEFFICIENTS 董荣, 李东升 数学物理学报(英文版). 2017 (6):  1841-1860.  DOI: 10.1016/S0252-9602(17)30111-X 摘要 ( 73 )   RICH HTML PDF   收藏 In this paper, a type of nonlinear elliptic equations with rapidly oscillatory coefficients is investigated. By compactness methods, we show uniform Hölder estimates of solutions in a C1 bounded domain. 参考文献 | 相关文章 | 计量指标

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THE INTEGRATION OF ALGEBROIDAL FUNCTIONS 孙道椿, 霍颖莹, 孔荫莹, 柴富杰 数学物理学报(英文版). 2017 (6):  1861-1869.  DOI: 10.1016/S0252-9602(17)30112-1 摘要 ( 70 )   RICH HTML PDF   收藏 In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros. 参考文献 | 相关文章 | 计量指标

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EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS 李全清, 吴鲜 数学物理学报(英文版). 2017 (6):  1870-1880.  DOI: 10.1016/S0252-9602(17)30113-3 摘要 ( 57 )   RICH HTML PDF   收藏 In this paper, we study the following generalized quasilinear Schrödinger equations with critical or supercritical growths -div(g2(u)∇u) + g(u)g'(u)|∇u|2 + V (x)u=f(x, u) + λ|u|p-2u, x ∈ RN, where λ > 0, N ≥ 3, g:R → R+ is a C1 even function, g(0)=1, g'(s) ≥ 0 for all s ≥ 0,???20170623???((g(s))/(|s|α-1)):=β > 0 for some α ≥ 1 and (α-1)g(s) > g'(s)s for all s > 0 and p ≥ α2*. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 using a change of variables and variational method. 参考文献 | 相关文章 | 计量指标