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2018年, 第38卷, 第1期　刊出日期：2018-02-25 上一期    下一期

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LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES 刘军, 杨大春, 袁文 数学物理学报(英文版). 2018 (1):  1-33.  DOI: 10.1016/S0252-9602(17)30115-7 摘要 ( 122 )   RICH HTML PDF   收藏 Let p∈(0, 1], q∈(0, ∞] and A be a general expansive matrix on Rn. Let HAp,q (Rn) be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q(Rn) in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley gλ*-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q(Rn). All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ*-function characterization of HAp,q (Rn) coincides with the best known one in the classical Hardy space Hp(Rn) or in the anisotropic Hardy space HAp (Rn). 参考文献 | 相关文章 | 计量指标

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INITIAL-BOUNDARY PROBLEM FOR THE 1-D EULER-BOLTZMANN EQUATIONS IN RADIATION HYDRODYNAMICS 张晶, 张永前 数学物理学报(英文版). 2018 (1):  34-56.  DOI: 10.1016/S0252-9602(17)30116-9 摘要 ( 81 )   RICH HTML PDF   收藏 We study the initial-boundary value problem for the one dimensional Euler-Boltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified Glimm scheme to construct the global approximate solutions (U△t,d, I△t,d) and prove that there is a subsequence of the approximate solutions which is convergent to the global solution. 参考文献 | 相关文章 | 计量指标

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ROBUST DEPENDENCE MEASURE FOR DETECTING ASSOCIATIONS IN LARGE DATA SET 蒋杭进, 吴琼莉 数学物理学报(英文版). 2018 (1):  57-72.  DOI: 10.1016/S0252-9602(17)30117-0 摘要 ( 101 )   RICH HTML PDF   收藏 In this paper, we proposed a new statistical dependency measure for two random vectors based on copula, called copula dependency coefficient (CDC). The CDC is proved to be robust to outliers and easy to be implemented. Especially, it is powerful and applicable to high-dimensional problems. All these properties make CDC practically important in related applications. Both experimental and application results show that CDC is a good robust dependence measure for association detecting. 参考文献 | 相关文章 | 计量指标

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THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA 王先甲, 董瑞, 陈琳 数学物理学报(英文版). 2018 (1):  73-92.  DOI: 10.1016/S0252-9602(17)30118-2 摘要 ( 136 )   RICH HTML PDF   收藏 Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner's Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two control strategies are proposed:compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a cooperator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can't prevent defection from being evolutionary stable strategy (ESS). On the other hand, compensation for the cooperator can't prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples. 参考文献 | 相关文章 | 计量指标

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DOOB'S INEQUALITY, BURKHOLDER-GUNDY INEQUALITY AND MARTINGALE TRANSFORMS ON MARTINGALE MORREY SPACES Kwok-Pun HO 数学物理学报(英文版). 2018 (1):  93-109.  DOI: 10.1016/S0252-9602(17)30119-4 摘要 ( 92 )   RICH HTML PDF   收藏 We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces. 参考文献 | 相关文章 | 计量指标

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DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES 孙美满, 严国政 数学物理学报(英文版). 2018 (1):  110-124.  DOI: 10.1016/S0252-9602(17)30120-0 摘要 ( 47 )   RICH HTML PDF   收藏 In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions. 参考文献 | 相关文章 | 计量指标

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SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS 刘颖博, Ingo WITT 数学物理学报(英文版). 2018 (1):  125-150.  DOI: 10.1016/S0252-9602(17)30121-2 摘要 ( 63 )   RICH HTML PDF   收藏 For the 2-D quasilinear wave equation  satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation (∂t2-△x)u+ satisfying null conditions with small initial data and the coefficients depending simultaneously on u and ∂u. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction. 参考文献 | 相关文章 | 计量指标

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YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES 程立新, 罗思捷 数学物理学报(英文版). 2018 (1):  151-156.  DOI: 10.1016/S0252-9602(17)30122-4 摘要 ( 78 )   RICH HTML PDF   收藏 In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C(K), then it can be equivalently renormed so that the set of normattaining functionals contains an infinite dimensional closed subspace of X* if and only if X* contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy. 参考文献 | 相关文章 | 计量指标

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EULER SCHEME AND MEASURABLE FLOWS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS 王志明 数学物理学报(英文版). 2018 (1):  157-168.  DOI: 10.1016/S0252-9602(17)30123-6 摘要 ( 81 )   RICH HTML PDF   收藏 For a stochastic differential equation with non-Lipschitz coefficients, we construct, by Euler scheme, a measurable flow of the solution, and we prove the solution is a Markov process. 参考文献 | 相关文章 | 计量指标

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A NOTE ON CONICAL KÄHLER-RICCI FLOW ON MINIMAL ELLIPTIC KÄHLER SURFACES 张雅山 数学物理学报(英文版). 2018 (1):  169-176.  DOI: 10.1016/S0252-9602(17)30124-8 摘要 ( 72 )   RICH HTML PDF   收藏 We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kähler-Ricci flow on a minimal elliptic Kähler surface converges in the sense of currents to a generalized conical Kähler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor. 参考文献 | 相关文章 | 计量指标

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CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION 宋威, 李林 数学物理学报(英文版). 2018 (1):  177-186.  DOI: 10.1016/S0252-9602(17)30125-X 摘要 ( 65 )   RICH HTML PDF   收藏 Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in[J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. (China) 24 (1995) 385-405] (or[W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 (2000) 29-36]). 参考文献 | 相关文章 | 计量指标

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EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW 汪承志, 张明书, 赵才地 数学物理学报(英文版). 2018 (1):  187-202.  DOI: 10.1016/S0252-9602(17)30126-1 摘要 ( 68 )   RICH HTML PDF   收藏 This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space. 参考文献 | 相关文章 | 计量指标

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SOLUTIONS TO QUASILINEAR HYPERBOLIC CONSERVATION LAWS WITH INITIAL DISCONTINUITIES 牛海萍, 王术 数学物理学报(英文版). 2018 (1):  203-219.  DOI: 10.1016/S0252-9602(17)30127-3 摘要 ( 79 )   RICH HTML PDF   收藏 We study the singular structure of a family of two dimensional non-self-similar global solutions and their interactions for quasilinear hyperbolic conservation laws. For the case when the initial discontinuity happens only on two disjoint unit circles and the initial data are two different constant states, global solutions are constructed and some new phenomena are discovered. In the analysis, we first construct the solution for 0 ≤ t < T*.Then, when T* ≤ t < T', we get a new shock wave between two rarefactions, and then, when t > T', another shock wave between two shock waves occurs. Finally, we give the large time behavior of the solution when t → ∞. The technique does not involve dimensional reduction or coordinate transformation. 参考文献 | 相关文章 | 计量指标

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ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS Kuo-Shou CHIU 数学物理学报(英文版). 2018 (1):  220-236.  DOI: 10.1016/S0252-9602(17)30128-5 摘要 ( 82 )   RICH HTML PDF   收藏 In this paper, we investigate the existence, uniqueness and the asymptotic equivalence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results. 参考文献 | 相关文章 | 计量指标

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THE HOMOGENEOUS POLYNOMIAL SOLUTIONS FOR THE GRUSHIN OPERATOR 刘海蓉 数学物理学报(英文版). 2018 (1):  237-247.  DOI: 10.1016/S0252-9602(17)30129-7 摘要 ( 54 )   RICH HTML PDF   收藏 In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant. 参考文献 | 相关文章 | 计量指标

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THE PLANCHEREL FORMULA FOR THE LINE BUNDLES ON SL(n+1, R)/S(GL(1, R)×GL(n, R)) 朱理 数学物理学报(英文版). 2018 (1):  248-268.  摘要 ( 45 )   RICH HTML PDF   收藏 In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL(n + 1, R) and H=S(GL(1, R)×GL(n, R)). The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk. 参考文献 | 相关文章 | 计量指标

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ON SOME ROTATIONALLY SYMMETRIC GRADIENT PSEUDO-KÄHLER-RICCI SOLITONS 段孝娟 数学物理学报(英文版). 2018 (1):  269-288.  摘要 ( 63 )   RICH HTML PDF   收藏 In this paper, we explicitly construct some rotationally symmetric gradient pseudo-Kähler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the "phase change" phenomenon caused by the variation of parameters. 参考文献 | 相关文章 | 计量指标

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GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY 杨兆星, 张国宝 数学物理学报(英文版). 2018 (1):  289-302.  摘要 ( 70 )   RICH HTML PDF   收藏 This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts (waves with speeds c > c*, where c=c* is the minimal speed) is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21]. 参考文献 | 相关文章 | 计量指标

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LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES Santhosh GEORGE, C. D. SREEDEEP 数学物理学报(英文版). 2018 (1):  303-314.  摘要 ( 56 )   RICH HTML PDF   收藏 In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general Hölder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. 参考文献 | 相关文章 | 计量指标

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CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES 涂强, 陈文艺 数学物理学报(英文版). 2018 (1):  315-332.  摘要 ( 43 )   RICH HTML PDF   收藏 In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents. 参考文献 | 相关文章 | 计量指标

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SOLVING COUPLED PSEUDO-PARABOLIC EQUATION USING A MODIFIED DOUBLE LAPLACE DECOMPOSITION METHOD Hassan Eltayeb GADAIN 数学物理学报(英文版). 2018 (1):  333-346.  摘要 ( 93 )   RICH HTML PDF   收藏 In this paper, the modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems. 参考文献 | 相关文章 | 计量指标

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PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL 徐亚娟, 王过京 数学物理学报(英文版). 2018 (1):  347-360.  摘要 ( 100 )   RICH HTML PDF   收藏 In this paper, we study the price of catastrophe options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model. We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae. 参考文献 | 相关文章 | 计量指标

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CASH SUBADDITIVE RISK MEASURES FOR PORTFOLIO VECTORS 刘红卫, 胡亦钧, 魏林晓 数学物理学报(英文版). 2018 (1):  361-376.  摘要 ( 71 )   RICH HTML PDF   收藏 In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated. 参考文献 | 相关文章 | 计量指标