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2015年, 第35卷, 第2期　刊出日期：2015-03-20 上一期    下一期

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DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS 陆云光, Christian KLINGENBERG, Ujjwal KOLEY, Xuezhou LU 数学物理学报(英文版). 2015 (2):  281-302.  DOI: 10.1016/S0252-9602(15)60001-7 摘要 ( 105 )   RICH HTML PDF(231KB) ( 812 )   收藏 We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions. 参考文献 | 相关文章 | 计量指标

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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE 周杰明, 邓迎春, 黄娅, 杨向群 数学物理学报(英文版). 2015 (2):  303-312.  DOI: 10.1016/S0252-9602(15)60002-9 摘要 ( 95 )   RICH HTML PDF(179KB) ( 1959 )   收藏 This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance (CEV) model. Assume that the insurer's surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term's explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained. 参考文献 | 相关文章 | 计量指标

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RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT 张帅琪, 刘国欣, 孙梅慈 数学物理学报(英文版). 2015 (2):  313-325.  DOI: 10.1016/S0252-9602(15)60003-0 摘要 ( 127 )   RICH HTML PDF(205KB) ( 458 )   收藏 This article deals with the problem of minimizing ruin probability under opti- mal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended gen- erator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained. 参考文献 | 相关文章 | 计量指标

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ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS Eid H. DOHA, Waleed M. ABD-ELHAMEED, Mahmoud A. BASSUONY 数学物理学报(英文版). 2015 (2):  326-338.  DOI: 10.1016/S0252-9602(15)60004-2 摘要 ( 109 )   RICH HTML PDF(196KB) ( 1143 )   收藏 Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given. 参考文献 | 相关文章 | 计量指标

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EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES 丁协平 数学物理学报(英文版). 2015 (2):  339-347.  DOI: 10.1016/S0252-9602(15)60005-4 摘要 ( 94 )   RICH HTML PDF(172KB) ( 931 )   收藏 In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature. 参考文献 | 相关文章 | 计量指标

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A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H2/H∞ CONTROL WITH RANDOM JUMPS 张启侠, 孙启良 数学物理学报(英文版). 2015 (2):  348-358.  DOI: 10.1016/S0252-9602(15)60006-6 摘要 ( 138 )   RICH HTML PDF(190KB) ( 347 )   收藏 A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps. 参考文献 | 相关文章 | 计量指标

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THREE PROBLEMS IN SEARCHING FOR A MOVING TARGET BETWEEN TWO SITES 余旌胡, 叶文敏 数学物理学报(英文版). 2015 (2):  359-365.  DOI: 10.1016/S0252-9602(15)60007-8 摘要 ( 88 )   RICH HTML PDF(149KB) ( 569 )   收藏 Suppose that a moving target moves randomly between two sites and its movement is modeled by a homogeneous Markov chain. We consider three classical problems: (1) what kind of strategies are valid? (2) what strategy is the optimal? (3) what is the infimum of expected numbers of looks needed to detect the target? Problem (3) is thoroughly solved, and some partial solutions to problems (1) and (2) are achieved. 参考文献 | 相关文章 | 计量指标

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CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION 李海霞, 韩玉柱, 高文杰 数学物理学报(英文版). 2015 (2):  366-374.  DOI: 10.1016/S0252-9602(15)60008-X 摘要 ( 106 )   RICH HTML PDF(178KB) ( 677 )   收藏 In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743). 参考文献 | 相关文章 | 计量指标

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THE SHARP JACKSON INEQUALITY FOR L2-APPROXIMATION ON THE PERIODIC CYLINDER 谷懿, 刘永平 数学物理学报(英文版). 2015 (2):  375-382.  DOI: 10.1016/S0252-9602(15)60009-1 摘要 ( 82 )   RICH HTML PDF(182KB) ( 1044 )   收藏 We consider Jackson inequality in L2(Bd×T,Wκ,μB (x)), where the weight function Wκ,μB (x)) is defined on the ball Bd and related to reflection group, and obtain the sharp Jackson inequality En-1,m-1(f)2≤Kn,m(τ, r)ωr(f, t)2,τ≥2τn,λ, where τn,λ is the first positive zero of the Gegenbauer cosine polynomial Cnλ(cosθ)(n∈N).d:\PDF\10.16381/j.cnki.issn1003-207x.2015.04.020.pdf 参考文献 | 相关文章 | 计量指标

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SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R2 王春花, 谢定一, 占丽萍, 张李攀, 赵良珮 数学物理学报(英文版). 2015 (2):  383-398.  DOI: 10.1016/S0252-9602(15)60010-8 摘要 ( 83 )   RICH HTML PDF(234KB) ( 749 )   收藏 We study the following nonlinear Schrödinger system  where P(r) and Q(r) are positive radial functions, μ >0,ν >0, and β∈R is a coupling constant. This type of system arises, particularly, in models in Bose-Einstein condensates theory. Applying a finite reduction method, we construct an unbounded sequence of nonradial positive vector solutions of segregated type when β is in some suitable interval, which gives an answer to an interesting problem raised by Peng and Wang in Remark 4.1 (Arch. Ration. Mech. Anal., 208(2013), 305-339). 参考文献 | 相关文章 | 计量指标

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CONTINUOUS SELECTIONS OF SOLUTION SETS OF FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS Aurelian CERNEA 数学物理学报(英文版). 2015 (2):  399-406.  DOI: 10.1016/S0252-9602(15)60011-X 摘要 ( 88 )   RICH HTML PDF(151KB) ( 1001 )   收藏 Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov's theorem for a fractional integro-differential inclusion involving Caputo's fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered. 参考文献 | 相关文章 | 计量指标

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DIFFERENTIAL INVERSE VARIATIONAL INEQUALITIES IN FINITE DIMENSIONAL SPACES 李为, 汪星, 黄南京 数学物理学报(英文版). 2015 (2):  407-422.  DOI: 10.1016/S0252-9602(15)60012-1 摘要 ( 134 )   RICH HTML PDF(204KB) ( 1030 )   收藏 In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under differ- ent conditions. Some existence theorems of Carathéodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given. 参考文献 | 相关文章 | 计量指标

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SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS 康东升, 罗婧, 史晓琳 数学物理学报(英文版). 2015 (2):  423-438.  DOI: 10.1016/S0252-9602(15)60013-3 摘要 ( 173 )   RICH HTML PDF(233KB) ( 1024 )   收藏 In this article, an elliptic system is investigated, which involves Hardy-type po- tentials, critical Sobolev-type nonlinearities, and critical Hardy-Sobolev-type nonlinearities. By a variational global-compactness argument, the Palais-Smale sequences of related approx- imation problems is analyzed and the existence of infinitely many solutions to the system is established. 参考文献 | 相关文章 | 计量指标

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OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION 费晨, 费为银 数学物理学报(英文版). 2015 (2):  439-458.  DOI: 10.1016/S0252-9602(15)60014-5 摘要 ( 183 )   RICH HTML PDF(262KB) ( 492 )   收藏 This article is concerned with a class of control systems with Markovian switching, in which an Itô formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results. 参考文献 | 相关文章 | 计量指标

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CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM 李浩光 数学物理学报(英文版). 2015 (2):  459-476.  DOI: 10.1016/S0252-9602(15)60015-7 摘要 ( 124 )   RICH HTML PDF(231KB) ( 394 )   收藏 In this article, we study the Cauchy problem for the linearized spatially homogeneous non-cutoff Boltzamnn equation with Maxwellian molecules. By using the spectral decomposition, we solve the Cauchy problem with initial datum in the sense of distribution, which contains the dual space of a Gelfand-Shilov class. We also prove that this solution belongs to the Gelfand-Shilov space for any positive time. 参考文献 | 相关文章 | 计量指标

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SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS 刘芳 数学物理学报(英文版). 2015 (2):  477-494.  DOI: 10.1016/S0252-9602(15)60016-9 摘要 ( 111 )   RICH HTML PDF(226KB) ( 404 )   收藏 In this article, we prove that viscosity solutions of the parabolic inhomogeneous equations (n+p)/put-ΔpNu=f(x,t) can be characterized using asymptotic mean value properties for all p≥1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a proble 参考文献 | 相关文章 | 计量指标

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PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE SQ(T) (1≤Q≤∞) 徐艳艳, 陈广贵, 甘莹, 许燕 数学物理学报(英文版). 2015 (2):  495-507.  DOI: 10.1016/S0252-9602(15)60017-0 摘要 ( 95 )   RICH HTML PDF(211KB) ( 341 )   收藏 Probabilistic linear (N, δ)-widths and p-average linear N-widths of Sobolev space W2r(T), equipped with a Gaussian probability measure μ, are studied in the metric of Sq(T) (1 ≤ q ≤ ∞), and determined the asymptotic equalities: and where 0< p <∞, δ∈ (0, 1/2 ], ρ >1, and Sq(T) is a subspace of S1(T), in which the Fourier series is absolutely convergent in ?q sense. 参考文献 | 相关文章 | 计量指标

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FORMULA OF GLOBAL SMOOTH SOLUTION FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE 曹高伟, 胡凯, 杨小舟 数学物理学报(英文版). 2015 (2):  508-526.  DOI: 10.1016/S0252-9602(15)60018-2 摘要 ( 92 )   RICH HTML PDF(207KB) ( 324 )   收藏 In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional(m-D) conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value. 参考文献 | 相关文章 | 计量指标