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20 March 2015, Volume 35 Issue 2 Previous Issue    Next Issue

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DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS Yunguang LU, Christian KLINGENBERG, Ujjwal KOLEY, Xuezhou LU Acta mathematica scientia,Series B. 2015, 35 (2):  281-302.  DOI: 10.1016/S0252-9602(15)60001-7 Abstract ( 105 )   RICH HTML PDF (231KB) ( 812 )   Save 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. References | Related Articles | Metrics

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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE Jieming ZHOU, Yingchun DENG, Ya HUANG, Xiangqun YANG Acta mathematica scientia,Series B. 2015, 35 (2):  303-312.  DOI: 10.1016/S0252-9602(15)60002-9 Abstract ( 95 )   RICH HTML PDF (179KB) ( 1959 )   Save 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. References | Related Articles | Metrics

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RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT Shuaiqi ZHANG, Guoxin LIU, Meici SUN Acta mathematica scientia,Series B. 2015, 35 (2):  313-325.  DOI: 10.1016/S0252-9602(15)60003-0 Abstract ( 127 )   RICH HTML PDF (205KB) ( 458 )   Save 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. References | Related Articles | Metrics

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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 Acta mathematica scientia,Series B. 2015, 35 (2):  326-338.  DOI: 10.1016/S0252-9602(15)60004-2 Abstract ( 109 )   RICH HTML PDF (196KB) ( 1143 )   Save 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. References | Related Articles | Metrics

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EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES Xieping DING Acta mathematica scientia,Series B. 2015, 35 (2):  339-347.  DOI: 10.1016/S0252-9602(15)60005-4 Abstract ( 94 )   RICH HTML PDF (172KB) ( 931 )   Save 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. References | Related Articles | Metrics

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A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H2/H∞ CONTROL WITH RANDOM JUMPS Qixia ZHANG, Qiliang SUN Acta mathematica scientia,Series B. 2015, 35 (2):  348-358.  DOI: 10.1016/S0252-9602(15)60006-6 Abstract ( 138 )   RICH HTML PDF (190KB) ( 347 )   Save 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. References | Related Articles | Metrics

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THREE PROBLEMS IN SEARCHING FOR A MOVING TARGET BETWEEN TWO SITES Jinghu YU, Wenmin YE Acta mathematica scientia,Series B. 2015, 35 (2):  359-365.  DOI: 10.1016/S0252-9602(15)60007-8 Abstract ( 88 )   RICH HTML PDF (149KB) ( 569 )   Save 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. References | Related Articles | Metrics

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CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION Haixia LI, Yuzhu HAN, Wenjie GAO Acta mathematica scientia,Series B. 2015, 35 (2):  366-374.  DOI: 10.1016/S0252-9602(15)60008-X Abstract ( 106 )   RICH HTML PDF (178KB) ( 677 )   Save 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). References | Related Articles | Metrics

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THE SHARP JACKSON INEQUALITY FOR L2-APPROXIMATION ON THE PERIODIC CYLINDER Yi GU, Yongping LIU Acta mathematica scientia,Series B. 2015, 35 (2):  375-382.  DOI: 10.1016/S0252-9602(15)60009-1 Abstract ( 82 )   RICH HTML PDF (182KB) ( 1044 )   Save 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 References | Related Articles | Metrics

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SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRÖDINGER SYSTEMS IN R2 Chunhua WANG, Dingyi XIE, Liping ZHAN, Lipan ZHANG, Liangpei ZHAO Acta mathematica scientia,Series B. 2015, 35 (2):  383-398.  DOI: 10.1016/S0252-9602(15)60010-8 Abstract ( 83 )   RICH HTML PDF (234KB) ( 749 )   Save 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). References | Related Articles | Metrics

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CONTINUOUS SELECTIONS OF SOLUTION SETS OF FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS Aurelian CERNEA Acta mathematica scientia,Series B. 2015, 35 (2):  399-406.  DOI: 10.1016/S0252-9602(15)60011-X Abstract ( 88 )   RICH HTML PDF (151KB) ( 1001 )   Save 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. References | Related Articles | Metrics

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DIFFERENTIAL INVERSE VARIATIONAL INEQUALITIES IN FINITE DIMENSIONAL SPACES Wei LI, Xing WANG, Nanjing HUANG Acta mathematica scientia,Series B. 2015, 35 (2):  407-422.  DOI: 10.1016/S0252-9602(15)60012-1 Abstract ( 134 )   RICH HTML PDF (204KB) ( 1030 )   Save 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. References | Related Articles | Metrics

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SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS Dongsheng KANG, Jing LUO, Xiaolin SHI Acta mathematica scientia,Series B. 2015, 35 (2):  423-438.  DOI: 10.1016/S0252-9602(15)60013-3 Abstract ( 173 )   RICH HTML PDF (233KB) ( 1024 )   Save 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. References | Related Articles | Metrics

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OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION Chen FEI, Weiyin FEI Acta mathematica scientia,Series B. 2015, 35 (2):  439-458.  DOI: 10.1016/S0252-9602(15)60014-5 Abstract ( 183 )   RICH HTML PDF (262KB) ( 492 )   Save 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. References | Related Articles | Metrics

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CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM Haoguang LI Acta mathematica scientia,Series B. 2015, 35 (2):  459-476.  DOI: 10.1016/S0252-9602(15)60015-7 Abstract ( 124 )   RICH HTML PDF (231KB) ( 394 )   Save 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. References | Related Articles | Metrics

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SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS Fang LIU Acta mathematica scientia,Series B. 2015, 35 (2):  477-494.  DOI: 10.1016/S0252-9602(15)60016-9 Abstract ( 111 )   RICH HTML PDF (226KB) ( 404 )   Save 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 References | Related Articles | Metrics

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PROBABILISTIC AND AVERAGE LINEAR WIDTHS OF SOBOLEV SPACE WITH GAUSSIAN MEASURE IN SPACE SQ(T) (1≤Q≤∞) Yanyan XU, Guanggui CHEN, Ying GAN, Yan XU Acta mathematica scientia,Series B. 2015, 35 (2):  495-507.  DOI: 10.1016/S0252-9602(15)60017-0 Abstract ( 95 )   RICH HTML PDF (211KB) ( 341 )   Save 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. References | Related Articles | Metrics

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FORMULA OF GLOBAL SMOOTH SOLUTION FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE Gaowei CAO, Kai HU, Xiaozhou YANG Acta mathematica scientia,Series B. 2015, 35 (2):  508-526.  DOI: 10.1016/S0252-9602(15)60018-2 Abstract ( 92 )   RICH HTML PDF (207KB) ( 324 )   Save 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. References | Related Articles | Metrics