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R!kpe_(u!kpeN}!kpe!kpe\OUSMOKExplicit Multisymplectic Method for a High Order Wave Equation of KdV TypeWANG JUNJIE;WANG XIUYING;!In this paper, we consider multisymplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multisymplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multisymplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.1709pef[xvzGA Kind of Boundary Value Problems for Stochastic Differential Equations/HU LING;WU ZHENG;WEI ZHANGZHE;WANG LIANGLONG;:In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions(in sense of mean value). Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and LeraySchauder fixed point theorem, respectively.128VExistence and Uniqueness of Fixed Points for Mixed Monotone Operators with ApplicationWU YUEXING;HUO YANMEI;In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.7CDiscrete ArzelAscoli Theorem on the Half Line and Its ApplicationLU YANQING;MA RUYUN;The compactness criterion in l_%={x()"l~"(0,"))lim t!" x(t)=x(")} is given and as an application,we study the existence of positive solutions of second order boundary value problems of difference equation on the half line by the fixedpoint theorem in cones.5DA Note on Homogenization of Parabolic Equation in Perforated Domains5YANG ZHANYING;SHU WAN;PAN ZHANGPING;PENG CHANQUAN;We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh(Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.(Math. Sci.), 2002, 112(1): 195 207). Moreover,these results generalize those obtained by Donato and Nabil(Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50: 115 144).64"Jclean and Strongly Jclean RingsXIANG YUEMING;OUYANG LUNQUN;Let R be a ring and J(R) the Jacobson radical. An element a of R is called(strongly) Jclean if there is an idempotent e " R and w " J(R) such that a = e + w(and ew = we). The ring R is called a(strongly) Jclean ring provided that every one of its elements is(strongly) Jclean. We discuss, in the present paper,some properties of Jclean rings and strongly Jclean rings. Moreover, we investigate Jcleanness and strongly Jcleanness of generalized matrix rings. Some known results are also extended.3Embedding Cartesian Product of Some Graphs in Books"YANG JIAO;SHAO ZELING;LI ZHIGUO;The book embedding of a graph G consists of placing the vertices of G in a line called spine and assigning edges of the graph to pages so that the edges assigned to the same page do not intersect. The number of pages is the minimum number in which the graph can be embedded. In this paper, we study the book embedding of the Cartesian product Pm Sn, Pm W<n, Cn Sm, Cn Wm, and get an upper bound of their pagenumber.5Oconvexity of OrliczBochner Spaces with Orlicz Norm.ZHOU CHENGHUA;GONG WANZHONG;ZHANG DAOXIANG;JIn this paper we give some characterizations of Oconvexity of Banach spaces, and show the criteria for Oconvexity in OrliczBochner function space L_M(, X) and OrliczBochner sequence space l_M(X_s) endowed with Orlicz norm.Moreover, we give a sufficient condition for the dual of such a space to have the fixed point property.uExponential Convergence of Finitedimensional Approximations to Linear Bondbased Peridynamic Boundary Value ProblemsWU HAO;;In this paper, we demonstrate that the finitedimensional approximations to the solutions of a linear bondbased peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.'Communications in Mathematical Research<ck>Aims and Scope Communications in Mathematical Research(CMR)is a comprehensive mathematical journal carrying original papers on pure and applied mathematics.It was launched in September,1985.The journal is formerly Northeastern Mathematical Journal(NMJ),and publishes quarterly.The primary purpose is to present the latest achievements in mathematical research and to promote of the journal international academic exchange.The Editorial
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