中国科学院数学与系统科学研究院期刊网

15 September 2007, Volume 50 Issue 5
    

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  • Rigidity of Reproducing ■[z]-Modules over the Unit Disk
    Xiao Xhun SHENG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 961-968. https://doi.org/10.12386/A2007sxxb0112
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,we investigate the rigidity of submodules of ■[z]-modules over the open unit disk.We prove that submodules of the space ■_α(0<α<1)are rigid,which is completely different from the case in the usual Hardy space.Then we prove that in the Dirichlet space,the rigidity of submodules also exists under some mild assumption.
  • The Fundamental Structure Theorem in Relative Twisting Hopf Modules and Relative Yetter-Drinfel'd Modules
    Xiao Li FANG(1); Jin Qi LI(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 969-980. https://doi.org/10.12386/A2007sxxb0113
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    In this paper,first we obtain new modules and eomodules constructions by the twisting method which plays an important role in the costructions of algebras and coalgebras.Then,in a more general case,we give the fundamental structure theorem in relative twisting Hopf modules.Lastly,we consider how to turn the twisting modules into relative Yetter-Drinfel'd modules and relative Hopf modules in HopfYD modules.
  • Blow-up of Solutions of Parabolic Problems with Nonlinear Boundary Conditions
    Xiao Jun LI(1); Cheng Kui ZHON
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 981-988. https://doi.org/10.12386/A2007sxxb0114
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    The purpose of this paper is to investigate the blow-up solutions of reaction- diffusion equations with nonlinear boundary conditions.Under some assumptions on the nonlinear terms f and g,we show that the solutions blow up in finite time.
  • Abstract Definition of JC~*-Algebra
    Xiao Chun FANG(1); Hai Tao YAN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 989-994. https://doi.org/10.12386/A2007sxxb0115
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    In this paper,the authors give an abstract definition of JC~*-algebra,and obtain the conditions for SC~*-algebra to be of typeП_k.
  • σ-Weak Mixing of Certain *-Endomorphism of Self-Adjoint Operator Algebras
    Xun Xiang GUO
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 995-998. https://doi.org/10.12386/A2007sxxb0116
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let A be a self-adjoint operator algebra of Hilbert space H,a be a*- endomorphism of A.If there exists a unit element e∈H such that lim_(→∞)〈α~n(a)h, h〉=〈ae,e〉for allα∈A and h∈H with‖h‖=1,then we sayαisσ-weak mixing with respect to A.In this paper,we establish a condition for an *-endomorphism to beσ-weak mixing.
  • Symbol Operator and the Speed of ApproximAtion by Compact Operator
    Qi Xiang YANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 999-100. https://doi.org/10.12386/A2007sxxb0117
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    In the traditional PDE problem,one approximates symbol by principal symbol in Taylor decomposition's way.In this paper,we apply appropriate wavelets to approximate the symbol operator by a very good compact operator,and such an operator converges very fast to the original symbol operator in the sense of operator's continuity norm.
  • Essentially Commuting Dual Toeplitz Operators on the Polydisk
    Tao YU; Guo Zheng CHENG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1007-101. https://doi.org/10.12386/A2007sxxb0118
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    We characterize essentially commuting dual Toeplitz operators with bounded measurable symbols and bounded pluriharmonic symbols on the Bergman space of the polydisk respectively.
  • Higher Order Integral Factors and Integrals of Ordinary Differential Equation(s) and Their Determination by Characteristic Set Method
    Temuerchaolu(1); Shan YIN(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1017-103. https://doi.org/10.12386/A2007sxxb0119
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The higher order integrals of general ordinary differential equations (ODEs) and their determination by Characteristic set method (Wu's method) are considered. Firstly,the concepts of higher order integral factors and the corresponding higher or- der integrals of ODEs,which are generalization of the concepts of usual integral factors and first integral of ODEs,are put forward.Secondly,a direct computing formula for higher order integral in term of its higher order integral factor is given,which makes the question of determining the (higher order) integrals reduce to the question of deter- mining the (higher order) integral factors.Thirdly,the differential form Characteristic set method is suggested to solve the over-determined system satisfied by the higher order integral factors.Finally,the construction theorems for second and third order ODEs which admit the higher order integrals and several concrete illustrative exam- ples are given.The results obtained in this article lead to a systematically mechanical algorithm to determine (higher order) integrals for a given ODEs and new application of Wu's method in differential fields is suggested.
  • Generalized Frames and Quotients of Generalized Frames
    Han LIU; Wei HE
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1031-104. https://doi.org/10.12386/A2007sxxb0120
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,we generalize the concepts of frames,frame homomorphisms, quotient frames and nuclei in the sense of category,and show that the category of frames is a reflective subcategory of the category of generalized frames.Moreover,we discuss the relation between the quotients of a generalized frame A and the nucleus functors on A.In particular,we prove that the category N(A) of all nucleus functors on A is a generalized frame.
  • Composition Operators on Dirichlet Spaces of Multiply Connected Domains
    Xiao Hong WANG(1); Xiao Feng W
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1041-104. https://doi.org/10.12386/A2007sxxb0121
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    In this paper,we are largely devoted to finding the boundedness property, Fredholm property,K-property of composition operators on Dirichlet space.
  • Stability and Convergence Problem of Ishikawa and Mann Iterative Sequences in Banach Spaces
    Shi Sheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1051-106. https://doi.org/10.12386/A2007sxxb0122
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Some equivalence theorems between convergence and stability of modi- fied Ishikawa and modified Mann iterative sequences with mean errors for asymptot- ically nonexpansive mappings in the intermediate sense and asymptotically pseudo- contractive mappings in Banach spaces are obtained,the results presented in this paper extend and improve some recent results.
  • 1-Lipschitz Mappings Between Unit Spheres of Banach Spaces
    Rui LIU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1063-107. https://doi.org/10.12386/A2007sxxb0123
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We discuss the extension problem of non-surjective 1-Lipschitz mappings between unit spheres,and obtain that,under some conditions,every 1-Lipschitz map can be extended to be a real linear isometric mapping on the whole space.This is the first time we study the 1-Lipschitz map extension problem on"general"Banach spaces.
  • A Note on Two Diophantine Equations y~2=nx(x~2±1)
    Hui Lin ZHU(1); Jian Hua CHEN(
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1071-107. https://doi.org/10.12386/A2007sxxb0124
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    In this paper,we use the results of Ljunggren,Cohn,Bennett and Walsh, Chen to give the bound and effective algorithm of positive integer solution number of two Diophantine equations.
  • Some Algebraic Properties of Bi-Cayley Graphs
    Hua ZOU; Ji Xiang MENG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1075-108. https://doi.org/10.12386/A2007sxxb0125
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    For a finite group G and a subset S(possibly,it contains the identity element) of G,the Bi-Cayley graph X=BC(G,S) of G with respect to S is defined as the bipartite graph with vertex set G×{0,1} and edge set {{(g,0),(sg,1)}:g∈G,s∈S}. In this paper,we investigate the relation between the eigenvaiues of Cayley graph D(G,S) and Bi-Cayley graph BC(G,S) for a finite abelian group.As a consequence, we determine the eigenvalues of Bi-Cayley graphs of cyclic groups.In addition,some asymptotic enumeration theorems are presented.
  • Some Theorems of Convergence in W_0~(1,x)L~(p(x)) (Q) Spaces and Their Conjugate Spaces
    Shu Jun SHI; Shu Tao CHEN; Yu
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1081-108. https://doi.org/10.12386/A2007sxxb0126
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Three theorems of convergence in W_0~(1,x)L~(p(x))(Q)spaces and their conjugate spaces are proved in this paper.Under weaker conditions,it is given that almost everywhere convergence implies weak convergence,and weak convergence implies strong convergence.
  • An Extension of Frigon's Fixed Point Theorem and Its Simplifyied Proof
    Xiao Yan LIU; Jin Xuan FANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1087-109. https://doi.org/10.12386/A2007sxxb0127
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    In 2000,Frigon established a fixed point theorem for generalized contraction in a complete gauge space.The purpose of this paper is to generalize this theorem and to give its straightforward proof.At the same time,we give a positive answer to an open question about convergency of iterative sequence for generalized contraction which is brought forward by Frigon.
  • On the Fundamental Groups of Complete Manifolds with Lower Quadratic Curvature Decay
    Yun Tao ZHANG(1); Xu XU(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1093-109. https://doi.org/10.12386/A2007sxxb0128
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    In this paper,we prove that a complete Riemannian manifold M~n with lower quadratic sectional curvature (or Ricci curvature) decay,if it has small linear diameter growth,then it has a finitely generated fundamental group.
  • Recurrent Markov Chains in Bi-infinite Random Environments
    LI Ying-Qiu
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1099-111. https://doi.org/10.12386/A2007sxxb0129
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    The two possible concepts of recurrence are introduced into the research field of Markov chains in bi-infinite random environments,and their connections and basic properties are discussed.Some criteria for states or chains to be recurrent are given.The existence of invariant measure of recurrent Markov chains in bi-infinite random environments are discussed.The concepts of positivity and nullity for Markov chains in bi-infinite random environments are firstly introduced,and their properties are discussed.Especially some criteria for states to be positive or null are given by making use of more powerful tools such as theories of invariant functions.
  • Distribution of Closed Orbits for a Class of Dispersing Billiards
    Hong Qiang XIA
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1111-111. https://doi.org/10.12386/A2007sxxb0130
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    We consider the billiard flows in R~3 with finitely many scatters with smooth boundary satisfying the visibility assumption and describe the asymptotic behavior of the distribution of closed orbits with an even collision number.
  • On S-points of Musielak-OrUcz Sequence Spaces
    Yun An CUI(1);
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1117-112. https://doi.org/10.12386/A2007sxxb0131
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper,criteria for S-points of Musielak-Orlicz sequence spaces are given.Moreover,as a corollary,the necessary and sufficient conditions for Musielak- Orlicz sequence spaces to have the S-property are obtained.
  • Spectral Theory of a New Kind of Non-Normal Operators
    Wan Gui SUN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1129-113. https://doi.org/10.12386/A2007sxxb0132
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    new kind of non-normal operators,the so-called u-scalar operators with complex spectra,is introduced.Such operators are proved to have Jordan-type decom- position.The relations between u-scalar operators with complex spectra and scalar- type spectral operators are discussed.And the construction and some examples of u-scalar operators with complex spectra are also given.
  • A Sphere Theorem with Positive Ricci Curvature and Reverse Volume Pinching
    Pei He WANG(1); Chun Li SHEN(2
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1135-114. https://doi.org/10.12386/A2007sxxb0133
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    Let M~n be a compact,simply connected n (≥3)-dimensional Riemannian manifold without boundary and S~n be the unit sphere in Euclidean space R~(n+1).We derive a new proof of a sphere theorem whenever the manifold concerned satisfies that the sectional curvature K_M is not larger than 1,while Ric(M)≥(n+2)/4 and the volume V(M) is not larger than 3/2(1+η)V(S~(2n)) for some positive numberηdepending only on n.
  • A Resolution of Some Mapping Classes
    Li Xin LIU(1); Chao Hui ZHANG(
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1141-115. https://doi.org/10.12386/A2007sxxb0134
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    Let S be a Riemann surface with at least one puncture a.There is a group H of mapping classes on S that fixes a and projects to the trivial mapping classes of ■=SU{a}.Let t_αdenote the Dehn twist along a simple closed curveαon S. In this paper we study the equation of mapping classes of S for X:(t_αoθ)~n o X= t_■~n,whereθ∈H is given.Since both (t_αoθ)~n and t_α~n project to the same Dehn twist t_■ along a simple loop ■,the above equation always has a solution in H.We give the necessary and sufficient condition for the equation to have a solution X=θ~(-n) for all sufficiently large n.We also characterize for an arbitrarily givenθ∈H a subset H′■ H such that the solution X=X_n for the equation eventually lies in H′.Finally, we study some compositions of simple mapping class and characterize that they are irreducible on a punctured pair of pants obtained from S by cutting along some simple curves.
  • The Essential Norm of a Composition Operator on the Bloch Space in Cn Unit Ball
    Shu Hong WU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1151-116. https://doi.org/10.12386/A2007sxxb0135
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    Let B~n be C~n unit ball andφ=(φ_1,φ_2,…,φ_n) a holomorphic self-map of B~n.An estimate of the essential norm of a composition operator C_φon the Bloch spaceβ(B~n) and the little Bloch spaceβ_0(B~n) is given in this paper.As a consequence,a necessary and sufficient condition for the composition operator C_φto be compact onβ(B~n) andβ_0(B~n) is obtained.
  • The Existence of Harmonic Solutions for Second Order n-Dimensional p-Laplacian Equations with a Deviating Argument
    Jian Jun ZHANG; Wen Bin LIU; H
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1161-117. https://doi.org/10.12386/A2007sxxb0136
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    In this paper,the existence of harmonic solutions for second order n- Dimensional p-Laplacian equations with a deviating argument is studied by using the topological degree theory.Sufficient conditions to guarantee the existence of harmonic solutions for the equation are obtained under having no restriction on the damping forces and some known results are improved.
  • Idempotency of Linear Combinations of Two Idempotent Operators
    Yan Ni CHEN; Hong Ke DU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1171-117. https://doi.org/10.12386/A2007sxxb0137
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    Let P and Q be two different idempotents on a Hilbert space.In this note,a complete solution is established to the problem of characterizing all situations, where a linear combination of P and Q is also an idempotent.Besides,we pointed out that the condition P_1P_2≠P_2P_1 of the statement (b) of the theorem in Baksalary and Baksalary (2000) can be deleted.
  • Average Onesided Widths of Anisotropic Sobolev and Besov Classes
    Zhu Yuan YANG(1); Zong Wen YAN
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1177-118. https://doi.org/10.12386/A2007sxxb0138
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    The paper concerns the average onesided widths of the anisotropic Sobolev and Besov classes.The weak asymptotic results are obtained for the corresponding quantities.
  • An Equation Involving the Smarandache Function
    Jin Ping MA(1); Bao Li LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1185-119. https://doi.org/10.12386/A2007sxxb0139
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    For any positive integer n,let S(n) denotes the Smarandache function,that is,S(n)=min{m:n|m!}.In this paper,we use the elementary methods to study the solutions of the equation∑_(d|n) S(d)=n,and give its all positive integer solutions.
  • Total Genus Distributions of Two Classes of 4-Regular Graphs
    Yan YANG; Yan Pei LIU
    Acta Mathematica Sinica, Chinese Series. 2007, 50(5): 1191-120. https://doi.org/10.12386/A2007sxxb0140
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    The total genus polynomial for a graph G shows the genus (orientable, nonorientable) distribution of the graph G.In this paper,We obtain the total genus polynomials for two new classes of 4-regular graphs by using the joint tree model of a graph embedding introduced by Yanpei Liu.And we deduce the total genus polynomials of two classes of graphs which had been done,these results are in much simpler forms in this paper.
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