中国科学院数学与系统科学研究院期刊网

15 January 2003, Volume 46 Issue 1
    

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  • On a Conjecture on Fixed Point Indices of Positive Mappings in Cones
    Dong Sheng LI,Kai Tai LI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 1-6. https://doi.org/10.12386/A2003sxxb0001
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    Under some additional conditions, we prove a conjecture on fixed point indices of positive mappings in cones proposed by Dancer E. N. and give an example to illustrate the application of the theory.
  • Explicit Expression of Smith's Determinant on Poset
    Bo Ying WANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 7-10. https://doi.org/10.12386/A2003sxxb0002
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    We introduce meet-function and join-function on a subset of a poset and use them to give some explicit expressions of Smith's determinant.
  • A Berry-Essen Inequality for the Kaplan-Meier L-Estimator
    Qi Hua WANG(1),Li Xing ZHU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 11-18. https://doi.org/10.12386/A2003sxxb0003
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    Let ^Fn be the Kaplan-Meier estimator of distribution function F. Let J(-) be measureable real-valued function. In this paper, U-statistic representation for Kaplan-Meier L-estimator, T(^Fn) = (?)xJ(^Fn(x))d^Fn(x), is derived. Furthermore, the representation is also used to establish a Berry-Essen inequality for T(^Fn).
  • Hausdorff Measure of Homogeneous Cantor Set
    Cheng Qin QU(1),Hui RAO(2),Wei
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 19-22. https://doi.org/10.12386/A2003sxxb0004
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    This paper gives the exact Hausdorff of measures a class of homogeneous Cantor sets.
  • A_r-Weighted Poincare-Type Inequalities for Differential Forms in Some Domains
    Shu Sen DING(1),Yun Ying GAI(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 23-28. https://doi.org/10.12386/A2003sxxb0005
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    We prove the weighted integral inequalities for differential forms, which can be considered as generalizations of the classical Poincare-type inequality.
  • On the Centers of Generalized Lienard System
    Chao Jie LIU,Xian Xi SHAO,Chen
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 29-034. https://doi.org/10.12386/A2003sxxb0006
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    This paper discusses the local and global centers of the generalized Lienard system, and gives two theorems which extend and improve on the related results of [1-3]. Moreover, the lemmas in this paper are also useful to the study of oscillation, stability of solution and existence of limit cycles of the generalized Lienard system.
  • The Pinching Theorems about Sectional Curvature of Submanifolds on Unit Sphere
    Ding Xing DING,Hong An SUN,Qin
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 37-48. https://doi.org/10.12386/A2003sxxb0007
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    Let M be a submanifold without umbilic point on unit sphere; its Moebius form Φ vanishes, in this paper the pinching theorems of sectional curvature about Moebius metric are obtained.
  • The Existence of Periodic Solutions for High Order Duffing Equations
    Wen Bing LIU(1),Yong LI(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 49-56. https://doi.org/10.12386/A2003sxxb0008
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    In this paper, the existence of periodic solutions for high order Duffing equations is studied by using degree theory and some known results are improved to some extent.
  • A Note on Noncommutative Chern Character for Dirac Operator
    Hui Tao FENG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 57-64. https://doi.org/10.12386/A2003sxxb0009
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    In this note by using an idea of Moscovici and the techniques of asymptotic expansions for heat kernels, an entire cyclic Chern character formula is given for a Dirac operator denned on a Clifford module.
  • On Approximation by Non-Periodic Neural and Translation Networks in L~p-w, Spaces
    Jian Li JIAN(1),Bao Huai SHENG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 65-74. https://doi.org/10.12386/A2003sxxb0010
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    The authors investigate the approximation of non-periodic functions in by a kind of s-dimensional network operator constructed by orthogonal algebraic polynomial. The upper bound of approximation is achieved and, in particular, the upper bound of approximation of the derivatives of the target functions by the corresponding derivatives of the translate and neural network operators is discussed.
  • Regularity of the Attractor for the Nonlinear Strain Wave Equation Coupled with Nonlinear Schrodinger Equation
    Ping GAO(1),Zheng De DAI(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 75-84. https://doi.org/10.12386/A2003sxxb0011
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    In this article, we study the reqularity of the attractor in Cauchy problem for a system of nonlinear strain wave equation coupled with nonlinear Schrodinger equation. Existence of the global attractor A0 in E0 and A0 is actally equal to the global strong attractor A1 in E1 are obtained by a new operator decomposition technique.
  • The Bergman Kernel Function on HUA Domains of the Fourth Type
    Wei Ping YIN,Bing Xin GUAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 85-94. https://doi.org/10.12386/A2003sxxb0012
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    We obtain explicit formulas of the Bergman kernels and holomorphic automorphism groups on HUA domains of the fourth type. And we also obtain of the explicit formula completely orthonormal system on semi-Reinhardt domain.
  • Quantifier Elimination for Complete Binary Trees
    Ji Qiang LIU(1),Dong Sheng LIA
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 95-102. https://doi.org/10.12386/A2003sxxb0013
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    The method of quantifier elimination has been one of the powerful tools in the computer science and algebraic model theory. In this article, we deal with the theory of complete binary trees. After givling a set of fomulas as the Basic Formulas, we use the layout formulas and finite covering to prove that the theory of complete binary trees admits quantifier elimination.
  • A Family of Nonnormal Cayley Digraphs
    Yan Quan FENG(1),Dian Jun WANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 103-108. https://doi.org/10.12386/A2003sxxb0014
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    We call a Cayley digraph (?)= Cay(G, S) normal for G if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(?) of (?). In this paper we determine the normality of Cayley digraphs of valency 2 on nonabelian groups of order 2p2 (p odd prime). As a result, a family of nonnormal Caylay digraphs is found.
  • Quasiperiodic Motions for Asymmetric Oscillators
    Xiao Ping YUAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 109-114. https://doi.org/10.12386/A2003sxxb0015
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    We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity , where a, b > 0, p(t) and is an unbounded function (see [1-19]).
  • On Rectifiable Curves in the Plane
    Shi Pan LU(1),Cheng Ming Lee(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 115-118. https://doi.org/10.12386/A2003sxxb0016
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    This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral.
  • Multiplicative Perturbation Theorems for Regularized Cosine Operator Functions
    Fang LI,Jing LIANG,Ti Jun XIAO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 119-130. https://doi.org/10.12386/A2003sxxb0017
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    In this paper, we investigate multiplicative perturbation of the regularized cosine operator functions. We obtain some multiplicative perturbation theorems for the regularized cosine operator functions without the density of the range of the regularizing operator C.
  • Isometries of the Preannihilators of Weakly Closed T(N)-Modules
    Jian Wen LUO(1),Fang Yan LU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 131-136. https://doi.org/10.12386/A2003sxxb0018
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    In this paper, we characterize the linear surjective isometrics between the preannihilators of weakly closed T(N)-modules. Let U and W be the weakly closed T(N)-modules determined by the left order homomorphisms N → N and N→N respectively, and let U(?) and W(?) be the preannihilators of U and W on a Hilbert space H respectively. We prove that the onto isometrics between the spaces U(?) and W(?) are of the form A→U1AV1* or A → U2A*V2, where Ui and Vi (i = 1,2) are unitary operators, if (0)* = (0)# = (0), dim(0)+ ≠ 1 and min{dim(H(?)H), dim(H(?) H)} ≥ 2.
  • Semisimple Extensions of Hopf Algebra and Homological Dimension of Invariants for Hopf Actions
    Jia Gui ZHU(1),Liang Yun ZHUAN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 137-142. https://doi.org/10.12386/A2003sxxb0019
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    Let H be a finite dimensional Hopf algebra acting on an algebra yl, and let AH denote the invariant subring of A and A#H the smash product. Assume that A/AH is a semisimple extension and A is a flat right AH-module. It is shown that if H* is unimodular and A has an element of trace one then WD(AH) = WD(A) = WD(A#H). Moreover, if A is a projective left and right AH-module, then LD(AH) = LD(A) = LD(A#H).
  • Regularity of a Class of Elliptic Equations with Singular Lower Order Terms
    Yong Yang JIN
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 143-152. https://doi.org/10.12386/A2003sxxb0020
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    A regularity result of a class of elliptic equations with singular lower term is obtained. The form of the equation is: Lu + vu =u, where L is a second order divergence elliptic operator, v belongs to some Morrey space and u, is a nonnegative Radon measure.
  • Conformal Deformations of Surfaces in K~(2+p) Preserving the Gauss Map
    Xin Xiao LI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 153-160. https://doi.org/10.12386/A2003sxxb0021
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    In this article, we shall give the necessary and suffcient conditions for a conformally immersed surface f : M →R2+p to be G*-deformable. After introducing the concept of adjoint form for /, the following results are proved: (1) If / is G*-deformable, then the normal bundle of / is flat and the adjoint form is closed; (2) When M is simply connected, then / is G*-deformable if it has flat normal bundle and closed adjoint form.
  • On the Fixed Point Existence and Uniqueness Theorems of Mixed Monotone Operators and Their Applications
    Yan Sheng WU,Guo Zhen LI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 161-166. https://doi.org/10.12386/A2003sxxb0022
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    In this paper, we firstly discuss the existence, uniqueness and non-symmetric iterative approximation of solution for a class of systems of mixed monotone operator equations, and obtain some new fixed point theorems of mixed monotone operators, increasing operators and decreasing operators which have no continuous and compact conditions. Secondly, we study the fixed point of mixed monotone operators which have a-concave and -a-convex conditions while the operators also have no continuous and compact conditions, and get a new result. Finally, we apply the new results presented in this paper to Hammerstein integral equations on RN (see [1-12]).
  • Positively Steady State and Hopf Bifurcation and Periodic Solution of 3-D Oregonator
    Zi Fan ZHANG,Suo Chun ZHANG
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 167-176. https://doi.org/10.12386/A2003sxxb0023
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    The positively steady state, Hopf bifurcation and existence of periodic solution of 3-D Oregonator are analysed. The topological equivalence of 3-D Oregonator to its 2-D simplified model is proved, which testifies that the investigation of 2-D model for the 3-D Oregonator is valid.
  • Singularity Methods of Periodic Systems of First Order
    Hong Bin CHEN,Shuang Liang DI
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 177-182. https://doi.org/10.12386/A2003sxxb0024
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    Consider the differential equation (?) + a(t)g(x) = h(t), where a(t) and h(t) are 1-periodic functions such that a(f) does not change sign, and g is a concave-convex type function. By using the singularity method we obtain a complete geometric structure of 1-periodic solution, and the exact multiplicity results. More precisely, the image of singularities consists of codimensional 1 manifold that divides the C[0, 1] into two open sets A1,A3: (1) for h(t) A1, the equation has a unique periodic solution. (2) for h(t) ∈ A3, the equation has exactly three periodic solutions. (3) Moreover, the image F(C) of cusp singularities C is a codimensional 2 manifolds of ∈ [0,1] such that for h(t) ∈ F(C), the equation has a unique periodic solution, and for h(t) ∈ F(E)\F(C), the equation has exactly two periodic solutions.
  • The Conformal Gauss Maps of Willmore Submanifolds
    Zhen GUO
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 183-188. https://doi.org/10.12386/A2003sxxb0025
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    In this paper we investigate the conformal Gauss map of submanifolds in sphere space and get, by Moebius invariants, the condition for this kind of map to be harmonic. In particular, we show that the conformal Gauss map of a 2-dimensional submanifold in sphere space is harmonic if and only if it is a Willmore submanifold.
  • Stancu Polynomials Defined on a Simplex and Best Polynomial Approximation
    Fei Long CAO(1),Zong Ben XU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 189-196. https://doi.org/10.12386/A2003sxxb0026
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    As a generalization of the famous Bernstein polynomials, a class of broader polynomials called the multivariate Stancu polynomials denned on the normal simplex is introduced. With the best polynomial approximation as a metric, we prove the approximation property, estimate the approximation rate and characterize the approximation order of the Stancu polynomials to any continuous functions. An inverse theorem of approximation for the Stancu polynomials is also proved.
  • Topological Group Acts Expansively on Continua
    En Hui SHI(1),Li Zhen ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 197-202. https://doi.org/10.12386/A2003sxxb0027
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    In this paper, the concept of expansive action of homeomorphism is generalized to the case of topological group, the expansiveness of a finitely generated topological group with discrete topology is studied and the following result is obtained: Z×Z can not acts expansively on the unit interval I, but the free product Z★Z can acts expansively on it.
  • The Enumeration of Rooted 4-Connected Triangulations
    Jun Liang CAI(1),Yan Pei LIU(2
    Acta Mathematica Sinica, Chinese Series. 2003, 46(1): 203-208. https://doi.org/10.12386/A2003sxxb0028
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    In this paper the enumeration of rooted cubic strong c-nets is studied. The explicit expressions of this kind of maps with the size and the valency of the root-face as parameters are derived. Moreover, these results are also the same as those of rooted 4-connected triangulations which are the dual maps of rooted cubic strong c-nets. Here, some of the corresponding results in [1, 2] are thus simplified or generalized properly.
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