中国科学院数学与系统科学研究院期刊网

15 January 2001, Volume 44 Issue 1
    

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  • Composition Operators on the Bloch Space of Several Complex Variables
    Ji Huai SHI,Luo LUO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 1-10. https://doi.org/10.12386/A2001sxxb0001
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    In this paper, we study the boundedness and compactness of composition operator on the Bloch space β（Ω）, Ω is a bounded homogeneous domain. For Ω＝Ｂｎ， we give the necessary and sufficient conditions for a composition operator C to be compact on β（Ｂn） or β0(Bn) .
  • Algebraic Independence by Approximation Method (II)
    Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 11-14. https://doi.org/10.12386/A2001sxxb0002
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    Let f(x) be a continued fraction with elements a_nx, where coefficients an are positive algebraic numbers. Using the criterion of [1] for any nonzero real algebraic numbers a1,..as, with distinct absolute values the algebraic independence of the values f(a1 ),... , f(as) is proved under certain assumption concerning only with an. For some transcendental numbers the algebraic independence of values is also established
  • The Generalized Maximum Density Index Sets of Primitive Matrices with d Nonzero Diagonal Entries
    Zheng Ke MIAO,Lin Qiang PAN,Ke
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 15-20. https://doi.org/10.12386/A2001sxxb0003
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    Let A be an n x n irreducible Boolean matrix with period p. In [1], the generalized maximum density index hA(k) is defined. Let DISn,d(k) = {hA(k) | A PMn(d)}, where PMn(d) is the set of all n x n primitive matrices with d nonzero entries exactly. In this paper, we show that Furthermore, we define the norm of A, denoted by (A), the numbers of 1 in A and describe the extremal matrices with minimum norm.
  • Quantifiers Elimination and Complexity for the Theory of Groups of Prime Orders
    Yun Fu SHEN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 21-28. https://doi.org/10.12386/A2001sxxb0004
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    We deal with the quantifier eliminations and corresponding computational complexities for the theory T of groups of prime orders over language We prove that T has the quantifier elimination property and give,an upper bound of the decision problem for theory T.
  • Harmonic Analysis in Classical Domains and Complex Clifford Analysis
    Sha HUANG,Yu Ying QIAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 29-36. https://doi.org/10.12386/A2001sxxb0005
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    In this paper, we using the results in Hua Luogeng and Lu Qikeng of harmonic analysis in classical domains for functions theorey of several complex variables, consider harmonic analysis in four kind classical domains for complex Clifford analysis and discuss the existence (uniqueness) of solutions of the two relevant boundary value problems and integral representation of the regular solutions of those problems.
  • On the Distribution and Number of Limit Cycles for Quadratic System with Two Foci
    Ping Guang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 37-44. https://doi.org/10.12386/A2001sxxb0006
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    In this paper it is prove that a quadratic system with two foci has at most one limit cycle around one of the two foci, and hence the limit cycles of the quadratic system with two fool must be (0, i)-distribution or (1, i)-distribution (i = 0, 1, 2,...).
  • Limit Molecular Lattices
    Yong Ming LI,Zhi Hui LI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 45-50. https://doi.org/10.12386/A2001sxxb0007
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    The notion of limit molecular lattice is introduced, it is proved that the category of limit molecular lattices is a Cartesian closed category containing the category of topological molecular lattices as a bireflective full subcategory and the category of limit spaces as a reflective and coreflective subcategory, respectively.
  • The Operation and the Basic Invariants on Long Curves
    Jian Cheng ZOU(1),Jian Yi ZHOU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 51-58. https://doi.org/10.12386/A2001sxxb0008
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    The formula of invariants with the operation of insertion and pushing are given on long curves.
  • On Vector-Valued Martingale Lipschitz Spaces P_λ~β(X)and P_∧~β(X)
    Lin YU,Pei De LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 59-68. https://doi.org/10.12386/A2001sxxb0009
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    The embeding relations between Banach-space-valued martingale spaces and and and the duals of martingale Hardy spaces and Dr(X) with small index are studied, the results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.
  • On Holomorphic Solutions of the Non-Linear Totally Characteristic Equations in High Dimensional Complex Domain
    Hua CHEN,Zhuang Chu LUO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 69-76. https://doi.org/10.12386/A2001sxxb0010
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    In this paper, we study a class of non-linear singular PDE in holomorphic functions defined on a high dimensional complex domain. Under certain assumptions, we proved the existence and uniqueness of the local holomorphic solution.
  • On the Solvability of Degenerate Quasilinear Parabolic Equations of Second Order
    Zhen Hai LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 77-84. https://doi.org/10.12386/A2001sxxb0011
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    In this paper, we consider a nonlinear degenerate quasilinear parabolic initial boundary value problems of second order. Using results from the theory of pseudomonotone operators, we show that there exists at least one weak solution in a suitable weighted Sobolev space.
  • On the 2kth Mean Value Formula of General Dedekind Sums
    Min XIE,Wen Peng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 85-94. https://doi.org/10.12386/A2001sxxb0012
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    The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the asymptotic property of general Dedekind sums, and give an interesting asymptotic formula.
  • On the Discrete Spectrum of a Class of Differential Operators
    Zhong WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 95-102. https://doi.org/10.12386/A2001sxxb0013
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    In this paper, 2nth order symmetric differential expressions with real valued coefficients are considered. Some results concerning the discreteness of spectrum of associated operators are obtained. Especially, the necessary and sufficient conditions are given which ensure that the spectrum of differential operators is discrete.
  • Injectiveness of a Mapping Generating Ring Derived Sequences and a Restoring Algorithm
    Yue Fei ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 103-110. https://doi.org/10.12386/A2001sxxb0014
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    The injectiveness of a mapping from primitive sequences over Z2n to its highest coordinate sequences is known [1]. In this paper,the above fact is generalized to primitive sequences over Galois rings using trace representation, and a restoring algorithm, which output the primitive sequence according to its characteristic polynomial and highest coordinate sequence, is given.
  • On the Number of Tournaments with Prescribed Score Vector
    Yao Ping HOU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 111-116. https://doi.org/10.12386/A2001sxxb0015
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    In this paper, we discuss the tournament matrix which can be interpreted as a competition where n participants play each other once in a match that can be end in ties. A player receives two points for each win and one point for each tie. We obtain the number of tournament matrices with special score vectors, and give the lower bound of the number for tournament matrices with strong score vectors and obtain the score vector with this lower bound.
  • On Hausdorff Measures of Self-Similar Sets
    Sheng You WEN(1),Shao Yuan XU(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 117-124. https://doi.org/10.12386/A2001sxxb0016
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    Some sufficient and necessary conditions for sets having the same Hausdorff content and Hausdorff measure are obtained. For the self-similar set satisfying the open set condition, it is proved that its Hausdorff content and Hausdorff measure are equal and a formula, which is convenient for use, of its Hausdorff measure is given. As applications, the Hausdorff measures of uniform Cantor sets are computed in a new way and the upper bound problem of the Hausdorff measure of the Koch curve is also discussed.
  • The Class Number of the Field Q(P_1~(1/2)，…，P_t~(1/2))(t≥4) Is Even
    Yan Ming DI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 125-130. https://doi.org/10.12386/A2001sxxb0017
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    In this paper, it is proved that the class number of the number field is even, where are different primes, all congruent to 1 modulo 4.
  • The Unique Solution for Discontinuous Nonlinear Volterra Type Integral Equations in Banach Spaces
    Li Shan LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 131-136. https://doi.org/10.12386/A2001sxxb0018
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    In this paper, the unique solution of the discontinuous nonlinear Volterra type integral equations in Banach spaces are investigated. In very weakly condition the unique solution of nonlinear Volterra type integral equations can be obtained by the uniformly limit of the iterative sequences is proved. The error estimate of the iterative sequences of approximation solutions is given. And then apply this result to the initial value problem of first order ordinary differential equations. The results obtained here improve and extend recent results.
  • Hopf Algebra Structures on Crossed Coproducts
    Zheng Ming JIAO,Shuan Hong WAN
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 137-148. https://doi.org/10.12386/A2001sxxb0019
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    In this paper a necessary and sufficient condition for the Smash product algebra structure and the crossed coproduct coalgebra structure to form a bialgebra was found. In particular, we also derive a sufficient condition for this new bialgebra to be a Hopf algebra.
  • Commutation Formulas of Two Lax Operator and Two Master Symmetries for KP Hierarchy
    Xin Shen GU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 149-158. https://doi.org/10.12386/A2001sxxb0020
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    This paper mainly concerns about the commutation formulas of Lax operators and masters symmetries for KP hierarchy. At first the quickly decaying function space is extended and the condition for operator to be Lax operator is discussed. On the basis of above work, the representation vector of Lax operator is found. Then, by studying the relationship among the Lax operator, Lax flow and the representa- tion vector of Lax operator, a method to calculate the representation vector of the Lie bracket of two Lax operators as well as a method to calculate the commutation of two master symmetries are obtained. At the end of this paper,a formula that can be used to obtain a symmetry from an arbitrary master symmetry is also given.
  • Logical Metric Spaces
    Guo Jun WANG(1),Wei WANG(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 159-168. https://doi.org/10.12386/A2001sxxb0021
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    Taking the valuation lattice to be the unit interval [0, 1] this paper introduced the concepts of truth degree and similarity degree for formulas by means of integrals, and then introduced on the set F consisting of all formulas a kind of pseudo-metric so as to offer a possible framework for approximate reasoning.
  • Extension of (1, σ) Derivations of Semiprime Rings
    Feng WEI(1),Feng Wen NIU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 169-174. https://doi.org/10.12386/A2001sxxb0022
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    This paper gives the propersitions of extension concerning automorphisms and derivations of semiprime rings. These results generalize some results of reference [1]. Then, through the idempotents in the generalized centroid of semiprime rings, topological space is established on the extended module of (1, ) derivations. From the point of view of topology we give the structure theorem concerning the extended module of (1, ) derivations.
  • On Sequence-Covering Compact Mappings
    Shou LIN(1),Peng Fei YAN(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 175-182. https://doi.org/10.12386/A2001sxxb0023
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    In this paper authors use the concepts of cs-networks, sequential-neighbor- hood networks, sequential-open networks and weak bases, discuss the relations among point-regular covers, uniform covers and point-star networks of point-finite covers in spaces, and establish the characterizations of images of metric spaces under some sequence-covering (compact) mappings. In particular, it is shown that the image of metric spaces under sequence-covering (or 1-sequence-covering) compact mappings is equivalent to the space with point-regular cs-networks, which answers a Tanaka's question.
  • The Research of P Dissipative Operator
    Li Xin TIAN(1),Zeng Rong LIU(2
    Acta Mathematica Sinica, Chinese Series. 2001, 44(1): 183-192. https://doi.org/10.12386/A2001sxxb0024
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    In this paper the authors solve the maximal dissipative extension representation of P dissipative operators in Banach space and get some nice application.
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