中国科学院数学与系统科学研究院期刊网

15 January 1999, Volume 42 Issue 1
    

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  • Characterizations on Two Dimensional Rings
    Fang Gui WANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 1-4. https://doi.org/10.12386/A1999sxxb0001
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    Let R be a domains. In this paper we prove that wgl(R)2 if and only if every w-module over R is flat, and if and only if every finite type w-module over R is projective.
  • Generalized Weight Approximation by Maximal Families with Applications
    Chong LI(1),Xing Hua WANG(2)
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 5-12. https://doi.org/10.12386/A1999sxxb0002
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    The nonlinear approximation problems with generalized weights are investigated. The maximal families of Kolmogorov and alternation type are characterized.Results on uniqueness elements and applications are also given.
  • Critieria of Biholomorphic Starlike Mappings
    Sheng GONG(1),Shi Kun WANG(2),
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 13-16. https://doi.org/10.12386/A1999sxxb0003
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    In this paper the sufficient and necessary condition that holomorphic mappings are starlike on bounded starlike circle domain is discussed.
  • Bergman Type Spaces and the Cesàro Operator
    Zhi Jing XIAO
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 17-22. https://doi.org/10.12386/A1999sxxb0004
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    In this paper, we give a characterization of Bergman type spaces, and the boundedness of the Cesaro operator on Bergman type spaces.
  • The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch_o=2 and Representation of Its q-hypergeometric Series
    Hong Zeng WEI(1),Yi Bin ZHANG(
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 23-34. https://doi.org/10.12386/A1999sxxb0005
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    Let Fq be a finite field with q=2t elements. In this paper, using singular symplectic and singular pseudo-symplactic geometry over Fq, we have given the sufficient and necessary condition of there exists solutions and the number of solutions X of rank k and solutions X to the equation XAXT=B over Fq. when A and B are symmetric matrices. Finally. we have obtained simple representations of enumerational formulas by q-hypergeometric series.
  • The Hausdorff Dimension of the Graph for a Fractal Interpolation Function
    Guan Tie DENG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 35-40. https://doi.org/10.12386/A1999sxxb0006
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    In this paper,we obtain a lower bound estimation about the Hausdorff dimension of the graph of a fractal interpolation function with the interpolation points
  • A Two-dimensional Hyperbolic System of Nonlinear Conservation Laws with Functional Solutions
    Jia Xin HU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 41-48. https://doi.org/10.12386/A1999sxxb0007
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    A two-dimensional hyperbolic system of nonlinear conservation laws was considered for any piecewise constant initial data having two discontinuity rays with the origin as vertex. One kind of new waves, which was labelled as the Dirac-contact wave, appeared in the solution. The entropy conditions for the Dirac-contact waves were given. The solutions on the Dirac-contact waves can be viewed as the bounded linear functionals on C(R2×R+).
  • Sequential Networks and the Sequentially Quotient Images of Metric Spaces
    Shou LIN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 49-54. https://doi.org/10.12386/A1999sxxb0008
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    In this paper the concept of sequential networks is introduced, the relations among that and the concepts of sequential quasi-bases and cs*-networks are established,and some new characterizations of the certain quotient images of metric spaces are obtained.
  • On Limit Cycles of Type I Equation of Quadratic Differential Systems (2)
    Xiao Gui LI
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 55-60. https://doi.org/10.12386/A1999sxxb0009
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    In this paper, the problem on limit cycles of Type I equation of quadratic differential systems dx/dt=-y+δx+lx2+mxy+ny2, dx/dt=x has been researched.It obtained the existential condition of limit cycles on large range when l≠0.
  • A Novel Dual Notion of a Banach Space: Lipschitz Dual Space
    Ji Gen PENG,Zong Ben XU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 61-70. https://doi.org/10.12386/A1999sxxb0010
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    A new dual space notion of a Banach space, named Lipschitz dual space,is introduced, and within the new introduced space framework, the concept of the Lipschitz dual operator of a nonlinear Lipschitz operator is further defined. It is proved that the Lipschitz dual space of any Banach space E is an ordinary dual space of a certain Banach space containing E in the isometric embeding sense, and that the Lipschitz dual operator of any nonlinear Lipscitz operator becomes linear and bounded.By means of these findings, a lot of important results in linear analysis and theorems on linear operators are generalized to nonlinear cases. Thereby, a completely new way to generalize the linear operator theory to the nonlinear case is developed. As examples,several new mean ergodic theorems of the uniformly Lipschitz operators are proved.
  • The Graded Radicals, Weakly Graded Radicals and Reflected Radicals
    Yao WANG,Yan Li REN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 71-76. https://doi.org/10.12386/A1999sxxb0011
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    In the category of general group-graded rings and graded-preserving ring homomorphisms, the characterizations of classical graded radical NG, LG, gG, rG and KG by means of elements are presented, the constructions of Nref, Lref, gref, rref and Kref are investigated and the relations between these graded radicals and their corresponding reflected radicals are discussed by introducing the weakly graded radicals.
  • Zonal Wavelets on the Heisenberg Group and the Orthogonal Decomposition for the Function Space
    Jian Xun HE(1),Li Zhong PENG(2
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 77-82. https://doi.org/10.12386/A1999sxxb0012
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    Let P=NAM be the minimal parabolic subgroup of SU(n+1,1), which can be regarded as the affine automorphism group of Hn. According to the admissible condition in [1], we give the zonal wavelets on Heisenberg group Hn. Using the wavelet transform, we get the other decomposition of orthogonal direct sum of Li (Un+1, dμl(z, t, ρ) ). Moreover, the orthogonal decomposition of L2(P, dμl (z,t, ρ, u) )is given.
  • The Closure of the Unitary Orbit of the Strongly Irreducible Operators in Continuous Nest Algebra
    You Qing JI(1),Chun Lan JIANG(
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 83-88. https://doi.org/10.12386/A1999sxxb0013
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    In this paper, N always denotes continuous nest, and T(N) = {T∈L(H),TMM: M∈N}. We describe the spectral picture of some strongly irreducible operators in T(N). and characterize the closure of the unitary orbit of the strongly irreducible operators in T(N).
  • Spectrum-Preserving Multiplicative Maps
    Wu JING
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 89-92. https://doi.org/10.12386/A1999sxxb0014
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    Let X and Y be Banach spaces. We show that a spectrum-preserving surjective multiplicative map from B(X) to B(Y) is of the form (T) = ATA-1 for an isomorphism A of X onto Y.
  • On a Diophantine Inequality Involving Prime Numbers
    Ying Chun CAI
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 93-98. https://doi.org/10.12386/A1999sxxb0015
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    Let. In this paper it is proved that there exists N(c)>0 such that for any N>N(c), the inequalityis solvable in prime numbers p1, p2, p3, where c1 is an absolute positive constant.
  • Pseudo-orbit-tracing and Completely Positive Entropy
    Run Sheng YANG(1),Su Lin SHEN(
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 99-104. https://doi.org/10.12386/A1999sxxb0016
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    Let f be a continuous map from compact metric space onto itself. In this paper, for f has completely positive entropy, we get a necessary condition and some equivalent conditions when f has the pseudo-orbit-tracing property.
  • Super-Brownian Motion and One Class of Nonlinear Differential Equations on Unbounded Domains
    Yan Xia REN(1),Rong WU(2),Chun
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 105-110. https://doi.org/10.12386/A1999sxxb0017
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    Let where a(x) and γ(x) are positive bounded integrable functions in D and We first establish a limit theorem of the super-Brownian motion X with parameters Then in Section 3 and 4, we study the structure of the set of all positive bounded solutions of the differential equation in a domain D (bounded or unbounded). All positive bounded solutions with Dirichlet boundary condition or stochastic Dirichlet boundary condition are represented in terms of the super-Brownian motion X.
  • Existence of Positive Solution for Singular Boundary Value Problem
    Hong Zhou WANG,Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 111-118. https://doi.org/10.12386/A1999sxxb0018
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    In this paper, we consider existence of positive solutions for singular boundary value problem by a fixed point theorem in cones. At last, we will prove a brief theorem on existence of positive solutions for singular problem in decreasing condition.
  • Regularity of very Weak Solutions for a Class of Nonlinear Elliptic Systems
    Shen Zhou ZHENG,Ai Nong FANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 119-121. https://doi.org/10.12386/A1999sxxb0019
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    In this paper, we improve the integrability of the derivatives of very weak solutions for a class of nonlinear elliptic systems (1.1). which satisfy. the controllable growth conditions (1.2)-(1.4).
  • On Structure of Ordered Fields Satisfying the Infinite-dimensional Real Nullstellensatz I
    Guang Xing Zeng
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 125-132. https://doi.org/10.12386/A1999sxxb0020
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    The purpose of this paper is to establish a theorem on structure of ordered fields satisfying the infinite-dimensional real Nullstellensatz. For the preliminaries, in the first part of this paper, a class of ordered groups, which have no gap of rank d for an infinite cardinal number d, is investigated. With the aid of Hahn Embeding Theorem,we give the structure of ordered groups without gap of rank d for an infinite cardinal numberd.
  • Implication Lattices and Their Fuzzy Implication Space Representation Theorem
    Guo Jun WANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 133-140. https://doi.org/10.12386/A1999sxxb0021
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    Taking the concept of L*-Lindenbaum algebra as background, this paper introduced the concepts of implication lattice and regular implication lattice and discussed their basic properties. On the other hand, this paper introduced the concept of fuzzy implication space that is generallization of the concept of zero-dimensional space in point set topology. The representation theorem of regular implication lattices by means of fuzzy implication spaces had been established, that can be seen as, in certain sense, a generalization of the famous Stone’s representation theorem.
  • C-wellposedness of the Complete Second Order Abstract Cauchy Problem and applications
    Ming Chu GAO
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 141-150. https://doi.org/10.12386/A1999sxxb0022
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    In this paper, we give sufficient and necessary conditions for operator ma trix to generate an exponentially bounded semigroup, where A1 and A0 are the coefficent operators of the complete sedond order abstract Cauchy problem (ACP2). we also give the relationship between the fact that generates an exponentially bounded semigroup and the C-wellposedness of semigroup and the C-wellposedness of (ACP2). Finally, we apply these,esult and those in [3] to discuss the C-wellposedness of a kind of (ACP2) with application background.
  • Mappings of Subalgebras of AF C~*-algedras which Preserve Idempotents, and Local Derivations
    Pei Sheng JI
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 151-154. https://doi.org/10.12386/A1999sxxb0023
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    It is proved that norm continuous linear mappings of subalgebras of AF C*-algebras which preserve idempotents are Jordan homomorphisms, and that local derivation from subalgebra A of AF C*-algebra E into an arbitrary normed E-bimodule M is derivation, which generalizes the result of Crist about local derivation.
  • Injectors, Bi-injectors, Flatjectors and Coflatjectors
    Xiao Sheng ZHU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 155-160. https://doi.org/10.12386/A1999sxxb0024
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    In this paper, hi-injectors are defined. Some new representations of injectors,flatjectors, perfect injectors and coflatjectors are given. Endomorphism ring S of finitely generated modules over R and some relations between ring R and ring S are discussed.
  • The Varieties of~*-regular Semigroups Generated by Mal’cev Products of Varieties of*-regular Semigroups
    Zhong Hao JIANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 161-166. https://doi.org/10.12386/A1999sxxb0025
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    In this paper, we will study*-regular semigroups from a universal perspective. First. we introduce the concept of a*-relational morphism and discuss some properties of*-relational morphisms. Then we describe the varieties of*-regular semigroups generated by Mal’cev products of varieties of*-regular semigroups in terms of *-relational morphisms. Last, using this description, we determine the varieties of the forms (uog), (uoReB) and (uoReg).
  • Extrapolation Theorem of Interpolation Spaces by Approximation
    Li Hua YANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 167-174. https://doi.org/10.12386/A1999sxxb0026
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    In this paper, an extrapolation theorem of interpolation spaces by approximation is established on a quasi-norm Abelian group. The results generalizes the extrapolation theorem by the best approximation of a family of normal approximation sets, which was found by Devore R. The conditions here is weakened. Moreover. the similar theorem by operator approximation can be set up by our results.
  • Quadrati Systems with Weak Pairing Infinitehyperbolic Saddles
    Ping Guang ZHANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 175-180. https://doi.org/10.12386/A1999sxxb0027
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    In this paper, we prove that a quadratic system with a weak focus and weak pairing infinitehyperbolic saddles has at most one limit cycle, and that if this system has a weak infinite homoclinic loop, then its stability is contrary to that of the singular point surrounded by it, and this system has no limit cycle in the region formed by it.
  • On the Spectral Completion of Operator Partial Matrices
    Jian Lian CUI,Jin Chuan HOU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 181-186. https://doi.org/10.12386/A1999sxxb0028
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    For a 2 by 2 operator partial matrix of the form with A, C and D given operators acting on suitable separable complex Hilbert spaces, the intersection and the union of the spectra of all completions are completely characterized.are completely characterized.
  • Some Preservation of Properties in Stability Theory of Module and its Fraction
    Han Pin WANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(1): 187-192. https://doi.org/10.12386/A1999sxxb0029
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    In this article, preservation of hall, class, bound and rank in stability theory of module is discussed. The following results are proved: 1) NR is the hall of A in MR if and only if NS-1R is the hall of A in MS-1R; 2) β(p) =β(q) if and only if β(pR)=β(qR), 3) cl(p) =cl(q) if and only if cl(pR)=cl(qR), 4) U(P)=U(pR). Some conditions which ensure preservation of hall, class, bound and rank between MR and its fracted module (S-1 M)s-1 R are also given.
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