中国科学院数学与系统科学研究院期刊网

15 May 1999, Volume 42 Issue 5
    

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  • Wei JIANG,Zu Xiu ZHENG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 769-780. https://doi.org/10.12386/A1999sxxb0104
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    In this paper, by using the D-inverse matrix, we give the fundamental solution, the constant variation formula and the general solution of degenerate for the degenerate difference system with delay. This will determine the fundamental theory for degenerate difference system with delay and will be extensively used in most Kinds of degenerate control system.
  • Zhi Xiang WU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 781-786. https://doi.org/10.12386/A1999sxxb0105
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    In this paper we use Horn funtor to characterize Artinian ring.
  • Zhi Cai XU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 787-794. https://doi.org/10.12386/A1999sxxb0106
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    Let M be spacelike hypersurface with constant mean curvature in de Sitter space, this paper gives some conditions which guarantee M is totally umbilic or isoparametric.
  • Xian Hua TANG,Jian She YU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 795-802. https://doi.org/10.12386/A1999sxxb0107
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    Consider the neutral differential equations with positive and negative coefficientsTwo sufficient conditions for the existence of positive solutions of Eq.(*) are obtained when R(t) + Q(s)ds 1 is not satisfied.
  • Long Guang HE
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 803-808. https://doi.org/10.12386/A1999sxxb0108
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    Let (Γ P, α, β) be a Poisson groupoid. If its each α-fiber intersects each βfiber not more than one point, then for any x ∈Γ, α(x) = u, β(x) = v, the characteristic distribution of Γ has a decomposition into direct product △(x)= △α(x) + △β(x),such that △α(x) tangents to α-fiber, △β(x) tangents to β-fiber, △α(x) and △β(x) are both Symplectic subspaces of △(x). Since the complete integrabilities of △α(x) and △β(x), there exist Symplectic submanifolds S and S of Symplectic leaf S, such that α: S→α(S) Su is Symplectic diffeomorphism and β: S→β(S) Sv is anti-Symplectic diffeomorphism. Where Su and Sv are Symplectic leaves of P.For general Poisson groupoids, we can obtain S and S with similar properties.Using these results to Symplectic groupoids, we can obtain some more concrete results.
  • Shu ZHU(1),Sheng Fan ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 809-814. https://doi.org/10.12386/A1999sxxb0109
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    This paper studies the damped and driven sine-Gordon equation with homogeneous Dirichlet boundary conditions. It is shown that in certain parameter region of damping and diffusing, for arbitrary nonautonomous and time-periodic driving force, the system has a unique periodic solution, which attracts any bounded set exponentially. Moreover, if the driving force is autonomous, the global attractor consists of only the unique equilibrium point which attracts any bounded set exponentially.
  • Yue Hui ZHANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 815-822. https://doi.org/10.12386/A1999sxxb0110
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    In this paper, the existence of triangular decompositions of Ringel dual algebras is proved by the concept of the exact Borel subalgebras.
  • Ren Xing NI(1),Chong LI(2)
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 823-826. https://doi.org/10.12386/A1999sxxb0111
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    The well posedness problems for simultaneous farthest points with respect to bounded subsets in Banach spaces are investigated. Under the Hausdorff metric of subsets, we proved that for a bounded closed subset K, The set of all convex compact sets A such that the simultaneous farthest points problem with respect to K is well posed is a dense Ge subset of the set of all convex compact subset.
  • Jin Jing LI(1),Shou Li JIANG(2
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 827-832. https://doi.org/10.12386/A1999sxxb0112
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    In this paper, we establish the characterizations of metric spaces under strong compact-covering(compact covering, strong sequence-covering) strong s-mappings. It is shown that the regular spaces with a locally countable k-network (strong k-network,csnetwork, cs*-network, compact-finite-partition network, sequence-finite-partition network) are mutually equivalent to the images of metric spaces under strong compactcovering (compact-covering, strong sequence-covering, sequence-covering, sequencequotient) strong s-mappings. In addition, we obtain some theorems on quotient strong s-images of metric spaces.
  • Yan XU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 833-838. https://doi.org/10.12386/A1999sxxb0113
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    Let F be a family of holomorphic functions in a domain G; a,b be two distinct finite complex numbers. In this paper, we prove that F is normal in G if f and f' share a, b IM in G, for every f ∈ F.
  • Hong Ji CHEN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 839-844. https://doi.org/10.12386/A1999sxxb0114
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    In this paper, we show that any A-module is a direct sum of a trivial module and a nosingular module, and give the structure of nonsingular module over infinitedimensional simple Novikov ajgebra of type (Ⅱ) and (Ⅲ) over a field F of characteristic 0.
  • Ji Sirendaoer
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 845-852. https://doi.org/10.12386/A1999sxxb0115
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    By introducing the adjoint coordinates, some non-regular high-order constrained flows for the Dirac hierarchy and their corresponding Lax representations and r-matrices are constructed. These constrained flows are also proved to be completely integrable in the sense of Liouville.
  • Xin Yi CHEN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 853-858. https://doi.org/10.12386/A1999sxxb0116
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    By constructing appropriate comparison functions on different areajs, Filippov's theorem is extended to the more generalized system
  • Han Fang ZHANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 859-862. https://doi.org/10.12386/A1999sxxb0117
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    In this paper, we first prove an algebraic inequality' then use its obtain a class of geometric inequalities of finite point sets on a sphere in the space of constant curvature , as its special case obtain the main result in the paper [3].
  • Fu Qing GAO,Yong Hong LIU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 863-872. https://doi.org/10.12386/A1999sxxb0118
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    In this paper, we discuss the large deviations for total occupation times of transient symmetric diffusion processes. We prove that total occupation times of transient symmetric diffusion processes satisfy the large deviation principle under uniformly elliptic condition.
  • Tu Sen HUANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 873-876. https://doi.org/10.12386/A1999sxxb0119
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    Conley gave two sufficient conditions of the existence of an attractor when he discussed attrastor-repeller pairs of a dynamical system on a topological space X in [1]. In this paper, we prove that these two sufficient conditions are, in fact, necessary. Further, we prove that any attractor defined by Conley must be asymptotically stable.
  • Wei WU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 877-882. https://doi.org/10.12386/A1999sxxb0120
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    In this paper, we present a complete proof of a theorem of submultiplication which claims that a*-algebra A with complete linear space norm such that ||x*x|| ||x||2 for x ∈ A and ||x*x|| = ||x||2 for normal ∈ E A is a C*-algebra. At the same time,a C*-equivalent version of the theorem is given.
  • Jin Fa CHEN(1),Ai Nong FANG(2)
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 883-888. https://doi.org/10.12386/A1999sxxb0121
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    In this paper, quasiregular mappings with double dilations was transformed into variational problems, its Euler-Lagrange equation was obtained, by using the equation, integral estimates for B-harmonic equation, Caccippoli inequality regularity and removability theorems for quasiregular mappings were established.
  • Ci Wen XU(1),Pu Xian HAN(2)
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 889-896. https://doi.org/10.12386/A1999sxxb0122
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    In this paper, we discuss the properties of the polar sets for (N -d) dimensional Generalized Wiener Processes and obtain some sufficient conditions and necessary conditions for a set to be a polar.
  • Cong Xin WU,Jun Jun LIAO
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 897-904. https://doi.org/10.12386/A1999sxxb0123
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    In this paper, we introduce 16 kinds of natural topologies on ∑(λ, μ), where ∑(λ,μ) denotes the algebra of the infinite matrix operators, which map the sequence space λ into another sequence space p. And we obtain a criterion for the continuity of the multiplication with respect to all kinds of topologies on ∑(λ,μ). Furthermore, with a detailed discuss of the continuity of the multiplication on ∑(ω, Ф), we study the toplogies for which the multiplication would never be continuous. As a result, the work of [1-3] is fully geneaxlized and developed.
  • Li Hong WANG,Jin De WANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 905-912. https://doi.org/10.12386/A1999sxxb0124
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    L1-estimation for time series is very important. Some properties of these estimators have been studied. However, some basic problems on this subject are left open. In this paper, we derive the limit distribution of the L1-estimators for stationary autoregressive models.
  • Jia Sheng XING
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 913-922. https://doi.org/10.12386/A1999sxxb0125
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    We consider the initial and mixed boundary value problems for the semiconductor equations with the initial value u0 ∈ (L2(G))2 in this paper, we prove the existence and uniqueness of generalized solutions for these problems.
  • Zong Guang LIU,Si Lei WANG
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 923-930. https://doi.org/10.12386/A1999sxxb0126
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    In this paper, we discussed the weak estimates for fractional integration on Herz-type spaces and established the Hardy-Littlewood-Sobolev theorems of fractional integration on Herz-type spaces completely together with Lu Shanzhen and Yang Dachun's strong estimates in [1].
  • Guo LI,Bai Li CHEN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 931-936. https://doi.org/10.12386/A1999sxxb0127
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    In this paper, the convergence of random products of a finite number of projection operators in Hilbert spaces is studied. The positive answer, under certain wild conditions, are given to two open problems concerning the convergence.
  • Fa Gui LIU
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 937-944. https://doi.org/10.12386/A1999sxxb0128
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    In this paper the author considers typical free boundary value problem for quasilinear hyperbolic system with dissipative term. Under certain assumptions, the global resolvabihty of C1 solution is obtained.
  • Xin Ping WANG,Jian Guo SI
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 945-950. https://doi.org/10.12386/A1999sxxb0129
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    Using Schauder and Banach's fixed point theorems, in this paper we discuss the existence, uniqueness and stability of continuous solutions of an iterative functional equation not in the polynomial-like form and extend the results of [1].
  • Wei Ping YIN
    Acta Mathematica Sinica, Chinese Series. 1999, 42(5): 951-960. https://doi.org/10.12386/A1999sxxb0130
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    The Bergman kernel function and holomorphic automorphism group for super-Cartan domain of the fourth type are given in explicit formulas.