中国科学院数学与系统科学研究院期刊网

15 April 2000, Volume 43 Issue 4
    

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  • Ming Chu GAO,Jin Chuan HOU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 577-588. https://doi.org/10.12386/A2000sxxb0074
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    In this paper, sufficient and necessary conditions are given for a smooth Prichard-Salamon systems (PS systems for short) to be admissibly stabilizabile with a compact admissible feedback. Applying this result, we give a parameter representation for all nonnegative solutions to the algebraic Riccati equation for a smooth PS system,generalizing the main result in [1] to smooth PS systems.
  • Shu Xing CHEN,Yi ZHOU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 589-598. https://doi.org/10.12386/A2000sxxb0075
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    In this paper we generalize global Sobolev inequality introduced by Klainer man in studying wave equation to the hyperbolic system case. We obtain severaJ decay estimate of solutions to hyperbolic system of first order by different norms of initial data. Particularly, the result mentioned in Theorem 1.5 offers an optimal decay rate of solutions, if the initial data belongs to the asigned weighted Sobolev space. In the proof of the theorem we reduce the estimate of solutions to hyperbolic system to the corresponding case for a scalar pseudodifferential equation of the first order, then we establish the required estimate by using microlocaJ analysis.
  • Chun Chao HUANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 599-604. https://doi.org/10.12386/A2000sxxb0076
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    Let Sm be a Sierpinski carpet with compression ratio 1/m(m≥ 4), Sn be the set of n-th order elementary squares to produce Sm, U be a subset in R2 with diameter |U| > 0. αn.(U) denotes the number of the elementary squares intersecting U in Sn. It will be shown that (s=logm 4) for large n by elementary method, therefore we obtain that , where Hs(Sm) denotes s-dimensional Hausdorff mearsure of Sm.
  • Rao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 605-610. https://doi.org/10.12386/A2000sxxb0077
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    In the present note the transcendence of values of certain functions expressed by infinite products at algebralc and transcendental points is given.
  • Zhong Yan LI
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 611-614. https://doi.org/10.12386/A2000sxxb0078
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    In this paper, we point out that the two * operations must be same if there are two * operations which make the same one real Banach algebra be a real C*-algebra at the same time. i.e. the * operation in a real C*-algebra is uniquely determined.
  • Gao Hua TANG,Miao Qing ZHAO,We
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 615-622. https://doi.org/10.12386/A2000sxxb0079
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    In this paper, it is proved that a commutative coherent local ring with maximal ideal m, which is finitely generated, is regular if and only if m can be generated by a regular R-sequence. Some corresponding results in [1] are generalized, and a method for constructing non-regular coherent local rings from regular coherent local rings is gived.
  • An Min MAO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 623-632. https://doi.org/10.12386/A2000sxxb0080
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    This paper studies the existence of positive solutions of singular boundary value problems of positive exponent superlinear Emden-Fowler equations. A necessary and sufficient condition for the existence of C1[0, 1] positive solutions is given by means of function approximation with the fixed point theorems.
  • Zuo Xin GAN,Wei Gao GE
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 633-638. https://doi.org/10.12386/A2000sxxb0081
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    In this paper, from the method of Lyapunov functional, the absolute stability of systems with delay and multiple non-linearities, is studied. Some practicaJ sufficient conditions are obtained, which generalize the results of [1]. A concise example illustrates the effectiveness of the results of this paper.
  • Zhi Qing HAN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 639-644. https://doi.org/10.12386/A2000sxxb0082
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    In this paper, we obtain two existence results for 2π-periodic solutions of the following sublinear ordinary differential equations at resonance: u(t) + m2u(t)+ G(t, u(t)) =0 under coercive conditions on G(t, u) by critical point theorem.
  • Yuan Qiu HUANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 645-652. https://doi.org/10.12386/A2000sxxb0083
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    This paper studies the relationship between the Betti deficiency and the vertex-induced subgraph of vertex partition of graphs, and obtains an expression on the upper bounds on the mtalmum genus of a graph in terms of the vertex-induced subgraphs for vertex partition. Therefore some now results on the maximum genus of graphs are given.
  • Zheng Gui Dai
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 653-658. https://doi.org/10.12386/A2000sxxb0084
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  • Shu Ling ZHANG,Cheng Lin WEN,Y
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 659-664. https://doi.org/10.12386/A2000sxxb0085
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    A new multiscal system method is proposed for signal processin with a B- Spline function based on the multiscal anaJysis thought.
  • Jian Xun HE(1),Li Zhong PENG(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 665-672. https://doi.org/10.12386/A2000sxxb0086
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    Let B2 be the unit ball of 2-dimensional complex plane C2, dμα(z) = dm(z)(α>-1) the weighted measure. From the view point of the Cauchy-Riemann operator and the triangle polynomial given in [1], we obtain an or thogonal decomposition and orthogonal basis, where A0(+,+) and A0(-, -) are the Bergman and anti-Bergman spaces respectively. This decomposition can be extended to L2(Bn, dμα(z)). In addi tion, we also obtain some results for Hankel type operators.
  • Qing CHEN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 673-676. https://doi.org/10.12386/A2000sxxb0087
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    We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space. A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.
  • Wen Zheng ZHAO
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 677-684. https://doi.org/10.12386/A2000sxxb0088
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    The double crossed-product Bτ■bH by Doi Y. constructed and bialgebra B■bH by Reshetikhim N. constructed are well known in [1, 3], in this paper we find necessary and sufficient conditions for the Bτ■H algebra structure and B■RH coalgebra structure on B■H to afford B■H a bialgebra structure (Let Bτ■H denote the resulting bialgebra). By use this result, we construct an intersting example B4τ■R KZ2. In the final we give characterization of Bτ■R H by introducing the mapping system.
  • Pei Long SHEN(1),Fu Yi LI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 685-694. https://doi.org/10.12386/A2000sxxb0089
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    In this paper, the supsolution and subsolution method and the positive op erators semigroups theory are applied to periodic solution problems for semilinear evo lution equations with mixed monotone or mixed quasimonotone nonlinear terms in Ba nach spaces. The results on the minimal and maximal coupled periodic (qusi)solution are obtained. These results generalize and extend the relevant results in ordinary differential equations and partial differential equations.
  • Meng FAN,Ke WANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 695-702. https://doi.org/10.12386/A2000sxxb0090
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    In this paper, it has been proved that, for linear neutral functional differential equations of D-operator type with infinite delay, there is a periodic solution if and only if there is a bounded solution. The results proved by Massera J. L., Chow S. N. and Makay M. are generalized.
  • Ji Hui ZHANG(1),Xue Bo LUO(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 703-710. https://doi.org/10.12386/A2000sxxb0091
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    In this paper, the nonlinear eigenvalue problems on the Heisenberg group are studied, by using Leray-Schauder degree, some etistence results and some properties for set of solutions are obtained.
  • Wan Li YANG(1),You Wei LI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 711-718. https://doi.org/10.12386/A2000sxxb0092
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    In this paper, using the methods in nonlinear analysis, this present paper,studies the quasilinear parabolic systems in population dynamics, and obtained the existence of the global solution.
  • Qi Gui YANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 719-726. https://doi.org/10.12386/A2000sxxb0093
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    This paper studies the global stability of Lienard type system (E): x = φ(h(y) - F(x)), y = -g(x) through Filippov transformation and new method. We obtain new a series of necessary and sufficient conditions under which the zero solution of system (E) is globally stable.
  • Qin Jie FAN(1),Hui WANG(2),Gon
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 727-732. https://doi.org/10.12386/A2000sxxb0094
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    In this paper, we consider chaos for the subsystems arising from substitutions of constant length on two symbols. We get the following results: (1) the subsystems from nonsingular substitutions of constant length are not Li-Yorke chaos; (2) the sub systems from singular substitutions of constant length axe Li-Yorke chaos.
  • Qiu Hui SHENG(1),Si Long PENG(
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 733-742. https://doi.org/10.12386/A2000sxxb0095
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    An inverse problem on matrix extension is studied in order to investigate the construction of bivariate wavelets. The main result can be stated as follows: suppose that m is a low-pass filter, then it can be extended to a unitary matrix (1.9) if it and only if it has the form of (3.1).
  • Liang Yun ZHANG(1),Jin Qi LI(2
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 743-750. https://doi.org/10.12386/A2000sxxb0096
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    In the paper [1], the writer has given the concept of twisting product, and has pointed out (Drinfel'd double) D(H) to be a twisting product of tensor prduct algebras. In this paper, we extend twisting product to twisting module, and give its basic structure theorem. Meanwhile, we first give the concept of the paired Hopf module, which is a development of the duality of Hopf module in [2].
  • Qian LU(1),Yong Xing GU(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 751-756. https://doi.org/10.12386/A2000sxxb0097
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    In this paper, the existence of the singular point related to normal criterion is widely proved for the meromorphic function of zero order on the unit disc, and thus, we obtain the follow result: suppose that f(z) is the meromorphic function on the unit disc and satisfies then there exists point eiθo (0≤θ0 <2π) such that for every positive ε>0, every integer n ≥ 1, and every finite complex number a(a ≠ 0), we have limr→1-0 n(r, θ0, ε, fl fn = a) = +∞.
  • Jin Jin LI(1),Wei Yuan CAI(2)
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 757-762. https://doi.org/10.12386/A2000sxxb0098
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    This paper gives some new characterizations of images of locally separable metric spaces under strong sequence-covering (resp. 1-sequence-covering or 2-sequence covering)s-mappings, and a sufficient condition for a space to be a sequence-covering (resp. compact-covering) s-image of a locally separable metric space.
  • Cong Quan YAN,Shun Hua SUN
    Acta Mathematica Sinica, Chinese Series. 2000, 43(4): 763-768. https://doi.org/10.12386/A2000sxxb0099
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    The paper studied the automorphism on the tensor product C(X)A of the continuously function algebra and some C*-algebra. When A is a unita1 C*-algebra with trivial center, the paper characterized completely the automorphism group on the C(X)A. By using K-theory of AF-algebra, the paper characterized the automorphism group on the tensor product of the C(X) and the compact ideal when X is a tottaly disconnected compact Hausdoof space.