中国科学院数学与系统科学研究院期刊网

15 June 2001, Volume 44 Issue 6
    

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  • Chun Shan ZHAO(1),Kai Tai LI(2
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 961-976. https://doi.org/10.12386/A2001sxxb0122
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    The global stability for large solutions to the evolution system of MHD type describing geophysical flow in three-dimensional bounded or unbounded domains was investigated. Under suitable conditions of the large solutions, it was shown that the large solutions were stable. Moreover, the stability of unforced two-dimensional MHD flow under three-dimensional perturbation was also obtained.
  • Zhong Kui LIU(1),Javed AHSAN(2
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 977-982. https://doi.org/10.12386/A2001sxxb0123
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    As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and (5, ≤) a strictly totally ordered monoid. We prove that (1) the ring [[RS≤_]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B(R) (the set of all idempotents of R) has a least upper bound in B(R), and (2) if (S,≤) also satisfies the condition that 0 ≤ s for any s∈5, then the ring [[RS≤_]] is weakly PP if and only if R is weakly PP.
  • Zhong Xuan LUO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 983-994. https://doi.org/10.12386/A2001sxxb0124
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    In this paper, the theory of generator basis of a prime module is investigated by establishing a new reduce theorem in module. For the cases of lower dimensions, the sufficient and necessary conditions for generator basis of a prime module are given. Some applications of the generator basis method in spline functions are given, and some interesting examples are presented in the paper.
  • Qiu Hui SHENG(1),Han Lin CHEN(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 995-100. https://doi.org/10.12386/A2001sxxb0125
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    Suppose that f(x) = (f1(x),... ,fr(x))T, a ? Rd is a vector-valued function satisfying the refinement equation f(x) with finite set of Zd and some r × r matricex Ck. The requirements for f to have accuracy p are given in terms of the symbol function m(ξ).
  • Qing Jie SUN,Wei Yi SU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1003-101. https://doi.org/10.12386/A2001sxxb0126
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    Dupain Y., France M. M. and Tricot C[1].defined and studied Steinhaus dimension of spirals by Steinhans theorem of integral geometry. We continue this study and show that Steinhaus dimension is not a "good" dimension.
  • Rao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1011-101. https://doi.org/10.12386/A2001sxxb0127
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    In this note using the radical-inverse function and the matrix construction certain finite point sets in [0,1]8 (s≥1) are defined, and the upper bound estimation of their discrepancy is given, and so the uniform distribution property of certain sequences consisting of these point sets is proved.
  • Jin Lin SHI
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1019-102. https://doi.org/10.12386/A2001sxxb0128
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    The Basic condition to linearize a nonlinear system x' = Ax + f(x) is that none of the real parts of characteristic roots of A is zero. The classical conclusion of linearization is only limited to the small neighborhood of origion[1]. Later, in [2,3], it is generalized to global space, however, it required that f(x) must be bounded. In [4] we free the limitation. In this paper, we further free the limitation that none of the real parts of characteristic roots of A is zero and prove that the global linearization can be realized with a proper structure of f(x).
  • Yuan Tong XU,Zhi Ming GUO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1027-103. https://doi.org/10.12386/A2001sxxb0129
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    In this paper, we introduce a new version of geometrical index of Zp, group action. By means of this index theory, we obtain the existence of subharmonics to a class of nonautonotnous functional differential equations. Meanwhile, we provide a new answer to the conjecture posed in [1] on the existence of subharmonic solutions to Hamiltonian systems.
  • Rong Kun ZHUANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1037-104. https://doi.org/10.12386/A2001sxxb0130
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    In this paper, the second order matrix differential system (P(t)Y')'+Q(t)Y = 0, t ∈ [t0, ∞] is considered, where P,Q and Y are n × n real matrix functions, P(t) and Q(t) are symmetric, and P(t) > 0, t ∈ [t0, ∞]. New oscillation criteria are only based on the information of a sequence of subinterval of [t0,∞), and different from most known results. Our results are sharper, and can be applied to extreme cases such as
  • Yu Wen WANG(1),Hui WANG(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1045-105. https://doi.org/10.12386/A2001sxxb0131
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    In this paper, we have first extended Riesz orthogonal decomposition theorem in Hilbert space to Banach space and obtained generalized orthogonal decomposition theorem in Banach Space. Then, we have discussed orthogonal cencept in Banach Space introduced by James R. C[1] and generalized orthogonal complemented subspace in Banach Space introduced by Nashed M. Z.[2]. Finally, a sufficient and necessary condition for a subspace to be generalized orthogonal complemented and a new character of Hibert space are given.
  • Lei LI(1),Cong Xin WU(2)
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1051-106. https://doi.org/10.12386/A2001sxxb0132
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    In this paper, we introduce two lower semicontinuous closed convex set-valued mappings relating to almost lower semicontinous set-valued mappings in Banach spaces, give several characteristics on the existence of continuous selections for set-valued mappings. As the corollaries, the results of Deutsch and Kenderov, De Blasi and Myjak, Przeslawski and Rybinski, Gutev and author about the existence of continuous selections are obtained again. On the basis this, we discuss the problem about the existence of homogenoous right inverses for linear operators from Banach space into normed spaces when the open mapping theorem does not hold.
  • Run Sheng YANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1063-106. https://doi.org/10.12386/A2001sxxb0133
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    For the topologically ergodic self-maps on compact metric space, this paper studies its properties, judging and relationship with chaos.
  • Jiao Wan LUO(1),Jian Hua SHEN(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1069-107. https://doi.org/10.12386/A2001sxxb0134
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    The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses. Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8].
  • Chun Gen LIU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1073-108. https://doi.org/10.12386/A2001sxxb0135
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    In this paper, by using the direct variational and the Gelerkin approximation methods, we study the dual Morse k-index theory of subquadratic Hamiltonian systems without conexity. As an application, we study the stability of closed characteristics on the strictly convex C2 conmpact hypersurface in R2n. We prove that under a relaxed pinched condition, there exists a strictly elliptic characteristic on .
  • Cai Sheng CHEN,Ru Yun WANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1089-109. https://doi.org/10.12386/A2001sxxb0136
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    In this paper, we consider the global existence, uniqueness and L∞ estimate of weak solution to the initial-boundary value problem for the doubly nonlinear parabolic equation ut = div with zero boundary condition. In particular, the behavior of solution as t and is investigated. We established the following results. If , then the solution u(t) exists and satisfies where are some positive constants depending on m, q, r, N.
  • Xu An ZHAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1099-110. https://doi.org/10.12386/A2001sxxb0137
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    In this paper, the cohomology endomorphisms of flag manifold G/T of compact simple Lie group G is completely classified, and the Lefschetz number of these endomorphisms are computed.
  • You Long YANG,Xiao Guang GAO
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1107-111. https://doi.org/10.12386/A2001sxxb0138
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    Hopenwasser A.[1] guessed that the operator set of the CSL algebra satisfying Ringrose condition just is its Jacobson radical; Davidson K. R.[2] proved that this conjecture is true on the width-two CSL. In this paper, the structure of Jacobson radical on the width-two CSL is described clearly, and an. aproach for analyzing the CSLs radical is provided. Let be a width-two CSL generated by nests M and N in a separable Hilbert space, and W = M∩ N. We prove an important relationship , where is the Jacobson radical of alga and Rw, are the Jacobson radical and the stronger radical of nest W respectively. Also, it has been derivedt that the sufficient and necessary conditions for are M ≠ K and M≠K⊥.
  • Qiu Yi DAI(1),Xian Zhong ZENG(
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1113-112. https://doi.org/10.12386/A2001sxxb0139
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    Cauchy problem for a class of singular semilinear parabolic systems is considered. Quenching critical exponent and quenching critical dimension of the above problem is evaluated.
  • Tian Shou ZHOU(1),Suo Chun ZHA
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1121-112. https://doi.org/10.12386/A2001sxxb0140
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    The paper proves the stability of in-phase solutions in the coupled Hodgkin-Huxley equations.
  • Zhi Tao ZHANG
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1127-113. https://doi.org/10.12386/A2001sxxb0141
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    In this paper, by making use of continuation method, we confirm the uniqueness of solutions for a class of semilinear elliptic equations.
  • Ci Wen XU
    Acta Mathematica Sinica, Chinese Series. 2001, 44(6): 1131-114. https://doi.org/10.12386/A2001sxxb0142
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    In this paper, we obtain the upper bounds and lower bounds of Hausdorff measure of image sets and graph sets for N-parameter d-dimensional generalized Brownian Sheet.