中国科学院数学与系统科学研究院期刊网

15 March 1991, Volume 7 Issue 1
    

  • Select all
    |
    Articles
  • Wang Zeke
    Acta Mathematica Sinica. 1991, 7(1): 1-3. https://doi.org/10.1007/BF02582986
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The convex hull of the vertices of a simplex and a point lying on the hyperplane spanned by the simplex is called a flat cone on the simplex. This paper proposes a natural way to simplicially triangulate flat cones on simplices and develops its applications to PL homotopy methods.
  • Wu Shaoping
    Acta Mathematica Sinica. 1991, 7(1): 4-12. https://doi.org/10.1007/BF02582987
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let L be a self-adjoint linear operator and N be the gradient of a functional ψ, which is almost quadratic. We first give a theorem on the surjectivity of the operator L+N, then apply the result to semilinear elliptic systems:
    We get the existence of weak solution in space L2(Ω) for any f1(x) in L2(Ω), when the function g has the behavior at infinity like au2+bv2+c‖u‖1/2‖v‖1/2, etc.
  • Mai Jiehua, Tang Yun
    Acta Mathematica Sinica. 1991, 7(1): 13-18. https://doi.org/10.1007/BF02582988
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    It was proved in [5] that every finite collapsible polyhedron admits of an injective metric. In this paper, by using some new techniques, we extend the conclusions in [5] to the infinite case.
  • Chen Mufa
    Acta Mathematica Sinica. 1991, 7(1): 19-37. https://doi.org/10.1007/BF02582989
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    This paper deals with the exponential L2-convergence for jump processes. We introduce some reduction methods and improve some previous results. Then we prove that for birth-death processes, exponential L2-convergence coincides indeed with exponential ergodicity which is widely studied in the Markov chain theory.
  • Chen Hua
    Acta Mathematica Sinica. 1991, 7(1): 38-50. https://doi.org/10.1007/BF02582990
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, I study the microlocal hypoellipticity for a class of totally characteristic operators (1.1). My main result is as follows: Under the conditions (Ⅰ), (Ⅱ), if the indicial operator of (1.1) is microlocally hypoelliptic in the complement of WFx(Pu(t,·)) for any u(t,x)∈Cb ([0,T], g), t∈[0, T], λ∈Z+, then the operator (1.1) is microlocally hypoelliptic in the variable x.
  • Li Boyu
    Acta Mathematica Sinica. 1991, 7(1): 51-61. https://doi.org/10.1007/BF02582991
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In 1985 I. Rival and N. Zaguia conjectured that in a chain complete poset having the finite cutset property every element belongs to an antichain cutset iff there is no alternating-cover cycle. In this paper a counterexample is given to show that the condition that there is no alternating-cover cycle is not sufficient and other two conditions on generalized alternating-cover paths are added to complete the characterization.
  • Wang Yanming
    Acta Mathematica Sinica. 1991, 7(1): 62-65. https://doi.org/10.1007/BF02582992
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By using the classification theorem of finite simple groups, we have shown that "If G is a finite group, H is a coprime operator group of G, CG(H)≤S(G), then G is solvable." As a direct corollary, we have completely proved the long-standing conjecture on fixed-point-free automorphism group.
  • Li Huiling, Huang Jianhua
    Acta Mathematica Sinica. 1991, 7(1): 66-74. https://doi.org/10.1007/BF02582993
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we discuss an amalgam (M11, SL2 (5)) of rank 2 and characteristic 3. Suppose G is a group generated by its two subgroups P1, P2, and suppose P1, P2 and their intersection satisfy some local group-theoretic conditions. Then, assuming that O3 (P1/O3(P1)) and O3′ (P2/O3(P2)) are isomorphic to M11 and SL2 (5) respectively, we give an explicit description about the structures of O3 (P1) and O3 (P2) and of the operations of Pi's on them. At this time, they have structures similar to those of some 3-local subgroups of the sporadic simple group Ly.
  • Zheng Zhiming
    Acta Mathematica Sinica. 1991, 7(1): 75-90. https://doi.org/10.1007/BF02582994
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper we discuss the time dependence of solutions of the equation (2.3). From it we will get the global qualitative analysis of the equation.
  • Li Banghe, Li Guisong
    Acta Mathematica Sinica. 1991, 7(1): 91-96. https://doi.org/10.1007/BF02582995
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let M be a manifold satisfying certain conditions which are weaker than those of E. Thomas[12], and f:MN be a map with codimension one or two. We give necessary and sufficient conditions for f to be homotopic to a map with maximal rank. As an application, we completely determine the codimension one or two immersions of Dold manifolds in real projective spaces.