中国科学院数学与系统科学研究院期刊网

15 September 1992, Volume 8 Issue 3
    

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  • Huang Cheng-gui
    Acta Mathematica Sinica. 1992, 8(3): 225-235. https://doi.org/10.1007/BF02582911
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    Suppose X and the coefficients A1,…,Am are n×n matrices.Let B be an mn×mn matrix as in (7).Let J be the Jordan canonical matrix of B and B=PJP-1.Let Ei denote the i×i unit matrix.V is defined by dV/dt=JV and V(t=0)=Emn.Then Z=PV satisfies dZ/dt=BZ.P* is a matrix which consists of the first n rows of P.The author proves: There is a solution of (1)↔there are an mn×n matrix C,an n×n matrix Q and an n×n function matrix N such that P*VC=QN,where det Q≠0 and N is defined by N(t=0)=En and dN/dt=RN,in which R is an n×n Jordan canonical matrix.There are three cases regarding the solutions of (1): No solution,finite k solutions,1<k<Cnm,and infinite solutions which contain j parameters,1<-j<-mn2.
  • Chuan Kuan Yuan
    Acta Mathematica Sinica. 1992, 8(3): 236-242. https://doi.org/10.1007/BF02582912
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    For infinite discrete groups,Effros introduced the notion of inner amenability which gives a new classification of discrete groups.The inner amenability is a considerably weaker condition than amenability,but closely related to the quite deep property Γ of groups.In this paper the author investigates the structures of inner amenable groups by theoretical set theory.A sequence of characterizations of inner amenable groups is given here by developing the well-known Folner's conditions for amenable locally compact groups.
  • Cheng Shihong
    Acta Mathematica Sinica. 1992, 8(3): 243-254. https://doi.org/10.1007/BF02582913
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    To estimate the exponent of a regularly varying d.f.F,the asymptotic behaviour of Hill's estimator has been extensively discussed.Under the assumption that the d.f.F is continuous,we obtain the large deviation theorem for Hill's estimator.
  • Shanyou Zhou
    Acta Mathematica Sinica. 1992, 8(3): 255-265. https://doi.org/10.1007/BF02582914
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    This paper deals with the closedness of generalized vertex operators defined by the central binomial coefficient under Lie bracket.The formula of Lie product of generalized vertex operators has also been obtained.
  • Li Weigu
    Acta Mathematica Sinica. 1992, 8(3): 266-272. https://doi.org/10.1007/BF02582915
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    In this paper,we give a necessary and sufficient condition for the one-parameter families of diffeomorphisms on S1 to be stable and a necessary condition for the multi-parameter families to be stable; and,moreover,we prove that phase-locking is a generic property of the one-parameter families of diffeomorphisms on S1.We also get a necessary and sufficient condition of phase-locking for the one-parameter families of integral diffeomorphisms on S1 which strengthens a result in [2].
  • Wang Xu-jia
    Acta Mathematica Sinica. 1992, 8(3): 273-291. https://doi.org/10.1007/BF02582916
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    In this paper we extend the results of Brezis and Nirenberg in [4] to the problem
    (A)
    where L is a uniformly elliptic operator,b(x)≥0,f(x,u) is a lower order perturbation of up at infinity.The existence of solutions to (A) is strongly dependent on the behaviour of aij (x),b(x) and f(x,u).For example,for any bounded smooth domain Ω,we have such that Lu=up possesses a positive solution in H01(Ω).

    We also prove the existence of nonradial solutions to the problem -Δu=f(|x|,u) in Ω,u>0 in Ω u=0 on ∂Ω,Ω=B(0,1).for a class of f(r,u).

  • Jiang Jiahe, Yang Changcheng
    Acta Mathematica Sinica. 1992, 8(3): 292-308. https://doi.org/10.1007/BF02582917
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    A coincidence theorem for a single-valued mapping in [3] is generalized as one for a strongly decomposable multivalued mapping.
  • Yan Shaozong, Chen Xiaoman
    Acta Mathematica Sinica. 1992, 8(3): 309-318. https://doi.org/10.1007/BF02582918
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    As we know,B.Sz-Nagy and C.Foins studied systematically contractions on Hilbert spaces and developed the harmonic analysis theory of operators on Hilbert spaces.Since 1950s,people paid great attention to the study of contractions on πk spaces.Only a few results have been obtained until today; in particular,the spectral theory of contractions on πk Spaces and corresponding harmonic analysis theory have left still unexplored.This paper,as a continuation of [1],[2],[6],in which the authors after discussing some problems such as the negative invariant subspaces and unitary dilations of contractions on complete spaces with indefinite metrics,establish the triangle model of contractions on πk spaces and furthermore,apply the triangle model to the study of spectral theory of contractions on πk spaces,which is essential to the harmonic analysis of operators on πk spaces.
  • Chen Weihuan
    Acta Mathematica Sinica. 1992, 8(3): 319-328. https://doi.org/10.1007/BF02582919
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    In this paper we give the volume of tubes around complex submanifolds in complex space form in terms of the technique of Jacobi fields.
  • Fu Bin
    Acta Mathematica Sinica. 1992, 8(3): 329-336. https://doi.org/10.1007/BF02582920
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    We construct an oracle A such that .So the polynomial time hierarchy is separated from the polynomial time probabilistic complexity class in relativization.