中国科学院数学与系统科学研究院期刊网

15 March 1990, Volume 6 Issue 1
    

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  • Hong Jiaxing, Liu Jiaqian
    Acta Mathematica Sinica. 1990, 6(1): 1-9. https://doi.org/10.1007/BF02108857
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    Let S1.1 denote the submanifold of Lorentz space R2.1,which is composed of all points l with l2=1 and let T1.1= R1.1/Z×Z.In this paper we study the existence of nontrivial harmonic maps from T1.1 to S1.1 and H2,and construct a harmonic map for any homotopy class of maps from T2 to S1.1.
  • Wang Duo
    Acta Mathematica Sinica. 1990, 6(1): 10-17. https://doi.org/10.1007/BF02108858
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    The differential equation
    in considered,where θ is a real parameter.We prove that Hopf bifurcation occurs at the nonzero foci and is always subcritical for any A in a subregion in the complex plane.
  • Wang Zhiqiang
    Acta Mathematica Sinica. 1990, 6(1): 18-23. https://doi.org/10.1007/BF02108859
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    In this paper,we introduce a Zp index theory.For any given positive integer p,we introduce a subset Ep of positive integers and define a family of index mappings σn,n∈Ep.We prove that this index theory possesses the similar properties as Z2 and S1 index theories do.In particular,by means of a Zp Borsuk-Ulam theorem given in one of our recent papers we prove that under some suitable conditions this theory also possesses dimensional property which is important in applications.As a simple application,we study the bifurcation problem of periodic solutions of nonautonomous Hamiltonian systems.
  • Zhu Yaochen
    Acta Mathematica Sinica. 1990, 6(1): 24-34. https://doi.org/10.1007/BF02108860
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    In the present paper we establish a criterion of algebraic independence of complex numbers θ1,...,θn over a field KC of finite transcendence type using a sequence of nonzero polynomials in several variables with integral coefficients,which satisfy simultaneously certain upper and lower estimates in different orders of magnitude at the point (ω1,...,ωq,θ1,...,θn),where {ω1,...,ωq} is a transcendence basis of K over C.
  • Cao Cewen
    Acta Mathematica Sinica. 1990, 6(1): 35-41. https://doi.org/10.1007/BF02108861
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    Harry-Dym's equation (HD)rt=(r-1/2)xxx is well-known for ies cusp soliton solutions.In this paper,relatoions are revealed HD and a completely integrable Hamkltonian system in Liouvile sense given by

    in the symplectic manifold (R2N,dpdp).Here <ξ,η〉 is the standard inner product in RN.
  • Zhao Xishun
    Acta Mathematica Sinica. 1990, 6(1): 42-46. https://doi.org/10.1007/BF02108862
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    In this paper,we prove that if ZFC is consistent,then so are the following theories:

    where MA denotes Martin's axiom.KT(ω2) the statement:"There exists an ω2-Kurepa tree",and SOCA,SOCA1,OCA and ISA are axioms introduced in [1].
  • Ton Daorong
    Acta Mathematica Sinica. 1990, 6(1): 47-56. https://doi.org/10.1007/BF02108863
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    In this paper we discuss the completions (G,τ) of a commutative l-group G with respect to the intrinsic topologies τ.We give some conditions under which τ is the intrinsic topology of the same type on G as τ and give the relations between these completions.
  • Wang Youning
    Acta Mathematica Sinica. 1990, 6(1): 57-64. https://doi.org/10.1007/BF02108864
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    In this paper,we establish a sharp inequality of the gradient of energy density.We use it in studying stability of domain and pinching of energy.And we get the sharp conclusion respectly.In addition,we connect the existence of non-constant totally geodesic maps with the construction of manifolds on topology and geometry.
  • Zheng Zukang
    Acta Mathematica Sinica. 1990, 6(1): 65-71. https://doi.org/10.1007/BF02108865
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    In this paper the limit points of the Kaplan-Meier estimator is discussed.We use the method of strong approximation to get the unit ball of the reproducing kernel Hilbert space.
  • Lin Qing
    Acta Mathematica Sinica. 1990, 6(1): 72-79. https://doi.org/10.1007/BF02108866
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    Let F=(fij)be an n×n matrix of Hentries,and define

    This type of operator plays an important role in Cowen-Douglas theory.We call it the imbedded operator with symbol F.In the paper [L],we have already shown that SF is a compact pertubation of Tz⊕ * In by BDF Theorem.In this paper,we begin to investigate the compact part of SF.We give a practical method to calculate this compact part when n=1 and F is any finite Blaschke product.
  • Yu Yanlin
    Acta Mathematica Sinica. 1990, 6(1): 80-86. https://doi.org/10.1007/BF02108867
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    This paper considers geodesic triangies in a Riemannian manifold M.First we imbed the set Σ of geodesic triangles in M into a big space E,then find some equations in E satisfied by tangent vectors of Σ.Finally we give an application of the result.
  • Yang Jingen
    Acta Mathematica Sinica. 1990, 6(1): 87-96. https://doi.org/10.1007/BF02108868
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    To each curve singularity there associates a tree with suitably defined weights and special paths.These combinatorial data reflect the topological properties of the singularity.It is shown that such a curve can be specified by several axioms,so that every tree satisfying these axioms arises from a curve singularity.