15 August 2004, Volume 20 Issue 4

    

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  Lacunary Measures and Self-similar Probability Measures in Function Spaces

  Hans TRIEBEL

  Acta Mathematica Sinica. 2004, 20(4): 577-588. https://doi.org/10.1007/s10114-004-0381-8

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  The paper deals with multifractal quantities for some types of Radon measures,especially self-similar probability measures,and their relations to Besov spaces.
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  Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow

  Ze Jun WANG

  Acta Mathematica Sinica. 2004, 20(4): 589-604. https://doi.org/10.1007/s10114-004-0379-2

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  In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in compressible flow.The corresponding mathematical model is the well-known Euler system.With the Newton iteration procedure and energy estimate,we give the local existence of the shock front solution to this problem.
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  Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

  Xiang Yu ZHOU, Wei Ming LIU

  Acta Mathematica Sinica. 2004, 20(4): 605-612. https://doi.org/10.1007/s10114-004-0376-5

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  Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vector bundle of rank r with trivial pull-back to W=Cⁿ-{0}.We prove the existence of a non-vanishing section of LE for some line bundle on X and study the vector bundles filtration structure of E.These generalize the results of D.Mall about structure theorem of such a vector bundle E.
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  Some Characterizations of the Properties LB^∞ and LB_∞

  Thuan Quang THAI

  Acta Mathematica Sinica. 2004, 20(4): 613-628. https://doi.org/10.1007/s10114-003-0299-6

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  The aim of this paper is to give some properties of the linear topological invariant Using these results we show that a nuclear Fréchet space F has the property LB_∞ if and only if every separately holomorphic function on an open subset U×V of E×F* has a local Dirichlet representation,where E is a nuclear Fréchet space with the property having a basis.
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  Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

  J. C. ROSALES, P. A. GARCíA-SÁNCHEZ, J. I. GARCíA-GARCíA, J. A. JIMÉNEZ MADRID

  Acta Mathematica Sinica. 2004, 20(4): 629-646. https://doi.org/10.1007/s10114-003-0298-7

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  For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps.We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup.Numerical semigroups with maximum and minimum number of this kind of gaps are described.
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  Uniqueness of Limit Cycle for the Quadratic Systems with Weak Saddle and Focus

  Shen Qi ZHAO, Ping Guang ZHANG

  Acta Mathematica Sinica. 2004, 20(4): 647-652. https://doi.org/10.1007/s10114-004-0380-9

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  It is proved that the quadratic system with a weak saddle has at most one limit cycle,and that if this system has a separatrix cycle passing through the weak saddle,then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it.
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  On the Characterizability of the Automorphism Groups of Sporadic Simple Groups by Their Element Orders

  A. R. MOGHADDAMFAR, A. R. ZOKAYI, M. R. DARAFSHEH

  Acta Mathematica Sinica. 2004, 20(4): 653-662. https://doi.org/10.1007/s10114-004-0352-0

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  For G a finite group,π_e(G) denotes the set of orders of elements in G.If Ω is a subset of the set of natural numbers,h(Ω) stands for the number of isomorphism classes of finite groups with the same set Ω of element orders.We say that G is k-distinguishable if h(π_e(G))=k<∞,otherwise G is called non-distinguishable.Usually,a 1-distinguishable group is called a characterizable group.It is shown that if M is a sporadic simple group different from M₁₂,M₂₂,J₂,He,Suz,M^cL and O'N,then Aut(M) is characterizable by its element orders.It is also proved that if M is isomorphic to M₁₂,M₂₂,He,Suz or O'N,then h(π_e(Aut(M)))∈{1,∞}.
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  Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure

  Hui Jun FAN

  Acta Mathematica Sinica. 2004, 20(4): 663-682. https://doi.org/10.1007/s10114-004-0375-6

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  This paper discusses the Cauchy problem of the equation
  
  with initial datum a measure.Under the assumption of the parameters,one proves the existence and non-existence of the non-negative generalized solution.
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  Modular Lie Superalgebras of H-type

  Yong Zheng ZHANG

  Acta Mathematica Sinica. 2004, 20(4): 683-694. https://doi.org/10.1007/s10114-004-0362-y

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  In this article the Z-graded transitive modular Lie superalgebra ⊕_i≥-1L_i,whose representation of L₀ in L_-1 is isomorphic to the natural representation of osp(L_-1),is determined.
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  Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations

  Quan Sen JIU, Cheng HE

  Acta Mathematica Sinica. 2004, 20(4): 695-708. https://doi.org/10.1007/s10114-003-0296-9

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  In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T].Five sufficient conditions are given.Our results are motivated by two main ideas:one is to control the accumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.
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  Definition of Measure-theoretic Pressure Using Spanning Sets

  Lian Fa HE, Jin Feng LV, Li Na ZHOU

  Acta Mathematica Sinica. 2004, 20(4): 709-718. https://doi.org/10.1007/s10114-004-0368-5

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  We introduce a new definition of measure-theoretic pressure for ergodic measures of continuous maps on a compact metric space.This definition is similar to those of topological pressure involving spanning sets.As an application,for C^1+α(α >0) diffeomorphisms of a compact manifold,we study the relationship between the measure-theoretic pressure and the periodic points.
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  Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

  Xi Cheng ZHANG

  Acta Mathematica Sinica. 2004, 20(4): 719-730. https://doi.org/10.1007/s10114-004-0353-z

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  In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-sure continuity of the solution.
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  Disk-like Tiles Derived from Complex Bases

  Jun LUO, Zuo Ling ZHOU

  Acta Mathematica Sinica. 2004, 20(4): 731-738. https://doi.org/10.1007/s10114-004-0354-y

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  For each positive integer k,the radix representation of the complex numbers in the base -k+i gives rise to a lattice self-affine tile T_k in the plane,which consists of all the complex numbers that can be expressed in the form ∑_j≥1d_j(-k+i)^-j,where d_j∈{0,1,2,…,k²}.We prove that T_k is homeomorphic to the closed unit disk {z∈C:|z|≤1} if and only if k≠2.
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  Viscosity Solutions of Monotonic Functional Parabolic PDE

  Wei An LIU, Gang LU

  Acta Mathematica Sinica. 2004, 20(4): 739-748. https://doi.org/10.1007/s10114-003-0241-y

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  In this paper,by the technique of coupled solutions,the notion of viscosity solution is extended to quasi-monotonic fully nonlinear parabolic equations with delay,which involves many models arising from optimal control theory,economy and finance,biology etc.The comparison,existence and uniqueness are proved.And the results are applied to the retarded Bellman equations.
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  Asymtotics of M-estmation in Non-linear Regression

  Ying YANG

  Acta Mathematica Sinica. 2004, 20(4): 749-760. https://doi.org/10.1007/s10114-004-0378-3

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  Consider the standard non-linear regression model y_i=g(x_i,θ₀)+ε_i,i=1,…,n where g(x,θ) is a continuous function on a bounded closed region X×Θ,θ₀ is the unknown parameter vector in ΘR⊂^p,{x₁,x₂,…,x_n} is a deterministic design of experiment and {ε₁,ε₂,…,ε_n} is a sequence of independent random variables.This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed.This result is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models.At the same time,we point out that Theorem 2 of Wang (1995) (J.of Multivariate Analysis,vol.54,pp.227-238,Corrigenda.vol.55,p.350) is not correct.
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  A Characterization of Homomorphisms Between Banach Algebras

  Jian Lian CUI, Jin Chuan HOU

  Acta Mathematica Sinica. 2004, 20(4): 761-768. https://doi.org/10.1007/s10114-004-0312-8

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  We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex Banach algebra onto another,we also show that the following statements are equivalent:(1) Φ is an homomorphism;(2) Φ is completely invertibility preserving;(3) Φ is 2-invertibility preserving.