15 September 1996, Volume 12 Issue 3

    

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  Chen Jingrun: A Brief Outline of His Life and Works

  Pan Chengtong, Wang Yuan

  Acta Mathematica Sinica. 1996, 12(3): 225-233. https://doi.org/10.1007/BF02106975

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  Chen Jingrun was born on 22 May,1933 in Fu Zhou in Fu Jian province of China.Chen's father Chen Yuanjun was a clerk in postoffice and his mother was passed away in 1947.Chen's family was comparatively poor since the income of his father was lower and the population of his family was comparatively large.
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  Algebraic surfaces of general type with K²=2p_g-1, p_g≥5

  Liu Xianfang

  Acta Mathematica Sinica. 1996, 12(3): 234-243. https://doi.org/10.1007/BF02106976

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  This paper mainly deals with minimal algebraic surfaces of general type with K²=2p_g-1. We prove that for p_g≥7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g≥13 all these surfaces are simply-connected.
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  Free Quadratic Bialgebra

  Hao Zhifeng, Tong Wenting

  Acta Mathematica Sinica. 1996, 12(3): 244-248. https://doi.org/10.1007/BF02106977

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  In this paper, we obtain the following main theorem for a free quadratic bialgebra J:

  (a) For p≠0,J is a pointed cosemisimple coalgebra. For p=0,J is a hyperalgebra.

  (b) For p≠0 and q≠0,J has antipode S iff p·q+2=0 and S(x)=x. For p=0 or q=0,J has antipode and S(x)=x.

  (c) All left J^*-modules are rational.

  Also, we give some applications in homological theory and algebraic K-theory.

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  The Braided Product of Ockham Algebras

  Fang Jie

  Acta Mathematica Sinica. 1996, 12(3): 249-253. https://doi.org/10.1007/BF02106978

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  In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L_i ∈MS(i=1, 2,…,n) then the Braided product of L_i(i=1, 2,…,n) exists if and only if L₁,…,L_n have isomorphic skeletons.
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  The Regularity of Lagrangians f(x, ξ)=|ξ|^α(x) with Hölder Exponents α(x)

  Fan Xianling

  Acta Mathematica Sinica. 1996, 12(3): 254-261. https://doi.org/10.1007/BF02106979

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  In this paper the regularity of the Lagrangians f(x, ξ)=|ξ|^α(x)(1<α₁≤α(x)≤α₂< +∞) is studied. Our main result: If α(x) is Holder continuous, then the Lagrangian f(x, ξ)=|ξ|^α(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.
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  Some New Results in Waring’s Problem

  Meng Zaizhao

  Acta Mathematica Sinica. 1996, 12(3): 262-267. https://doi.org/10.1007/BF02106980

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  Let G(k) denote the smallest number s such that every sufficiently large natural number is the sum of, at most,s k-th powers of natural numbers. In this paper, we give new bounds for G(12),G(13) and G(19).
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  Geometric Parameters Corresponding to Representations of the Classical Groups with Integral Infinitesimal Characters

  Hou Zixin, Zhao Qiang

  Acta Mathematica Sinica. 1996, 12(3): 268-284. https://doi.org/10.1007/BF02106981

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  In this paper we calculate the orbits of flag manifolds of the complex classical groups under the action of the sets of fixed points of Cartan involutions, and determine all the geometric parameters corresponding to representations of the classical groups with integral infinitesimal characters, which are used to discuss Arthur conjecture and the Langlands classification of the irreducible admissible representations of real classical groups(see[1]).
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  Extremal Quasiconformal Mappings Compatible with Fuchsian Groups

  Shen Yuliang

  Acta Mathematica Sinica. 1996, 12(3): 285-291. https://doi.org/10.1007/BF02106982

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  For every torsion free Fuchsian group Γ with Poincaré's Θ-operator norm ||Θ_Γ||=1, it is proved that there exists an extremal Beltrami differential of Γ which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.
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  A Necessary Condition for the Consistency of LAD Estimate

  Chen Xiru, Wu Yuehua, Zhao Lincheng

  Acta Mathematica Sinica. 1996, 12(3): 292-297. https://doi.org/10.1007/BF02106983

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  If in the linear model (1) the random errors e₁, e₂,… satisfy assumption (B) (See Section 1), then a necessary condition for the consistency of the LAD estimate of β₀ is .
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  The Riemannian Geometry of Superminimal Surfaces in Complex Space Forms

  Shen Yibing

  Acta Mathematica Sinica. 1996, 12(3): 298-313. https://doi.org/10.1007/BF02106984

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  This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.
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  Global Attractors for the Initial Value Problems of Cohn-Hilliard Equations on Compact Manifolds

  Guo Boling, Wang Youde

  Acta Mathematica Sinica. 1996, 12(3): 314-325. https://doi.org/10.1007/BF02106985

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  In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.
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  Choice of Optimal Trimming Proportion by the Random Weighting Method

  Shi Jian, Zheng Zhongguo

  Acta Mathematica Sinica. 1996, 12(3): 326-336. https://doi.org/10.1007/BF02106986

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  In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the distribution of some adaptive estimator is also obtained.