15 December 2000, Volume 16 Issue 4

    

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  Moving Symplectic Curves in Kähler-Einstein Surfaces

  Jingyi Chen, Gang Tian

  Acta Mathematica Sinica. 2000, 16(4): 541-548. https://doi.org/10.1007/s101140000075

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  We derive a parabolic equation for the Kähler angle of a real surface evolving under the mean curvature flow in a Kähler-Einstein surface and show that a symplectic curve remains symplectic with the flow.
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  On the Average Number of Unitary Factors of Finite Abelian Groups (Ⅱ)

  Wenguang Zhai

  Acta Mathematica Sinica. 2000, 16(4): 549-554. https://doi.org/10.1007/s101140000085

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  Let t(G)be the number of unitary factors of finite abelian group G.In this paper we prove T(x)=Σ|G|≤xt(G)=main terms+o(x^(1+2k)/3+4k+εfor any exponent pair (k,1/2+2k),which improves on the exponent 9/25 obtained by Xiaodong Cao and the author.
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  More on Bounding Introspection in Modal Nonmonotonic Logics

  Xishun Zhao, Decheng Ding

  Acta Mathematica Sinica. 2000, 16(4): 555-564. https://doi.org/10.1007/s101140000086

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  By L,we denote the set of all propositional formulas.Let C be the set of all clauses.Define C₀=C∪{﹁Lη:η∈C} In Sec.2 of this paper,we prove that for normal modal logics S,the notions of (S,C₀)-expansions and S-expansions coincide.In Sec.3,we prove that if I consists of default clauses then the notions of S-expansions for I and (S,C)-expansions for I coincide.To this end,we first show,in Sec.3,that the notion of S-expansions for I is the same as that of (S,L)-expansions for I.
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  Asymptotic Behavior of Forced Nonlinear Delay Differential Equations with Impulses

  Jiaowan Luo, Jianhua Shen

  Acta Mathematica Sinica. 2000, 16(4): 565-572. https://doi.org/10.1007/s101140000087

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  The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses
  
  Our results,which hold for linear and nonlinear equations,forced and unforced equations,impulsive and nonimpulsive equations,improve and generalize the known results recently obtained in [8].
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  PP-Rings of Generalized Power Series

  Zhongkui Liu, Javed Ahsan

  Acta Mathematica Sinica. 2000, 16(4): 573-578. https://doi.org/10.1007/s1011400000884

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  As a generalization of power series rings,Ribenboim introduced the notion of the rings of generalized power series.Let R be a commutative ring,and (S,≤) a strictly totally ordered monoid.We prove that (1) the ring[[R^S,≤]]of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B(R)(the set of all idempotents of R) has a least upper bound in B(R),and (2) if(S,≤)also satisfies the condition that 0≤s for any s∈S,then the ring [[R^S,≤]] is weakly PP if and only if R is weakly PP.
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  Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

  Yiming Long, Shiqing Zhang

  Acta Mathematica Sinica. 2000, 16(4): 579-592. https://doi.org/10.1007/s101140000007

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  In this paper,we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R³ or R² are precisely the planar equilateral triangle circular solutions found by J.Lagrange in 1772,and that the variational minimization solutions of the circular restricted 3-body problem in R³ or R² are also planar equilateral triangle circular solutions.
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  L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

  Yong Ding, Dashan Fan, Yibiao Pan

  Acta Mathematica Sinica. 2000, 16(4): 593-600. https://doi.org/10.1007/s101140000015

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  We give the L^p-boundedness for a class of Marcinkiewicz integral operators μ_Ω,μ_Ω^*,λ and μ_Ω,S related to the Littlewood–Paley g-function,g_λ^*-function and the area integral S,respectively.These operators have the kernel functions Ω∈H¹(S^n-1),the Hardy space on S^n-1.The results in this paper substantially improve and extend the known results.
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  A Note on the Singular Limit of the Exact Contrôllability of Dissipative Wave Equations

  Yuping Tang, Xu Zhang

  Acta Mathematica Sinica. 2000, 16(4): 601-612. https://doi.org/10.1007/s101140000055

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  In this note we analyze the exact Contrôllability of singularly perturbed damped wave equations under more general geometric Contrôl condition than that of [1].We show that the null Contrôllability of the heat equation can be obtained as a singular limit of the exact Contrôllability of such sorts of wave equations.
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  A Besov Estimate for Multilinear Singular Integrals

  Wengu Chen

  Acta Mathematica Sinica. 2000, 16(4): 613-626. https://doi.org/10.1007/s101140000059

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  The main purpose of this paper is to prove a good λ inequality for a multilinear singular integral in R_n.
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  The Asymptotics of the Heat Semigroup for a General Bounded Domain with Mixed Boundary Conditions

  E. M. E. Zayed

  Acta Mathematica Sinica. 2000, 16(4): 627-636. https://doi.org/10.1007/s101140000058

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  Small-time asymptotics of the trace of the heat semigroup θ(t)=Σ_ν=1^∞exp(-tμ_ν) where {μ_ν} are the eigenvalues of the negative Laplacian-△=-Σ_β=1²(∂/∂x^β)² in the (x¹,x²)-plane,is studied for a general bounded domain Ω with a smooth boundary ∂Ω,where a finite number of Dirichlet,Neumann and Robin boundary conditions,on the piecewise smooth parts Г_i(i=1,…,n) of ∂Ω such that ∂Ω=U_i=1ⁿ=1Г_i,are considered.Some geometrical properties associated with Ω are determined.
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  Functional Limit Theorems for C-R Increments of k-Dimensional Brownian Motion in Hölder Norm

  Qicai Wei

  Acta Mathematica Sinica. 2000, 16(4): 637-654. https://doi.org/10.1007/s101140000080

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  In this paper,based on large deviation formulas established in stronger topology generated by Hölder norm,we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hölder norm.
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  A Remark on Multilinear Oscillatory Singular Integrals

  Shanzhen Lu, Dunyan Yan

  Acta Mathematica Sinica. 2000, 16(4): 655-668. https://doi.org/10.1007/s101140000081

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  In this paper,we study multilinear oscillatory singular integrals with rough kernel,and give a criterion of certain boundedness for this kind of operator.
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  Hua’s Theorem on Prime Squares in Short Intervals

  Jianya Liu, Tao Zhan

  Acta Mathematica Sinica. 2000, 16(4): 669-690. https://doi.org/10.1007/s101140000077

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  It is proved that every large integer N≡5(mod24) can be written as N=p₁²+…+p₅²with each prime p_j satisfying |p_j-√N/5|≤N^11/23+ε.This gives a short interval version of Hua's theorem on the quadratic Waring-Goldbach problem.
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  Central Limit Theorems for Asymptotically Negatively Associated Random Fields

  Lixin Zhang

  Acta Mathematica Sinica. 2000, 16(4): 691-710. https://doi.org/10.1007/s101140000084

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  The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition.Results obtained improve a central limit theorem of Roussas [11] for negatively associated fields and the main results of Su and Chi[18],and also include a central limit theorem for weakly negatively associated random variables similar to that of Burton et al.[20].
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  Convergence of Monotone Iterations for Differential Problem

  Tadeusz Jankowski

  Acta Mathematica Sinica. 2000, 16(4): 711-720. https://doi.org/10.1007/s101140000083

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  We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter.Existence of extremal solutions to such problems is proved.