15 September 1999, Volume 15 Issue 3

    

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  Skew Pairing, Cocycle Deformations and Double Crossproducts

  Huixiang Chen

  Acta Mathematica Sinica. 1999, 15(3): 225-234.

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  In this paper,we give a suffcient condition for double crossproduct X A to be X _τA for some skew pairingτif X A is a 2-cocycle deformation of X A.Then we give a suffcient and necessary condition for X A to be X _τA by using natural isomorphism terminology.
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  Strong Limit Theorems for Oscillation Moduli of PL-Process and Cumulative Hazard Process under Truncation and Censorship with Applications

  Liuquan Sun, Yong Zhou

  Acta Mathematica Sinica. 1999, 15(3): 235-244.

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  In this paper we obtain exact rates of uniform convergence for oscillation moduli and Lipschitz-1/2 moduli of PL-process and cumulative hazard process when the data are subject to left truncation and right censorship.Based on these results,the exact rates of uniform convergence for various types of density and hazard function estimators are derived.
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  On the Mean Value Formula of Dedekind Sums

  Xiali He, Wenpeng Zhang

  Acta Mathematica Sinica. 1999, 15(3): 245-254.

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  The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums,and to give a sharper mean value formula.
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  Topological Structures of ω-subsets in Symplectic Groups

  Yiming Long

  Acta Mathematica Sinica. 1999, 15(3): 255-268.

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  All the symplectic matrices possessing a fixed eigenvalue ω on the unit circle form a hypersurface in the real symplectic group Sp(2n).This paper is devoted to the study of the topological structures of this hypersurface and its complement in Sp(2n).
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  Tangential Developable Surfaces as Bonnet Surfaces

  Ioannis M. Roussos

  Acta Mathematica Sinica. 1999, 15(3): 269-276.

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  We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature,in the three-dimensional Euclidean space.We give a general criterion for these surfaces and use it to determine the tangential developable surfaces of this kind.They are determined implicitly by elliptic integrals of the third kind.Only the tangential developable surfaces of circular helices are explicit examples for which we completely determine the above unique nontrivial isometry.
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  Harmonic Maps from Kähler Manifolds

  Yuanlong Xin

  Acta Mathematica Sinica. 1999, 15(3): 277-292.

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  Some Liouville type theorems for harmonic maps from Kähler manifolds are obtained.The main result is to prove that a harmonic map from a bounded symmetric domain(except R_IV(2))to any Riemannian manifold with finite energy has to be constant.
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  On Ohtsuki’s Invariants of Integral Homology 3-Spheres

  Xiaosong Lin, Zhenghan Wang

  Acta Mathematica Sinica. 1999, 15(3): 293-316. https://doi.org/10.1007/BF02650726

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  We provide some more explicit formulae to facilitate the computation of Ohtsuki's rational invariants λ_n of integral homology 3-spheres extracted from Reshetikhin-Turaev SU(2) quantum invariants. Several interesting consequences will follow from our computation of λ₂. One of them says that λ₂ is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ₁ is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained from surgery on knots by using the Jones polynomial.
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  A Two-Dimensional Hyperbolic System of Nonlinear Conservation Laws with Functional Solutions

  Jiaxin Hu

  Acta Mathematica Sinica. 1999, 15(3): 317-332. https://doi.org/10.1007/BF02650727

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  A two-dimensional hyperbolic system of nonlinear conservation laws is considered for any piecewise constant initial data having two discontinuity rays with the origin as vertex. One kind of new waves, which is labeled the Dirac-contact wave, appears in the solution. The entropy conditions for the Dirac-contact waves are given. The solutions on the Dirac-contact waves can be viewed as the bounded linear functionals on C₀^∞ (R² ×R₊).
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  Idempotent Completions of Operator Partial Matrices

  Jinchuan Hou, Heydar Radjavi, Peter Rosenthal

  Acta Mathematica Sinica. 1999, 15(3): 333-346. https://doi.org/10.1007/BF02650728

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  Necessary and sufficient conditions are obtained for operator partial 2 × 2 matrices to have an idempotent completion, and all such completions are parametrically represented.
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  Representation of Congruences on Regular Semigroups with Inverse Transversals

  Limin Wang, Xilin Tang

  Acta Mathematica Sinica. 1999, 15(3): 347-352. https://doi.org/10.1007/BF02650729

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  For a regular semigroup with an inverse transversal, we have Saito's structure W(I,S^o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I,S^o and Λ. The structure of images of this type of semigroups is also presented.
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  Nash Inequalities for General Symmetric Forms

  Mufa Chen

  Acta Mathematica Sinica. 1999, 15(3): 353-370. https://doi.org/10.1007/BF02650730

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  This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincaré and the logarithmic Sobolev inequalities in the present context.
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  On Minimal Graph Evolutions in the Hyperbolic Space

  Li Ma

  Acta Mathematica Sinica. 1999, 15(3): 371-374. https://doi.org/10.1007/BF02650731

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  We study here minmal graph evolutions in the hyperbolic space and prove that there exists a unique smooth solution.
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  On Self-Adjointness of the Product of Two Second-Order Differential Operators

  Zhijiang Cao, Jiong Sun, D. E. Edmunds

  Acta Mathematica Sinica. 1999, 15(3): 375-386. https://doi.org/10.1007/BF02650732

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  In this paper, the problem of self-adjointness of the product of two differential operators is considered. A number of results concerning self-adjointness of the product L₂ L₁ of two second-order self-adjoint differential operators are obtained by using the general construction theory of self-adjoint extensions of ordinary differential operators.
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  On a Diophantine Inequality Involving Prime Numbers (Ⅲ)

  Yingchun Cai

  Acta Mathematica Sinica. 1999, 15(3): 387-394. https://doi.org/10.1007/BF02650733

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  Let 1<c<11/10. In the present paper it is proved that there exists a number N(c)>0 such that for each real number N>N(c) the inequality |p₁^c+p₂^c+p₃^c-N|-1/c(11/10-c)log^c₁N is solvable in prime numbers p₁,p₂,p₃, where c₁ is some absolute positive constant.
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  K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex

  Song Li

  Acta Mathematica Sinica. 1999, 15(3): 395-406. https://doi.org/10.1007/BF02650734

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  An inverse theorem for the best weighted polynomial approximation of a function in (S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in , wherew_α is a Jacobi-type weight on S, 0<p ≤ ∞,S is a simplex and W_λ is a Freud weight. For Ditzian-Totik K-functionals on L_p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression.
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  Singular Limit for Stochastic Reaction-Diffusion Equation and Generation of Random Interfaces

  T. Funaki

  Acta Mathematica Sinica. 1999, 15(3): 407-438. https://doi.org/10.1007/BF02650735

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  Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R². The solution converges to one of the two stable phases {+1,-1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.