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Lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： LI Chong 1 and WANG Xinghua 2.1. Center for Mathematical Sciences, zhejiang university, hangzhou 310027,{2. 2. department of mathematics, hangzhou university, hangzhou 31002.,{2. Center for Mathematical Sciences Zhejiang University Hangzhou China department of mathematics Hangzhou University Hangzhou China

The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.

Extension of a quantized enveloping algebra by a Hopf algebra

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Science china mathematics 2010年第5期53卷 300-307页

作者： WU ZhiXiang department of mathematics,{2. university,hangzhou 310027,china department of mathematics Zhejiang University Hangzhou China

Suppose that H is a Hopf algebra,and g is a generalized Kac-Moody algebra with Cartan matrix A =(aij)I×I,where I is an index set and is equal to either {1,2....,n} or the natural number set *** f,g be two mappings from I to G(H),the set of group-like elements of H,such that the multiplication of elements in the set {f(i),g(i)|i ∈I} is *** we define a Hopf algebra Hgf Uq(g),where Uq(g) is the quantized enveloping algebra of g.

关键词： quantum enveloping algebra Hopf algebra Kac-Moody algebra

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science china mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics,{2. hangzhou 310027, china department of mathematics, zhejiang Normal university Jinhua 32.004, china department of mathematics Zhejiang University Hangzhou China department of mathematics Zhejiang Normal University Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

Inverse minimum spanning tree problem and reverse shortest-path problem with discrete values

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Progress in Natural Science:Materials International 2006年第6期16卷 649-655页

作者： LIU Longcheng and HE Yong (department of mathematics,{2., hangzhou 310027, china State Key Laboratory of CAD & CG,{2., hangzhou 310027, china) department of mathematics Zhejiang University Hangzhou 310027 China State Key Laboratory of CAD and CG Zhejiang University Hangzhou 310027 China

In this paper, we consider two network improvement problems with given discrete values: the inverse minimum spanning tree problem and the reverse shortest-path problem, where the decrements of the weight of the edges are given discrete values. First, for the three models of the inverse minimum spanning tree problem (the sum-type, the bottleneck-type and the constrained bottleneck-type), we present their respective strongly polynomial algorithms. Then, we show that the reverse shortest-path problem is strongly NP-complete.

关键词： minimum spanning tree shortest-path problem inverse problem reverse problem computational complexity.

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of mathematics,Linyi Normal {2.,Linyi 2.6005,Shandong,china department of mathematics,zhejiang {2.,hangzhou 310027,china department of mathematics Linyi Normal University Linyi China department of mathematics Zhejiang University Hangzhou China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms

GLOBAL EXISTENCE AND ASYMPTOTICS BEHAVIOR OF SOLUTIONS FOR A RESONANT KLEIN-GORDON SYSTEM IN TWO SPACE DIMENSIONS

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Chinese Annals of mathematics,Series B 2005年第1期26卷 89-104页

作者： XUERUYING FANGDAOYUAN departmentofmathematics ZhejiangUniversityHangzhou310027China departmentofmathematics ZhejiangUniversityHangzhou310027China

The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t... 详细信息

关键词： Klein-Gordon equation Asymptotic behavior Global existence

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α

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Chinese Annals of mathematics,Series B 2005年第3期26卷 361-378页

作者： FANGDAOYUAN WANGCHENGBO departmentofmathematics ZhejiangUniversityHangzhou310027China

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed re... 详细信息

关键词： Semilinear wave equation Low regularity Local well-posedness Ill-posedness

Constructing a quasi-Legendre basis based on the C-Bézier basis

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Progress in Natural Science:Materials International 2005年第6期15卷 559-563页

作者： HUANG Yu* and WANG Guozhao(department of mathematics,{2., hangzhou 310027, china) department of mathematics Zhejiang University Hangzhou 310027 China

In the space Γ_n=span｛sint,cost,1,t,t2.…,t n-2.｝, a C-Bézier basis is constructed by an integral approach. However, the C-Bézier basis is not orthogonal. For some applications, we construct an orthogonal basis based on the C-Bézier basis, which has remarkable properties similar to that of the Legendre basis. Then we derive the transformation matrices that convert the C-Bézier basis and the orthogonal basis into each other. As an example of application, we apply this orthogonal basis to the degree reduction approximation of the C-Bézier curves.

关键词： C-Bézier basis orthogonal basis basis transformations degree reduction.

Simple proofs of the Bedrosian equality for the Hilbert transform

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Science china mathematics 2009年第3期52卷 507-510页

作者： WANG SiLei department of mathematics,{2., hangzhou 310027, china department of mathematics Zhejiang University Hangzhou China

Two simple proofs of Bedrosian theorem are given.

关键词： Hilbert transform Bedrosian theorem filter 42.2. 42.2.