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ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

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Chinese Annals of mathematics,Series B 2000年第3期21卷 351-358页

作者： YANG HAITAO(department of mathematics, zhejiang university, hangzhou 310027, china.) WU SHAOPING(department of mathematics, zhejiang university, hangzhou 310027, china.) department of mathematics Zhejiang University Hangzhou 310027 China

By making use of Variational method, the authors obtain some results about existence of multiple positive solutions and their asymptotic behavior as the parameter →＋∞ for a semilinear elliptic problem in RN.

关键词： Critical point Asymptotic behavior Concentration

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, zhejiang university, hangzhou 310027, china State Key Laboratory of CAD & CG, zhejiang university, 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.

REMARKS ON h-TRANSFORM AND DRIFT

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Chinese Annals of mathematics,Series B 1998年第4期19卷 473-478页

作者： YING JIANGANG (department of mathematics, zhejiang university, hangzhou 310027, china.) department of mathematics Zhejiang University Hangzhou 310027 China

The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a diffe... 详细信息

关键词： Right processes Revuz measures h-transform

Circular β ensembles,CMV representation,characteristic polynomials

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Science china mathematics 2009年第7期52卷 1467-1477页

作者： SU ZhongGen department of mathematics,zhejiang university,hangzhou 310027,china department of mathematics Zhejiang University Hangzhou China

In this note we first briefly review some recent progress in the study of the circular β ensemble on the unit circle,where β > 0 is a model *** the special cases β = 1,2 and 4,this ensemble describes the joint probability density of eigenvalues of random orthogonal,unitary and sympletic matrices,*** general β,Killip and Nenciu discovered a five-diagonal sparse matrix model,the CMV *** representation is new even in the case β = 2;and it has become a powerful tool for studying the circular β *** then give an elegant derivation for the moment identities of characteristic polynomials via the link with orthogonal polynomials on the unit circle.

关键词： characteristic polynomials circular β ensembles CMV representation moment identity 15A52

Mean size formula of wavelet subdivision tree on heisenberg group

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Applied mathematics(A Journal of Chinese Universities) 2008年第3期23卷 303-312页

作者： WANG Guo-mao department of mathematics,zhejiang university,hangzhou 310027,china department of mathematics,hangzhou Dianzi university,hangzhou 310018,china. department of mathematics Zhejiang University Hangzhou China department of mathematics Hangzhou Dianzi University Hangzhou China

The purpose of this paper is to investigate the mean size formula of wavelet packets （wavelet subdivision tree） on heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on heisenberg group and the subdivision tree on the heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.

关键词： heisenberg group wavelet packets subdivision tree joint spectral radius stability

Rigidity for rational maps with Cantor Julia sets

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Science china mathematics 2008年第1期51卷 79-92页

作者： ZHAI Yu department of mathematics, zhejiang university, hangzhou 310027, china department of mathematics Zhejiang University Hangzhou China

In this paper, we prove that two rational maps with the Cantor Julia sets are quasicon- formally conjugate if they are topologically conjugate.

关键词： Cantor Julia set rigidity puzzle piece bounded shape quasiconformally conjugate 37F12

Local orthogonal transform for a class of acoustic waveguides

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Progress in Natural Science:Materials International 2007年第10期17卷 1136-1146页

作者： Zhu Jianxin and Li Peng(department of mathematics, zhejiang university, hangzhou 310027, china) department of mathematics Zhejiang University Hangzhou 310027 China

There are some curved interfaces in acoustic waveguides. To compute wave propagation along the waveguides with some marching methods, flattening of the internal interfaces is needed. In this paper, a local orthogonal coordinate transform and an equation transform are constructed to solve the two-dimensional helmholtz equation for the waveguides bounded by a flat top, a flat bottom and two curved internal interfaces with three layered media. The curved internal interfaces are flattened by the local orthogonal coordinate transform, and the corresponding transformed helmholtz equation can be solved by some marching methods. This treatment can be extended in multilayered medium waveguides. The one-way reformulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides with multilayered medium structure.

关键词： helmholtz equation local orthogonal transform DtN reformulation marching method internal interface one-way reformulation.

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,zhejiang 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

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 university,Linyi 276005,Shandong,china department of mathematics,zhejiang university,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