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The fundamental solution of the Keldysh typeoperator

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Science China Mathematics 2009年第9期52卷 1829-1843页

作者： CHEN ShuXing School of mathematical sciences, Fudan university, Shanghai 200433, China 1. School of mathematical sciences Fudan University Shanghai 200433 China

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2 u}} {{\partial x^2 }} + y\frac{{\partial ^2 u}} {{\partial y^2 }} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \frac{1} {2} $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha < \frac{1} {2} $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

关键词： mixed type equation Keldysh operator fundamental solution finite part of divergent integral 35M10 35A08

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (School of mathematical sciences,Fudan university,Shanghai 200433,China Institute of Computational Mathematics,Chinese Academy of sciences,Beijing 100080,China School of mathematical sciences Fudan University Shanghai 200433 China Institute of Computational Mathematics Chinese Academy of Sciences Beijing 100080 China

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Comparison of CSC method and the B-net method for deducing smoothness condition

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Progress in Natural Science:Materials International 2009年第1期19卷 25-31页

作者： Renhong Wang,Kai Qu Institute of mathematical sciences,Dalian university of Technology,Dalian 116024,China [a]Institute of mathematical sciences Dalian University of Technology Dalian 116024 China

The first author of this paper established an approach to study the multivariate spline over arbitrary partition,and presented the so-called conformality method of smoothing cofactor(the CSC method).Farin introduced the B-net method which is suitable for studying the multivariate spline over simplex *** paper indicates that the smoothness conditions obtained in terms of the B-net method can be derived by the CSC method for the spline spaces over simplex partitions,and the CSC method is more capable in some sense than the B-net method in studying the multivariate spline.

关键词： Multivariate spline Smoothing cofactor Global conformality condition B-net method Smoothness condition

A note on periodic solutions for semi-ratio-dependent predator-prey systems

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 1-8页

作者： LIU Xiu-xiang School of mathematical sciences, South China Normal university, Guangdong 510631, China School of mathematical sciences South China Normal University Guangdong China

This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results.

关键词： Periodic solutions predator-prey system functional response.

On maximal injective subalgebras in a wΓ factor

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Science China Mathematics 2008年第11期51卷 2089-2096页

作者： HOU ChengJun School of mathematical sciences, Qufu Normal university, Shandong 273165, China 1. School of mathematical sciences Qufu Normal University Qufu Shandong 273165 China

Let $ \mathcal{L} $ (F ?) × α ? be the crossed product von Neumann algebra of the free group factor $ \mathcal{L} $ (F ?), associated with the left regular representation λ of the free group F ? with the set {u r : r ∈ ?} of generators, by an automorphism α defined by α(λ(u r )) = exp(2πri)λ(u r ), where ? is the rational number set. We show that $ \mathcal{L} $ (F ?) × α ? is a wΓ factor, and for each r ∈ ?, the von Neumann subalgebra $ \mathcal{A}_r $ generated in $ \mathcal{L} $ (F ?) × α ? by λ(u r ) and υ is maximal injective, where υ is the unitary implementing the automorphism α. In particular, $ \mathcal{L} $ (F ?) × α ? is a wΓ factor with a maximal abelian selfadjoint subalgebra $ \mathcal{A}_0 $ which cannot be contained in any hyperfinite type II1 subfactor of $ \mathcal{L} $ (F ?) × α ?. This gives a counterexample of Kadison’s problem in the case of wΓ factor.

关键词： von Neumann algebra maximal injective subalgebra crossed product wΓ factor 46L10

Some scaled limit theorems for an immigration super-Brownian motion

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Science China Mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei School of mathematical sciences,Beijing Normal university,Beijing 100875,China 1. School of mathematical sciences Beijing Normal University Beijing 100875 China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue *** first prove a functional central limit theorem,and then study the l... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation 60J80 60F05

Wavelets associated with Hankel transform and their Weyl transforms

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Science China Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, School of mathematical sciences, Peking university, Beijing 100871, China 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science China Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 Department of mathematical sciences,Huzhou university,Huzhou 313000,China 2 School of mathematical sciences,Fudan university,Shanghai 200433,China 1. Department of mathematical sciences Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

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Science China Mathematics 2007年第6期50卷 761-772页

作者： Duan-zhi ZHANG School of mathematical sciences, Peking university, Beijing 100871, China 1. School of mathematical sciences Peking University Beijing 100871 China

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s... 详细信息

关键词： brake orbit Maslov-type index relative Morse index dual variational method 58E05 70H05 34C25