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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 2.0433,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

Local Existence of Smooth Solutions to the FENE Dumbbell Model

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 501-520页

作者： Ge YANG11school of Mathematical sciences, fudan university, shanghai 2.0433, china. school of Mathematical sciences Fudan University Shanghai 200433 China

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.

关键词： Fokker-Planck equation FENE model Degenerate parabolic equations Regularity

Hyperbolic positive mass theorem under modified energy condition

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Science china Mathematics 2008年第12期51卷 2189-2197页

作者： XIE NaQing Institute of Mathematics, school of Mathematical sciences, fudan university, shanghai 2.0433, china Institute of Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang... 详细信息

关键词： positive mass theorem modified energy condition modified asymptotically hyperbolic 83C40 53C27

Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of Mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI school of Mathematical sciences, fudan university, shanghai 2.0433, china school of Mathematics and Statistics, Northeast Normal university, Changchun 130024, china. school of Mathematical sciences Fudan University Shanghai 200433 China school of Mathematics Statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

Invariant tori for asymptotically linear impact oscillators

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Science china Mathematics 2006年第5期49卷 669-687页

作者： QIAN Dingbian & SUN Xiying school of Mathematical sciences, Suzhou university, Suzhou 215006, china Laboratory of Mathematics for Nonlinear sciences, fudan university, shanghai 2.0433, china school of Mathematical sciences Suzhou University Suzhou 215006 China Laboratory of Mathematics for Nonlinear sciences Fudan University Shanghai 200433 China

The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.

关键词： invariant tori, boundedness of solutions, quasi-periodic solution, impact oscillator.

Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china Mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong school of Mathematical sciences, fudan university, shanghai 2.0433, china school of Mathematics, Sichuan university, Chengdu 610064, china Department of Applied Mathematics, shanghai university of Finance & Economics, shanghai 2.0433, china school of Mathematical sciences Fudan University Shanghai 200433 China school of Mathematics Sichuan University Chengdu 610064 China Department of Applied Mathematics Shanghai University of Finance & Economics Shanghai 200433 China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-

Semantic Search among Heterogeneous Biological Databases Based on Gene Ontology

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Acta Biochimica et Biophysica Sinica 2004年第5期36卷 365-370页

作者： Shun-Liang CAO, Lei QIN1, Wei-Zhong HE1, Yang ZHONG2, Yang-Yong ZHU, and Yi-Xue LI1,3* Department of Computing and Information Technology, fudan university, shanghai 2.0433, china shanghai Center for Bioinformation 1 Technology, shanghai 200235, china school of life sciences, fudan university, shanghai 2.0433, china Bioinformation Center of shanghai Institutes for Biological sciences, the Chinese Academy of sciences, shanghai 200031, china Department of Computing and Information Technology Fudan University Shanghai China

Semantic search is a key issue in integration of heterogeneous biological databases. In this paper, we present a methodology for implementing semantic search in BioDW, an integrated biological data warehouse. Two tables are presented: the DB2GO table to correlate Gene Ontology (GO) annotated entries from BioDW data sources with GO, and the semantic similarity table to record similarity scores derived from any pair of GO terms. Based on the two tables, multifarious ways for semantic search are provided and the corresponding entries in heterogeneous biological databases in semantic terms can be expediently searched.

关键词： Gene Ontology semantic search BioDW

Dynamics of Primary Events in the Photocycle of Excited Bacteriorhodopsin

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Acta Biochimica et Biophysica Sinica 2004年第11期36卷 724-728页

作者： Jun-Jun LU, Ming MING, Yi YANG, Jia WU, Bo LI, Jian-Dong DING, Qing-Guo LI, and Shi-Xiong QIANDepartment of Physics, fudan university, shanghai 2.0433, china Department of Macromolecular Science, Key Laboratory of Molecular Engineering of Polymers, fudan university, shanghai 2.0433, china Department of Physiology and Biophysics, school of life sciences, fudan university, shanghai 2.0433, china Department of Physics Fudan University Shanghai 200433 China

Transient dynamic behavior of the excited bacteriorhodopsin (BR), which was isolated from the strain H. salinarum, was studied at excitation wavelength from 585 to 639 nm. With the one-color femtosecond (fs) pump-probe technique, we revealed the primary events in BR's photocycle that took place in an ultrafast time scale. From the analysis of the decay components of the dynamical traces, it was evident that the isomerization of the retinal

关键词： bacteriorhodopsin transient dynamics primary events femtosecond laser pump-probe technique

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of Mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of Mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu, china school of Mathematical sciences, fudan university, shanghai 2.0433, china school of Mathematics and System sciences, Shandong university, Jinan 250100, china. Department of Mathematics China University of Mining Technology Xuzhou 221008 Jiangsu China school of Mathematical sciences Fudan University Shanghai 200433 China school of Mathematics System sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs