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ALGEBRAIC-GEOMETRY FOUNDATION FOR CONSTRUCTING SMOOTH INTERPOLANTS ON CURVED SIDES ELEMENT

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Journal of Computational Mathematics 1995年第4期13卷 343-350页

作者： Z.X. Luo(Institute of mathematical sciences, Dalian university of Technology, Dalian, China) DALIAN UNIV TECHNOL INST MATH SCIDALIANPEOPLES R CHINA

The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively f... 详细信息

关键词： CAGD Wang Rational ALGEBRAIC-GEOMETRY FOUNDATION FOR CONSTRUCTING SMOOTH INTERPOLANTS ON CURVED SIDES ELEMENT

The Nother and Riemann-Roch type theorems for piecewise algebraic curve

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Science China Mathematics 2007年第2期50卷 165-182页

作者： Yi-sheng LAI & Ren-hong WANG College of Statistics and Mathematics, zhejiang Gongshang university, Hangzhou 310018, China Institute of mathematical sciences, Dalian university of Technology, Dalian 116024, China College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou China Institute of mathematical sciences Dalian University of Technology Dalian China

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, the Nother type theorems for Cμpiecewise algebraic curves are obtained. The theory of the linear series of sets of places on the piecewise algebraic curve is also established. In this theory, singular cycles are put into the linear series, and a complete series of the piecewise algebraic curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the algebraic curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions, and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cμpiecewise algebraic curves and the degree, the genus and the smoothness of the curves, hence the Riemann-Roch type theorem of the Cμpiecewise algebraic curve is established.

关键词： Piecewise algebraic curve place cycle complete linear series.

OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE

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Acta Mathematica Scientia 2008年第3期28卷 604-612页

作者：闻国椿 School of mathematical sciences Peking University

The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.

关键词： Oblique derivative problems nonlinear mixed equations parabolic degeneracy

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational Mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of System Science, Academy of Mathematics and System sciences, Chinese Academy of sciences, Beijing, 100080, China School of mathematical sciences, Peking university, Beijing 100871, China) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

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Acta Mathematica Scientia 2007年第3期27卷 663-672页

作者：闻国椿 School of mathematical sciences Peking University

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.

关键词： Boundary value problems nonlinear elliptic equations parabolic degeneracy

Expression and Identification of Mutated Osteoprotegerin in Culture Cells and Larvae of Silkworm

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Acta Biochimica et Biophysica Sinica 2004年第5期36卷 331-335页

作者： Hai-Long XIAO, Yong-Feng JIN, and Yao-Zhou ZHANG1* Institute of Biochemistry, College of Life sciences, zhejiang university, Hangzhou 310029, China College of Life sciences, zhejiang university of Science & Technology, Hangzhou 310018, China College of Life sciences Zhejiang University of Science & TechnologyHangzhou 310018China Institute of Biochemistry College of Life SciencesZhejiang UniversityHangzhou 310029China

The mutated osteoprotegerin (OPG-372) gene was inserted into the baculovirus transfer vector pBacPAK8, and the recombinant plasmid was co-transfected with linearized Bm-BacPAK6 virus DNA into BmN cells, then homologous recombination occurred inside the cells. The recombinant virus BmNPV-OPG- 372 was screened and identified by Southern blotting. The recombinant human OPG-372 was expressed in cultured cells and the larvae of silkworm by inoculation of recombinant virus. The expression products were run on the SDS-PAGE and their immunoreactivities were determined by Western blotting. It was found that a 42 kD recombinant protein was expressed in BmN cells and a 46 kD one in larvae respectively. The bioactivi- ties of the recombinant proteins were determined by hypocalcemic effect assay in the mice. The results showed that the recombinant proteins had a significant hypocalcemic effect on mice sera.

关键词： OPG-372 silkworm baculovirus expression system hypocalcemic effect

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 200433, 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

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

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Acta Mathematica Scientia 2008年第3期28卷 513-522页

作者：叶俊 Department of mathematical sciences Tsinghua University

The purpose of this article is to obtain the quasi-stationary distributions of the δ（δ 〈 2）-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin （2001）. It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a （4 - δ）- dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.

关键词： Radial Ornstein-Uhlenbeck process quasi-stationary distribution quasiinvariant

Local Gromov-Witten invariants of canonical line bundles of toric surfaces

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Science China Mathematics 2010年第6期53卷 1571-1582页

作者： YANG Fei & ZHOU Jian Department of mathematical sciences,Tsinghua university,Beijing 100084,China 1. Department of mathematical sciences Tsinghua University Beijing 100084 China

We define and compute by localizating the local equivariant Gromov-Witten invariants of the canonical line bundles of toric surfaces,not necessarily Fano.

关键词： local Gromov-Witten invariants localization partition function geometric engineering