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THE CAPACITY DENSITY AND THE HAUSDORFF DIMENSION OF FRACTAL SETS

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 43-50页

作者： Xu You (institute of Mathematics, fudan university, shanghai 200433, shanghai, china). fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

This paper defines the upper capacity densities of the subsets of R￣n, gets uniform lower bound of the upper capacity densities for -almost all points of the Hausdorff s-sets or the analytic sets with Hausdorff dimen... 详细信息

关键词： Capacity density Hausdorff dimension Fractal set.

Averaging of Hamilton-Jacobi equation in infinite dimensions and application

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Chinese Science Bulletin 1998年第1期43卷 30-32页

作者： WANG Shihong institute of Mathematics, fudan university, shanghai 200433, china fudan university Institute of Mathematics Shanghai China

The averaging of Hamilton_Jacobi equation with fast variables in viscosity solution sense in infinite dimensions is studied. It is proved that viscosity solution of the original equation converges to viscosity solution of the averaged equation and this result is applied to study the limit problem of the value function for optimal control problem with fast variables.

关键词： infinite dimensions averaging of HJB equation viscosity solution optimal control problem value function.

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

CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 181-192页

作者： HUANG ZHAOBO(institute of Mathematics, fudan university, shanghai 200433, shanghai, china) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

This paper gives the intrinsic character of the classification for AF-algebras defined by *** and G. K. Pedersen in terms of their dimension groups.

关键词： AF-algebra Demension group Classification.

GROUP ACTIONS ON VON NEUMANN REGULAR RINGS

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 235-240页

作者： ZHANG YINHUO(institute of Mathematics,fudan university, shanghai 200433, china) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

Let A be a ring with indentity, G a finite group of automorphisms of A. The main result of this paper is that A/AG is Galois if and only if it is Frobenius and the module AGA (or AAG)is faithful. Moreover if |G| is in... 详细信息

关键词： Von Neumann regular ring Extension Group Automorphism.

HOPF ALGEBRAIC APPROACH TO THE n LINEARLY RECURSIVE SEQUENCES

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 141-146页

作者： LIANG GUI(institute of Mathematics, fudan university, shanghai 200433, china) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

It is proved that a linearly recursive sequence of n indices over field F (n≥1) is automatically a product of n linearly recursive sequences of 1-index over F by the theory of Hopf *** the way, the correspondence bet... 详细信息

关键词： Hopf algebra Linearly recursive sequence Recursive relation.

PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS,KAUP-NEWELL AND PCF SYSTEMS

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Chinese Annals of Mathematics,Series B 1999年第2期20卷 195-204页

作者： ZHOU ZIXIANG(institute of Mathematics, fudan university, shanghai 200433) fudan Univ Inst Math Shanghai 200433 Peoples R China

FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) *** some other reductions, sufficiency and necessity of more constraints are proved.

关键词： Darboux transformation Spectral parameters u(p q) reduction

ON TAYLOR'S CONJECTURE ABOUT THE PACKING MEASURES OF CARTESIAN PRODUCT SETS

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Chinese Annals of Mathematics,Series B 1996年第1期17卷 121-126页

作者： XU YOU REN FUYAO(institute of Mathematics, fudan university, shanghai 200433, china.) fudan UNIV INST MATHSHANGHAI 200433PEOPLES R CHINA

It is proved that if E R, F Rn, then P(E x F,12) ≤c. P(E, 1)P(E, 2), where P(, ) denotes the -packing measure, belongs to a class of Hausdorff functions, the positive constat c deponds only on 1,2 and n.

关键词： Packing measure Hausdorff measure Cartesian product set

A note on Jacobi-Eisenstein series

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Chinese Science Bulletin 1998年第14期43卷 1163-1165页

作者： WANG Juping institute of Mathematics, fudan university, shanghai 200433, china institute of Mathematics Fudan University Shanghai China

The so_called Jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagie... 详细信息

关键词： Jacobi Eisenstein series Jacobi form Fourier coefficient