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Toeplitz Operators on Dirichlet Spaces

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Acta Mathematica Sinica,English Series 2001年第4期17卷 643-648页

作者： Yu Feng LU Shun Hua SUN department of Applied mathematics, Dalian university of Technology, Dalian 116024, P. R. china department of mathematics, sichuan university, chengdu 610064, P. R. china department of mathematics, sichuan university, chengdu 610064, P. R. china department of Applied mathematics Dalian University of Technology Dalian 116024 P. R. China department of mathematics Sichuan University Chengdu 610064 P. R. China

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Diric... 详细信息

关键词： Dirichlet space Toeplitz operator Compact operator Strong operator topology

Strongly Zero-Dimensional Locales

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Acta Mathematica Sinica,English Series 2002年第1期18卷 47-54页

作者： KOU Hui LUO Mao Kang department of mathematics. sichuan university, chengdu 610064. P. R. china department of mathematics Sichuan University Chengdu P. R. China

New kinds of strongly zero-dimensional locales are introduced and characterized, which are different from Johnstone's, and almost all the topological properties for strongly zero-dimensional spaces have the pointloss localic forms. Particularly. the Stone-Cech compactification of a strongly zero-diluensional locale is stongly zero-dimensional.

关键词： Locale Strongly zero-dimensional Compactification

Diffusion Equation on Fractals:Three-Dimensional Case

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Communications in Nonlinear Science and Numerical Simulation 1999年第3期4卷 3-5页

作者： Qiuhua ZENG and Houqiang LI(department of Physics, sichuan university, chengdu 610064, china) department of Physics Sichuan University ChengDu 610064 China

IntroductionInrecentyearsthephenomenonofunusualtrajnsport-prop***onindisorderedmediaorfractalmedia,anomalousdiffusionistheoretic... 详细信息

IntroductionInrecentyearsthephenomenonofunusualtrajnsport-prop***onindisorderedmediaorfractalmedia,anomalousdiffusionistheoretic...

关键词： comb model probability density diffusion on fractals

Anomalous Fractional Diffusion Equation forTransport Phenomena

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 99-104页

作者： Qiuhua ZENG Houqiang LI De LIU(department of Physics, sichuan university, chengdu 610064, china) department of Physics Sichuan University ChengDu 610064 China

We derive the standard diffusion equation from the continuity equationand by discussing the defectiveness of earlier proposed equations, we get the generalizedfractional diffusion equation for anomalous diffusion.

关键词： fractal lattice probability density fractal anomalous diffusion

Representation of Integers by Ternary Quadratic Forms

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Acta Mathematica Sinica,English Series 2001年第4期17卷 715-720页

作者： De Lang LI Chun Lai ZHAO department of mathematics, sichuan university, chengdu 610064, P. R. china department of mathematics, Peking university, Beijing 100871, P. R. china 四川大学数学系四川成都北京大学数学系北京

In this paper we give a formula for the number of representations of some square-free integers by certain ternary quadratic forms and estimate the lower bound of the 2-power appearing in this number.

关键词： Congruent elliptic curve Tate-Shafarevich group Modular form Class number

Integrated optimization methods in multisensor decision and estimation fusion

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Science china(Information Sciences) 2012年第3期55卷 545-550页

作者： LUO YingTing, SHEN XiaoJing & ZHU YunMin College of mathematics, sichuan university chengdu, 610064, china 1. College of mathematics Sichuan University Chengdu 610064 China

This paper presents a significant integrated optimization point of view behind the following three successful decision and estimation fusion results: 1) a unified fusion rule for networked sensor decision systems; 2) optimal sensor data quantization for estimation fusion and 3) integrated multi-target data association tracking systems. More precisely speaking, the integrated optimization method in 1) derives a unified objective function optimizing only sensor rules given a unified fusion rule; the method in 2) derives a unified objective function optimizing both the sensor quantization rule and the final estimation in the MSE sense, and the method in 3) integrates all associated targets and their valid observations into a whole random measurement matrix dynamic system so that the optimal random matrix Kalman filtering can be applied to estimate the states of all associated targets.

关键词： integrated optimization decision fusion estimation fusion data association

The Space of Maps from a Locally Compact Space to a Banach Space

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Acta Mathematica Sinica,English Series 1997年第3期13卷 333-336页

作者： Wang Yangeng (department of mathematics,sichuan university,chengdu 610064,china) department of mathematics Sichuan University

The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open *** this paper we prove that C（X,Y）is an absolute retract if X is a locally compact separable metric space and Y a convex set in a Banach *** the above fact we know that C（X,Y）is homomorphic to Hilbert space l2 if X is a locally compact separable metric space and Y a separable Banach space;in particular,C（Rn,Rm） is homomorphic to Hilbert space l2.

关键词： Absolute retract Function space Infinite-dimensional manifold

Theoretical study of the potential energy surface and the highly excited rovibra-tional spectroscopy of H_2S molecule

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Chinese Science Bulletin 2001年第8期46卷 650-652页

作者： XIE Junkai & YAN Guosendepartment of Chemistry, sichuan Normal university, chengdu 610066, china department of Chemistry, sichuan university, chengdu 610064, china department of Chemistry Sichuan Normal University Chengdu China department of Chemistry Sichuan University Chengdu China

This note reports the potential energy surface of H2S that has been refined by using SCF-CI approach and the high-resolution experimental data. The calculated splitting values of the local mode vibration states pair close to observed values. This vibration state calculation has shown that there are no obvious non-Born Oppenheimer effects occurring in the lower vibration states of the system.

关键词： potential energy surface local mode vibration state non- Born Oppenheimer effect.

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 200433, china School of mathematics, sichuan university, chengdu 610064, china department of Applied mathematics, Shanghai university of Finance & Economics, Shanghai 200433, 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-