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Combinatorial Invariants on Planar Graphs

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Acta Mathematica Sinica,English Series 1995年第2期11卷 211-220页

作者： Liu Yanpei Institute of applied Mathematics Academia Sinica beijing, 100080 china Institute of applied Mathematics Academia Sinica Beijing People's Republic of China

This paper introduces three kinds of operators on planar graphs with binary weights on edges, for which combinatorial invariants on two kinds of equivalences are found. Further, it is shown that the Jones polynomial and the bracket polynomial which are proved to be new topological invariants on knots in topology become special cases. Moreover, these invariants are a kind of generalization of Tutte polynomial on graphs.

关键词： link Combinatorial Invariants on Planar Graphs

Quasi-Homeomorphisms and Measures of Finite Energy Integrals of Generalized Dirichlet Forms

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Acta Mathematica Sinica,English Series 2000年第2期16卷 325-336页

作者： Wei Sun Institute of applied Mathematics,Chinese Academy of Sciences,beijing,100080,P.R.china Institute of applied Mathematics Chinese Academy of Sciences Beijing 100080 P. R. China

We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.

关键词： Generalized Dirichlet form Quasi-homeomorphism Measure of finite energy integral

Dissipative Transitions between Bloch Bands

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Journal of Materials Science & Technology 1999年第4期15卷 363-365页

作者： Xangeng ZHAO(Institute of applied Physics and Computational Mathematics, beijing 100088, china)E-mail:zhaoxg@*** Inst Appl Phys & Computat Math Beijing 100088 Peoples R China

We study the effect of dissipative transport of two-band systems in a static electric field. With the help of numerical solutions of a stochastic Liouville equation for the density matrix, we find that the Markoffian dephasing will take electrons which are initially located in one band to equal population of the two bands, instead of undergoing Zener resonance, as they do in the absence of scattering.

关键词： Rev Dissipative Transitions between Bloch Bands

Latest progress on interactions between VLF/ELF waves and energetic electrons in the inner magnetosphere

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Science china Earth Sciences 2010年第3期53卷 317-326页

作者： XIAO FuLiang1,2, ZONG QiuGang3. SU ZhenPeng4, TIAN Tian3.& ZHENG HuiNan4 1 School of Physics and Electronic Sciences, Changsha University of Science and Technology, Changsha 410004, china 2 State Key Laboratory of Space Weather, Chinese Academy of Sciences, beijing 100190, china 3.Institute of Space Physics and {3. Technology, Peking University, beijing 100871, china 4 CAS Key Lab for Basic Plasma Science, School of Earth and Space Sciences, University of Science and Technology of china, Hefei 23.026, china 1. School of Physics and Electronic Sciences Changsha University of Science and Technology Changsha 410004 China2. State Key Laboratory of Space Weather Chinese Academy of Sciences Beijing 100190 China3. Institute of Space Physics and Applied Technology Peking University Beijing 100871 China4. CAS Key Lab for Basic Plasma Science School of Earth and Space Sciences University of Science and Technology of China Hefei 230026 China

Interactions between very/extremely low frequency (VLF/ELF) waves and energetic electrons play a fundamental role in dynamics occurring in the inner magnetosphere. Here, we briefly discuss global properties of VLF/ELF waves, along with the variability of the electron radiation belts associated with wave-particle interactions and radial diffusion. We provide cases of electron loss and acceleration as a result of wave-particle interactions primarily due to such waves, and particularly some preliminary results of 3. evolution of phase space density from our currently developing 3. code. We comment on the existing mechanisms responsible for acceleration and loss, and identify several critical issues that need to be addressed. We review latest progress and suggest open questions for future investigation.

关键词： wave-particle interaction VLF/ELF waves energetic electrons acceleration and loss inner magnetosphere

A Polyhedral Theory on Graphs

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Acta Mathematica Sinica,English Series 1994年第2期10卷 136-142页

作者： Liu Yanpei Institute of applied Mathematics Academia Sinica beijing, 100080 china 1. Institute of applied Mathematics Academia Sinica 100080 Beijing China

This paper provides a polyhedral theory on graphs from which the criteria of Whit- ney and MacLane for the planarity of graphs are unified, and a brief proof of the Gauss crossing conjecture is obtained.

关键词： Math A Polyhedral Theory on Graphs

Latent ancestral graph of structure vector autoregressive models

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Journal of Systems Engineering and Electronics 2010年第2期21卷 233-238页

作者： Wei Gao1,2and Zheng Tian2,3.1.School of Statistics,Xi’an University of Finance&Economics,Xi’an 710061,P.R.china 2.Department of applied Mathematics,Northwestern Polytechnical University,Xi’an 710072,P.R.china 3.State Key Laboratory of Remote Sensing Science,Institute of Remote Sensing Applications,Chinese Academy of Sciences,{3. 100101,P.R.china School of Statistics Xi'an University of Finance & EconomicsXi'an 710061P.R.China Department of applied Mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China Department of applied Mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing ApplicationsChinese Academy of SciencesBeijing 100101P.R.China

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

关键词： multivariate time series latent ancestral graph itera- tive conditional fitting.

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(r,k)-catching code

Chinese Science Bulletin 1998年第10期43卷 812-815页

作者： LI Anping Institute of applied Mathematics, Chinese Academy of Sciences, beijing 100080, china Institute of applied Mathematics Chinese Academy of Sciences Beijing China

A collection of r_words on an alphabet of n letters is called (r,k)_catching code if for every r_word w there is one selected member v such that v coincides with w in at least k places. How large is the smallest size of the (r,k)_catching code and how to find the minimal (r,k)_\%catching code? Some methods are advanced to construct such codes.

关键词： catching code.

Centralizers and Iterate Radicals of Morse-Smale Diffeomorphisms of the Circle

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Acta Mathematica Sinica,English Series 1995年第1期11卷 1-11页

作者： Zhang Meirong Department of applied Mathematics Tsinghua University beijing,100084 china Department of applied Mathematics Tsinghua University Beijing People's Republic of China

In this paper,we will use the embedding flows in[1],[2]to give a complete descrip- tion of the smooth centralizers and iterate radicals of all C^r(r≥2)Morse-Smale diffeomorphisms of the circle S^*** a result,we prove... 详细信息

关键词： Centralizers and Iterate Radicals of Morse-Smale Diffeomorphisms of the Circle TDFs

ANALYSIS OF BOUNDARY LAYER SINGULARITYIN A NONLINEAR DIFFUSION PROBLEM

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Acta Mathematica Scientia 1999年第4期19卷 431-441页

作者：何成 Acad Sinica Inst Appl Math Beijing 100080 Peoples R China

In this paper, the author analyzes the singularity of a boundary layer in a nonlinear diffusion problem. Results show when the limiting solution satisfies the boundary condition, there is no boundary singularity. Otherwise, the boundary layer exists, and its thickness is proportional to epsilon(1/2), here epsilon is a small positive real parameter.

关键词： boundary layer singularity nonlinear diffusion problem