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Eigenvalues, inequalities and ergodic theory

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Chinese Science Bulletin 2000年第9期45卷 769-774页

作者： CHEN Mufadepartment of mathematics,{2., beijing 100875, china department of mathematics Beijing Normal University Beijing China

This paper surveys the main results obtained during the period 1992.1999 on three aspects mentioned in the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e. the first non-trivial eigenvalue) of elliptic operators in Euclidean space, Laplacian on Riemannian manifolds or Markov chains (?). Here, a probabilistic method -coupling method is adopted. The new formula is a dual of the classical variational formula. The last formula is actually equivalent to Poincare inequality. To which, there are closely related logarithmic Sobolev inequality, Nash inequality, Liggett inequality and so on. These inequalities are treated in a unified way by using Cheeger’s method which comes from Riemannian geometry. This consists of ?2. The results on these two aspects are mainly completed by the author joint with F. Y. wang. Furthermore, a diagram of the inequalities and the traditional three types of ergodicity is presented (?3). The diagram extends the ergodic

关键词： eigenvalue inequality ergodic theory Markov process.

A trust region algorithm for bilevel programing problems

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Chinese Science Bulletin 1998年第10期43卷 820-824页

作者： LIU Guoshan 1, HAN Jiye 2.and wang Shouyang 3 1. department of {2., beijing normal university, beijing 100875, china 2. Institute of Applied {2., Chinese Academy of Sciences, beijing 100080, china 3. Institute of Systems Science, Chi department of mathematics Beijing Normal University Beijing China Institute of Applied mathematics Chinese Academy of Sciences Beijing China Institute of Systems Science Chinese Academy of Sciences Beijing China

A trust region algorithm is proposed for solving bilevel programming problems where the lower level programming problem is a strongly convex programming problem with linear constraints. This algorithm is based on a tr... 详细信息

关键词： bilevel programming problem trust region algorithm global convergence.

Existence and Multiplicity of Periodic Solutions of the Second-Order Differential Equations with Jumping Nonlinearities

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Acta Mathematica Sinica,English Series 2002年第3期18卷 615-624页

作者： Zai Hong wang department of {2., Capital normal university. beijing 100037. P. R. china department of mathematics Capital Normal University Beijing P. R. China

We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions.

关键词： Periodic solution Jumping nonlinearities Spectrum curve Time map

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Science china mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & wang Mingxindepartment of {2., Southeast university, Nanjing 2.0018, china department of {2., Xuzhou normal university, Xuzhou 2.1116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 2. and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 2.andnq + (n + 1)p 2.+mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures

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Science china mathematics 2010年第4期53卷 895-904页

作者： wang FengYu 1,2.1 School of Mathematical Sciences,beijing {2. university,beijing 100875,china 2.department of mathematics,Swansea university,Singleton Park,Swansea SA2.8PP,UK 1. School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Department of Mathematics Swansea University Singleton Park Swansea SA2 8PP UK

By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically *** conditions,as well as the ... 详细信息

关键词： intrinsic ultracontractivity intrinsic super-Poincar’e inequality Riemannian manifold diffusion semigroup

Implementation of a multiple round quantum dense coding using nuclear magnetic resonance

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Science china(Physics,Mechanics & Astronomy) 2005年第6期48卷 706-715页

作者： ZHANG Jingfu1, XIE Jingyi2. wang Chuan1, DENG Zhiwei3, LU Zhiheng4, & LONG Guilu1,5 1. Key Laboratory For Quantum Information and Measurements of MOE, department of Physics, Tsinghua {2., beijing 100084,china 2. department of Materials Science and Engineering, beijing normal university, beijing 100875, china 3. Testing and Analytical Center, beijing normal university, beijing 100875,china 4. department of Physics, beijing normal university, beijing 100875, china 5. Key Laboratory For atomic and Molecular Nanosciences, Tsinghua {2., beijing 100084,china 1. Key Laboratory For Quantum Information and Measurements of MOE Department of Physics Tsinghua University 100084 Beijing China 2. department of Materials science and Engineering Beijing Normal University 100875 Beijing China 3. Testing and Analytical Center Beijing Normal University 100875 Beijing China 4. department of Physics Beijing Normal University 100875 Beijing China 5. Key Laboratory For Atomic and Molecular Nanosciences Tsinghua University 100084 Beijing China

A multiple round quantum dense coding scheme based on the quantum phase estimation algorithm is proposed and implemented in a three qubit nuclear magnetic resonance (NMR) quantum computer. Using an m + 1 qubit system, Bob can transmit one of 2.+1 messages to Alice, through manipulating only one qubit and exchanging it between Alice and Bob for m rounds. The information capacity is enhanced to m + 1 bits as compared to m bits in a classical scheme. The scheme has been demonstrated in NMR system, and the experimental results show a good agreement between theory and experiment.

关键词： quantum dense coding, multiple round, nuclear magnetic resorance

Effects of enhancing p2.^(waf1) on proliferation and expression of G1 cyclins and CDKs in human breast cancer cells

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Chinese Science Bulletin 1999年第16期44卷 1489-1493页

作者： SANG Jianli, wang Yongchao and YE Yingjiang1. Laboratory of Cell Biology , department of Biology ,{2. , beijing 100875 , china 2. The Second Hospital, beijing Medical university, beijing 100044, china Laboratory of Cell Biology Department of Biology Beging Normal University Beijing China The Second Hospital Beijing Medical University Beijing China

The cyclin-dependent kinase inhibitor p2.( waf1/cip1/sdi1) is an important negative regulator in control of cell cycle. Its functions of inhibiting cancer cell growth and its effects on expression of Gl phase cyclins and related CDKs are a worthy topic for study. The plasmid expressing p2. with high level was transformed to human breast cancer cells, and the expression of p2. in cells was enhanced, then the cell growth rate, anchorage-independent growth and tu-morigenecity were tested, at the same time the expression levels of cyclinD1, CDK4,

关键词： p2.waf1 breast cancer cell cyclin CDK.

Perceptions and Controversies on Cholera in the Traditional Chinese Medicine Field in the Late Qing Dynasty

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Chinese Medicine and Culture 2024年第2期7卷 143-151页

作者： GUO shiqiang WU Haohuan WU Yinghua The department of History College of Liberal Arts Of Jinan UniversityGuangzhou 510632China Jinan university Library Jinan UniversityGuangzhou 510632China

At the beginning of the initial cholera outbreak in china,wang Qingren(王清任),after years of clinical trials,became an early representative who discovered the infectious characteristics and observed the course of cholera in the field of traditional Chinesse medicine(TCM).Kou Langao(寇兰皋)and Xu Zimo(徐子默),both medical practitioners,constructed a diagnosis and treatment system for cholera with cold patterns under the theory of *** represented“School of Cholera with Cold Patterns”(SCCP).In the 1860s,with the influence of wang Shixiong’s(王士雄)studies on the nature of cholera under the theory of epidemic febrile disease,the“School of Cholera with Heated Patterns”(SCHP)prevailed *** two schools complemented each other in theories and contributed to the integrity of TCM in cholera diagnosis and *** reviewing previous literature,books,clinical cases,and historical materials in medical field,this article aims 1)to summarise the influence of TCM on the cognitive development towards cholera in the late Qing dynasty;2.to explore the origin of the controversy between SCCP and SCHP from historical evidence;3)to summarize the historical lessons from the debate over cholera in TCM based on the principle of treatment based on pattern identification,and offer suggestions for the current prevention and treatment of new diseases using TCM.

关键词： Traditional Chinese medicine Cholera School of Cholera with Cold Patterns School of Cholera with Heated Patterns wang Shixiong Xu Zimo

Superprocesses arising from interactive stochastic flows

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Science china mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & LI Zhanbing Medical School, Shantou university, Shantou 515063, china {2. of mathematics, Bejing normal university, beijing 100875, china Medical School Shantou University Shantou 515063 China department of mathematics Bejing Normal University Beijing 100875 China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g... 详细信息

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.