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Uniqueness and local stability for the inverse scattering problem of determining the cavity

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Science china Mathematics 2005年第8期48卷 1113-1123页

作者： FENG Lixin & MA Fuming LMAM, school of mathematical sciences, Peking university, Beijing 100871, china school of mathematical sciences, Heilongjiang university, Harbin 150080, china school of mathematical sciences, Jilin university, Changchun 130012, china 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 2. school of mathematical sciences Heilongjiang University 150080 Harbin China 3. school of mathematical sciences Jilin University 130012 Changchun China

Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper.

关键词： uniqueness, stability, Maxwell's equations, inverse scattering problem.

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational Mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (school of mathematical sciences, Peking university, Beijing 100871, china) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

Maslov P-Index Theory for a Symplectic Path with Applications

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 441-458页

作者： Chungen LIU school of Mathematics and LPMC Nankai University Tianjin 300071 China.

The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an appli... 详细信息

关键词： Hamiltonian system Symplectic path Maslov P-index Non-periodicboundary problem

CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES

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Acta Mathematica Scientia 2010年第3期30卷 919-931页

作者：王珊珊张春生吴荣 school of mathematical sciences and LPMC Nankai University

In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.

关键词： Probability of ruin the perturbed classical surplus model Oscillation recursive calculation

Rational points and zeta functions of some curves over finite fields

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Science china Mathematics 2010年第11期53卷 2855-2863页

作者： WANG Long1, & LUO JinQuan2,3 1Department of mathematical sciences, Tsinghua university, Beijing 100084, china 2school of mathematical sciences, Yangzhou university, Yangzhou 225002, china 3Division of mathematical sciences, school of Physical and mathematical sciences, Nanyang Technology university, 637371, Singapore 1. Department of mathematical sciences Tsinghua University Beijing 100084 China2. School of Mathematical Sciences Yangzhou University Yangzhou 225002 China3. Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technology University Singapore 637371 Singapore

In this paper we study the number of rational points on some curves over finite fields. Moreover, zeta functions of the associated function fields are evaluated explicitly.

关键词： exponential sum rational point rational place zeta function

The Isometric Extension of an Into Mapping from the Unit Sphere S(e_((2))~∞)to S(L^1(μ))

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1721-1724页

作者： Guang Gui DING school of mathematical Science and LPMC,nankai university,tianjin 300071,P.R.china

This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometric mapping from th... 详细信息

关键词： isometric mapping isometric extension

Observation of modulated spontaneous emission of Rhodamine 6G in low refractive index contrast 1D-periodic gelatin film

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中国科学：物理学、力学、天文学英文版 2010年第1期53卷 54-58页

作者： LI Wei 1 , ZHANG XinZheng 1 , WANG ZhenHua 1 , WU Qiang 1 , LIU LongChang 1 , XU JingJun 1 & Tang BaiQuan 2 1 The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics school, nankai university, tianjin 300457, china 2 school of Physics, nankai university, tianjin 300071, china 1. The MOE Key Laboratory of Weak-Light Nonlinear Photonics TEDA Applied Physics School Nankai University Tianjin 300457 China2. School of Physics Nankai University Tianjin 300071 China

The modulation of the spontaneous emission of Rhodamine 6G has been observed in one-dimensional periodic dielectric structure of dichromated gelatin film with refractive index contrast as low as 0.01. The spontaneous emission is enhanced at the band edges and inhibits in the band gap, which agree well with the theoretical analysis on the redistribution of the fractional local density of optical states.

关键词： density of states refractive index contrast spontaneous emission

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灵光独耀:沈宗灵与中国法理学

中国法律评论 2024年第4期 149-154页

作者： Peking university Law school 北京大学法学院

在其诸多弟子的追忆中,沈宗灵先生一生专心治学、淡泊名利,由此常常对世事保持一种有意的疏离。“灵光独耀,迥脱根尘”,或许便是这位法理学大家的灵魂写照。壹“经国济民”:沈宗灵的早年岁月1923年2月24日,沈宗灵出生于浙江杭州的一个... 详细信息

在其诸多弟子的追忆中,沈宗灵先生一生专心治学、淡泊名利,由此常常对世事保持一种有意的疏离。“灵光独耀,迥脱根尘”,或许便是这位法理学大家的灵魂写照。壹“经国济民”:沈宗灵的早年岁月1923年2月24日,沈宗灵出生于浙江杭州的一个商人家庭,后随家人迁居上海。

关键词：沈宗灵淡泊名利法理学浙江杭州灵光

Views on “Principle of limitation of physical quantities and cyclic universe”

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Science china(Physics,Mechanics & Astronomy) 2010年第9期53卷 1772-1774页

作者： LI LianGang Department of Physics,school of sciences,tianjin university,tianjin 300072,china 1. Department of Physics School of Sciences Tianjin University Tianjin 300072 China

This paper presents an analysis of a paper entitled "Principle of limitation of physical quantities and cyclic universe" and proposes different results for some formulae from that *** addition,this paper shows that the principle of limits coupling may lead to an approximation of current theories(i.e.,quantum theory and relativistic theory),which have interesting correlations with the Plank formula and the special theory of relativity.

关键词： principle of limitation of physical quantities limits coupling formulae Plank formula theory of relativity