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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 {2. 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192.年2.2.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192.年2.2.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

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. Department of physics, Tsinghua university, {2. 100084, china 2. Department of physics, peking university, beijing 100871, china) Department of physics Tsinghua University Beijing 100084 China Department of physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

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 {2., 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

Abrupt climate change and collapse of ancient civilizations at 2.00BC-2.00BC

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Progress in Natural Science:Materials International 2005年第10期15卷 46-52页

作者： WANG Shaowu (Department of Atmospheric Science, school of physics, {2. university, beijing 100871, china) Department of Atmospheric Science School of Physics Peking University Beijing 100871 China

Plentiful evidence of historical, archaeological and palaeoclimatic studies proved that an abrupt change from wetter to drier climate occurred over the Nile Valley,the Mesopotamia, the Indus Valley and Huanghe River Valley at 2.00BC-2.00BC. The abrupt change was developed based on the general lowering of temperature in the middle latitudes, and was a strong cold event since the beginning of the Megathermal (8.5-3.0 kaBP). Collapse of Nile civilization appeared at the First Intermediate Period (2.81BC-2.40BC). Civilization of Mesopotamia began collapse following the disintegration of Akkadian Empire. This process lasted to the foundation of Babylon Kingdom from 2.00BC to 1900BC. Indus civilization abruptly fell off at 1800BC. A widespread alternation of archaeological cultures happened in china at ca. 2.00BC except only in its central part. Longsheng culture was replaced by the Erlitou culture, which is now acknowledged in china as Xia Culture. Foundation of Xia Dynasty at 2.70BC opened a new chapter in the development of Chinese civilization. Studies indicated that abrupt climate change may be caused by the weakening of the Thermohaline Circulation (THC).

关键词： 2.00BC-2.00BC abrupt climate change collapse of ancient civilization.

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

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Science china(physics,Mechanics & Astronomy) 2004年第6期47卷 676-684页

作者： WANG Jing & ZENG Jinyan Department of physics,Tsinghua university,{2. 100084,china school of physics,peking university,{2. 100871,china Department of physics Tsinghua University Beijing 100084 China school of physics Peking University Beijing 100871 China

The symmetry and |m| partial-wave analysis for two-dimensional (2.) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef |m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off |m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f |m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off |m|(θ) on the positive real |m| axis.

关键词： two-dimensional Coulomb scattering, |m| partial-wave, Regge pole.

REGULARITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATION

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Chinese Annals of Mathematics,Series B 2003年第4期24卷 529-540页

作者： CHEN YEMIN school of Mathematics, peking {2., beijing 100871, china. peking Univ Sch Math Beijing 100871 Peoples R China

In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n... 详细信息

关键词： Regularity Dirichlet problem Degenerate Weighted spaces

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2. & GUO Maozheng~(1,3) 1. school of Mathematical Sciences,peking {2.,beijing 100871,china 2. Department of Mathematics,Yantai {2.,Yantai 2.4005,china 3. LMAM,peking {2.,beijing 100871,china 1. school of Mathematical Sciences Peking University 100871 Beijing China 2. Department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2. )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2. ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

Kinetic characteristics of continuous flow polymerase chain reaction chip: A numerical investigation

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Science china(Technological Sciences) 2010年第7期53卷 1967-1972页

作者： WANG ShiYing1 & WANG Wei2.3 1 school of physics, {2. university, beijing 100871, china 2.Institute of Microelectronics, {2. university, beijing 100871, china 3 National Key Laboratory of Science and Technology on Micro/Nano Fabrication, beijing 100871, china 1. school of physics Peking University Beijing 100871 China2. Institute of Microelectronics Peking University Beijing 100871 China3. National Key Laboratory of Science and Technology on Micro/Nano Fabrication Beijing 100871 China

Continuous flow PCR (polymerase chain reaction) chip holds impressive advantages compared to micro chamber PCR chip. In order to have better understanding of kinetic characteristics of continuous flow PCR chip, a comprehensive mathematical model is presented in this paper, including melting, annealing and extension phases of a typical PCR process which has the essence of a convection-diffusion-reaction system. Using this model, we can simulate the PCR process in series of reaction cycles. Numerical results show that the average sample velocity plays a significant role in affecting the amplification efficiency. Also, appropriate combination of the PCR mixture is important for high-quality DNA amplification. Giving a large initial DNA concentration range, the continuous flow PCR scheme holds excellent real-time detection ability theoretically. The present numerical model bridges the temperature distribution to the real DNA amplification, and thereby is able to successfully predict continuous flow PCR properties which are important for the chip design.

关键词： continuous flow PCR chip numerical simulation convection-diffusion-reaction system

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第5期16卷 437-444页

作者： (Department of Mathematics, peking university,{2., china) beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production