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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

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 university,{2. 100871,china 2. department of Mathematics,Yantai university,Yantai 2.4005,china 3. LMAM,peking university,{2. 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.

The numerical method for three-dimensional impact with friction of multi-rigid-body system

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Science china(Physics,Mechanics & Astronomy) 2006年第1期49卷 102-118页

作者： ZHAO Zhen1,2. LIU Caishan2.& CHEN Bin2.1. beijing Institute of Graphic Communication, beijing 102.00,{2. 2. department of Mechanics & Engineering Science, peking university, beijing 100871,{2. beijing Institute of Graphic Communication Beijing 102600 China department of Mechanics & Engineering Science Peking University Beijing 100871 China

The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid nu- merical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tan- gential movement modes varied with the normal impulse during collision.

关键词： multi-rigid body, impact, friction.

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 473-478页

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

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2.. It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

Dynamic mechanisms of the post-seismic deformation following large events:Case study of the 1999 Chi-Chi earthquake in Taiwan of china

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Science china Earth Sciences 2009年第11期52卷 1813-1824页

作者： ZHU ShouBiao1,2.& CAI YongEn2.1 Institute of Crustal Dynamics, china Earthquake Administration, beijing 100085, china 2.department of Geophysics, peking university, beijing 100871, china 1. Institute of Crustal Dynamics China Earthquake Administration Beijing 100085 China 2. department of Geophysics Peking University Beijing 100871 China

The mechanism of postseismic deformation related to strong earthquakes is important in geodynamics, and presumably afterslip or viscoelastic relaxation is responsible for the postsesimic deformation. The 1999 Chi-Chi, Taiwan of china, earthquake occurred in the region where GPS observation station is most densely deployed in the world. The unprecedented GPS data provides a unique opportunity to study the physical processes of postseismic deformation. Here we assume that the interactions of viscoelastic relaxation, afterslip, fault zone collapse, poroelastic rebound, flow of underground fluids, and all these combined contribute to the surface displacements following the main shock. In order to know the essence of the postseismic deformation after the strong event, fault zone collapse, poroelastic rebound, flow of underground fluids, and so on, are represented equivalently by the variations of the focal medium properties. Therefore, the viscoelastic relaxation, afterslip, and the variations of the equivalent focal medium properties are inverted by applying the GPS temporal series measurement data with viscoelastic finite element method. Both the afterslip rate distribution along the fault and the afterslip evolution with time are obtained by means of inversion. Also, the preliminary result suggests that viscosities of the lower crust and the upper mantle in Taiwan region is 2.7×1018 and 4.2.102. Pa·s, respectively. Moreover, the inversion results indicate that the afterslip contributing to postseismic deformation of 44.6% in 450 days after the Chi-Chi earthquake, with 34.7% caused by the viscous relaxation and 2..7% by other factors such as fault zone collapse, poroelastic rebound, and the flow of liquids.

关键词： mechanism of postseismic deformation viscoelastic finite element method GPS temporal series data Chi-Chi earthquake

Neuroimaging studies of self-reflection

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Progress in Natural Science:Materials International 2004年第4期14卷 10-16页

作者： ZHU Ying(department of Psychology, peking university,{2., china) peking Univ Dept Psychol Beijing 100871 Peoples R China

This paper reviews some basic findings and methodological issues in neuroimaging studies of self-referential processing. As a general rule, making judgments about one’s self, inclusive of personality trait adjectives or current mental states (person’ s preferences, norms, aesthetic values and feeling) uniformly generates medial prefrontal activations, regardless of stimulus materials (words or pictures) and modality (visual or auditory). Cingulate activations are also observed in association with most self-referential processing. Methodological issues include treating self-referential processing as either representing one’s own personality traits or representing one’s own current mental states. Finally, self-referential processing could be considered as implement of "I think therefore I am" approach to neuroimaging the self.

关键词： self self-referential processing medial prefrontal cortex cingulate brain image.

Two applications of generalized Carleson measures to meromorphic Besov-type spaces

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Chinese Science Bulletin 1998年第15期43卷 1260-1264页

作者： TAN Haiou 1 and XIAO Jie 2.1. department of Mathematics, Wuyi university, Jiangmen 52.02.,{2. 2. School of Mathematical Sciences, peking university, beijing 100871,{2. department of Mathematics Wuyi University Jiangmen China School of Mathematical Sciences Peking University Beijing China

The generalized Carleson measures are used to characterize the meromorphic Besov_type spaces and to explore some inclusions between these spaces.

关键词： generalized Carleson measures meromorphic Besov_type spaces.

Oblique Derivative Problems for Second OrderNonlinear Equations of Mixed Type inMultiply Connected Domains

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 281-284页

作者： Guochun WEN(department of Mathematics, peking university,{2., china) department of Mathematics Peking University Beijing 100871 China

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=02.LiaredeadedasLI={x=;)05x51}L:={x=--y+hi,hi... 详细信息

关键词： oblique derivative problems quasinonlinear equations of mixed type mul-tiply connected domains.

The refined theory of transversely isotropic piezoelectric rectangular beams

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Science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 473-486页

作者： GAO Yang1 & WANG Minzhong2.1. College of Science, china Agricultural university, {2. 100083, china 2. State Key Laboratory for Turbulence and Complex Systems and department of Mechanics and Engi- neering Science, peking university, beijing 100871, china 1. College of Science China Agricultural University Beijing 100083 China 2. State Key Laboratory for Turbulence and Complex Systems and department of Mechanics and Engineering Science Peking University Beijing 100871 China

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

关键词： rectangular beams, the refined theory, piezoelectric, transversely isotropic.