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DISTRIBUTION OF THE (0,∞) ACCUMULATIVE LINES OF MEROMORPHHIC FUNCTIONS

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Chinese Annals of Mathematics,Series B 1994年第4期15卷 453-462页

作者： WU SHENGJIAN(department of Mathematics, beijing university,beijing 100871, china.) 北京大学数学系北京 100871

Suppose that f(z) is a meromorphic function of order and of lower order μin the plane. Let ρ be a positive number such that .(1) If f(l)(z) () has ρ() finite nonzero deficient values ai (i =1,…,p) with deficiencies δ(ai, f(l)), then f(z) has a (0, ∝) accumulative line of order inany angular domain whose vertex is at the origin and whose magnitude is larger than(2) If f(z) has only p ()(0, ∝) accumulative lines of order : arg z = θk (θ1<θ2…<θp<2π, θp+1 = θ1 + 2π), then , where , providedthat has a finite noasero deficient value.

关键词： Meromorphic function Accumulative line Order.

|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,beijing 100084,china School of Physics,Peking university,beijing 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 (2D) 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.

The Laplacian spectral radii of unicyclic and bicyclic graphs with n vertices and k pendant vertices

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Science china Mathematics 2010年第8期53卷 2135-2142页

作者： GUO JiMing department of Applied Mathematics,china university of petroleum,Dongying 25.061,china department of Applied Mathematics China University of Petroleum Dongying China

In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.

关键词： Laplacian matrix Laplacian spectral radius unicyclic graph bicyclic graph

From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

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Journal of Materials Science & Technology 1999年第4期15卷 315-319页

作者： Shaojun LIU(department of physics, beijing Normal university, beijing 100875. china)Xiaobo WEI(department of Physics, Liuzhou College of Education, Liuzhou 5.5.05. china)Zhaodou CHEN Jun CAI and Benkun MA(department of Physics, beijing Normal university, department of Physics Beijing Normal University Beijing 100875 China department of Physics Liuzhou College of Education Liuzhou 545005 China

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

关键词： Rev Li Chen From the Green’s Function in Tight-Binding Representation to Interatomic Many-body Potentials body

The information entropy of a static dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU ChengZhou Institute of Theoretical Physics, Binzhou university, Binzhou 25.600, china department of Physics, beijing Normal university, beijing 100875. china Institute of Theoretical Physics Binzhou University Binzhou China department of Physics Beijing Normal University Beijing China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity

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, beijing 100871, china) department of Mathematics Peking University Beijing 100871 China

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=05.5.}L:={x=--y+hi,hi... 详细信息

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=05.5.}L:={x=--y+hi,hi5.5.i+（aZ--hi）/2}La={x=y+a...

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

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of Mathematics, beijing Normal university, beijing 100875. china.) 北京师范大学北京 100875

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su department of Mathematics, Tsinghua university, beijing 100084, china. department of Mathematics Tsinghua University Beijing 100084 China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

CONVERGENCE PROPERTIES OF A MODIFIED BFGSALGORITHM FOR MINIMIZATION WITHARMIJO-GOLDSTEIN STEPLENGTHS

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Journal of Computational Mathematics 1999年第6期17卷 645-652页

作者： Nai-yang Deng Zheng-feng Li(department of Mathematics, beijing Agricultural Engineering university, beijing 100083,china) 北京农业工程大学数学系北京 100083 北京农业工程大学数学系北京

The line search strategy is crucial for an efficient unconstrained optimization algorithm. One of the reason why the Wolfe line searches is recommended lies in that it ensures positive definiteness of BFGS updates. When gradient information has to be obtained costly, the Armijo-Goldstein line searches may be preferred. To maintain positive difiniteness of BFGS updates based on the Armijo-Goldstein line searches, a slightly modified form of BFGS update is proposed by I.D. Coope and C.J. Price (Journal of Computational Mathematics, 13 (1995., 15.-160), while its convergence properties is open up to now. This paper shows that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches.

关键词： BFGS methods convergence superlinear convergence