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WEIERSTRASS REPRESENTATION FORSURFACES WITH PRESCRIBED NORMALGAUSS MAP AND GAUSS CURVATURE IN H^3

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Chinese Annals of mathematics,Series B 2004年第4期25卷 567-586页

作者： SHISHUGUO Instituteofmathematics FudanUniversityShanghai200433China.

The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal ***, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.

关键词： Hyperbolic space Hyperbolic Gauss map Normal Gauss map Weier-strass representation Harmonic map

Resonance between automorphic forms and exponential functions

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Science china mathematics 2010年第9期53卷 2463-2472页

作者： REN XiuMin1,& YE YangBo1,2 1school of mathematics,shandong university,jinan 250100,china 2Department of mathematics,The university of Iowa,Iowa City,Iowa 52242-1419,USA school of mathematics Shandong University Jinan China Department of mathematics The University of Iowa Iowa City USA

Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier *** this paper,the exponential sum X2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of siz... 详细信息

关键词： automorphic form exponential sum resonance

Optical waveguides in LiNbO_3 and stoichiometric LiNbO_3 crystals by proton exchange

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Science china(Physics,Mechanics & Astronomy) 2008年第10期51卷 1479-1488页

作者： LI ShiLing College of Physics and Engineering, Qufu Normal university, Qufu 273165, china school of Physics and Microelectronics, shandong university, jinan 250100, china College of Physics and Engineering Qufu Normal University Qufu China school of Physics and Microelectronics Shandong University Jinan China

The formation of optical planar waveguides in LiNbO3 and stoichiometric LiNbO3 crystals by proton exchange was reported. The prism-coupling method was used to characterize the dark-line spectroscopy at the wavelength of 633 and 1539 nm, re-spectively. The mode optical near-field outputs from proton-exchanged LiNbO3 and SLN waveguides at 633 nm were presented. The mode field from stoichiometric LiNbO3 (SLN) waveguide is lighter and more uniform than that from LiNbO3 waveguide, which means the quality of the waveguide in SLN crystal is better than that of the LiNbO3 waveguide. For proton-exchanged LiNbO3 waveguides, the evo-lution of the refractive index profile with annealing was presented. The disorder profiles of Nb atoms in proton-exchanged LiNbO3 waveguides were obtained by Rutherford backscattering/channeling technique. It is shown that the longer the exchange time, the larger the displacement of Nb atoms.

关键词： optical waveguide proton exchange LiNbO3 crystal stoichiometric LiNbO3 crystal

SMALLEST g-SUPERSOLUTION FOR BSDE WITH CONTINUOUS DRIFT COEFFICIENTS

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Chinese Annals of mathematics,Series B 2000年第3期21卷 359-366页

作者： LIN QINGQUAN (school of mathematics and System Science, shandong university, jinan 250100, china.) PENG SHIGE(school of mathematics and System Science, shandong university, jinan 250100, china.) E-mail: Linqingquan@math. sdu. cn Peng@sdu. edu. cn school of mathematics and System Science Shandong University Jinan 250100 China

The authors prove the existence and uniqueness of smallest g-supersolution with an equality constrains on (y, z) for one demensional stochastic differential equations whose drift coefficients are continuous and linear... 详细信息

关键词： Backward stochastic differentail equation g-supersolution Constraint

THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR-SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

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Journal of Systems Science & Complexity 2003年第1期16卷 30-45页

作者： YUAN Yirang (Institute of mathematics, shandong university, jinan 250100, china) (Instilute of mathematics Shandong University Jinan 250100

For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and *** order estimates in L^2 norm are derived for the error in the approximate *** methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.

关键词： Multicomponent displacement 3-dimensional compressibility operator-splitting characteristics finite element optimal order L2 error estimates.

A polynomial algorithm for finding (g,f)-colorings orthogonal to stars in bipartite graphs

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Science china mathematics 2005年第3期48卷 322-332页

作者： LIU Guizhen & DENG Xiaotie Department of mathematics, shandong university, jinan 250100, china Department of Computer Science, The City university of Hong Kong, Hong Kong, china Department of mathematics Shandong University Jinan China Department of Computer Science The City University of Hong Kong Hong Kong China

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤f(x)for every vertex x of V(G). A(g,f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a(g, f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.

关键词： bipartite graph, (g, f)-coloring, (g, f)-factor, orthogonal coloring.

THREE-POINT BOUNDARY VALUE PROBLEMSFOR A CLASS OF THREE ORDER DIFFERENTIAL INCLUSIONS

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Systems Science and Mathematical Sciences 1998年第2期11卷 144-149页

作者： ZHANG Fubao(Department of mathematics, shandong university, jinan 250100, china) 山东大学数学系山东济南

Some existence theorems of three-point boundary value problems for a class ofthree order differential inclusions are obtained by means of the topological degree theory forset-valued mappings and an improved Wirtinger’s inequality. The results, even restrictedto the case of differential equations, have generized and improved on the related results in[1]. Particularlyt a problem raised in Remark 5 in if] is answered definitely.

关键词： Three-point boundary value differential inclusion topological degree.

Repetitious-Hot-Pressing Technique in Hot-Pressing Process

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Journal of Materials Science & Technology 2003年第5期19卷 486-488页

作者： Shixue SONG, Xing AI, Wei GAO and Jun ZHAO1)school of Mechanical Engineering, shandong university, jinan 250061, china2)school of Science, jinan university, jinan 250022, china school of Mechanical Engineering Shandong University Jinan 250061 China school of Science Jinan University Jinan 250022 China

A new pressing method was proposed for hot-pressing process. Experimental results indicated that the porosity in Al2O3/TiC/ Ni/Mo (hereafter called AI2O3/TiC composite) composite compacts decreases by 6% after adopting this new technique, compared to traditional hot-pressing technique under the same sintering temperature. The flexural strength and Vicker hardness increase from 883 MPa to 980 MPa and from 16 GPa to 21.1 GPa, respectively. A theoretical model was given to analyze the densification mechanism of the composite in the process of repetitious-hot-pressing.

关键词： Hot-pressing sintering Repetitious-hot-pressing sintering Composite

Ground state and polaron and bipolaron excited states in polydiacetylene

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Science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 430-439页

作者： LI Yuan1, HU Guichao1, XIA Caijuan1, LIU Desheng1,2 & XIE Shijie1,2 1. school of Physics and Microelectronics, shandong university, jinan 250100, china 2. National Key Laboratory of Crystal Materials, shandong university, jinan 250100, china school of Physics and Microelectronics Shandong University Jinan China National Key Laboratory of Crystal Materials Shandong University Jinan China

The electronic properties of ground state and charged excited states of nondegenerate polydiacetylene were investigated by means of a tight-binding model. The parameters of the model were obtained by comparison of the experimental and other theoretical results. It was found that there is a stable dimerized structure of polydiacetylene in ground state and the doping induces the nonlinear excitations, such as polarons and bipolarons. In order to compare the stability of polaron and bipolaron, the creation energy and binding energy were separately defined. By neglecting the electron-electron Coulomb interaction, a bipolaron is more stable than two independent polarons.

关键词： dimerization, polaron, bipolaron, binding energy.