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Smoothing Newton Algorithm for Linear Programming over Symmetric Cones

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Transactions of tianjin university 2009年第3期15卷 216-221页

作者：刘晓红倪铁 school of sciences Tianjin University

By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm... 详细信息

关键词： linear programming symmetric cone Euclidean Jordan algebra smoothing algorithm

ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n=p

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Acta Mathematica Scientia 2006年第2期26卷 209-219页

作者：姚仰新沈尧天 school of mathematical sciences South china university of Technology Guangzhou 510640China

This article deals with the problem-△pu=λ｜u｜p/-2｜x｜pIn^p R/｜x｜＋f（x,u）,x∈Ω;u=0,x∈δΩ,where n = p. The authors prove that a Hardy inequality and the constant （p/p-1）^p is optimal. They also prove the ex... 详细信息

关键词： Elliptic equation Hardy inequality critical singularity Mountain PassLemma

Modal identification of system driven by lévy random excitation based on continuous time AR model

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Science china(Technological sciences) 2009年第12期52卷 3649-3653页

作者： DU XiuLi 1,2 &WANG FengQuan 1 1 College of Civil Engineering,Southeast university,Nanjing 210096,china 2 school of mathematical sciences,Nanjing Normal university,Nanjing 210097,china College of Civil Engineering Southeast University Nanjing 210096 China school of mathematical sciences Nanjing Normal University Nanjing 210097 China

Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random *** structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified *** by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of ***,the modal parameters are identified by eigen *** results show that the method not only has high precision and robustness but also has very high computing efficiency.

关键词： modal identification uniformly modulated function CAR model lévy process exact maximum likelihood estimator

On semisymmetric cubic graphs of order 6p^(2)

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Science china Mathematics 2004年第1期47卷 1-17页

作者： LU Zaiping, WANG Changqun & XU MingyaoLMAM, school of mathematical sciences, Peking university, Beijing 100871, china Department of Mathematics, Zhengzhou university, Zhengzhou 450052, chinaPresent address: Department of Mathematics, Qufu Normal university, Qufu 273165, china. 1. LMAM School of Mathematical Sciences Peking University 100871 Beijing China 3. Department of Mathematics Zhengzhou University 450052 Zhengzhou China

A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.

关键词： (G-)semisymmetric graph, symmetric graph, bi-Cayley graph, regular covering, group action.

INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

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Acta Mathematica Scientia 2010年第3期30卷 830-840页

作者：贺小明邹文明 school of sciences Central University for Nationalities Department of mathematical sciences Tsinghua University

In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ｜x｜^2^-μ=α｜x｜^s^-｜μ｜^2＊（s）-2u＋βα（x）｜u｜^r-2u,x∈R^n. By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α,β.

关键词： Singular elliptic equation Multiple solutions Critical Sobolev-Hardy exponent Minimax method

Threading dislocation density comparison between GaN grown on the patterned and conventional sapphire substrate by high resolution X-ray diffraction

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Science china(Physics,Mechanics & Astronomy) 2010年第3期53卷 465-468页

作者： ZHANG YuChao1, XING ZhiGang2, MA ZiGuang2, CHEN Yao2, DING GuoJian2, XU PeiQiang2, DONG ChenMing3, CHEN Hong2 & LE XiaoYun1 1 school of Physics and Nuclear Energy Engineering, Beihang university, Beijing 100190, china 2 Renewable Energy Laboratory, Institute of Physics, Chinese Academy of sciences, Beijing 100190, china 3 school of Information and Communication, tianjin Polytechnic university, tianjin 300160, china 1. school of Physics and Nuclear Energy Engineering Beihang University Beijing 100190 China2. Renewable Energy Laboratory Institute of Physics Chinese Academy of Sciences Beijing 100190 China3. School of Information and Communication Tianjin Polytechnic University Tianjin 300160 China

GaN epifilms are grown on the patterned sapphire substrates (PSS) (0001) and the conventional sapphire substrates (CSS) (0001) by metal-organic chemical vapor deposition (MOCVD) using a novel two-step growth. High resolution X-ray diffraction (HR-XRD) is used to investigate the threading dislocation (TD) density of the GaN epifilms. The TD density is calculated from the ω-scans full width at half maximum (FWHM) results of HR-XRD. The edge dislocation destiny of GaN grown on the PSS is 2.7×108 cm-2, which is less than on the CSS. This is confirmed by the results of atomic force microscopy (AFM) measurement. The lower TD destiny indicates that the crystalline quality of the GaN epifilms grown on the PSS is improved compared to GaN epifilms grown on the CSS. The residual strains of GaN grown on the PSS and CSS are compared by Raman Scattering spectra. It is clearly seen that the residual strain in the GaN grown on PSS is lower than on the CSS.

关键词： GaN patterned sapphire substrate threading dislocation XRD

VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION

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Acta Mathematica Scientia 2010年第3期30卷 949-962页

作者：温焕尧丁时进 school of mathematical sciences South China Normal University

In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Cinzburg-Landau equation in a smooth bounded domain Ω （R^2,that is ,Эtuε=j,k=1∑2（ajkЭxkuε）xj＋ε^2^-b（x）（1-｜uε｜^2）uε,x∈Ω,and conclude that each vortex,bj（t）（j=1,2,…,N）satisfies dt^-dbj（t）=-（a（bj（t））^-a1k（bj（t））Эxka（bj（t））,a（aj（t））^-a2k（bj（t））Эxka（bj（t）））,where a（x）=√a11a22-a12^2. We prove that all the vortices are pinned together to the critical points of a（x）. Furthermore, we prove that these critical points can not be the maximum points.

关键词： Anisotropic Ginzburg-Landau equation Gronwall inequality vortex dynamics

A new Early Cretaceous lizard with well-preserved scale impressions from western Liaoning, china

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Progress in Natural Science:Materials International 2005年第2期15卷 67-73页

作者： JI Shu’an*(school of Earth and Space sciences, Peking university, Beijing 100871, china) school of Earth and Space sciences Peking University Beijing 100871 China

A new small lizard, Liaoningolacerta brevirostra gen. et sp. nov., from the Early Cretaceous Yixian Formation of western Liaoning is described in detail. The new specimen was preserved not only by the skeleton, but also by the exceptionally clear scale impressions. This lizard can be included within the taxon Scleroglossa based on its 26 or more presacrals, cruciform interclavicle with a large anterior process, moderately elongated pubis, and slightly notched distal end of tibia. The scales vary evidently in size and shape at different parts of body: small and rhomboid ventral scales, tiny and round limb scales, and large and longitudinally rectangular caudal scales that constitute the caudal whorls. This new finding provides us with more information on the lepidosis of the Mesozoic lizards.

关键词： new genus Squamata skeleton lepidosis Early Cretaceous western Liaoning

New feature extraction in gene expression data for tumor classification

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Progress in Natural Science:Materials International 2005年第9期15卷 861-864页

作者： HE Renya, CHENG Qiansheng**, WU Lianwen and YUAN Kehong(LMAM, school of mathematical sciences, Institute of Molecular Medicine, Peking university, Beijing 100871, china) LMAM School of Mathematical Sciences Institute of Molecular Medicine Peking University Beijing 100871 China

Using gene expression data to discriminate tumor from the normal ones is apowerful method. However, it is sometimes difficult because the gene expression data are in highdimension and the object number of the data sets is very small. The key technique is to find a newgene expression profiling that can provide understanding and insight into tumor related cellularprocesses. In this paper, we propose a new feature extraction method based on variance to the centerof the class and employ the supportvector machine to recognize the gene data either normal ortumor. Two tumor data sets are used to demonstrate the effectiveness of our methods. The resultsshow that the performance has been significantly improved.

关键词： tumor classification support vector machine (SVM) bioinformatics featureextraction gene expression