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ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS

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Journal of Computational Mathematics 2003年第2期21卷 157-166页

作者： Zhibing Chen9+(Department of Mathematics, normal college, Shenzhen university, Shenzhen 518060, china) Department of Mathematics Normal College Shenzhen University Shenzhen 518060

A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

关键词： Generalized inverse for matrices Neville-type Rational interpolants.

Level Set interface treatment and its application in Euler method

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Science china(physics,Mechanics & Astronomy) 2010年第2期53卷 227-236页

作者： WU KaiTeng1,2,HAO Li3,WANG Cheng4 & ZHANG Li1,2 1 Numerical Simulation Sichuan Higher School Key Laboratory,Neijiang normal university,Neijiang 641112,china 2 college of Mathematics and Information Science,Neijiang normal university,Neijiang 641112,china 3 college of Science,Beijing university of Civil Engineering and Architecture,Beijing 100044,china 4 State Key Laboratory of Explosion Science and technology,Beijing Institute of technology,Beijing 100081,china Numerical Simulation Sichuan Higher School Key Laboratory Neijiang Normal University Neijiang China college of Mathematics and Information Science Neijiang Normal University Neijiang China college of Science Beijing University of Civil Engineering and Architecture Beijing China State Key Laboratory of Explosion Science and technology Beijing Institute of Technology Beijing China

Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-order WENO spatial discretization and third-order TVD Runge-Kutta time discretization methods are used. Shock-wave action on bubble,implosion and velocity field Shock effect bubbles; implosion and velocity field are simulated by means of LS-MMIC3D programmed by C++. Nu-merical results show that the Level Set interface treatment method is effective and feasible for multi-material interface treatment in comparison with the WENO method.

关键词： Euler method Level Set method shock-wave action on bubble implosion numerical simulation

Scenario simulation and forecast of land use/cover in northern china

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Chinese Science Bulletin 2008年第9期53卷 1401-1412页

作者： LI YueChen 1,2,3 & HE ChunYang 3 1 college of Geographical Science, Chongqing normal university, Chongqing 400047, china 2 college of Resources and Environmental Science, Chongqing university, Chongqing 400044, china 3 college of Resources Science & technology, Beijing normal university, Beijing 100875, china college of Geographical Science Chongqing Normal University Chongqing China college of Resources and Environmental Science Chongqing University Chongqing China college of Resources Science & technology Beijing Normal University Beijing China

Modeling land use/cover scenario changes and its potential impacts on structure and functions of ecosystem in typical regions are helpful to understanding the interactive mechanism between land use/cover system and ecosystem. Based on the analysis of the existing land use/cover simulation and forecast models, a land use/cover scenario dynamics model by the integration of System Dynamics (SD) model, Back Propagation Neural Network (BPNN) and Cellular Automata (CA) model is developed with land use/cover scenario changes in northern china in the next 30 years and simulated in this paper. The model is to simulate the land use/cover scenario demands by using a SD model at first, and then allocating the land use scenario patterns at the local scale with the considerations of land use/cover suitability, inheritance ability and neighborhood effect by using BPNN-CA model to satisfy the balance between land use/cover scenario demands and supplies. It integrates the advantages of SD, BPNN and CA. Macro-driving factors and the micro-spatial pattern are also fully taken into account. The BPNN simplifies the identification of the factors’ weights used in CA model and improves the reliability of the simulation results. The simulation accuracy of the model developed in this paper was found to be about 74%. It suggests that the model has the ability to reflect the complexity of land use/cover system at different scales to some extent and it is a useful tool for assessing the potential impacts of land use system on ecosystem. The simulated results also indicate that the urban land, water area and forest will increase significantly, and farmland and unable land will decrease gradually. Obvious land use/cover changes will take place in the farming-pastoral zone and the southeast area of northern china.

关键词：土地利用中国北方细胞自动机系统动力学

Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip

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Chinese Annals of Mathematics,Series B 2006年第6期27卷 657-674页

作者： Shuliang SHUI Deming ZHU college of Mathematics Physics and Information Engineering Zhejiaag Normal University Jinhua 321004 Zhejiang China college of Sciences Shanghai University Shanghai 200436 China Department of Mathematics East China Normal University Shanghai 200062 China

四块维的向量地里的 Heteroclinic 分叉被建立一个本地人调查一个不平的异种诊所附近的坐标循环。这个异种诊所环有一条主要异种诊所轨道；拿轨道的一条非主要的异种诊所轨道扭动。存在，不存在，共存；1-heteroclinic 环的唯一， 1-hom... 详细信息

四块维的向量地里的 Heteroclinic 分叉被建立一个本地人调查一个不平的异种诊所附近的坐标循环。这个异种诊所环有一条主要异种诊所轨道；拿轨道的一条非主要的异种诊所轨道扭动。存在，不存在，共存；1-heteroclinic 环的唯一， 1-homoclinic 轨道；1-periodic 轨道被学习。双重或三方面的 1-periodic 轨道的存在也被获得。

关键词：分歧环路非谐振周期轨道向量场

The Research of Scattering Cross-Section and Energy-Extraction in FEL

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Chinese Journal of Lasers 1995年第1期B4卷 25-29页

作者： ZHU Jiaqing (Department of physics,Central china normal university,Wuhan,430070,china) Central china normal Univ Wuhan China

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ＴｈｅＲｅｓｅａｒｃｈｏｆＳｃａｔｔｅｒｉｎｇＣｒｏｓｓ－ＳｅｃｔｉｏｎａｎｄＥｎｅｒｇｙ－ＥｘｔｒａｃｔｉｏｎｉｎＦＥＬＴｈｅＲｅｓｅａｒｃｈｏｆＳｃａｔｔｅｒｉｎｇＣｒｏｓｓ－ＳｅｃｔｉｏｎａｎｄＥｎｅｒｇｙ－ＥｘｔｒａｃｔｉｏｎｉｎＦＥＬ￥ＺＨ...

关键词： free-electron laser scattering cross-section

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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Science china Mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of Mathematics, East china normal university, Shanghai 200062, china college of Mathematics & Information Science, Northwest normal university, Lanzhou 730070, china Department of Mathematics East China Normal University Shanghai China college of Mathematics & Information Science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

Preparation of Cu-SiO_2 composite aerogel by ambient drying and the influence of synthesizing conditions on the structure of the aerogel

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Chinese Science Bulletin 2011年第7期56卷 685-690页

作者： LI GuiAn, ZHU TingLiang, DENG ZhongXun, ZHANG YaJuan, JIAO Fei & ZHENG HaiRong college of physics and Information technology, Shaanxi normal university, Xi’an 710062, china college of physics and Information technology Shaanxi Normal University Xi’an China

A copper-doped silica composite aerogel with high specific surface area was prepared using a sol-gel method at ambient pressure. A drying control chemical additive (DCCA) N,N-dimethylformamide (DMF) was introduced to the composite sol of tetraethyl orthosilicate (TEOS) and copper nitrate (Cu(NO3)2·3H2O) during the synthesizing process. The influence of the preparation conditions including Cu loading, catalyst concentration and heat treatment on the structure of copper-doped silica was investigated. The results showed that the obtained aerogel particles were uniformly distributed. The pore diameter was in a range of 2 to 15 nm. Heavier Cu loading benefited the formation of CuO crystalline, and reduced the specific surface area and pore diameter. When the catalyst concentration was high, the aggregation of Si-O network was reduced with the increase of it. The composite aerogel exhibited a good thermal stability after the heat treatment at high temperature.

关键词：复合气凝胶铜掺杂凝胶结构合成条件 Si02 常压正硅酸乙酯溶胶凝胶法

ALMOST PERIODICITY FOR AN IMPULSIVE PURE DELAY LOGISTIC EQUATION

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Annals of Differential Equations 2009年第3期25卷 316-322页

作者： Chunhua Feng (college of Mathematical Science,guangxi normal university,guilin 541004,guangxi) Zhenkun Huang (Science college,Jimei university,Xiamen 361021,Fujian) college of Mathematical Science Guangxi Normal UniversityGuilin 541004Guangxi Science college Jimei UniversityXiamen 361021Fujian

By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic so... 详细信息

关键词： delay impulsive differential equation almost periodic solution existence

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

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Communications in Theoretical physics 2007年第7期48卷 19-22页

作者： DING Ning FANG Jian-Hui WANG Peng ZHANG Xiao-Ni college of physics Science and technology,china university of Petroleum,Dongying 257061,china college of physics Science and technology China University of Petroleum Dongying 257061 China

Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are *** exact invariants induced directly from the Lie symmetryof the system without perturbation are *** perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[***.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.

关键词： Lie symmetry perturbation adiabatic invariant general holonomic mechanical’system