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Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

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Applied Mathematics(A Journal of Chinese Universities) 2015年第1期30卷 1-16页

作者： cheng xiao-liang YU Yuan-jie Department of Mathematics Zhejiang University

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin in- verse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.

关键词： Inverse problem Robin coefficient differentiability the Gauss-Newton method.

AN EFFECTIVE CONTINUOUS ALGORITHM FOR APPROXIMATE SOLUTIONS OF LARGE SCALE MAX-CUT PROBLEMS

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Journal of Computational Mathematics 2006年第6期24卷 749-760页

作者： cheng-xian Xu xiao-liang Feng-min Xu Department of Mathematics Xi 'an Jiaotong University Xi ' an 710049 China

An effective continuous algorithm is proposed to find approximate solutions of NP-hard max-cut problems. The algorithm relaxes the max-cut problem into a continuous nonlinear programming problem by replacing n discrete constraints in the original problem with one single continuous constraint. A feasible direction method is designed to solve the resulting nonlinear programming problem. The method employs only the gradient evaluations of the objective function, and no any matrix calculations and no line searches are required. This greatly reduces the calculation cost of the method, and is suitable for the solution of large size max-cut problems. The convergence properties of the proposed method to KKT points of the nonlinear programming are analyzed. If the solution obtained by the proposed method is a global solution of the nonlinear programming problem, the solution will provide an upper bound on the max-cut value. Then an approximate solution to the max-cut problem is generated from the solution of the nonlinear programming and provides a lower bound on the max-cut value. Numerical experiments and comparisons on some max-cut test problems （small and large size） show that the proposed algorithm is efficient to get the exact solutions for all small test problems andwell satisfied solutions for most of the large size test problems with less calculation costs.

关键词： Max-cut problems Algorithm Feasible direction method Laplacian matrix,Eigenvectors.

A modified Tikhonov regularization method for a Cauchy problem of a time fractional diffusion equation

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Applied Mathematics(A Journal of Chinese Universities) 2019年第3期34卷 284-308页

作者： cheng xiao-liang YUAN Le-le liang Ke-wei School of Mathematical Sciences Zhejiang University

In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering *** illposedness of the Cauchy problem is explained by its solution in frequency ***,the problem is formulated into a minimization problem with a modified Tikhonov regularization *** gradient of the regularization functional based on an adjoint problem is deduced and the standard conjugate gradient method is presented for solving the minimization *** error estimates for the regularized solutions are obtained under Hp norm priori bound ***,numerical examples illustrate the effectiveness of the proposed method.

关键词： Cauchy problem time-fractional diffusion equation a modified Tikhonov regularization method conjugate gradient method error estimates

Two algorithms for two-phase Stefan type problems

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 298-308页

作者： LIAN xiao-peng cheng xiao-liang HAN Wei-min Dept. of Math. Zhejiang Univ. Hangzhou 310027 China Dept. of Math. University of Iowa Iowa City IA 52242 USA

In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are *** analysis of their convergence is presented and the upper bounds of the convergence rates are *** numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.

关键词： relaxation method Uzawa algorithm variational inequality two-phase Stefan type problem

On the optimal harvesting of size-structured population dynamics

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Applied Mathematics(A Journal of Chinese Universities) 2013年第2期28卷 173-186页

作者： LIU Yan cheng xiao-liang HE Ze-rong Department of mathematics Zhejiang University Institute of Operational Research and Cybernetics Hangzhou Dianzi University

This work is concerned with a kind of optimal control problem for a size-structured biological population ***-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point *** and uniqueness of optimal control are shown by functional analytical *** conditions describing the optimal strategy are established via tangent and normal cones *** results are of the first ones for this novel structure.

关键词： Body size population model optimal harvest maximum principle normal cone.

A SIMPLE FINITE ELEMENT METHOD FOR THE REISSNER-MINDLIN PLATE

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Journal of Computational Mathematics 1994年第1期12卷 46-54页

作者： cheng xiao-liang (Department of Mathematics, Hangzhou University, Hangzhou, Zhejiang, China) HANGZHOU UNIV DEPT MATHHANGZHOUPEOPLES R CHINA

A simple finite element method for the Reissner-Mindlin plate model in the primitive variables is presented and analyzed. The method uses conforming linear finite elements for both the transverse displacement and rotation. It is proved that the method converges with optimal order uniformly with respect to *** is simpler and more economical than the Arnold-Falk element[1].

关键词： Math A SIMPLE FINITE ELEMENT METHOD FOR THE REISSNER-MINDLIN PLATE IV

Research and Application of an Electro-hydraulic Synchronous Control System for Bridge Lifting

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International Journal of Plant Engineering and Management 2009年第1期14卷 1-7页

作者： ZHANG cheng-pu xiao Ju-liang School of Mechanical Engineering Tianjin University Tianjin 300072 China

With the increase of bridge reconstruction schemes, synchronous lifting of a bridge is more and more widely used. In order to solve the problems associated with the synchronoas lifting of a bridge, a multi-cylinder synchronous lifting power and monitoring system has been developed. This is a distributed control system, which is com- posed of an industrial computer workstation, a programmable logical controller and a hydraulic control system. The system can achieve distributed control and centralized operation of actuators, and centralized management of infor- mation. It not only can implement multi-cylinder synchronous lifting with an unbalanced load, but also can moni- tor the pressure, displacement and stress at each lifting point. The performance of the multi-cylinder synchronous system is verified through its application to several bridge lifting engineering projects. The details of such a project are given.

关键词： synchronous lifting of a bridge multi-cylinder synchronization distributed control system

The Ephemeral 10β-OH Trifluoromethanesulfonates of 7-Epi Paclitaxel Analogs─A New Example for Anchimeric Assistance

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Chinese Chemical Letters 1998年第1期9卷 29-33页

作者： Wei Shuo FANG Qi cheng FANG and xiao Tian liang (Institute of Materia Medica, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100050 ) Chinese Acad Med Sci Inst Mat Med Beijing 100050 Peoples R China Peking Union Med Coll Beijing 100050 Peoples R China

Two rearranged products, dienone 4 and 10-oxo product 5 were obtained upon attempted 10β-OSO2SO2CF3 formation from 3. The formation of compound 5 can be explained by anchimeric assistance of 7α-OH. Reduction of 4 ... 详细信息

关键词： rearrange anchimeric assistance neighboring group participation

Preliminary Studies on Acylation of 10β-OH and 7α-OH in 7-Epi-10-deacetylpaclitaxel

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Chinese Chemical Letters 1997年第10期8卷 847-848页

作者： Wei Shuo FANG Qi cheng FANG and xiao Tian liang (Institute of Materia Medica , Chinese Academy of Medical Sciences & Peking Union Medical College.Beijing 100050) CHINESE ACAD MED SCI INST MAT MEDBEIJING 100050PEOPLES R CHINA BEIJING UNION MED COLL BEIJING 100050PEOPLES R CHINA

10β-OH can be acylated cleanly when 7α-OH is also free, and thus a facile access to semisynthesis of 7-epi-paclitaxel was proposed. A 2's, 3's-oxazoline paclitaxel analog was serendipitously synthesized

关键词： OH in 7-Epi-10-deacetylpaclitaxel TES Preliminary Studies on Acylation of 10