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作者： Huang, Yunqing Li, Jichun Yang, Wei Hunan Key Laboratory for Computation and Simulation in Science Engineering Xiangtan University Hunan 411105 China Department of Mathematical Sciences University of Nevada Las Vegas Las Vegas NV 89154-4020 United States

We investigate the well-posedness of a perfectly matched layer model developed by Cohen and Monk [Comput Methods Appl Mech Eng 1.9 (1.99), 1.7-21.]. A new time-domain finite element method is proposed to solve the model. A novel feature of the scheme is that the number of unknowns is reduced to two from four in the original form. The scheme's effectiveness is demonstrated through numerical experiments. © 201. Wiley Periodicals, Inc.

关键词： Maxwell equations

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Protein folding kinetic order prediction from amino acid sequence based on horizontal visibility network

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Current Bioinformatics 2016年第2期11卷 173-185页

作者： Zhao, Zhi-Qin Yu, Zu-Guo Anh, Vo Wu, Jing-Yang Han, Guo-Sheng Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University XiangtanHunan411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQ4001 Australia School of Science Xi’an Shiyou University 18 Second Dianzi Road Yanta District Xi’anShaanxi710065 China

Protein folding is one of the most important problems in molecular biology. The kinetic order of protein folding is one of the main aspects of the folding process. Previous methods for predicting protein folding kinetic order require to use the information on tertiary or predicted secondary structure of a protein. In this paper, based on physicochemical properties of amino acids, we propose an approach to predict the protein folding kinetic order from the primary structure of a protein using support vector machine combined with principal component analysis. The horizontal visibility network, Hilbert-Huang transform, global descriptor, and Lempel-Ziv complexity are used to extract features in our approach. To evaluate our approach, the leave-one-out cross-validation test is employed on two widely-used data sets ("IvankovData" and "ZhengData" data sets) consisting of two-state and multi-state proteins. The overall accuracies of prediction can reach 83.87% for "IvankovData" data set and 85% for "ZhengData" data set respectively. Comparisons with the existing methods show that the present approach performs better on the "IvankovData" data set. These results indicate that the present approach is effective and valuable for predicting protein folding kinetic order. Based on factor analysis, we find that the length of protein sequence, hydrophobicity and hydrophilicity of amino acids are important features in our approach. © 201. Bentham science Publishers

关键词： Hilbert-Huang transform

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Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions

Spectral collocation method for a class of fractional diffus...

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作者： Wang, Junjie Xiao, Aiguo Bu, Weiping Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory for Intelligent Computing and Information Processing of Education Ministry Xiangtan University Hunan China School of Mathematics and Statistics Pu'er University Yunnan China

In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end-points, it can not be well approximated by classical polynomial basis functions. We first give nonclassical interpolants based on the associated Jacobi-Gauss points and obtain the corresponding fractional differentiation matrices. Second, we prove the convergence for the developed spectral collocation method. Finally, several numerical examples are considered to demonstrate the validity and applicability of the developed basis functions. © 2020 John Wiley & Sons, Ltd.

关键词： Polynomials

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Hybrid Allen-Cahn-based lattice Boltzmann model for incompressible two-phase flows: The reduction of numerical dispersion

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Physical Review E 2019年第2期99卷 023302-023302页

作者： Yang Hu Decai Li Licong Jin Xiaodong Niu Shi Shu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 People's Republic of China

In this work a phase field-lattice Boltzmann model for incompressible two-phase flows is presented. In this model, the interface tracking equation is a linear combination of the local and nonlocal Allen-Cahn equations. We also propose a multiple-relaxation-time lattice Boltzmann model for solving the hybrid Allen-Cahn equation. The second-order convergence rate of the present model in space is validated by simulating the diagonal translation of circular interface. Three other numerical tests, including static bubble immersed in another fluid, bubble rising under gravity, and droplet splashing on a thin liquid film, are simulated to verify the performance of the present model in reducing the numerical dispersion. The numerical results indicate that the order parameter fluctuation can be reduced by one order of magnitude in bulk region.

关键词： Multiphase flows Lattice-Boltzmann methods

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Two classes of implicit–explicit multistep methods for nonlinear stiff initial-value problems

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Applied Mathematics and computation 2014年 247卷 47-60页

作者： Aiguo Xiao Gengen Zhang Xing Yi School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China

The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit–explicit (IMEX) methods are often applied to these problems, i.e. the stiff and non-stiff terms are discretized by using implicit and explicit methods, respectively. In this paper, we mainly consider the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, and present two classes of the IMEX multistep methods by combining implicit one-leg methods with explicit linear multistep methods and explicit one-leg methods, respectively. The order conditions and the convergence results of these methods are obtained. Some efficient methods are constructed. Some numerical examples are given to verify the validity of the obtained theoretical results.

关键词： Stiff problems Singular perturbation problems Implicit–explicit multistep methods One-leg methods Linear multistep methods Convergence

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High time resolution observation and statistical analysis of atmospheric light extinction properties and the chemical speciation of fine particulates

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science China Chemistry 2010年第8期53卷 1801-1808页

作者： YAO TingTing1.HUANG XiaoFeng1.HE LingYan1.HU Min2,SUN TianLe1.XUE Lian1.LIN Yun1.ZENG LiWu1.& ZHANG YuanHang2 1.0} {1. for Urban Habitat Environmental science and Technology,School of Environment and Energy,Peking University Shenzhen Graduate School,Shenzhen 51.055,China 2State key Joint {1. of Environmental simulation and Pollution Control College of Environmental sciences and engineering,Peking University,Beijing 1.0871.China 1. Key Laboratory for Urban Habitat Environmental Science and Technology School of Environment and Energy Peking University Shenzhen Graduate School Shenzhen 518055 China2. State Key Joint Laboratory of Environmental Simulation and Pollution Control College of Environmental Sciences and Engineering Peking University Beijing 100871 China

In recent years,the visibility deterioration caused by regional fine particulate pollution becomes one of the crucial air pollution problems in the urban areas of our *** rapid variation of visibility and fine particulates make it difficult to estimate the relationship between them precisely and accurately unless high time resolution observation data can be *** study aims to fill this gap in the field of atmospheric science by establishing a formula using multiple linear *** fitting goodness (R2=0.91.,n=31.7) was obtained using 1. min average of high-resolution real-time light scattering coefficients,light absorption coefficients,main chemical speciation concentration in PM1.and some meteorological parameters from 1. Jan to 1. Feb,*** shows that the average light extinction coefficient during the observation in the winter of Shenzhen was measured to be 290 ± 1.3 Mm?1.consisting of 72% of light scattering and 21. of *** terms of the percentage contribution of PM1.chemical species to the total light extinction,the organic matter was estimated to be most with an average of 45%,followed by ammonium sulfate with an average of 24%.The contributions of black carbon and ammonium nitrate were 1.% and 1.%,***,the diurnal variation of light extinction was investigated as well in this study.

关键词： light extinction PM1 chemical speciation high time resolution multiple linear regressions

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Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method

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Applied Mathematics 2013年第1期4卷 113-118页

作者： Yin Yang College of Civil Engineering and Mechanics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.

关键词： Legendre Pseudo-Spectral Method Multi-Order Fractional Differential Equations Caputo Derivative

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Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes

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Numerical Mathematics(Theory,Methods and Applications) 2024年第1期17卷 210-242页

作者： Yu Xiong Yanping Chen Jianwei Zhou Qin Liang School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China School of Mathematics and Statistics Linyi University Linyi 276005P.R.China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal *** virtual element method is H1.conforming and exact *** virtue of these properties and the topological degree argument,we rigorously prove the well-posedness of the proposed discrete *** con-vergence analysis is carried out,which imply that the error estimate for the velocity in energy norm does not explicitly depend on the *** experiments on various polygonal meshes validate the accuracy of the theoretical analysis and the asymptotic pressure robustness of the proposed scheme.

关键词： Optimal error estimates divergence-free virtual element nonlinear damping term.

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Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

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Frontiers of Mathematics in China 2012年第3期7卷 397-413页

作者： Yanping CHEN Zuliang LU Ruyi GUO School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China College of Civil Engineering and Mechanics Xiangtan UniversityXiangtan 411105China School of Mathematics and Statistics China Three Gorges UniversityChongqing 404000China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105China

The goal of this paper is to study a mixed finite element approximation of the general convex optimal control problems governed by quasilinear elliptic partial differential equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a priori error estimates both for the state variables and the control variable. Finally, some numerical examples are given to demonstrate the theoretical results.

关键词： A priori error estimate quasilinear elliptic equation generalconvex optimal control problem triangular mixed finite element method

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A Posteriori Error Estimates for hp Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 469-493页

作者： Jinling Zhang Yanping Chen Yunqing Huang Fenglin Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Statistics Xinyang Normal UniversityNo.237 Nanhu RoadShihe DistrictXinyangHenan 464000China

This paper investigates an optimal control problem governed by an elliptic equation with integral control and state *** control problem is approxi-mated by the hp spectral element method with high accuracy and geometricﬂ*** conditions of the continuous and discrete optimal control problems are presented,*** a posteriori error estimates both for the control and state variables are established in *** addition,illustrative numerical examples are carried out to demonstrate the accuracy of theoretical results and the validity of the proposed method.

关键词： Elliptic equations optimal control control-state constraints a posteriori error esti-mates hp spectral element method.

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