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arXiv 2023年

作者： Feng, Fang Yu, Yue School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Xiangtan University Hunan Xiangtan411105 China

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in the penalty term, as well as presents an automated mesh-dependent selection of the penalty parameter. Drawing inspiration from the modified Morley finite element methods, we leverage the conforming interpolation technique to handle the lower part of the bilinear form. Through our analysis, we establish optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case. © 2023, CC BY-NC-ND.

关键词： Numerical methods

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Whole-proteome based phylogenetic tree construction with inter-amino-acid distances and the conditional geometric distribution profiles

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Molecular phylogenetics and evolution 2015年 89卷 37-45页

作者： Xian-Hua Xie Zu-Guo Yu Guo-Sheng Han Wei-Feng Yang Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China School of Mathematics and Computer Science Gannan Normal University Jiangxi 341000 PR China. Electronic address: xxianhua@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: yuzuguo@***. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China. Electronic address: korea10282003@***. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China. Electronic address: yangweifeng09@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: v.anh@qut.edu.au.

There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 29 genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.

关键词： Alignment-free whole-proteome comparison Conditional geometric distribution profile Inter-amino-acid distances Phylogenetic tree

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Exponentially Accurate Rayleigh–Ritz Method for Fractional Variational Problems

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Journal of computational and Nonlinear Dynamics 2015年第5期10卷 051009页

作者： Mao, Zhi Xiao, Aiguo Wang, Dongling Yu, Zuguo Shi, Long Hunan Key Laboratory for Computationand Simulation in Science and Engineering Xiangtan UniversityXiangtan Hunan 411105 China School of Mathematics Northwest UniversityXi’an Shaanxi 710127 China

A high accurate Rayleigh–Ritz method is developed for solving fractional variational problems (FVPs). The Jacobi poly-fractonomials proposed by Zayernouri and Karniadakis (2013, “Fractional Sturm–Liouville Eigen-Problems: Theory and Numerical Approximation,” J. Comput. Phys.,252(1), pp. 495–517.) are chosen as basis functions to approximate the true solutions, and the Rayleigh–Ritz technique is used to reduce FVPs to a system of algebraic equations. This method leads to exponential decay of the errors, which is superior to the existing methods in the literature. The fractional variational errors are discussed. Numerical examples are given to illustrate the exponential convergence of the method.

关键词： Errors Integration methods Algorithms Rayleigh-Ritz methods

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Hamiltonian Boundary Value Methods (HBVMs) for functional differential equations with piecewise continuous arguments

arXiv

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arXiv 2024年

作者： Gurioli, Gianmarco Wang, Weijie Yan, Xiaoqiang Università degli Studi di Firenze Florence Italy School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan411105 China

In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the reference differential equation along the shifted and scaled Legendre polynomial orthonormal basis, working on a suitable extension of Hamiltonian Boundary Value Methods. Within the design of the methods, a proper generalization of the perturbation results coming from the field of ordinary differential equations is considered, with the aim of handling the case of FDEPCAs. The error analysis of the devised family of methods is performed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to give evidence to the theoretical findings and show the effectiveness of the obtained resolution *** Codes 65L05, 65L03, 65L06, 65P10 Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Finite difference and sinc-collocation approximations to a class of fractional diffusion-wave equations

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Journal of Applied Mathematics 2014年第1期2014卷

作者： Mao, Zhi Xiao, Aiguo Yu, Zuguo Shi, Long Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Mathematics and Information Engineering Department Tongren University Tongren Guizhou 554300 China

We propose an efficient numerical method for a class of fractional diffusion-wave equations with the Caputo fractional derivative of order α. This approach is based on the finite difference in time and the global sinc collocation in space. By utilizing the collocation technique and some properties of the sinc functions, the problem is reduced to the solution of a system of linear algebraic equations at each time step. Stability and convergence of the proposed method are rigorously analyzed. The numerical solution is of 3 - α order accuracy in time and exponential rate of convergence in space. Numerical experiments demonstrate the validity of the obtained method and support the obtained theoretical results. © 2014 Zhi Mao et al.

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Cubic spline collocation method for fractional differential equations

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Journal of Applied Mathematics 2013年第1期2013卷

作者： Yang, Shui-Ping Xiao, Ai-Guo Department of Mathematics Huizhou University Guangdong 516007 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105 China

We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence, and the stability of this method for IVPs of FDEs are obtained. Some numerical examples verify our theoretical results. © 2013 Shui-Ping Yang and Ai-Guo Xiao.

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Synthesis of N-confused Porphyrin Derivatives with Substituted 3-C Position

Synthesis of N-confused Porphyrin Derivatives with Substitut...

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中国化学会第八届全国无机化学学术会议

作者： Bin Liu Xiaofang Li Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Hunan Province College Key Laboratory of QSAR/QSPR School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan Hunan 411201China Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Hunan Province College Key Laboratory of QSAR/QSPR School of Chemistry and Chemical Engineering Hunan University of Science

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Hm-CONFORMING VIRTUAL ELEMENTS IN ARBITRARY DIMENSION

arXiv

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arXiv 2021年

作者： Huang, Xuehai Chen, Chunyu Wei, Huayi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics Shanghai University of Finance and Economics Shanghai200433 China

The Hm-conforming virtual elements of any degree k on any shape of polytope in n with m, n ≥ 1 and k ≥ m are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest degree case k = m, the set of degrees of freedom only involves function values and derivatives up to order m − 1 at the vertices of the polytope. The inverse inequality and several norm equivalences for the Hm-conforming virtual elements are rigorously proved. The Hm-conforming virtual elements are then applied to discretize a polyharmonic equation with a lower order term. With the help of the interpolation error estimate and norm equivalences, the optimal error estimates are derived for the Hm-conforming virtual element *** Codes 65N12, 65N15, 65N22, 65N30 Copyright © 2021, The Authors. All rights reserved.

关键词： Degrees of freedom (mechanics)

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An Accurate, Robust and Efficient Convection-Pressure Flux Splitting Scheme for Compressible Euler Flows

SSRN

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SSRN 2023年

作者： Hu, Lijun Tan, Shide Li, Long Yuan, Haizhuan School of Mathematics and Statistics Hengyang Normal University Hunan Hengyang421002 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

The Roe's flux difference splitting scheme has been a popular shock-capturing method in computational fluid dynamics due to its high resolution for various discontinuities. However, it fails to satisfy the entropy condition and will encounter different forms of instability while calculating shock wave problems, such as the occurrence of post-shock oscillation in simulations of slowly moving shock waves and the carbuncle phenomenon in simulations of multidimensional strong shock waves. A simple flux difference splitting scheme based on the idea of convection-pressure splitting is proposed in the present work. The flux of the 3D Euler equations is split into the convection part and the pressure part with application of the Toro-Vazquez splitting procedure. The pressure subsystem has a complete set of linearly independent eigenvectors and thus it is solved by the conventional flux difference splitting method which is based on the eigenstructure of the system. The weakly hyperbolic convection subsystem, however, does not have a complete set of linearly independent eigenvectors and it is solved by the flux difference splitting scheme based on the generalized eigenvectors. In order to improve the resolution for contact discontinuities, a strategy combining the THINC reconstruction with the BVD algorithm is employed to minimize the density difference in the numerical dissipation term of the convection flux. Results of stability analysis show that the proposed scheme can effectively attenuate the numerical error and thus suppress the multidimensional shock instability. A comprehensive range of numerical simulations for classical 1D, 2D and 3D benchmark test problems demonstrate that the proposed scheme satisfies the entropy condition and positivity-preserving, possesses high resolution for contact discontinuities, and, more importantly, is free from the post-shock oscillation of slowly moving shock waves and the instability of multidimensional strong shock waves. © 2023, Th

关键词： Eigenvalues and eigenfunctions

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Correlating the Structure and Optical Absorption Properties of Au76（SR）44 Cluster

Correlating the Structure and Optical Absorption Properties ...

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第九届计算纳米科学与新能源材料国际研讨会

作者： Zhongyun Ma P.Wang G.Zhou J.Tang H.Li Y.Pei Department of Chemistry Key Laboratory of Environmentally Friendly Chemistry and Applications of Ministry of EducationXiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied MathematicsXiangtan University School of Materials Science and Engineering Central South University

The atomic structure of recently synthesized thiolate-protected Au cluster is theoretically predicted via a simple structural rule summarized from the crystal structures of thiolate-protected Au（SR）, Au（SR） and Au（SR） clusters. We find that the Au（SR）（N = 7） and recently reported Au（SR）（N = 4）, Au（SR）（N = 3）, Au（SR）（N = 2） and Au（SR）（N = 1） belong to a family of homologous Au（SR） cluster whose Au-cores follow one-dimensional polytetrahedral growth pathway. The Au（SR） cluster is predicted to contain an anisotropic face-centered cubic（FCC） Au-core, which can be viewed as combination of two helical tetrahedra-Au4 chains and is remarkably different from the well-known spherical Au-core in ligand protected gold clusters in the size region of 1-2 nm. The intense near infrared（NIR） absorption of Au（SR） is attributed to the synergistic effect of anisotropic Au-core structure and ligand protections. A plausible cluster-to-cluster transformation mechanism is further suggested.

关键词： thiolated-protected gold nanocluster Au76SR44 face-centered cubic near infrared adsorption

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