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arXiv 2017年

作者： Yue, Xiaoqiang Xu, Yehong Shu, Shi Liu, Menghuan Bu, Weiping School of Mathematics and Computational Science Xiangtan University Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain Ω. Firstly, a fully discrete scheme is obtained by the linear FE method in both temporal and spatial directions, and many characterizations on the resulting matrix are established. Secondly, the condition number estimation is proved, an adaptive algebraic multigrid (AMG) method is further developed to lessen computational cost and analyzed in the classical framework. Finally, some numerical experiments are implemented to reach the saturation error order in the L2(Ω) norm sense, and present theoretical confirmations and predictable behaviors of the proposed algorithm.35R11, 65F10, 65F15, 65N55 Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity

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AN EFFICIENT NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO DERIVATIVES

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Journal of Computational Mathematics 2016年第2期34卷 113-134页

作者： Shuiping Yang Aiguo Xiao 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

In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 〈β〈 αa 〈 1 are two parameters associated with the fractional differential equations.

关键词： Fractional differential equations Caputo derivatives Spline collocation method Convergence Stability.

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DLTree: efficient and accurate phylogeny reconstruction using the dynamical language method

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Bioinformatics (Oxford, England) 2017年第14期33卷 2214-2215页

作者： Qi Wu Zu-Guo Yu Jianyi Yang Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan China. School of Mathematical Sciences Nankai University Tianjin China.

SUMMARY:A number of alignment-free methods have been proposed for phylogeny reconstruction over the past two decades. But there are some long-standing challenges in these methods, including requirement of huge computer memory and CPU time, and existence of duplicate computations. In this article, we address these challenges with the idea of compressed vector, fingerprint and scalable memory management. With these ideas we developed the DLTree algorithm for efficient implementation of the dynamical language model and whole genome-based phylogenetic analysis. The DLTree algorithm was compared with other alignment-free tools, demonstrating that it is more efficient and accurate for phylogeny reconstruction. AVAILABILITY AND IMPLEMENTATION:The DLTree algorithm is freely available at http://***. CONTACT:yuzuguo@*** or yangjy@***. SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.

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PDϑControl Strategy for a Fractional-Order Chaotic Financial Model

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Complexity 2019年第1期2019卷

作者： Changjin Xu Maoxin Liao Peiluan Li Qimei Xiao Shuai Yuan Guizhou Key Laboratory of Economics System Simulation Guizhou University of Finance and Economics Guiyang 550004 *** School of Mathematics and Physics University of South China Hengyang 421001 *** School of Mathematics and Statistics Henan University of Science and Technology Luoyang 471023 *** Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha 410114 *** School of Mathematics and Statistics Central South University Changsha 410083 ***

In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriate P D ϑ controller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability.

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A novel genome signature based on inter-nucleotide distances profiles for visualization of metagenomic data

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Physica A: Statistical Mechanics and its Applications 2017年 482卷 87-94页

作者： Xian-Hua Xie Zu-Guo Yu Yuan-Lin Ma Guo-Sheng Han Vo Anh 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 Xiangtan Hunan 411105 China Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques Gannan Normal University Jiangxi 341000 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

There has been a growing interest in visualization of metagenomic data. The present study focuses on the visualization of metagenomic data using inter-nucleotide distances profile. We first convert the fragment sequences into inter-nucleotide distances profiles. Then we analyze these profiles by principal component analysis. Finally the principal components are used to obtain the 2-D scattered plot according to their source of species. We name our method as inter-nucleotide distances profiles (INP) method. Our method is evaluated on three benchmark data sets used in previous published papers. Our results demonstrate that the INP method is good, alternative and efficient for visualization of metagenomic data.

关键词： Alignment-free method Inter-nucleotide distance Metagenome Visualization

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Multifractal analysis and topological properties of a new family of weighted Koch networks

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Physica A: Statistical Mechanics and its Applications 2017年 469卷 695-705页

作者： Da-Wen Huang Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c ) in the limit of large generation t ; the second smallest eigenvalue μ 2 and the maximum eigenvalue μ n are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ 2 is approximately a quartic polynomial of c and μ n = 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c . We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

关键词： Weighted Koch networks Modified sandbox algorithm Multifractal analysis Topological property

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Fractal and multifractal analyses of bipartite networks

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Scientific reports 2017年第1期7卷 45588页

作者： Jin-Long Liu Jian Wang Zu-Guo Yu Xian-Hua Xie Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia.

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

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An adaptive BDDC algorithm in variational form for mortar discretizations

arXiv

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arXiv 2017年

作者： Peng, Jie Shu, Shi Wang, Junxian School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problems with high varying and random coefficients. Some vector-valued auxiliary spaces and operators with essential properties are defined to describe the variational algorithm, and the coarse space is formed by using a transformation operator on each interface. Compared with the adaptive BDDC algorithms for conforming Galerkin approximations, our algorithm is more simple, because there is not any continuity constraints at subdomain vertices in the mortar method involved in this paper. The condition number of the preconditioned system is proved to be bounded above by a user-defined tolerance and a constant which is dependent on the maximum number of interfaces per subdomain, and independent of the mesh size and the contrast of the given coefficients. Numerical results show the robustness and efficiency of the algorithm for various model problems.65N30, 65F10, 65N55 Copyright © 2017, The Authors. All rights reserved.

关键词： Number theory

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Efficient Synthesis of Isoquinolines by AgNO3-Catalyzed Sequential Imination-Annulation of 2-Alkynyl Aldehydes with Ammonium Bicarbonate

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Chinese Journal of Chemistry 2016年第9期34卷 857-860页

作者： Yunhui Zhao Mingjian Luo Yubo Li Xiong Liu Zilong Tang Keqin Deng Gang Zhao Hunan Province College Key Laboratory of QSAR/QSPR School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan Hunan 411201 China Key Laboratory of Synthetic Chemistry of Natural Substances Shanghai Institute of Organic Chemistry Chinese Academy of Sciences Shanghai 200032 China Key Laboratory of Theoretical Chemistry and Molecular Simulation Ministry of Education Xiangtan Hunan 411201 China

An operationally simple approach for the tandem synthesis of isoquinolines by the reaction of o-alkynylalde- hydes with ammonium bicarbonate via Ag-catalyzed 6-endo-dig ring closure is described. The reaction conditions and the scope of the reaction are examined, and a variety of substituted isoquinolines are prepared in moderate to excellent yields.

关键词： isoquinolines annulation imination silver nitrate o-alkynyl aldehydes

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Computational design of GeSe/graphene heterojunction based on density functional theory

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Materials Research Express 2018年第3期6卷

作者： Congsheng Xu Jianmei Yuan Dandan Wang Yuliang Mao Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 People's Republic of China Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 People's Republic of China Authors to whom any correspondence should be addressed.

Based on density functional theory, we computational designed the hetero junction composed by GeSe monolayer and graphene. The effects of interlayer coupling, strains and electric fields on the electronic structures of the designed GeSe/graphene (G/g) hetero structure are explored. We demonstrated that both the intrinsic electric properties of the GeSe monolayer and graphene are well preserved in G/g hetero structure. It is found that an energy gap of 0.17 eV in graphene is opened by decreasing the interlayer distance in G/g hetero structure. The height of Schottky barrier can be effectively tuned by the interlayer distance between GeSe monolayer and graphene. Moreover, we found that applying in-plane strains and the electric fields perpendicular to the G/g hetero structure can control the Schottky barriers at the G/g interface. Our results predict that the ultra-thin G/g hetero structure can be used as two-dimensional semiconductor-based optoelectronic devices.

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