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TWO-GRID ALGORITHM OF H^(1)-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of computational Mathematics 2022年第5期40卷 667-685页

作者： Tianliang Hou Chunmei Liu Chunlei Dai Luoping Chen Yin Yang School of Mathematics and Statistics Beihua UniversityJilin 132013China College of Science Hunan University of Science and EngineeringYongzhou 425199China School of Mathematics Southwest Jiaotong UniversityChengdu 611756China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element *** use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal ***,a priori error estimates and some superclose properties are ***,a two-grid scheme is presented and its convergence is *** the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal ***,a numerical experiment is implemented to verify theoretical results of the proposed *** theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).

关键词： Semilinear parabolic integro-differential equations H^(1)-Galerkin mixed finite element method A priori error estimates Two-grid Superclose.

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Crystal structures and theoretical investigation of anti-/syn-2,4-diphenylpentane-and 2,4-di-p-tolylpentane-2,4-diols

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Journal of Central South University 2012年第5期19卷 1219-1225页

作者：焦银春曹晨忠赵小林 School of Chemistry and Chemical Engineering Central South University School of Chemistry and Chemical Engineering Hunan University of Science and Technology Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Hunan University of Science and Technology

2,4-diphenylpentane- and 2,4-di-p-tolylpentane-2,4-diols were investigated employing experimental and density functional theory （DFT） method at B3LYP/6-31G （d） level. The structure of syn-2,4-di-p-tolylpentane-2,4-diol （2b） was characterized by X-ray diffraction and compared with the crystal structures of anti- and syn-2,4-diphenylpentane-2,4-diols （la and lb）. X-ray diffraction indicates that inter and intra-molecular hydrogen bonds are formed in the crystal structures. There is n-n staking interaction in lb and 2b. Good linear correlations and similar results are found between the experimental 1H and 13C NMR chemical shifts （6~exp） and GIAO （Gauge Independent Atomic Orbital） method calculated magnetic isotropic shielding tensors （acalc）. HOMO and LUMO molecular orbitals were calculated at the same levels with the different results. UV-vis absorption spectra of the compounds were recorded in EtOH, MeCN, n-BuOH and cyclohexane with different dielectric constants. It is found that the solvent effect is obvious when e is 24.85（EtOH）, 35.69（MeCN） and it is weak when e is decreased to 17.33（n-BuOH）, 1.18 （cyclohexane）.

关键词： X-ray crystallography hydrogen bonds nuclear magnetic resonance （NMR） density function theory （DFT） UV-visabsorption solvent effect

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Secondary structure element alignment kernel method for prediction of protein structural classes

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Current Bioinformatics 2014年第3期9卷 253-257页

作者： Han, Guo-Sheng Yu, Zu-Guo Anh, Vo 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 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q 4001 Australia

In this paper, we aim at predicting protein structural classes for low-homology data sets based on predicted secondary structures. We propose a new and simple kernel method, named as SSEAKSVM, to predict protein structural classes. The secondary structures of all protein sequences are obtained by using the tool PSIPRED and then a linear kernel on the basis of secondary structure element alignment scores is constructed for training a support vector machine classifier without parameter adjusting. Our method SSEAKSVM was evaluated on two low-homology datasets 25PDB and 1189 with sequence homology being 25% and 40%, respectively. The jackknife test is used to test and compare our method with other existing methods. The overall accuracies on these two data sets are 86.3% and 84.5%, respectively, which are higher than those obtained by other existing methods. Especially, our method achieves higher accuracies (88.1% and 88.5%) for differentiating the α+ β class and the α/β class compared to other methods. This suggests that our method is valuable to predict protein structural classes particularly for low-homology protein sequences. The source code of the method in this paper can be downloaded at http://***/myphp/math/research/source/SSEAK_source_***. © 2014 Bentham science Publishers.

关键词： Support vector machines

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Space-time finite element adaptive AMG for multi-term time fractional advection diffusion equations

Space-time finite element adaptive AMG for multi-term time f...

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

In this study, we construct a space-time 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 associated condition number estimation (Formula presented.) is derived, where τn and h, respectively, are the current time and space step sizes. Next, we propose a lossless in robustness and adaptive algebraic multigrid (AMG) with (Formula presented.) computational cost and (Formula presented.) matrix-free storage, in contrast to classical AMG with (Formula presented.), where M is the number of spatial segments. Meanwhile, uniform convergence analyses on the two-level V(0,1)-cycle of classical and adaptive AMGs are provided. Finally, we demonstrate the optimal error order of space-time FE approximations in the L2(Ω) norm sense, present theoretical confirmations and predictable behaviors of the proposed algorithm in numerical experiments. © 2019 John Wiley & Sons, Ltd.

关键词： Matrix algebra

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IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

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Journal of computational Mathematics 2021年第4期39卷 599-620页

作者： Bin Huang Aiguo Xiao Gengen Zhang School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta ***,the general order conditions up to order 3 are ***,for the nonlinear sti initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems,the corresponding errors of the implicit-explicit methods are *** last,some numerical examples are given to verify the validity of the obtained theoretical results and the e ectiveness of the methods.

关键词： Sti di erential equations Implicit-explicit Runge-Kutta-Rosenbrock method Order conditions Convergence

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Novel nanoporous palladium catalyst for electroreduction of hydrogen peroxide

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Rare Metals 2011年第4期30卷 332-336页

作者： YI Qingfeng NIU Fengjuan School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan 411201 China Key Laboratory of Theoretical Chemistry and Molecular Simulation （Ministry of Education of China） Hunan University of Science and Technology Xiangtan 411201 China

Titanium-supported nanoporous palladium catalyst （Pd/Ti） was prepared by a hydrothermal method using PdC12 as a precursor, ethylenediamine tetraacetic acid （EDTA） as a ligand, and formaldehyde as a reduction agent. Complex Pd-EDTA^2- is favorable for the formation of Pd particles with nanoscale sizes. The electroactivity of the Pd/Ti catalyst towards the electroreduction of hydrogen peroxide in 1 mol/L NaOH solution was evaluated by voltammetric techniques. Both linear scan voltammetric and chronoamperometric data present significantly large steady-state reduction current density of the hydrogen peroxide electroreduction on the prepared Pd/Ti catalyst. The results show that the prepared Pd/Ti catalyst is an effective electrocatalyst for the electroreduction of hydrogen peroxide in alkaline media.

关键词： electrocatalysis nanoporous materials palladium hydrogen peroxide fuel cells

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Boosting catalytic oxidation of H₂S over activated carbon optimized by the synergistic effect of rich defects and nitrogen sites

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Surfaces and Interfaces 2025年 68卷

作者： Liu, Xin Zhao, Minghui Liu, Dongxu Yang, Jianxiao Han, Yinghui Sultana, Rabia Mohamed, Yasser M.A. Nazer, Hossam A.El Elnazer, Ahmed A. Zhang, Xin College of Ecology and Environment Nanjing Forestry University Nanjing 210037 China College of Resources and Environment University of Chinese Academy of Sciences Beijing 101408 China Hunan Province Key Laboratory for Advanced Carbon Materials and Applied Technology College of Materials Science and Engineering Hunan University Changsha 410082 China State Key Joint Laboratory of Environment Simulation and Pollution Control Research Center for Eco-Environmental Sciences Chinese Academy of Sciences Beijing 100085 China Photochemistry Department National Research Centre Dokki Giza 12622 Egypt Geological Sciences Department National Research Centre Dokki Giza 12622 Egypt

H2S selective catalytic oxidation has been considered as the most efficient method for the removal of residual H2S in Claus tail gas. Carbon materials were regarded as a promising candidate for the reaction. However, ... 详细信息

H₂S selective catalytic oxidation has been considered as the most efficient method for the removal of residual H₂S in Claus tail gas. Carbon materials were regarded as a promising candidate for the reaction. However, its performance was rather poor. This study implemented an approach to enhance the catalytic performance of activated carbon catalysts through the synergy effect of rich defects and nitrogen species. The addition of phenanthroline, a nitrogen-containing compound increased the nitrogen content in the carbon framework, and annealing under an NH₃ atmosphere generated abundant surface defects. The pyridinic nitrogen species and defects facilitated the adsorption of H₂S. Moreover, the defects can also promote the generation of superoxide radicals, further resulting in the production of SO₂ and improving the catalytic performance through the Claus reaction. The best catalytic performance was achieved with the C-N-5 catalyst, and the sulfur yield was maintained higher than 95 % even at 220 °C. Furthermore, the oxygen-containing groups on the surface of carbon materials were the reactive oxygen species and the reaction obeyed the MvK mechanism, i.e., the adsorbed H₂S reacted with the oxygen-containing groups to form elemental sulfur, while the consumed oxygen-containing groups were regenerated by molecular oxygen. © 2025

关键词： Activated carbon Defects H2S catalytic oxidation Nitrogen doping Reaction mechanism

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An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation

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Communications in computational Physics 2014年第7期16卷 491-515页

作者： Peimeng Yin Yunqing Huang Hailiang Liu Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105P.R.China Iowa State University Mathematics DepartmentAmesIA 50011USA.

An iterative discontinuous Galerkin(DG)method is proposed to solve the nonlinear Poisson Boltzmann(PB)*** first identify a function space inwhich the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations,while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution *** the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB *** precisely,we use one initial guess when the Debye parameter l=O(1),and a special initial guess for l≪1 to ensure *** iterative parameter is carefully chosen to guarantee the existence,uniqueness,and convergence of the *** particular,iteration steps can be reduced for a variable iterative *** one and two-dimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases of l=O(1)and l≪***(m+1)th order of accuracy for L2 and mth order of accuracy for H1 for Pm elements are numerically obtained.

关键词： Poisson-Boltzmann equation nonlinear existence uniqueness DDG methods numerical flux.

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Analytical solutions for Earth discontinuous coverage of satellite constellation with repeating ground tracks

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Chinese Journal of Aeronautics 2022年第10期35卷 275-291页

作者： Xiangyue HE Haiyang LI College of Aerospace Science and Engineering National University of Defense TechnologyChangsha 410073China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha 410073China

This paper presents an analytical model for calculating the Earth discontinuous coverage of satellite constellation with repeating ground tracks by integrating and extending the application of coverage region and route ***,the visibility condition for a ground point is represented as a coverage region in the two-dimension map of visibility properties,and the trajectories of satellites with circular orbits and repeating ground tracks are converted to several inclined lines in the *** analyzing the intersections of the lines and the edge of the coverage region,the coverage durations for the ground point can be *** on the point coverage,the variations of coverage characteristics along the parallel are analyzed,and the regional or global coverage characteristics of constellations can be *** examples show that the proposed method can accurately and rapidly calculate the coverage characteristics,*** time and coverage *** calculated results are extremely close to those of the Satellite Tool Kit(STK)and are also superior to the existing research *** proposed analytical model can be a useful tool for constellation design and coverage performance analysis.

关键词： Analytical model Coverage region Earth discontinuous coverage Repeating ground track Satellite constellation Two-dimension map of visibility properties

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Discovery of New Metastable Patterns in Diblock Copolymers

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Communications in computational Physics 2013年第7期14卷 443-460页

作者： Kai Jiang Chu Wang Yunqing Huang Pingwen Zhang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871P.R.China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105P.R.China

The ordered patterns formed bymicrophase-separated block copolymer systems demonstrate periodic symmetry,and all periodic structures belong to one of 230 space *** on this fact,a strategy of estimating the initial values of self-consistent field theory to discover ordered patterns of block copolymers is *** particular,the initial period of the computational box is estimated by the Landau-Brazovskii model as *** planting the strategy into the whole-space discrete method,several new metastable patterns are discovered in diblock copolymers.

关键词： Metastable patterns diblock copolymers self-consistent field theory(SCFT) space group theory initial values

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