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Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

Advances in Applied Mathematics and Mechanics 2015年第6期7卷 796-817页

作者： Jiangxing Wang Ziqing Xie Chuanmiao Chen Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

An implicit discontinuous Galerkin method is introduced to solve the timedomain Maxwell’s equations in *** Maxwell’s equations in metamaterials are represented by integral-differential *** scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal *** fully discrete numerical scheme is proved to be unconditionally *** polynomial of degree at most p is used for spatial approximation,our scheme is verified to converge at a rate of O(τ^(2)+h^(p)+1/2).Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

关键词： Maxwell’s equations metamaterials fully disctete DG method L2-stability L2-error estimate.

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SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

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Acta Mathematica Scientia 2017年第6期37卷 1803-1816页

作者：孔凡超罗治国 Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China) College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

关键词： solitary wave periodic wave Mawhin＇s continuation theorem time：varyingdelay nonlinear sources

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Generalized Christoffel Functions for Power Orthogonal Polynomials

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 819-832页

作者： Xie TAO Yan LIANG Guangdong Country Garden School College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China)Hunan Normal University

In this paper we extend the Christoffel functions to the case of power orthogonal *** existence and uniqueness as well as some properties are given.

关键词： generalized Christoffel function existence uniqueness gaussian quadrature formula Christoffel number

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EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

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Acta Mathematica Scientia 2013年第6期33卷 1639-1651页

作者：周杰明莫晓云欧辉杨向群 College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal University Department of Mathematics Hunan University of Finance and Economics

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

关键词： compound binomial model main claim by-claim dividend random income

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First principles calculation on electronic structure,chemical bonding,elastic and optical properties of novel tungsten triboride

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Journal of Central South University 2014年第2期21卷 500-505页

作者：王一夫夏庆林余燕 Key Laboratory of High Performance Computing and Stochastic Information Processing of Ministry of Education of China (College of Mathematics and Computer Science Hunan Normal University) School of Physics and Electronics Central South University

The electronic structures,chemical bonding,elastic and optical properties of the novel hP24 phase WB3 were investigated by using density-functional theory(DFT) within generalized gradient approximation(GGA).The calculated energy band structures show that the hP24 phase WB3 is metallic *** density of state(DOS) and the partial density of state(PDOS) calculations show that the DOS near the Fermi level is mainly from the W 5d and B 2p *** analysis suggests that the chemical bonding in hP24-WB3 has predominantly covalent characteristics with mixed covalent-ionic *** physical properties,such as lattice constant,bulk modulus,shear modulus and elastic constants Cij were *** elastic modulus E and Poisson ratio υ were also *** results show that hP24-WB3 phase is mechanically stable and behaves in a brittle *** analysis of all optical functions reveals that WB3 is a better dielectric material,and reflectivity spectra show that WB3 can be promised as good coating material in the energy regions of 8.5-11.4 eV and 14.5-15.5 eV.

关键词： hP24-WB3 first principles calculation electronic structure chemical bonding elastic properties optical properties

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DTCWT-based zinc fast roughing working condition identification

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Chinese Journal of Chemical Engineering 2018年第8期26卷 1721-1726页

作者： Zhuo He Zhaohui Tang Zhihao Yan Jinping Liu College of Information Science and Enineering Central South University Changsha 410083China Key Laboratory of High Performance Computing and Stochastic Information Processing of Ministry of Education of China College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

The surface texture of mineral flotation froth is well acknowledged as an important index of the flotation *** surface texture feature closely relates to the flotation working conditions and hence can be used as a visual indicator for the zinc fast roughing working condition. A novel working condition identification method based on the dual-tree complex wavelet transform(DTCWT) is proposed for process monitoring of zinc fast ***-level DTCWT is implemented to decompose the froth image into different directions and resolutions in advance, and then the energy parameter of each sub-image is extracted as the froth texture feature. Then, an improved random forest integrated classification(i RFIC) with 10-fold cross-validation model is introduced as the classifier to identify the roughing working condition, which effectively improves the shortcomings of the single model and overcomes the characteristic redundancy but achieves higher generalization performance. Extensive experiments have verified the effectiveness of the proposed method.

关键词： DTCWT Working condition Integrated classification model Zinc fast roughing

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Parseval Frame Wavelet Multipliers in L^2(R^d)

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Chinese Annals of Mathematics,Series B 2012年第6期33卷 949-960页

作者： Zhongyan LI Xianliang SHI College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)Ministry of Education of ChinaHunan Normal Univer-sity Department of Mathematics and Physics North China Electric PowerUniversity

Let A be a d x d real expansive matrix. An A-dilation Parseval frame wavelet is a function φ E n2 （Rd）, such that the set {｜det A｜n/2φ（Ant -l）：n ∈ Z, l∈ Zd} forms a Parseval frame for L2 （Rd）. A measurable function f is called an A-dilation Parseval frame wavelet multiplier if the inverse Fourier transform of fφ is an A-dilation Parseval frame wavelet whenever φ is an A-dilation Parseval frame wavelet, where φ denotes the Fourier transform of φ. In this paper, the authors completely characterize all A-dilation Parseval frame wavelet multipliers for any integral expansive matrix A with ｜ det（A）｜= 2. As an application, the path-connectivity of the set of all A-dilation Parseval frame wavelets with a frame MRA in L2（Rd） is discussed.

关键词： Parseval frame wavelet Wavelet multiplier Frame multiresolutionanalysis

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Pointwise Convergence of Wavelets of Generalized Shannon Type

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Acta Mathematica Sinica,English Series 2013年第12期29卷 2343-2354页

作者： Xian Liang SHI Wei WANG College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China)Hu’nan Normal University School of Sciences Central South University of Forestry and Technology

In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.

关键词： Shannon type wavelet wavelet expansions pointwise convergence

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SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

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Acta Mathematica Scientia 2014年第5期34卷 1357-1376页

作者：汪波谢资清张智民 College of Mathematics and Computer Science and Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) Hunan Normal University Beijing Computational Science Research Center Department of Mathematics Wayne State University

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O？τr＋1＋hk＋1/2？ are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r＋1 in temporal variable t.

关键词： Maxwell equations dispersive media space-time DG method L2-stability L2-error estimate

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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

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Acta Mathematica Scientia 2015年第2期35卷 303-312页

作者：周杰明邓迎春黄娅杨向群 School of Mathematical Sciences Nankai University College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal University College of Business Administration Hunan University

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

关键词： Constant elasticity of variance Hami!ton-Jacobi-Bellman equation jump-diffusion process exponential utility reinsurance

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