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

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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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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DOUBLE-MARKOV RISK MODEL

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Acta Mathematica Scientia 2013年第2期33卷 333-340页

作者：莫晓云周杰明欧辉杨向群 College of Mathematics and Computer Science Hunan Normal University Hunan University of Finance and Economics College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Education Ministry of China)Hunan Normal University

Given a new Double-Markov risk model DM = （μ, Q, v, H; Y, Z） and Double-Markov risk process U = {U（t）, t 〉 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.

关键词： Q process Markov chain Double-Markov risk characterization survival prob-ability recursion formula

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Local L^(2) theory of the fractional Navier-Stokes equations and the self-similar solution

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Science China mathematics 2023年第3期66卷 503-570页

作者： Baishun Lai Jingyue Li Xiaoxin Zheng Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematical Sciences Beihang UniversityBeijing 100191China

This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is *** particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the local regularity of the non-local Stokes operator. Secondly, as an important application to the local L^(2)theory, we give a second construction of large self-similar solutions of the hypo-dissipative Navier-Stokes system along with the Leray-Schauder degree theory.

关键词： local energy weak solution self-similar solution Leray-Schauder degree theory

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The Spectrality of a Class of Fractal Measures on R^(n)

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Acta Mathematica Sinica,English Series 2023年第5期39卷 952-966页

作者： Jing Cheng LIU Zhi Yong WANG Yao LIU Ya SHI Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081P.R.China School of Mathematics and Statistics Hunan First Normal UniversityChangsha 410205P.R.China

Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by ***)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are ***,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.

关键词： Fractal spectral measure orthogonal exponentials Fourier transform spectrum

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MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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Acta Mathematica Scientia 2024年第4期44卷 1594-1608页

作者： Lulu FANG Jihua MA Kunkun SONG Xin YANG School of Mathematics and Statistics Nanjing University of Science and TechnologyNanjing210094China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction *** study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial *** a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

关键词： continued fractions product of partial quotients Hausdorff dimension

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On n-Coherent Rings and （n, d）-Injective Modules

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Algebra Colloquium 2015年第2期22卷 349-360页

作者： Dongdong Zhang Baiyu Ouyang Department of Mathematics Zhejiang Normal University Jinhua Zhejiang 321004 China Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) College of Mathematics and Computer Science Hunan Normal University Changsha Hunan 410081 China

Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.

关键词： (n d)-injective left R-module (n d)-flat right R-module left n-coherent ring

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TIME-EXTRAPOLATION ALGORITHM （TEA） FOR LINEAR PARABOLIC PROBLEMS

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Journal of Computational mathematics 2014年第2期32卷 183-194页

作者： Hongling Hu Chuanmiao Chen Kejia Pan 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 Changsha 410081 China School of Mathematics and Statistics Central South University Changsha 410083 China

The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.

关键词： Parabolic problem Crank-Nicolson scheme Error estimates Time-extrapolationalgorithm CG-iteration.

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A Total Variation Based Method for Multivariate Time Series Segmentation

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Advances in Applied mathematics and Mechanics 2023年第2期15卷 300-321页

作者： Min Li Yumei Huang Youwei Wen School of Mathematics and Statistics Center for Data ScienceLanzhou UniversityLanzhouGansu 730000China School of Mathematics and Statistics Hunan Normal UniversityChangshaHunan 410081China and Key Laboratory of Computing and Stochastic Mathematics(LCSM)Ministry of Education of China

Multivariate time series segmentation is an important problem in data mining and it has arisen in more and more practical applications in recent *** task of time series segmentation is to partition a time series into segments by detecting the abrupt changes or anomalies in the time *** time series segmentation can provide meaningful information for further data analysis,prediction and policy decision.A time series can be considered as a piecewise continuous function,it is natural to take its total variation norm as a prior information of this time *** this paper,by minimizing the negative log-likelihood function of a time series,we propose a total variation based model for multivariate time series *** iterative process is applied to solve the proposed model and a search combined the dynamic programming method is designed to determine the *** experimental results show that the proposed method is efficient for multivariate time series segmentation and it is competitive to the existing methods for multivariate time series segmentation.

关键词： Multivariate time series segmentation total variation dynamic programming

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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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