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Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science china mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. department of mathematics,Wuhan university,Wuhan 430072.{2. 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational mathematics,Beijing 100088. china 1. department of mathematics Wuhan University 430072 Wuhan China 2. Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

Pairwise entanglement and local polarization of Heisenberg model

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Science china(Physics,Mechanics & Astronomy) 2008年第10期51卷 1515-1522页

作者： xi xiaoQiang1,2. ZHANG Tao3, YUE RuiHong3,4 & LIU WuMing2.1 {2. of Applied mathematics and Physics, xi’an Institute of Post and Telecommunications, xi’an 710061, china 2.Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, china 3 Institute of Modern Physics, northwest university, xi’an 710069, china 4 {2. of Physics, Ningbo {12., Ningbo 3152.1, china department of Applied mathematics and Physics Xi’an Institute of Post and Telecommunications Xi’an 710061 China Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing 100080 China Institute of Modern Physics Northwest University Xi’an 710069 China department of Physics Ningbo University Ningbo 315211 China

The characteristics of pairwise entanglement and local polarization (LP) are dis-cussed by studying the ground state (states) of the Heisenberg XX model. The re-sults show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2.for odd qubit); LP and the prob-ability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412.(for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.

关键词： Heisenberg XX model local polarization pairwise entanglement

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing university, Beijing,{2.) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2.. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词： Biharmonic equations Convergent boundaries Shape functions Vertices Interpolation Weighting functions Integers

Homological Transfer between Additive Categories and Higher Differential Additive Categories

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1325-1344页

作者： xi TANG Zhao Yong HUANG School of Science Guilin University of Aerospace TechnologyGuilin 541004P.R.China department of mathematics Nanjing UniversityNanjing 210093P.R.China

Given an additive category C and an integer n≥*** higher differential additive category consists of objects X in C equipped with an endomorphism ϵ_(X)satisfying ϵ_(X)^(n).Let R be a,finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(t^(n))-*** is proved that a finitely generated left R-module M isτ-rigid(respectively,(support)τ-tilting,almost completeτ-tilting)if and only if so is T(M)as a left R[t]/(t^(n))-***,R isτm-selfinjective if and only if so is R[t]/(t^(n)).

关键词： Higher differential objects Wakamatsu tilting subcategories G_(ω)-projective modules sup-portτ-tilting modules τ_(m)-selfinjective algebras precluster tilting subcategories

Northernmost paleo-tethyan oceanic basin in Tibet:Geo-chronological evidence from ^(40)Ar/^(39)Ar age dating of Dur'ngoi ophiolite

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Chinese Science Bulletin 2001年第14期46卷 1203-1205页

作者： CHEN Liang, SUN Yong, PEI xianzhi, GAO Ming, FENG Tao, ZHANG Zhongqing & CHEN Wen1. Laboratory of Continental Dynamics, northwest university, xi’an 710069, china 2. department of Geology, northwest university, xi’an, 710069, china 3. Institute of Geology, Chinese Academy of Geological Sciences, Beijing, 100037, china Laboratory of Continental Dynamics Northwest University Xi’an China department of Geology Northwest University Xi’an China Institute of Geology Chinese Academy of Geological Sciences Beijing China

Whole rock 40Ar/39Ar age dating has been conducted on a basalt sample from Dur’ngoi ophiolite, Qinghai Province, which was reported to be the northernmost pa-leo-tethyan oceanic basin in Tibet. A high temperature pla-teau age (345.3±7.9 Ma) with an isochorn age (336.6±7.1 Ma) has been obtained, representing the eruption time of oceanic crust Considering related geological settings, the new age provides constraints on the northernmost pa-leo-tethyan suture zone in Tibet and the tectonic evolution of Paleo-tethys in Northeast Tibet and adjacent areas.

关键词： Dur’ngoi ophlolite 40Ar -39Ar age Paleo-tethys.

Geometric Parameters Corresponding to Representations of the Classical Groups with Integral Infinitesimal Characters

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Acta Mathematica Sinica,English Series 1996年第3期12卷 268-284页

作者： Hou Zixin, department of mathematics Nankai {2. Tianjin, 300071 chinaZhao Qiang, department of mathematics Peking {2. Beijing, 100871 china and department of mathematics northwest Normal {2. Lanzhou, 730070 china department of mathematics Nankai University Tianjin China department of mathematics Peking University Beijing China department of mathematics Northwest Normal University Lanzhou China

In this paper we calculate the orbits of flag manifolds of the complex classical groups under the action of the sets of fixed points of Cartan involutions, and determine all the geometric parameters corresponding to representations of the classical groups with integral infinitesimal char- acters, which are used to discuss Arthur conjecture and the Langlands classification of the irreducible admissible representations of real classical groups(see[1])

关键词： Extended groups Strong real forms E-groups Geometric parameters

Two applications of generalized Carleson measures to meromorphic Besov-type spaces

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Chinese Science Bulletin 1998年第15期43卷 1260-1264页

作者： TAN Haiou 1 and xiAO Jie 2.1. department of mathematics, Wuyi {2., Jiangmen 52.02., china 2. School of Mathematical Sciences, Peking {2., Beijing 100871, china department of mathematics Wuyi University Jiangmen China School of Mathematical Sciences Peking University Beijing China

The generalized Carleson measures are used to characterize the meromorphic Besov_type spaces and to explore some inclusions between these spaces.

关键词： generalized Carleson measures meromorphic Besov_type spaces.

Biorthogonal multiple wavelets generated by vector refinement equation

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Science china mathematics 2007年第7期50卷 1015-1025页

作者： Song LI~(1+) Jun xiAN~2.1 department of mathematics,Zhejiang {2.,Hangzhou 31002.,china 2.department of mathematics,Sun Yat-Sen {2.,Guangzhou 5102.5,china 1. department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Sun Yat-Sen University Guangzhou 510275 China

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2.(\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

关键词： refinement equation biorthogonal multiple wavelets refinable function vector 42.40 41A10 41A15 41A2.

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2.& DING NanQing3 1department of mathematics, Zhejiang university, Zhejiang 31002.,{2. 2.0}, Zhejiang university of Technology, Zhejiang 31002.,{2. 3department of mathematics, Nanjing university, Nanjing 2.0093,{2. 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module