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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2.& ZHOU Heng 1,2.1. department of Mechanics, Tianjin university, Tianjin 300072. {2. 2. Liu-Hui Center of Applied mathematics, Nankai university and Tianjin university, Tianjin 300072. {2. department of Mechanics Tianjin University Tianjin China Liu-Hui Center of Applied mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

Commission Strategy of the Auction House

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Wuhan university Journal of Natural Sciences 2006年第3期11卷 507-510页

作者： WANG Yan~ 1,2.1. College of Economics, Fudan university, shanghai 2.0433, {2. 2. School of mathematics and Statistics, Wuhan university , Wuhan 430072. Hubei, {2. College of Economics Fudan University Shanghai China School of mathematics and Statistics Wuhan University Wuhan Hubei China

In a SIPV model, when the commission proportion is not certain, but related with bargain price, generally, it is a linear function of the bargain price, this paper gives bidders＇ equilibrium bidding strategies in the first-and secondprice auctions. We find that the equilibrium strategies in second-price auction are dominant strategies. For seller or auction house, whether the fixed proportion or the unfixed proportion is good is not only related with constant item and the linear coefficient of the linear function, the size of the fixed commission proportion, but also related with the value of the item auctioned. So, in the practical auctions, the seller and the auction house negotiated with each other to decide the commission rules for their own advantage.

关键词： auction commission proportion Bayesian equilibrium bidding strategy

A new sieve for distinct coordinate counting

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Science china mathematics 2010年第9期53卷 2351-2362页

作者： LI JiYou1 & WAN DaQing2.1department of mathematics,{2. Jiao Tong university,{2. 2.02.0,china 2.0} of mathematics,university of California,Irvine,CA 92.97-3875,USA department of mathematics Shanghai Jiao Tong University Shanghai China department of mathematics University of California Irvine USA

We present a new sieve for the distinct coordinate counting *** significantly improves the classical inclusion-exclusion sieve for this problem,in the sense that the number of terms is reduced from 2.k 2. to k!,and reduced further to p(k) in the symmetric case,where p(k) denotes the number of partitions of *** an illustration of applications,we give an in-depth study of a basic example arising from coding theory and graph theory.

关键词： sieve distinct coordinate counting

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china 2. department of mathematics, Beijing Normal {2., Beijing 100875, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

An interpolating boundary element-free method (IBEFM) for elasticity problems

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 758-766页

作者： REN HongPing 1 , CHENG YuMin 2.& ZHANG Wu 1 1 School of Computer Engineering and Science, shanghai university, shanghai 2.0072. china 2.shanghai Institute of Applied mathematics and Mechanics, shanghai university, shanghai 2.0072. china School of Computer Engineering and Science Shanghai University Shanghai China shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai China

The paper begins by discussing the interpolating moving least-squares (IMLS) method. Then the formulae of the IMLS method obtained by Lancaster are revised. On the basis of the boundary element-free method (BEFM), combining the boundary integral equation method with the IMLS method improved in this paper, the interpolating boundary element-free method (IBEFM) for two-dimensional elasticity problems is presented, and the corresponding formulae of the IBEFM for two-dimensional elasticity problems are obtained. In the IMLS method in this paper, the shape function satisfies the property of Kronecker δ function, and then in the IBEFM the boundary conditions can be applied directly and easily. The IBEFM is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution to the nodal variables. Thus it gives a greater computational precision. Numerical examples are presented to demonstrate the method.

关键词： moving least-squares (MLS) approximation interpolating moving least-squares (IMLS) method boundary integral equation meshless method boundary element-free method (BEFM) interpolating boundary element-free method (IBEFM) elasticity problem

Codes From Strongly Regular (α,β)-reguli

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Journal of shanghai Jiaotong university(Science) 2008年第4期13卷 491-494页

作者：李秀丽 department of mathematics Shanghai Jiaotong University

Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-regul... 详细信息

关键词： two-weight codes strongly regular (α,β)-reguli

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2.1 Nonlinear Mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contem- porary Applied mathematics School of Mathematical Sciences, Fudan {2., shanghai 2.0433, china. 2.School of Mathematical Sciences, Fudan {2., shanghai 2.0433, china department of mathematics, North {2. of china, Taiyuan 030051, china. Nonlinear Mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contemporary Applied mathematics School of Mathematical Sciences Fudan University Shanghai China School of Mathematical Sciences Fudan University Shanghai China department of mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2.and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992.. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2.∑i=1n δx^^2. is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2. with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

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Acta Mathematica Scientia 2010年第3期30卷 713-725页

作者：曾宪忠刘振海 department of mathematics and Computational Science Hunan University of Science and Technology department of mathematics Central South University

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2.） is its critical exponent provided max{-1, [ （1- m ）n- 2. / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

关键词： Degenerate parabolic equations exterior domains -inhomogeneous dirichlet boundary conditions critical exponent blow-up global existence

Howe duality in Dunkl superspace

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Science china mathematics 2010年第12期53卷 3153-3162页

作者： REN GuangBin 1,2.1 department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china 2.department of mathematics, {2. of Aveiro, Aveiro 3810-193, Portugal department of mathematics University of Science and Technology of China Hefei China department of mathematics University of Aveiro Aveiro Portugal

In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2. on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.

关键词： Dunkl operators superspace Fischer decomposition Dirac operator

Online uniform machine covering with the known largest size

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Progress in Natural Science:Materials International 2007年第11期17卷 1271-1278页

作者： Cao Shunjuan1,2.and Tan Zhiyi1,3(1. department of mathematics, Zhejiang {2., Hangzhou 31002., china 2. department of mathematics, Zhejiang Forestry {2., Hangzhou 311300, china 3. State Key Laboratory of CAD & CG, Zhejiang {2., Hangzhou 31002., china) department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Zhejiang Forestry University Hangzhou 311300 China State Key Laboratory of CAD and CG Zhejiang University Hangzhou 310027 China

This paper investigates the semi-online scheduling problem with the known largest size on two uniform machines. The objective is to maximize the minimum machine completion time. Both lower bounds and algorithms are given. Algorithms are optimal for the majority values of s≥1, where s is the speed ratio of the two machines. The largest gap between the competitive ratio and the lower bound is about 0.064. Moreover, the overall competitive ratio 2.matches the overall lower bound.

关键词： scheduling and covering uniform machine design and analysis of algorithm online competitive ratio