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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 {2. of mathematical sciences, fudan univ.r.ity, shanghai 2.043., China. 2.{2. of mathematical sciences, fudan univ.r.ity, shanghai 2.043., China Department of Mathematics, North {12. 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 200433 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

Local 3-cocycles of von Neumann algebras

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Science China Mathematics 2007年第9期50卷 1240-1250页

作者： Cheng-jun HOU~(1+) Ben-yin FU~2.1 school of mathematical {2.,Qufu Normal univ.r.ity,Qufu 2.3165,China 2.school of mathematical {2.,fudan univ.r.ity,shanghai 2.043.,China 1. school of mathematical {2. Qufu Normal University Qufu 273165 China 2. school of mathematical sciences Fudan University Shanghai 200433 China

We show that every local 3-cocycle of a von Neumann algebra $\mathcal{r}$ into an arbitrary unital dual $\mathcal{r}$ -bimodule $\mathcal{S}$ is a 3-cocycle.

关键词： von Neumann algebra dual bimodule local 3-cocycle 3-cocycle 46L10

A new scheme of digital communication using chaotic signals in MIMO channels

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Science China(Information sciences) 2012年第10期55卷 2183-2193页

作者： MA HuanFei 1 & KAN HaiBin 2.1 school of mathematical {2.,Soochow univ.r.ity,Suzhou 2.5006,China 2.school of Computer Science,fudan univ.r.ity,shanghai 2.043.,China 1. school of mathematical {2. Soochow University Suzhou 215006 China 2. school of Computer Science Fudan University Shanghai 200433 China

This paper proposes a new digital communication scheme,which uses chaotic signals based on the adaptive synchronization and parameter identification technique of chaotic systems reported *** to the multi signal character,this scheme combines the chaotic signal transmission with the MIMO channel technique in a wireless environment,which is different from the traditional chaotic communication *** a practical perspective,an outline of modulation,channel model,demodulation and non-coherent detection is ***,system performance is evaluated by simulations,and improvements on this scheme are also discussed.

关键词： chaotic modulation chaotic digital communication mapping parameters MIMO channel

The fundamental solution of the Keldysh typeoperator

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Science China Mathematics 2009年第9期52卷 1829-1843页

作者： CHEN ShuXing school of mathematical {2., fudan univ.r.ity, shanghai 2.043., China 1. school of mathematical {2. Fudan University Shanghai 200433 China

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2.u}} {{\partial x^2.}} + y\frac{{\partial ^2.u}} {{\partial y^2.}} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \frac{2. {2. $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singular{2. than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha rac{2. {2. $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

关键词： mixed type equation Keldysh operator fundamental solution finite part of divergent integral 35M10 35A08

riemann boundary value problems and reflection of shock for the Chaplygin gas

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Science China Mathematics 2012年第4期55卷 671-685页

作者： CHEN ShuXing 1,& QU AiFang 2.1 school of mathematical {2.,fudan univ.r.ity,shanghai 2.043.,China 2.Wuhan Institute of Physics and Mathematics,Chinese Academy of {2.,Wuhan 430071,China 1. school of mathematical {2. Fudan University Shanghai 200433 China2. Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China

In this paper,we study two-dimensional riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex *** prove that the riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a *** result can be applied to solving the problem of shock reflection by a ramp.

关键词： riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2.1. Department of Mathematics, shanghai Normal univ.r.ity, shanghai 2.02.4, China 2. Laboratory of Mathematics for Nonlinear sciences and Institute of Mathematics, fudan univ.r.ity, shanghai 2.043., China Department of Mathematics Shanghai Normal University Shanghai China Laboratory of Mathematics for Nonlinear sciences and Institute of Mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

Local Existence of Smooth Solutions to the FENE Dumbbell Model

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Chinese Annals of Mathematics,Series B 2012年第4期33卷 501-520页

作者： Ge YANG11school of mathematical {2., fudan univ.r.ity, shanghai 2.043., China. school of mathematical {2. Fudan University Shanghai 200433 China

The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.

关键词： Fokker-Planck equation FENE model Degenerate parabolic equations regularity

Commission Strategy of the Auction House

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Wuhan univ.r.ity 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 univ.r.ity, shanghai 2.043., China 2. {2. of Mathematics and Statistics, Wuhan univ.r.ity , Wuhan 430072. Hubei, China College of Economics Fudan University 200433 Shanghai China school of Mathematics Statistics Wuhan University 430072 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

Paleoceanographic evolution recorded in the northern South China Sea since 4 Ma

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Science China Earth sciences 2005年第12期48卷 2166-2173页

作者： HUANG Baoqi1,2. JIAN Zhimin2.& WANG Pinxian2.1. school of Earth and Space sciences, Peking {2., Beijing 100871, China 2. Laboratory of Marine Geology, Tongji {2., shanghai 2.0092. China 1. school of Earth and Space sciences Peking University 100871 Beijing China 2. Laboratory of Marine Geology Tongji University 200092 Shanghai China

Upper water structure over the last 4 million years in the northern South China Sea (SCS) was reconstructed by sea surface temperature (SST) and primary productivity estimated by changes in the abundance of planktonic foraminifer, planktonic foraminifer transfer function, and the accumulation rate of benthic foraminifera. results of SST and primary productivity show that SST gradually decreased since 4 Ma, but differential seasonal temperature and primary productivity increased in steps mainly at about 3.1, 2.7, 2.1, 1.6, 0.9 and 0.5 Ma. Comparison with tectonics and orbital variations indicates that phased rising of the Tibet since 3.6 Ma, closing of Panama and Indonesian seaways, and orbital changes were responsible for the changes of upper water structure in the SCS, respectively.

关键词： northern South China Sea, upper water structure, Late Pliocene, planktonic foraminifer, ODP 1146.