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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 School of Mathematical sciences, fudan university, Shanghai 2.04.3, China. 2.School of Mathematical sciences, fudan university, Shanghai 2.04.3, China Department of Mathematics, North {4. 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

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 2.04.3, China 2. School of Mathematics and Statistics, Wuhan {4. , Wuhan 4.0072. 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

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 sciences,Qufu Normal university,Qufu 2.3165,China 2.School of Mathematical sciences,fudan university,Shanghai 2.04.3,China 1. School of Mathematical sciences 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 4.L10

Phylogeographic analysis of human papillomavirus 58

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Science China(Life sciences) 2009年第12期52卷 1164-1172页

作者： LI YanYun1, LI ZuoFeng2. HE YiFeng1, KANG Yu1, ZHANG XiaoYan1, CHENG MingJun1, ZHONG Yang2. 3· & XU CongJian1· 1 Obstetrics and Gynecology Hospital of fudan university, Shanghai 2.0011, China 2.Shanghai Bioinformation Research Center, Shanghai 2.02.5, China 3 School of Life sciences, fudan university, Shanghai 2.04.3, China Obstetrics and Gynecology Hospital of fudan university Shanghai 200011 China Shanghai Bio-information Research Center Shanghai 200235 China School of Life sciences Fudan University Shanghai 200433 China

Human papillomavirus 58 (HPV58) is one type of HPV with high risk of causing cervical cancer. Unusually high prevalence of HPV58 has been reported in Asia, Africa and some other areas. However, due to the scattered distribution of global data, in addition to the lack of data of some HPV58 high-incidence nations and regions, like China's Mainland, a comprehensive analysis of the global geographical distribution of HPV58 remains blank so far. In this study, HPV58 from the human cervical cancer tissue was detected in China's Mainland, and 14.new HPV58-E6/L1 gene sequences were obtained. Moreover, phylogeographic analysis has been conducted combining the HPV58 sequences that have been deposited in GenBank since 1985. The study result shows that the sequences detected from the Shanghai, Jiangsu and Sichuan areas are homologous with those found in the past from Hong Kong and Xi'an, China, as well as Japan and other Southeast Asian areas. Furthermore, Western Africa is considered to be the "root" source of the HPV58 variant, while China's Mainland and Southeast Asia are "transit points" and the new sources of HPV58 after receiving the isolates from the "root" source; like HPV16 and HPV18, the HPV58 might also be one of the major HPV types associated with the development and spread of cervical cancer.

关键词： human papillomavirus 58 (HPV58) cervical cancer phylogeography molecular evolution

The adsorption isotherms, IR and ^(2.)Si MAS NMR spectra of modified MCM-4. molecular sieves

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Chinese Science Bulletin 1997年第10期42卷 828-832页

作者： LONG Yingcai, DONG Weiyang, XU Taiming, GAO Xiaoqin, XIE Guangen and SUN Yaojun1. Department of Chemistry, fudan university, Shanghai 2.04.3, China 2. Centre of Analysis and Measurement, fudan university, Shanghai 2.04.3, China Department of Chemistry Fudan University Shanghai China Centre of Analysis and Measurement Fudan University Shanghai China

RECENTLY a new family of mesoporous molecular sieves,M4.S,was reported by researchers atMobil R&D *** a member of the family,MCM-4.,which exhibits a hexagonalarray of uniform channel mesopores,has been *** channel size can be variedfrom approximately 1.5 nm to greater than 10 nm by choosing different surfactants,auxiliarychemicals(1,3,5-trimethylbenzene)in the reactant,and by changing the reaction *** wall thickness of this kind of molecular sieve is in the range of 0.3 to 1.3 nm esti-

关键词： MCM-4. surface modification adsorption isotherm IR 2.Si MAS NMR.

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 sciences,Soochow university,Suzhou 2.5006,China 2.School of Computer Science,{2. university,Shanghai 2.04.3,China 1. School of Mathematical sciences 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

IL-12.4. is not required for islet allograft rejection

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Acta Pharmacologica Sinica 2006年第8期27卷 1065-1070页

作者： En-guang BI~(2.5) Wei SHI~(3,5) Jia ZOU~2.Zhen-hua HAO~3 Zhen-hu LI~2.Duan CAI~3 Hua-qun ZHANG~3 Bing SUN~(2.4.6) ~2.aboratory of Molecular Cell Biology Shanghai institutes for Biological sciences,Chinese Academy of sciences,Graduate School of the Chinese Academy of sciences,Shanghai 2.0031,China ~3the Huashan Hospital of{4.,Shanghai 2.004.,China ~4.-institutes of Shanghai Universities Immunology Division,Shanghai 2.002..China Laboratory of Molecular Cell Biology Shanghai Institutes for Biological Sciences Chinese Academy of Sciences Graduate School of the Chinese Academy of Sciences Shanghai 200031 China

Aim:To investigate whether IL-12.4. plays a crucial role in regulating islet al-lograft rejection in a streptozotocin(STZ)-induced diabetes mouse ***:C57BL/6 and IL-12.4. gene knockout mice were selected as recipient mice,towhich the diabetes was induced with a treatment of STZ(150-2.0 mg/kg)by asingle ip ***/c mice were selected as donor mice and islet cells wereisolated from the *** 500 islets were transplanted into recipient mice be-neath the capsule of the left *** the islet transplantation the glu-cose from the mice sera was monitored and the rejection rate of islets was ***:STZ could induce diabetes in the recipient mice within 1 *** of allograft islets,the increased glucose in wild-type(WT)micereturned to normal level and was maintained for 10 ***,the rejectionrate of islet allograft between IL-12.4.-deficient mice and WT mice was ***:The results suggested that,although islet allograft rejection is be-lieved to be Th1-cell predominant,the Th1 response inducer,IL-12.and IL-2. arenot essential to induce islet allograft rejection.

关键词： Th1 cells Th2.cells islets of Langerhans transplantation homologous transplantation IL-12.4.-deficient mice

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 sciences,fudan {2.,Shanghai 2.04.3,China 2.Wuhan Institute of Physics and Mathematics,Chinese Academy of sciences,Wuhan 4.0071,China 1. School of Mathematical sciences 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

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 sciences, fudan university, Shanghai 2.04.3, China 1. School of Mathematical sciences 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{4. {4. $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha 4. {4. $ 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