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Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long department of mathematics, china {3. of Mining and technology, Xuzhou 221008, china Institute of mathematics, Fudan {3., Shanghai 20043., china School of mathematics and System Sciences, Shandong {3., Jinan 250100, china department of mathematics China University of Mining and Technology Xuzhou China Institute of mathematics Fudan University Shanghai China School of mathematics and System Sciences Shandong University Jinan China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

Simultaneously inducing synthesis of semiconductor selenium multi-armed nanorods and nanobars through bio-membrane bi-templates

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Science china Chemistry 2004年第6期47卷 507-511页

作者： LI Li1, WU Qingsheng1 DING Yaping2 & LI Ping3.1. department of Chemistry, Tongji university, Shanghai 200092, china 2. department of Chemistry, Shanghai university, Shanghai 20043., china 3. department of Food, Anhui Agricultural university, hefei 23.03., china department of Chemistry Tongji University Shanghai China department of Chemistry Shanghai University Shanghai China department of Food Anhui Agricultural University Hefei China

Multi-armed nanorods and nanobars of semiconductor selenium were simultane- ously synthesized in the light of biomineralization process through bio-membrane bi-templates of rush at room temperature. The multi-armed nanorods are 60 nm in diameter and 1.5 μm in length; the nanobars are 150 nm in diameter and 1000—1100 nm in length. The XRD pattern indicates that these nanocrystals were crystallized in the hexagonal structure with lattice constants a = 0.43. nm, c = 0.495 nm. The possible formation mechanism was investigated.

关键词： selenium, multi-armed nanorods, nanobars, bio-membrane, bi-templates.

A blow-up criterion for classical solutions to the compressible Navier-Stokes equations

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Science china mathematics 2010年第3期53卷 671-686页

作者： HUANG XiangDi 1 & XIN ZhouPing 2, 1 department of mathematics, university of Science and {3. of china, hefei 23.026, china 2 department of mathematics, The Chinese university of Hong Kong, Hong Kong, china department of mathematics University of Science and Technology of China Hefei China department of mathematics The Chinese University of Hong Kong Hong Kong China

In this paper, we obtain a blow-up criterion for classical solutions to the 3.D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the id... 详细信息

关键词： blow-up classical solutions compressible Navier-Stokes

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2 ,DU Jin-yuan 1,3.1. School of mathematics and Statistics, Wuhan university, Wuhan 43.072, Hubei, china 2. School of mathematics and Computer, Ningxia university, Yinchuan 750021, Ningxia, china 3. department of mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, china School of mathematics and Statistics Wuhan University Wuhan Hubei China School of mathematics and Computer Ningxia University Yinchuan Ningxia China department of Mathematies Hubei Institute for Nationalities Enshi Hubei China

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order

An experimental study on the self-adaption mechanism used by evolutionary programming

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Progress in Natural Science:Materials International 2008年第4期18卷 481-486页

作者： Jingsong He a,b, a department of Electronic Science and technology, university of Science and technology of china, hefei 23.027, china b Nature Inspired Computation and Application Laboratory, university of Science and technology of china, hefei 23.027, china department of Electronic Science and technology University of Science and Technology of China Hefei 230027 China Nature Inspired Computation and Application Laboratory University of Science and Technology of China Hefei 230027 China

Evolutionary programming (EP) is one of the most important methods for numerical optimization. Its main technique is the combi- nation of mutations and the self-adaption mechanism. In the past years, studies on EP focused on how to improve the effciency of muta- tions with different probability distributions, and few of them touched on the question that the self-adaption mechanism did not work sometimes, but simply followed the original suggestion. So far, no experimental results have shown why this is a question. This paper firstly gives a primary analysis on the behavior of the self-adaption mechanism, and then presents experimental evidences to show why its adaptive ability is doubtful.

关键词： Evolutionary programming Cauchy mutation Self-adaption mechanism

THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES

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Acta Mathematica Scientia 2006年第2期26卷 255-264页

作者：招燕燕陈祖墀 department of mathematics university of Science and {3. of china Hefei 230026China

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop... 详细信息

关键词： Weak solution strongly degenerate quasilinear parabolic equation 2000 MR Subject Classification 3.K55 3.K60 3.K65

Finite groups in which elements of the same order outside the center are conjugate

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Science china mathematics 2007年第10期50卷 1493-1500页

作者： Xing-zhong YOU~1 Guo-hua QIAN~2 Wu-jie SHI~(3.) ~1 School of mathematics and Computing Science,Changsha university of Science and technology,Changsha 410076,{3. ~2 department of mathematics,Changshu Institute of technology,Changshu 215500,{3. ~3.School of mathematics,Suzhou university,Suzhou 215006,{3. School of mathematics and Computing Science Changsha University of Science and Technology Changsha China department of mathematics Changshu Institute of Technology Changshu China School of mathematics Suzhou University Suzhou China

We prove that if G is a finite group in which the elements of the same order outside the center are conjugate, then either G is abelian or G ≌ S3.

关键词： finite group, rational group, conjugacy class

A Remark on Computing the Tame Kernel of Quadratic Imaginary Fields

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Acta Mathematica Sinica,English Series 2002年第3期18卷 513-516页

作者： Xue Jun GUO Guang Tian SONG department of mathematics, university of Science and {3. of china, hefei, Anhui 23.026, P. R. china department of mathematics University of Science and Technology of China Hefei Anhui P. R. China

In this paper, we discuss a method to compute the tame kernel of a number field. Confining ourselves to an imaginary quadratic field, we prove that _υ:K_2~S F/K_2~S F→k~* is bijective when N_υ>8δ_D^6.

关键词： Tame kernel Quadratic imaginary fields GTT Theorem

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science china mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2 & WANG YuZhu 3. 1 department of mathematics, Zhejiang university, Hangzhou 3.0027, {3. 2 department of mathematics, university of California at Los Angeles, CA 90095, USA 3.department of mathematics, Shanghai Jiao Tong university, Shanghai 200248, {3. department of mathematics Zhejiang University Hangzhou China department of mathematics University of California at Los Angeles Los Angeles USA department of mathematics Shanghai Jiao Tong University Shanghai China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution