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INSTANTANEOUS SHRINKING AND LOCALIZATION OF FUNCTIONS IN Y_λ(m,p,q,N) AND THEIR APPLICATIONS

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 361-380页

作者： YUAN HONGJUN institute of Mathematics, Jilin university, Changchun 130023, china. institute of Mathematics Jilin University Changchun 130023 China

The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equation ut = △um-uq, m > 0, q > 0 and the p-Laplace equation ut = div(|△u|p-2△u)-uq, P > 1, q > 0. In particular, as an application of the results, the necessary and sufficient condition for the solutious of the above p-Laplace equation with nonnegative finite Borel measures as initial conditions to have the instantaneous shrinking property of the support is obtained. This is an answer to an open problem posed by R. Kersner and A. Shishkov.

关键词： Porous medium equation p-Laplace equation Instantaneous shrinking Localization property Support

ON TWO CONJECTURES OF THE QUADRATIC DIFFERENTIAL SYSTEMS

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Chinese Annals of Mathematics,Series B 1997年第4期18卷 429-434页

作者： ZHANG XIANG institute of Mathematics,Nanjing Normal university,Nanjing 210097,china 南京师范大学数学所江苏南京

Two conjectures in the qualitative theory of quadratic differential systems are proved under certain conditions.

关键词： Quadratic system Limit cycle Dulac function

ORDER PROPERTIES AND CONSTRUCTION OF SYMPLECTIC RUNGE-KUTTA METHODS

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Journal of Computational Mathematics 2000年第6期18卷 645-656页

作者： Shou-fu Li (institute for Computational and Applied Mathematics, Xiangtan university, Xiangtan 411105, china) 湘潭大学湖南湘潭 411105

The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p + l(1 less than or equal to p less than or equal to s - 1) provided that the simplifying conditions C(p) (or D(p) with non-zero weights) and B(2p + l) hold, where 1 0, 1, 2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(p) and D(p) with 0 s. Then this method is symplectic if and only if either p = s or the nonlinear stability matrix M of the method has an (s - p) x (s - p) chief submatrix (M) over cap = 0. (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has been designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying C(p),D(p) and B(2p + l) can be easily computed, where 1 I P less than or equal to s, 0 less than or equal to l less than or equal to 2, s less than or equal to 2p + l less than or equal to 2s.

关键词： numerical analysis symplectic Runge-Kutta methods simplifying conditions order results

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 university of Mining and Technology, Xuzhou 221008, china institute of Mathematics, Fudan university, Shanghai 200433, china School of Mathematics and System Sciences, Shandong university, 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.

Conduction Properties and Scattering Mechanisms in F-doped Textured Transparent Conducting SnO_2 Films Deposited by APCVD

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Journal of Materials Science & Technology 1997年第1期13卷 50-56页

作者： Deheng ZHANG(Dept. of Physics, Shandong university, Jinan 250100, china)Honglei MA(institute of Optoelectronic Materials and Devices, Shandong university, Jinan 250100, china) Dept. of Physics Shandong University Jinan 250100 China institute of Optoelectronic Materials and Devices Shandong University Jinan 250100 China

Transparent conducting F-doped texture SnO2 films with resistivity as low as 5× 10-4 Ω ·cm,with carrier concentrations between 3.5 × 1020 and 7× 1020 cm-3 and Hall mobilities from 15.7 to 20.1 cm2/(V/s) have been prepared by atmosphere pressure chemical vapour deposition (APCVD). These polycrystalline films possess a variable preferred orientation, the polycrystallite sizes and orientations vary with substrate temperature. The substrate temperature and fluorine flow rate dependence of conductivity, Hall mobility and carrier conentration fOr the resultingfilms have been obtained. The temperature dependence of the mobiity and carrier concentrationhave been measured over a temperature range 16～400 K. A systematically theoretical analysis on scattering mechanisms for the highly conductive SnO2 films has been given. Both theoretical analysis and experimental results indicate that for these degenerate, polycrystalline SnO2 ：F films in the low temperature range (below 100 K), ionized impurity scattering is main scattering mechanism. However, when the temperature is higher than 100 K, the lattice vibration scattering becomes dominant. The grain boundary scattering makes a small contribution to limit the mobility of the films.

关键词： SnO cm Conduction Properties and Scattering Mechanisms in F-doped Textured Transparent Conducting SnO2 Films Deposited by APCVD

Interaction between a Nanovirus-like Component and the Tobacco Curly Shoot Virus/Satellite Complex

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Acta Biochimica et Biophysica Sinica 2005年第1期37卷 25-31页

作者： Pei-Jun WU Xue-Ping ZHOU~* institute of Biotechnology Zhejiang university,Hangzhou 310029,china institute of Biotechnology Zhejiang UniversityHangzhou 310029 China

The biological role of DNA1,a nanovirus-like component shown to be associated with thebegomovirus/satellite complex,has not yet been ***,we demonstrated that DNAl of Tobaccocurly shoot virus isolate Y35(TbCSV-Y35)attenuated leaf-curling symptoms induced by TbCSV-Y35 orTbCSV-Y35 plus Y35 DNAβ in the early stage of symptom development and induced leaf cluster at a laterstage of symptom development in Nicotiana benthamiana *** leaf disc assay demonstrated thatTbCSV-Y35 DNA 1 replicated *** blot analysis revealed that TbCSV-Y35 DNA 1 re-duced viral DNA *** DNA accumulation was not reduced when plants were co-inoculatedwith TbCSV-Y35 DNAβ,but the TbCSV-Y35 DNAβ level was dramatically reduced in the presence ofTbCSV-Y35 DNA *** determine whether the interaction between TbCSV/satellite complex and DNA 1 hadisolate specificity,DNAI of TbCSV isolate Y132 was cloned and *** was found to have 75%nucleotide sequence identity with TbCSV-Y35 DNA *** tests showed that TbCSV-Y 132 DNA 1 hadno effect on the symptoms induced by TbCSV-Y35 or TbCSV-Y35 and Y35 DNAβ in ***,although Y 132 DNA1 could replicate in these plants.

关键词： Tobacco curly shoot virus DNA1 DNAβ symptom replication interaction

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of Computational Mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for Mathematical Sciences, Kyoto university, Japan Department of Mathematics, Peking university, Beijing 100871, china) 北京大学数学系北京

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

P-twisted affine Lie algebra and its realizations by twisted vertex operators

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Science china Mathematics 2005年第Z1期48卷 295-305页

作者： LU Keping, CHU Yanjun, ZHENG Zhujun & DONG Wenfeng institute of Mathematics, Henan university, Kaifeng 475001, china USTC Shanghai institute for Advanced Studies, university of Science and Technology of china, Shanghai 201315, china institute of Mathematics Henan University Kaifeng China USTC Shanghai institute for Advanced Studies University of Science and Technology of China Shanghai China

In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.

关键词： P-twisted affine Lie algebra, twisted vertex operator, extended P-twisted afline algebra.

The information entropy of a static dilaton black hole

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Science china(Physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU ChengZhou institute of Theoretical Physics, Binzhou university, Binzhou 256600, china Department of Physics, Beijing Normal university, Beijing 100875, china institute of Theoretical Physics Binzhou University Binzhou China Department of Physics Beijing Normal University Beijing China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity