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Monomial Hopf algebras over fields of positive characteristic

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Science china mathematics 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu institute of mathematics, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080,{3. department of mathematics, University of Science and Technology of{3., Hefei 23.026,{3. institute of mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China department of mathematics University of Science Technology of china Hefei 230026 China

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

关键词： monomial coalgebra, Gaussian binomial coefficient, monomial Hopf algebra.

FeCl_3.AlCl_3.UR催化合成草莓酯

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香料香精化妆品 1999年第3期 14-16页

作者：但悠梦余爱农湖北民族学院化工系恩施445000

以乙酸乙酸乙酯和１，２一丙二醇为原料，在新型高分子复合催化剂ＦｅＣＩ３－ＡＩＣＩ３－ＵＲ的催化作用下合成了新型香料草莓酯。在最佳条件下，草莓酯的收率可达８８．５％。

关键词：高分子复合催化剂 FeCl3.AlCl3.UR 催化合成草莓脂合成香料

Harmonic maps with potential from complete manifolds

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Chinese Science Bulletin 1998年第21期43卷 1780-1786页

作者： CHEN Qun mathematics department, Central china Normal University, Wuhan 43.079, china institute of mathematics, Fudan University, Shanghai 20043., china mathematics department Central China Normal University Wuhan China institute of mathematics Fudan University Shanghai China

Harmonic maps with potential from complete manifolds are considered. This is a new kind of maps more general than the usual harmonic maps relating to many interesting problems such as equilibrium system of ferromagnetic spin chain and Neumann motion. Aiming at the general properties, the author derives basic gradient estimates and then Liouville type results for these maps, which are interesting in constrast to those of the usual harmonic maps for the presence of potentials.

关键词： harmonic maps potential ferromagnetic chain gradient estimate.

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 20043., china School of mathematics and System Sciences, Shandong University, Jinan 250100, china 1. department of mathematics China University of Mining and Technology Xuzhou 221008 China 2. institute of mathematics Fudan University Shanghai 200433 China 3. School of mathematics and System Sciences Shandong University Jinan 250100 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.

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang department of mathematics,East china Normal University,Shanghai 200241,{3. Division of Computational Science,E-institute of Shanghai Universities,Shanghai Normal Benyu Guo department of mathematics,Shanghai Normal University,Shanghai 20023.,{3. Division of Computational Science,E-institute of Shanghai Universities,Shanghai,{3. department of mathematics East China Normal University Shanghai 200241 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China department of mathematics Shanghai Normal University Shanghai 200234 China Division of Computational Science E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Gerbes and twisted orbifold quantum cohomology

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Science china mathematics 2008年第6期51卷 995-1016页

作者： PAN JianZhong~1 RUAN YongBin~(2,3. YIN XiaoQin~(1,3.) 1 institute of mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,{3. 2 department of mathematics,University of Wisconsin-Madison,WI 53.06,USA 3.department of mathematics,The Hong Kong University of Science and Technology,Hong Kong,{3. institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China department of mathematics University of Wisconsin-Madison WI 53706 Madison USA department of mathematics The Hong Kong University of Science and Technology Hong Kong China

In this paper,we construct an orbifold quantum cohomology twisted by a flat gerbe. Then we compute these invariants in the case of a smooth manifold and a discrete torsion on a global quotient orbifold.

关键词： gerbe orbifold quantum cohomology 53.45

The existence of global solution and their weak limit of generalized Ginzburg-Landau equations in two dimensions

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Progress in Natural Science:Materials International 2006年第5期16卷 458-463页

作者： YANG Ling'e and GUO Boling (department of mathematics, Foshan University, Foshan 528000, china {3. of Applied Physics and Computational mathematics, Beijing 100088, china) [a]department of mathematics Foshan University Foshan China [b]institute of Applied Physics and Computational mathematics Beijing China

By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid lim- it to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrodinger equations.

关键词： Ginzburg-Landau equation global solution inviscid limits.

TWO-WEIGHT NORM INEQUALITY FOR IMAGINARY POWERS OF A LAPLACE OPERATOR

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Journal of Systems Science & Complexity 2006年第3期19卷 403-408页

作者： Jianlin ZHANG department of mathematics and Physics,Zhongyuan institute of Technology,Zhengzhou 450007,{3. department of mathematics,Beijing institute of Technology,Beijing 100081,{3.. department of mathematics and Physics Zhongyuan Institute of Technology Zhengzhou 450007 China

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.

关键词： Ap condition Laplace operator weighted norm inequality.

ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEIGAO(department of Applied mathematics, Beijing institute of Technology, Beijing 100081,{3..) LI CUIZHE(department of Applied mathematics, Beijing institute of Technology, Beijing 100081,{3..) YU YUANHONG(Inditute of Applied mathematics, Acad department of Applied mathematics Beijing Institute of Technology Beijing 100081 China institute of Applied mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point