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A characterization of the finite simple groups with set of indices of their maximal subgroups

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Science China Mathematics 2004年第4期47卷 508-522页

作者： LI XianhuaDepartment of Mathematics, Suzhou University, Suzhou 215006, China (email: xhli@***) 1. Department of Mathematics Suzhou University 215006 Suzhou China

We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups.

关键词： Finite simple group, maximal subgroup, index.

Stereoselective synthesis of 3-butylphtalide via CBS catalytic reduction

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Chinese Chemical Letters 2007年第6期18卷 653-655页

作者： Geng Xu[a] Zhan Zhu Liu[a]&email:liuzhanzhu@*** Jing Hua Yang[a] Shi Zhi Chen[a] Hui Ying Yang[b]&email:yanghuiying@*** [a]Institute of Materia Medica Peking Union Medical College & Chinese Academy of Medical Science Beijing 100050 China [b]National Institute for the Control of Pharmaceutical and Biological Products Beijing 100050 China

Optically active 3-butylphtalide of high enantiomeric excesses (up to 93% e.e.) was synthesized from the reduction of o-pentanoylbenzoic ester with borane using B-methyloxyoxazaborolidine (1b) as the chiral catalyst.

关键词： Stereoselective synthesis 3-Butylphtalide CBS catalytic reduction o-Pentanoylbenzoic ester

Entropy Function for Multifractal Thermodynamics

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 83-86页

作者： Qiuhua ZENG (Department of Physics, Sichuan University, Chengdu 610064, China) email: nonlinear@*** Department of Physics Sichuan University Chengdu 610064 China

The theory on multifractal thermodynamics has been studied by the method of series expansion. The method is able to overcome the shortages of Kohmoto’s steepest desent method and the results have general meanings.

关键词： multifractal thermodynamics classical thermodynamics entropy function

Development of multidimensional sequence operation theory with applications to risk evaluation in power system generation scheduling

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Science China(Technological Sciences) 2008年第6期51卷 724-734页

作者： ChongQing Kang&email:cqkang@*** GaoFeng Yang Qing Xia State Key Lab of Power Systems Department of Electrical Engineering Tsinghua University Beijing 100084 China Yangjiaping Power Supply Bureau Chongqing Electric Power Corporation Chongqing 400050 China

Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state; multi-attribute analysis, which is often the case in actual power system practice. To address this problem, multidimensional sequence operation theory (MSOT) is developed. On the basis of previous research, this paper first categorizes the situations by the number of state variables; the number of attribute values,; defines the multidimensional sequence for single state variable; multiple attribute values, as well as the multidimensional sequence for multiple state variables; multiple attribute values. Corresponding to those definitions, four types of operations between two discrete multidimensional sequences are derived respectively. Therefore, the sequence is extended from single dimensional to multidimensional, establishing an integrated theory of multidimensional sequence operation. In particular, the basic single dimension SOT can be viewed as a special case of MSOT with only one state variable; one attribute value. Finally, the paper demonstrates the effectiveness of MSOT through an example of risk evaluation in power system generation scheduling.

关键词： power system multidimensional sequence operation theory vector Hadamard products uncertainty

Some New Approaches to Duffing Equation with Strongly and High Order Nonlinearity (II) Parametrized Perturbation Technique

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 78-83页

作者： Jihuan HE (Shanghai institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China) email: glliu@*** Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

For the strongly nonlinear equations without small parameter, a transformation u = v can be introduced for the nonlinear equation L(u) + N(u) = 0, where L and N are general linear and nonlinear differential operators respectively, P is sufficiently small. Therefore, a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter P, thus various traditional perturbation techniques can be applied. By Lindstedt-Poincare method, a perturbation solution for Duffing equation with sib order nonlinearity is obtained, which is valid not only for the small parameter E in the equation, but also for very large values of E.

关键词： perturbation technique nonlinear equation

Theoretical study on the size consistency of the second and third order energies of the multireference perturbation theory

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Science China Chemistry 2007年第4期50卷 483-487页

作者： CHEN FeiWu Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, China (email: chenfeiwu@***) 1. Department of Chemistry University of Science and Technology Beijing Beijing 100083 China

The size consistency of the second and third order energies of the multireference perturbation theory(Chen F, Davidson E, Iwata S. Int J Quant Chem, 2002, 86: 256) is investigated theoretically with a su-per-molecular model composed of N-hydrogen molecules separated by a large distance. It is found that the two perturbation series corresponding to two Hamiltonian partitions are not size consistent at the second and third order. However, two size consistent forms are suggested for two Hamiltonian parti-tions at the second order, if some approximations to the denominators of the original second order energies are assumed.

关键词： size consistency multireference perturbation theory

Approximate Analytical Solution of Blasius' Equation

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 75-78页

作者： Jihuan HE (Shanghai institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China) email:glliu@*** Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

The Blasius’ equation, with boundary conditions, is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth’s numerical solution reveal... 详细信息

关键词： nonlinear technique variational iteration method Blasius’ flow variational technique

Approximate Analytical Solution of Blasius'Equation

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 260-263页

作者： Jihuan HE(Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072, China)email: glliu@*** Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The Blasius’ equation f"’ + ff"/2=0, with boundary conditions f(0) =f,(0)0, f’ (+∞)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison w... 详细信息

关键词： nonlinear technique variational iteration method Blasius’ flow variational technique

A Variational Model for an AsymptoticMagnetohydrodynamic System

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 176-179页

In the present paper an asymptotic gas magnetohydrodynamic system isformulated in veriational principles for the first time via the semi-inverse method proposedby He. Thus, a new theoretical basis for the trite elemen... 详细信息

关键词： variational technique semi-inverse method unsteady flow magnetohydrodynamic