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Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. department of Mathematics, beijing normal university,{2., china 2. Institute of Applied Physics and Computational Mathematics, beijing 100080, china 1. department of Mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational Mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

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Science china(Physics,Mechanics & Astronomy) 2005年第2期48卷 150-157页

作者： XU Quan1 & TIAN Qiang2.1. Scientific and Technological Office, Daqing Teacher College, Daqing 163712. china 2. department of Physics ,{2., beijing 100875, china Scientific and Technological Office Daqing Teacher College Daqing 163712 China department of Physics Beijing Normal University Beijing 100875 China

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2.) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

关键词： two-dimensional nonlinear lattice, quasi-one-dimensional nonlinear lattice, kink-soliton, antikink-soliton.

Theoretical study on thermal decomposition of azoisobutyronitrile in ground state

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Science china Chemistry 2004年第5期47卷 373-380页

作者： SUN Chengke1,2. ZHAO Hongmei1 & LI Zonghe1 1. department of Chemistry, beijing normal university,{2., china 2. department of Chemistry, Qujing normal College, Qujing 655000, china 1. department of Chemistry Beijing Normal University 100875 Beijing China 2. department of Chemistry Qujing Normal College 655000 Qujing China

The thermal decomposition mechanisms of azoisobutyronitrile (AIBN) in the ground state have been investigated systematically. Based on the potential energy surfaces (PES) of various possible dissociation paths obtained using the semiempirical AM1 method with partial optimization, the density function theory B3LYP/6-311G* method was employed to optimize the geometric parameters of the reactants, the intermediates, the products and the transition states, which were further confirmed by the vibrational analysis. The obtained results show that the re- action process of the two-bond (three-body) simultaneous cleavage Me2.CN)C─ N=N─ C(CN)Me2. 2.e2.CN)C?+N2.is much more favorable than the reaction process of the two one- bond asynchronous cleavage Me2.CN)CN=N─C(CN)Me2.? Me2.CN)CN=N?+ Me2.CN)C?? Me2.CN)C?+ N2. It was suggested that the electron shrinking effect of double bond (─N=N─) in AIBN and the stabilities of the Me2.CN)C?radical as well as N2.molecule are main factors of leading to the reaction proceeding in the former pathway. The calculation results were consistent with all the experimental facts.

关键词： azoisobutyronitrile, radicals, thermal decomposition, density function theory (DFT).

Optimal reactions for the synthesis of superheavy nucleus ^(2.0)Hs

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Science china(Physics,Mechanics & Astronomy) 2006年第6期49卷 641-648页

作者： LIU Zuhua1,3 & BAO Jingdong1,2.1. Key Laboratory of Beam Technology and Material Modification of Ministry of Education, beijing normal university, beijing 100875,{2. 2. Physics department, beijing normal university, beijing 100875,{2. 3.{2. Institute of Atomic Energy, beijing 102.13,{2. Key Laboratory of Beam Technology Material Modification of Ministry of Education Beijing Normal University Beijing 100875 China Physics department Beijing Normal University Beijing 100875 China china Institute of Atomic Energy Beijing 102413 China

The superheavy nucleus 2.0Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 2.8Cm(2.Mg,4n)2.0Hs, 2.4Pu(30Si,4n)2.0Hs, 2.8U(36S,4n)2.0Hs and 2.6Ra(48Ca,4n)2.0Hs using a two-parameter Smoluchowski equation. It is found from our results that 2.6Ra(48Ca,4n)2.0Hs and 2.8U(36S,4n)2.0Hs are two optimal reactions for the synthesis of the superheavy nucleus 2.0Hs due to their large negative Q-values.

关键词： diffused fusion barrier,Smoluchowski equation,superheavy nuclei.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of Mathematics, beijing normal university,{2., china 2. department of Mathematics, Neijiang Teacher's College, Neijiang 641112. china) beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Solvation effects on brain uptakes of isomers of ^(99m)Tc brain imaging agents

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Chinese Science Bulletin 2002年第21期47卷 1786-1791页

作者： JIA Hongmei, MA Xiaohui, WANG Cunxin & LIU Boli1. department of Chemistry, beijing normal university,{2., china 2. Center for Biomedical Engineering, beijing Polytechnic university, beijing 10002., china 1. department of Chemistry Beijing Normal University Beijing 100875 China 2. Center for Biomedical Engineering Beijing Polytechnic University Beijing 100022 China

Analysis of electrostatic hydration free energies of the isomers of the 99mTc-BAT and 99mTc-DADT complexes is carried out using the computer simulation technique. The results show that not only a correlation exists between the logarithm of the brain uptake and the electrostatic hydration free energy for the isomers of 99mTc-brain radiopharmaceu-ticals, but also a linear relationship exists between the logarithm of the ratio of the brain uptake of the syn isomer to that of the anti one and the difference between the electrostatic hydration free energy of the syn-isomer and that of the anti one. Furthermore, the investigation on the important factors influencing the brain uptakes of 99mTc-radiophar-maceuticals and the reasons of the different biodistribution of the isomers of the 99mTc-complexes is explored at the molecular level. The results may provide a reference for the rational drug design of brain imaging agents.

关键词： 99mTc-brain imaging agent isomer brain uptake electro-static hydration free energy.

Approach to synthesis of novel chiral 3-chloro-2.5H)- furanone and its application in asymmetric reactions

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Chinese Science Bulletin 2000年第8期45卷 711-716页

作者： HUANG Hui & CHEN Qinghua1. department of Chemistry, Tonghua Teacher’s College, Tonghua 134002. china 2. department of Chemistry, beijing normal university, beijing 100875, china department of Chemistry Tonghua Teacher’s College Tonghua China department of Chemistry Beijing Normal University Beijing China

The synthetic method of the novel chiral synthon, 5-/-menthyloxy-3-chloro-2.(5H)-furanone 5a and its application in asymmetric reactions were investigated. 5a is easily obtained in highly optical purity, and acts as a stable acceptor of Michael addition with oxygen nucleophiles in tandem double Michael addition / internal nucieophilic substitution to offer the spiro-cyclopropane derivative containing four stereogenic centers 8, which it is difficult to obtain by routine methods. The synthetic methods for 5a and 8 are reported in detail and the new compounds are identified on the basis of their analytical data and spectroscopic data, such as UV, IR, H NMR,13 C NMR, MS and elementary analysis. The absolute configuration of the interesting spiro-cyclopropanes, spiro [1-chloro-4-(/-menthyloxy)-5-oxo-6-oxa-biscyclo[3.1.0]hexane-2.3i(4’-/-menthyloxy-5’-/-menthyloxy- butyrolactone)] 8 was established by X-ray crystallography. This result can provide important synthetic strategy in synthesis of some complex

关键词： new chiral synthon. 5-l-menthyloxy-3-chloro-2.(5H)-furanone absolute configuration spiro-cyclopropane derivative containing multiple chiral centers.

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of Mathematics, university of Science and Technology of{2., Hefei 2.002.,{2. 2. department of Mathematics, beijing normal university, beijing 100875,{2. department of Mathematics University of Science and Technology of China Hefei China department of Mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of Mathematics, Chinese Academy of Sciences, beijing 100080, china 2. {2. of Mathematics, beijing normal university, beijing 100875, china Institute of Mathematics Chinese Academy of Sciences Beijing China department of Mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.