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Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N_(2.molecule

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 385-398页

作者： REN Weiyi1,2. SUN Weiguo1, HOU Shilin3 & FENG Hao4 1. institute of Physics, College of Chemical Engineering, Sichuan university, Chengdu 610065, {2. 2. institute of theoretical Physics, xihua normal university, nanchong 63.002. china 3. Department of Physics, {2. Oceanography university, Qingdao 2.6003, {2. 4. College of Physics, Sichuan university, Chengdu 610065, {2. institute of Physics College of Chemical Engineering Sichuan University Chengdu China institute of theoretical Physics Xihua Normal University Nanchong China Department of Physics China Oceanography University Qingdao China College of Physics Sichuan University Chengdu China

It is usually very difficult to directly obtain molecular dissociation energy De and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein’s energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of N2.molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree excellently with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.

关键词： vibrational energy, dissociation energy, nitrogen molecule, algebraic method.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. Department of Mathematics,Inner Mongolia normal university, Huhhot 01002., {2. 2. Department of Mathematics, Harbin institute of Technology, Harbin 150006, {2. Department of Mathematics Inner Mongolia Normal University Huhhot China Department of Mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

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, Beijing 100875, {2. 2. institute of Applied Physics and Computational Mathematics, Beijing 100080, {2. Department of Mathematics Beijing Normal University Beijing China institute of Applied Physics and Computational Mathematics Beijing 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.

Three industries and wastewater and COD discharge of Beijing

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Journal of Environmental Sciences 2000年第4期12卷 474-477页

作者： WANG Yan 1, WANG Hong rui 2. NING Da tong 2.(1. Beijing Municipal Research institute of Environmental Protection, Beijing 100037, china 2. institute of Environmental Sciences, Beijing normal university, Beijing 100875, china) 北京市环境保护所北京 1 0 0 0 3 北京师范大学北京 1 0 0 875

With the swift development of economy, the water quality of Beijing is becoming worse day by day and hampers the sustainable development obviously. In this paper, the current conditions of the municipal wastewater structure in the industrial sectors are analysed and discussed in terms of the indicators, such as direct wastewater\|discharge coefficient, complete wastewater\|discharge coefficient, direct discharge coefficient of COD and complete discharge coefficient of COD, by taking a year of 1990s as the base year. Some countermeasures are studied and the corresponding recommendations are put forward in order to improve the water environment in Beijing. This provides a scientific ground for coordinating the relationship between the aquatic environment and economic growth in this city.

关键词： direct wastewater discharge coefficient (DWDC) complete wastewater discharge coefficient (CWDC) direct discharge coefficient of COD(DDC of COD) complete discharge coefficient of COD (CDC of COD)

Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese Science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei Department of Mathematics, Qufu normal university, Qufu 2.3165, {2. 2. institute of Mathematics, Shantou university, Shantou 515063, {2. Department of Mathematics Qufu Normal University Qufu China institute of Mathematics Shantou University Shantou China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

DFT study of the conductance of molecular wire:The effect of coupling geometry and intermolecular interaction on the transport properties

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Science china Chemistry 2006年第6期49卷 492-498页

作者： QI Yuanhua1,2. GUAN Daren1 & LIU Chengbu1 1. institute of theoretical Chemistry, Shandong {2., Jinan 2.0100, china 2. School of Physics and Microelectronics, Shandong {2., Jinan 2.0061, china institute of theoretical Chemistry Shandong University Jinan China School of Physics and Microelectronics Shandong University Jinan China

The density functional theory (DFT) combining with the non-equilibrium Green functions (NEGF) method is applied to the study of the electronic transport properties for a Di-thiol-benzene (DTB) molecule coupled to two Au(111) surfaces. The dependence of the transport properties on the bias, the coupling geometry of the molecule-electrode interface, and the intermolecular interaction are examined in detail. The results show that the existence of the hydrogen atom at the end of the DTB molecule would significantly decrease the transmission coefficients, and then the differential conductance (dI/dV). By changing the position of the DTB molecule located between two electrodes a maximum value of calculated current is observed. It is also found that the intermolecular interaction will strongly influence the transport properties of the system studied.

关键词： non-equilibrium Green functions method, transmission spectrum, the molecular projected selfconsistent Hamiltonian, projected density of state.

Global convergence property of s-dependent GFR conjugate gradient method

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Chinese Science Bulletin 1998年第23期43卷 1959-1965页

作者： WANG Changyu 1,2.and ZHANG Yuzhong\+1 1. institute of Operations Research in Qufu normal {2., Qufu 2.3165, china 2. institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, china institute of Operations Research Qufu Normal University Qufu China institute of Applied Mathematics Chinese Academy of Sciences Beijing China

An \%S\%_dependent GFR method and a generalized conjugate gradient method are designed. Two estimated values of upper bounds for the ratio of β k to β FR k are given. The two convergence theorems are proved. The global convergent properties of \%s\%_dependent GFR method are obtained adopting several choice strategies of steplength and some results in recent literature are extended.

关键词： steplength linear search global convergence conjugate gradient.

Calculating soil moisture by remote sensing and analyzing hydrologic cycle process in the Yellow River basin

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Science china(Technological Sciences) 2004年第Z1期47卷 1-13页

作者： YANG Shengtian1 & LIU Changming1, 2.1. School of Environmental Sciences, Beijing normal university, Beijing 100875, {2. 2. institute of Geographic Science and Natural Resources Research, Beijing 100101, {2. School of Environmental Sciences Beijing Normal University Beijing China institute of Geographic Science and Natural Resources Research Beijing China

Based on the AVHRR pathfinder remote sensing data, soil moisture, precipitation and evaporation during the period of 1982.1998, soil moisture of all layers of soil-profile (0—1 m) in the Yellow River basin over the 17 years are calculated by the remote sensing model of calculating soil water. The Yellow River basin is divided into seven subcatchments as control sections at the location of six hydrologic stations (Lanzhou, Toudaoguai, Longmen, Sanmenxia, Huayuankou and Lijin). After calculating soil moisture and obtaining runoff data and precipitation data, the dynamical features of hydrological cycle in the Yellow River basin are analyzed for the period from 1982.to 1988 using water balance method. The conclusions are as follows: It is feasible to calculate the soil water on the macro-scale, in the soil profile with temporal continuity by means of remote sensing and survey in land. Some values of the key water cycle factors in the Yellow River are obtained, which include the annual precipitation of 4000 km3, the evapotranspiration of 3000-3500 km3, and the soil moisture transformation of ?500- 500 km3. Consequently, we analyzed the process of the water cycle in the Yellow River over the 17 years, and the results show that the segment upstream of Lanzhou city is a relatively humid region, and the area of internal waters and the reaches of Shanshan is the most desiccated region. Therefore, the runoff in the depth process is intensive and the runoff-generating process is weak in more arid regions.

关键词： the Yellow River, soil moisture, remote sensing, hydrologic cycle.

The geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1,2. 1 Department of Mathematics,East china normal {2.,Shanghai 2.0062.china 2.institute of theoretical Computing,East china Narnal {2.,Shanghai 2.0062.china Department of Mathematics East China Normal University Shanghai China institute of theoretical Computing East China Narnal University Shanghai China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2. is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C12 05C2.