B_2分子X~3Σ_g~-和A~3Σ_u~-态的势能函数

使用SAC/SAC-CI方法,利用D95(d),6-311g**以及cc-PVTZ等基组,对B2分子的基态(X3Σg-)和第一激发态(A3Σu-)的平衡结构和谐振频率进行了优化计算.通过对3个基组的计算结果的比较,得出了D95(d)基组为3个基组中的最优基组的结论;使用D95(d)基组,利用SAC的GSUM(Group Sum of Operators)方法对基态(X3Σg-),SAC-CI的GSUM方法对激发态(A3Σu-)进行单点能扫描计算,用正规方程组拟合Murrell-Sorbie函数,得到了相应电子态的完整势能函数;从得到的势能函数计算了与基态(X3Σg-)和第一激发态(A3Σu-)相对应的光谱常数(Be,αe,ωe和ωeχe),结果与实验数据吻合.     

THE QUALITATIVE CONTENT OF RENEWABLE RESOURCE MODELS

This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model.     

Modification of the surface state of rough substrates by two different varnishes and influence on the reflected light

Modification of the visual appearance when a rough surface is covered by a varnish is mostly attributed to the levelling of the substrate surface, which depends on the molecular weight of the varnish. The topography of varnished surfaces, however, has never been measured directly. Surfaces of varnishes applied over glass substrates of varying roughness were studied, therefore, using mechanical profilometry. Two different varnishes made with a low and a high molecular weight resin were studied. Both varnishes lower the r.m.s. roughness of the substrates and filter the high spatial frequencies. These results are amplified for the varnish containing the low molecular weight resin. The light reflected by the varnished samples is modelled from these topographical data. Its angular distribution, calculated from the probability density of slopes is presented, taking into account separately the air/varnish and the varnish/substrate interfaces. These analyses are presented in a back-scattering configuration. They show that varnishing significantly reduces the angular width of the reflected light and that this effect is magnified for the low molecular weight resin. Modelling furthermore shows that the influence of the roughness of the varnish/substrate interface is negligible in the total reflected light.     

二项式光场与级联三能级原子的量子纠缠

利用量子熵理论，研究了二项式光场与级联三能级原子的量子纠缠，讨论了光场与原子的初始参量对其量子纠缠性质的影响.结果表明，利用二项式光场的特性，可以揭示从相干态到数态之间的所有态光场与三能级原子相互作用时的量子纠缠性质.选择适当的系统参数可以制备稳定的光场-原子qutrit纠缠态. 关键词： 二项式光场 级联三能级原子 光场熵 量子纠缠     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model

The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Three types of maximally entangled states for a two-particle system

Foratwo-particle(spin1/2)systemthespinstateisdescribedusingavectorinafour-dimensionalHilbertspace.Inangularmomentumcouplingtheory[1],theangularmomentumuncouplingandcouplingrepresentationsareusuallyadopted.WhilethesimultaneouseigenstatesoftheCSCO(s1z,s2z),12,12,12and12,arechosenasthebasisofangularmomentumuncouplingscheme,thesimultaneouseigenstatesoftheCSCO(2,zSS),,SM(12=+Sss),arechosenasthebasisofangularmomentumcouplingscheme,1212100,2轾=-臌1212110,2轾=+臌121211,1,1.=-=Thefo…     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.