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.     

设计性、研究性实验对学生创新能力的培养

根据设计性、研究性实验的特点,从几个方面、不同的角度,阐述了设计性、研究性实验对学生创新能力培养的作用与意义。     

一种新的奇偶非线性相干态的位相统计性质

根据Pegg-Barnett位相定义, 计算了一种新的奇偶非线性相干态的位相概率分布函数, 利用数值计算方法研究了它们的位相统计性质. 数值计算结果表明：新的奇偶非线性相干态的位相特性与通常奇偶相干态的位相特性截然不同.     

Focusing and diffraction by an optical lens and a small circular aperture

Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, analytical expressions for the transversal and axial field distribution of plane waves propagating through a thin lens followed by a small circular aperture are derived and used to study the focusing and diffraction properties of plane waves. Some special cases of our general result are discussed, and illustrative numerical calculation results are given. It is found that the vectorial nonparaxial approach should be applied if the aperture dimension is comparable with the wavelength or the focusing is strong.     

Surface structures formed by individual adsorption and coadsorption of Mn and Bi on Cu(0 0 1), studied by LEED

We have studied the individual adsorption of Mn and Bi, and their coadsorption on Cu(0 0 1) by low-energy electron diffraction (LEED). For Mn, we have determined the c(2 × 2) structure formed at 300 K, whose structure had been determined by several methods. We reconfirmed by a tensor LEED analysis that it is a substitutional structure and that a previously reported large corrugation (0.30 Å) between substitutional Mn and remaining surface Cu atoms coincides perfectly with the present value. In the individual adsorption of Bi, we have found a c(4 × 2) structure, which is formed by cooling below ∼250 K a surface prepared by Bi deposition of ∼0.25 ML coverage at 300 K where streaky half-order LEED spots appear. The c(4 × 2) structure has been determined by the tensor LEED analysis at 130 K and it is a substitutional structure. In the coadsorption, we found a c(6 × 4) structure, which has been determined by the tensor LEED analysis. It is very similar to the previously determined structure of the c(6 × 4) formed by coadsorption of Mg and Bi, and embedded MnBi₄ clusters are arranged in the top Cu layer instead of MgBi₄. Large lateral displacements of Bi atoms in the c(6 × 4)-(Mn + Bi) suggest that the Mn atoms undergo the size-enhancement caused by their large magnetic moment.     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

Remote stereocontrol by the sulfinyl group: Mukaiyama aldol reactions of (S)-2-[2-(p-tolylsulfinyl)phenyl]acetaldehyde in the asymmetric synthesis of β-hydroxyacids and 1,3-diols

(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)₃ yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes.     

Hankel convolution operators on entire functions and distributions

In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration.