Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation

We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods.     

Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.     

多自由度测试技术的发展

介绍目前较常用的多种多自由度测试技术，给出每种测试技术的测试原理和应用场合，比较各种技术的优缺点和适用范围，讨论该技术发展的方向。     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

邻苯二甲酸二丁酯对雌二醇与血清组分结合的影响

利用紫外分光光度法测定了邻苯二甲酸二丁酯 (DBP)、雌二醇 (E2 )与血清组分 3种物质间两两结合的二元体系和三元体系结合常数。结果表明 ,DBP、血清组分和 E2 三者之间能两两结合 ,其中以 E2 与血清组分的结合能力最强。当三者处于同一体系中 ,随着 DBP浓度的增加 ,E2 与血清组分 - DBP二元体系间的结合常数也逐渐增加 ,其最大值高出正常 E2 与血清组分结合常数 (7.5 4× 10 4mol-1· L )近一个数量级。这表明 ,DBP的存在可能不会与 E2 对血清组分进行竞争结合 ,但由于本身的结合特点 ,会减少血液中游离E2 的含量 ,从而影响细胞内雌激素的平衡     

An inverse spectral problem for a nonsymmetric differential operator: Reconstruction of eigenvalue problem

In this paper, an algorithm is established to reconstruct an eigenvalue problem from the given data satisfying certain conditions. These conditions are proved to be not only necessary but also sufficient for the given data to coincide with the spectral characteristics corresponding to the reconstructed eigenvalue problem.     

On‐line Determination of Particle Size Distributions in Flowing Dispersions

Emulsions are of great importance to industry. They are involved in many engineering operations, including chemical reactions, extraction, emulsification and suspension polymerization, etc. However, an important problem for these processes is how to control the size distribution of the dispersed phase. Indeed, off‐line analysis of the emulsion may generate uncertainties due to sampling and dilution of the product, which are likely to change the dispersion state and physico‐chemical properties. In this work, an on‐line optical method is proposed to characterize dispersed media in real flowing conditions. This method is based on the time‐analysis of back‐scattered light fluctuations. The present paper deals with the development of this method and its application to dispersions of alumina in water. The results obtained with the on‐line optical method are compared with those acquired by classical laser light scattering and microscopy.     

同轴双无衍射光的理论与实验

提出同轴双无衍射光的概念。如果两束汇聚角略有不同的同轴无衍射光同时存在，则它们相互之间叠加干涉后产生一种纵向呈周期变化的光场结构，这是一种新的光束空间分布，这种光束在横向仍是一种同心环光斑，可用于精密对准。而在不同纵向位置，这些同心环的强度分布是不同的，且是周期性变化的。同轴双无衍射光的轴向周期性可用于沿光束传播方向的定位。文中提出了双环缝法、分段圆锥透镜法、正弦相位环光栅法等实现同轴双无衍射光的理论与实验方法，分析了同轴双无衍射光的横向与纵向传播的衍射光斑特性，理论计算与实验测量的结果基本相符合。     

C++QED: an object-oriented framework for wave-function simulations of cavity QED systems

We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting qua ntum dynamics in general. The user is provided with a number of “elements”, e.g. pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.     

类型γ射线能谱指纹的识别机理

放射源的辐射指纹能起到标识和鉴别放射性物体的作用.在涉及核弹头不可逆销毁过程的深度核裁军核查中,核弹头的辐射指纹对标识和鉴别裁减下来的核弹头将起到关键作用.预先研究辐射指纹的有关技术,如识别机理的研究,将有助于深度核裁军的核弹头核查技术发展.以实验室放射源为研究对象,探索了类型γ射线能谱指纹的同一性识别机理.类型γ射线指纹识别机理的研究,就是要找出一种合适的方法,以较高的置信度,描述两个正在进行比较的γ射线指纹是否为同一放射源的指纹.采用了谱形比较法,并用谱相似度概念来描述两个指纹的相似程度.在谱形比较思想的指导下,编制了放射源类型指纹识别软件,并通过放射源同一性的识别实验验证了软件的有效性,同时研究了谱相似度随统计涨落和测量条件,如时间、源强和本底等因素的变化情况.研究结果表明:1)用相似度概念来描述两个指纹的相似程度,回答两个待比较的γ射线能谱是否代表同一类型放射源,是切实可行的;2)该识别机理只具备识别放射源类型的能力,而对同一类型、差异甚微的放射源个体还不能识别 关键词： γ射线能谱指纹 辐射指纹 识别机理 核查技术