Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

将A-L理论推广到无限维李代数

为使由Alhassid与Levine所提出的动力学李代数方法（简称A－L理论）能适用于更多的散射体系，在h(∞)中引入了有效集合C（有限维）的概念．按照微扰理论的意义，C中的代数元所对应的群参量是较低次微扰的结果，而不属于C的代数元所对应的群参量则相当于较高次做扰所产生的修正结果．因此可以近似地利用C来代替h(∞)．这样，不仅简化了计算程序并且对于很多具有现实意义的散射过程的计算成为可能．     

共线散射体系A+BC的平-振能量传递──无限维李代数处理方法

利用无限维李代数方法处理了在BC分子能谱中含有二级与三级非简谐项的散射体系A＋BC的平-振能量传递问题，获得了散射过程的含有主要动力学参量的跃迁矩阵元和跃迁几率的解析表达式     

Rapid and simple method for determination of Nepsilon-(carboxymethyl)lysine and Nepsilon-(carboxyethyl)lysine in urine using gas chromatography/mass spectrometry

A new procedure was developed to determine in urine the concentrations of N(epsilon)-(carboxymethyl)lysine (CML) and N(epsilon)-(carboxyethyl)lysine (CEL), the major products of oxidative modification of glycated proteins, to assess levels of oxidative stress in physiological systems. The urine samples were acetonitrile-deproteinized, then derivatized by ethylchloroformate, and N(O,S)-ethoxycarbonyl ethyl esters of amino acids were analysed by isotope dilution gas chromatography/mass spectrometry. Recovery averaged 89%. Linearity was excellent (r = 0.998-0.999) in the 0.5-25 micromol/L range for CML and CEL. The limit of detection of this assay was 0.1 micromol/L (corresponding to 0.20 pmol of CML or CEL on column). Intra-day and inter-day precisions were likewise excellent, with relative standard deviations <4.63 and <6.15%, respectively. Accuracy of CML and CEL determination (15 micromol/L) was 2.9 and 5.9% of the estimated theoretical value. The time from obtaining the urine sample to determination of the concentration from the chromatographic peak was 80 min or less. This method is sensitive, reproducible, accurate, relatively cheap and very simple. It can be useful for laboratories involved in the diagnosis and monitoring of age-related chronic diseases.     

Design of a combined ozone/electron beam process for waste water and economic feasibility of the process

A design of a combined ozone/electron beam irradiation process for treating a 50 m³/h waste water stream from a molasses processing is discussed. Moreover, a cost evaluation of such a process in comparison to a conventional ozonation/biology treatment process has been performed to assess the potential of the irradiation process for technical use. Although the result of this comparison is not bad for the irradiation process an implementation into a full scale plant would not seem to be the thing to do in the present case.     

On solving sparse band systems with three algorithms of the ABS family

In this paper, we examine three algorithms in the ABS family and consider their storage requirements on sparse band systems. It is shown that, when using the implicit Cholesky algorithm on a band matrix with band width 2q+1, onlyq additional vectors are required. Indeed, for any matrix with upper band widthq, onlyq additional vectors are needed. More generally, ifa _kj 0,j>k, then thejth row ofH _i is effectively nonzero ifj>i>k. The arithmetic operations involved in solving a band matrix by this method are dominated by (1/2)n ² q. Special results are obtained forq-band tridiagonal matrices and cyclic band matrices.The implicit Cholesky algorithm may require pivoting if the matrixA does not possess positive-definite principal minors, so two further algorithms were considered that do not require this property. When using the implicit QR algorithm, a matrix with band widthq needs at most 2q additional vectors. Similar results forq-band tridiagonal matrices and cyclic band matrices are obtained.For the symmetric Huang algorithm, a matrix with band widthq requiresq–1 additional vectors. The storage required forq-band tridiagonal matrices and cyclic band matrices are again analyzed.This work was undertaken during the visit of Dr. J. Abaffy to Hatfield Polytechnic, sponsored by SERC Grant No. GR/E-07760.     

Reachable and controllable sets for two-dimensional,linear, discrete-time systems

We consider two-dimensional discrete-time linear systems with constrained controls. We propose a simple polynomial time procedure to give an exact external representation of theN-step reachable set and controllable set. The bounding hyperplanes are explicitly derived in terms of the data of the problem. By using a result in computational geometry, all the calculations are made in polynomial time in contrast to classical methods. The limit case asN is also investigated.     

Coulomb scattering of an electron by a monopole

The Coulomb scattering of an electron by a magnetic monopole is analyzed using a lowest-order quantum perturbation approximation suggested by a two-potential Lagrangian form for classical electromagnetism, generalized through the use of spacetime algebra to include magnetic monopoles. Good agreement with existing conventional analyses of this problem is demonstrated.1. Work supported by Department of Energy contract DE-AC03-76SF00515.2. The idea to employ spacetime algebra (sometimes called Dirac algebra) to incorporate magnetic monopoles into classical electromagnetic theory was proposed by de Faria-Rosaet al. [3].3. This is a factori difference between the definition of 5 by Eq. (3) and that by Bjorken and Drell [6]. Since a cross section (without interference terms) is being calculated, we can ignore this distinction.     

过硫酸盐活化高级氧化新技术

过硫酸盐在热、光、过渡金属催化等条件激活下产生强氧化性的硫酸根自由基·SO₄^-。基于·SO₄^-的过硫酸盐活化“高级氧化技术”在环境污染治理领域的应用,是刚刚发展起来的崭新的研究方向,具有广阔的应用前景。本文在分析其基本原理的基础上,综述了过硫酸盐活化技术在国内外土壤地下水有机污染原位修复、难降解有机废水处理等环境污染治理方面的研究进展,并就存在问题进行了研究展望。