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     

Structural chemistry of bimetallic hydride complexes of titanium and aluminium: I. Crystal and molecular structure of [(η5-C5H5)2,Ti(μ-H)2AlH2]2(CH3)2NCH2CH2N(CH3)2C6H6

The structure of a titanium aluminium hydride complex of composition [(C₅H₅)₂TiAlH₄]₂(CH₃)₂NC₂H₄N(CH₃)₂C₆H₆ has been determined by X-ray diffraction. The complex forms triclinic crystals with unit cell dimensions a = 8.406(2), b = 10.117(2), c = 11.269(3) Å; α = 112.01(2)°, β = 109.25(2)°, γ = 87.04(2)°, space group P$\text{1}$, Z = 2 and density d = 1.21 g/cm³. The structure was refined to give a discrepancy index R = 0.056. The crystals are composed of centrosymmetric molecules of (Cp₂TiAlH₄)₂TMEDA (Cp = η⁵-cyclopentadienyl) and molecules of crystal benzene. Two moieties of Cp₂TiH₂AlH₂ are linked by a tetramethylethylenediamine molecule (r_AlN 2.11 Å). The aluminium atom is bonded to a titanium atom by a double hydride bridge (r_AlH b = 1.8, 1.6 Å, r_TiH b = 1.6 Å), and has trigonal bipyramidal stereochemistry, [H₄N] (r_AlH t = 1.6 Å).     

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.     

Finitely maxitive T-conditional possibility theory: Coherence and extension

Starting from the axiomatic definition of finitely maxitive T-conditional possibility (where T is a continuous triangular norm), the paper aims at a comprehensive and self-contained treatment of coherence and extension of a possibilistic assessment defined on an arbitrary set of conditional events. Coherence (or consistence with a T-conditional possibility) is characterized either in terms of existence of a linearly ordered class of finitely maxitive possibility measures (T-nested class) agreeing with the assessment, or in terms of solvability of a finite sequence of nonlinear systems for every finite subfamily of conditional events. Coherence reveals to be a necessary and sufficient condition for the extendibility of an assessment to any superset of conditional events and, in the case of T equal to the minimum or a strict t-norm, the set of coherent values for the possibility of a new conditional event can be computed solving two optimization problems over a finite sequence of nonlinear systems for every finite subfamily of conditional events.     

Classification of extensions of torus algebra II

We use extension theory and algebraic methods to give a complete characterization of extensions of torus algebra by stable Cuntz algebras,and prove certain classification theorems of these extension algebras.     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.