The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

k-边覆盖对策及其核心

本文针对从图的k-边覆盖问题引出的合作对策模型，利用线性规划对偶理论得到了其核心非空的一个充分条件和构造核心分配的多项式时间算法，并将这一结果推广到了一般的k-集合覆盖对策模型中．     

三级近似束流光学计算程序

为了精确计算束流在离子光学系统中的传输,用Visual FORTRAN 6.5语言编写了一个计算程序,长约13000行. 此程序可以计算由三圆筒单透镜、三膜片单透镜、双元筒透镜、均匀场静电加速管、磁四极透镜、六极磁铁、静电四极透镜、偏转磁铁、螺线管透镜、ExB~正交电磁场分析器、静电偏转器、漂浮管、QWR(Quarter Wave Resonators)和SLR(Split Loop Resonators)射频加速元件等元件任意组成的离子光学系统. 粒子轨迹的计算可精确到三级近似. 粒子的分布类型也可以有多种选择. 程序具有最优化计算功能,即可以自动调整元件的参数,以实现所需要的光学条件. 各元件之后的横向和纵向相图以及系统的束流包络线以图形方式显示在屏幕上.     

On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program

In this paper an algorithm is developed to generate all nondominated extreme points and edges of the set of objective values of a multiple objective linear program. The approach uses simplex tableaux but avoids generating unnecessary extreme points or bases of extreme points. The procedure is based on, and improves, an algorithm Dauer and Liu developed for this problem. Essential to this approach is the work of Gal and Kruse on the neighborhood problem of determining all extreme points of a convex polytope that are adjacent to a given (degenerate) extreme point of the set. The algorithm will incorporate Gal's degeneracy graph approach to the neighborhood problem with Dauer's objective space analysis of multiple objective linear programs.     

在线氧含量分析中的自动反吹

为解决在线氧含量分析测试仪表常被聚合物堵塞的问题，提出了自动反吹的时序分配和实施控制方案，从而为安全生产提供了保障。     

Theory of reflectance measurements in quantitative evaluation in TLC and HPTLC. 1. Multilayer model of reflectance and transmittance

In the approach described in this paper, the layer of adsorbent is divided into n sublayers. The radiation density in each sublayer is given by the sum of the transmittance and the reflectance of the adjacent sublayers. Absorption of light by the layer or the substance will diminish this radiation density. Depending upon the factors of reflectance and transmittance some light will pass to the adjacent sublayers. Two polynomials are derived from this readily understood formulation to calculate the reflectance or the transmittance of a layer of finite thickness. The algorithms given describe the reflectance and transmittance encountered in practical measurements with large amounts of substance per spot, as well as with small amounts. There are no restrictions with respect to nonideal scattering or reflection by the adsorbent layer support.     

An efficient ab initio gradient program

An ab initio Hartree-Fock gradient program is described. It is characterized by (1) efficiency of the gradient evaluation, and (2) capability of handling higher angular momentum (d andf) basis functions. The latter are constructed from shifted Cartesian Gaussian p-type primitives. A satisfactory solution is presented for the problems connected with the neglect of small integrals in a gradient program. Methods for increasing the efficiency of the SCF procedure are discussed.     

乙醇在杂多酸上的氧化、脱水和程序升温脱附研究

合成了两个系列具有Keggin结构的12-钒钼磷酸和钨钼磷酸,研究了它们对乙醇氧化、脱水的催化反应。借助程序升温脱附技术研究了反应物及产物乙醇、乙烯、乙醚等在样品上的程脱作用。讨论了钨、钒取代部分钼原于后对杂多酸酸性及氧化性能的影响。     

Co(II) Schiff碱载氧载氮性能研究

运用INDO－UHF计算方法研究了CO(Ⅱ) Schiff碱的载氧特性，结果表明，Co(Ⅱ)与O_2的作用是通过σ键组合，并具有较明显的反铁磁性耦合作用, 论证了作为第五轴向配体在可逆载氧过程中的必要性，对比研究了Co－N_2的相互作用. 计算表明，CO(Ⅱ)的Schiff碱络合物可能作为氧氮分离的活性物质，从而具有一定的、潜在的工业应用价值.     

建立在群对称轨道(SMO)及特征组态(CD)基础上的CI方法与程序发展

ISMO－CDCI方法点群理论，特别是不可约张量方法，在量子化学理论方法发展以及简化概念与计算方面，发挥了重要作用．但在国外的量子化学计算程序（如G94）中，在后自洽场（opt－SCF）计算方面，很少用到对称约化．在文献中，只见有关hbeltah群（DZh与它的子群）对称约化用于组态相关计算的报导．由于多重耦合系数的计算复杂，蜕化不可约表示多体问题的对称约化难于得到解决．我们提出了一个统一与普遍的方法，它能解决所有分子体系多体相关的点群对称约化问题［‘－6］，这个方法的核心是群对称轨道（SMO）概念的提出．SMO的基本特…