Computational results on an algorithm for finding all vertices of a polytope

This paper provides answers to several questions raised by V. Klee regarding the efficacy of Mattheiss' algorithm for finding all vertices of convex polytopes. Several results relating to the expected properties of polytopes are given which indicate thatn-polytopes defined by large numbers of constraints are difficult to obtain by random processes, the expected value of the number of vertices of polytope is considerably less than Klee's least upper bound the expected performance of Mattheiss' algorithm is far better than Klee's upper bound would suggest.     

Pyrolysis Analysis and Kinetics of Crude Oils

This research presents the results of an experimental study on the determination of pyrolysis behaviour and kinetics of six crude oils by differential scanning calorimetry (DSC) and thermogravimetry (TG/DTG). Crude oil pyrolysis indicated two main temperature ranges where loss of mass was observed. The first region between ambient to 400°C was distillation. The second region between 400 and 600°C was visbreaking and thermal cracking. Arrhenius-type kinetic model is used to determine the kinetic parameters of crude oils studied. It was observed that as crude oils gets heavier (°API decreases) cracking activation energy increases. Activation energy of cracking also show a general trend with asphaltene content. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermoanalytical characterization of polyphenylacetylene: III. Use of modulated differential scanning calorimetry (MDSC)

Four polyphenylacetylene samples, synthesized using different C₆H₅OH/Mo molar ratios, were investigated thermoanalytically by modulated temperature differential scanning calorimetry (MTDSC) in order to clarify a non-reversible exothermic event observed between 473 and 523 K on normal DSC. A stepwise, non-reversible change in heat capacity suggests the presence of internal reactions within the sample, that are followed by decomposition with loss of volatile products.     

Study of a Catalytic Mechanism in Additive Differential Pulse Techniques

The new electrochemical double pulse technique, known as additive differential normal pulse voltammetry (ADNPV) when there is no restriction on the duration of both pulses, and additive differential pulse voltammetry (ADPV) when t₂?t₁, has been applied to a pseudo‐first‐order catalytic mechanism. The expressions obtained here are applicable to planar and spherical electrodes, of any radius. This is of great interest since the size of the electrode plays an important role in the preponderating of diffusive and kinetics processes. The signal obtained with this technique presents the same morphological characteristics as the triple pulse technique, double differential pulse voltammetry (DDPV) and is more advantageous than DDPV and than the double pulse one, differential pulse voltammetry (DPV).     

Perfect equilibria in stochastic games

We examine stochastic games with finite state and action spaces. For the -discounted case, as well as for the irreducible limiting average case, we show the existence of trembling-hand perfect equilibria and give characterizations of those equilibria. In the final section, we give an example which illustrates that the existence of stationary limiting average equilibria in a nonirreducible stochastic game does not imply the existence of a perfect limiting average equilibrium.Support was provided by the Netherlands Organization for Scientific Research NWO via the Netherlands Foundation for Mathematics SMC, Project 10-64-10.     

Partially and totally asynchronous algorithms for linear complementarity problems

A unified treatment is given for partially and totally asynchronous parallel successive overrelaxation (SOR) algorithms for the linear complementarity problem. Convergence conditions are established and compared to previous results. Convergence of the partially asynchronous method for the symmetric linear complementarity problem can be guaranteed if the relaxation factor is sufficiently small. Unlike previous results, this relaxation factor interval does not depend explicitly on problem size.This material is based on research supported by the Air Force Office of Scientific Research Grant No. AFOSR-89-0410.The author wishes to thank the referee for pointing out how to improve the bound (12). The same technique can be used to reduce the factorn in Ref. 5, p. 553, to .     

Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.     

On a class of least-element complementarity problems

The present paper studies the linear complementarity problem of finding vectorsx andy inR ₊ ⁿ such thatc + Dx + y 0,b – x 0 andx ^T (c + Dx + y) = y ^T (b – x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of least-element solution is presented. Finally, applications and computational experience with its implementation are discussed.Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.     

高能闪光照相中影响光程确定的几个因素

 利用闪光照相基本原理和成像原理，在直接记录法和转换屏记录法的情况下，研究了闪光照相中影响X射线在材料中光程确定的主要因素。结果表明，影响光程确定的几个因素是：散射效应、光源角分布效应、立体角效应和能谱效应。对于高能闪光照相，散射效应是影响光程确定的最主要因素，散射的存在使光程的测量值比实际值降低20%～40%。因此必须在做CT之前，对散射的影响进行修正。     

基于激光诱导击穿光谱(LIBS)的煤灰熔点快速检测

炉内结渣是影响火电机组和气化工艺可靠运行的关键因素之一,准确预测灰熔点可以提前调整炉膛出口温度以避免结渣。本论文采用激光诱导击穿光谱（LIBS）采集煤灰样中金属元素的光谱,分别建立煤灰中的金属元素的谱线强度与煤灰熔点的随机森林模型、支持向量机回归模型和线性回归模型,直接预测煤灰熔点温度。采用基于马氏距离(MD)的异常数据剔除算法和基于稀疏矩阵的基线估计与降噪算法（BEADS）,对粉煤灰样的全光谱数据进行了预处理。随机森林模型对粉煤灰熔点的预测平均相对误差（MRE）为54.74%,支持向量机回归模型的预测平均相对误差为60.08%,而线性回归模型的预测平均相对误差达到了9.78%。研究结果表明,线性回归模型对煤灰熔点的预测结果更准确。