The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

Synthesis of pyridine derivatives by reactions of α,β-unsaturated nitriles with 2-oxo-cycloalkano carbothioic acid anilides

Summary The tandem Michael addition-cyclization of 2-oxo-cycloalkane carbothioic acid anilides1–3 to benzylidenemalononitrile4 yielded spiroannulated pyridines5–7. Reaction of acrylonitrile with2 and3 gave 2,2-disubstituted Michael adducts14,15, whereas with1 led to 2,2,5-tri(2-cyanoethyl)-cyclopentanone11.

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Synthese von Pyridinderivaten durch Reaktionen von ,-ungesättigten Nitrilen mit 2-Oxo-cycloalkano-thiokohlensäure-aniliden

Zusammenfassung Die Michael Tandem-Addition-Cyclisierung von 2-Oxo-cycloalkano-thiokohlensäure-aniliden1–3 mit Benzylidenmalononitril4 ergab die spiroannelierten Pyridine5–7. Reaktion von Acrylnitril mit2 und3 ergab die 2,2-disubstituierten Michael-Addukte14,15, wohingegen mit1 2,2,5-Tri(2-cyanethyl)-cyclopentanon11 erhalten wurde.

     

Direct and stepwise intercalation of alkylalcohols intoα-zirconium phosphate

Intercalation of alkylalcohols into -zirconium phosphate was investigated at 25°C and/or under reflux.n-Alcohols having two to five carbons and 2-propanol were taken up at 25°C. These alcohols, andn-hexanol and heptanol, also intercalated under reflux.n-Alcohols having eight to eighteen carbon atoms intercalated when a stepwise method was employed. 2-Butanol and tertiary amylalcohols intercalated under reflux using a butanol intercalate as a starting material. Ethanol-to-butanol intercalates were unstable at room temperature, losing alcohols and changing to -zirconium phosphate. The particle size of the -zirconium phosphate did not affect the intercalation of alcohols.     

A configuration interaction study of phosphine using bonded functions

A computational study is made of the effect of basis set upon the energy, properties and inversion barrier of the phosphine molecule. The calculations are performed at both the SCF and CI level. The flexibility of the double zeta basis is discussed in the light of the results.     

O（^3P）原子与丙醛和正丁醛化学反应动力学研究

我们已对O(~3p)原子和酮类分子化学反应速率常数进行了系列测定,分析讨论了羰基对O(~3p)抽提氢原子反应速率的影响,关于O(~3p)与醛类分子反应速率的测定也有报道。本文用流动微波放电-化学发光光子计数方法测定O(~3p)原子与丙醛和正丁醛化学反应速率常数及其与温度的关系,并由动力学数据对醛基中C—H键的离解能进行了讨论。     

正交试验法研制多烷基二氢化茚

双环苯型麝香化合物对香料工业具有重要意义。如粉檀麝香是合成麝香料。而1,1,2,3,3,5-六甲基-2.3-二氢化茚(HMI)则是制备粉檀麝香的母体化合物, 其经酰化后即可得到粉檀麝香。本文以对甲基异丙苯和2-甲基-丁烯-[2]为原料, 合成了HMI。     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

The inclusion complex of piromidic acid with dimethyl-β-cyclodextrin in aqueous solution and in the solid state

Inclusion complex formation of piromidic acid (PA) with dimethyl--cyclodextrin (DM--CD) in aqueous solution and in the solid state was confirmed by the solubility method, differential scanning calorimetry (DSC) and proton nuclear magnetic resonance (¹H-NMR) spectroscopy. The apparent stability constant,K _c , of the complex was estimated to be 244 M^–1. The stoichiometry of the complex was given as the ratio 1:2 of PA to DM--CD. The dissolution rate of the PA/DM--CD complex was much greater than that of intact PA.Presented at the Fourth International Symposium on Inclusion Phenomena and the Third International Symposium on Cyclodextrins, Lancaster, U.K., 20–25 July 1986.     

Synthetic receptors based on calix[4]arene functionalized at the lower rim in molecular recognition of dicarboxylic, α-hydroxycarboxylic,and α-amino acids

New calix[4]arenes, di- and tetrasubstituted at the lower rim, with different functional groups were synthesized. They were studied as carriers of a series of dicarboxylic and -hydroxycarboxylic acids through a liquid impregnated membrane. The calix[4]arenes under study are capable of molecular recognition of oxalic acid in the series of structurally similar dicarboxylic and -hydroxycarboxylic acids. The regularities found make it possible to change purposefully the receptor ability of 1,3-disubstituted calix[4]arenes by variation of the nature of substituents.