Seminormality and upper semicontinuity in optimal control

This paper concerns the concept of upper semicontinuity of variable sets, precisely the variant of Kuratowski's definition of upper semicontinuity that Cesari has denoted as property (Q). This concept has been used by Cesari in most of his papers on existence theorems for optimal solutions, and later used by Olech, Lasota and Olech, Brunovsky, Baum, Suryanarayana, and Angell. First, criteria are given for property (Q) in addition to those which had been already given previously. Then, it is shown that a slight restriction in the concept can be expressed in a form which is similar to Tonelli's concept of seminormality for free problems of the calculus of variations. Thus, the property (Q) appears to be a generalization to Lagrange problems of control of the well-known concept of seminormality for free problems.This research was partially supported by AFOSR Research Project No. 69-1662.     

Microwave-assisted synthesis of symmetric and asymmetric viologens

Viologens are generally synthesized by N-alkylating 4,4′-bipyridine with alkyl halides. Under conventional heating conditions, however, their synthesis suffers from long reaction times and, often, low yields. In this work, symmetric and asymmetric viologens were synthesized under the assistance of microwave irradiation in good to excellent yields and in short reaction times.     

Molecular-cluster studies of defects in silicon lattices

Summary Ab initio HF-SCF-LCAO calculations have been performed on Si _n H _2n+n (n=1 to 5) by means of four different basis sets. Total energies, first ionization potentials, minimum-energy geometries and torsional barriers of rotation around the Si−Si bond have been computed in order to test the accuracy of the basis sets used.

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Riassunto Sono stati eseguiti calcoliab initio HF-LCAO-SCF su composti della famiglia dei silani lineari (Si _n H _2n+2 ,n=1, ..., 5) mediate quatro differenti insiemi di funzioni di base. Sono state calcolate energie totali, primi potenziali di ionizzazione, geometrie al minimo di energia e barriere torsionali attorno al legame Si−Si per poter verificare l'accuratezza degl'insiemi di funzioni di base usati.

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Резюме Сначала проводятся вычисления HF-SCF-LCAO в семействе соединений Si _n H _2n+1 (n от 1 до 5), используя четыре различных базисных системы. С целью проверки точнсти использованных базисных систем систем бычислены полные знергии, первые потенциалы ионизации, геометрии с минимльной энергией и барьеры врашения вокруг связи Si−Si.

     

The nonequilibrium Lorentz gas

We study the conductivity of a Lorentz gas system, composed of a regular array of fixed scatterers and a point-like moving particle, as a function of the strength of an applied external field. In order to obtain a nonequilibrium stationary state, the speed of the point particle is fixed by the action of a Gaussian thermostat. For small fields the system is ergodic and the diffusion coefficient is well defined. We show that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At larger values of the field we observe a variety of possible dynamics, including the breakdown of ergodic behavior, and later the existence of a single stable trajectory for the largest fields. We also study the behavior of the system as a function of the orientation of the array of scatterers with respect to the external field. Finally, we present a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain. The consequences of this behavior for the ergodicity of the system are explored. (c) 1995 American Institute of Physics.     

Maximally homogeneous para-CR manifolds

We define the notion of a (weak) almost para-CR structure on a manifold M as a distribution HM ⊂ TM together with a field K ∈ Γ(End(HM)) of involutive endomorphisms of HM. If K satisfies integrability conditions, then (HM, K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.Mathematics Subject Classifications (1991): 53C15, 53D99, 58A14