Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

Polynuclear manganese grids and clusters—A magnetic perspective

High nuclearity paramagnetic, spin-coupled transition metal clusters and grids are fascinating chemists and physicists partly because of their structural beauty, and the challenge of creating them, but also because of their novel physical properties. Magnetic interactions between the spin centers are a primary focus. This review will examine a selection of Mn(II) polynuclear grids and clusters, with nuclearities in the range Mn₄ to Mn₉. Theoretical treatments of the magnetic properties are discussed, and approaches to solving the exchange problem for ‘large’ spin systems related to computational difficulties. A freely available software package (MAGMUN4.1) is presented as a means of dealing simply with spin-coupled clusters in general, and symmetry reduction methods are discussed briefly as a means of dealing with ‘large’ spin systems.     

The European Eco-Management and Audit Scheme Accreditation – an overview

 Environmental quality is still deteriorating in the EU and worldwide despite all the Directives and Regulations in this field over the past 20 years. The European Community has devised a new approach to this problem with the introduction of the Eco-Management and Audit Scheme Regulation. This Regulation provides industry with an opportunity to demonstrate that it can achieve continuous improvement in its environmental performance through a voluntary scheme which is not based on the traditional command and control mechanisms of Directives. This paper gives an overview of the steps involved in implementing the European Eco-Management and Audit Scheme and the role of accreditation in supporting the scheme.     

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

Cyclic homology for schemes

Using hypercohomology, we can extend cyclic homology from algebras to all schemes over a ring . By `extend' we mean that the usual cyclic homology of any commutative algebra agrees with the cyclic homology of its corresponding affine scheme.

     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

On the modelling of solid state reactions.Synthesis of YAG

There is a model of yttrium aluminium garnet (YAG) synthesis presented in this article. The developed model is based on nonlinear reaction–diffusion partial differential equations. The solution was carried out numerically using finite difference techniques. We got dependability curves for diffusion and reaction rates and offered possible method to localize values of diffusion and reaction rate constants precisely enough.AMS subject classification: 35K57, 65M06     

On obtaining localized bonding schemes from delocalized molecular-orbital wave functions

A straightforward procedure is proposed for expanding a molecular orbital determinantal wave function into a set of determinantal wave functions composed of atomic orbitals localized at the atoms of a molecule. By employing this method, atomic orbital determinants and their weights can be derived for a molecule from the computed molecular-orbital wave function. The procedure permits the interpretation of a molecular orbital determinantal wave function in terms of bonding schemes related to the classic resonance structures used by organic chemists. By using the unrestricted molecular orbital determinant, bonding schemes and their weights are obtained for butadiene, the butadiene radical cation and the acrylonitrile radical anion. Their dominant bonding schemes are in accord with the relevant resonance structures for these molecules. For the butadiene radical cation and the acrylonitrile anion they are shown to be compatible with the accepted mechanisms of the electrochemical coupling reactions of butadiene and acrylonitrile. Received: 7 August 1996 / Accepted: 18 March 1997