Molecular properties with dual basis set methods

The dual basis set approach has proven to be very successful for accurately estimating total energies with large basis sets. This study extends the applications of this technique to the calculation of molecular properties, including energy derivatives with respect to nuclear positions and to an external electric field. All energy derivatives have been calculated numerically via finite-differences. Molecular gradients and Hessians as well as dipole moments and polarizabilites have been calculated at the HF and MP2 levels using two alternative versions of the dual basis set method. The accuracy of these approaches is discussed in the context of quality of basis sets used in calculations. It is shown that even quite poor results obtained with the 6-311G basis set are significantly improved in dual basis set calculations with the 6-311G(d,p) and 6-311G(3df,3dp) basis sets.     

On the interaction of the Dirac oscillator with the Aharonov–Casher system in topological defect backgrounds

In this paper, we study the influence of the Aharonov–Casher effect [Y. Aharonov, A. Casher, Phys. Rev. Lett. 53 (1984) 319] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov–Casher geometric phase. We also discuss the influence of curvature and torsion on the relativistic energy levels and the Dirac spinors due to the topology of the cosmic string and cosmic dislocation spacetimes.     

LCAO-MO Calculation of Dipole Transition Moment of Some First-Row Transition Metal Tetroxy Anions

Abstract

Recently very encouraging results of semiempirical parameteric calculation of dipole transition moments of the lowest energy t₁ ? 2e (¹A₁ - ¹T₂) transition of permanganate and chromate ions have been reported. In the case of vanadate ion, which is isoelectronic with the permanganate and chromate ion, no such study of spectral intensities appears to have been reported so far. A parameteric calculation in terms of a single parameter β, the ligand mixing coefficient using Richardson's orbitals⁴ and both dipole velocity and dipole length operators have been reported in the present paper.     

Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ^d (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d2.     

Time-marching numerical schemes for the electric field integral equation on a straight thin wire

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.     

Nonmonotone stabilization methods for nonlinear equations

We are concerned with defining new globalization criteria for solution methods of nonlinear equations. The current criteria used in these methods require a sufficient decrease of a particular merit function at each iteration of the algorithm. As was observed in the field of smooth unconstrained optimization, this descent requirement can considerably slow the rate of convergence of the sequence of points produced and, in some cases, can heavily deteriorate the performance of algorithms. The aim of this paper is to show that the global convergence of most methods proposed in the literature for solving systems of nonlinear equations can be obtained using less restrictive criteria that do not enforce a monotonic decrease of the chosen merit function. In particular, we show that a general stabilization scheme, recently proposed for the unconstrained minimization of continuously differentiable functions, can be extended to methods for the solution of nonlinear (nonsmooth) equations. This scheme includes different kinds of relaxation of the descent requirement and opens up the possibility of describing new classes of algorithms where the old monotone linesearch techniques are replace with more flexible nonmonotone stabilization procedures. As in the case of smooth unconstrained optimization, this should be the basis for defining more efficient algorithms with very good practical rates of convergence.This material is partially based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410, National Science Foundation Grant CCR-91-57632, and Istituto di Analisi dei Sistemi ed Informatica del CNR.     

Image space analysis of generalized fractional programs

The solution of a particular nonconvex program is usually very dependent on the structure of the problem. In this paper we identify classes of nonconvex problems involving either sums or products of ratios of linear terms which may be treated by analysis in a transformed space. In each class, the image space is defined by a mapping which associates a new variable with each original ratio of linear terms. In the image space, optimization is easy in certain directions, and the overall solution may be realized by sequentially optimizing in these directions.In addition to these ratio problems, we also show how to use image space analysis to treat the subclass of problems whose objective is to optimize a product of linear terms. For each class of nonconvex problems, we present an algorithm that locates global solutions by computing both upper and lower bounds on the solution and then solving a sequence of linear programming sub-problems. We also demonstrate the algorithms described in this paper by solving several example problems.     

Near optimality of stochastic control in systems with unknown parameter processes

Stochastic control for systems with an unknown parameter is considered in this paper. The underlying problem is to minimize a functional subject to a system described by a singularly perturbed differential equation with an unknown parameter process driven by fast fluctuating random disturbances. This problem arises in the context of stochastic adaptive control, adaptive signal processing, and failure-prone manufacturing systems. Due to the nature of the wide-bandwidth noise processes, identifying the parameter process for eacht is very hard since the driving noise changes very rapidly. An alternative approach is used, and an auxiliary control problem is introduced to overcome the difficulties. By means of weak convergence methods and comparison control techniques, nearly optimal controls are obtained.This research was supported in part by the National Science Foundation under Grant DMS-9022139 and DMS-9224372.     

A parallel method for finding the global minimum of univariate functions

We describe a new parallel method for solving global optimization problems. The formulation of the decision rules of this method is presented. We examine convergence conditions of the proposed algorithm and establish conditions which guarantee a considerable speedup with respect to the sequential version of the algorithm. We also present some numerical experiments executed on Alliant FX/80 for one class of multiextremal functions.The authors are greatly indebted to R. G. Strongin who stimulated the fulfillment of this research. They also would like to thank the anonymous referees for their useful suggestions.The research of the first author was partially supported by Grant 9494/NC/89 from the Italian Government under the Italian-Soviet Agreement about the Cultural and Scientific Exchange in 1990–1991. He thanks the Systems Department, University of Calabria, where he was a Visitor.     

一类非线性单调型方程的区域分裂法

本文考虑了一类非线性单调问题的加性Schwgrz交替法和异步平行算法,并得到了在能量模意义下的收敛性结果,最后还讨论了格式的有限元离散。