ON THE GLOBAL ATTRACTIVITY FOR A NEUTRAL DIFFERENCE EQUATION WITH TWO DELAYS

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Subdivision of simplices relative to a cutting plane and finite concave minimization

In this article, our primary concern is the classical problem of minimizing globally a concave function over a compact polyhedron (Problem (P)). We present a new simplicial branch and bound approach, which combines triangulations of intersections of simplices with halfspaces and ideas from outer approximation in such a way, that a class of finite algorithms for solving (P) results. For arbitrary compact convex feasible sets one obtains a not necessarily finite but convergent algorithm. Theoretical investigations include determination of the number of simplices in each applied triangulation step and bounds on the number of iterations in the resulting algorithms. Preliminary numerical results are given, and additional applications are sketched.     

Crystal Structures of Analogs of threo-Methylphenidate

The crystal structures of the chloride salts of five analogs of threo-methylphenidate have been obtained. Four of these have different substituents on the phenyl ring while the fifth is the ethyl ester of methylphenidate. All five structures have similar three-dimensional conformations and these are compared with the global minimum obtained by MM2-87 calculations. There is good agreement between the crystal structures and the computed global minimum with the major difference being the presence of a chloride counterion in the crystal structures that prevents the carbonyl oxygen from approaching the equatorial ammonium hydrogen as closely as in the computed global minimum.     

一类齐三次系统的全局结构

本文讨论了一类齐三次系统的全局结构，并给出了它们的系数条件．     

Simulated annealing for constrained global optimization

Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generateany point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by anadaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.This material is based on work supported by a NATO Collaborative Research Grant, no. 0119/89.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance:the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O-Br bonds more prone to dissociation.     

Effects of substituents on activation parameters in SN2 reactions at aliphatic carbon in solution

Changes of the activation parameters in aliphatic S_N2 reactions with anionic and neutral nucleophiles in various solvents, ΔH^≠ and ΔS^≠, were correlated with σ constants of the substituents. The resultant δΔH^≠ and δΔS^≠ reaction constants are linearly related for variations of substituents at the substrate, leaving group and nucleophile. Correlations of δΔH^≠ versus δΔS^≠ allow the estimation of the contribution of changes of the internal enthalpy, δΔH, to the enthalpy reaction constant, δΔH^≠, which gives a single linear dependence on the Hammett ρ reaction constants. The deviations from the dependence of δΔH versus ρ can be interpreted in terms of changes in the transition state structure in S_N2 reactions. The results obtained show that the substituent effects on the charge development in the transition state are governed by the magnitude of δΔH. Copyright © 2009 John Wiley & Sons, Ltd.     

Complete Solutions and Extremality Criteria to Polynomial Optimization Problems

This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications, Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore, a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples.