Publication list

The helium atom in its ground state, subject to strong magnetic fields, is treated using a variational method. Trial functions consisting of Gaussians with nonlinear parameters variationally optimized are used. The form of these functions is a generalized s-symmetry-state properly modified to admit spatial deformation along the direction on which the magnetic field is applied. © 1994 John Wiley & Sons, Inc.     

Harmonic mappings of the Sierpinski gasket to the circle

Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.

     

The Implications of Cognitive-style Findings for Operational Research

Cognitive style refers to differences that can be perceived in individuals due to differing cognitive structures. There has been a large amount of research on how cognitive style affects managerial decision-making, particularly in the context of management information systems, but little or no attempt to relate these findings to operational research. This paper reviews the findings of cognitive-style research from the perspective of operational research, and draws a number of useful inferences concerning the matching of OR aids to managers, the presentation of information and recommendations, the use and acceptance of OR, and the structure of OR groups. Further, it is argued that cognitive-style findings help to give a justification to the move towards ‘soft’ approaches to analysis.     

Theory of interfacial phase transitions in surfactant systems

The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday.     

The Henderson Approximation and the Mass Action Law of Guldberg and Waage

Using contemporary accounts, we describe the scope of the Henderson approximation, and its relationship to the mass action law of Guldberg & Waage. The Henderson approximation, apparently written in logarithmic form by Hasselbalch, has the same form as the mass action law, but has a completely different meaning and a much more restricted range of applicability. The Guldberg-Waage law is the fundamental mass action relationship valid for all chemical equilibria, whereas the Henderson approximation is useful only within a limited range of a sufficiently concentrated two-component buffer mixture.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Spectral manifestations of distorted forms of Pd-porphin at helium temperatures: The effect of the matrix

The occurrence of two noninteracting forms of Pd-porphin in the ground electronic state in a wide number of Shpolskii matrices maintained at liquid helium temperature was observed with the help of the finestructure phosphorescence spectra of these systems. The ratio between these forms can be varied in wide limits by choosing a particular matrix, which indicates that the matrix plays a significant role in the conformation formation of the tetrapyrrole macrocycle. Based on comparison both with the resonance Raman spectra and with the results of investigations of metal complexes of porphin by the selective spectroscopy methods, the shortwavelength spectral form has been shown to correspond to the planar molecular structure, whereas the longwavelength form has been attributed to a nonplanar molecular structure with the distortion of the porphin macrocycle of the saddle type. The results obtained indicate that the methods of fine structure spectroscopy make it possible to efficiently study distorted molecular structures stabilized in solid matrices at low temperatures.