Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

An efficient electrophilic N-amination utilizing in situ generated chloramine under phase transfer conditions

An efficient, one-pot, phase transfer N-amination technology was developed. The protocol utilizes chloramine, an inexpensive and safe electrophilic aminating agent potentially viable for commercial manufacturing.     

A critical review of the chemical kinetics of SF4, SF5, and S2F10 in the gas phase

The gas phase chemical kinetics of SF₄, SF₅, and S₂F₁₀ are reviewed with particular emphasis on relevance to the general problem of the dielectric breakdown of SF₆. Specific reaction systems treated are SF₄ + F₂, SF₅ + SF₅, and the pyrolysis of S₂F₁₀. Computer modeling calculations were carried out to arrive at the best estimates of rate parameters. Based on the results of these calculations, sets of recommended rate parameters are provided. The major discrepancies and problems in establishing the kinetic data base are described. Thermochemical consequences of different model calculations are given.     

Improving the Fundamental Theorem of Algebra

Theorems 2 and 3 establish the minimum algebraic conditions necessary for a field to be algebraically closed, and they can therefore be said to “optimize” the Fundamental Theorem of Algebra. But each specific“degree implication” is a first-order consequence of the axioms for fields, and could have been discovered two centuries ago; the existence of these finitary relationships appears to have been unsuspected by practically everyone, with one important exception.     

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.     

Enumeration of inequivalent irreducible Goppa codes

We consider irreducible Goppa codes over F_q of length qⁿ defined by polynomials of degree r, where q is a prime power and n,r are arbitrary positive integers. We obtain an upper bound on the number of such codes.     

Network externalities in a dynamic monopoly

We reconsider the role of network externalities in a dynamic spatial monopoly where the firm must invest in order to accumulate capacity, while consumers may have either linear or quadratic preferences. We (1) characterise saddle point equilibria, (2) prove that the extent of market coverage is increasing in the network effect and (3) unlike the existing static literature on the same problem, the monopolist may not make introductory price offers. Then, we briefly deal with the socially optimal solution, showing that, in general, a planner would serve more consumers than a profit-seeking monopolist.      

Developing professional judgement with the aid of a ‘low-profile’ group support system

This paper reports positive results from an application of one type of group support system (GSS) to a training application. Reviews of the findings of other trials of GSS have been mixed, and inconclusive. We describe the results of a series of seven training sessions in a field-based application of group process support. The subjects were professionals working in various agencies concerned with the welfare of older people. A ‘low-profile’ type of group support system, based on wireless handsets, was used. This design enabled responses from each participant to be input and displayed anonymously. Each session was aimed at stimulating a dialogue focused on the reasons for differences of judgement, as displayed on a single projected feedback screen. Changes of individual judgements were recorded for subsequent analysis and comparison with already known ‘expert judgements’. Frequent changes of judgement were recorded. A significant proportion of these were related to an improvement, which could not be explained as simply the result of conforming behaviour. We propose that the mode of operation and design of a ‘low-profile’ GSS have the potential to create a learning environment by reducing personal anxieties while encouraging group-based learning with focussed conversation. We conclude that this type of GSS design is particularly suited to ‘selective’-type tasks in groups.     

On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.