Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

The increasing problem of hepatitis C virus infection

The widespread incidence of hepatitis C (HCV) infection throughout the community is of concern. Although many of those infected will not suffer significantly from their infection, up to one-third will have liver disease, fatigue and oral health problems. General dental practitioners need to be aware of the precautions necessary in treating people with severe liver disease. This paper discusses the issues associated with treating patients who have HCV infection including the importance of preventive programs to reduce dental pathology and maximise oral health.

Hemiplegic shoulder pain: defining the problem and its management

Purpose: Hemiplegic shoulder pain can affect up to 70% of stroke patients and can have an adverse impact on rehabilitation outcomes. This article aims to review the literature on the suggested causes of hemiplegic shoulder pain and the therapeutic techniques that can be used to prevent or treat it. On the basis of this review, the components of an optimal management programme for hemiplegic shoulder pain are explored. Method: English language articles in the CINAHL and MEDLINE databases between 1990 and 2000 were reviewed. These were supplemented by citation tracking and manual searches. Results: A management programme for hemiplegic shoulder pain could comprise the following components: provision of an external support for the affected upper limb when the patient is seated, careful positioning in bed, daily static positional stretches, motor retraining and strapping of the scapula to maintain postural tone and symmetry. Conclusions: Research is required to evaluate the effectiveness of the components of the proposed management programme for the prevention and treatment of hemiplegic shoulder pain and to determine in what combination they achieve the best outcomes.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.