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.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

The future of cognitive and behavioral therapies in the prevention and early management of psychosis: Opportunities and risks

Behavioral and cognitive interventions for people with psychosis have a long and distinguished history, although the evidence for their application to young people remains limited. We anticipate that the next decades will show substantial research into psychological intervention for this population. Important targets will include the management of environmental stressors, reduction of substance misuse, and promotion of early treatment. Psychological management of positive symptoms, depression, and suicidal behavior will continue to be critical objectives. Important secondary prevention goals will be the retention of cognitive functioning, vocational options, social skills, and social network support, including appropriate family support. We expect primary prevention to include both universal programs and interventions for adolescents at particularly high risk. Technical innovations will include increasing use of Internet-based intervention and behavior cueing devices. Pressures for intervention brevity will continue, as will problems with the systematic delivery of effective procedures.

Teledermatology: a review

Teledermatology holds great potential for revolutionizing the delivery of dermatology services, providing equitable service to remote areas and allowing primary care physicians to refer patients to dermatology centres of excellence at a distance. However, before its routine application asa service tool, its reliability, accuracy and cost-effectiveness need to be verified by rigorous evaluation. Teledermatology can be applied in one of two ways: it may be conducted in real-time, utilizing videoconferencing equipment, or by store-and-forward methods, when transmitted digital images or photographs are submitted with a clinical history. While there is a considerable range of reported accuracy and reliability, evidence suggests that teledermatology will become increasingly utilized and incorporated into more conventional dermatology service delivery systems. Studies to date have generally found that real-time dermatology is likely to allow greater clinical information to be obtained from the patient. This may result in fewer patients requiring conventional consultations, but it is generally more time-consuming and costly to the health service provider It is often favoured by the patient because of the instantaneous nature of the diagnosis and management regimen for the condition, and it has educational value to the primary care physician. Store-and-forward systems of teledermatology often give high levels of diagnostic accuracy, and are cheaper and more convenient for the health care provider, but lack the immediacy of patient contact with the dermatologist, and involve a delay in obtaining the diagnosis and advice on management. It is increasingly likely that teledermatology will prove to be a significant tool in the provision of dermatology services in the future. These services will probably be provided by store-and-forward digital image systems, with real-time videoconferencing being used for case conferences and education. However, much more research is needed into the outcomes and Limitations of such a service and its effect on waiting lists, as well as possible cost benefits for patients, primary health care professionals and dermatology departments.