Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Profiling "new" communication technologies in adolescence

In an overview of some of the central issues concerning the impact and effects of new technology in adolescence, this article questions the reality of the net generation before considering the interplay of new and old technologies, the internet as both communication and lifestyle resource, and newer technologies like text messaging and webcams.

Adolescent risk behaviors and communication research - Current directions

Examples of recent research into adolescent risk behaviors from a variety of disciplines and methodologies, denoting the range of researchers interested in this area and whose interest in communication and language articulates and exemplifies the extent of the field, are surveyed in this article.

Beyond hearing aid fitting: improving communication for older adults

Many older adults with hearing impairment continue to have substantial communication difficulties after being fitted with hearing aids, and many do not choose to wear hearing aids. Two group communication education programs aimed at such older people are described. The 'Keep on Talking' program has a health promotion focus, and is aimed at maintaining communication for older adults living in the community. An experimental group (n=120) attended the program, and a control group (n=130) received a communication assessment but no intervention. Significant improvements were found in the experimental participants in terms of knowledge about communication changes with age and about strategies to maintain communication skills. At the follow-up evaluation at 1 year, 45% of the experimental group, compared to 10% of the control group, had acted to improve their communication skills. The 'Active Communication Education' program focuses on the development of problem-solving strategies to improve communication in everyday life situations. Preliminary outcomes have been assessed on a small scale (n=14) to date. It is concluded that communication programs represent an important adjunct to, or supplement for, the traditional approach that focuses on hearing aid fitting.

Differential modes of alaryngeal communication and long-term voice outcomes following pharyngolaryngectomy and laryngectomy

Patterns of vocal rehabilitation for 37 pharyngolaryngectomy patients and 55 total laryngectomy patients over a 5-year period were compared. An electrolarynx (EL) was introduced as the initial communication mode immediately after surgery for 98% of patients, with 30% of pharyngolaryngectomy and 74% of laryngectomy patients subsequently developing tracheoesophageal speech (TES) as their primary mode of communication. Follow-up with 14 of 37 pharyngolaryngectomy patients and 36 of 55 laryngectomy patients was conducted 1-6 years following surgery and revealed that 90% of the pharyngolaryngectomy patients maintained the use of TES in the long term compared to 69% of the laryngectomy group. Long-term outcomes relating to communication disability and handicap did not differ significantly between the two surgical groups, however the laryngectomy patients had significantly higher levels of wellbeing. Across the whole group of patients, statistical comparison revealed that patients using TES had significantly lower levels of disability, handicap and distress than EL users. Considering that lower levels of disability, handicap and distress are associated with TES, and the data supports that suitably selected patients can maintain functional TES in the long term, increased application of this form of communication rehabilitation should be encouraged where viable for the pharyngolaryngectomy population. Copyright (C) 2003 S. Karger AG, Basel.

Identifying the communication activities of older people with aphasia: Evidence from naturalistic observation

Background: Increasingly there is a call from clinicians and researchers for measures that document the impact of aphasia on a person's everyday communication. Do existing assessments of communication disability adequately sample communication activities relevant to our clients? Communication skills and networks change with age. A need exists to determine the everyday communication activities of older people and in particular those with aphasia. Aims: The primary aim of this study was to describe and compare the everyday communication activities of older people with aphasia and healthy older people who are living in the community. A secondary aim was to investigate the content validity of the American Speech-Language Hearing Association Functional Assessment of Communication Skills for Adults (ASHA FACS, 1997) for older Australians. Methods & Procedures: Naturalistic observation was the method of choice for detailing the everyday communication of 15 older people with chronic aphasia following stroke and a matched group of 15 healthy older people who were living in the community. Researchers, in the role of participant observer, took field notes for 8 hours, over three occasions within a week. A total of 240 hours of observation have been coded in terms of communication activity, topic, communication partners, and place of communication. A brief 5-day diary served to check the representativeness of the observational data. After each hour of observation, the researcher checked which ASHA FACS items had been observed. Outcomes & Results: Naturalistic observation provided a rich, rigorous, and systematic methodology for detailing the dynamics and complexities of authentic communication. The most common communication activities for both groups were conversations at home and in social groups. Real-life communication was revealed to serve the dual purposes of transaction and interaction. Results indicate that older people with aphasia engage in similar communication activities to healthy older people although differences were evident in the frequency of communication and in specific activities such as story telling, writing, commenting, and acknowledging. ASHA FACS items were generally relevant to older Australians living in the community. Conclusions: This study demonstrated that communication activity is multifaceted in terms of the type of communication and contextual factors. The observational data describe the effects of aphasia on a person's everyday communication activity and reveal the impact of aphasia on the social functions of communication including sharing information, maintaining and establishing relationships, and telling one's story. Functional communication assessment requires a greater focus on the interactional and uniquely interpersonal aspects of social communication.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.