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.

The case for emotional intelligence in organizational research

Since its popularization by Goleman (1995), the concept of emotional intelligence has been the subject of ongoing controversy, so it is understandable that the model we proposed, which includes emotional intelligence as a moderator variable, would attract its share of criticism.

Is emotional intelligence training for leaders justified?

In this paper, we present the results of a qualitative study of subordinate perceptions of leaders. The study represents a preliminary test of a model based on Affective Events Theory, which posits that leaders who are seen to be effective shape the affective events that determine employees' attitudes and behaviours in the workplace. Within this framework, we argue that effective leaders ameliorate employees' hassles by providing frequent, small emotional uplifts. The resulting positive affective states are then proposed to lead to more positive employee attitudes and behaviours, and more positive regard for the leader. Importantly, leaders who demonstrate these ameliorating behaviours are likely to require high levels of emotional intelligence, defined in terms of the ability to recognise, understand, and manage emotions in self and others. To investigate this model, we conducted interviews and focus groups with 10 leaders and 24 employees. Results confirmed that these processes do indeed exist in the workplace. In particular, leaders who were seen by employees to provide continuous small emotional uplifts were consistently held to be the most effective. Study participants were especially affected by negative events (or hassles). Leaders who failed to deal with hassles or, worse still, were the source of hassles, were consistently seen to be less effective. We conclude with a discussion of implications for practicing managers, and suggest that our exploratory findings provide justification for emotional intelligence training as a means to improve leader perceptions and effectiveness. [Abstract from author]

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Effects of physical activity on emotional well-being among older Australian women - Cross-sectional and longitudinal analyses

Objective: To explore relationships between physical activity and mental health cross-sectionally and longitudinally in a large cohort of older Australian women. Method: Women in their 70s participating in the Australian Longitudinal Study on Women's Health responded in 1996 (aged 70-75) and in 1999 (aged 73-78). Cross-sectional data were analyzed for 10,063 women and longitudinal data for 6472. Self-reports were used to categorize women into four categories of physical activity at each time point as well as to define four physical activity transition categories across the 3-year period. Outcome variables for the cross-sectional analyses were the mental health component score (MCS) and mental health subscales of the Medical Outcomes Study Short Form (SF-36). The longitudinal analyses focused on changes in these variables. Confounders included the physical health component scale (PCS) of the SF-36, marital status, body mass index (BMI) and life events. Adjustment for baseline scores was included for the longitudinal analyses. Results: Cross-sectionally, higher levels of physical activity were associated with higher scores on all dependent variables, both with and without adjustment for confounders. Longitudinally, the effects were weaker, but women who had made a transition from some physical activity to none generally showed more negative changes in emotional well-being than those who had always been sedentary, while those who maintained or adopted physical activity had better outcomes. Conclusion: Physical activity is associated with emotional well-being among a population cohort of older women both cross-sectionally and longitudinally, supporting the need for the promotion of appropriate physical activity in this age group. (C) 2003 Elsevier Science Inc. All rights reserved.