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.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

The acquisition of movement skills: Practice enhances the dynamic stability of bimanual coordination

During bimanual movements, two relatively stable inherent patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p = 0.025). These changes were still observed one week (p = 0.05) and two months (p = 0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p = 0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout. (C) 2001 Elsevier Science B.V. All rights reserved.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers

The blending of coals has become popular to improve the performance of coals, to meet specifications of power plants and, to reduce the cost of coals, This article reviews the results and provides new information on ignition, flame stability, and carbon burnout studies of blended coals. The reviewed studies were conducted in laboratory-, pilot-, and full-scale facilities. The new information was taken in pilot-scale studies. The results generally show that blending a high-volatile coal with a low-volatile coal or anthracite can improve the ignition, flame stability and burnout of the blends. This paper discusses two general methods to predict the performance of blended coals: (1) experiment; and (2) indices. Laboratory- and pilot-scale tests, at least, provide a relative ranking of the combustion performance of coal/blends in power station boilers. Several indices, volatile matter content, heating value and a maceral index, can be used to predict the relative ranking of ignitability and flame stability of coals and blends. The maceral index, fuel ratio, and vitrinite reflectance can also be used to predict the absolute carbon burnout of coal and blends within limits. (C) 2000 Elsevier Science Ltd. All rights reserved.