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.

The effect of moderate aerobic exercise and relaxation on secretory immunoglobulin A

A deficiency in secretory immunoglobulin A (sIgA) is associated with recurrent upper respiratory tract infections both in the general community and in elite athletes. The aim of this paper was to investigate the effect of aerobic exercise and relaxation on various indices of sIgA in 12 male and 8 female adults who varied in levels of recreational activity. Salivary samples were obtained before, immediately after and 30 minutes after an incremental cycle ergometer test to fatigue. after 30 minutes of cycling at 30% or 60 % of maximum heart rate, and after 30 minutes of relaxation with guided imagery. Each session was run on a separate day. When expressed in relation to changes in salivary flow rate, sIgA did not change after exercise. However, both the absolute concentration and secretion rate of sIgA increased during relaxation (167 +/- 179 mug ml(-1), p < 0.001: and 37 +/- 71 g(.)min(-1), p < 0.05 respectively). Nonspecific protein increased more than sIgA during incremental exercise to fatigue (decrease in the sIgA/protein ratio 92 +/- 181 g(.)mg protein(-1), p(0.05), but sIgA relative to protein did not change during relaxation. Our findings suggest that sIgA secretion rate is a more appropriate measure of sIgA than sIgA relative to protein, both for exercise and relaxation. These data suggest the possibility of using relaxation to counteract the negative effects of intense exercise on sIgA levels.

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.

Stability of nest range, home range and movement of the northern bettong (Bettongia tropica) following moderate-intensity fire in a tropical woodland, north-eastern Queensland

Nest use, home-range characteristics and nightly movements by the northern bettong (Bettongia tropica) were examined before and after a low- to moderate-intensity fire in sclerophyll woodland in north-eastern Australia using radio-telemetry. In all, 23 animals were radio-tracked at three-month intervals between February 1995 and May 1996. During November 1995 a low- intensity experimental fire burned the entire home range of most animals. The northern bettong appeared fairly catholic in choice of nest site, with a variety of nest locations and nesting materials used. Prior to the fire, nests were generally located in areas of dense cover, such as the skirts of grass trees (46%) or grass close to a log (29%). After fire removed most ground cover in the nesting areas of most animals, bettongs used remaining shelter such as boulder piles (45%), recently fallen trees (8%) and patches of unburnt vegetation (21%). Nest areas (10.1 ha) of males were significantly larger than those of females (5.4 ha). Home ranges of both sexes were large (59 ha) and most ranges lacked distinct core areas, suggesting that bettongs used all parts of their home ranges equally. High mean rates of nightly movement by the northern bettong indicated that large distances were moved within home ranges during nightly foraging. No significant fire-related changes were detected in home-range size, home-range location, nest-area location or mean rates of nightly movement, suggesting that the northern bettong is well adapted to the low- and medium-intensity fires that characterise its habitat.

Habitat complexity, spatial interference, and "minimum risk distribution": a framework for population stability

In the past century, the debate over whether or not density-dependent factors regulate populations has generally focused on changes in mean population density, ignoring the spatial variance around the mean as unimportant noise. In an attempt to provide a different framework for understanding population dynamics based on individual fitness, this paper discusses the crucial role of spatial variability itself on the stability of insect populations. The advantages of this method are the following: (1) it is founded on evolutionary principles rather than post hoc assumptions; (2) it erects hypotheses that can be tested; and (3) it links disparate ecological schools, including spatial dynamics, behavioral ecology, preference-performance, and plant apparency into an overall framework. At the core of this framework, habitat complexity governs insect spatial variance. which in turn determines population stability. First, the minimum risk distribution (MRD) is defined as the spatial distribution of individuals that results in the minimum number of premature deaths in a population given the distribution of mortality risk in the habitat (and, therefore, leading to maximized population growth). The greater the divergence of actual spatial patterns of individuals from the MRD, the greater the reduction of population growth and size from high, unstable levels. Then, based on extensive data from 29 populations of the processionary caterpillar, Ochrogaster lunifer, four steps are used to test the effect of habitat interference on population growth rates. (1) The costs (increasing the risk of scramble competition) and benefits (decreasing the risk of inverse density-dependent predation) of egg and larval aggregation are quantified. (2) These costs and benefits, along with the distribution of resources, are used to construct the MRD for each habitat. (3) The MRD is used as a benchmark against which the actual spatial pattern of individuals is compared. The degree of divergence of the actual spatial pattern from the MRD is quantified for each of the 29 habitats. (4) Finally, indices of habitat complexity are used to provide highly accurate predictions of spatial divergence from the MRD, showing that habitat interference reduces population growth rates from high, unstable levels. The reason for the divergence appears to be that high levels of background vegetation (vegetation other than host plants) interfere with female host-searching behavior. This leads to a spatial distribution of egg batches with high mortality risk, and therefore lower population growth. Knowledge of the MRD in other species should be a highly effective means of predicting trends in population dynamics. Species with high divergence between their actual spatial distribution and their MRD may display relatively stable dynamics at low population levels. In contrast, species with low divergence should experience high levels of intragenerational population growth leading to frequent habitat-wide outbreaks and unstable dynamics in the long term. Six hypotheses, erected under the framework of spatial interference, are discussed, and future tests are suggested.

Detection and stability of Japanese encephalitis virus RNA and virus viability in dead infected mosquitoes under different storage conditions

A semi-nested polymerase chain reaction (PCR) was evaluated for detection of Japanese encephalitis (JE) virus in infected mosquitoes stored under simulated northern Australian summer conditions. The effect of silica gel, thymol, and a combination of the two on RNA stability and virus viability in dead mosquitoes were also examined. While JE virus RNA was relatively stable in mosquitoes held for up to 14 days after death, viable virus was not detected after day 1. Thymol vapor inhibited fungal contamination. Detection of single mosquitoes infected with JE virus in large pools of mosquitoes was also investigated. Single laboratory-infected mosquitoes were detected in pools of less than or equal to200 mosquitoes and in pools diluted to 0.2/100 and 0.1/100 mosquitoes, using the semi-nested PCR. However, the ability to detect live virus decreased as pool size increased. The semi-nested PCR proved more expensive than virus isolation for pools of 100 mosquitoes. However, the semi-nested PCR was faster and more economical using larger pools. Results indicate that surveillance of JE virus in mosquitoes using the semi-nested PCR is an alternative to monitoring seroconversions in sentinel pigs.

Patterns of change and stability in the gender division of household labour in Australia, 1986-1997

Recent research in Australia and overseas has suggested that we are witnessing a convergence of men's and women's time on domestic labour activities. But there is disagreement about whether this is due to women reducing their time on housework or men increasing their time on housework. This article addresses these issues using national survey data collected in Australia in 1986, 1993 and 1997. The results show some changes in the proportional responsibilities of men and women in the home with men reporting a greater share of traditional indoor activities. But overall both men and women are spending less time on housework. In particular, women's time on housework has declined by six hours per week since 1986. Hence, while the gender gap between men's and women's involvement in the home is getting smaller, it is not the result of men increasing their share of the load, but is due to the large decline in women's time spent on domestic labour. There is also evidence of change in the relationship. between paid and unpaid work for women. Women's hours of,paid labour had a greater impact on their involvement in domestic labour in 1997 compared to a decade earlier. The article concludes that women's increased labour force involvement in combination with changing patterns and styles, of consumption is leading to some changes in the gender-division:of household labour, but not in the direction anticipated by earlier commentators on the domestic division of labour.