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.

Perceived constraints and social support for active leisure among mothers with young children

Evidence suggests that women who are mothers of young children have lower levels of physical activity than women of similar age who do not have children (Brown, Lee, Mishra, & Bauman, 2000). The purposes of this study were to explore the factors that constrain mothers of young children from being more physically active, and the relationship between physical activity and levels of social support available to the women. The empirical basis for this examination was provided through a study of activity levels and barriers to physical activity experienced by a sample of 543 mothers of young children from differing socioeconomic backgrounds. The data indicate that: (a) more than two-thirds of the mothers were inadequately active in their leisure time for health benefit; (b) while the vast majority of mothers expressed a desire to be more active, they were inhibited in their ability to act out their leisure preferences by a combination of structural (e.g., lack of time, money, energy) and ideological influences (e.g., sense of commitment to others); (c) access to social support (from partners, family, and friends) was seen to place some women in a better position than others to negotiate constraints that inhibit leisure participation; and (d) within groups of varying socioeconomic status (SES) there was wide variation in the amount of time spent each week in active leisure.

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.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Estimating economic relationships subject to firm- and time-varying equality and inequality constraints

Applied econometricians often fail to impose economic regularity constraints in the exact form economic theory prescribes. We show how the Singular Value Decomposition (SVD) Theorem and Markov Chain Monte Carlo (MCMC) methods can be used to rigorously impose time- and firm-varying equality and inequality constraints. To illustrate the technique we estimate a system of translog input demand functions subject to all the constraints implied by economic theory, including observation-varying symmetry and concavity constraints. Results are presented in the form of characteristics of the estimated posterior distributions of functions of the parameters. Copyright (C) 2001 John Wiley Sons, Ltd.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

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.

Probing the time course of nonlinear discriminations during human electrodermal conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning; schedule (A-, B-, AB+) and a second in a negative patterning schedule (A+, B+, AB-). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during non-reinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning. (C) 2001 Elsevier Science (USA).

Syntactic and pragmatic constraints on processing relative clauses

Thc oen itninteureasc ttioo nb eo fa pcreangtmraal tiiscs uaen di ns ymnotadcetlisc ocfo nsestnrtaeinnctse processing. It is well established that object relatives (1) are harder to process than subject relatives (2). Passivization, other things being equal, increases sentence complexity. However, one of the functions of the passive construction is to promote an NP into the role of subject so that it can be more easily bound to the head NP in a higher clause. Thus, (3) is predicted to be marginally preferred over (1). Passiviazation in this instance may be seen as a way of avoiding the object relative construction. 1. The pipe that the traveller smoked annoyed the passengers. 2. The traveller that smoked the pipe annoyed the passengers. 3.The pipe that was smoked by the traveller annoyed the 4.The traveller that the pipe was smoked by annoyed the 5.The traveller that the lady was assaulted by annoyed the In (4) we have relativization of an NP which has been demoted by passivization to the status of a by-phrase. Such relative clauses may only be obtained under quite restrictive pragmatic conditions. Many languages do not permit relativization of a constituent as low as a by-phrase on the NP accessibility hierarchy (Comrie, 1984). The factors which determine the acceptability of demoted NP relatives like (4-5) reflect the ease with which the NP promoted to subject position can be taken as a discourse topic. We explored the acceptability of sentences such as (1-5) using pair-wise judgements of samddifferent meaning, accompanied by ratings of easeof understanding. Results are discussed with reference to Gibsons DLT model of linguistic complexity and sentence processing (Gibson, 2000)

Fluid-mobile trace element constraints on the role of slab melting and implications for Archaean crustal growth models

We use published and new trace element data to identify element ratios which discriminate between arc magmas from the supra-subduction zone mantle wedge and those formed by direct melting of subducted crust (i.e. adakites). The clearest distinction is obtained with those element ratios which are strongly fractionated during refertilisation of the depleted mantle wedge, ultimately reflecting slab dehydration. Hence, adakites have significantly lower Pb/Nd and B/Be but higher Nb/Ta than typical arc magmas and continental crust as a whole. Although Li and Be are also overenriched in continental crust, behaviour of Li/Yb and Be/Nd is more complex and these ratios do not provide unique signatures of slab melting. Archaean tonalite-trondhjemite-granodiorites (TTGs) strongly resemble ordinary mantle wedge-derived arc magmas in terms of fluid-mobile trace element content, implying that they-did not form by slab melting but that they originated from mantle which was hydrated and enriched in elements lost from slabs during prograde dehydration. We suggest that Archaean TTGs formed by extensive fractional crystallisation from a mafic precursor. It is widely claimed that the time between the creation and subduction of oceanic lithosphere was significantly shorter in the Archaean (i.e. 20 Ma) than it is today. This difference was seen as an attractive explanation for the presumed preponderance of adakitic magmas during the first half of Earth's history. However, when we consider the effects of a higher potential mantle temperature on the thickness of oceanic crust, it follows that the mean age of oceanic lithosphere has remained virtually constant. Formation of adakites has therefore always depended on local plate geometry and not on potential mantle temperature.

Genetic constraints on the evolution of mate recognition under natural selection

Field populations of Drosophila serrata display reproductive character displacement in cuticular hydrocarbons (CHCs) when sympatric with Drosophila birchii. We have previously shown that the naturally occurring pattern of reproductive character displacement can be experimentally replicated by exposing field allopatric populations of D. serrata to experimental sympatry with D. birchii. Here, we tested whether the repeated evolution of reproductive character displacement in natural and experimental populations was a consequence of genetic constraints on the evolution of CHCs. The genetic variance-covariance (G) matrices for CHCs were determined for populations of D. serrata that had evolved in either the presence or absence of D. birchii under field and experimental conditions. Natural selection on mate recognition under both field and experimental sympatric conditions increased the genetic variance in CHCs consistent with a response to selection based on rare alleles. A close association between G eigenstructure and the eigenstructure of the phenotypic divergence (D) matrix in natural and experimental populations suggested that G matrix eigenstructure may have determined the direction in which reproductive character displacement evolved during the reinforcement of mate recognition.