On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Dependence of transient dynamics in a class-C laser upon variation of inversion with time

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser. [S1050-2947(97)07112-6].

Do migrants' remittances decline over time? Evidence from Tongans and Western Samoans in Australia

There is concern that Pacific Island economies dependent on remittances of migrants will endure foreign exchange shortages and falling living standards as remittance levels fall because of lower migration rates and the belief that migrants' willingness to remit declines over time. The empirical validity of the remittance-decay hypothesis has never been tested. From survey data on Tongan and Western Samoan migrants in Sydney, this paper estimates remittance functions using multivariate regression analysis. It is found that the remittance-decay hypothesis has no empirical validity, and migrants are motivated by factors other than altruistic family support, including asset accumulation and investment back home.

Two-body and three-body abrasion: A critical discussion

It is argued that the common classification of abrasive wear into 'two-body abrasion' and 'three-body abrasion' is seriously flawed. No definitions have been agreed upon for these terms, and indeed there are two quite different interpretations, the implications of which are mutually inconsistent. In the dominant interpretation, the primary thrust of the two-body/three-body concept is to describe whether the abrasive particles are constrained (two-body) or free to roll (three-body). In this view, two-body abrasion is generally much more severe than three-body. The alternative interpretation emphasises the presence (three-body) or absence (two-body) of a rigid counterface backing the abrasive. In this view, three-body abrasion is equated to high-stress (or grinding) abrasion and is generally more severe than two-body (low-stress) abrasion. This paper recommends that the 'two-body/three-body' terminology be abandoned, to be replaced by an alternative classification scheme based directly upon the manifest severity of wear. (C) 1998 Elsevier Science S.A.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Experimental control of single-mode laser chaos by using continuous, time-delayed feedback

Control of chaos in the single-mode optically pumped far-infrared (NH3)-N-15 laser is experimentally demonstrated using continuous time-delay control. Both the Lorenz spiral chaos and the detuned period-doubling chaos exhibited by the laser have been controlled. While the laser is in the Lorenz spiral chaos regime the chaos has been controlled both such that the laser output is cw, with corrections of only a fraction of a percent necessary to keep it there, and to period one. The laser has also been controlled while in the period-doubling chaos regime, to both the period-one and -two states.

Dissociation between skin conductance orienting and secondary task reaction time: Time course with a visual discrimination task

A dissociation between two putative measures of resource allocation skin conductance responding, and secondary task reaction time (RT), has been observed during auditory discrimination tasks. Four experiments investigated the time course of the dissociation effect with a visual discrimination task. participants were presented with circles and ellipses and instructed to count the number of longer-than-usual presentations of one shape (task-relevant) and to ignore presentations of the other shape (task-irrelevant). Concurrent with this task, participants made a speeded motor response to an auditory probe. Experiment 1 showed that skin conductance responses were larger during task-relevant stimuli than during task-irrelevant stimuli, whereas RT to probes presented at 150 ms following shape onset was slower during task-irrelevant stimuli. Experiments 2 to 4 found slower RT during task-irrelevant stimuli at probes presented at 300 ms before shape onset until 150 ms following shape onset. At probes presented 3,000 and 4,000 ms following shape onset probe RT was slower during task-relevant stimuli. The similarities between the observed time course and the so-called psychological refractory period (PRF) effect are discussed.

Retinal and lenticular ultrastructure in the aestivating salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) with special reference to a new type of photoreceptor mosaic

The salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) is endemic to southwestern Australia and inhabits shallow, freshwater pools which evaporate during the hot summer months. Burrowing into the substrate in response to falling water levels allows these fish to aestivate for extended periods of time while encapsulated in a mucous cocoon even when the pools contain no water. Only a few minutes after a major rainfall, these fish emerge into relatively clear water which subsequently becomes laden with tannin, turning the water black and reducing the pH to approximately 4.3. As part of a large study of the visual adaptations of this unique species, the retinal and lenticular morphology of the aestivating salamanderfish is examined at the level of the light and electron microscopes. The inner retina is highly vascularised by a complex system of vitreal blood vessels, while the outer retina receives a blood supply by diffusion from a choriocapillaris. This increased retinal blood supply may be an adaptation for reducing the oxygen tension during critical periods of aestivation. Large numbers of Muller cells traverse the thickness of the retina from the inner to the outer limiting membranes. The ganglion cells are arranged in two ill-defined layers, separated from a thick inner nuclear layer containing two layers of horizontal cells by a soma-free inner plexiform layer. The photoreceptors can be divided into three types typical of many early actinopterygian representatives; equal double cones, small single cones and large rods (2:1:1). These photoreceptors are arranged into a unique regular square mosaic comprising a large rod bordered by four equal double cones with a small single cone located at the corner of each repeating unit. The double cones may optimise perception of mobile prey which it tracks by flexion of its head and neck and the large rods may increase sensitivity in the dark tannin-rich waters in which it lives. Each single cone also possesses a dense collection of polysomes and glycogen (a paraboloid) beneath its ellipsoid, the first such finding in teleosts. The retinal pigment epithelium possesses melanosomes, pha,oocytes and a large number of mitochondria. The anatomy of the retina and the photoreceptor mosaic is discussed in relation to the primitive phylogeny of this species and its unique life history.

In vivo dynamics of axon pathfinding in the Drosophila CNS: A time-lapse study of an identified motoneuron

We developed a system for time-lapse observation of identified neurons in the central nervous system (CNS) of the Drosophila embryo. Using this system, we characterize the dynamics of filopodia and axon growth of the motorneuron RP2 as it navigates anteriorly through the CNS and then laterally along the intersegmental nerve (ISN) into the periphery. We find that both axonal extension and turning occur primarily through the process of filopodial dilation. In addition, we used the GAL4-UAS system to express the fusion protein Tau-GFP in a subset of neurons, allowing us to correlate RP2's patterns of growth with a subset of axons in its environment. In particular, we show that RP2's sharp lateral turn is coincident with the nascent ISN. (C) 1998 John Wiley & Sons, Inc.