Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Sediment yield and impacts from river catchments to the Great Barrier Reef lagoon

Land use intensification is estimated to result in an overall increase in sediment delivery to the Great Barrier Reef lagoon by a factor of approximately four. Modelling suggests that, following land use intensification, croplands cause the greatest increase of sediment yield and sediment concentration, whereas erosion of grazing land is the main contemporary source of sediments, primarily owing to the large spatial extent of this land use. The spatial pattern of sediment yield to the coast after land use intensification is strongly correlated with the pattern under natural conditions, although the greatest increase is estimated to have occurred in the wet-dry catchments. Sediment transport and resuspension processes have led to the development of a strongly sediment-partitioned shelf, with modern mud-rich sediments almost exclusively restricted to the inner and inner-middle shelf, northward-facing embayments and in the lee of headlands. Elevated sediment concentrations increase the potential transport rates of nutrients and other pollutants. Whether increased sediment supply to the coastal zone has impacted on reefs remains a point of contention. More sediment load data need to be collected and analysed in order to make detailed estimates of catchment yields and establish the possible sediment impact on the Great Barrier Reef.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

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.

Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces

In the present paper, we establish two fixed point theorems for upper semicontinuous multivalued mappings in hyperconvex metric spaces and apply these to study coincidence point problems and minimax problems. (C) 2002 Elsevier Science (USA). All rights reserved.

Catheter effects in organ perfusion experiments

In a typical isolated organ perfusion experiment, a substance is injected upstream of an organ and then collected at some distance downstream. To reach the organ from the injection site, and then from the organ to the collector, a solute passes through catheters, usually tubes with circular cross-sections. Catheters cause distortion to the concentration-time profile of the perfusion. In this paper, we analyse catheter distribution kinetics from a mathematical point of view, develop the function most suitable for modeling this distribution and successfully apply this function to experimental data. (C) 2002 Academic Press.

Cloud-point extraction and preconcentration of cyanobacterial toxins (microcystins) from natural waters using a cationic surfactant

A new cloud-point extraction and preconcentration method, using a cationic, surfactant, Aliquat-336 (tricaprylyl-methy;ammonium chloride), his-been developed for the determination of cyanobacterial toxins, microcystins, in natural waters. Sodium sulfate was used to induce phase separation at 25 degreesC. The phase behavior of Aliquat-336 with respect to concentration of Na2SO4 was studied. The cloud-point system revealed a very high phase volume ratio compared to other established systems of nonionic, anionic, and cationic surfactants: At pH 6-7, it showed an outstanding selectivity in ahalyte extraction for anionic species. Only MC-LR and MC-YR, which are known to be predominantly anionic, were extracted (with averaged recoveries of 113.9 +/- 9% and 87.1 +/- 7%, respectively). MC-RR, which is likely to be amphoteric at the above pH range, was. not cle tectable in.the extract. Coupled to HPLC/UV separation and detection, the cloud-point extraction method (with 2.5 mM Aliquat-336 and 75 mM Na2SO4 at 25 degreesC) offered detection limits of 150 +/- 7 and 470 +/- 72 pg/mL for MC-LR and MC-YR, respectively, in 25 mL of deionized water. Repeatability of the method was 7.6% for MC-LR and 7.3% for MC-YR: The cloud-point extraction process can be. completed within 10-15 min with no cleanup steps required. Applicability of the new method to the determination of microcystins in real samples was demonstrated using natural surface waters, collected from a local river and a local duck pond spiked with realistic. concentrations of microcystins. Effects of salinity and organic matter (TOC) content in the water sample on the extraction efficiency were also studied.

Analysis of the wind field and heat budget in an alpine lake basin during summertime fair weather conditions

Observational data collected in the Lake Tekapo hydro catchment of the Southern Alps in New Zealand are used to analyse the wind and temperature fields in the alpine lake basin during summertime fair weather conditions. Measurements from surface stations, pilot balloon and tethersonde soundings, Doppler sodar and an instrumented light aircraft provide evidence of multi-scale interacting wind systems, ranging from microscale slope winds to mesoscale coast-to-basin flows. Thermal forcing of the winds occurred due to differential heating as a consequence of orography and heterogeneous surface features, which is quantified by heat budget and pressure field analysis. The daytime vertical temperature structure was characterised by distinct layering. Features of particular interest are the formation of thermal internal boundary layers due to the lake-land discontinuity and the development of elevated mixed layers. The latter were generated by advective heating from the basin and valley sidewalls by slope winds and by a superimposed valley wind blowing from the basin over Lake Tekapo and up the tributary Godley Valley. Daytime heating in the basin and its tributary valleys caused the development of a strong horizontal temperature gradient between the basin atmosphere and that over the surrounding landscape, and hence the development of a mesoscale heat low over the basin. After noon, air from outside the basin started flowing over mountain saddles into the basin causing cooling in the lowest layers, whereas at ridge top height the horizontal air temperature gradient between inside and outside the basin continued to increase. In the early evening, a more massive intrusion of cold air caused rapid cooling and a transition to a rather uniform slightly stable stratification up to about 2000 m agl. The onset time of this rapid cooling varied about 1-2 h between observation sites and was probably triggered by the decay of up-slope winds inside the basin, which previously countered the intrusion of air over the surrounding ridges. The intrusion of air from outside the basin continued until about mid-night, when a northerly mountain wind from the Godley Valley became dominant. The results illustrate the extreme complexity that can be caused by the operation of thermal forcing processes at a wide range of spatial scales.

Comparison of adsorption capacity of p-Cresol & p-Nitrophenol by activated carbon in single and double solute

Adsorption of p-Cresol and p-Nitrophenol by untreated activated carbon in single and multisolute solutions was carried out at 301 K and at controlled pH conditions. In acidic conditions, well below the pK(a) of both solutes, it was observed that the adsorbate solubility and the electron density of aromatic rings influenced the extent of adsorption by affecting the extent of London dispersion forces. The fitted parameters obtained from single-solute Langmuir equation show that Q(max) and the adsorption affinity of carbon for the compound with low pK(a) decrease more significantly. In higher solution pH conditions, on the other hand, it was found that electrostatic forces played a significant role on the extent of adsorption. The presence of another compound decreases Q(max) and the adsorption affinity of carbon for the principal compound. The effect of pH, on the carbon surface and on the solute molecules, must be considered. Adsorption of the solute at higher pH values was found to be dependent on the concentration of anionic form of the solute. The isotherm data were fitted to the Langmuir isotherm equation for both single and double solute solutions.

Osmoregulative capacity in birdseed millet under conditions of water stress. I. Variation in Setaria italica and Panicum miliaceum

Experiments involving 14 accessions of Panicum miliaceum L. (Proso millet) and 11 accessions of Setaria italica L. (Foxtail millet) have demonstrated variability in the degree of osmoregulative capacity among these accessions. Birdseed millet is generally claimed to be sensitive to drought stress, apparently because of a shallow root system. Accessions with high osmoregulative capacity demonstrate at least some drought tolerance. Osmoregulative capacity was measured on flag leaves of headed millet plants in pots undergoing water stress in a controlled environment chamber. Osmoregulative capacity was determined from the relationship between osmotic potential and leaf water potential; and the logarithmic relationship between osmotic potential and relative water content. The group of accessions of S. italica showed an overall level of osmoregulative capacity which was greater than that observed for the group of P. miliaceum accessions. Four accessions of S. italica (108042, 108463, 108541 and 108564) and one accession of P. miliaceum (108104) demonstrated high osmoregulative capacity. Differences of 1.05 MPa or more between observed and estimated osmotic potential were found at relative water contents of 80 % among these accessions. The extent of osmoregulative capacity was associated with osmotic potential at full turgor and the rate of decline in osmotic potential as leaf water potentail declined.

Randomized comparison of the quality of realtime fetal ultrasound images transmitted by ISDN and by IP videoconferencing

We compared the quality of realtime fetal ultrasound images transmitted using ISDN and IP networks. Four experienced obstetric ultrasound specialists viewed standard recordings in a randomized trial and rated the appearance of 30 fetal anatomical landmarks, each on a seven-point scale. A total of 12 evaluations were performed for various combinations of bandwidths (128, 384 or 768 kbit/s) and networks (ISDN or IF). The intraobserver coefficient of variation was 2.9%, 5.0%, 12.7% and 14.7% for the four observers. The mean overall ratings by each of the four observers were 4.6, 4.8, 5.0 and 5.3, respectively (a rating of 4 indicated satisfactory visualization and 7 indicated as good as the original recording). Analysis of variance showed that there were no significant interobserver variations nor significant differences in the mean scores for the different types of videoconferencing machines used. The most significant variable affecting the mean score was the bandwidth used. For ISDN, the mean score was 3.7 at 128 kbit/s, which was significantly worse than the mean score of 4.9 at 384 kbit/s, which was in turn significantly worse than the mean score of 5.9 at 768 kbit/s. The mean score for transmission using IP was about 0.5 points lower than that using ISDN across all the different bandwidths, but the differences were not significant. It appears that IP transmission in a private (non-shared) network is an acceptable alternative to ISDN for fetal tele-ultrasound and one deserving further study.

Point source inoculation of Mesocyclops (Copepoda : Cyclopidae) gives widespread control of Ochlerotatus and Aedes (Diptera : Culicidae) immatures in service manholes and pits in North Queensland, Australia

This study details the novel application of predacious copepods, genus Mesocyclops, for control of Ochlerotatus tremulus (Theobald) group and Aedes aegypti (L.) mosquito larvae in subterranean habitats in north Queensland, Australia. During June 1997, 50 Mesocyclops sp. I were inoculated into one service manhole in South Townsville. Wet season rainfall and flooding in both 1998 and 2000 was responsible for the dispersal of copepods via the underground pipe system to 29 of 35 manholes over an area of 1.33 km(2). Significant reductions in Aedes and Ochlerotatus larvae ensued. In these habitats, Mesocyclops and Metacyclops were able to survive dry periods, when substrate moisture content ranged from 13.8 to 79.9%. At the semiarid inland towns of Hughenden and Richmond, cracking clay soil prevents drainage of water from shallow service pits where Oc. tremulus immatures numbered from 292-18,460 per pit. Introduction of Mesocyclops copepods into these sites during May 1999 resulted in 100% control of Oc. tremulus for 18 mo. One uninoculated pit subsequently became positive for Mesocyclops with resultant control of mosquito larvae.

Stressful animal housing conditions and their potential effect on sympathetic neurotransmission in mice

Although the sympathetic nervous system (SNS) plays a major role in mediating the peripheral stress response, due consideration is not usually given to the effects of prolonged stress on the SNS. The present study examined changes in neurotransmission in the SNS after exposure of mice (BALB/c) to stressful housing conditions. Focal extracellular recording of excitatory junction currents (EJCs) was used as a relative measure of neurotransmitter release from different regions of large surface areas of the mouse vas deferens. Mice were either group housed (control), isolation housed (social deprivation), group housed in a room containing rats (rat odor stress), or isolation housed in a room containing rats (concurrent stress). Social deprivation and concurrent stressors induced an increase of 30 and 335% in EJC amplitude, respectively. The success rate of recording EJCs from sets of varicosities in the concurrent stressor group was greater compared with all other groups. The present study has shown that some common animal housing conditions act as stressors and induce significant changes in sympathetic neurotransmission.

Behavioural responses of two native Australian fish species (Melanotaenia duboulayi and Pseudomugil signifer) to introduced poeciliids (Gambusia holbrooki and Xiphophorus helleri) in controlled conditions

Experimental treatments to compare behavioural responses included native fish species only, natives plus one exotic species and natives plus both exotic species. The mosquitofish, Gambusia holbrooki frequently attacked both native species, but tended to nip Melanotaenia duboulayi (especially small individuals) and chase Pseudomugil signifer The frequency of attacks by G. holbrooki on M. duboulayi rose when all four fish species were present. When food was added, all four species showed a strong increase in aggression, especially in the four-species treatment, where there were significant increases in the frequency of attacks by the swordtail Xiphophorus helleri on M. duboulay and by M. duboulayi on G. holbrooki, and of conspecific attacks by M. duboulayi. Increased attack frequency was associated with aggregation closer to the water's surface, regardless of the presence of food. The results support the hypothesis that introduced poeciliids can have deleterious competitive effects on native species. However, while juvenile M. duboulayi were particularly vulnerable to the secondary, effects of fin-nipping, R signifer appeared to be more susceptible to physical displacement and reduced food capture success.