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.

Effects of the solute ionization on the adsorption of aromatic compounds from dilute aqueous solutions by activated carbon

Adsorption of four dissociating aromatic compounds and one nondissociating compound on a commercial activated carbon is investigated systematically. All adsorption experiments were carried out in pH-controlled aqueous solutions. The adsorption isotherms are fitted to the binary homogeneous Langmuir model, where the concentrations of the molecular and the ionic species in the liquid phase are expressed in terms of the sum of the two and the degree of solute ionization. Examination of the relationships between the solution pH, the degree of ionization of the solutes, and the model parameters is found to give new insights into the adsorption process. Furthermore, this is used to correlate the variation of the monolayer capacity with the solution pH.

The strength of concentrated Mg-Zn solid solutions

Solid solution effects on the hardness and flow stress have been studied for zinc contents between 0.2 and 2.4 at% (0.5 and 6.9 wt%) in Mg. The alloys were grain refined with 0.6 wt% zirconium to ensure a similar grain size at all compositions. The hardness increases with the zinc content as Hv(10) (kg mm(-2)) = 9 Zn (at%) + 33. At low solute concentrations the (0.2%) proof strength does not change significantly with concentration. At concentrations above 0.7 at%, within the supersaturated solid solution region, the rate of solid solution hardening is high, following a c(2) rule, where c is the atom fraction of Zn. It is suggested that short-range order may account for most of the observed strengthening in concentrated Mg-Zn alloys.

Effects of surface chemistry on aromatic compound adsorption from dilute aqueous solutions by activated carbon

Adsorption of one nondissociating and four dissociating aromatic compounds onto three untreated activated carbons from dilute aqueous solutions were investigated. All adsorption experiments were preformed in pH-controlled solutions. The experimental isotherms were analyzed using the homogeneous Langmuir model. The surface chemical properties of the activated carbons were characterized using a combination of water adsorption, X-ray photoemission spectroscopy, and mass titration. These data give rise to a new insight into the adsorption mechanism of aromatic solutes, in their molecular and ionic forms, onto untreated activated carbons. It was found that, for the hydrophilic activated carbons, the dominant adsorption forces were observed to be dipolar interactions when the solutes were in their molecular form whereas dispersive forces, such as pi-pi interactions, were most likely dominant in the case of the basic hydrophobic carbons. However, when the solutes were in their ionic form adsorption occurs in all cases through dispersive forces.

Aerosolization of protein solutions using thermal inkjet technology

Vapotronics Inc. is developing the thermal inkjet (TIJ) technology used extensively in the printer industry to create a digital aerosol inhaler for the inhalation of therapeutics for local and systemic delivery. The operation of thermal inkjet printers requires generation of high temperatures and vaporization of the liquid formulation to effect droplet ejection. A study was conducted to develop formulations that would permit the generation of aerosols of therapeutic proteins without damage to the inkjet system or degradation of the proteins. Two proteins, human growth hormone and insulin, were formulated and aerosolized. The aerosol was collected and subjected to assays to compare the physicochemical and biological activities of these proteins before and after aerosolization. In each case, there was no significant changes to the proteins as a result of the aerosolization, providing evidence that TIJ can be used for aerosolizing solutions of protein therapeutics.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

NEW Solutions: An Australian health promotion programme for people with mental illness

The prevalence of people who are overweight or obese is continuing to rise. This is a key risk indicator of preventable morbidity and mortality resulting from many diseases. The increase in the number of obese people is associated with dietary practices and a reduction in physical activity. There is a need to implement strategies for the reduction of obesity in at-risk groups. People with a mental illness are at high risk of many physical illnesses related to behavioural factors, which include poor diet and lack of exercise. Health promotion programmes need to be incorporated into mental-health services to improve the general health and wellbeing of people with a mental illness. An Australian psychiatric rehabilitation service developed and implemented a health promotion programme, NEW Solutions, which aimed to address issues related to weight gain, dietary practice and physical inactivity.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Reforming the law of medical negligence: Solutions in search of a problem

The Commonwealth Government's Principles Based Review of the Law of Negligence recently recommended reforms aimed at limiting liability and damages arising from personal injury and death, in response to the growing perception that the current system of compensating personal injury had become financially unsustainable. Recent increases in medical liability and damages have eroded the confidence of doctors and their professional bodies, with fears of unprecedented desertion from and reduced recruitment into high risk areas, and one of the primary foci of the review concerned medical negligence. The article analyses proposals to redefine the principles necessary for the finding of negligence, against the terms of reference of the review. The article assumes that for the foreseeable future, Australia will persist with tort-based compensation for personal injury rather than developing a no-fault scheme. If the suggested changes to the fundamental principles of negligence are unlikely to reduce medical liability, greater attention might be given to the processes which come into play after the finding of negligence, where reform is more likely to benefit both plaintiffs and defendants.

Characterization of the surface stickiness of fructose-maltodextrin solutions during drying

A probe tack test has been used for the in situ characterization of the surface stickiness of hemispherical drops with an initial radius of 3.5 mm while drying. Surface stickiness of drops of fructose and maltodextrin solutions dried at 63degreesC and 95degreesC was determined. The effect of addition of maltodextrin on fructose solution-was studied with fructose/maltodextrin solid mass ratios of 4: 1, 1: 1, and 1:4. Pure fructose solutions remained completely sticky and failed cohesively even when their moisture approached zero. Shortly after the start of drying, the surface of the maltodextrin drops formed a skin, which rapidly grew in thickness. Subsequently the drop surface became completely nonsticky probably due to transformation of outer layers into a glassy material. Addition of malto,dextrin significantly altered the surface stickiness of drops of fructose solutions, demonstrating its use as an effective drying aid.