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.

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.

Neural control of the heart: developmental changes in ionic conductances in mammalian intrinsic cardiac neurons

The expression and properties of ionic channels were investigated in dissociated neurons from neonatal and adult rat intracardiac ganglia. Changes in the hyperpolarization-activated and ATP-sensitive K+ conductances during postnatal development and their role in neuronal excitability were examined. The hyperpolarization-activated nonselective cation current, I-h, was observed in all neurons studied and displayed slow time-dependent rectification. An inwardly rectifying K+ current, I-K(I), was present in a population of neurons from adult but not neonatal rats and was sensitive to block by extracellular Ba2+. Using the perforated-patch recording configuration, an ATP-sensitive K+ (K-ATP) conductance was identified in greater than or equal to 50% of intracardiac neurons from adult rats. Levcromakalim evoked membrane hyperpolarization, which was inhibited by the sulphonylurea drugs. glibenclamide and tolbutamide. Exposure to hypoxic conditions also activated a membrane current similar to that induced by levcromakalim and was inhibited by glibenclamide. Changes in the complement of ion channels during postnatal development may underlie observed differences in the function of intracardiac ganglion neurons during maturation. Furthermore, activation of hyperpolarization-activated and KATP channels in mammalian intracardiac neurons may play a role in neural regulation of the mature heart and cardiac function during ischaemia-reperfusion. (C) 2002 Elsevier Science B.V All rights reserved.

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.

Improving the ionic conductivity of yttria-stabilised zirconia electrolyte materials

Low-temperature anneals (1200 degreesC for 40 h) of 8 mol% yttria-stabilised zirconia, prior to the samples being sintered at 1500 degreesC, had the effect of improving the ionic conductivity of the specimens. The presence Of SiO2 in the specimens was shown to be detrimental, however. Irrespective of the SiO2 content, this type of heat treatment also leads to improvements in conductivity. Extensive microstructural analysis provided indication of the mechanism of this phenomenon. This included selective formation of zircon, relief of sintering strain leading to the formation of coherent grain boundaries and segregation effects. (C) 2002 Elsevier Science B.V All rights reserved.

Oxide ionic conductivity and microstructures of Sm- or La-doped CeO2-based systems

The concept of crystallographic index termed the effective index is suggested and applied to the design of ceria (CeO2)-based electrolytes to maximize oxide ionic conductivity. The suggested index considers the fluorite structure, and combines the expected oxygen vacancy level with the ionic radius mismatch between host and dopant cations. Using this approach, oxide ionic conductivity of Sm- or La-doped CeO2-based system has been optimized and tested under operating conditions of a solid oxide fuel cell. In the observation of microstructure in atomic scale, both Sm-doped CeO2 and La-doped CeO2 electrolytes had large micro-domains over 10 nm in the lattice. On the other hand, Sm or La and alkaline earth co-doped CeO2-based electrolytes with high effective index had small micro-domains around 1-3 nm in the microstructure. The large micro-domain would prevent oxide ion from passing through the lattice. Therefore, it is concluded that the improvement of ionic conductivity is reflected in changes of microstructure in atomic scale. (C) 2002 Elsevier Science B.V. 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.