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.

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.

Analysis of the sequence and expression of a second putative acetylcholinesterase cDNA from organophosphate-susceptible and organophosphate-resistant cattle ticks

The cattle tick, Boophilus microplus, is a major pest of cattle in Australia, Central and South America, and parts of Africa and Asia. Control of ticks with organophosphates (OPs) and carbamates, which target acetylcholinesterases (AChE), led to evolution of resistance to these pesticides. Alleles at the locus studied here, AChE2, from OP-susceptible female ticks from Australia and Mexico differed at 46 of 1689 nucleotide positions (20 putative amino acid differences) whereas alleles from three strains of OP-resistant ticks from Australia differed with the allele from the Australian susceptible ticks at six to 13 nucleotide positions (three to six putative amino acid differences). However, the role, if any, of these polymorphisms in the OP-resistance phenotype is unknown. Certainly none of the polymorphisms correspond to sites in ACK that are involved in catalysis or binding of acetylcholine in other organisms. Both of the AChE loci of B. microplus, AChE1 and AChE2, are apparently expressed in synganglia; AChE1 is also expressed in salivary glands and ovaries, in OP-susceptible and OP-resistant ticks. This seems to contradict studies of enzyme kinetics, which indicated that only one form of AChE was present in the synganglia, the site of the action of OPs, in this species of tick. (C) 2002 Elsevier Science Ltd. All rights reserved.

Effects of paternal drinking, conduct disorder and childhood home environment on the development of alcohol use disorders in a Thai population

Aims To identify influences on the development of alcohol use disorders in a Thai population, particularly parental drinking and childhood environment. Design Case-control study. Setting A university hospital, a regional hospital and a community hospital in southern Thailand. Participants Ninety-one alcohol-dependents and 177 hazardous/harmful drinkers were recruited as cases and 144 non-or infrequent drinkers as controls. Measurements Data on parental drinking, family demographic characteristics, family activities, parental disciplinary practice, early religious life and conduct disorder were obtained using a structured interview questionnaire. The main outcome measure was the subject's classification as alcohol-dependent, hazardous/harmful drinker or non-/infrequent drinker. Findings A significant relationship was found between having a drinking father and the occurrence of hazardous/harmful drinking or alcohol dependence in the subjects. Childhood factors (conduct disorder and having been a temple boy, relative probability ratios, RPRs and 95% CI: 6.39, 2.81-14.55 and 2.21, 1.19-4.08, respectively) also significantly predicted alcohol dependence, while perceived poverty and ethnic alienation was reported less frequently by hazardous/harmful drinkers and alcohol-dependents (RPRS and 95% CIs = 0.34, 0.19-0.62 and 0.59, 0.38-0.93, respectively) than the controls. The relative probability ratio for the effect of the father's infrequent drinking on the son's alcohol dependence was 2.92 (95% CI = 1.42-6.02) and for the father's heavy or dependent drinking 2.84 (95% CI=1.31-6.15). Conclusions Being exposed to a light-drinking, father increases the risk of a son's alcohol use disorders exhibited either as hazardous-harmful or dependent drinking. However, exposure to a heavy- or dependent-drinking father is associated more uniquely with an increased risk of his son being alcohol-dependent. The extent to which this is seen in other cultures is worthy of exploration.

Second primary oesophageal cancer following radiation for breast cancer

The management of 12 women who presented with a second primary oesophageal cancer following radiotherapy for breast cancer was reviewed. It was concluded that nine cases fitted the classical description of a radiation-induced malignancy. Most cases were successfully managed with combined modality therapy in spite of their previous radiotherapy. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Selling Queensland at the Glasgow international exhibition of 1901

Queensland was one of two states of the newly-federated Australia to mount official courts at the Glasgow International Exhibition of 1901, the largest world expo held in Great Britain to that date. In exhibiting at Glasgow, then the second city of the British Empire, Queensland sought to draw emigrants and investment from Britain. The court, funded by the Queensland Department of Mines, was mostly a display of mineral wealth, and the state's agricultural and pastoral resources were poorly represented. The 'prettily designed' court presented a rose-coloured view of a land endowed with boundless wealth and resources. This in no way reflected the realities of life back home, in a year of environmental and economic disaster, and of political and social upheaval. Though the exhibit failed to bring tangible benefits, it is an important record of Queensland aspirations and concerns at the time of Federation. It has special interest as the last occasion when Queensland exhibited in its own right, rather than as part of the Commonwealth of Australia.

The tourism-leisure behavioural continuum

Tourism and leisure have historically been studied in isolation, but recent researchers attempt to understand the relationship between them. However, there have been few comparisons of how people behave in their environments. This paper provides a conceptual model of the relationship based oil a critical review of the current literature oil pleasure-oriented environments. The model indicates that despite potential differences in observable behavior, there is a commonality between the underlying influences that define how people behave during their leisure and tourism experiences. Therefore, the paper concludes that these should not be regarded as separate phenomenon. (C) 2002 Elsevier Science Ltd. All Lights reserved.