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.

Effects of dietary level of protein, lysine and methionine and strain of bird on production and egg yolk cholesterol

The effects of dietary level of protein (151, 181 g/kg), lysine (nil, 10g L-lysine hydrochloride/kg) and methionine (nil, 5g DL-methionine/kg) on the production performance and egg yolk cholesterol of two strains of birds were studied for 12 weeks. Birds fed on the high protein diet had higher body weight gain, feed conversion ratio (FCR), rate of lay, egg weight and mass and yolk weight and mass. A high lysine diet decreased feed intake and improved FCR. High dietary level of methionine increased egg yolk cholesterol. There were differences between strains of laying bird in feed intake, rate of lay, egg and yolk weights and egg cholesterol content. It is concluded that strain of bird and dietary level of protein and lysine influenced the production performance of birds. Whilst, egg yolk cholesterol was not reduced by any of the factors studied.

Are wing size, wing shape and asymmetry related to field fitness of Trichogramma egg parasitoids?

The effects of wing shape, wing size, and fluctuating asymmetry in these measures oil the field fitness of T. nr. brassicae and T. pretiosum were investigated. Trichogramma wasps mass-reared on eggs of the factitious host Sitotroga cerealella were released in tomato paddocks and those females ovipositing on Helicoverpo spp. eggs were recaptured. Comparisons of the recaptured group with a sample from the release population were used to assess fitness. Wing data were obtained by positioning landmarks on mounted forewings. Size was then measured as the centroid size computed from landmark distances, while Procrustes analysis followed by principal component analysis was used to assess wing shape. Similar findings were obtained for both Trichogramma species: fitness of wasps was strongly related to wing size and some shape dimensions, but not to the asymmetries of these measures. Wasps which performed well in the field had larger wings and a different wing shape compared to wasps from the mass reared population. Both size and the shape dimensions were linearly associated with fitness although there was also some evidence for non-linear selection on shape. The results suggest that wing shape and wing size are reliable predictors of field fitness for these Trichogramma wasps.

Composition and energy density of eggs from two species of freshwater turtle with twofold ranges in egg size

Lipid, protein, ash, carbohydrate and water content and energy density of eggs were measured from different clutches over a range of egg size in two species of freshwater turtle. Dry egg contents consisted of protein (54-60%), lipid (25-31%) and ash (5-6%) while carbohydrate was found to be negligible (

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.

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.

The value of screening in siblings of patients with abdominal aortic aneurysm

Objectives. This study aimed to determine the incidence of abdominal aortic aneurysm (AAA) in a large group of siblings of Australian AAA patients to determine if screening in this group is justified. Methods. 1254 siblings of 400 index AAA patients were identified and offered aortic ultrasound screening. An age and sex matched control group was recruited from patients having abdominal CT scans for non-vascular indications. AAA was defined by an infrarenal aortic diameter of greater than or equal to3 cm or a ratio of the infrarenal to suprarenal aortic diameter of greater than or equal to2.0. A ratio of 1.0-1.5 was considered normal, and a ratio of >1.5 to

Effect of type of grain and oil supplement on the performance, blood lipoproteins, egg cholesterol and fatty ccids of laying hens

The effects of type of grain (wheat vs. sorghum) and oil supplement/kg diet [0, 20g olive oil (OL), 20g safflower oil (SO), 10 g OL plus 10 g SO (OLSO)], over a 12-week period on the performance, plasma and lipoproteins lipids [cholesterol (C), triglycerides (TG), phospholipid (P)], and yolk C and fatty acids concentrations of laying hens were studied. Hens fed on the sorghum diet had significantly (P

The value of idiosyncratic markers and changes to conserved tRNA sequences from the mitochondrial genome of hard ticks (Acari: Ixodida: Ixodidae) for phylogenetic inference

Idiosyncratic markers are features of genes and genomes that are so unusual that it is unlikely that they evolved more than once in a lineage of organisms. Here we explore further the potential of idiosyncratic markers and changes to typically conserved tRNA sequences for phylogenetic inference. Hard ticks were chosen as the model group because their phylogeny has been studied extensively. Fifty-eight candidate markers from hard ticks ( family Ixodidae) and 22 markers from the subfamily Rhipicephalinae sensu lato were mapped onto phylogenies of these groups. Two of the most interesting markers, features of the secondary structure of two different tRNAs, gave strong support to the hypothesis that species of the Prostriata ( Ixodes spp.) are monophyletic. Previous analyses of genes and morphology did not strongly support this relationship, instead suggesting that the Prostriata is paraphyletic with respect to the Metastriata ( the rest of the hard ticks). Parallel or convergent evolution was not found in the arrangements of mitochondrial genes in ticks nor were there any reversals to the ancestral arthropod character state. Many of the markers identified were phylogenetically informative, whereas others should be informative with study of additional taxa. Idiosyncratic markers and changes to typically conserved nucleotides in tRNAs that are phylogenetically informative were common in this data set, and thus these types of markers might be found in other organisms.