Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (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

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.

The paternity of the price-quality 'value map'

In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer 'value maps'. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the 'quality' axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.

A molecular phylogeny of the Australian skink genera Eulamprus, Gnypetoscincus and Nangura

Skinks from the genera Eulamprus, Gnypetoscincus and Nangura are a prominent component of the reptile fauna of the mesic forests of the east coast of Australia and have been the subject of numerous ecological studies. Highly conserved morphology and the retention of ancestral traits have limited our understanding of the relationships within and among these genera beyond an initial identification of species groups within Eulamprus. To address this deficit and to explore the relationships between Eulamprus and the monotypic genera Nangura and Gnypetoscincus, sections of two mitochondrial genes (ND4 and 16S rRNA) were sequenced and subjected to Bayesian phylogenetic analysis. This phylogenetic analysis supports recognition of the three species groups proposed for Eulamprus (murrayi, quoyii and tenuis) and indicates that this genus is paraphyletic, with Gnypetoscincus and Nangura being proximal to basal lineages of the tenuis group. To resolve these and broader problems of paraphyly, we suggest that each of the species groups from 'Eulamprus' should be recognised as a distinct genus. The phylogenetically and ecologically distinct water skinks of the quoyii group would be retained within Eulamprus and the diverse species of the tenuis group allocated to Concinnia. We suggest placing the monophyletic murrayi group, endemic to the rainforests of central eastern Australia, in a new genus ( yet to be formally described). The sequencing data also revealed the existence of a genetically divergent but morphologically cryptic lineage within E. murrayi and substantial diversity within E. quoyii. There is evidence for two major habitat shifts from rainforest towards drier habitats, one leading to the quoyii group and the second defining a clade of three species within the tenuis complex. These ecological transitions may represent adaptations to general drying across eastern Australia during the late Miocene - Pliocene. Each of the major areas of east coast tropical or subtropical rainforest contains multiple phylogenetically diverse endemic species, reflecting the long-term persistence and high conservation value of wet forest habitats in each area.

Effects of heat treatment on the nutritional value of raw soybean selected for low trypsin inhibitor activity

1. Two broiler experiments and a layer experiments were conducted on Kunitz trypsin inhibitor (Kti) soybeans (SB) of low trypsin inhibitor (TI) activity to determine their nutritive value when included as mash in least-cost poultry diets. 2. Experiment 1 compared chick performance on the Kti or raw SB using a commercial full-fat SB meal (FFSBM) and a solvent extracted SB meal (SBM) as controls during a 20 d experimental period. Broiler experiment 2 compared Kti and raw SB, non-steamed, or steam-pelleted with and without DL-methionine supplementation added to every treatment containing 170 g SB/kg. For each broiler experiment the levels of each SB were 70, 120 and 170 g/kg with the control birds fed only 170 g SB/kg. 3. The layer experiment, compared steam-pelleted Kti and raw SB against a non-steamed Kti and raw SB each fed at two levels (70 and 110 g/kg) x 30 replicates from 29 weeks of age for 19 weeks in a completely randomised design. Production parameters were measured when diets were formulated to contain minimum required specifications and calculated apparent metabolisable energy (AME). At the completion of each trial, 2 broiler birds from each cage and 5 layer birds per treatment were killed, weighed, and their liver and pancreas weighed. 4. Both broiler experiments indicated that production parameters on the Kti SB treatments were significantly lower (P < 0.05) than on the two commercial control SB treatments. However, the Kti treatments were superior to the raw SB treatments. 5. Pancreas weight increased with increasing inclusion of both raw and Kti SB, suggesting that a TI was causing the depression in performance. The AME of the Kti SB was similar to that of commercial FFSB meal. After steam conditioning, the raw SB meal AME value of 9.5 MJ/kg dry matter (DM) was improved to 14.1 MJ/kg DM by reduced TI activity, but this AME improvement with TI activity reduction, plus the supplementation with DL-methionine on birds fed the raw SB had no effect (P > 0.05) on any parameter evaluated in experiment 2. 6. The layer experiment showed that hens on the Kti SB treatments had significantly greater live weight gain (LWG), egg weight and daily egg mass than birds given raw SB. A reduced food intake (FI) was observed in the Kti treatments but egg mass was generally similar to that on the FFSB control diet, indicating that Kti SB supported excellent egg production at an inclusion of 110 g/kg. The depressed performance observed for broiler chicks suggest that younger birds are more susceptible to the effects of SB TI.