Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

The appearance of a second genotype of Japanese encephalitis virus in the Australasian region

In mid-January 2000, the reappearance of Japanese encephalitis (JE) virus activity in the Australasian region was first demonstrated by the isolation of JE virus from 3 sentinel pigs on Badu Island in the Torres Strait. Further evidence of JE virus activity was revealed through the isolation of JE virus from Cidex gelidus mosquitoes collected on Badu Island and the detection of specific JE virus neutralizing antibodies in 3 pigs from Saint Pauls community on Moa Island. Nucleotide sequencing and phylogenetic analyses of the premembrane and envelope genes were performed which showed that both the pig and mosquito JE virus isolates (TSOO and TS4152, respectively) clustered in genotype I, along with northern Thai, Cambodian, and Korean isolates. All previous Australasian JE virus isolates belong to genotype II, along with Malaysian and Indonesian isolates. Therefore, for the first time, the appearance and transmission of a second genotype of JE virus in the Australasian region has been demonstrated.

The nature and evolution of the association among digeneans, molluscs and fishes

Patterns of association of digenean families and their mollusc and vertebrate hosts are assessed by way of a new database containing information on over 1000 species of digeneans for lift-cycles and over 5000 species from fishes. Analysis of the distribution of digenean families in molluscs suggests that the group was associated primitively with gastropods and that infection of polychaetes, bivalves and scaphopods are all the results of host-switching. For the vertebrates. infections of agnathans and chondrichthyans are apparently the result of host-switching from teleosts. For digenean families the ratio of orders of fishes infected to superfamilies of molluscs infected ranges from 0.5 (Mesometridae) to 16 (Bivesiculidae) and has a mean of 5.6. Individual patterns of host association of 13 dipenean families and superfamilies are reviewed. Two, Bucephalidae and Sanguinicolidae. are exceptional in infecting a range of first intermediate hosts qualitatively as broad as their range of definitive hosts. No well-studied taxon shows narrower association with vertebrate than with mollusc clades. The range of definitive hosts of digeneans is characteristically defined by eco-physiological similarity rather than phylogenetic relationship. The range of associations of digenean families with mollusc taxa is generally much narrower. These data are considered in the light of ideas about the significance of different forms of host association. If Manter's Second Rule (the longer the association with a host group, the mure pronounced the specificity exhibited by the parasite group) is invoked, then the data may suggest that the Digenea first parasitised molluscs before adopting vertebrate hosts. This interpretation is consistent with most previous ideas about the evolution of the Digenea but contrary to current interpretations based on the monophyly of the Neodermata. The basis of Manter's Second Rule is. however, considered too flimsy for this interpretation to be robust. Problems of the inference of the evolution of patterns of parasitism in the Neodermata al-e discussed and considered so intractable that the truth may be presently unknowable. (C) 2001 Australian Society for Parasitology Inc. Published by Elsevier Science Ltd. All rights reserved.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

The cloning and characterization of a second alpha-amylase of A-hydrophila JMP636

Aims: The aim of this study was to identify, clone and characterize the second amylase of Aeromonas hydrophila JMP636, AmyB, and to compare it to AmyA. Methods and Results: The amylase activity of A. hydrophila JMP636 is encoded by multiple genes. A second genetically distinct amylase gene, amyB, has been cloned and expressed from its own promoter in Escherichia coli. AmyB is a large alpha-amylase of 668 amino acids. Outside the conserved domains of alpha-amylases there is limited sequence relationship between the two alpha-amylases of A. hydrophila JMP636 AmyA and AmyB. Significant (80%) similarity exists between amyB and an alpha-amylase of A. hydrophila strain MCC-1. Differences in either the functional properties or activity under different environmental conditions as possible explanations for multiple copies of amylases in JMP636 is less likely after an examination of several physical properties, with each of the properties being very similar for both enzymes (optimal pH and temperature, heat instability). However the reaction end products and substrate specificity did vary enough to give a possible reason for the two enzymes being present. Both enzymes were confirmed to be alpha-type amylases. Conclusions: AmyB has been isolated, characterized and then compared to AmyA. Significance and Impact of Study: The amylase phenotype is rarely encoded by more than one enzyme within one strain, this study therefore allows the better understanding of the unusual amylase production by A. hydrophila.

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.