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.

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.

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.

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.

Was there a second adaptive radiation of giant tortoises in the Indian Ocean? Using mitochondrial DNA to investigate speciation and biogeography of Aldabrachelys (Reptilia, Testudinidae)

A radiation of five species of giant tortoises (Cylindraspis ) existed in the southwest Indian Ocean, on the Mascarene islands, and another (of Aldabrachelys ) has been postulated on small islands north of Madagascar, from where at least eight nominal species have been named and up to five have been recently recognized. Of 37 specimens of Madagascan and small-island Aldabrachelys investigated by us, 23 yielded significant portions of a 428-base-pair (bp) fragment of mitochondrial (cytochrome b and tRNA-Glu), including type material of seven nominal species (A. arnoldi, A. dussumieri, A. hololissa, A. daudinii, A. sumierei, A. ponderosa and A. gouffei ). These and nearly all the remaining specimens, including 15 additional captive individuals sequenced previously, show little variation. Thirty-three exhibit no differences and the remainder diverge by only 1-4 bp (0.23-0.93%). This contrasts with more widely accepted tortoise species which show much greater inter- and intraspecific differences. The non-Madagascan material examined may therefore only represent a single species and all specimens may come from Aldabra where the common haplotype is known to occur. The present study provides no evidence against the Madagascan origin for Aldabra tortoises suggested by a previous molecular phylogenetic analysis, the direction of marine currents and phylogeography of other reptiles in the area. Ancient mitochondrial DNA from the extinct subfossil A. grandidieri of Madagascar differs at 25 sites (5.8%) from all other Aldabrachelys samples examined here.