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.

Polarised infrared and differential scanning calorimetry studies on oriented vinyl pipe materials

The molecular orientation in a conventionally extruded PVC pipe, a uniaxially oriented PVC pipe and a biaxially oriented PVC pipe has been studied via Infrared dichroism. The degree of order or crystallinity has also been studied by Differential Scanning Calorimetry and also via Infrared Spectroscopy. The fundamental structural difference between the conventional and oriented pipes was that polymer chains were preferentially aligning in the hoop direction for oriented pipes whereas they were fairly isotropic in the conventional pipe with a slight preferential alignment in the axial direction. Analysis of the C-Cl stretching mode indicated that the uniaxially oriented pipe had much higher alignment of the C-Cl bond in the axial direction than the biaxial pipe, which correlates with higher fracture toughness for circumferential cracking in the biaxial pipe. Both DSC and Infrared spectroscopy detected little change in the crystallinity or order in the oriented pipes compared to the conventionally extruded pipes. (C) 2002 Kluwer Academic Publishers.

Differential regulation of twitching motility and elastase production by Vfr in Pseudomonas aeruginosa

Vfr, a homolog of Escherichia coli cyclic AMP (cAMP) receptor protein, has been shown to regulate quorum sensing, exotoxin A production, and regA transcription in Pseudomonas aeruginosa. We identified a twitching motility-defective mutant that carries a transposon insertion in vfr and confirmed that vfr is required for twitching motility by construction of an independent allelic deletion-replacement mutant of vfr that exhibited the same phenotype, as well as by the restoration of normal twitching motility by complementation of these mutants with wild-type vfr. Vfr-null mutants exhibited severely reduced twitching motility with barely detectable levels of type IV pili, as well as loss of elastase production and altered pyocyanin production. We also identified reduced-twitching variants of quorum-sensing mutants (PAK lasl::Tc) with a spontaneous deletion in vfr (S. A. Beatson, C. B. Whitchurch, A. B. T. Semmler, and J. S. Mattick, J. Bacteriol., 184:3598-3604,2002), the net result of which was the loss of five residues (EQERS) from the putative cAMP-binding pocket or Vfr. This allele (VfrDeltaEQERS) was capable of restoring elastase and pyocyanin production to wild-type levels in vfr-null mutants but not their defects in twitching motility. Furthermore, structural analysis of Vfr and VfrDeltaEQERS in relation to E. coli CRP suggests that Vfr is capable of binding both cAMP and cyclic GMP whereas VfrDeltaEQERS is only capable of responding to cAMP. We suggest that Vfr controls twitching motility and quorum sensing via independent pathways in response to these different signals, bound by the same cyclic nucleotide monophosphate-binding pocket.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

The differential role of alcohol expectancies, drinking refusal self-efficacy and coping resources in predicting alcohol consumption in community and clinical samples

This study explored the relationship between coping, alcohol expectancies and drinking refusal self-efficacy in predicting drinking behaviour in both community and clinical samples. These variables were found to have differential effects in their association with frequency and volume of alcohol consumption across the two samples. Generally, drinking refusal self-efficacy was a more salient factor in relation to frequency and volume of community drinking, while coping and expectancies were more strongly associated with frequency of drinking sessions by problem drinkers. The interaction between expectancies and drinking refusal self-efficacy was related to volume of consumption in both groups, while coping and expectancies interacted in their association with frequency in the clinical group. The findings are discussed with regard to the different patterns of cognitive variables governing the decision to drink and the amount consumed in each drinking session, which may differentiate community and problem drinkers.

Differential sorting and fate of endocytosed GPI-anchored proteins

In this paper, we studied the fate of endocytosed glycosylphosphatidyl inositol anchored proteins (GPI-APs) in mammalian cells, using aerolysin, a bacterial toxin that binds to the GPI anchor, as a probe. We find that GPI-APs are transported down the endocytic pathway to reducing late endosomes in BHK cells, using biochemical, morphological and functional approaches. We also find that this transport correlates with the association to raft-like membranes and thus that lipid rafts are present in late endosomes (in addition to the Golgi and the plasma membrane). In marked contrast, endocytosed GPI-APs reach the recycling endosome in CHO cells and this transport correlates with a decreased raft association. GPI-APs are, however, diverted from the recycling endosome and routed to late endosomes in CHO cells, when their raft association is increased by clustering seven or less GPI-APs with an aerolysin mutant. We conclude that the different endocytic routes followed by GPI-APs in different cell types depend on the residence time of GPI-APs in lipid rafts, and hence that raft partitioning regulates GPI-APs sorting in the endocytic pathway.

Induction of birth in the bandicoot (Isoodon macrourus) with prostaglandin and oxytocin

As in eutherians, maturation of the fetal pituitary and adrenal glands together with an increase in prostaglandin and mesotocin or oxytocin production initiates birth in marsupials. in this study, prostaglandin (Lutalyse) or oxytocin (Syntocinon) were administered to pregnant bandicoots at 05:00 h on the calculated day of birth and the resultant effects were filmed for analysis. The administration of prostaglandin caused the bandicoot to adopt the birth position several minutes after injection (n = 2). However, the bandicoot did not give birth for several hours. Birth occurred at a similar time of day to that observed for untreated bandicoots (n = 7), between 08:00 h and 12:00 h. After an injection of oxytocin, the bandicoot assumed the birth position and birth occurred within several minutes. The young were alive while still connected to their allantoic stalks. However, they were unable to attach to the teats and did not survive (n = 4). The induced young were the colour of venous blood and died soon after the umbilicus was separated, indicating that the cardiopulmonary system of these neonates was underdeveloped and inadequate to maintain life. The results from this study demonstrate that prostaglandin is required to prepare the bandicoot for birth, and mesotocin is required for contraction of the uterus and for birth to occur.

Polyethylene flow prediction with a differential multi-mode Pom-Pom model

We report the first steps of a collaborative project between the University of Queensland, Polyflow, Michelin, SK Chemicals, and RMIT University; on simulation, validation and application of a recently introduced constitutive model designed to describe branched polymers. Whereas much progress has been made on predicting the complex flow behaviour of many - in particular linear - polymers, it sometimes appears difficult to predict simultaneously shear thinning and extensional strain hardening behaviour using traditional constitutive models. Recently a new viscoelastic model based on molecular topology, was proposed by McLeish and Larson (1998). We explore the predictive power of a differential multi-mode version of the pom-pom model for the flow behaviour of two commercial polymer melts: a (long-chain branched) low-density polyethylene (LDPE) and a (linear) high-density polyethylene (HDPE). The model responses are compared to elongational recovery experiments published by Langouche and Debbaut (1999), and start-up of simple shear flow, stress relaxation after simple and reverse step strain experiments carried out in our laboratory.

Study on diffusion and flow of benzene, n-hexane and CCl4 in activated carbon by a differential permeation method

In this paper the diffusion and flow of carbon tetrachloride, benzene and n-hexane through a commercial activated carbon is studied by a differential permeation method. The range of pressure is covered from very low pressure to a pressure range where significant capillary condensation occurs. Helium as a non-adsorbing gas is used to determine the characteristics of the porous medium. For adsorbing gases and vapors, the motion of adsorbed molecules in small pores gives rise to a sharp increase in permeability at very low pressures. The interplay between a decreasing behavior in permeability due to the saturation of small pores with adsorbed molecules and an increasing behavior due to viscous flow in larger pores with pressure could lead to a minimum in the plot of total permeability versus pressure. This phenomenon is observed for n-hexane at 30degreesC. At relative pressure of 0.1-0.8 where the gaseous viscous flow dominates, the permeability is a linear function of pressure. Since activated carbon has a wide pore size distribution, the mobility mechanism of these adsorbed molecules is different from pore to pore. In very small pores where adsorbate molecules fill the pore the permeability decreases with an increase in pressure, while in intermediate pores the permeability of such transport increases with pressure due to the increasing build-up of layers of adsorbed molecules. For even larger pores, the transport is mostly due to diffusion and flow of free molecules, which gives rise to linear permeability with respect to pressure. (C) 2002 Elsevier Science Ltd. All rights reserved.

Adolescents' perceptions of differential parenting: Links with attachment style and adolescent adjustment

The study examines whether adolescent twins' attachment style mediates the association between their perceptions of differential parental treatment and their reported adjustment. Data from a survey of 174 adolescent twins are used to assess the links between twins' reports of differential parental affection and differential parental control, their attachment style, and their reported personal self-esteem, social self-esteem, and anxiety. Twins' reports of having been disfavored in comparison with their co-twin were associated with attachment insecurity, anxiety, and lower personal self-esteem. Attachment was found to mediate the association between the twins' reports of differential parental affection and their reported anxiety and personal self-esteem. The strongest evidence for mediation was found for twins' reports of differential maternal affection in predicting adolescent twins' anxiety.

Osteonectin/SPARC induction by ectopic beta(3) integrin in human radial growth phase primary melanoma cells

Expression of the beta(3) integrin subunit in melanoma in situ has been found to correlate with tumor thickness, the ability to invade and metastasize, and poor prognosis. Transition from the radial growth phase (RGP) to the vertical growth phase (VGP) is a critical step in melanoma progression and survival and is distinguished by the expression of beta(3), integrin. The molecular pathways that operate in melanoma cells associated with invasion and metastasis were examined by ectopic induction of the beta(3), integrin subunit in RGP SBcl2 and WM1552C melanoma cells, which converts these cells to a VGP phenotype. We used cDNA representational difference analysis subtractive hybridization between beta(3)-Positive and -negative melanoma cells to assess gene expression profile changes accompanying RGP to VGP transition. Fourteen fragments from known genes including osteonectin (also known as SPARC and BM-40) were identified after three rounds of representational difference analysis. Induction of osteonectin was confirmed by Northern and Western blot analysis and immunohistochemistry and correlated in organotypic cultures with the beta(3)-induced progression from RGP to VGP melanoma. Expression of osteonectin was also associated with reduced adhesion to vitronectin, but not to fibronectin. Osteonectin expression was not blocked when melanoma cells were cultured with anti-alpha(v)beta(3) LM609 mAb, mitogen-activated protein kinase, or protein kinase C inhibitors, indicating that other signaling pathway(s) operate through a(v)beta(3) integrin during conversion from RGP to VGP.