Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

Influence of adsorbate interaction on transport in confined spaces

This article provides a review of the recent theory of transport in nanopores developed in the author's laboratory. In particular the influence of fluid-solid interactions on the transport coefficient is examined, showing that such interactions reduce the value of the coefficient by almost an order of magnitude in comparison to the Knudsen theory for non-interacting systems. The activation energy and potential energy barriers for diffusion in smooth pores with a one-dimensional potential energy profile are also discussed, indicating the inadequacy of the commonly used assumption of proportionality between the activation energy and heat of adsorption or the minimum pore potential energy. A further feature affected by fluid-solid interactions is the nature of the reflection of fluid molecules colliding with a pore wall surface, varying from being nearly specular - such as in carbon nanotubes - to nearly diffuse for amorphous solids. Diffuse reflection leads to momentum loss and reduced transport coefficients. However, fluid-solid interactions do not affect the transport coefficient in the single-file diffusion regime when the surface reflection is diffuse, and the transport coefficient in this case is largely independent of the adsorbed density.

Student Difficulties with units in differential equations in modelling contexts

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless failed to apply that knowledge when needed. In addition, few students were able to determine the units of a proportionality factor in a simple equation. These results indicate that lecturers of modelling courses cannot take this foundational knowledge for granted and should explicitly include it in instruction.

Playing in continuous spaces: Some analysis and extension of population-based incremental learning

As an alternative to traditional evolutionary algorithms (EAs), population-based incremental learning (PBIL) maintains a probabilistic model of the best individual(s). Originally, PBIL was applied in binary search spaces. Recently, some work has been done to extend it to continuous spaces. In this paper, we review two such extensions of PBIL. An improved version of the PBIL based on Gaussian model is proposed that combines two main features: a new updating rule that takes into account all the individuals and their fitness values and a self-adaptive learning rate parameter. Furthermore, a new continuous PBIL employing a histogram probabilistic model is proposed. Some experiments results are presented that highlight the features of the new algorithms.

Languaging the worker:globalized governmentalities in/of language in peripheral spaces

In the introduction to the special issue “Languaging the worker: globalized governmentalities in/of language in peripheral spaces”, we take up the notion of governmentality as a means to interrogate the complex relationship between language, labor, power and subjectivity in peripheral multilingual spaces. Our aim here is to argue for the study of governmentality as a viable and growing approach in critical sociolinguistic research. As such, in this introduction, we first discuss key concepts germane to our interrogations, including the notions of governmentality, languaging, peripherality and language worker. We proceed to map out five ethnographically and discourse-analytically informed case studies. These examine diverse actors in different settings pertaining to the domain of work. Finally we chart how the case studies construe the issue of languaging the worker through a governmentality frame.

Visual field defects in Alzheimer's disease patients may reflect differential pathology in the primary visual cortex

The aim of this study was to test the hypothesis that differences in density of senile plaques (SP) and neurofibrillary tangles (NFT) in the cuneal and lingual gyri of area V1 of the visual cortex could explain the predominantly inferior visual field defects seen in patients with Alzheimer's disease (AD). The density of SP and NFT was measured in the cuneal and lingual gyri of 18 AD patients. In 7/18 (39%) patients, the density of SP and/or NFT was significantly greater in the cuneal compared with the lingual gyri. In 3/18 (17%) patients, densities were greater in the lingual than the cuneal gyri and in 8/18 (44%) patients there were no significant differences among gyri. The data suggest that pathological differences between cuneal and lingual gyri could contribute to the reported visual field defects in some AD patients.

Differential birefringence in Bragg gratings in multicore fiber under transverse stress

We present experimental measurements of the peak splitting of the reflection spectra of fiber Bragg gratings as a result of birefringence induced by transverse loading of a multicore fiber. Measurements show that the splitting is a function of the applied load and the direction of the load relative to the azimuth of the fiber. A model for calculating the stress in the fiber that is due to an applied load is in good agreement with our experimental observations.

Differential Equations in Abstract Cones

We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.