Pure mathematics for engineers,

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Encyclopaedia of pure mathematics.

Articles reprinted from Encyclopaedia metropolitana.

A complete course of pure mathematics /

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Questions in pure mathematics proposed at the B.A. and B.Sc. pass and honours examinations of the University of London. With complete solutions.

Mode of access: Internet.

Genetic algorithms in statistical tolerancing

An important aspect in manufacturing design is the distribution of geometrical tolerances so that an assembly functions with given probability, while minimising the manufacturing cost. This requires a complex search over a multidimensional domain, much of which leads to infeasible solutions and which can have many local minima. As well, Monte-Carlo methods are often required to determine the probability that the assembly functions as designed. This paper describes a genetic algorithm for carrying out this search and successfully applies it to two specific mechanical designs, enabling comparisons of a new statistical tolerancing design method with existing methods. (C) 2003 Elsevier Ltd. All rights reserved.

Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Valerian does not appear to reduce symptoms for patients with chronic insomnia in general practice using a series of randomised n-of-I trials

Objectives: To investigate the effectiveness of valerian for the management of chronic insomnia in general practice. Design: Valerian versus placebo in a series of n-of-1 trials, in Queensland, Australia. Results: Of 42 enrolled patients, 24 (57%) had sufficient data for inclusion into the n-of-1 analysis. Response to valerian was fair for 23 (96%) participants evaluating their 'energy level in the previous day' but poor or modest for all 24 (100%) participants' response to 'total sleep time' and for 23 (96%) participants' response to 'number of night awakenings' and 'morning refreshment'. As a group, the proportion of treatment successes ranged from 0.35 (95% CI 0.23, 0.47) to 0.55 (95% CI 0.43, 0.67) for the six elicited outcome sleep variables. There was no significant difference in the number (P = 0.06), distribution (P = 1.00) or severity (P = 0.46) of side effects between valerian and placebo treatments. Conclusions: Valerian was not shown to be appreciably better than placebo in promoting sleep or sleep-related factors for any individual patient or for all patients as a group. (C) 2003 Elsevier Ltd. All rights reserved.

All's fair in love and war - but not contract

Changes to Queensland's unfair terms in consumer contracts expected - nature of the changes outlined - protections given to consumers, with respect to unfair contracts, in Victoria and the United Kingdom.

'Slippage' is not a dirty word: Considering the usefulness of Giddens' notion of knowledgeability in understanding the possibilities for teacher education

The attempt to understand the relationship between messages intended and messages received has been an enduring issue in teacher education. For the past three decades researchers have made forays into understanding this enduring issue, and in the process have drawn on various explanatory frameworks, one of them being socialisation. In this paper we work with Giddens' structuration theory as well as his concept of knowledgeability as analytical frameworks for understanding the relationship between messages intended (by the teacher educator) and messages received (by the student-teachers). Our discussion is informed by the findings of a study that investigated student-teachers' interpretations of the pedagogical process of a physical education teacher education course. Data generated from conversations with, and observations of, the student-teachers indicated that there was considerable “slippage” between the teacher educator's critical pedagogy inspired intentions and what was understood by the student-teachers.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

The Debreu Gap Lemma and some generalizations

In this paper we study the Debreu Gap Lemma and its generalizations to totally ordered sets more general than (R, less than or equal to). We explain why it is important in economics to study utility functions which may not be real-valued and we build the foundations of a theory of continuity of such generalized utility functions. (C) 2004 Published by Elsevier B.V.

Ergot of rye - the first specific for migraine

Over the past decade the various triptan derivatives have been accepted as the most effective available agents for relieving migraine attacks. Prior to that, for a period of half a century, ergotamine was the only 'specific' available for this purpose. In 1918, Stoll had isolated it from the various alkaloids present in extracts of the sclerotia of the fungus Claviceps purpurea (ergot), which grow on rye and, to a lesser extent, on other grasses. By 1925 ergotamine was beginning to be used to treat migraine attacks. However, as ergotamine was present in extracts of ergot, which had been used to treat migraine first, In Italy in 1862, and then by Edward Woakes (11868) in England, and after him by Albert Eulenburg in Germany (1883), the drug had actually come into unrecognised use for the disorder more than half a century before ergotamine itself was known to exist. Unfortunately, because of ergotamine's chemical and pharmacokinetic properties, extracts of ergot of rye were incapable of producing consistent therapeutic results, so that general acceptance that the first specific substance for migraine treatment existed had to wait until pure ergotamine was available for administration. (C) 2003 Elsevier Ltd. All rights reserved.

Nutrient partitioning during treatment of tuberculosis: gain in body fat mass but not in protein mass

Background: Tuberculosis is an important cause of wasting. The functional consequences of wasting and recovery may depend on the distribution of lost and gained nutrient stores between protein and fat masses. Objective: The goal was to study nutrient partitioning, ie, the proportion of weight change attributable to changes in fat mass (FM) versus protein mass (PM), during anti mycobacterial treatment. Design: Body-composition measures were made of 21 men and 9 women with pulmonary tuberculosis at baseline and after 1 and 6 mo of treatment. All subjects underwent dual-energy X-ray absorptiometry and deuterium bromide dilution tests, and a four-compartment model of FM, total body water (TBW), bone minerals (BM), and PM was derived. The ratio of PM to FM at any time was expressed as the energy content (p-ratio). Changes in the p-ratio were related to disease severity as measured by radiologic criteria. Results: Patients gained 10% in body weight (P < 0.001) from baseline to month 6. This was mainly due to a 44% gain in FM (P < 0.001); PM, BM, and TBW did not change significantly. Results were similar in men and women. The p-ratio decreased from baseline to month 1 and then fell further by month 6. Radiologic disease severity was not correlated with changes in the p-ratio. Conclusions: Microbiological cure of tuberculosis does not restore PM within 6 mo, despite a strong anabolic response. Change in the p-ratio is a suitable parameter for use in studying the effect of disease on body composition because it allows transformation of such effects into a normal distribution across a wide range of baseline proportion between fat and protein mass.

Design of artificial myocardial microtissues

Cultivation technologies promoting organization of mammalian cells in three dimensions are essential for gene-function analyses as well as drug testing and represent the first step toward the design of tissue replacements and bioartificial organs. Embedded in a three-dimensional environment, cells are expected to develop tissue-like higher order intercellular structures (cell-cell contacts, extracellular matrix) that orchestrate cellular functions including proliferation, differentiation, apoptosis, and angiogenesis with unmatched quality. We have refined the hanging drop cultivation technology to pioneer beating heart microtissues derived from pure primary rat and mouse cardiomyocyte cultures as well as mixed populations reflecting the cell type composition of rodent hearts. Phenotypic characterization combined with detailed analysis of muscle-specific cell traits, extracellular matrix components, as well as endogenous vascular endothelial growth factor (VEGF) expression profiles of heart microtissues revealed (1) a linear cell number-microtissue size correlation, (2) intermicrotissue superstructures, (3) retention of key cardiomyocyte-specific cell qualities, (4) a sophisticated extracellular matrix, and (5) a high degree of self-organization exemplified by the tendency of muscle structures to assemble at the periphery of these myocardial spheroids. Furthermore (6), myocardial spheroids support endogenous VEGF expression in a size-dependent manner that will likely promote vascularization of heart microtissues produced from defined cell mixtures as well as support connection to the host vascular system after implantation. As cardiomyocytes are known to be refractory to current transfection technologies we have designed lentivirus-based transduction strategies to lead the way for genetic engineering of myocardial microtissues in a clinical setting.