The mathematics of Arthur Cayley with particular reference to linear algebra

This thesis is principally concerned with Arthur Cayley's work on Invariant Theory, but also considers his contribution to matrix algebra and other algebraic systems, drawing on sources including unpublished letters between Cayley and his contemporary, J. J. Sylvester. The history of modern linear algebra and Cayley's part in its development has been extensively researched in the last decade by Thomas Hawkins. However, little has been written on Cayley's contribution to Invariant Theory, a subject to which he constantly reverted over a period of fifty years. In comparison, his work on Matrix Theory was a minor interest. The focal points in Cayley's passage through Invariant theory are investigated with reference being made, inter alia, to his correspondence with J. J. Sylvester which affords special insights into both the development of this Theory and the nature of their collaboration. Where appropriate, particulars of Sylvester's own work are given. Biographical details are included where these are believed to be unpublished or otherwise not generally available. A survey of Cayley's mathematical thought is offered in so far as it may be determined from his scattered remarks. Cayley pursued his algebraic researches on two distinct levels. First, he absorbed himself in calculation which led him to the combinatorial aspects of Invariant Theory and, secondly, he displayed a remarkable proclivity for systemisation, although this expressed itself in the classification of specific forms rather than in the development of an abstract theory as with the German algebraists. The basic text contains four chapters on Cayley's work in approximate chronological order followed by a final chapter on his general mathematical thinking. The Appendices include a statistical survey of his work, a bibliography of manuscripts, including, of course, his letters to Sylvester and a number of, little known photographs associated with Cayley and his times

Design dis-integration Silent, Partial, and Disparate Design

Michael Porter’s frameworks for analysing and planning competitive differentiation (Porter 1980, 1985) are established ‘textbook’ tools, widely taught to business students today. As the claim of design’s strategic importance is increasingly heard, we ask where does design fit in established strategy thinking? This paper documents a proposed conceptual model based on Porter’s value chain model for strategic planning. The concept outlined is the result of the first stage of a larger study of design’s potential role at strategic level and the difficulties faced by organisations in exploiting design strategically. This exploratory phase comprised a review of literature on design management and models of strategy, followed by nineteen interviews with senior design professionals. These then informed a novel revision of the value chain diagram reflecting the strategic role of design, and the identification of three key phenomena concerning design integration (silent design, partial design and disparate design). These phenomena are also represented in modified versions of the value chain. This overall project follows a research approach based on the design research method and on procedural action research, and aims to develop a tool or method to help organisations increase design integration. This project is ongoing, and the results will be published separately. Keywords: Strategic; value chain; silent; partial; disparate; integrated</p

A systematic review of randomized controlled trials of telehealth and digital technology use by community pharmacists to improve public health

Community pharmacists (CPs) continue to have an important role in improving public health, however, advances in telehealth and digital technology mean that the methods by which they support their customers and patients are changing. The primary aim of this study was to identify which telehealth and digital technology tools are used by CPs for public health purposes and determine if these have a positive impact on public health outcomes. A systematic review was carried out using databases including PubMed and ScienceDirect, covering a time period from April 2005 until April 2020. The search criteria were the following: randomized controlled trials, published in English, investigating the delivery of public health services by community pharmacists using a telehealth or digital tool. Thirteen studies were included out of 719 initially identified. Nine studies detailed the use of telephone prompts or calls, one study detailed the use of a mobile health application, two studies detailed the use of a remote monitoring device, and one study detailed the use of photo-aging software. Public health topics that were addressed included vaccination uptake (n = 2), smoking cessation (n = 1), hypertension management (n = 2), and medication adherence and counseling (n = 8). More studies are needed to demonstrate whether or not the use of novel technology by CPs can improve public health

Reactivity to sustainability metrics: A configurational study of motivation and capacity

Previous research on reactivity – defined as changing organisational behaviour to better conform to the criteria of measurement in response to being measured – has found significant variation in company responses towards sustainability metrics. We propose that reactivity is driven by dialogue, motivation and capacity in a configurational way. Empirically, we use fuzzy set Qualitative Comparative Analysis (fsQCA) to analyse company responses to the sustainability index FTSE4Good. We find evidence of complimentary and substitute effects between motivation and capacity. Based on these effects we develop a typology of reactivity to sustainability metrics, which also theorises the use of metrics as tools for performance feedback and the building of calculative capacity. We show that when reactivity is studied configurationally, we can identify previously underacknowledged types of responses. We discuss the theoretical and practical implications for studying and using sustainability metrics as governance tools for responsible behaviour

Methodological diversity and theoretical integration: Research in design fixation as an example of fixation in research design?

ABSTRACT: Over the last three decades, design fixation research has emerged as a distinct and productive area of design creativity research, and of design research more generally. In studying an applied aspect of human behaviour, fixation research is unusually restricted in its methodological choices, primarily adopting experimental and statistical approaches. The few relevant qualitative studies remain isolated from the core experimental literature. This limited diversity and limited integration restricts our ability to interpret the relevance of prior work, plan new studies and impact practice. By viewing research as a creative design activity, I argue that the fixation research community is well placed to study and change its own behaviour, and also to inform the behaviour of other research disciplines.This work was partly supported by the UK’s Engineering and Physical Sciences Research Council (EP/K008196/1)

Arthur Cayley as Sadleirian Professor: A Glimpse of Mathematics Teaching at 19th-Century Cambridge

AbstractThis article contains the hitherto unpublished text of Arthur Cayley's inaugural professorial lecture given at Cambridge University on 3 November 1863. Cayley chose a historical treatment to explain the prevalent basic notions of analytical geometry, concentrating his attention in the period (1638–1750). Topics Cayley discussed include the geometric interpretation of complex numbers, the theory of pole and polar, points and lines at infinity, plane curves, the projective definition of distance, and Pascal's and Maclaurin's geometrical theorems. The paper provides a commentary on this lecture with reference to Cayley's work in geometry. The ambience of Cambridge mathematics as it existed after 1863 is briefly discussed.Copyright 1999 Academic Press.Cet article contient le texte jusqu'ici inédit de la leçon inaugurale de Arthur Cayley donnée à l'Université de Cambridge le 3 novembre 1863. Cayley choisit une approche historique pour expliquer les notions fondamentales de la géométrie analytique, qui existaient alors, en concentrant son attention sur la période 1638–1750. Les sujets discutés incluent l'interpretation géométrique des nombres complexes, la théorie des pôles et des polaires, les points et les lignes à l'infini, les courbes planes, la définition projective de la distance, et les théorèmes géométriques de Pascal et de Maclaurin. L'article contient aussi un commentaire reliant cette leçon à l'oeuvre de Cayley en géométrie. L'atmosphère des mathématiques à Cambridge après 1863 est brièvement discutée.Copyright 1999 Academic Press.MSC Classification: 01A55, 01A72, 01A73