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Theory, but also considers his contribution to matrix algebra and other algebraic systems, drawing on sources including unpublished letters between Cayley and his contemporary, J. J. Sylvester.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 Biographical details are included where these are believed to be unpublished or otherwise not generally available.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

Regional index of sustainable economic well-being development project: final report

This report presents results from a development project carried out by nef (the new economics foundation) on behalf of emda (the East Midlands Development Agency) and Natural England, to improve the methodologies used in the calculation of the R-ISEW (Regional Index of Sustainable Economic Well-Being)

A Configurational Theory of Generalized Exchange in Stakeholder-Oriented Firms

Recent developments in stakeholder theory have refined our understanding of value creation via bilateral reciprocity. Generalized exchange is another important microfoundational mechanism in value creation, but because of the potential for free-riding it is surprising that some stakeholders contribute more resources to a firm’s value-creating nexus than would be expected based on contractual obligations, and even beyond what bilateral reciprocity would predict. This paper aims to identify the minimum conditions that promote generalized exchange in a firm’s value-creating nexus. Because generalized exchange is causally complex—it can occur in multiple contexts and through various combinations of explanatory factors—a configurational theorizing approach is applied. We identify four combinations of attributes that consistently promote generalized exchange and limit free-riding behavior, such that generalized exchange can make a net positive difference in a firm’s nexus: the entrepreneurial logic (high rewards, strong institutional drivers), the conformity logic (powerful sanctions, strong institutional drivers), the influencer logic (powerful sanctions, individual or firm drivers), and the identification logic (high rewards, individual or firm drivers). This work provides an important additional explanation for why stakeholder-oriented firms tend to have higher performance, and can also help managers devise policies for increasing the amount of generalized exchange exhibited among their firm’s stakeholders

Hip Fractures in Long-Term Care: Is the Excess Explained by the Age and Gender Distribution of the Residents?

Introduction. This study compares hip fracture rates in Long Term Care (LTC) residents with those in the community to determine if their high rate of fracturing reflects the extreme age and predominantly female nature of that population. Methods. Hospital discharge data in London Ontario (population 350,000) and Statistics Canada data were used to correct the hip fracture rate in the LTC setting for age and gender. Results. The risk of hip fracture is 1.8 times greater in LTC than in the community for people of similar age and gender. The rate in women is 1.5 times higher whereas in men it is 4.3 times higher. In the oldest residents, the risk in men exceeds that of women in LTC. Conclusion. The high hip fracture rate in LTC is not just a reflection of the age and predominantly female nature of this population. The oldest men in LTC are a particularly high risk group, deserving more attention

Corporate social counterpositioning: How attributes of social issues influence competitive response

Research Summary Whilst existing research generally assumes corporate social responsibility (CSR) is seen as universally positive, firms increasingly adopt practices, and take stands, on highly polarizing social issues (e.g., gun-control, LGBTQ rights, abortion). To better understand this phenomenon, we develop a theory about when firms will emulate, ignore, or oppose each other's CSR efforts, based on attributes of the underlying social issue (its salience and polarization), the level of market competition, and the substantiveness of CSR. Our theory predicts several distinct equilibrium outcomes, including the potential for social counter-positioning, whereby rival firms take advantage of socio-political polarization to horizontally differentiate by taking opposing stances on a polarizing issue. Counterpositioning is more likely when salience is high, but agreement is low, when markets are competitive, and when CSR is largely symbolic. Managerial Summary Firms increasingly find themselves drawn, willingly or not, to taking stances on a controversial social issue (e.g., gun rights, abortion), though doing so risks alienating (some) stakeholders. In this paper, we develop a theory of why, when, and how firms should take a stance on a polarizing issue. We argue that firms profit from doing so when (1) the issue is salient, (2) markets are competitive, and (3) the actions are mostly symbolic. We also show that taking a stance on polarizing issues creates opportunities for the firms' competitors to counter their ideological positioning, strengthening weaker rivals in the process. Thus, in competitive markets, taking clear stances on polarizing, salient issues can segment the market, increasing the profits of all firms, and, potentially, intensifying polarization

Hip Fracture Types in Men and Women Change Differently with Age

BACKGROUND: Hip fractures are expensive and a frequent cause of morbidity and mortality in the elderly. In most studies hip fractures have been viewed as a unitary fracture but recently the two main types of fracture (intertrochanteric and subcapital) have been viewed as two fractures with a different etiology and requiring a different approach to prevention. The relative proportion of intertrochanteric fractures increases with age in women. In previous studies no particular pattern in men has been noted. In this study, we explored changes in the relative proportion of the two fracture types with age in the two genders. METHODS: Patients of 50 years and older, with a diagnosis of hip fracture, discharged from two local acute care hospitals over a 5 year period (n = 2150) were analyzed as a function of age and gender to explore the relative proportions of intertrochanteric and subcapital fractures, and the change in relative proportion in the two genders with age. RESULTS: Overall, for the genders combined, the proportion of intertrochanteric fractures increases with age (p = .007). In women this increase is significant (p \u3c .001), but in men the opposite pattern is observed, with the proportion of intertrochanteric fractures falling significantly with age (p = .025). CONCLUSIONS: The pattern of hip fractures is different in men and women with aging. It is likely that the pattern difference reflects differences in type and rate of bone loss in the genders, but it is conjectured that the changing rate and pattern of falling with increasing age may also be important. The two main hip fracture types should be considered distinct and different and be studied separately in studies of cause and prevention