An introduction to HKR character theory

The generalized character theory of Hopkins, Kuhn, and Ravenel is an important tool in the study of Morava E-theory and higher height phenomena in chromatic homotopy theory. In this paper, we provide an introduction to HKR character theory with many examples, applications, and alternative points of view.Comment: 23 page

PaL Diagrams: A Linear Diagram-Based Visual Language

Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based reasoning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowledge gap, we present and formalise Point and Line (PaL) diagrams, an extension of simple linear diagrams containing points, thus providing a formal foundation for an effective visual language.We prove that PaL diagrams are exactly as expressive as monadic first-order logic with equality, gaining, as a corollary, an equivalence with the Euler diagram extension called spider diagrams. The method of proof provides translations between PaL diagrams and sentences of monadic first-order logic

Gentle Guardian of the Mentally Ill: The Story of One Missourian

In July of this year Dr. Emmett F. Hoctor, superintendent of Farmington State Hospital in Missouri, retired from this post after 38 years of dedicated tabors. Mr. Jack Stapleton, Jr., reporting for The Farmington Press, contributed the following interesting tribute to this devoted Catholic physician whose years of zealous care of the mentally ill at the Farmington institution are a source of edification to all who know him. The article is reprinted with the kind permission of the editor of The Farmington Press

Do academics doubt their own research?

When do experts doubt or question their own previously published research and why? An online survey was designed and distributed across academic staff and postgraduate research students at different universities in Great Britain. Respondents (n = 202 - 244) identified the likelihoods of six different (quasi) hypothetical occurrences causing them to doubt or question work they have published in peer reviewed journals. They are: two objective and two semi-objective citation based metrics, plus two semi-objective metrics based on verbalised reactions. Only limited support is found from this study to suggest that the authors of primary research would agree with any judgements made by others about their research based on these metrics. The occurrence most likely to cause respondents to doubt or question their previously published research was where the majority of citing studies suggested mistakes in their work. In a multivariate context, only age and nationality are significant determinants of doubt beyond average likelihoods. Understanding and acknowledging what makes authors of primary research doubt their own research could increase the validity of those who pass judgement

Investigating the Effects of Flue Gas Injection, Hot Water Distribution, and Fill Distribution on Natural Draft Wet Cooling Tower Performance

Natural draft wet cooling towers (NDWCT) are a common method of heat removal in powerplants. This study employs a numerical cooling tower model developed by Eldredge, Benton & Hodgson (1997) to examine whether utilizing nonuniform water, fill profiles, and flue gas injection can improve NDWCT efficiency. The results show that each of these variables can be optimized to lower outlet water temperature. Within the range tested for each parameter, the water profile had the most significant effect on outlet water temperature, followed by the flue gas temperature and then the fill profile. The optimum parameter combination reduced the predicted outlet water temperature by 0.5 °C which corresponds to annual fuel savings of up to 55 million dollars and 1.83 million metric tons of carbon dioxide for fossil plants in the United States