A Factorial Power Variation of Fermat\u27s Equation

We consider a variant of Fermat\u27s well-known equation xn+yn=zn. T his variant replaces the usual powers with the factorial powers defined by xn=x(x-1)...(x-(n-1)). For n=2 we characterize all possible integer solutions of the equation. For n=3 we show that there exist infinitely many non-trivial solutions to the equation. Finally we show there exists no maximum n for which xn+yn = zn has a non-trivial solution

The Evolution of AM CVn Binary Systems

AMCVn-type binary systems are a class of ultracompact, accreting binary system. Each system consists of a white dwarf accreting helium-dominated material from a compact donor star, which may be degenerate or semi-degenerate. Due to the position of these binary systems within late binary evolution, they provide an opportunity to constrain poorly understood aspects of binary evolution such as common envelope evolution and the merger rate of double white dwarf binaries (the favoured progenitors of type Ia supernovae). Despite the growing number of known AMCVn systems, details of the prior evolution of these systems remain poorly constrained, with several competing models. The objective of this thesis is to use observations of AMCVn binaries to explore their prior evolution. I present an in-depth study of Gaia14aae, the only known fully-eclipsing AMCVn system. High-speed photometry allows me to model the system and deduce its component stellar masses and radii. Phase-resolved spectroscopy provides an independent test of the photometric results, and allows me to probe the origin of the line emission seen in many AMCVn systems. The properties of Gaia14aae make it clear that the donor is not degenerate, and suggest an unusual evolutionary origin in which the system is descended from a short-period cataclysmic variable. I present the discovery of SDSS J1351-0643, a 16 minute orbital period binary which was observed by the K2 project. Several periods with physical origins are identified, allowing me to estimate the mass ratio of the component stars. From the literature, I compile all known mass ratio measurements and compare these with evolutionary models. The results suggest that AMCVn donor stars across the population are more inflated than has been previously expected, and that few, if any, donor stars are fully degenerate. Acknowledging the need for a greater number of well-characterised systems in order to fully explore this suggestion, I present spectroscopy of five AMCVn binaries and short-period cataclysmic variables. Four of these systems show potential to be well characterised with further observations. The results in this thesis, in line with other recent results, suggest that the importance of the helium star donor channel and the evolved CV channel of AMCVn formation have historically been underestimated. The importance of the white dwarf donor channel has either been overestimated, or mechanisms that heat and inflate the donor have been overlooked. Future studies to find and characterise new AMCVn binaries will help to further explore these questions

The Politicization of Judicial Elections and its Effect on Judicial Independence

This article presents the proceedings of the Cleveland-Marshall College of Law Symposium, The Politicization of Judicial Elections and Its Effect on Judicial Independence and LGBT Rights, held October 21, 2011. The idea for the conference stemmed from the November 2010 Iowa judicial election, in which three justices were voted out of office as a result of joining a unanimous ruling, Varnum v. Brien, that struck down, on equal protection grounds, a state statute limiting marriage rights to heterosexual couples. The conference addresses whether the backlash that occurred in Iowa after the Varnum decision might undermine judicial independence in jurisdictions where judges are elected. Daniel Takoji, professor of law at the Ohio State University\u27s Moritz College of Law, discusses, the role of money in judicial elections and more broadly its effect on judicial independence. Cleveland-Marshall College of Law Professor Susan Becker provides an overview of the struggle for LGBT rights, and discusses various factors that likely have influenced and will continue to influence judicial independence when addressing LGBT rights. Camilla Taylor, of Lambda Legal, who successfully litigated the Varnum decision through the Iowa courts, discusses her efforts in Iowa prior to litigating the Varnum case and whether the backlash that occurred after Varnum might affect Lambda\u27s efforts to challenge laws affecting LGBT rights in other states where judges are elected. The Hon. Marsha K. Temus recounts her experience and offers her unique perspective on whether politicized judicial elections might undermine judicial independence

Diffusion in congress: measuring the social dynamics of legislative behavior

While there is a substantial literature highlighting the presence of social dynamics in legislatures, we know very little about the precise processes that generate these social dynamics. Yet, whether social dynamics are due to peer pressure, frequency of interaction, or genuine learning, for example, has important implications for questions of political representation and accountability. We demonstrate how a recent innovation can be used to study the diffusion of behavior within legislatures. In particular, we study diffusion within the U.S. House of Representatives by looking at the dynamic process underlying discharge petitions. The discharge procedure shares many characteristics with other forms of legislative behavior, yet it has one important advantage when it comes to studying social dynamics: we can observe when members decide to sign petitions. Based on data from 1995 to 2014, we find that the social dynamics underlying the discharge procedure tend to involve the rational evaluation of information conveyed by the behavior of previous petition signatories

Polysemy in the mental lexicon : Relatedness and frequency affect representational overlap.

Funding The reported research and the writing of this paper were sup-ported by a grant awarded by the Graduate School in the College of Life Sciences and Medicine in Aberdeen.Peer reviewedPostprin

Disease monitoring and biosecurity

Understanding and detecting diseases of amphibians has become vitally important in conservation and ecological studies in the twenty-fi rst century. Disease is defi ned as the deviance from normal conditions in an organism. The etiologies (causes) of disease include infectious, toxic, traumatic, metabolic, and neoplastic agents. Thus, monitoring disease in nature can be complex. For amphibians, infectious, parasitic, and toxic etiologies have gained the most notoriety. Amphibian diseases have been linked to declining amphibian populations, are a constant threat to endangered species, and are frequently a hazard in captive breeding programs, translocations, and repatriations. For example, a group of viruses belonging to the genus Ranavirus and the fungus Batrachochytrium dendrobatidis are amphibian pathogens that are globally distributed and responsible for catastrophic population die-offs, with B. dendrobatidis causing known species extinctions (Daszak et al. 1999; Lips et al. 2006; Skerratt et al. 2007). Some infectious diseases of amphibians share similar pathological changes; thus, their detection, recognition, and correct diagnosis can be a challenge even by trained veterinary pathologists or experienced herpetologists. This chapter will introduce readers to the most common amphibian diseases with an emphasis on those that are potentially or frequently lethal, and the techniques involved in disease monitoring. It will also outline methods of biosecurity to reduce the transmission of disease agents by humans. We start by covering infectious, parasitic, and toxic diseases. Next, surveillance methods are discussed, including methods for sample collection and techniques used in disease diagnosis. Finally, biosecurity issues for preventing disease transmission will be covered, and we provide protocols for disinfecting fi eld equipment and footwear

Thrombotic and Thromboembolic Complications in Patients with Adult Congenital Heart Disease

Improved medical and surgical interventions have increased the longevity of patients with congenital heart defects and most such patients live into adulthood. Thrombotic and thromboembolic complications constitute a major cause of mortality and morbidity in patients with adult congenital heart disease (ACHD). Such events include acute coronary syndromes, ischemic stroke (cardioembolic due to thrombus formation in the systemic ventricle, secondary to atrial arrhythmias, or due to paradoxical embolism), and venous thromboembolism. Some thrombotic phenomena are also specific to patients with ACHD, such as those related to Fontan circulation. We provide a succinct overview of thrombotic and thromboembolic complications in patients with ACHD, focusing on stroke and venous thromboembolic events

Analysis of EZproxy server logs to visualise research activity in Curtin’s online library

© 2019, Emerald Publishing Limited. Purpose: The purpose of this paper is to develop data visualisation proof of concept prototypes that will enable the Curtin University Library team to explore its users’ information-seeking behaviour and collection use online by analysing the library’s EZproxy logs. Design/methodology/approach: Curtin Library’s EZproxy log file data from 2013 to 2017 is used to develop the data visualisation prototypes using Unity3D software. Findings: Two visualisation prototypes from the EZproxy data set are developed. The first, “Global Visualisation of Curtin Research Activity”, uses a geographical map of the world as a platform to show where each research request comes from, the time each is made and the file size of the request. The second prototype, “Database Usage Visualisation”, shows the use of the library’s various subscription databases by staff and students daily, over a month in April 2017. Research limitations/implications: The paper has following limitations: working to a tight timeline of ten weeks; time taken to cleanse noise data; and requirements for storing and hosting the voluminous data sets. Practical implications: The prototypes provide visual evidence of the use of Curtin Library’s digital resources at any time and from anywhere by its users, demonstrating the demand for the library’s online service offerings. These prototype evidence-based data visualisations empower the library to communicate in a compelling and interesting way how its services and subscriptions support Curtin University’s missions. Originality/value: The paper provides innovative approaches to create immersive 3D data visualisation prototypes to make sense of complex EZproxy data sets

Relationship of VO2 Peak, Body Fat Percentage, and Power Output Measured During Repeated Bouts of a Wingate Protocol

The principle of specificity would indicate that being aerobically trained would not necessarily enhance performance in events relying principally on oxygen-independent metabolic pathways (i.e. “anaerobic” exercise). Body fatness may be associated with aerobic and anaerobic performance. VO2 Peak was determined with a graded cycle ergometry and, in a separate session 4 consecutive Wingate power tests (3 min recovery) in 31 males. Pearson correlations were calculated for VO2 Peak and Body Fat Percentage with Peak Power, Mean Power, Minimum Power, Fatigue Index, Peak Heart Rate, and Recovery Heart Rate. No significant correlations were found for VO2 Peak or Body Fat Percentage with Peak Power on any bout (p\u3e0.05). Significant correlations were found for VO2 Peak and Body Fat Percentage with Mean Power, Minimum Power, and Fatigue Index. Significant correlations were found for VO2 Peak with delta values of power performance and heart rates (peak and 3 min recovery). Results indicate that VO2 Peak is associated with repeated anaerobic performance, possibly due to greater capacity to recover between bouts. Body Fat Percentage was correlated with measures of power performance (strongest relationships existing in the earlier bouts), but is not strongly correlated with either the heart rate response to power performance or the change in performance over successive bouts