A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

An Integrated Architecture for Corrosion Monitoring and Testing, Data mining, Modeling and Diagnostics/Prognostics

It has been established that corrosion is one of the most important factors causing deterioration and decreased performance and reliability in critical aerospace and industrial systems. Corrosion monitoring, detection, and quantification are recognized as key enabling technologies to reduce the impact of corrosion on the integrity of aircraft and industrial assets. Accurate and reliable detection of corrosion initiation and propagation, with specified false alarm rates, requires novel tools and methods, including verifiable simulation and modeling methods. This paper reports an experimental investigation of the detection and quantification of pitting corrosion on aluminum alloy panels using 3D surface metrology methods and image processing techniques. Panel surfaces were evaluated by laser microscopy and stylus-based profilometry to characterize global and local surface features. Promising imaging and texture features were extracted and compared between coated and uncoated aluminum panels at different exposure times under accelerated corrosion conditions. Image processing, information processing, and data mining techniques were utilized to evaluate the presence and extent of pitting corrosion. A new modeling framework for corrosion stages is introduced that emphasizes the representation of pitting corrosion and ultimately the crack formation process. Detection and prediction of the evolution of corrosion stages relies on data, a particle filtering method, and the corrosion propagation model. Results from these experimental studies demonstrate the efficacy of this proposed methodology

Anthropology and GIS: Temporal and Spatial Distribution of the Philippine Negrito Groups

The Philippine negrito groups comprise a diverse group of populations speaking over 30 different languages, who are spread all over the archipelago, mostly in marginal areas of Luzon Island in the north, the central Visayas islands, and Mindanao in the south. They exhibit physical characteristics that are different from more than 100 Philippine ethnolinguistic groups that are categorized as non-negritos. Given their numbers, it is not surprising that Philippine negritos make up a major category in a number of general ethnographic maps produced since the nineteenth century. Reports from various ethnological surveys during this period, however, have further enriched our understanding regarding the extent and distribution of negrito populations. Using the data contained in these reports, it is possible to plot and create a map showing the historical locations and distribution of negrito groups. Using geographic information systems (GIS), the location and distribution of negrito groups at any given time can be overlaid on historical or current maps. In the present study, a GIS layer was compiled and extracted from the 2000 Philippine Census of population at the village level and overlaid on existing maps of the Philippines. The maps that were generated from this project will complement ongoing anthropological and genetic studies of negrito groups that inhabit different locations within the Philippine archipelago

Land Law, Property Ideologies and the British-Irish relationship

English and Irish land law are deeply influenced by the historical context of the British-Irish relationship, yet property scholarship comparing the two jurisdictions is surprisingly rare. The current Brexit negotiations provide a timely reminder of the strategic importance of property and trade relations between the two countries; and of their related-but-different legal cultures. In this article we examine how the property cultures of England and Ireland were shaped by the politics and practices of land tenure, by competing economic and property ideologies, and by the influence of both on national identity and statehood in both jurisdictions. The article reveals the role of local contexts and events in shaping land reform, and demonstrates the fertile potential of the comparative frame to contextualise each jurisdiction’s doctrines and practices. As domestic land law systems are drawn together in the context of emerging EU jurisdiction over areas like mortgage credit, each jurisdiction’s underpinning ideological commitments have important implications for the ease – or not – of attempts to harmonize member state practices. We explain the alignments and divergences between domestic underpinnings of Irish and English law, and reflect on the implications of our findings for contemporary property problems in the context of evolving economic and political relationships between the UK and Ireland

Risk Factors for Urosepsis in Older Adults

Objective: To identify factors that predispose older adults to urosepsis and urosepsis-related mortality. Method: A systematic search using PubMed and CINAHL databases. Articles that met inclusion criteria were assessed using the Strengthening the Reporting of OBservational studies in Epidemiology (STROBE) criteria and were scored on a 4-point Likert-type scale. Results: A total of 180 articles were identified, and six met inclusion criteria. The presence of an internal urinary catheter was associated with the development of urosepsis and septic shock. Although a number of factors were examined, functional dependency, number of comorbidities, and low serum albumin were associated with mortality across multiple studies included in this review. Discussion: Little scientific evidence is available on urosepsis, its associated risk factors, and those factors associated with urosepsis-related mortality in older adults. More research is warranted to better understand urosepsis in this vulnerable population in an effort to improve the quality of patient care

Hypergeometric analogues of the arithmetic-goemetirc mean iteration

The arithmetic-geometric mean iteration of Gauss and Legendre is the two-term iteration a_n+1=(a_n+b_n)/2 and b_n+1 = [formula could not be replicated] with a_o:=1 and b_o:=x. The common limit is ₂F₁(½,½;1;1−x²)^-1 and the convergence is quadratic. This is a rare object with very few close relatives. There are however three other hypergeometric functions for which we expect similar iterations to exist, namely:₂F₁(½−s₁,½ + s; 1;·) with s=1/3, 1/4, 1/6. Our intention is to exhibit explicitly these iterations and some of their generalizations. These iterations exist because of underlying quadratic or cubic transformations of certain hypergeometric functions, and thus the problem may be approached via searching for invariances of the corresponding second-order differential equations. It may also be approached by searching for various quadratic and cubic modular equations for the modular forms that arise on inverting the ratios of the solutions of these differential equations. In either case, the problem is intrinsically computational. Indeed, the discovery of the identities and their proofs can be effected almost entirely computationally with the aid of a symbolic manipulation package, and we intend to emphasize this computational approach