Geometric Algebras for Euclidean Geometry

The discussion of how to apply geometric algebra to euclidean $n$-space has been clouded by a number of conceptual misunderstandings which we first identify and resolve, based on a thorough review of crucial but largely forgotten themes from $19^{th}$ century mathematics. We then introduce the dual projectivized Clifford algebra $\mathbf{P}(\mathbb{R}^*_{n,0,1})$ (euclidean PGA) as the most promising homogeneous (1-up) candidate for euclidean geometry. We compare euclidean PGA and the popular 2-up model CGA (conformal geometric algebra), restricting attention to flat geometric primitives, and show that on this domain they exhibit the same formal feature set. We thereby establish that euclidean PGA is the smallest structure-preserving euclidean GA. We compare the two algebras in more detail, with respect to a number of practical criteria, including implementation of kinematics and rigid body mechanics. We then extend the comparison to include euclidean sphere primitives. We conclude that euclidean PGA provides a natural transition, both scientifically and pedagogically, between vector space models and the more complex and powerful CGA.Comment: 25 pages, 4 figures in Advances in Applied Clifford Algebras, pages 1--24, 2016, online at link.springer.co

The Principles of Exchange Rate Determination in an International Finance Experiment

This paper reports the first experiments designed to explore the behavior of economies with prominent features of international finance. Two “countries,” each with its own currency, were created. International trade could take place only through the operation of markets for currency. The law of one price and the flow of funds theory of exchange rate determination were used to produce general equilibrium models that captured much of the behavior of the economies. Prices of goods, as well as the exchange rate, evolve over time toward the predictions of the models. However, both the law of one price and purchasing power parity can be rejected for reasons that do not appear in the literature. Patterns of international trade were as predicted by the law of comparative advantage

On helicity fluctuations and the energy cascade in turbulence

Recent conjectures concerning the correlation between regions of high local helicity and low dissipation are examined from a rigorous theoretical standpoint based on the Navier-Stokes equations. It is proven that only the solenoidal part of the Lamb vector omega x u (which is directly tied to the nonlocal convection and stretching of vortex lines) contributes to the energy cascade in turbulence. Consequently, it is shown that regions of low dissipation can be associated with either low or high helicity, a result which disproves earlier speculations concerning this direct connection between helicity and the energy cascade. Some brief examples are given along with a discussion of the consistency of these results with the most recent computations of helicity fluctuations in incompressible turbulent flows

Discussion of turbulence modelling: Past and future

The full text of a paper presented at the Whither Turbulence Workshop (Cornell University, March 22-24, 1989) on past and future trends in turbulence modeling is provided. It is argued that Reynolds stress models are likely to remain the preferred approach for technological applications for at least the next few decades. In general agreement with the Launder position paper, it is further argued that among the variety of Reynolds stress models in use, second-order closures constitute by far the most promising approach. However, some needed improvements in the specification of the turbulent length scale are emphasized. The central points of the paper are illustrated by examples from homogeneous turbulence

Coordinating Loan Repayment Assistance Programs with New Federal Legislation

For decades, law school administrators, faculty members, students and graduates have worried about the problem of the ever-increasing cost of attendance at the nation’s law schools, and the rapidly rising average debt of graduating law students. The problem was particularly acute for students who desired careers in public service, because starting salaries in the government and non-profit sectors failed to keep pace with the increase in educational debt of law school graduates. In response, many law schools created loan repayment assistance programs (LRAPs), through which they subsidized loan repayment for some or all of their graduates who undertook public service jobs or careers. Most of these programs are insufficiently funded to meet the needs of their graduates who desire to use them, and demand for financial assistance for lower-income graduates has particularly accelerated as the recession that began in 2008 caused private sector firms to reduce their hiring, prompting more student interest in public sector employment. In addition, many law schools had no LRAP programs at all. Fortunately, Congress has significantly alleviated this problem, passing four laws between 2005 and 2010 that collectively reduce the debt repayment burdens on graduates, particularly (though not exclusively) those in public service. The new legislation also makes it possible for law schools to create or restructure LRAP programs in a way that provides a great deal of debt relief to graduates in public service at the lowest possible cost to the law school. As of this writing (in the summer of 2010), at least seven law schools—the University of California at Berkeley, Georgetown, UCLA, Duke, Northwestern, Virginia, and Suffolk—have altered their LRAP programs to take maximum advantage of the federal legislation, and several others are currently considering modifications. This article, together with an associated web-based calculator, provides guidance for law school administrators and faculty members who desire to coordinate law school LRAP benefits with those provided by federal law, and for law students and alumni who might want to suggest LRAP improvements to their schools

Mapping and Distribution of Torpedograss and Evaluating the Effectiveness of Torpedograss Management Activities in Lake Okeechobee, Florida

Thousands of hectares of native plants and shallow open water habitat have been displaced in Lake Okeechobee’s marsh by the invasive exotic species torpedograss ( Panicum repens L.). The rate of torpedograss expansion, it’s areal distribution and the efficacy of herbicide treatments used to control torpedograss in the lake’s marsh were quantified using aerial color infra red (IR) photography.(PDF has 6 pages.

Chapter 16 - Federations of Labor, pp. 360-388

The Catherwood Library and ILR School at Cornell are pleased to again make available an extremely important index of major labor union publications, long out of print. It is Lloyd G. Reynolds and Charles C. Killingsworth\u27s Trade Union Publications: The Official Journals, Convention Proceedings and Constitutions of International Unions and Federations, 1850-1941. Baltimore, The John Hopkins Press, 1944

Subject Index (International Labor Organization - Massachusetts Labor Relations Board), pp. 392-486

The Catherwood Library and ILR School at Cornell are pleased to again make available an extremely important index of major labor union publications, long out of print. It is Lloyd G. Reynolds and Charles C. Killingsworth\u27s Trade Union Publications: The Official Journals, Convention Proceedings and Constitutions of International Unions and Federations, 1850-1941. Baltimore, The John Hopkins Press, 1944

Index of Unions in Volume I, pp. 389-405

The Catherwood Library and ILR School at Cornell are pleased to again make available an extremely important index of major labor union publications, long out of print. It is Lloyd G. Reynolds and Charles C. Killingsworth\u27s Trade Union Publications: The Official Journals, Convention Proceedings and Constitutions of International Unions and Federations, 1850-1941. Baltimore, The John Hopkins Press, 1944