Second Order Superintegrable Systems in Three Dimensions

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, the system is second order superintegrable. Such systems have remarkable properties. Typical properties are that 1) they are integrable in multiple ways and comparison of ways of integration leads to new facts about the systems, 2) they are multiseparable, 3) the second order symmetries generate a closed quadratic algebra and in the quantum case the representation theory of the quadratic algebra yields important facts about the spectral resolution of the Schr\"odinger operator and the other symmetry operators, and 4) there are deep connections with expansion formulas relating classes of special functions and with the theory of Exact and Quasi-exactly Solvable systems. For n=2 the author, E.G. Kalnins and J. Kress, have worked out the structure of these systems and classified all of the possible spaces and potentials. Here I discuss our recent work and announce new results for the much more difficult case n=3.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Reconsidering the Value

This article is a think piece that asks educators to reexamine ideas around outcomes of visual arts programs.  The view that the value of a visual arts education consists primarily in transferrable skills, defined as those valued by business, is, the author suggests, not the appropriate metric.  Instead, a number of outcomes are presented and rationalized

The Best He Could, As Fast As He Could: The World War II Experiences of Wesley Crawley, Bryant College, ‘36

This paper focuses on the wartime experiences of Wesley Crawley, a 1936 graduate of Bryant College and one of three Crawley brothers to graduate from Bryant and serve in World War II. In addition to interviews with Crawley that took place in 2009, the paper draws from the letters that Crawley received from the Bryant Service Club as well as the letters that he and his family wrote to the Club. After graduating from U.S. Army Officer Candidate School in Ft. Monmouth, New Jersey, Crawley was sent to North Africa where, in 1943, he was briefly captured, but later released, by the Germans. He spent much of the remainder of the war in Italy, France, and eventually Germany. Following the war, Crawley returned to his home in Fall River, Massachusetts where he worked for the Fall River National Bank, retiring as Vice President in 1983

Thinking Continental: Writing the Planet One Place at a Time by Tom Lynch, Susan Naramore Maher, Drucilla Wall, and O. Alan Weltzien

Review of Thinking Continental: Writing the Planet One Place at a Time by Tom Lynch, Susan Naramore Maher, Drucilla Wall, and O. Alan Weltzien, eds

Exploring the Locus of Anthropos in Market Ecology: When the Homo Politicus Converses with the Homo Economicus

The dilemma of the anthropos confuses him as to the advantage of the market to his existence. The market anthropos is seen as homo economicus, a self-interested, utility-maximizing individual. This popular belief is critically analyzed as to its nuances insofar as the homo politicus of John Rawls is concerned. The life of the market anthropos seeks consensus towards societal cooperation and justice. Popularly held to be dissenting, this paper seeks to explore their possible convergence in the light of the nuances predicated by Adam Smith and Rawls. Ultimately, it is argued that the anthropos in either startum of politics or market is not differentiated but is one and the same, contextually apart but anthropologically integrated. The cooperative homo politicus can also be a cooperative homo econonomicus just as both can be selfishly motivated and utilitarianist