Defect correction from a galerkin viewpoint

We consider the numerical solution of systems of nonlinear two point boundary value problems by Galerkin's method. An initial solution is computed with piecewise linear approximating functions and this is then improved by using higher—order piecewise polynomials to compute defect corrections. This technique, including numerical integration, is justified by typical Galerkin arguments and properties of piecewise polynomials rather than the traditional asymptotic error expansions of finite difference methods

Some Comments on Branes, G-flux, and K-theory

This is a summary of a talk at Strings2000 explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.Comment: 10pp., late

The Psychagogic Work of Examples in Plato's Statesman

This paper concerns the role of examples (paradeigmata) as propaedeutic to philosophical inquiry, in light of the methodological digression of Plato’s Statesman. Consistent with scholarship on Aristotle’s view of example, scholars of Plato’s work have privileged the logic of example over their rhetorical appeal to the soul of the learner. Following a small but significant trend in recent rhetorical scholarship that emphasizes the affective nature of examples, this essay assesses the psychagogic potential of paradeigmata, following the discussion of example in Plato’s Statesman. I argue that, by creating an expectation for finding similarities, the use of examples in philosophical pedagogy cultivates in the soul of the learner a desire to discern the intelligible principles the ground experiential knowledge. Thus, examples not only serve as practice at the dialectician’s method of abstraction, but also cultivate a dialectical ethos, characterized by the desire to know the logoi of all things

Side-looking radar in urban research - A case study

Capabilities of side-looking radar in urban researc

A prediction of 3-D viscous flow and performance of the NASA low-speed centrifugal compressor

A prediction of the 3-D turbulent flow in the NASA Low-Speed Centrifugal Compressor Impeller has been made. The calculation was made for the compressor design conditions with the specified uniform tip clearance gap. The predicted performance is significantly worse than that predicted in the NASA design study. This is explained by the high tip leakage flow in the present calculation and by the different model adopted for tip leakage flow mixing. The calculation gives an accumulation for high losses in the shroud/pressure-side quadrant near the exit of the impeller. It also predicts a region of meridional backflow near the shroud wall. Both of these flow features should be extensive enough in the NASA impeller to allow detailed flow measurements, leading to improved flow modelling. Recommendations are made for future flow studies in the NASA impeller

The Campaign to Arrest Ed Shann’s Influence in Western Australia

Shann towered over the discipline of economics in the state of Western Australia in the first third of the twentieth century. He was the foundation professor in history and economics from 1913 to 1931 and inaugural professor of economics from 1931 to 1934 at the University of Western Australia (UWA); he set the curriculum for the subjects that constituted the economics major that was offered at UWA over this period and ensured that it had a market-driven, policy-oriented and historical flavour; he trained a generation of bright young men and women—such as John La Nauze, Nugget Coombs, Merab Harris, Paul Hasluck, Arthur Tange and Alexander Reid—who drew upon his teachings (even when they disagreed with certain elements of it) to guide their actions as servants of the public; he exploited his contacts in the commercial and professional world of Perth to draw men of intellect, but not formal economic training, into the newly established local branch of the Economic Society of Australia and New Zealand in 1925; he established close contacts with local men of finance, including Alfred Davidson of the Bank of New South Wales, in a way that eventually allowed him (and his students!) to provide policy advice at a national level; and he used his power as an administrator, at one time acting as the Vice Chancellor of the university, to establish a faculty of law and a diploma in journalism, both of which thereafter had close associations with the economics discipline at UWA. Shann, in short, created the discipline of economics in Western Australia in his own image. Unfortunately, however, a number of powerful identities in Perth resented the free-market commentaries that Shann dispensed in the public domain and before his students, and hence orchestrated a public campaign to arrest his influence. In this paper I provide an account of Shann’s influence in Western Australia from 1913 to 1934 and trace the campaign waged against him (and economics) which eventually induced him to leave this state

Balanced Topological Field Theories

We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of ``iterated superspaces'' that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space.Comment: 40 pages, harvmac, references added, to appear in Commun. Math. Phy