Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

Domains of holomorphy for irreducible unitary representations of simple Lie groups

We classify the domains of holomorphy of all Harish-Chandra modules of irreducible unitary representations of simple non-compact Lie groups.Comment: revised version, to appear in Invent. math., 14 page

Control of clover infertility in sheep

A summary of practices recommended for the control of infertility caused by subterranean clover in West Australian sheep. PROLONGED grazing of green subterranean clover pastures often reduces ewe fertility. In more extreme cases, obvious signs of clover disease occur

Group Invariant Solutions Without Transversality

We present a generalization of Lie\u27s method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and independent variables. The theoretical basis for our method is provided by a general existence theorem for the invariant sections, both local and global, of a bundle on which a finite dimensional Lie group acts. A simple and natural extension of our characterization of invariant sections leads to an intrinsic characterization of the reduced equations for the group invariant solutions for a system of differential equations. The characterization of both the invariant sections and the reduced equations are summarized schematically by the kinematic and dynamic reduction diagrams and are illustrated by a number of examples from fluid mechanics, harmonic maps, and general relativity. This work also provides the theoretical foundations for a further detailed study of the reduced equations for group invariant solutions

Towards predicting biomechanical consequences of jaw reconstruction

Abstract — We are developing dynamic computer models of surgical jaw reconstructions in order to determine the effect of altered musculoskeletal structure on the biomechanics of mastication. We aim to predict post-reconstruction deficits in jaw motion and force production. To support these research goals we have extended our biomechanics simulation toolkit, ArtiSynth [1], with new methods relevant to surgical planning. The principle features of ArtiSynth include simulation of constrained rigid-bodies, volume-preserving finite-element methods for deformable bodies, contact between bodies, and muscle models. We are adding model editing capabilities and muscle activation optimization to facilitate progress on postsurgical simulation. Our software and research directions are focused on upper-airway and cranio-facial anatomy, however the toolset and methodology are applicable to other musculoskeletal systems. I

Emotive Captioning and Access to Television

Closed captioning has been enabling access to television for people who are deaf and hard of hearing since the early 1970s. Since that time, technology and people’s demands have been steadily improving and increasing. Closed captioning has not kept up with these changes. We present the results of a study that used graphics, colour, icons and animation as well as text, emotive captions, to capture more of the sound information contained in television content. deaf and hard of hearing participants compared emotive and conventional captions for two short video segments. The results showed that there was a significant difference between deaf and hard of hearing viewers in their reaction to the emotive captions. Hard of hearing viewers seemed to enjoy them and find them interesting. deaf viewers had a strong dislike for them although they did see some potential for intermittent use of emotive captions or for use with children’s programs