Wednesday, December 1, 2010 - 11:00am - 11:45am
David Keyes (King Abdullah University of Science & Technology)
Eulerian formulations of problems with interfaces avoid the subtleties
of tracking and remeshing, but do they complicate solution of the
discrete equations, relative to domain decomposition methods that
respect the interface? We consider two different interface problems –
one involving cracking and one involving phase separation. Crack
problems can be formulated by extended finite element methods (XFEM),
in which discontinuous fields are represented via special degrees of
Monday, November 10, 2014 - 3:30pm - 3:55pm
Mirkó Visontai (Google Inc.)
In joint work with Carla Savage, we studied the inversion sequence representation of Eulerian polynomials and their generalizations. This led us to new recurrences for the generalized Eulerian polynomials and their refinements.

These recurrences, combined with a relaxed notion of interlacing polynomials, called compatible polynomials, can be used to prove that all zeros of the generalized Eulerian polynomials are real. A slight modification of this method settles a conjecture of Brenti from 1994 in the affirmative.
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