31 research outputs found
Genus Topology of the Cosmic Microwave Background from WMAP
We have independently measured the genus topology of the temperature
fluctuations in the cosmic microwave background seen by the Wilkinson Microwave
Anisotropy Probe (WMAP). A genus analysis of the WMAP data indicates
consistency with Gaussian random-phase initial conditions, as predicted by
standard inflation.Comment: PDF: http://www.astro.virginia.edu/~wnc5c/WMAPtopology.pd
A conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of
Sturm-Liouville problems and generalize in this sense the classical families of
Hermite, Laguerre and Jacobi. They also generalize the family of CPRS
orthogonal polynomials. We formulate the following conjecture: every
exceptional orthogonal polynomial system is related to a classical system by a
Darboux-Crum transformation. We give a proof of this conjecture for codimension
2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this
analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The
classification includes all cases known to date plus some new examples of
X2-Laguerre and X2-Jacobi polynomials
Mouse Chromosome 11
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46996/1/335_2004_Article_BF00648429.pd