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1. with M. Jarden, σ-fields, PJM 185 (1998) 307–313. H(ilbert)'s I(rreducibility) T(heorem) is a diophantine limitation statement that applies to any number field. A field K satisfies HIT if for any finite collection of nonconstant maps (of degree at least 2) from algebraic curves, there are values of K not in the image of any K points from any of the curves. The paper's main examples are g-Hilbertian fields: Fields K that are not the union of images on K points on finitely many degree at least 2 maps on curves of genus at most g, yet there are g' > g for which this statement fails. Pending as of October 16, 2007. sigmahilb.html %-%-% sigmahilb.pdf

2. with S. R. Valluri (West. Ont. Univ.), Chebychev Derived Spindown Parameters for Gravitational Wave Signals from Pulsars, to appear Canadian J. Physics. As of 10/10/07, noone has yet detected gravity waves, though General Relativity has predicted them for 80 years. Their most likely identifiable source is spinning neutron stars – weighty, yet tinier than the earth, stellar objects – by integrating space-perturbating data over long periods (several months at least). Such integration must cancel inter-solar-system data, and account for the neutron spin slowing with time. Neutron stars are a final stage for solar masses between standard red-giants and black holes. Inserting into the master equations parameters to detect what is involved in their spin-down is the topic of this paper. April3CJPFriedValluri.pdf

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