SO(10) SUSY GUTs with mainly axion cold dark matter: implications for cosmology and colliders

Supersymmetric grand unified theories based on the gauge group SO(10) are highly motivated. In the simplest models, one expects t-b-\tau Yukawa coupling unification, in addition to gauge, matter and Higgs unification. Yukawa unification only occurs with very special GUT scale boundary conditions, leading to a spectra with ~10 TeV first and second generation scalars, TeV-scale third generation scalars, and light gauginos. The relic density of neutralino cold dark matter is calculated to be 10^2-10^4 times higher than observation. If we extend the theory with the PQWW solution to the strong CP problem, then instead a mixture of axions and axinos comprises the dark matter, with the measured abundance. Such a solution solves several cosmological problems. We predict a rather light gluino with m(gluino)~300-500 GeV that should be visible in either Tevatron or forthcoming LHC run 1 data. We would also expect ultimately a positive result from relic axion search experiments.Comment: 6 pages plus 2 .eps figures; invited talk given at Axions 2010 meeting, University of Florida, Jan. 15-17, 201

Convex Bodies of Constant Width and Constant Brightness

In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in $\R^3$ with constant width, constant brightness, and boundary of class $C^2$ is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.Comment: 20 page

Varieties of Ontological Argument

I consider what I hope are increasingly sophisticated versions of ontological argument, beginning from simple definitional forms, through three versions to be found in Anselm, with their recent interpretations by Malcolm, Plantinga, Klima and Lowe. I try to show why none of these work by investigating both the different senses of necessary existence and the conditions under which logically necessary existence can be brought to bear. Although none of these arguments work, I think that they lead to interesting reflections on the nature of definition, on the conditions for possessing the property of necessary existence and point towards a different, neo-Platonic ground for God’s meeting the criteria for being logically necessary

Selective Use of the Executive Immunity Power: A Denial of Due Process?

Attacks on the government\u27s power to grant immunity to cooperative witnesses have been premised on several grounds, including the due process clause of the fifth amendment. It is upon this clause that the United States District Court of the Southern District of New York based a decision that a defendant was denied due process when the government refused to immunize him after granting immunization to its own witnesses. This article examines traditional arguments against challenging a prosecutor\u27s immunity discretion, the procedural and substantive factors necessary in substantiating a defendant\u27s due process claim, and the effect of immunization on the government\u27s burden of proof in future prosecutions