On the "Universal" N=2 Supersymmetry of Classical Mechanics

In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular we try to shed some light on a N=2 "universal" supersymmetry which seems to have an interesting interplay with the concept of ergodicity of the system. To study the geometry better we make this susy local and clarify pedagogically several issues present in the literature. Secondly, in order to prepare the ground for a better understanding of its relation to ergodicity, we study the system on constant energy surfaces. We find that the procedure of constraining the system on these surfaces injects in it some local grassmannian invariances and reduces the N=2 global susy to an N=1.Comment: few misprints fixed with respect to Int.Jour.Mod.Phys.A vol 16, no15 (2001) 270

Newtonian M(atrix) Cosmology

A Newtonian matrix cosmology, correspoding to the BFSS model of eleven-dimensional M-theory in the IMF as a (0+1) M(atrix) model is constructed. Interesting new results are obtained, such as the existence of (much sought for in the past) static solutions. The possible interpretation of the off-diagonal entries as a background geometry is also briefly discussed.Comment: 9 pages, Latex2

Holography and the C-Theorem

We review the geometric definition of C-function in the context of field theories that admit a holographic gravity dual.Comment: Contribution to the proceedings of the TMR 2000 Paris Conferenc

Prospects for radio detection of extremely high energy cosmic rays and neutrinos in the Moon

We explore the feasibility of using the Moon as a detector of extremely high energy (>10^19 eV) cosmic rays and neutrinos. The idea is to use the existing radiotelescopes on Earth to look for short pulses of Cherenkov radiation in the GHz range emitted by showers induced just below the surface of the Moon when cosmic rays or neutrinos strike it. We estimate the energy threshold of the technique and the effective aperture and volume of the Moon for this detection. We apply our calculation to obtain the expected event rates from the observed cosmic ray flux and several representative theoretical neutrino fluxes.Comment: 11 pages, Latex, aipproc.sty and epsfig.sty. 5 ps figures. Talk presented by J. Alvarez-Muniz at the 1st International Workshop on Radio Detection of High Energy Particles (RADHEP-2000), UCLA, November 2000. Some typos corrected. Fig.4 caption extende

Irreversible Investment, Incremental Capital Accumulation, and Price Uncertainty

We consider optimal incremental capital accumulation in the presence of investment irreversibility and general price uncertainty. We present a set of general conditions under which the optimal capital accumulation path can be explicitly characterized in terms of an ordinary threshold rule stating that investment is optimal whenever the underlying price exceeds a capital-dependent threshold. We also present a set of general conditions under which increased price volatility expands the region where investment is suboptimal and decreases both the expected cumulative present value of the marginal revenue product of capital and the value of the future expansion options.Price uncertainty, irreversible investment, incremental capital accumulation.

Killings, Duality and Characteristic Polynomials

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved.Comment: 14 pages, Late