Stability study of a model for the Klein-Gordon equation in Kerr spacetime

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon equation, describing the propagation of a scalar field of mass $\mu$ in the background of a rotating black hole. Rigorous results proof the stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters $a$ extremely close to 1. Among others, the paper derives a model problem for the equation which supports the instability of the field down to $a/M \approx 0.97$.Comment: Updated version, after minor change

Inflation and the quantum measurement problem

We propose a solution to the quantum measurement problem in inflation. Our model treats Fourier modes of cosmological perturbations as analogous to particles in a weakly interacting Bose gas. We generalize the idea of a macroscopic wave function to cosmological fields, and construct a self-interaction Hamiltonian that focuses that wave function. By appropriately setting the coupling between modes, we obtain the standard adiabatic, scale-invariant power spectrum. Because of central limit theorem, we recover a Gaussian random field, consistent with observations

Colación del MS. 197 (P. Vergilii Maronis Bucolica Georgicon Aeneidos) del Archivo Capitular de Vic

El objeto del presente trabajo es presentar la primera y única colación exhaustiva del más antiguo de los manuscritos virgilianos existentes en España, el MS. 197 del Archivo Capitular de Vic1. Hace más de un siglo y medio, Ch. G. Heyne2 dejó escritas las siguientes y desmoralizadoras palabras: “Codicum virgilianorum, qui nondum cum vulgata scriptura comparati in bibliothecis passim latent ... adThe author presents the first view of the oldest Virgilian manuscript custodied in Spain (11th Century), which she has denominated Ausonensis. She states the convenience of taking into account this manuscript in Virgil’s future editions

Dynamic analysis of the GEOS satellite

The assumed modes method is used to investigate the stability of the GEOS satellite. The system is discretized by representing the continuous displacement by finite series of space-dependent admissible functions multiplied by time-dependent generalized coordinates. The spatial dependence is eliminated by integration over the elastic domains, so that the testing functional reduces to a testing function. The sign properties of the testing function are then tested and the equilibrium defined as nontrivial. In considering the stability of small motions about nontrivial equilibrium, it is shown that if the analysis performed by ignoring the motion of the mass center indicates stability, then the system remains stable if the motion of the mass center is included

Superconnections, theta series, and period domains

We use superconnections to define and study some natural differential forms on the period domain D that parametrizes polarized Hodge structures of given type on a rational quadratic vector space V. These forms depend on a choice of vectors v_{1},...,v_{r} \epsilon V and have a Gaussian shape that peaks on the locus where v_{1},...,v_{r} become Hodge classes. We show that they can be rescaled so that one can form theta series by summing over a lattice L^{T} C V^{T}. These series define differential forms on arithmetic quotients Γ\D. We compute their cohomology class explicitly in terms of the cohomology classes of Hodge loci in Γ\D. When the period domain is a hermitian symmetric domain of type IV, we show that the components of our forms of appropriate degree recover the forms introduced by Kudla and Millson. In particular, our results provide another way to establish the main properties of these forms