The Automorphism Group of a Simple Tracially AI Algebra

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group .     

Modeling of astigmatic-elliptical beam shaping during fs-laser waveguide writing including beam truncation and diffraction effects

In this work, we report a model for accurately calculating the focal volumes corresponding to astigmatic elliptical beams used in fs-laser waveguide writing. The model is based on the use of the ABCD matrix formalism for the propagation of a Gaussian beam. The code includes the effects of propagation on the astigmatic elliptical beam, and the effects of beam truncation and diffraction at the entrance pupil of the focusing objective due to beam clipping when overfilling the pupil. The results predict that for a given astigmatism value and propagation distance it is possible to efficiently suppress the astigmatic focus closer to the surface. This explains previous experimental results where single structure waveguides with controllable aspect-ratio were fabricated using astigmatic-elliptical beams. Furthermore, we investigate the respective roles of astigmatism and beam propagation, as well as the strong impact of truncation and diffraction effects caused by clipping the beam at the pupil of the focusing optics. Finally, based on the results from our model, we present some practical considerations in terms of beam propagation and phase wrapping constraints.     

Unified Field Theoretical Models from Generalized Affine Geometries III

In this work the underlying structure of new type of Unified Field Theoretical model introduced in by the authors is elucidated and analyzed from the geometrical and group theoretical point of view. Our goal is to take advantage of the geometrical and topological properties of this theory in order to determine the minimal group structure of the resultant spacetime manifold able to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined and important physical consequences enumerated. In the case of spacetime with torsion the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed based in the important cases of tratorial, totally antisymmetric and general torsion fields.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

A measurement of the neutral current electroweak parameters using the fermilab narrow band neutrino beam

We report a measurement of the electroweak parameters sin₂θ ^w and ? based on the ratios of neutral current to charged current events measured in the Fermilab narrow-band neutrino beam at energies of 30–240 GeV. The data are fully corrected for radiative effects, heavy-quark production, and other effects. The best value for sin₂θ ^w obtained, sin₂θ ^w =0.239±0.011, is consistent with the most recent values fromW andZ production, as well as from other neutrino experiments.     

Situations in traffic — how quickly they change

Spatio-temporal correlations of traffic intensity are analyzed employing data collected for the motorway M-30 around Madrid during one week in January 2009. We found that the lifetime of these correlations is the shortest in the evening between 6:00 p.m. and 8:00 p.m. This lifetime represents a new indicator for the amount of attention that is demanded by drivers in given traffic conditions.     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.     

High‐energy‐resolution diced spherical quartz analyzers for resonant inelastic X‐ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X‐ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.