A note on ideal spaces of Banach Algebras

In a previous paper the second author introduced a compact topology on the space of closed ideals of a unital Banach algebra A. If A is separable then this topology is either metrizable or else neither Hausdorff nor first countable. Here it is shown that this topology is Hausdorff if A is the algebra of once continuously differentiable functions on an interval, but that if A is a uniform algebra then this topology is Hausdorff if and only if A has spectral synthesis. An example is given of a strongly regular, uniform algebra for which every maximal ideal has a bounded approximate identity, but which does not have spectral synthesis.Comment: 9 pages plain te

Cosmologies with Two-Dimensional Inhomogeneity

We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar field, or alternatively with perfect fluid, can be constructed using this algorithm. Some families of solutions and the applications of the algorithm are discussed.Comment: 9 pages, one postscript figur

The interaction between jets and clouds in the 3CR galaxies

From the HST/WFPC2 3CR Snapshot Survey, data taken with the filter F555W, F702W and narrow-ramp, a set of galaxies with noticeable extended structure were selected (e.g. 3C 79, 3C 135, 3C 234, etc). All of these objects show large regions of [OIII] λ 5007˚A emission (narrow ramp filter) and the broad-band filters data show similar structures indicating the presence of strong emission in several lines over these regions. The morphology observed seems to be related (e.g. same position angle, direct overlapping or similar shape) with the radio-jet. For some candidates with these properties GMOS/Gemini spectroscopy was taken. These data (both HST direct imaging and Gemini spectroscopy) can be tested with diagnostic diagrams and total UV photons budget to understand the source of energy that is ionizing the gas. This source of ionization was commonly believed to be the UV photons emitted by the powerful active galactic nuclei (AGN), but several of these objects show clearly that shocks produced by the radio jet are the main cause of the observed gas line emission. We show in this work, the results obtained over some of these radio-galaxies: 3C 135, 3C 180, 3C 234 and 3C 284.Fil: Hägele, G. F.. Universidad Autónoma de Madrid; EspañaFil: Feinstein Baigorri, Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Macchetto, D. F.. Space Telescope Science Institute; Estados UnidosFil: Montero, F.. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

On the Entropy and the Density Matrix of Cosmological Perturbations

We look at the transition to the semiclassical behaviour and the decoherence process for the inhomogeneous perturbations in the inflationary universe. Two different decoherence mechanisms appear: one dynamical, accompanied with a negligible, if at all, entropy gain, and the other, effectively irreversible dephasing, due to a rapid variation in time of the off-diagonal density matrix elements in the post-inflationary epoch. We thus settle the discrepancies in the entropy content of perturbations evaluated by different authors.Comment: LaTeX2e with the epsf packag

Penrose Limits, the Colliding Plane Wave Problem and the Classical String Backgrounds

We show how the Szekeres form of the line element is naturally adapted to study Penrose limits in classical string backgrounds. Relating the "old" colliding wave problem to the Penrose limiting procedure as employed in string theory we discuss how two orthogonal Penrose limits uniquely determine the underlying target space when certain symmetry is imposed. We construct a conformally deformed background with two distinct, yet exactly solvable in terms of the string theory on R-R backgrounds, Penrose limits. Exploiting further the similarities between the two problems we find that the Penrose limit of the gauged WZW Nappi-Witten universe is itself a gauged WZW plane wave solution of Sfetsos and Tseytlin. Finally, we discuss some issues related to singularity, show the existence of a large class of non-Hausdorff solutions with Killing Cauchy Horizons and indicate a possible resolution of the problem of the definition of quantum vacuum in string theory on these time-dependent backgrounds.Comment: Some misprints corrected. Matches the version in print. To appear in Classical & Quantum Gravit

Return to Play Following Shoulder Stabilization: A Systematic Review and Meta-analysis.

BackgroundAnterior shoulder instability can be a disabling condition for the young athlete; however, the best surgical treatment remains controversial. Traditionally, anterior shoulder instability was treated with open stabilization. More recently, arthroscopic repair of the Bankart injury with suture anchor fixation has become an accepted technique.HypothesisNo systematic reviews have compared the rate of return to play following arthroscopic Bankart repair with suture anchor fixation with the Bristow-Latarjet procedure and open stabilization. We hypothesized that the rate of return to play will be similar regardless of surgical technique.Study designSystematic review; Level of evidence, 4.MethodsWe performed a systematic review and meta-analysis focused on return to play following shoulder stabilization. Inclusion criteria included studies in English that reported on rate of return to play and clinical outcomes following primary arthroscopic Bankart repair with suture anchors, the Latarjet procedure, or open stabilization. Statistical analyses included Student t tests and analyses of variance.ResultsSixteen papers reporting on 1036 patients were included. A total of 545 patients underwent arthroscopic Bankart repair with suture anchors, 353 with the Latarjet procedure, and 138 with open repair. No significant difference was found in patient demographic data among the studies. Patients returned to sport at the same level of play (preinjury level) more consistently following arthroscopic Bankart repair (71%) or the Latarjet procedure (73%) than open stabilization (66%) (P < .05). Return to play at any level and postoperative Rowe scores were not significantly different among studies. Recurrent dislocation was significantly less following the Latarjet procedure (3.5%) than after arthroscopic Bankart repair (6.6%) or open stabilization (6.7%) (P < .05).ConclusionThis systematic review demonstrates a greater rate of return to play at the preinjury level following arthroscopic Bankart repair and the Latarjet procedure than open stabilization. Despite this difference, >65% of all treated athletes returned to sport at their preinjury levels, with other outcome measures being similar among the treatment groups. Therefore, arthroscopic Bankart repair, the Latarjet procedure, and open stabilization remain good surgical options in the treatment of the athlete with anterior shoulder instability