Metallicity determination in gas-rich galaxies with semiempirical methods

A study of the precision of the semiempirical methods used in the determination of the chemical abundances in gas-rich galaxies is carried out. In order to do this the oxygen abundances of a total of 438 galaxies were determined using the electronic temperature, the $R_{23}$ and the P methods. The new calibration of the P method gives the smaller dispersion for the low and high metallicity regions, while the best numbers in the turnaround region are given by the $R_{23}$ method. We also found that the dispersion correlates with the metallicity. Finally, it can be said that all the semiempirical methods studied here are quite insensitive to metallicity with a value of $8.0\pm0.2$ dex for more than 50% of the total sample. \keywords{ISM: abundances; (ISM): H {\sc ii} regions}Comment: 26 pages, 9 figures and 2 tables. To appear at AJ, January 200

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Geometric inequalities from phase space translations

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality, and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup, and argue that it implies fast convergence towards the fixed point for a large class of initial states.Comment: 37 pages; updated to match published versio

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

Hypercontractive measures, Talagrand's inequality, and influences

We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context

Structural and nuclear characterizations of defects created by noble gas implantation in silicon oxide

Thermally grown silicon oxide layer was implanted at room temperature with 300keV Xe at fluences ranging from 0.5 to 5x10$^16$Xe/cm$^2$. Bubbles created after Xe-implantation provided a low-k silicon oxide that has potential use as a dielectric material for interconnects in Si integrated circuits. Transmission Electron Microscopy (TEM), Rutherford Backscattering Spectrometry (RBS) and Positron Annihilation Spectroscopy (PAS) were used to provide a comprehensive characterization of defects (bubbles, vacancy, gas atoms and other types of defects) created by Xe implantation in $SiO_2$ layer. These measurements suggest that the bubbles observed with TEM for all fluences were a consequence of the interaction between Xe and vacancies (V), with $V_nXe_m$ complexes created in the zone where V and Xe profiles overlap. Negatively charged defects such as ($Si-O^-$, $Si-O-O^-$ and $O_2^-$) are also created after implantation

Study of the optimal conditions for NV- center formation in type 1b diamond, using photoluminescence and positron annihilation spectroscopies

We studied the parameters to optimize the production of negatively-charged nitrogen-vacancy color centers (NV-) in type~1b single crystal diamond using proton irradiation followed by thermal annealing under vacuum. Several samples were treated under different irradiation and annealing conditions and characterized by slow positron beam Doppler-broadening and photoluminescence (PL) spectroscopies. At high proton fluences another complex vacancy defect appears limiting the formation of NV-. Concentrations as high as 2.3 x 10^18 cm^-3 of NV- have been estimated from PL measurements. Furthermore, we inferred the trapping coefficient of positrons by NV-. This study brings insight into the production of a high concentration of NV- in diamond, which is of utmost importance in ultra-sensitive magnetometry and quantum hybrid systems applications

Type-based termination of recursive definitions

This paper introduces "lambda-hat", a simply typed lambda calculus supporting inductive types and recursive function definitions with termination ensured by types. The system is shown to enjoy subject reduction, strong normalisation of typable terms and to be stronger than a related system "lambda-G" in which termination is ensured by a syntactic guard condition. The system can, at will, be extended to also support coinductive types and corecursive function definitions.Information Society Technologies (IST) - Fifth Framework Programm (FP5) - TYPES.Fundação para a Ciência e a Tecnologia (FCT) – PRAXIS XXI/C/EEI/14172/98.INRIA-ICCTI.Estonian Science Foundation (ETF) - grant no. 4155

Moments of unconditional logarithmically concave vectors

We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.Comment: 14 page

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1