418 research outputs found

    Hitchin characters and geodesic laminations

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    For a closed surface S, the Hitchin component Hit_n(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group pi_1(S) to the Lie group PSL_n(R). We construct a parametrization of the Hitchin component that is well-adapted to a maximal geodesic lamination on the surface. This is a natural extension of Thurston's parametrization of the Teichmueller space of S by shear coordinates associated to a maximal geodesic lamination, corresponding to the case n=2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.Comment: 67 pages, 9 figures. Version 2: Minor polish (misprints, etc.) prior to submissio

    Length functions of Hitchin representations

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    Given a Hitchin representation \rho \colon \pi_1(S) \to \PSL_n(\mathbb{R}), we construct nn continuous functions \ell_i^\rho \colon \mathcal \CH(S) \to \mathbb{R} defined on the space of H\"older geodesic currents \CH(S) such that, for a closed, oriented curve Îł\gamma in SS, the ii--th eigenvalue of the matrix \rho(\gamma)\in \PSL_n(\mathbb{R}) is of the form ±exp ℓiρ(Îł)\pm \mathrm{exp}\, \ell_i^\rho(\gamma): such functions generalize to higher rank Thurston's length function of Fuchsian re\presentations. Identities, diffe\rentiability properties of these lengths ℓiρ\ell_i^\rho, as well as applications to eigenvalue estimates, are also considered.Comment: 16 pages, 2 figures, final version to appear in Algebraic and Geometric Topolog

    RANS computations of tip vortex cavitation

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    Some two-dimensional (2D) exfoliated zeolites are single- or near single-unit cell thick silicates that can function as molecular sieves. Although they have already found uses as catalysts, adsorbents and membranes precise determination of their thickness and wrinkling is critical as these properties influence their functionality. Here we demonstrate a method to accurately determine the thickness and wrinkles of a 2D zeolite nanosheet by comprehensive 3D mapping of its reciprocal lattice. Since the intensity modulation of a diffraction spot on tilting is a fingerprint of the thickness, and changes in the spot shape are a measure of wrinkling, this mapping is achieved using a large-angle tilt-series of electron diffraction patterns. Application of the method to a 2D zeolite with MFI structure reveals that the exfoliated MFI nanosheet is 1.5 unit cells (3.0 nm) thick and wrinkled anisotropically with up to 0.8 nm average surface roughness. © 2015 Macmillan Publishers Limited

    Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

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    Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð„with constraintsð ð ð„ „ ðandðŽð„ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

    Hyperoxemia and excess oxygen use in early acute respiratory distress syndrome : Insights from the LUNG SAFE study

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    Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Concerns exist regarding the prevalence and impact of unnecessary oxygen use in patients with acute respiratory distress syndrome (ARDS). We examined this issue in patients with ARDS enrolled in the Large observational study to UNderstand the Global impact of Severe Acute respiratory FailurE (LUNG SAFE) study. Methods: In this secondary analysis of the LUNG SAFE study, we wished to determine the prevalence and the outcomes associated with hyperoxemia on day 1, sustained hyperoxemia, and excessive oxygen use in patients with early ARDS. Patients who fulfilled criteria of ARDS on day 1 and day 2 of acute hypoxemic respiratory failure were categorized based on the presence of hyperoxemia (PaO2 > 100 mmHg) on day 1, sustained (i.e., present on day 1 and day 2) hyperoxemia, or excessive oxygen use (FIO2 ≄ 0.60 during hyperoxemia). Results: Of 2005 patients that met the inclusion criteria, 131 (6.5%) were hypoxemic (PaO2 < 55 mmHg), 607 (30%) had hyperoxemia on day 1, and 250 (12%) had sustained hyperoxemia. Excess FIO2 use occurred in 400 (66%) out of 607 patients with hyperoxemia. Excess FIO2 use decreased from day 1 to day 2 of ARDS, with most hyperoxemic patients on day 2 receiving relatively low FIO2. Multivariate analyses found no independent relationship between day 1 hyperoxemia, sustained hyperoxemia, or excess FIO2 use and adverse clinical outcomes. Mortality was 42% in patients with excess FIO2 use, compared to 39% in a propensity-matched sample of normoxemic (PaO2 55-100 mmHg) patients (P = 0.47). Conclusions: Hyperoxemia and excess oxygen use are both prevalent in early ARDS but are most often non-sustained. No relationship was found between hyperoxemia or excessive oxygen use and patient outcome in this cohort. Trial registration: LUNG-SAFE is registered with ClinicalTrials.gov, NCT02010073publishersversionPeer reviewe

    Search for heavy resonances decaying to two Higgs bosons in final states containing four b quarks