24,019 research outputs found

    Closed ideals in some algebras of analytic functions

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    We obtain a complete description of closed ideals of the algebra \mathcal{D}\cap \mathrm{lip}_\alpha}, 0<α≀1/2,0<\alpha\leq{1/2}, where D\mathcal{D} is the Dirichlet space and \mathrm{lip}_\alpha} is the algebra of analytic functions satisfying the Lipschitz condition of order α.\alpha.Comment: 19 page

    Two Body Relaxation in Simulated Cosmological Haloes

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    This paper aims at quantifying discreetness effects, born of finite particle number, on the dynamics of dark matter haloes forming in the context of cosmological simulations. By generalising the standard calculation of two body relaxation to the case when the size and mass distribution are variable, and parametrising the time evolution using established empirical relations, we find that the dynamics of a million particle halo is noise-dominated within the inner percent of the final virial radius. Far larger particle numbers (~ 10^8) are required for the RMS perturbations to the velocity to drop to the 10 % level there. The radial scaling of the relaxation time is simple and strong: t_relax ~ r^2, implying that numbers >> 10^8 are required to faithfully model the very inner regions; artificial relaxation may thus constitute an important factor, contributing to the contradictory claims concerning the persistence of a power law density cusp to the very centre. The cores of substructure haloes can be many relaxation times old. Since relaxation first causes their expansion before recontraction occurs, it may render them either more difficult or easier to disrupt, depending on their orbital parameters. It may thus modify the characteristics of the subhalo distribution and effects of interactions with the parent. We derive simple closed form formulas for the characteristic relaxation times, as well as for the weak N-scaling reported by Diemand et al. when the main contribution comes from relaxing subhaloes (abridged).Comment: 11 Pages, 7 figs, Monthly Notices styl

    Growth and optical characterisation of multilayers of InGaN quantum dots

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    We report on the growth (using metal-organic vapour phase epitaxy) and optical characterization of single and multiple layers of InGaN quantum dots (QDs), which were formed by annealing InGaN epilayers at the growth temperature in nitrogen. The size and density of the nanostructures have been found to be fairly similar for uncapped single and three layer QD samples if the GaN barriers between the dot layers are grown at the same temperature as the InGaN epilayer. The distribution of nanostructure heights of the final QD layer of three is wider and is centred around a larger size if the GaN barriers are grown at two temperatures (first a thin layer at the dot growth temperature, then a thicker layer at a higher temperature). Micro-photoluminescence studies at 4.2 K of capped samples have confirmed the QD nature of the capped nanostructures by the observation of sharp emission peaks with full width at half maximum limited by the resolution of the spectrometer. We have also observed much more QD emission per unit area in a sample with three QD layers, than in a sample with a single QD layer, as expected

    A Hopf Index Theorem for foliations

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    We formulate and prove an analog of the Hopf Index Theorem for Riemannian foliations. We compute the basic Euler characteristic of a closed Riemannian manifold as a sum of indices of a non-degenerate basic vector field at critical leaf closures. The primary tool used to establish this result is an adaptation to foliations of the Witten deformation method.Comment: 26 page

    An Explicative and Predictive Study of Employee Attrition using Tree-based Models

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    We develop tree-based models to estimate the probability of an employee leaving a firm during a job transition from a dataset of anonymously submitted resumes through Glassdoor’s online portal. Dataset construction and summary statistics are first summarized followed by a more in depth examination through four exploratory studies. Insights provided by these studies are then used to engineer features that serve as input into subsequent attrition related predictive models. We finally perform a thorough search through several dozen binary classification techniques in the cases of an original and extended feature set. We find tree-based methods including random forests and light gradient boosted trees provide the overall strongest predictive performance. Finally, we summarize ROC curves for several such models and describe future potential research directions

    Nature and Nurture in Dark Matter Halos

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    Cosmological simulations consistently predict specific properties of dark matter halos, but these have not yet led to a physical understanding that is generally accepted. This is especially true for the central regions of these structures. Recently two major themes have emerged. In one, the dark matter halo is primarily a result of the sequential accretion of primordial structure (ie `Nature'); while in the other, dynamical relaxation (ie `Nurture') dominates at least in the central regions. Some relaxation is however required in either mechanism. In this paper we accept the recently established scale-free sub-structure of halos as an essential part of both mechanisms. Consequently; a simple model for the central relaxation based on a self-similar cascade of tidal interactions, is contrasted with a model based on the accretion of adiabatically self-similar, primordial structure. We conclude that a weak form of this relaxation is present in the simulations, but that is normally described as the radial orbit instability.Comment: 25 pages, 3 figures, fig with parts 1 to d, fig 3 with parts a to
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