Positive eigenvalue-eigenvector of nonlinear positive mappings

We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein- Rutman theorem is presented, and a simple iteration process {T^kx/｜｜T^kx｜｜} （ x ∈ P^＋） is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert＇s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.     

EVALUATION OF DEGENERATE SCALE FOR N-GON CONFIGURATION IN ANTIPLANE ELASTICITY

This paper provides a solution for the degenerate scale for N-gon configuration in antiplane elasticity using the conformal mapping function, and the lower and upper bounds for the degenerate scale for N = 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 100, 150 and 200, are evaluated.     

Nonlinear Electrodynamics and Magnetic Black Holes

A model of nonlinear electrodynamics with two parameters, coupled with general relativity, is investigated. We study the magnetized black hole and obtain solutions. The asymptotic of the metric and mass functions at and , and corrections to the Reissner‐Nordström solution are found. We investigate thermodynamics of black holes and calculate the Hawking temperature and heat capacity of black holes. It is shown that there are phase transitions and at some parameters of the model black holes are stable.     

The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings $f \in TL^{\alpha}_H,$ which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z|<1\}.$ Moreover, denoting the subclass $TS^{\alpha}_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f \in TS^α_H,$ and their covering theorems.     

Optical characteristics of m-plane InGaN/GaN multiple quantum well grown on LiAlO2 (1 0 0) by MOVPE

We investigate the optical properties of m-plane InGaN/GaN multiple quantum well grown on LiAlO₂ substrate by metal organic vapor phase epitaxy. Polarization-dependent photoluminescence and polarization-dependent photoluminescence excitation measurements have been performed at low temperature to study the optical absorption and emission characteristics. The main emission band possesses large polarization anisotropy which may be attributed to the anisotropic biaxial strain. We found the optical emission is not influenced by the polarization-induced electric field from the excitation-dependent photoluminescence measurements. From our results, we attribute the low-temperature emission band around 3.2 eV to interband transition in the quantum well. Besides, the mechanism of the main emission band is associated with interband transition and subsequent carrier localization. The realization of good-quality non-polar GaN-based devices can then be expected in near future.     

Uncertainty evaluation of continuous noise sampling

An area of current interest and topic of multiple publications is the assessment of uncertainty in estimating long-term indicators from measurements made for periods of time of less than 1 year. In this work, these prior investigations have been used as a starting point.Based on measurements made during one whole year at 26 sampling points with variables of urban and traffic characteristics, it was considered two aims related to uncertainty in the estimation of the annual L_den. The strength of this study is the large amount of data, which allows to simulate real measurements by sampling data from random days. Thus, it was studied in detail the predictive ability of the expressions proposed in the literature. Associated with this objective, then it was sought to evaluate the uncertainty associated with the estimation of annual L_den when random days of sampling were much lower than a full year.The results indicate the need for further progress in the theoretical determination of uncertainty. Second, the results made it able to estimate the uncertainty for the L_den indicator based on the number days sampled randomly.     

Measurement network for urban noise assessment: Comparison of mobile measurements and spatial interpolation approaches

This paper investigates the relevance of different interpolation techniques to improve the spatial resolution of urban noise maps, in complement to measurements achieved at fixed stations. Interpolation techniques based on mobile measurements are compared to usual spatial interpolations techniques, namely Inverse Distance Weighting and Kriging. The analyses rely on a measurement campaign, which consisted of nearly 8 h of geo-referenced mobile noise measurements performed at random moments of the day, conducted simultaneously with continuous measurements collected at five fixed stations located on the inner city of Gent, Belgium.Firstly, a procedure is proposed to build a noise map with a high spatial resolution (one point every 5 m). The procedure relies on both mobile and fixed measurements: the mobile measurements are used to capture spatial variations on the network, and the measurements at fixed stations are used to capture the temporal variations. The map produced is then used as reference to compare the interpolation techniques based on a significantly more sparse measurement set.The spatial interpolation techniques tested fail in predicting accurately the noise level variations within streets. The explanation given is that they do not offer a sufficient covering of the network, and assume spatial variations which are not coherent with traffic dynamics or street configurations. Inversely, mobile measurements cover the entire network. As a result, they allow a more accurate prediction of noise levels even if very short samples are used, provided that the procedure used to estimate noise levels includes a spatial aggregation, which aims at smoothing the high spatial variations inevitable with short samples. Moreover, mobile measurements can advantageously be used to optimize, through a Genetic Algorithm, the locations where to install fixed stations, promising an efficient noise monitoring at reduced operational costs.     

Linear quantification calibration of crystallinity at subpercent and its evaluation based on spectral and spatial information inherited in Raman chemical images

In this paper, the author reported two methods to extract spectral or spatial information inherited in the Raman chemical images for linear quantification calibration of crystallinity. The two approaches reported quantification results according to the spectral mean score of overall pixels or the spatial percentage of the pixels with a score greater than and equal to the threshold of the chemical images, respectively. From this study, it can be concluded that, first, sampling method for data collection in mapping has to be optimized to achieve linear quantification calibration through simple univariate analysis approaches. Second, the ordinary way of evaluating/validating a linear quantification technique by best linear correlation coefficient (R²) and root‐mean‐square error of calibration is disputable and has to be reconsidered. Lastly, with further consideration of root‐mean‐square relative error of calibration and predicted crystallinity at subpercent, it was found that the spectral mean score method cannot generate reliable quantification results at subpercent crystallinity. Copyright © 2014 John Wiley & Sons, Ltd.     

Bipotential versus return mapping algorithms: Implementation of non associated flow rules

Numerical implementation of constitutive laws involves specific incremental methods. The “return mapping” (Simo and Hughes, 1998) and the “bipotential” (de Saxcé, 1992) are one of those, associated respectively to two different classes of materials: the General Standard Materials (GSM) for the return mapping and the Implicit Standard Materials (ISM) for the bipotential.The objective of this paper is then to compare the implementation of those both methods in the case of non associated flow rules in plasticity.In the first section, the properties of the different previous material classes will be recalled and the methods of “return mapping” and “bipotential” will be detailed. The comparison of both methods is realised on the non linear kinematic hardening rule of Armstrong–Frederick (Armstrong and Frederick, 1966) in a second section and the details are given in a third part. The numerical implementation is realised in Abaqus/Standard 6.11 by the means of a UMat subroutine and the practical simple case of tension–compression is analysed in a last section.     

Selective depiction of susceptibility transitions using Laplace-filtered phase maps

In this work, we aim to demonstrate the ability of Laplace-filtered three-dimensional (3D) phase maps to selectively depict the susceptibility transitions in an object. To realize this goal, it is first shown that both the Laplace derivative of the z component of the static magnetic field in an object and the Laplacian of the corresponding phase distribution may be expected to be zero in regions of constant or linearly varying susceptibility and to be nonzero when there is an abrupt change in susceptibility, for instance, at a single point, a ridge, an interface, an edge or a boundary. Next, a method is presented by which the Laplace derivative of a 3D phase map can be directly extracted from the complex data, without the need for phase unwrapping or subtraction of a reference image. The validity of this approach and of the theory behind it is subsequently demonstrated by simulations and phantom experiments with exactly known susceptibility distributions. Finally, the potential of the Laplace derivative analysis is illustrated by simulations with a Shepp-Logan digital brain phantom and experiments with a gel phantom containing positive and negative focal susceptibility deviations.