Rosenblatt distribution subordinated to gaussian random fields with long-range dependence

The Karhunen-Lo\`eve expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields on R^d displaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution when d=1. Several properties of this new distribution are obtained. Specifically, its series representation in terms of independent chi-squared random variables is given, the asymptotic behavior of the eigenvalues, its L\`evy-Khintchine representation, as well as its membership to the Thorin subclass of self-decomposable distributions. The existence and boundedness of its probability density is then a direct consequence.Comment: This paper has 40 pages and it has already been submitte

Completely dark galaxies: their existence, properties, and strategies for finding them

There are a number of theoretical and observational hints that large numbers of low-mass galaxies composed entirely of dark matter exist in the field. The theoretical considerations follow from the prediction of cold dark matter theory that there exist many low-mass galaxies for every massive one. The observational considerations follow from the observed paucity of these low-mass galaxies in the field but not in dense clusters of galaxies; this suggests that the lack of small galaxies in the field is due to the inhibition of star formation in the galaxies as opposed to the fact that their small dark matter halos do not exist. In this work we outline the likely properties of low-mass dark galaxies, and describe observational strategies for finding them, and where in the sky to search. The results are presented as a function of the global properties of dark matter, in particular the presence or absence of a substantial baryonic dark matter component. If the dark matter is purely cold and has a Navarro, Frenk and White density profile, directly detecting dark galaxies will only be feasible with present technology if the galaxy has a maximum velocity dispersion in excess of 70 km/s, in which case the dark galaxies could strongly lens background objects. This is much higher than the maximum velocity dispersions in most dwarf galaxies. If the dark matter in galaxy halos has a baryonic component close to the cosmic ratio, the possibility of directly detecting dark galaxies is much more realistic; the optimal method of detection will depend on the nature of the dark matter. A number of more indirect methods are also discussed.Comment: 12 pages, 4 figures, MNRAS in pres

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

Anode Fabrication for Solid Oxide Fuel Cells: Electroless and Electrodeposition of Nickel and Silver into Doped Ceria Scaffolds

© 2016 The Authors.A novel fabrication method using electroless and electrodeposited Ni/Ag/GDC for SOFC anodes is presented. First a porous Ce0.9Gd0.1O2-x (GDC) scaffold was deposited on a YSZ electrolyte by screen printing and sintering. The scaffold was then metallized with silver using Tollens reaction, followed by electrodeposition of nickel from a Watts bath. The electrodes (Ni/Ag/GDC) were tested in both symmetrical and fuel cell configurations. The microstructures of the Ni/Ag/GDC anodes were analyzed using scanning electron microscopy (SEM) and energy dispersive x-ray spectroscopy (EDX). Nano-particles of Ni formed in the porous GDC scaffold provided triple phase boundaries (TPB). The electronic conductivity of the Ni/Ag/GDC (3.5/24.7/71.8 vol%) electrode was good even at relatively low Ni volume fractions. The electrochemical performance was examined in different concentrations of humidified hydrogen (3% H2O) and over a range of temperatures (600-750 °C). The total area specific resistance (ASR) of the anode at 750 °C in humidified 97 vol% H2 was 1.12 Ω cm2, with low-frequency polarization (R-l) as the largest contributor. The electrodes were successfully integrated into a fuel cell and operated in both H2 and syngas

Study of the derivative expansions for the nuclear structure functions

We study the convergence of the series expansions sometimes used in the analysis of the nuclear effects in Deep Inelastic Scattering (DIS) proccesses induced by leptons. The recent advances in statistics and quality of the data, in particular for neutrinos calls for a good control of the theoretical uncertainties of the models used in the analysis. Using realistic nuclear spectral functions which include nucleon correlations, we find that the convergence of the derivative expansions to the full results is poor except at very low values of $x$

The Stars in M15 Were Born with the r-process

High-resolution spectroscopy of stars on the red giant branch (RGB) of the globular cluster M15 has revealed a large (~1 dex) dispersion in the abundances of r-process elements such as Ba and Eu. Neutron star mergers (NSMs) have been proposed as a major source of the r-process. However, most NSM models predict a delay time longer than the timescale for cluster formation. One possibility is that a NSM polluted the surfaces of stars in M15 long after the cluster finished forming. In this case, the abundances of the polluting elements would decrease in the first dredge-up as stars turn on to the RGB. We present Keck/DEIMOS abundances of Ba in 66 stars along the entire RGB and the top of the main sequence. The Ba abundances have no trend with stellar luminosity (evolutionary phase). Therefore, the stars were born with the Ba that they have today, and Ba did not originate in a source with a delay time longer than the timescale for cluster formation. In particular, if the source of Ba was a NSM, it would have had a very short delay time. Alternatively, if Ba enrichment took place before the formation of the cluster, an inhomogeneity of a factor of 30 in Ba abundance needs to be able to persist over the length scale of the gas cloud that formed M15, which is unlikely