On the Poisson Process of Order k Space

2010 Mathematics Subject Classification: 60E05, 62P05.

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Transient distributions of composition and temperature in a gas-solid packed bed reactor by near-infrared tomography

Near-infrared diffuse tomography was used in order to observe dynamic behaviour of flowing gases by measuring the 3D distributions of composition and temperature in a weakly scattering packed bed reactor, subject to wall effects and non-isothermal conditions. The technique was applied to the vapour phase hydrogen isotopic exchange reaction in a hydrophobic packing of low aspect ratio made of platinum on styrene divinyl benzene sulphonate copolymer resin. The results of tomography revealed uneven temperature and composition maps of water and deuterated water vapours in the core-packed bed and in the vicinity of the wall owing to flow maldistribution. The dynamic lag between the near-wall water vapour and deuterated water vapour compositions were observed suggesting that the convective transfer which was significant near the wall at the start, owing to high porosity, was also effective at large conversions. (C) 2012 Elsevier B.V. All rights reserved.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Probability distributions of number of children and maternal age at various order births using age-specific fertility rates by birth order

In this study, a simple analytical framework to find the probability distributions of number of children and maternal age at various order births by making use of data on age-specific fertility rates by birth order was proposed. The proposed framework is applicable to both the period and cohort fertility schedules. The most appealing point of the proposed framework is that it does not require stringent assumptions. The proposed framework has been applied to the cohort birth order-specific fertility schedules of India and its different regions and period birth order-specific fertility schedules, including the United States of America, Russia, and the Netherlands, to demonstrate its usefulness.

Measurement of the K + - pi + pi - e + - (-) v e form factors and of the pi pi scattering length a 0 0

The quark condensate is a fundamental free parameter of Chiral Perturbation Theory ($chi PT$), since it determines the relative size of the mass and momentum terms in the power expansion. In order to confirm or contradict the assumption of a large quark condensate, on which $chi PT$ is based, experimental tests are needed. In particular, the $S$-wave $pipi$ scattering lengths $a_0^0$ and $a_0^2$ can be predicted precisely within $chi PT$ as a function of this parameter and can be measured very cleanly in the decay $K^{pm} to pi^{+} pi^{-} e^{pm} stackrel{mbox{tiny(---)}}{nu_e}$ ($K_{e4}$). About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were analysed and 342,859 $K_{e4}$ candidates were selected. The background contamination in the sample could be reduced down to 0.3% and it could be estimated directly from the data, by selecting events with the same signature as $K_{e4}$, but requiring for the electron the opposite charge with respect to the kaon, the so-called ``wrong sign'' events. This is a clean background sample, since the kaon decay with $Delta S=-Delta Q$, that would be the only source of signal, can only take place through two weak decays and is therefore strongly suppressed. The Cabibbo-Maksymowicz variables, used to describe the kinematics of the decay, were computed under the assumption of a fixed kaon momentum of 60 GeV/$c$ along the $z$ axis, so that the neutrino momentum could be obtained without ambiguity. The measurement of the form factors and of the $pipi$ scattering length $a_0^0$ was performed in a single step by comparing the five-dimensional distributions of data and MC in the kinematic variables. The MC distributions were corrected in order to properly take into account the trigger and selection efficiencies of the data and the background contamination. The following parameter values were obtained from a binned maximum likelihood fit, where $a_0^2$ was expressed as a function of $a_0^0$ according to the prediction of chiral perturbation theory: f'_s/f_s = 0.133+- 0.013(stat)+- 0.026(syst) f''_s/f_s = -0.041+- 0.013(stat)+- 0.020(syst) f_e/f_s = 0.221+- 0.051(stat)+- 0.105(syst) f'_e/f_s = -0.459+- 0.170(stat)+- 0.316(syst) tilde{f_p}/f_s = -0.112+- 0.013(stat)+- 0.023(syst) g_p/f_s = 0.892+- 0.012(stat)+- 0.025(syst) g'_p/f_s = 0.114+- 0.015(stat)+- 0.022(syst) h_p/f_s = -0.380+- 0.028(stat)+- 0.050(syst) a_0^0 = 0.246+- 0.009(stat)+- 0.012(syst)}+- 0.002(theor), where the statistical uncertainty only includes the effect of the data statistics and the theoretical uncertainty is due to the width of the allowed band for $a_0^2$.

Global distributions of diatoms abundance, biovolume and biomass - Gridded data product (NetCDF) - Contribution to the MAREDAT World Ocean Atlas of Plankton Functional Types

This study is a first effort to compile the largest possible body of data available from different plankton databases as well as from individual published or unpublished datasets regarding diatom distribution in the world ocean. The data obtained originate from time series studies as well as spatial studies. This effort is supported by the Marine Ecosystem Data (MAREDAT) project, which aims at building consistent data sets for the main PFTs (Plankton Functional Types) in order to help validate biogeochemical ocean models by using converted C biomass from abundance data. Diatom abundance data were obtained from various research programs with the associated geolocation and date of collection, as well as with a taxonomic information ranging from group down to species. Minimum, maximum and average cell size information were mined from the literature for each taxonomic entry, and all abundance data were subsequently converted to biovolume and C biomass using the same methodology.

Catalogue of nineteen books of the highest importance, from the library of the late Earl of Carysfort, K.P., sold by order of the owner, Col. D.J. Proby, and with the consent of the trustees and of the court.

The collection was sold at auction by Sotheby, Wilkinson & Hodge, July, 1923.

Dispersal and seasonal distributions of black-faced impala in the Etosha National Park, Namibia

Factors affecting the seasonal distribution of the vulnerable black-faced impala at Etosha National Park, Namibia and the spread of the impala in the park since their translocation there in the 1970s were studied in the hot dry season of 2000 and the wet season of 2001 in order to provide information for future translocations of this antelope. In the 30 years since their release in the park, black-faced impala appear to have dispersed a maximum of 31.5 km from their initial release sites, effectively forming five subpopulations based on their five initial release sites. The mean minimum distance that impala had dispersed between water holes since their release was 7.11 +/- 1.47 km. Black-faced impala concentrated strongly around water holes; more than 50% were within 1 km of water holes in both seasons. Changes in population densities in different habitats may have resulted from seasonal movements of impala between adjacent habitats. The role of initial release sites in determining the distribution of threatened species such as the black-faced impala is discussed in light of its importance for future translocations.

Distributions of lesser mealworm (Coleoptera: Tenebrionidae) in litter of a compacted earth floor broiler house in subtropical Queensland, Australia

Distributions of lesser mealworm, Alphitobius diaperinus (Panzer) (Coleoptera: Tenebrionidae), in litter of a compacted earth floor broiler house in southeastern Queensland, Australia, were studied over two flocks. Larvae were the predominant stage recorded. Significantly low densities occurred in open locations and under drinker cups where chickens had complete access, whereas high densities were found under feed pans and along house edges where chicken access was restricted. For each flock, lesser mealworm numbers increased at all locations over the first 14 d, especially under feed pans and along house edges, peaking at 26 d and then declining over the final 28 d. A life stage profile per flock was devised that consisted of the following: beetles emerge from the earth floor at the beginning of each flock, and females lay eggs, producing larvae that peak in numbers at 3 wk; after a further 3 to 4 wk, larvae leave litter to pupate in the earth floor, and beetles then emerge by the end of the flock time. Removing old litter from the brooder section at the end of a flock did not greatly reduce mealworm numbers over the subsequent flock, but it seemed to prevent numbers increasing, while an increase in numbers in the grow-out section was recorded after reusing litter. Areas under feed pans and along house edges accounted for 5% of the total house area, but approximately half the estimated total number of lesser mealworms in the broiler house occurred in these locations. The results of this study will be used to determine optimal deployment of site-specific treatments for lesser mealworm control.

Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV

Measurements of inclusive charged-hadron transverse-momentum and pseudorapidity distributions are presented for proton-proton collisions at sqrt(s) = 0.9 and 2.36 TeV. The data were collected with the CMS detector during the LHC commissioning in December 2009. For non-single-diffractive interactions, the average charged-hadron transverse momentum is measured to be 0.46 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 0.9 TeV and 0.50 +/- 0.01 (stat.) +/- 0.01 (syst.) GeV/c at 2.36 TeV, for pseudorapidities between -2.4 and +2.4. At these energies, the measured pseudorapidity densities in the central region, dN(charged)/d(eta) for |eta|

Quantitative structural refinement of mn K edge XANES in LaMnO3 and CaMnO3 perovskites

The special magnetotransport properties of hole doped manganese perovskites originate from a complex interplay among structural, magnetic and electronic degree of freedom. In this picture the local atomic structure around Mn ions plays a special role and this is the reason why short range order techniques like X-ray absorption spectroscopy (XAS) have been deeply exploited for studying these compounds. The analysis of near edge region features (XANES) of XAS spectra can provide very fine details of the local structure around Mn, complementary to the EXAFS, so contributing to the full understanding of the peculiar physical properties of these materials. Nevertheless the XANES analysis is complicated by the large amount of structural and electronic details involved making difficult the quantitative interpretation.This work exploits the recently developed MXAN code to achieve a full structural refinement of the Mn K edge XANES of LaMnO3 and CaMnO3 compounds; they are the end compounds of the doped manganite series LaxCa1-xMnO3, in which the Mn ions are present only in one charge state as Mn3+ and Mn4+ respectively. The good agreement between the results derived from the analysis of near edge and extended region of the XAS spectra demonstrates that a quantitative picture of the local structure call be obtained from structural refinement of Mn K edge XANES data in these crystalline compounds. The XANES analysis offers, in addition.. the possibility to directly achieve information on the topology of local atomic structure around the absorber not directly achievable from EXAFS.