By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of 1 n Kn.x; x/ for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials. We then show that these hypotheses are always valid for erg...

A general construction for σ−finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of fn ∗ (λ) will imply the existence of a σ−finite invariant measure for the map f which is absolutely continuous with respect to λ, a measure on the phase space describing the sets of measure zero. Furthermore we will...

In 2004, Rodr'{i}guez-Lallena and '{U}beda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and '{U}beda-Flores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized Rodr'{i}guez-Lallena and '{U}beda-Flores' study to any given copula family. But ther...

We study fluctuations of the error term for number integer lattice points lying inside a three-dimensional Cygan–Korányi ball large radius. prove that term, suitably normalized, has limiting value distribution which is absolutely continuous, and we provide estimates decay rate corresponding density on real line. In addition, establish existence all moments normalized these are given by density.

A distribution function F(x) is said to be unimodal [l, p. 157] if there exists at least one value x = a such that F(x) is convex for xa. The point x = a is called the vertex of the distribution. In particular, if F(x) is absolutely continuous, then the corresponding probability density function p(x) = F'{x) is nondecreasing for xa. In the present...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

For applications in spatial statistics, an important property of a random set X in R k is its rst contact distribution. This is the distribution of the distance from a xed point 0 to the nearest point of X, where distance is measured using scalar dilations of a xed test set B. We show that, if B is convex and contains a neighbourhood of 0, the rst contact distribution function F B is absolutely...

The problem of eliminating the statistical fluctuations and extracting the event dynamics from event-by-event analysis is discussed. New moments Gp (for continuous distribution), and Gq,p (for anomalous distribution) are proposed, which are experimentally measurable and can eliminate the Poissonian type statistical fluctuations to recover the dynamical moments Cp and Cq,p. In this way, the dyna...

Transitions in behaviour across a continuous distribution of organisms can provide valuable information on how variation in behaviour is maintained. We used analyses developed for interspecific hybrid zones to examine geographic variation in colony founding strategy in the desert seed-harvester ant, Messor pergandei. Newly mated females initiate new colonies either alone (haplometrosis) or coop...

The monophthongization of /ay/ in the Southern United States is disfavored by following voiceless consonants (PRICE) relative to voiced or word-final environments (PRIZE). If monophthongization is the trigger for the Southern Shift (Labov, 2010) and chain shifts operate as predicted by a modular feedforward phonological theory (cf. Bermúdez-Otero, 2007), this implies PRICE and PRIZE must be two...