The distribution of the absolute maximum of the discontinuous stationary random process with Raileigh and Gaussian components

The purpose of this research is to find the asymptotically exact expressions for the distribution function and for the probability that the absolute maximum of the sum of statistically independent homogeneous Gaussian and Rayleigh random processes with nondifferentiable covariance function will exceed the specified threshold. In this study, the applicability boundaries of the introduced theoretical formulas are also determined by means of statistical simulation. The recommendations are presented concerning the application of the obtained expressions depending on the observation interval length and the interrelation of Gaussian and Rayleigh components of the analyzed random process. © 2019, International Association of Engineers. All rights reserve

On Classification of QCD defects via holography

We discuss classification of defects of various codimensions within a holographic model of pure Yang-Mills theories or gauge theories with fundamental matter. We focus on their role below and above the phase transition point as well as their weights in the partition function. The general result is that objects which are stable and heavy in one phase are becoming very light (tensionless) in the other phase. We argue that the $\theta$ dependence of the partition function drastically changes at the phase transition point, and therefore it correlates with stability properties of configurations. Some possible applications for study the QCD vacuum properties above and below phase transition are also discussed.Comment: 21 pages, 2 figure

DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT

Consider the Cauchy problem for the Korteweg-de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. Numerical and analytical methods show that the obtained using renormalization formal asymptotics, corresponding to rarefaction waves, is an asymptotic solution of the KdV equation. The graphs of the asymptotic solutions are represented, including the case of non-monotonic initial data

Estimating the parameters of the Sgr A* black hole

The measurement of relativistic effects around the galactic center may allow in the near future to strongly constrain the parameters of the supermassive black hole likely present at the galactic center (Sgr A*). As a by-product of these measurements it would be possible to severely constrain, in addition, also the parameters of the mass-density distributions of both the innermost star cluster and the dark matter clump around the galactic center.Comment: Accepted for publication on General Relativity and Gravitation, 2010. 11 Pages, 1 Figur