We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self tim...

Some work has been done in the past on the estimation of reliability characteristics of Rayleigh distribution based on complete and censored samples. But, traditionally it is assumed that the available data are performed in exact numbers. However, in real world situations, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to ...

A five-parameter distribution called Beta Generalized Weibull (BGW) distribution is introduced. Beta Generalized Exponential (BGE), Beta Weibull (BW), Generalized or Exponentiated Weibull (GW or EW), Generalized Rayleigh (GR), Beta Exponential (BE), Generalized Exponential (GE), Weibull, Rayleigh and Exponential are its sub models. The cumulative distribution function (cdf) and the probability ...

In this paper, we present novel closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of ratio of random variable and product of two random variables for the cases where random variables are Rayleigh, Weibull, Nakagami-m and α-μ distributed. An application of obtained results in performance analysis of multi-hop wireless communication syst...

Steady natural convection flow in an inclined square cavity filled with a porous medium has been investigated. It is assumed that the cavity is heated on one wall and cooled from an adjacent wall, while the other two walls are adiabatic. The governing dimensionless partial differential equations have been solved numerically for the stream function, isotherms, and the local and average Nusselt n...

We model buoyancy-driven convection with chimneys – channels of zero solid fraction – in a mushy layer formed during directional solidification of a binary alloy in two dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chi...

Non-Gaussian distributions occur in systems that do not follow strictly the prescriptions of standard statistics. Important example of non-Gaussian statistics is distribution which was introduced by Lord Rayleigh in connection with the problem of interference of harmonic oscillations with random phases [1, 2]. This distribution is known also as Wigner's surmise distribution giving a remarkably ...

We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning recovery of Lamé parameters in slab beneath traction-free surface. employ Markushevich substitution, while data are captured Jost function, and we point out parallels corresponding for Schrödinger equation. The function can be identified spectral data. derive Gel’fand-Levitan ...

This paper deals with the Sum-Of-Sinusoids (SOS)-based simulation method for generating timecorrelated Rayleigh fading processes. Five of the most accepted and recently proposed SOS-based Rayleigh fading models have been analyzed and compared. We have used the mean and the maximum power margin quality measures to assess the accuracy of the autocorrelation function (ACF) of the generated process...