The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the correlation links between signal irregularities and formulated for continuous signals, is discussed. It is shown that the mathematical notions of Dirac δ and Heavisi...

With the goal of maximizing thermoelectric (TE) figure merit $ZT$, Mahan and Sofo [Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] found that optimal transport distribution (TD) is a delta function. Materials, however, have TDs appear to always be finite non-diverging. Motivated by this observation, study focuses on deriving what bounded TD, which determined boxcar function for $ZT$ Heaviside po...

In the sense of distributions, derivative Heaviside unit step function $H(t)$ is a generalized Dirac-$\delta$ distribution. If velocity $V(t)$ flat plate impulsive, as $V(t)=H(t)$ (i.e., it suddenly set into motion with at $t=0^+$), then its acceleration $V'(t)=\delta(t)$. The distribution has no point values. However, when forcing term an ODE (in $t$), contributes to solution. recently publish...

We consider a model of stochastically interacting particles on 2~, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate 7/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this ...

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V]=(1/T)integral(T)(0)dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T-->infinity at fixed r we obtain P(r,T) approximately exp[-theta(r)T], where theta(r) is a large-deviatio...

Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundame...