Self‐organized criticality of cellular automata model; absorbtion in finite‐time of supercritical region into the critical one

In this work, it is studied the evolution and time behavior of solutions to nonlinear diffusion equation in where , d ≥ 1, and H is the Heaviside function. For d = 1,2,3, this equation describes the dynamics of self‐organizing sandpile process with critical state ρ_c. The main conclusion is that the supercritical region is absorbed in a finite‐time in the critical region . Copyright © 2013 John Wiley & Sons, Ltd.     

A PDE approach to image restoration problem with observation on a meager domain

We present here a new nonlinear PDE approach to image restoration (the inpainting problem) using a meager blurred image or a finite number of observation points. To this end, one uses a least square approach with the H⁻¹ distributional metric. Some important theoretical and numerical results are provided in this paper.     

An extension of coherent sheaves defined outside holomorphically convex compact sets

We show that a coherent analytic sheaf ${\mathcal F}$ with prof ${{\mathcal F}\geq 2}$ defined outside a holomorphically convex compact set K in a 1-convex space X admits a coherent extension to the whole space X if, and only if, the canonical topology on ${H^1(X \setminus K,{\mathcal F})}$ is separated.     

Exergy of nuclear radiation — a quantum statistical thermodynamics approach

The exergy of nuclear radiation is evaluated by using a simple quantum statistical thermodynamic approach. Only radiation particles with non-zero rest mass are considered (i.e. protons, neutrons, alpha and beta particles). The exergy and the exergy flux involve efficiency-like factors affecting the internal energy and the energy flux, respectively. These factors are generally different from both the usual Carnot factor and the Petela-Landsberg-Press factor that appears in the exergy of blackbody radiation. The efficiency-like factors are higher in the case of charged rather than neutral particles and in the case of enclosed rather than free radiation. The results are compared with those obtained previously by using a classical thermodynamic theory.      

A method constructing density functions: The case of a generalized Rayleigh variable

In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 25 (1989), pp. 209–215) namely, if X is a positive continuous random variable with a finite mean-value E(X), then a new density is set to be f ₁(x) = xf(x)/E(X), where f(x) is the probability density function of X. The new generalized Rayleigh variable is obtained using a generalized form of the exponential distribution introduced by Isaic-Maniu and the present author as f(x).     

Stochastic wave equations with dissipative damping

We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping.