0 i 1 LINEAR SCALE - SPACE I : BASIC THEORY 1

Linear Scale - Space I : Basic Theory 1

Sample Path Regularity for One-Dimensional for Diffusion Processes

1. Basic Assumptions. Assume that (i) {Tt} is a strongly-continuous semigroup of bounded linear operators on the Banach space B = C0(I) = { f continuous on I = [0, 1] : f(0) = f(1) = 0 } (ii) If f(x) ≥ 0 and f ∈ B, then Ttf(x) ≥ 0 and Ttf(x) ≤ maxy∈I f(y). In general, the infinitesimal generator of a strongly-continuuous semigroup of linear operators Tt on any Banach space B is defined by Af = ...

Sample Path Regularity for One-Dimensional Diffusion Processes

1. Basic Assumptions. Assume that (i) {Tt} is a strongly-continuous semigroup of bounded linear operators on the Banach space B = C0(I) = { f continuous on I = [0, 1] : f(0) = f(1) = 0 } (ii) If f(x) ≥ 0 and f ∈ B, then Ttf(x) ≥ 0 and Ttf(x) ≤ maxy∈I f(y). In general, the infinitesimal generator of a strongly-continuuous semigroup of linear operators Tt on any Banach space B is defined by Af = ...

A physics-free introduction to quantum error correcting codes

Research in the field of quantum algorithms and quantum error correction is progressing at an astounding rate. There are many good papers on both subjects, but reading even a few of these may seem a daunting task to the newcomer. The aim of this paper is to give a leisurely introduction to the basic theory of quantum error correcting codes without appealing to even the most basic notions in phy...

On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity

A general model of the equations of generalized thermoelasticity   for an infinite space weakened by a finite linear opening Mode-I crack is solving. The material is   homogeneous and has isotropic properties of elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, the Lord-Şhulman...