Approximate Symmetries

Abstract

In polymeric, biological and other similar absorbers diffusion contributes significantly to the Mossbauer linewidths. A simple expression has been derived for the optimum thickness for such single-line absorbers. The optimum thickness yields a Mossbauer spectrum having the highest value of the ratio of the depth of spectrum to the statistical errors in background count, in a given experimental time.

On geometry of solutions to approximate equations and their symmetries

“…There are several approaches to the notion of approximate symmetry of a differential equation. In this work we base on that introduced in [1] and it was introduced in details by a series of authors (see, for instance, surveys [2], [3]). However, our approach differs a little from that employed by these authors and our approach is more geometric and is based on the notion of a manifold over the algebra of dual numbers.…”

“…We begin with preliminary ideas and definitions introduced and studied first in [1]. Assume that we have the equation ( , ) = 0, where is some smooth or even analytic function depending on a variable , which can be a vector one, = ( 1 , 2 .…”

“…This direction is initiated by paper [1] and then it was continued in many other works. The main aim of the present paper is not to study new examples or to calculate the symmetries for new equations, but to construct a geometric approach for studying these equations and symmetries and to develop the corresponding methodology.…”

Approximate Waiting-Time for a Thin Liquid Drop Spreading under Gravity

“…al. [1,2]. Another approach is that of finding approximate conditional symmetries admitted by the model equation as presented by Mahomed and Qu [13].…”

Approximate Symmetry Reduction Approach: Infinite Series Reductions to the KdV-Burgers Equation

“…The first method due to Baikov et al [7,8] generalizes symmetry group generators to perturbation forms. For the second method proposed by Fushchich and Shtelen [9], dependent variables are expanded in perturbation series and the approximate symmetry of the original equation is decomposed into an exact symmetry of the system resulted from the perturbation.…”