Let K ⊂ R be a self-similar or self-affine set, let μ be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R. Under various assumptions (such as separation conditions or we assume that the transformations are small perturbations or that K is a so called Sierpiński sponge) we prove theorems of the following types, which...

We give a self–contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framewor...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

The interaction between the Earth’s magnetic field and the solar wind plasma results in a natural plasma confinement system which stores energy. Dissipation of this energy through Joule heating in the ionosphere can be studied via the Auroral Electrojet (AE) index. The apparent broken power law form of the frequency spectrum of this index has motivated investigation of whether it can be describ...

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...

All image processing applications of the self-affine mapping system (SAMS) were developed based on the attraction and repellence behaviours. In this paper, we provide some analytical justifications for these properties. Besides, it is shown that the cost function of SAMS sometimes have multiple equivalent solutions which may produce ambiguity. We improve the cost function of self-affine snake a...