The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

By making use of a suite of programs for designing profile geometry, cutter geometry and predicting the thermodynamic performance of a twin screw compressor, this paper investigates techniques of obtaining an optimised rotor cutter blade design. The techniques for using different geometric schemes for setting clearances are explained, and the techniques for optimising main manufacturing paramet...

In this paper, we define and study generalizations of expansiveness, namely n- $$\aleph _0$$ -expansiveness, continuum-wise expansive meagre expansiveness for non-autonomous discrete dynamical systems. We discuss various properties such systems give necessary examples. prove results related to non-existence -expansive system on certain spaces. also relation between meagre-expansive

Expansive soils have high compressibility, swelling, and shrinkage properties. So we need an effective method to improve soil conditions when the structure is built on it. This paper presents results of research effect substitution ceramic waste physical properties expansive soil. Soil improvement using construction will contribute reducing amount conserving natural resources. The stages includ...

It is shown that for any expansive, integer valued 2×2 matrix, there exists a (multi-)wavelet whose Fourier transform is compactly supported and smooth. A key step is showing that for almost every equivalence class of integrally similar matrices there is a representative A which is strictly expansive in the sense that there is a compact set K which tiles the plane by integer translations and su...

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...

In this survey, we review some old and new results initiated with the study of expansive mappings. From a variational perspective, convergence analysis almost-expansive curves sequences governed by an evolution equation monotone or non-monotone type. Finally, propose two well-defined algorithms to remedy shortcomings concerning ill-posedness expansive-type systems.

A general framework for investigating topological actions of Z d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R d. Here we completely describe this expansive behavior for the class of algebraic Z d-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an alg...