Related papers: Groupoid Methods in Wavelet Analysis
We give a detailed description of the local commutant approach to wavelet theory using operator algebraic methods. We include a new result on interpolation pairs of wavelet sets: Every pair in the generalized Journe family of wavelet sets…
Groupoids graded by the groupoid of bijections between finite sets admit generating functions which encode the groupoid cardinalities of their graded components. As suggested in the work of Baez and Dolan, we use analytic continuation of…
We use the idea of partial Gauss decomposition to study structures related to $U_q(\widehat{{{\frak{gl}}}(n-1)})$ inside $U_q(\widehat{{{\frak{gl}}}(n)}) $. This gives a description of $U_q(\widehat{{{\frak{gl}}}(n)})$ as an extension of…
We present natural and general ways of building Lie groupoids, by using the classical procedures of blowups and of deformations to the normal cone. Our constructions are seen to recover many known ones involved in index theory. The…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this…
p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems
We use the DPW method to obtain the associate family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential.
We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
We introduce and study knotoids. Knotoids are represented by diagrams in a surface which differ from the usual knot diagrams in that the underlying curve is a segment rather than a circle. Knotoid diagrams are considered up to Reidemeister…
We introduce wavelets, curvelets and multiresolution analysis techniques to assess the symmetry of X ray driven imploding shells in ICF targets. After denoising X ray backlighting produced images, we determine the Shell Thickness Averaged…
The investigation into the scattering of plane waves by a periodic array of parallel cylinders utilizes the method of cylindrical wave decomposition, thereby reducing the problem complexity to a series of linear algebraic equations. This…
A detailed simple model is applied to study a metallic cluster. It is assumed that the ions and delocalized electrons are distributed randomly throughout the cluster. The delocalized electrons are assumed to be degenerate. A spherical ball…
Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots.
Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is…
In these lecture notes we present connections between the theory of iterated function systems, in particular those attractors that are graphs of multivariate real-valued fractal functions, foldable figures and affine Weyl groups, and…
A new method for the study of resonant behavior - using wave-packet dynamics - is presented, based on the powerful window operator technique. The method is illustrated and quantified by application to the astrophysically-important example…