Results 1 to 10 of about 361 (122)

Refining perovskite structures to pair distribution function data using collective Glazer modes as a basis [PDF]

IUCrJ, 2022
Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the ...
Sandra Helen Skjærvø, Martin A. Karlsen, Riccardo Comin, Simon J. L. Billinge   +3 more
doaj   +2 more sources

On the power and promise of resonant diffraction for powders [PDF]

Structural Dynamics
Significantly more information is available if X-ray scattering and spectroscopic techniques are combined. In crystallography, structural information is encoded in the intensity of Bragg peaks, with the complex scattering power of each atom given by f(Q ...
Kevin H. Stone, Sikhumbuzo M. Masina
doaj   +2 more sources

The Sobolev Regularity of Refinable Functions

Journal of Approximation Theory, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amos Ron, Zuowei Shen
exaly   +2 more sources

Orthogonality criteria for compactly supported refinable functions and refinable function vectors

Journal of Fourier Analysis and Applications, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jeffrey Lagarias
exaly   +3 more sources

On the Exact Evaluation of Integrals of Wavelets

Mathematics, 2023
Wavelet expansions are a powerful tool for constructing adaptive approximations. For this reason, they find applications in a variety of fields, from signal processing to approximation theory.
Enza Pellegrino, Chiara Sorgentone, Francesca Pitolli   +2 more
doaj   +1 more source

Refinable Trapezoidal Method on Riemann–Stieltjes Integral and Caputo Fractional Derivatives for Non-Smooth Functions

Fractal and Fractional, 2023
The Caputo fractional α-derivative ...
Gopalakrishnan Karnan, Chien-Chang Yen
doaj   +1 more source

Biorthogonal Wavelet on a Logarithm Curve ℂ

Journal of Mathematics, 2021
According to the length-preserving projection and Euler discretization method, biorthogonal wavelet function on a smooth curve C is constructed in this paper, such as a logarithm curve.
Xiaohui Zhou, Gang Wang
doaj   +1 more source

A Brief Survey of the Graph Wavelet Frame

Complexity, 2022
In recent years, the research of wavelet frames on the graph has become a hot topic in harmonic analysis. In this paper, we mainly introduce the relevant knowledge of the wavelet frames on the graph, including relevant concepts, construction methods, and
Jie Zhou, Zeze Zhang
doaj   +1 more source

Refinement equations and spline functions [PDF]

Advances in Computational Mathematics, 2008
In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution of powers of a fixed number modulo 1, and show the nonexistence of a non-trivial {\bf C}^{\infty} solution of the refinement equation with non-integer dilations.
Arturas Dubickas, Zhiqiang Xu 0001
openaire   +3 more sources

Approximation by crystal-refinable functions [PDF]

Geometriae Dedicata, 2019
Let $Γ$ be a crystal group in $\mathbb R^d$. A function $φ:\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $Γ-$refinable) if it is a linear combination of finitely many of the rescaled and translated functions $φ(γ^{-1}(ax))$, where the {\em translations} $γ$ are taken on a crystal group $Γ$, and $a$ is an expansive ...
Ursula Molter, María del Carmen Moure, Alejandro Quintero   +2 more
openaire   +4 more sources