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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 +3 more
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On the power and promise of resonant diffraction for powders [PDF]
Structural DynamicsSignificantly 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
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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 +2 more
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Fractal and Fractional, 2023 The Caputo fractional α-derivative ...
Gopalakrishnan Karnan, Chien-Chang Yen
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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
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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
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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.
Dubickas, Artūras, Xu, Zhiqiang
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Approximation by crystal-refinable functions [PDF]
Geometriae Dedicata, 2019 Let $ $ be a crystal group in $\mathbb R^d$. A function $ :\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $ -$refinable) if it is a linear combination of finitely many of the rescaled and translated functions $ ( ^{-1}(ax))$, where the {\em translations} $ $ are taken on a crystal group $ $, and $a$ is an ...
Ursula Molter +2 more
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Totally positive refinable functions with general dilation M [PDF]
, 2017 We construct a new class of approximating functions that are M-refinable and provide shape preserving approximations. The refinable functions in the class are smooth, compactly supported, centrally symmetric and totally positive.
GORI, Laura, PITOLLI, Francesca
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Bell-shaped nonstationary refinable ripplets [PDF]
, 2015 We study the approximation properties of the class of nonstationary refinable ripplets introduced in \cite{GP08}. These functions are solution of an infinite set of nonstationary refinable equations and are defined through sequences of scaling masks that
Pitolli, Francesca
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