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Current developments and trends in quantum crystallography. [PDF]

Acta Crystallogr B Struct Sci Cryst Eng Mater
Krawczuk A, Genoni A.
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How many holes can locally linearly independent refinable function vectors have?

, 2017
Plonka-Hoch, Gerlind, Levesley, J., Anderson, I. J., Mason, J. C.   +3 more
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Multiwavelet Frames from Refinable Function Vectors

Advances in Computational Mathematics, 2003
A \(d\)-refinable function vector \(\phi = (\phi_1, \ldots, \phi_r)^T\) satisfies the refinement equation \[ \phi = | d| \sum_{k \in {\mathbb Z}} a_k \phi(d\cdot - k), \] where \(r\) is the multiplicity, \(d\) the dilation factor, and \(a\) is the finitely supported sequence of \(r\times r\) matrices.
Han, Bin, Mo, Qun
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Smoothness of refinable function vectors on ℝn

International Journal of Wavelets, Multiresolution and Information Processing, 2017
Let [Formula: see text] be a dilation matrix, an [Formula: see text] expansive matrix that maps [Formula: see text] into itself. Let [Formula: see text] be a finite subset of [Formula: see text] and for [Formula: see text] let [Formula: see text] be [Formula: see text] complex matrices.
Ramazan Tinaztepe, Denise Jacobs, Christopher Heil   +2 more
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Refinable Function Vectors

SIAM Journal on Mathematical Analysis, 1998
Dependence of properties of refinable function vectors on their refinement masks is studied. In particular, necessary and sufficient conditions for the convergence of cascade algorithms, for the stability and orthonormality of refinable vectors are found.
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Construction of refinable function vector via GTST

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xie, Changzhen, Yang, Shouzhi
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Analysis and Construction of Multivariate Interpolating Refinable Function Vectors

Acta Applicandae Mathematicae, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Bin, Zhuang, Xiaosheng
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Multivariate symmetric refinable functions and function vectors

International Journal of Wavelets, Multiresolution and Information Processing, 2016
For any symmetry group [Formula: see text], any appropriate matrix dilation (compatible with [Formula: see text]) and any appropriate symmetry center [Formula: see text] we give an explicit method for the construction of [Formula: see text]-symmetric with respect to the center [Formula: see text] refinable masks which have sum rule of an arbitrary ...
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Local linear independence of refinable vectors of functions

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions is said to be refinable if it satisfies the vector refinement equation where a is a finitely supported sequence of r × r matrices called the refinement mask. A complete characterization for the local linear independence of the shifts
Goodman, T. N. T., Jia, R.-Q., Zhou, D.-X.   +2 more
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Multivariate Balanced Vector-Valued Refinable Functions

2003
Vanishing moments of sufficiently high order and compact supports of reasonable size contribute to the great success of wavelets in various areas of applications, particularly in signal and image processing. However, for multi—wavelets, polynomial preservation of the refinable function vectors does not necessarily imply annihilation of discrete ...
Charles K. Chui, Qingtang Jiang
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