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Journal of Computational Physics, ISSN 0021-9991, 05/2017, Volume 337, pp. 42 - 61
In this paper, we present a fast time adaptive numerical method for interface tracking. The method uses an explicit multiresolution description of the... 
Adaptive methods | Interface tracking | Multiresolution analysis | Fast algorithms | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TRAVEL-TIME | REGULARITY | PHYSICS, MATHEMATICAL | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Methods | Numerical analysis | Usage | Algorithms
Journal Article
Sbornik: Mathematics, ISSN 1064-5616, 10/2006, Volume 197, Issue 9-10, pp. 1529 - 1558
For an arbitrary positive integer n refinable functions on the positive half-line, R+ are defined, with masks that are Walsh polynomials of order 2(n) - 1. The... 
MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
SIAM journal on mathematical analysis, ISSN 1095-7154, 1998, Volume 29, Issue 2, pp. 511 - 546
We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one... 
Wavelet | Second generation wavelet | Lifting scheme | Multiresolution | MULTIRESOLUTION ANALYSES | MATHEMATICS, APPLIED | COMPACTLY SUPPORTED WAVELETS | ORTHONORMAL BASES | SPACES | second generation wavelet | REPRESENTATION | DECOMPOSITION | lifting scheme | 2-SCALE DIFFERENCE-EQUATIONS | SPLINE WAVELETS | FILTER BANKS | wavelet | multiresolution | SCALING FUNCTIONS
Journal Article
Reviews of geophysics (1985), ISSN 8755-1209, 1997, Volume 35, Issue 4, pp. 385 - 412
Wavelet transforms originated in geophysics in the early 1980s for the analysis of seismic signals. Since then, significant mathematical advances in wavelet... 
GEOCHEMISTRY & GEOPHYSICS | FOREST CANOPY | TURBULENT COHERENT MOTIONS | MULTICOMPONENT DECOMPOSITION | FRACTIONAL BROWNIAN-MOTION | SAMPLING THEORY | SIGNAL ANALYSIS | REPRESENTATION | SPATIAL RAINFALL FIELDS | 2-SCALE DIFFERENCE-EQUATIONS | TRANSFORMS
Journal Article
Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 03/2008, Volume 20, Issue 3, pp. 639 - 657
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2014, Volume 287, Issue 5-6, pp. 546 - 560
It is known that there is no orthonormal wavelet belonging to C∞ and having exponential decay. In this paper, we shall construct new wavelets having Gevrey... 
subexponential decay | Wavelets | Gevrey class | 46E10 | 42C40 | Subexponential decay | MATHEMATICS | BAND-LIMITED WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
Applied and computational harmonic analysis, ISSN 1063-5203, 2003, Volume 15, Issue 2, pp. 89 - 116
We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this... 
MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
Numerische Mathematik, ISSN 0029-599X, 10/2014, Volume 128, Issue 2, pp. 339 - 375
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 09/2014, Volume 548, Issue C, pp. 25 - 53
Journal Article
Journal Article
International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, 01/2018, Volume 16, Issue 1
Journal Article
Constructive approximation, ISSN 1432-0940, 2004, Volume 20, Issue 3, pp. 399 - 463
A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction.... 
Wavelet | Subdivision | Normal mesh | Normal multiresolution | Lifting | Philosophy | MATHEMATICS | subdivision | normal mesh | normal multiresolution | REGULARITY | lifting | wavelet | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2013, Volume 438, Issue 5, pp. 2107 - 2126
Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with... 
Dilation equation | Asymptotic analysis | Radix-rational sequence | Rational formal power series | Joint spectral radius | Self-similarity | MATHEMATICS, APPLIED | REGULARITY | MATRICES | MELLIN TRANSFORMS | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Algebra | Algorithms | Operator Algebras | Mathematics | Computer Science | Discrete Mathematics
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 7, pp. 1845 - 1851
An algorithm for constructing a pair of biorthogonal two-direction refinable function and the corresponding biorthogonal two-direction wavelet is presented. In... 
Two-direction refinable function | Two-direction wavelet | Biorthogonal | Dilation factor | MATHEMATICS, APPLIED | two-direction refinable function | REGULARITY | two-direction wavelet | biorthogonal | dilation factor | 2-SCALE DIFFERENCE-EQUATIONS | Algorithms | Wavelet | Dilation | Construction | Mathematical models | Mathematical analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 207, Issue 1, pp. 83 - 89
The concept of general two-scale similarity transform (GTST) is introduced. By applying GTST, we present an algorithm of constructing a class of balanced... 
Balanced order | Refinable function vector | GTST | Symmetry | EXISTENCE | MATHEMATICS, APPLIED | DESIGN | MULTISCALING FUNCTIONS | MULTI-WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS | REGULARITY | APPROXIMATION ORDER | MULTIWAVELETS | Algorithms
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 2004, Volume 338, Issue 4, pp. 321 - 326
The goal of this Note is to present some theoretical results for the nonlinear multiscales representations concerning the smoothness characterization through... 
MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
Izvestiya: Mathematics, ISSN 1064-5632, 10/2006, Volume 70, Issue 5, pp. 975 - 1013
We introduce the notion of a summable fractal curve generated by a finite family of affine operators. This generalizes well-known notions of affine fractals... 
MATHEMATICS | REGULARITY | PRODUCTS | MATRICES | REFINEMENT EQUATIONS | JOINT SPECTRAL-RADIUS | SUBDIVISION SCHEMES | 2-SCALE DIFFERENCE-EQUATIONS
Journal Article
Energy Exploration & Exploitation, ISSN 0144-5987, 6/2012, Volume 30, Issue 3, pp. 417 - 433
Journal Article
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