Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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01 May 1993
TL;DR: In this paper, a wavelet method for the multiresolution representation of parametric curves and surfaces was developed, and a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions was constructed.
Abstract: We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used filters. We also give examples of the applications of the wavelet approach: these include the derivation of compact hierarchical curve and surface representations using modified wavelet compression, identifying smooth sections of surfaces and a subdivision-like intersection algorithm for discrete plane curves.
6 citations
TL;DR: In this article, the authors discuss some facts on generalized Gibbs states and their related KMS-like conditions and propose some extended versions of the Heisenberg algebraic dynamics, deducing some of their properties that are useful for our purposes.
Abstract: Motivated by the growing interest in PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended versions of the Heisenberg algebraic dynamics, deducing some of their properties that are useful for our purposes.
6 citations
TL;DR: In this article, a biorthogonal series expansion and a numerical finite difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques.
Abstract: A biorthogonal series expansion and a numerical finite-difference approximation are applied to the problem of steady Stokes flow in a driven sector of 10° total angle, providing mutual support of the theoretical techniques. For this problem the method of biorthogonal series is faster, cheaper, and more accurate.
6 citations
TL;DR: In this article, the authors considered the Schrodinger operator with integrable potential and analyzed the convergence rate of the biorthogonal expansion of an absolutely continuous function in the root functions of this operator with its Fourier trigonometric series.
Abstract: We consider the one-dimensional Schrodinger operator with integrable potential. We analyze the rate of the uniform equiconvergence of the biorthogonal expansion of an absolutely continuous function in the root functions of this operator with its Fourier trigonometric series on a compact set. For this convergence rate, we obtain an estimate depending on the modulus of continuity of the potential. We extract subclasses of absolutely continuous functions on which these estimates can be improved.
6 citations
01 Nov 2011
TL;DR: The result showed the effect of wavelets proprieties on classification process and the Symelt wavelets are the optimum wavelets for the face classification with four levels.
Abstract: The selection of appropriate wavelets is an important target for any application In this paper, wavelets functions are examined in order to choose the best wavelet for face classification process and for finding the optimal number of levels of decomposition Seven wavelet functions namely Symelt, Daubechig, Coiflets, Mayer Discrete, Biorthogonal, Reverse Biorthogonal and Haar were tested with different number of decomposition levels and different number of biggest coefficients is selected to reduce the huge feature dimension, and then the Euclidean Distance Method (EDM) was used for classification process Also a statistical method has been proposed to produce new metric of features coefficients, the experiments brought about 40% improvements in comparison to the method that accounts the biggest coefficients from the four levels of decompositions The experiments have been performed on Olivetti Research Laboratory database (ORL) and Yale University database (YALE) The result showed the effect of wavelets proprieties on classification process and the Symelt wavelets are the optimum wavelets for the face classification with four levels
6 citations