Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for subject:(decimation method). Showing records 1 – 2 of 2 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Lal, Nishu. Spectral Zeta Functions of Laplacians on Self-Similar Fractals.

Degree: Mathematics, 2012, University of California – Riverside

This thesis investigates the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar Sturm – Liouville operator associated with a fractal self-similar measure on the half-line. In the latter case, C. Sabot discovered the relation between the spectrum of this operator and the iteration of a rational map of several complex variables, called the renormalization map. We obtain a factorization of the spectral zeta function of such an operator, expressed in terms of the Dirac delta hyperfunction, a geometric zeta function, and the zeta function associated with the dynamics of the corresponding renormalization map, viewed either as a polynomial function on the complex plane (in the first case) or (in the second case) as a polynomial on the complex projective plane. Our first main result extends to the case of the fractal Laplacian on the unbounded Sierpinski gasket a factorization formula obtained by M. Lapidus for the spectral zeta function of a fractal string and later extended by A. Teplyaev to the bounded (i.e., finite) Sierpinski gasket and some other decimable fractals. Furthermore, our second main result generalizes these factorization formulas to the renormalization maps of several complex variables associated with fractal Sturm – Liouville operators. Moreover, as a corollary, in the very special case when the underlying self-similar measure is Lebesgue measure on [0, 1], we obtain a representation of the Riemann zeta function in terms of the dynamics of a certain polynomial on the complex projective plane, thereby extending to several variables an analogous result by A. Teplyaev.

Subjects/Keywords: Mathematics; Analysis on fractals; decimation method; Dirac delta hyperfunction; fractal Sturm-Liouville operators; multivariable complex dynamics; spectral zeta functions

…2.2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Decimation Method… …the eigenvalue equation −∆µ u = λu, and discovered the decimation method which establishes… …the harmonic extension. 2.3 The Decimation Method We have seen in the above section that… …fractals are defined similarly via a suitable approximation. The decimation method is a process… …m−1 via the decimation method and the remaining eigenvalues are called the initial… 

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lal, N. (2012). Spectral Zeta Functions of Laplacians on Self-Similar Fractals. (Thesis). University of California – Riverside. Retrieved from http://www.escholarship.org/uc/item/888903d2

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Thesis, University of California – Riverside. Accessed January 23, 2021. http://www.escholarship.org/uc/item/888903d2.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Web. 23 Jan 2021.

Vancouver:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Internet] [Thesis]. University of California – Riverside; 2012. [cited 2021 Jan 23]. Available from: http://www.escholarship.org/uc/item/888903d2.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Thesis]. University of California – Riverside; 2012. Available from: http://www.escholarship.org/uc/item/888903d2

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Scipioni, Angel. Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets.

Degree: Docteur es, Systèmes électroniques, 2010, Université Henri Poincaré – Nancy I

La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore

The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that…

Advisors/Committee Members: Schweitzer, Patrick (thesis director).

Subjects/Keywords: Ondelettes; Principe d'incertitude de Heisenberg; Pavage temps-Fréquence; Moments; Régularité; Support compact; Fonction d'échelle; Fonction d'ondelette; Approximations; Détails; Résolution; Filtre QMF; Coefficients de Daubechies; Analyse; Reconstruction; Précurseur; Algorithme de Mallat; Convolution; Décimation; Symétrisation; Orthogonalisation; Gram Schmidt; Filtres frontières; Complexité; Décomposition modale empirique; Méthode R/S; Analyse des fluctuations redressées; Fractal; Auto-Similarité; Plasma; Bruit Gaussien fractionnaire; Mouvement Brownien fractionnaire; Ultrason; Wavelets; Heisenberg uncertainty principle; Time-Frequency tiles; Vanishing moments; Regularity; Compact support; Scaling function; Wavelet function; Approximations; Details; Resolution; QMF filters; Daubechies coefficients; Analysis; Reconstruction; Precursor; Mallat algorithm; Convolution; Decimation; Mirroring; Orthogonalization; Gram Schmidt; Boundary filters; Complexity; Empirical Modal Decomposition; R/S method; Detrended fluctuations Analysis; Fractal; Self-Similarity; Plasma; Fractional Gaussian noise; Fractional Brownian motion; Ultrasound; 530.44; 515.243 3

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Scipioni, A. (2010). Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets. (Doctoral Dissertation). Université Henri Poincaré – Nancy I. Retrieved from http://www.theses.fr/2010NAN10125

Chicago Manual of Style (16th Edition):

Scipioni, Angel. “Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets.” 2010. Doctoral Dissertation, Université Henri Poincaré – Nancy I. Accessed January 23, 2021. http://www.theses.fr/2010NAN10125.

MLA Handbook (7th Edition):

Scipioni, Angel. “Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets.” 2010. Web. 23 Jan 2021.

Vancouver:

Scipioni A. Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets. [Internet] [Doctoral dissertation]. Université Henri Poincaré – Nancy I; 2010. [cited 2021 Jan 23]. Available from: http://www.theses.fr/2010NAN10125.

Council of Science Editors:

Scipioni A. Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles : Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targets. [Doctoral Dissertation]. Université Henri Poincaré – Nancy I; 2010. Available from: http://www.theses.fr/2010NAN10125

.