Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Il teorema di Chebyshev

Dopo aver introdotto alcune nozioni della teoria della probabilità, ho esposto il teorema di Chebyshev ed alcuni teoremi ad esso collegati. Ho infine analizzato un'applicazione legata alle strategie d'investimento.

Orthogonality relations for Chebyshev polynomials,

"C00-1469-0154."

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Polynômes de Kazhdan-Lusztig et cohomologie d'intersection des variétés de drapeaux

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Polynômes de Kazhdan-Lusztig et cohomologie d'intersection des variétés de drapeaux

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Étude du nombre de polynômes irréductibles dans les corps finis avec certaines contraintes imposées aux coefficients

L'objectif de ce mémoire est de dénombrer les polynômes irréductibles unitaires sur un corps fini en prescrivant des contraintes sur les coefficients. Dans les prochaines pages, il sera question de fixer simplement des coefficients, ou simplement de fixer leur signe, leur cubicité ou leur quarticité.

Étude du nombre de polynômes irréductibles dans les corps finis avec certaines contraintes imposées aux coefficients

L'objectif de ce mémoire est de dénombrer les polynômes irréductibles unitaires sur un corps fini en prescrivant des contraintes sur les coefficients. Dans les prochaines pages, il sera question de fixer simplement des coefficients, ou simplement de fixer leur signe, leur cubicité ou leur quarticité.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Future directions in this field are also discussed.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Metodología de diseño de filtros CRF/SCF basada en modelos de resonadores BAW acoplados acústicamente

La creixent utilització de sistemes de comunicacions mòbils ha impulsat la demanda de filtres passabanda miniaturitzats d'elevades prestacions operant en el rang de freqüències de microones. Els Film Bulk Acoustic Resonators (FBAR) estan esdevenint la principal alternativa als filtres basats en ressonadors Surface Acoustic Wave (SAW) o als basats en ressonadors ceràmics. Els Stacked Crystal Filters (SCF) i els Coupled Resonator Filters (CRF) són configuracions FBAR que permeten assolir una excel·lent atenuació en la banda de refús. Aquest treball presenta un innovador circuit equivalent elèctric que modela el CRF. Llavors, es desenvolupa una metodologia de síntesi de filtres per al SCF i per al CRF utilitzant els seus circuits equivalents elèctrics. La metodologia de disseny presentada permet obtenir les dimensions de l'estructura del filtre acústic partint de les especificacions del filtre i de les restriccions pròpies de la tecnologia. S'han implementat diferents respostes de Chebyshev per a sistemes de comunicacions reals per tal de validar el procediment de disseny dels filtres obtenint els resultats esperats.

Disseny d'un sistema de filtrat d'àudio

Tant el medi transmissor com els equips d'enregistrament o reproducció de so introdueixen components de soroll d'alta freqüència als senyals. En aquest treball de final de carrera (TFC), s'ha dissenyat i implementat un sistema de filtrat d'àudio encaminat a filtrar aquestes components d'alta freqüència. Donat que l'oïda humana no pot percebre sons de més de 20 kHz, s'ha considerat aquest límit com a freqüència màxima a mantenir en la senyal.S'ha començat estudiant el senyal problema a través del seu espectre de freqüències simulat mitjançant la transformada discreta de Fourier (DFT, en anglès). Una vegada identificades les components d'alta freqüència a atenuar, s'han estudiat les diferents opcions de filtre passabaix.Inicialment, s'ha valorat la possibilitat del disseny de filtres analògics de Butterworth o Chebyshev, o de filtres digitals de tipus IIR (Infinite Impulse Response) basats en els primers. Tanmateix, malgrat assolir les especificacions en magnitud, mitjançant aquest filtres no s'obté una fase lineal en la banda de pas. Per això, s'ha realitzat un disseny de filtre digital tipus FIR (Finite Infinite Response) que compleix estrictament amb les especificacions i presenta una fase lineal en la banda de pas. S'ha simulat el comportament d'aquest filtre amb el senyal problema per tal d'assegurar el seu correcte funcionament.A continuació, s'ha implementat aquest últim disseny en llenguatge C i compilat per un microcontrolador de l'empresa Microchip. S'han realitzat proves de simulació mitjançant Stimulus del programa MPLAB. En definitiva, s'ha dissenyat un filtre passabaix de tipus FIR per acondicionar una senyal d'àudio que posteriorment s'ha implementat en un microcontrolador de Microchip.