No description available.

Thesis (doctoral)--Georg-August-Universität zu Göttingen, 1919. / Cover title. Vita. Includes bibliographical references (p. [47]).

Let {Ij} be an interval partition of the integers, f(x) a function on the circle group T and S(f) = (sum |f j|2)1/2 where fˆ j = fˆ cIj . In their 1995 paper, Hare and Klemes showed that, for fixed p ∈ (1, infinity), there exist lambdap > 1 and Ap, Bp > 0 such that if l(Ij+1)/ l(Ij) ≥ lambdap, where l(Ij) is the length of the interval Ij, then Ap∥ f∥p ≤ ∥S( f)∥p ≤ Bp∥ f∥p. That is, {Ij} is a Littlewood-Paley (p) partition. Since the intervals need not be adjacent, these partitions may be viewed as permutations of lacunary intervals. Partitions like these can be induced by subsets of sums of permuted lacunary sequences. In this thesis, we present two main results. First, complementary to the aforementioned work of Hare and Klemes who proved that sums of permuted lacunary sequences were Littlewood-Paley (p) partitions (for large enough ratio), we prove the surprising result that there are sums of permuted lacunary sequences of fixed ratio that cannot be obtained by iterating sums of permuted lacunary sequences of larger ratio finitely many times. The proof of this statement is based on the ideas developed in the 1989 paper of Hare and Klemes, especially with respect to the definition of a tree and to the theorem on the equivalency of a finitely generated partition and the absence of certain trees. These special sums may then be viewed as the critical test case for further progress on the conjecture of Hare and Klemes that sums of permuted lacunary sequences are Littlewood-Paley (p) partitions for any p. Secondly, we use the non-branching case of the method of Hare and Klemes developed in their 1992 and 1995 papers, and further developed by Hare in a general setting in 1997, to prove a result of Marcinkiewicz on iterated lacunary sequences in the case p = 4. This shows that the method introduced by Hare and Klemes can potentially be adapted to partitions other than those they were originally applied to. As well, in considering the proof given by Hare and Klemes (and by Hare in a general setting) that lacunary sequences are Littlewood-Paley (4) partitions, we present a slight variation on one of the computations which may be useful in regard to sharp versions of some of these computations, but otherwise follows the same pattern as that of the above papers. Finally, we prove an elementary property of the finite union of lacunary sequences.

Thesis (AE. E.D.)--Polytechnic Institute of Brooklyn, 1945. / Cover title. Reproduced from typewritten copy.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Ciência da Computação. / Made available in DSpace on 2012-10-20T10:06:07Z (GMT). No. of bitstreams: 1 192002.pdf: 536710 bytes, checksum: 9e40ddaa8a7c8e6259ff6b9eeaccb70c (MD5) / A solução de equações diferenciais nem sempre pode ser obtida em forma fechada. Em geral, faz-se necessário utilizar aproximações numéricas que tornem o problema solúvel computacionalmente. O método numérico escolhido na resolução do problema deve apresentar rápida convergência, consistência, estabilidade e baixo custo computacional. Dentre os métodos numéricos existentes para a resolução aproximada de equações diferenciais, consideramos os denominados métodos espectrais. Os métodos espectrais utilizam séries truncadas de funções suaves (infinitamente diferenciáveis) para representar a solução. Se o problema envolve dados suaves e condições de contorno periódicas, podemos conseguir uma rápida convergência (espectral) utilizando expansões em séries de Fourier. A convergência espectral é alcançada quando o erro de truncamento entre a série (com um número finito N de termos) e a solução exata, decai a zero mais rapidamente que qualquer potência de 1/N. As expansões espectrais para problemas não-periódicos (em domínios simples e finitos), geralmente utilizam séries em termos de polinômios de Chebyshev ou Legendre. Tais representações apresentam limitações quando precisamos resolver problemas transientes, pois o adensamento de pontos nodais próximo aos contornos implica na necessidade de pequenos passos no tempo para satisfazer a condição CFL.

A technique has been developed for studying surface waves on liquids. The measuring device employed Fourier analyzes the surface wave being studied. This property of the technique has been verified by three independent tests. The method developed has been applied to the study of the Rayleigh-Taylor instability of fluid surfaces. The results of this study are in good agreement with theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

This thesis consists of two unrelated parts. In the first part of this thesis, we give explicit expressions for the Fourier coefficients of Eisenstein series E∗(z, s, χ) twisted by modular symbols ⟨γ, f⟩ in the case where the level of f is prime and equal to the conductor of the Dirichlet character χ. We obtain these expressions by computing the spectral decomposition of an automorphic function closely related to E∗(z, s, χ). We then give applications of these expressions. In particular, we evaluate sums such as Σχ(γ)⟨γ, f⟩, where the sum is over γ ∈ Γ∞\Γ0(N) with c^2 + d^2 < X, with c and d being the lower-left and lower-right entries of γ respectively. This parallels past work of Goldfeld, Petridis, and Risager, and we observe that these sums exhibit different amounts of cancellation than what one might expect. In the second part of this thesis, given an elliptic curve E and a point P in E(R), we investigate the distribution of the points nP as n varies over the integers, giving bounds on the x and y coordinates of nP and determining the natural density of integers n for which nP lies in an arbitrary open subset of {R}^2. Our proofs rely on a connection to classical topics in the theory of Diophantine approximation.

<p>This work is devoted to trigonometric series with monotone coefficients. The main problem is to study conditions under which a given series is the Fourier series of an integrable (or continuous) function.</p>

This work is devoted to trigonometric series with monotone coefficients. The main problem is to study conditions under which a given series is the Fourier series of an integrable (or continuous) function.