Thesis (M.A.)--Marshall University, 2004. / Title from document title page. Document formatted into pages; contains vi, 39 p. Includes abstract. Includes bibliographical references (p. 39).

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9963453.

Ulm, Univ., Diss., 2008.

Ulm, Univ. Diss., 2006.

Two common classes of filter functions in use today, Butterworth functions and Chebyshev functions, are based upon solutions to special cases of the Sturm-Liouville equation. Here, solutions to several other special cases of the Sturm-Liouville equation were used to develop filter functions, and the properties of the resulting filters were examined. The following functions were explored: Chebyshev functions of the second kind, untraspherical functions of the second and third kinds, Hermite functions, and Legendre functions. Filter functions were developed for each of the first five polynomials in each series of functions, and magnitude and phase responses were tabulated and plotted. One of the classes of functions, the Hermite functions, led to filters which have a significant advantage over the commonly used Chebyshev filters in passband magnitude response, and were essentially the same as Chebyshev filters in stopband magnitude response and phase response.

A análise desenvolvida no presente trabalho lida com o peculiar acesso do jovem Goethe à questão da subjetividade enquanto uma problemática que, em tempos modernos, traz todo um conjunto de dilemas e contradições em si. O tratamento da participação do autor no que é chamado de discurso moderno da subjetividade se dá, primeiramente, através da identificação de sua apropriação crítica de códigos culturais que lhe foram contemporâneos (como o Pietismo e a Empfindsamkeit), e, em um segundo momento, pela análise detida de seus dois romances do Sturm und Drang. A presente análise confronta, sobretudo, certas categorias tradicionalmente empregadas pela historiografia literária com o fim de generalizar um único modelo antropológico supostamente compartilhado por autores do Sturm und Drang isto é, o modelo do Genie e do indivíduo autônomo pertencente a uma época de crescente ênfase no ideal burguês de Bildung. Não apenas Goethe não compartilharia o mesmo entusiasmo de seus contemporâneos pelo individualismo enquanto valor em si, como também seus dois retratos romanescos desse individualismo sugerem a experiência moderna do Eu como uma entidade potencialmente autodefinidora como um aparato conceitual insuficiente, uma noção permeada por pressuposições metafísicas enganadoras que poderia e deveria ser reconsiderada. O famoso caso trágico de Werther, o indivíduo titânico para o qual não há lugar possível no mundo, é exemplar de tal insuficiência, e o fato de que Goethe continua a lidar com a imagem do ser à procura de seu cerne mais íntimo no romance seguinte, Wilhelm Meisters theatralische Sendung, é tomado como prolongamento de sua participação no corrente discurso filosófico da subjetividade do final do século XVIII. Estes romances são aqui tomados, assim, como dois momentos distintos ainda que de certa forma complementares, ou ao menos coerentes em relação um ao outro do acesso goethiano à problemática. / The analysis developed in the present work deals with the peculiar way the young Goethe portrayed the experience of subjectivity as an issue which, in modern times, brings a whole set of dilemmas and contradictions within itself. The treatment of the author\'s participation in what is here called the modern discourse of subjectivity is developed, first off, through the identification of his critical appropriation of certain cultural codes contemporary to him (such as the Pietistic movement and the Empfindsamkeit), and, in a second moment, through a direct analysis of his two Sturm und Drang novels. The present analysis confronts, above all, certain categories that are traditionally employed by the German literary historiography with the ends of generalizing a single anthropological model supposedly shared by Sturm und Drang authors e.g., the model of the Genie and autonomous individual of an age of growing emphasis upon a bourgeois ideal of Bildung. Against this approach, my claim is that not only Goethe does not share the same enthusiasm held by his contemporaries toward individualism as a value in itself, as his two novelistic portrayals of it suggests the modern experience of the I as the potentially self-defining entity as an insufficient conceptual apparatus, a notion surrounded by deceitful metaphysical presuppositions which could and should be reconsidered. The well-known tragic case of Werther, the titanic subject to whom there could not be any space in the ordinary world, is exemplar of such an insufficiency, and the fact that Goethe continues dealing with the image of the self in search for his innermost core in his following novel, Wilhelm Meisters theatralische Sendung, is taken as a completion of his participation in the ongoing philosophical discourse of subjectivity of the late eighteenth century. These novels are taken, therefore, as two different moments even though they end up being somewhat complementary, or at least coherent in relation to each other of the Goethian access to this issue.

O presente trabalho trata do problema de isolar zeros de polinômios complexos. Muitos algoritmos calculam zeros polinomiais, a partir de regiões iniciais disjuntas, cada uma contendo um único zero. Entretanto o problema de obter tais regiões ainda e alvo de estudo, uma vez que as soluções propostas ainda não são satisfatórias. A obtenção de regiões disjuntas, denominada de isolamento de raízes está diretamente relacionada com a contagem (enumeração) do número de raízes numa determinada região do plano complexo. Algoritmos para enumerar e isolar raízes de polinômios complexos são analisados, desenvolvidos e implementados. A proposta de uma modificação no método numérico de Wilf e realizada, na qual se usa basicamente Seqüências de Sturm e o principio do argumento da analise complexa. Um enfoque algébrico e dado para o algoritmo, visando enumerar zeros de forma exata dentro de um retângulo. Diversas melhorias foram introduzidas, principalmente no tratamento da presença de zeros nas fronteiras de um retângulo alvo de pesquisa. O desempenho do algoritmo proposto e avaliado tanto nos aspectos teórico como pratico, através da determinação da complexidade teórica e através de testes experimentais. A abrangência do algoritmo também e verificada, através da realização de testes com polinômios mal condicionados. Uma comparação deste algoritmo com um recente trabalho e também realizada, mostrando a adequação deles de acordo com o tipo de polinômio. / In this thesis, the problem of isolating polynomial complex zeros is treated. There are many algorithms to calculate polynomial zeros, having previously isolated regions, each containning only one zero. Despite of this, the problem of obtainning such regions is still unsatisfactory. This problem, called root isolation, requires number of root in a given region of the complex plane. Algorithms to enumerate and isolate complex polynomial roots are analised, developed and implemented. A modified Wilf method is given, in with Sturm Sequences and the principle of argument is used. An algebraic approach is given, with the aim to enumerate zeros inside a rectangle in an exact way. Several improvements are introduced, mainly to treat zeros on the boundary of the rectangle. The performance of this new algorithm is evaluated theoretical as well as practice point of view, by means experimental tests. The robustness of the algorithm is verified by means of tests with ill-conditioned polynomials. The algorithm proposed is compared with a recent paper, presenting the performance of both, according different polynomial classes.

In this thesis, we consider the following one dimensional p-Laplacian eigenvalue problem: -((y¡¦/s)^(p-1))¡¦+(p-1)(q-£fw)y^(p-1)=0 a.e. on (0,1) (0.1) and satisfy £\y(0)+ £\ ¡¦ (y¡¦(0)/s(0))=0 £]y(1)+£]¡¦ (y¡¦(1)/s(1))=0 (0.2) where f^(p-1)=|f|^p-2 f=|f|^p-1 sgnf; £\, £\¡¦, £], £]¡¦ ∈R such that £\^2+£\¡¦^2>0 and£]^2+£]¡¦^2>0; and the functions s,q,w are required to satisfy (1) s,q,w∈L^1(0,1); (2) for 0≤x≤1, we have s≥0,w≥0 a.e.; (3) for any x∈ (0,1), ¡ì_0^1 s(t)dt>0, ¡ì_0^x w(t)dt>0,and¡ì_x^1 w(t)dt>0; (4) if for some x_1<x_2,we have¡ì_ x1^x2 w(t)dt=0,then¡ì_ x1^x2 |q(t)|dt=0; (5) for all n∈N, there is a partition {£a_i^(n)}_i=1 ^2n of [0,1] such that for any 0<k≤n-1, ¡ì_£a_2k^(n)^ £a_2k+1^(n) w>0 and ¡ì_£a_2k+1^(n)^ £a_2k+2^(n) s>0. We call the above conditions Atkinson conditions, first introduce in [1].There conditions include the case when s,q,w∈L^1(0,1) and s,w>0 a.e. We use a generalized Prufer substitution and Caratheodory theorem to prove the existence and uniqueness for the solution of the initial value problem of (0.1) above. Then we generalize the Sturm oscillation theorem to one dimensional p-Laplacian and establish the Sturm-Liouville properties of the p-Laplacian operators with L^1 coefficient functions. Our results filled up some gaps in Binding-Drabek [3].

Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, 2009. / Kaynakça var.

A revision of the author's Thesis (doctoral--Marburg, 1976). / Includes bibliographical references (p. 518-535).