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Semigrupos numéricos e suas características / Numerical semigroups and their featuresPortes, Leonardo Alcântara 01 October 2013 (has links)
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Previous issue date: 2013-10-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The objective of this work is to show the structure of numerical semigroups and their characteristics, showing the completion of these in a P:A: (arithmetic progressions). Then we show the curiosities of some semigroups and many examples to facilitate understanding of this structure is presented. / O objetivo deste trabalho é mostrar a estrutura de semigrupos numéricos e suas características, mostrando a finalização destes em uma P:A: (progressões aritméticas).Em seguida mostrar a curiosidades de alguns semigrupos e realizar muitos exemplos para facilitar o entendimento desta estrutura. Por fim mostramos a estrutura para generalizar o número de Frobenius em alguns semigrupos e para a quantidade de elementos presente nos semigrupos até a chegada deste número.
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Evolution equations and vector-valued Lp spaces: Strichartz estimates and symmetric diffusion semigroups.Taggart, Robert James, Mathematics & Statistics, Faculty of Science, UNSW January 2008 (has links)
The results of this thesis are motivated by the investigation of abstract Cauchy problems. Our primary contribution is encapsulated in two new theorems. The first main theorem is a generalisation of a result of E. M. Stein. In particular, we show that every symmetric diffusion semigroup acting on a complex-valued Lebesgue space has a tensor product extension to a UMD-valued Lebesgue space that can be continued analytically to sectors of the complex plane. Moreover, this analytic continuation exhibits pointwise convergence almost everywhere. Both conclusions hold provided that the UMD space satisfies a geometric condition that is weak enough to include many classical spaces. The theorem is proved by showing that every symmetric diffusion semigroup is dominated by a positive symmetric diffusion semigoup. This allows us to obtain (a) the existence of the semigroup's tensor extension, (b) a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and (c) an holomorphic functional calculus for the extension's generator. The ergodic theorem is used to prove a vector-valued version of a maximal theorem by Stein, which, when combined with the functional calculus, proves the pointwise convergence theorem. The second part of the thesis proves the existence of abstract Strichartz estimates for any evolution family of operators that satisfies an abstract energy and dispersive estimate. Some of these Strichartz estimates were already announced, without proof, by M. Keel and T. Tao. Those estimates which are not included in their result are new, and are an abstract extension of inhomogeneous estimates recently obtained by D. Foschi. When applied to physical problems, our abstract estimates give new inhomogeneous Strichartz estimates for the wave equation, extend the range of inhomogeneous estimates obtained by M. Nakamura and T. Ozawa for a class of Klein--Gordon equations, and recover the inhomogeneous estimates for the Schr??dinger equation obtained independently by Foschi and M. Vilela. These abstract estimates are applicable to a range of other problems, such as the Schr??dinger equation with a certain class of potentials.
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Amalgamation of inverse semigroups and operator algebrasHaataja, Steven P. January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (site viewed on Feb. 6, 2007). PDF text: iv, 86 p. : ill. UMI publication number: AAT 3218333. Includes bibliographical references. Also available in microfilm and microfiche format.
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Completely regular semiringsSchumann, Rick 16 July 2013 (has links) (PDF)
Vollständig reguläre Halbgruppen weisen eine stark regelmäßige Struktur auf, die verschiedenste Zerlegungsmöglichkeiten gestatten. Ziel dieser Dissertation ist es, diese strukturelle Regelmäßigkeit auf Halbringe zu übertragen und die gewonnenen Algebren zu untersuchen. Mehrere Charakterisierungen werden herausgearbeitet, aufgrund derer es sich herausstellt, dass die Klasse aller vollständig regulären Halbringe eine Varietät bilden, deren Untervarietäten in der Folge untersucht werden. Zentrale Bedeutung haben dabei vollständig einfache Halbringe, deren Analyse einen der Schwerpunkte der Arbeit darstellt. Es zeigt sich, dass diese Bausteine vollständig regulärer Halbringe untereinander eine feste Struktur besitzen, selber aber auch als Zusammensetzung von isomorphen Halbringen aufgefasst werden können. Außerdem werden orthodoxe Halbringe, also Halbringe, deren idempotente Elemente einen Unterhalbring bilden, betrachtet. Zunächst wird dabei wieder auf mehrere Teilklassen eingegangen, bevor abschließend für beliebige vollständig reguläre Halbringe eine Beschreibung der kleinsten Kongruenz angegeben wird, deren Faktorhalbring orthodox ist.
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Regeneration of Elliptic Chains with Exceptional Linear SeriesPflueger, Nathan K 06 June 2014 (has links)
We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of Eisenbud, Harris, and Komeda on the existence of Weierstrass points with certain semigroups, by refining their dimension estimate in light of combinatorial considerations. Both results are proved by constructing chains of elliptic curves, joined at pairs of points differed by carefully chosen orders of torsion, and smoothing these chains. These arguments lead to several combinatorial problems of separate interest. / Mathematics
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Evolution equations and vector-valued Lp spaces: Strichartz estimates and symmetric diffusion semigroups.Taggart, Robert James, Mathematics & Statistics, Faculty of Science, UNSW January 2008 (has links)
The results of this thesis are motivated by the investigation of abstract Cauchy problems. Our primary contribution is encapsulated in two new theorems. The first main theorem is a generalisation of a result of E. M. Stein. In particular, we show that every symmetric diffusion semigroup acting on a complex-valued Lebesgue space has a tensor product extension to a UMD-valued Lebesgue space that can be continued analytically to sectors of the complex plane. Moreover, this analytic continuation exhibits pointwise convergence almost everywhere. Both conclusions hold provided that the UMD space satisfies a geometric condition that is weak enough to include many classical spaces. The theorem is proved by showing that every symmetric diffusion semigroup is dominated by a positive symmetric diffusion semigoup. This allows us to obtain (a) the existence of the semigroup's tensor extension, (b) a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and (c) an holomorphic functional calculus for the extension's generator. The ergodic theorem is used to prove a vector-valued version of a maximal theorem by Stein, which, when combined with the functional calculus, proves the pointwise convergence theorem. The second part of the thesis proves the existence of abstract Strichartz estimates for any evolution family of operators that satisfies an abstract energy and dispersive estimate. Some of these Strichartz estimates were already announced, without proof, by M. Keel and T. Tao. Those estimates which are not included in their result are new, and are an abstract extension of inhomogeneous estimates recently obtained by D. Foschi. When applied to physical problems, our abstract estimates give new inhomogeneous Strichartz estimates for the wave equation, extend the range of inhomogeneous estimates obtained by M. Nakamura and T. Ozawa for a class of Klein--Gordon equations, and recover the inhomogeneous estimates for the Schr??dinger equation obtained independently by Foschi and M. Vilela. These abstract estimates are applicable to a range of other problems, such as the Schr??dinger equation with a certain class of potentials.
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On evolution equations in Banach spaces and commuting semigroups /Alsulami, Saud M. A. January 2005 (has links)
Thesis (Ph.D.)--Ohio University, June, 2005. / Includes bibliographical references (p. 96-102)
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On evolution equations in Banach spaces and commuting semigroupsAlsulami, Saud M. A. January 2005 (has links)
Thesis (Ph.D.)--Ohio University, June, 2005. / Title from PDF t.p. Includes bibliographical references (p. 96-102)
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The theory of integrated empathiesBrown, Thomas John. January 2005 (has links)
Thesis (PhD.(Mathematics))-University of Pretoria, 2005. / Includes bibliographical references. Available on the Internet via the World Wide Web.
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Um modelo matemático de suspensão de pontesFigueroa López, Rodiak Nicolai [UNESP] 20 March 2009 (has links) (PDF)
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figueroalopez_rn_me_sjrp.pdf: 751046 bytes, checksum: 50788892bf3e9440cb207b1489c88d57 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho vamos estudar um modelo matemático que descreve as oscilações não lineares de uma ponte suspensa. Este modelo é dado por um sistema de equações diferenciais parciais que estão acopladas. Basicamente, estudaremos a existência e unicidade da solução fraca do sistema. Usaremos a teoria de operadores maximais monótonos para modelo linear e os semigrupos fortemente contínuos de contração para o modelo não linear. / In this work we study a mathematical model which describes the nonlinear oscillations of a bridge suspended. This model is given by a system of partial di®erential equations which are coupled. Basically, we study the existence and uniqueness of weak solution of the system. We use the theory of maximal monotone operators to model linear and strongly continuous semigroups of contraction for the nonlinear model.
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