Berlin, Humboldt-University, Diss. 2002.

SANTOS, Edjan Fernandes dos. Medidas e forma em geometria . 2015. 61 f. Dissertação (Mestrado em Matemática em Rede Nacional) – Centro de Ciências, Universidade Federal do Ceará, Juazeiro do Norte, 2015. / Submitted by Erivan Almeida (eneiro@bol.com.br) on 2015-12-15T13:01:29Z No. of bitstreams: 1 2015_dis_efsantos.pdf: 2235474 bytes, checksum: 976431d2a4782cb88fd52234af9d0839 (MD5) / Approved for entry into archive by Rocilda Sales(rocilda@ufc.br) on 2015-12-15T13:35:51Z (GMT) No. of bitstreams: 1 2015_dis_efsantos.pdf: 2235474 bytes, checksum: 976431d2a4782cb88fd52234af9d0839 (MD5) / Made available in DSpace on 2015-12-15T13:35:51Z (GMT). No. of bitstreams: 1 2015_dis_efsantos.pdf: 2235474 bytes, checksum: 976431d2a4782cb88fd52234af9d0839 (MD5) Previous issue date: 2015 / The work initially brings a historical approach, Greece (with the Pythagoreans), with the mathematician Eudoxus, referring to perhaps the greatest mathematical work, Euclid’s books. Then bring definitions and constructions of the real numbers as a complete body, the concepts of tiny, supreme, infinite sequences especially the convergent, Cauchy sequences and the three fundamental theorems for the calculus course, the annulment of the theorem, the intermediate value and Weierstrass. Soon after, we define metric and metric space in the plan, we show that the process of comparing an arbitrary segment with another set as unit leads to various types of positive real numbers: integers, rational and irrational, where the notion of measurable and immeasurable segment is explained. The area calculation for plane figures, where the usual formulas for the areas of simple polygons are presented, we present and application, Pick’s formula, without demonstration of the theorem, simple, fun, practical and efficient for area calculation, one this mathematical discipline of content throughout basic education in Brazil always present in external evaluation as OBMEP. / O trabalho traz inicialmente uma abordagem histórica, da Grécia (com os pitagóricos), com o matemático Eudoxo, fazendo referência a talvez à maior obra matemática, os livros de Euclides. Em seguida, trazemos definições e construções sobre os números reais com um corpo completo, os conceitos de ínfimo, supremo, sequências infinitas com destaque as convergentes, sequência de Cauchy e os três teoremas fundamentais para o curso de cálculo, o teorema do anulamento, do valor intermediário e de Weierstrass. Logo após, definimos métrica e espaço métrico no plano, mostramos que o processo de comparar um segmento arbitrário com outro fixado como unidade nos conduz aos diversos tipos de números reais positivos: inteiros, racionais e irracionais, onde a noção de segmento comensurável é explicada. O cálculo de área para figuras planas, onde são apresentadas as fórmulas usuais para as áreas dos polígonos mais simples, apresentamos uma aplicação, a fórmula de Pick, sem demonstração do teorema, simples, divertida, prática e eficiente para o cálculo de área, um conteúdo da disciplina de matemática presente em todo o ensino básico do Brasil sempre presente em avaliações externas como a OBMEP.

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La création de nouveaux matériaux, aux propriétés souhaitées, peut être obtenue par la combinaison de deux, trois ou plusieurs composants. L'évolution des matériaux, l'amélioration de leurs performances et l´extension de leurs fonctionnalités provoquent ainsi une augmentation de la variété des matériaux disponibles: c´est désormais l´usage qui détermine les propriétés du matériau et non l´inverse. L'ajout de nanoparticules dans un polymère peut entraîner, quantitativement via la nanostructuration du polymère et qualitativement via leurs surfaces réactives, de nouvelles caractéristiques, qui ne se limitent pas à la simple addition des propriétés de chaque composant. Les interactions entre la surface des nanoparticules et les molécules du polymère peuvent être notamment à la base de la formation d´interphases, présentant des propriétés différentes de celles du polymère massif. Afin de comprendre l´influence des nanoparticules dans les propriétés mécaniques, optiques et diélectriques du composite et plus particulièrement dans la création d´interphases, ce travail s´est intéressé à des systèmes composés de particules d´Al2O3 et de SiO2 dans une résine d´époxyde. De tels matériaux, a priori simples, affichent des résultats surprenants présentés dans cette thèse. / Creation of new materials with tailor-made properties can be achieved by the combination of two, three or more components. Their development, improvement in performance and the extension of their functionalities have enlarged the diversity of these materials: The desired purpose will define the properties of the used materials and not vice-versa. The inclusion of nanoparticles in a polymer can lead quantitatively via the occurring local structure and qualitatively via the reactive surfaces of the particles to new physical properties, which are not just a simple superposition of the properties of the single components. The interactions between the nanoparticles´ surfaces and the polymer molecules are the reason for the formation of interphases, which differ in their specificities from the polymer bulk. To understand the effect of nanoparticles on the mechanical, optical and dielectric properties of composites, and moreover the formations of interphases, an, at first believed, rather simple nanocomposite produced by including Al2O3- or SiO2- nanoparticles in an industrially common epoxy resin is studied. Such materials, a priori simples show surprising results, which will be discussed in this PhD Thesis.

Made available in DSpace on 2016-06-02T20:28:28Z (GMT). No. of bitstreams: 1 5584.pdf: 648891 bytes, checksum: 48f40694ad94f3de818b195847493b1f (MD5) Previous issue date: 2013-08-22 / Financiadora de Estudos e Projetos / Our main goal in this work is to present an abstract version of Cauchy-Kowalevski theorem and use it to solve the periodic Cauchy problem for the Camassa-Holm equation. / Nosso objetivo principal neste trabalho é apresentar uma versão abstrata do Teorema de Cauchy-Kowalevski, e utilizá-lo para resolver o problema de Cauchy periódico para a equação de Camassa-Holm.

This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.

Thesis (M.A.)--Boston University / In this paper, several numerical methods, instructive for the calculation of the approximate solutions of differential equations, are exhibited to be convergent. In the first two methods (Picard's Method and the Cauchy-Euler method), the theoretical importance of numerical solutions is demonstrated by establishing existence and uniqueness theorems for the linear differential equation of the first order dy/dx = f(x,y) subject to the following conditions: The equation is considered in some region of xy space containing a point (xo,yo) and in addition to being continuous, f(x,y) is assumed to satisfy a Lipschitz condition with respect to y, i.e. |f(x,y1)-f(x,y2)| < k|y1 - y2| where k is called the Lipschitz constant [TRUNCATED]

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 88-95)

This work consists of three chapters. In the first chapter, a brief overview is made on the history of the modern kinetic theory of elastic and dilute gases since the early stages of Maxwell and Boltzmann. In addition, I short exposition on the complexities of the theory of granular media is presented. This chapter has the objectives of contextualize the problems that will be studied in the remainder of the document and, somehow, to exhibit the mathematical complications that may arise in the inelastic gases (not present in the elastic theory of gases). The rest of the work presents two self-contained chapters on different topics in the study of the Boltzmann equation. Chapter 2 focuses in studying and extending the propagation of regularity properties of solutions for the elastic and homogeneous Boltzmann equation following the techniques introduced by A. Bobylev in 1997 and Bobylev, Gamba and Panferov in 2002. Meanwhile, chapter 3 studies the existence and uniqueness of the inelastic and inhomogeneous Cauchy problem of the Boltzmann equation for small initial data. A new set of global in time estimates, proved for the gain part of the inelastic collision operator, are used to implement the scheme introduced by Kaniel and Shinbrot in the late 70’s. This scheme, known as Kaniel and Shinbrot iteration, produces a rather simple and beautiful proof of existence and uniqueness of global solutions for the Boltzmann equation with small initial data. / text

Bibliography: leaves 110-115. / iv, 115 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1999