Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T11:10:07Z No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) / Made available in DSpace on 2016-03-28T11:10:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2015-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Morphic numbers are numbers related to the form and, somehow, they establish a conception of beauty, aesthetics and harmony. These numbers have important of applications in various branches of knowledge, such as geometry, arithmetic, architecture, and engineering. There are only two morphic numbers, the golden number and the plastic number. The rst one has been studied since ancient Greece, and the second one has only become a subject of interest in the twentieth century, what makes the plastic number a relatively new branch of research. In this work, we will analyze a data collection concerning arithmetic, algebraic or geometric properties of these numbers, by establishing a straight relation between the morphic numbers and the Fibonacci and Padovan sequences. / Os números mór cos são números relacionados à forma e que, de alguma maneira, estabelecem uma concepção de beleza, estética e harmonia. Esses números possuem uma série de aplicações em vários ramos do conhecimento, como geometria, aritmética, arquitetura e engenharia. Existem apenas dois números mór cos, o número de ouro e o número plástico, o primeiro deles é estudado desde a antiga Grécia e o segundo passou a ser estudado no século XX, o que torna o assunto relativamente novo. Traremos neste trabalho uma coleção de informações acerca desses números, sejam propriedades aritméticas, algébricas ou geométricas, estabelecendo um paralelo muito forte entre os mesmos e também como eles se relacionam com as sequências de Fibonacci e Padovan.

Made available in DSpace on 2014-12-17T15:15:05Z (GMT). No. of bitstreams: 1 CarlosAAA.pdf: 386122 bytes, checksum: 5912e9682005147cb0db6bc16a139bab (MD5) Previous issue date: 2007-06-15 / In this work we present a theoretical study about the properties of magnetic polaritons in superlattices arranged in a periodic and quasiperiodic fash?ons. In the periodic superlattice, in order to describe the behavior of the bulk and surface modes an effective medium approach, was used that simplify enormously the algebra involved. The quasi-periodic superlattice was described by a suitable theoretical model based on a transfer-matrix treatment, to derive the polariton's dispersion relation, using Maxwell's equations (including effect of retardation). Here, we find a fractal spectra characterized by a power law for the distribution of the energy bandwidths. The localization and scaling behavior of the quasiperiodic structure were studied for a geometry where the wave vector and the external applied magnetic field are in the same plane (Voigt geometry). Numerical results are presented for the ferromagnet Fe and for the metamagnets FeBr2 and FeCl2 / Neste trabalho apresentamos um estudo te?rico sobre as propriedades dos polaritons magn?ticos em super-redes organizadas em padr?es peri?dico e quasiperi?dico. Na super-rede peri?dica, objetivando descrever o comportamento destes modos, tanto no volume quanto na superf?cie, foi utilizada a teoria do meio efetivo, que facilita enormemente a ?lgebra envolvida. Para a superrede quasi-peri?dica usamos um conveniente modelo te?rico baseado no trata mento da matriz-tranfer?ncia, para derivar a rela??o de dispers?o, utilizando as equa??es de Maxwell (incluindo efeitos de retardamento). Aqui, encontramos um espectro fractal caracterizado por uma lei de pot?ncia para a distribui??o de bandas de energia. A localiza??o e o comportamento de escala da estrutura quasi-peri?dica s?o estudadas numa geometria onde o vetor de onda e o campo aplicado est?o no mesmo plano (geometria de Voigt). Resultados num?ricos s?o apresentados para o ferromagneto Fe e para os metamagnetos FeBr2 e FeCl2

Orientador: José Plínio de Oliveira Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T02:14:38Z (GMT). No. of bitstreams: 1 Spreafico_ElenVivianiPereira_D.pdf: 1192138 bytes, checksum: 2b12cd351b94a0f2f7ec24fc172305c9 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho, colaboramos com provas combinatórias que utilizam a contagem e a q-contagem de elementos em conjuntos de ladrilhamentos com restrições. Na primeira parte do trabalho utilizamos os ladrilhamentos para demonstrar algumas identidades da teoria das partições, dentre elas, o Teorema dos Números Triangulares e o Teorema q-análogo da Série q-Binomial. Na segunda parte do trabalho apresentamos interpretações combinatórias, via ladrilhamento, para algumas identidades envolvendo os números de Jacobsthal e os números generalizados de Jacobsthal . Na terceira parte do trabalho são dadas novas identidades envolvendo os números q-análogos de Jacobsthal e encontramos generalizações para essas novas identidades. Por fim, definimos duas novas sequências: números de Fibonacci generalizados e números de Lucas generalizados e, utilizando ladrilhamentos, estabelecemos e demonstramos novas identidades envolvendo esses números / Abstract: In this work we present combinatorial proofs by making use of tilings. In the first part we use tilings to prove some identities on Partitions Theory, including Triangular Numbers' Theorem and q-analogue of q-Binomial Theorem. In the second part we present combinatorial interpretations, using tilings, for some identities involving Jacobsthal numbers and generalized Jacobsthal numbers. Next we find new identities involving an q-analogue of Jacobsthal numbers and generalizations for these new identities. Finally, we define two new sequences: generalized Fibonacci numbers and generalized Lucas numbers, and using tilings, we prove new identities involving these numbers / Doutorado / Matematica Aplicada / Doutora em Matemática Aplicada

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Min teori är att en av förklaringarna till naturens positiva inverkan på oss ligger i att naturen är lättläst för oss när vi avkodar vår omgivning. I naturen finns det matematiska mönster som återkommer och upprepar sig. Fibonaccis talserie, Gyllene snittet, Fyllotaxisspiralen och framförallt fraktaler. De här mönstren hjälper oss att registrera och ta in information från det vi ser i vår omvärld för att förstå den men också för att avgöra om det finns några faror eller om vi är på en trygg plats.   Inom forskning där försökspersonernas ögonrörelser studerades fann man att vi automatiskt fäster blicken vid mönster med den fraktala dimensionen 1,3 - 1,5. Vidare försök visade att testpersonerna blev som mest avslappnade när de fick se bilder med ett D-värde inom det spannet. Ytterligare stöd för växters hälsofrämjande inverkan fann jag i en rapport från ett försök där testpersonerna fick vidröra olika material med förbundna ögon. Man ville mäta både psykiska och fysiska reaktioner. Testpersonerna fick dels skatta sina upplevelser utifrån 10 par motsatsord och dels mättes deras syremättnad i blodet och det cerebrala blodflödet. Den psykologiska delen av försöket gav ett neutralt resultat men de fysiska mätvärdena indikerade att försökspersonerna blev stressade av att vidröra metall och blev mer avslappnade när de vidrörde levande växtmaterial i form av ett blad. Slutsatsen blev att fysisk kontakt med växtmaterial kan ha en lugnande effekt, trots att försökspersonen inte vet att det är växtmaterial den vidrör.   Genom att föra in dessa mönster i bostadsgården skulle den bli mer hälsofrämjande för den urbana människan. Eftersom örtskiktet idag är underrepresenterat i dessa bostadsområden har jag valt att lägga fokus på perenner som skulle lyfta in de fraktala och matematiska mönstren i den miljön. / My theory is that one of the explanations for the nature's positive impact on us is that nature is easy to read when we decode our surroundings. In nature there are mathematical patterns that recur and repeat themselves like the Fibonacci numbers, Golden Ratio, Phyllotaxis spiral and especially fractals. These patterns help us to record and take in information from what we see in our surroundings to understand it but also to determine if there is something scary or if we are in a safe place.   In research where they investigated the subjects’ eye movements it was found that we automatically attach our gaze at pattern of the fractal dimension 1.3 – 1.5. Further experiments showed that the test subjects where the most relaxed when they saw pictures with a dimension value within that range. I found additional support for plant health effects in a report from an experiment in which test subjects touched different materials blindfolded. The research team wanted to measure both psychological and physical reactions. The test subjects were instructed to value their experiences based on 10 pairs of word opposites and additionally their oxygen saturation in the blood and the cerebral blood flow were monitored. The psychological part of the trail gave a neutral result, but the physical measurements indicated that the subjects were stressed by touching metal and were more relaxed when they touched living plant material (a fresh leaf). The conclusion was that physical contact with plant material can have a calming effect, even though the subject does not know it is plant material it touches.   By bringing in these patterns to apartment house courtyards they would become more health promoting for the urban human. Since the herbal layer is underrepresented in these areas today, I have chosen to focus on perennials that would bring in the fractal and mathematical patterns in this environment.

This master's report addresses the conceptual and material investigations that were explored within my artistic research made at the University of Texas at Austin between 2011 and 2014. These works are a confluence of adornment, sculpture and installation art. These pieces incorporate ancient and contemporary metalworking techniques with raw, organic material. The notion of elegant ornamentation is expanded beyond the body into the adornment of architecture. The potential for transformation and reinvention within found elements is explored within this work. The natural resources I work with have gone through a cycle, which is interrupted when the objects are removed from the earth. I see my process in relationship to alchemical concepts of transmutation. Through manipulation, common matter evolves into precious material. The refined, meticulous craftsmanship conveys a sense of reverence and honor towards the common material. This intervention with the material is an act of preservation and veneration. This work explores my sense of intrigue about the extraordinary potential of mundane materials, and investigates conventional notions of material value. / text

Dans cette thèse, nous étudions l'enveloppe convexe des arbres binaires à racine sur n feuilles.Ce sont les arbres de Huffman dont les feuilles sont labellisées par n caractères. à chaque arbre de Huffman T de n feuilles, nous associons un point xT , appelé point de Huffman, dans l'espace Qn où xT est le nombre d'arêtes du chemin reliant la feuille du ième caractère et la racine.L'enveloppe convexe des points de Huffman est appelé Huffmanoèdre. Les points extrêmes de ce polyèdre sont obtenus dans un premier temps en utilisant l'algorithme d'optimisation qui est l'algorithme de Huffman. Ensuite, nous décrivons des constructions de voisinages pour un point de Huffman donné. En particulier, une de ces constructions est principalement basée sur la construction des sommets adjacents du Permutoèdre. Puis, nous présentons une description partielle du Huffmanoèdre contenant en particulier une famille d'inégalités définissant des facettes dont les coefficients, une fois triés, forment une suite de Fibonacci. Cette description bien que partielle nous permet d'une part d'expliquer la plupart d'inégalités définissant des facettes du Huffmanoèdre jusqu'à la dimension 8, d'autre part de caractériser les arbres de Huffman les plus profonds, i.e. une caractérisation de tous les facettes ayant au moins un plus profond arbre de Huffman comme point extrême. La contribution principale de ce travail repose essentiellement sur les liens que nous établissons entre la construction des arbres et la génération des facettes / In this thesis, we study the convex hull of full binary trees of n leaves. There are the Huffman trees, the leaves of which are labeled by n characters. To each Huffman tree T of n leaves, we associate a point xT , called Huffman point, in the space Qn where xT i is the lengths of the path from the root node to the leaf node marked by the ith character. The convex hull of the Huffman points is called Huffmanhedron. The extreme points of the Huffmanhedron are first obtained by using the optimization algorithm which is the Huffman algorithm. Then, we describe neighbour constructions given a Huffman point x. In particular, one of these constructions is mainly based on the neighbour construction of the Permutahedron. Thereafter, we present a partial description of the Huffmanhedron particularly containing a family of inequalities-defining facets whose coeficients follows in some way the law of the well-known Fibonacci sequence. This description allows us, on the one hand, to explain the most of inequalities-defining facets of the Huffmanhedron up to the dimension 8, on the other hand, to characterize the Huffman deepest trees, i.e a linear characterization of all the facets containing at least a Huffman deepest tree as its extreme point. The main contribution of this work is essentially base on the link what we establish between the Huffman tree construction and the facet generation.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-04-11T12:39:47Z No. of bitstreams: 2 Dissertação - Carlos Alirio Rico Acevedo - 2018.pdf: 1289579 bytes, checksum: 0b60c803c3d9f6f61772e58e7d624086 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-04-12T11:29:32Z (GMT) No. of bitstreams: 2 Dissertação - Carlos Alirio Rico Acevedo - 2018.pdf: 1289579 bytes, checksum: 0b60c803c3d9f6f61772e58e7d624086 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-04-12T11:29:32Z (GMT). No. of bitstreams: 2 Dissertação - Carlos Alirio Rico Acevedo - 2018.pdf: 1289579 bytes, checksum: 0b60c803c3d9f6f61772e58e7d624086 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-03-16 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Let $ k \geq 2.$ an integer. The recurrence $ \fk{n} = \sum_ {i = 0}^k \fk{n-i} $ for $ n> k $, with initial conditions $F_{-(k-2)}^{(k)}=F_{-(k-3)}^{(k)}=\cdots=F_{0}^{(k)}=0$ and $F_1^{ (k)} = 1$, which is called the $k$-generalized Fibonacci sequence. When $ k = 2 ,$ we have the Fibonacci sequence $ \{ F_n \}_{n\geq 0}.$ We will show that the equation $F_{n}^{x}+F_{n+1}^x=F_{m}$ does not have no non-trivial integer solutions $ (n, m, x) $ to $ x> 2 $. On the other hand, for $ k \geq 3,$ we will show that the diophantine equation $\epi$ does not have integer solutions $ (n, m, k, x) $ with $ x \geq 2 $. In both cases, we will use initially Matveev's Theorem, for linear forms in logarithms and the reduction method due to Dujella and Pethö, to limit the variables $ n, \; m $ and $ x $ at intervals where the problem is computable. In addition, in the case for $ k\geq 3 $, we will use the fact that the dominant root the $k$-generalized Fibonacci sequence is exponentially close to 2 to bound $k$, a method developed by Bravo and Luca. / Seja $k\geq 2$ inteiro, considere-se a recorrência $\fk{n}=\sum_{i=0}^{k}\fk{n-i}$ para $n>k$, com condições iniciais $F_{-(k-2)}^{(k)}=F_{-(k-3)}^{(k)}=\cdots=F_{0}^{(k)}=0$ e $F_{1}^{(k)}=1$, que é a sequência de Fibonacci $k$-generalizada. No caso quando $k=2$, é dizer, para a sequência de Fibonacci $\{F_n\}_{n\geq 0}$, vai-se mostrar que a equação $F_{n}^{x}+F_{n+1}^x=F_{m}$ não possui soluções inteiras não triviais $(n,m,x)$ para $x>2$. Por outro lado para, $k\geq 3$ se mostrar que a equação diofantina $\epi$ não possui soluções inteiras $(n,m,k,x)$ com $x\geq 2$. Em ambos casos, inicialmente são usados resultados como o Teorema de Matveev, para formas lineares em logaritmos e o método de redução de Dujella e Pethö, para limitar as variáveis $n, \; m$ e $x$ em intervalos onde o problema seja computável. Adicionalmente, no caso para $k\geq 3$ é usado que a raiz dominante da sequência de Fibonacci $k$-generalizada e exponencialmente próxima a 2, para limitar $k$, o que é um método desenvolvido por Bravo e Luca.

Orientador: Prof. Dr. Jeferson Cassiano / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016. / Neste trabalho de dissertação, apresentamos uma linha de pesquisa envolvendo a incomensurabilidade com um estudo de caso do número de ouro; sua definição, suas aplicações, sua relação com o pentagrama e com a sequência de Fibonacci e também suas curiosidades que o relacionamos com a arte e a natureza. O objetivo é mostrar como este tema pode vir a ser abordado entre os alunos do Ensino Fundamental e Medio de forma prática e interativa. / In this dissertation, we present a line of research involving incommensurable with a case study of the number of gold, its defnition, its applications, its relationship with the pentagram and the Fibonacci sequence and its curiosities that relate to art and nature. The goal is to show how this theme might be broached among students of middle school and high school in a practical and interactive way.