Orientador: Rodney Carlos Bassanezi / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T16:18:31Z (GMT). No. of bitstreams: 1 Dias_AlbertoFaustino_M.pdf: 1122688 bytes, checksum: a62e35c5bae8f636d723761c61dcfcd7 (MD5) Previous issue date: 2015 / Resumo: Apresentamos neste trabalho, uma relação existente entre a despretensiosa Sequência de Fibonacci e o Número de Ouro, conhecido também como Razão Áurea ou Número Áureo. Neste mesmo contexto, tratamos de um modelo variacional discreto através das Equações de Diferenças e contínuo através das Equações Diferenciais Lineares, problematizado pelo crescimento populacional de escargots, em cuja solução aparece o Número de Ouro. Para fundamentação deste trabalho utilizamos pesquisa bibliográfica constituída de livros e publicações diversas, cujo embasamento reside principalmente nos autores, Rodney C. Bassanezzi, Maurício Zahn, William E. Boyce e Richard C. Diprima. O princial objetivo deste trabalho foi dar uma abordagem contínua ao modelo variacional discreto gerado pelo crescimento populacional dos escargots / Abstract: In this work, an existing relationship between the unpretentious Fibonacci sequence and the Golden Mean, also known as the Golden Ratio or Golden Number. In this same context, we deal with a discrete variational model through the differences and continuous equations through Linear Differential Equations, questioned by population growth escargots, whose solution appears the Golden Mean. For reasons of this work we use literature consists of books and publications whose foundation lies mainly in authors, Rodney C. Bassanezzi, Mauritius Zahn, William E. Boyce and Richard C. DiPrima. The princial objective was to give a continuous approach to the discrete variational model generated by population growth of snails / Mestrado / Matematica Aplicada e Computacional / Mestre em Matemática Aplicada e Computacional

Published Article / In the 13th century an Italian mathematician Fibonacci, also known as Leonardo da Pisa, identified a sequence of numbers that seemed to be repeating and be residing in nature (http://en.wikipedia.org/wiki/Fibonacci) (Kalman, D. et al. 2003: 167). Later a golden ratio was encountered in nature, art and music. This ratio can be seen in the distances in simple geometric figures. It is linked to the Fibonacci numbers by dividing a bigger Fibonacci value by the one just smaller of it. This ratio seems to be settling down to a particular value of 1.618 (http://en.wikipedia.org/wiki/Fibonacci) (He, C. et al. 2002:533) (Cooper, C et al 2002:115) (Kalman, D. et al. 2003: 167) (Sendegeya, A. et al. 2007). Artificial Intelligence or neural networks is the science and engineering of using computers to understand human intelligence (Callan R. 2003:2) but humans and most things in nature abide to Fibonacci numbers and the golden ratio. Since Neural Networks uses the same algorithms as the human brain does, the aim is to experimentally proof that using Fibonacci numbers as weights, and the golden rule as a learning rate, that this might improve learning curve performance. If the performance is improved it should prove that the algorithm for neural network's do represent its nature counterpart. Two identical Neural Networks was coded in LabVIEW with the only difference being that one had random weights and the other (the adapted one) Fibonacci weights. The results were that the Fibonacci neural network had a steeper learning curve. This improved performance with the neural algorithm, under these conditions, suggests that this formula is a true representation of its natural counterpart or visa versa that if the formula is the simulation of its natural counterpart, then the weights in nature is Fibonacci values.

Submitted by SAMUEL VILELA DE LIMA FRANCISCO null (samvilela@hotmail.com) on 2017-02-28T23:58:46Z No. of bitstreams: 1 TCC - Vesão final - Samuel vilela de lima.pdf: 6672918 bytes, checksum: a9b85452d594c16d9cfe679f612d0561 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-03-07T13:33:10Z (GMT) No. of bitstreams: 1 francisco_svl_me_sjrp.pdf: 6672918 bytes, checksum: a9b85452d594c16d9cfe679f612d0561 (MD5) / Made available in DSpace on 2017-03-07T13:33:10Z (GMT). No. of bitstreams: 1 francisco_svl_me_sjrp.pdf: 6672918 bytes, checksum: a9b85452d594c16d9cfe679f612d0561 (MD5) Previous issue date: 2017-02-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Apresentamos, neste trabalho, um estudo sobre um número que tem fascinado muitos estudiosos ao longo da história da humanidade, o Número de Ouro. Este número é representado pela letra grega (lê-se: "Fi") no qual alguns estudiosos atribuem-se que foi escolhido em homenagem ao grande escultor grego Fídias. Mostramos um pouco do contexto histórico, algumas de suas propriedades e a sua relação intrínseca com a sequência de Fibonacci. Desenvolvemos neste trabalho uma metodologia de natureza teórica e prática, na qual realizamos algumas construções geométricas relacionando-as com a Razão Áurea, retratando assim, como o conteúdo de construções geométricas e a geométrica em que foi perdendo espaço no ensino fundamental ao longo do tempo, e buscamos o resgate deste conteúdo no panorama atual da educação. Tendo como objetivo principal o de promover a reflexão da importância desse número através do projeto desenvolvido paralelamente às aulas de matemática para alunos do ensino fundamental. / We present, in this work, a study on a number that has fascinated many scholars throughout the history of humanity, the Gonden Number. This number is represented by the Greek letter phi (reads: "Fi") in which some scholars are attributed that it was chosen in honor of the great Greek sculptor Fídias. We show some of the historical context, some of its properties and its intrinsic relation with the Fibonacci Sequence. In this work we develop a methodology of theoretical and practical nature, in which we perform some geometric constructions relating them to the Golden Ratio, thus portraying, as the content of geometric constructions and the geometric in which it lost space in elementary education over time, And we seek the rescue of this content in the current panorama of education. Its main objective is to promote the reflection of the importance of this number through the project developed parallel to the mathematics classes for elementary school students.

In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are examiningthe so called Pisano period, which is the period for the Fibonacci sequence considered modulo n to repeatitself. The theory shows that it suces to compute Pisano periods for primes. We are also looking atthe same problems for the generalized Pisano period, which can be described as the Pisano period forthe generalized Fibonacci sequence.

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As an alternative to the Fibonacci heap, and a variation of the 2-3 heap data structure by Tadao Takaoka, this research presents the 3-4 heap data structure. The aim is to prove that the 3-4 heap, like its counter-part 2-3 heap, also supports n insert, n delete-min, and m decrease-key operations, in O(m + nlog n) time. Many performance tests were carried out during this research comparing the 3-4 heap against the 2-3 heap and for a narrow set of circumstances the 3-4 heap outperformed the 2-3 heap. The 2-3 heap has got a structure based on dimensions which are rigid using ternary linking and this path is made up of three nodes linked together to form a trunk, and the trunk is permitted to shrink by one. If further shrinkage is required then an adjustment is made by moving a few nodes from nearby positions to ensure the heaps rigid dimensions are retained. Should this no longer be the case, then the adjustment will trigger a make-up event, which propagates to higher dimensions, and requires amortised analysis. To aid amortised analysis, the trunk is given a measurement value called potential and this is the number of comparisons required to place each node into its correct position in ascending order using linear search. The divergence of the 3-4 heap from the 2-3 heap is that the trunk maximum is increased by one to four and is still permitted to shrink by one. This modified data structure will have a wide range of applications as the data storage mechanism used by graph algorithms such as Dijkstra's 'Single Source Shortest Path'.

Thesis (M.M.)--Bowling Green State University, 2009. / Document formatted into pages; contains 1 score (vi, 29 p.) For clarinet, bassoon, and chamber orchestra (two trumpets, two horns, tenor trombone, bass trombone, percussion, piano, harp, and strings (six first violins, six second violins, four violas, four cellos, and two basses) Includes bibliographical references.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2016-08-25T20:38:32Z No. of bitstreams: 1 DaniloOliveiraPedreira_TESE.pdf: 7943420 bytes, checksum: 3266c07efadf03619e0cc898cba272f8 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2016-08-25T23:57:40Z (GMT) No. of bitstreams: 1 DaniloOliveiraPedreira_TESE.pdf: 7943420 bytes, checksum: 3266c07efadf03619e0cc898cba272f8 (MD5) / Made available in DSpace on 2016-08-25T23:57:40Z (GMT). No. of bitstreams: 1 DaniloOliveiraPedreira_TESE.pdf: 7943420 bytes, checksum: 3266c07efadf03619e0cc898cba272f8 (MD5) Previous issue date: 2016-02-19 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Materiais em nanoescala compostos por ?tomos de boro, carbono e nitrog?nio apresentam propriedades ?nicas e podem ser ?teis no desenvolvimento de novas tecnologias. Nesta tese, investigamos algumas propriedades de nanofitas BCN com arranjo quasiperi?dico dado por uma sequ?ncia Fibonacci. Analisamos propriedades como: estabilidade estrutural, densidade eletr?nica de estados, calor espec?fico eletr?nico, estrutura de bandas e gap de energia. Realizamos c?lculos de primeiros princ?pios baseados na teoria do funcional da densidade implementado como no c?digo SIESTA. Os resultados mostraram que nanofitas com maior gera??o Fibonacci tendem a apresentar um valor fixo para a energia de forma??o. A densidade eletr?nica de estados foi utilizada para calcular o calor espec?fico. Encontramos um comportamento oscilat?rio do calor espec?fico eletr?nico, para o regime de baixas temperaturas. Analisamos a estrutura de bandas para determinar o gap de energia. O gap de energia apresenta oscila??es como fun??o do ?ndice n da gera??o Fibonacci. Nosso trabalho sugere que uma escolha apropriada dos blocos de constru??o da sequ?ncia quasiperi?dica do material pode levar a um controle do gap de energia para nanofitas quasiperi?dicas. / Nanoscale materials composed of boron, nitrogen, and carbon have unique properties and may be useful in new technologies. In this thesis, we investigate some properties of BCN nanoribbons constructed according to the Fibonacci quasiperiodic sequence. We analyze properties such as structural stability, electronic density of states, electronic specific heat, band structure, and energy band gap. We have performed first-principles calculations based on density functional theory implemented in the SIESTA code. The results showed that nanoribbons present a fixed value of the formation energy. The electronic density of states was used to calculate the specific heat. We found an oscillatory behavior of the electronic specific heat, in the low temperature regime. We analyze the electronic band structure to determine the energy band gap. The energy band gap oscillates as a function of the Fibonacci generation index n. Our work suggest that appropriate choice of the building block materials of the quasiperiodic sequence, may lead to a tuneable band gap of the quasiperiodic nanoribbons.

Submitted by Marcos Samuel (msamjunior@gmail.com) on 2017-05-31T15:41:16Z No. of bitstreams: 1 Dissertação - José Jackson.pdf: 1298423 bytes, checksum: 911920da0ec3ff9bfb3648ed45a64b32 (MD5) / Approved for entry into archive by Vanessa Reis (vanessa.jamile@ufba.br) on 2017-06-06T14:37:43Z (GMT) No. of bitstreams: 1 Dissertação - José Jackson.pdf: 1298423 bytes, checksum: 911920da0ec3ff9bfb3648ed45a64b32 (MD5) / Made available in DSpace on 2017-06-06T14:37:44Z (GMT). No. of bitstreams: 1 Dissertação - José Jackson.pdf: 1298423 bytes, checksum: 911920da0ec3ff9bfb3648ed45a64b32 (MD5) / Este trabalho pretende destacar a importância da utilização das sequências Fibonacci como ferramenta que irá auxiliar em alguns temas do ensino da Matemática, em especial o ensino médio. O professor de Matemática, com sua habilidade e bem orientado, deverá provocar no aluno a construção dos conceitos matemáticos utilizando essas sequências. No entanto, na sala de aula, o docente deve trabalhar com resoluções de problemas que despertem e provoquem no aluno a vontade de aprender, levando-o a perceber as ligações com os conteúdos afi ns. Além de auxiliar no ensino aprendizagem dos conte udos propostos, temos a possibilidades de explorar alguns aspectos da História da matemática, objetivando introduzir e complementar os conteúdos do currículo. Temos também a oportunidade, neste trabalho de conclusão, de apresentar e demonstrar como as sequências Fibonacci se conectam com os conteúdos da disciplina.