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

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

This master’s report seeks to increase knowledge of complex numbers and how to identify complex roots graphically. The reader will obtain a greater understanding of the history of complex numbers, the definition of a complex number and a few of the field properties of complex numbers. Readers will also be enlightened on how to visibly detect complex roots of polynomials of the second, third and fourth degree. / text

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Este trabalho apresenta a construção dos conjuntos dos números naturais, inteiros, racionais e reais, buscando contemplar uma mediação entre alunos e professores do ensino médio que possa contribuir em uma abordagem facilitadora para o processo de ensino e aprendizagem. A construção dos conjuntos numéricos é feita de modo progressivo, apresentando leis e propriedades que definem cada um deles. Os capítulos apresentam teoremas que são provados de modo que o leitor possa conseguir, efetivamente, estabelecer um elo entre a teoria matemática e suas abstrações iniciais inerentes aos estudantes em formação. / This work presents the construction of the sets of natural, integer, rational and real numbers, aiming to contemplate a mediation between high school students and teachers that can contribute to an easy approach to the teaching and learning processes. The construction of the numerical sets is done progressively presenting laws and properties that define each one of them. The chapters present theorems that are proven so that the reader can effectively establish a link between mathematical theory and its initial abstractions inherent in the students in formation.

Economic theory does not always specify the functional relationship between dependent and explanatory variables, or even isolate a particular set of covariates. This means that model uncertainty is pervasive in empirical economics. In this paper, we indicate how Bayesian semi-parametric regression methods in combination with stochastic search variable selection can be used to address two model uncertainties simultaneously: (i) the uncertainty with respect to the variables which should be included in the model and (ii) the uncertainty with respect to the functional form of their effects. The presented approach enables the simultaneous identification of robust linear and nonlinear effects. The additional insights gained are illustrated on applications in empirical economics, namely willingness to pay for housing, and cross-country growth regression.

Membrane wings are used both in nature and small aircraft as lifting surfaces. For these low Reynolds number applications, separated flows are common and are the main sources of unsteadiness. Adaptability of the membrane wing is known to improve the vehicle performance; and membrane compliancy in animal wings such as bats contributes significantly to their astonishing flights. Yet, the aerodynamic characteristics of the membranes are still largely unknown. An experimental study of flexible membranes at low Reynolds numbers was undertaken. Two-dimensional membrane aerofoils were investigated, with particular focus on the unsteady aspects. Membrane deformation, flow fields and fluid-structure interaction were examined over a range of angles of attack and freestream velocities. A comprehensive study of the effect of membrane pre-strain and excess length was carried out. Low aspect ratio membrane wings were investigated for rectangular and nonslender delta wings. The amplitude and mode of membrane vibration are found to be dependent mainly on the location and the unsteadiness level of the shear layer. The results indicate a strong coupling of unsteady flow with the membrane oscillation. With increasing Reynolds number, the separated shear layer becomes more energetic and closer to the surface. The membrane not only has smaller size of the separation region compared to a rigid aerofoil, but also excites the roll-up of large vortices which might lead to delayed stall. The membrane aerofoils with excess length exhibit higher vibration modes, earlier roll-up and smaller separated region, compared to the ones with pre-strain. This smaller separated region delays the onset of membrane vibrations to a larger incidence. For the low aspect ratio membrane wings, the combination of tip vortices and leading-edge vortex shedding results in a mixture of streamwise and spanwise vibrational modes. The flexibility benefits the rectangular wing more than the delta wing by increasing the maximum normal force and the force slope by a larger amount. Similar to the two-dimensional membrane aerofoils, the Strouhal numbers of the oscillations are on the order of unity, and there is a coupling with the wake instabilities in the post-stall region. Stronger tip vortices on membrane wings contribute significantly to total lift enhancement.

Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an attempt to generalize Lehr's result we show that the set M(r) is closed under multiplication by rational numbers. We also show that M(r) is not closed under addition.

Lam, Ho Yin Theodore. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 59-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Shift spaces and Symbolic Dynamical systems --- p.8 / Chapter 2.1 --- Shift spaces --- p.8 / Chapter 2.2 --- Symbolic dynamical systems --- p.10 / Chapter 3 --- β-expansion --- p.12 / Chapter 3.1 --- Expansion of real numbers --- p.12 / Chapter 3.2 --- Ergodic theory of f-expansion with independent digits --- p.16 / Chapter 3.3 --- β-expansion --- p.22 / Chapter 3.3.1 --- Ergodic theory of β-expansion --- p.22 / Chapter 3.3.2 --- Properties of β-expansion --- p.28 / Chapter 3.3.3 --- The normalizing function F(β) --- p.34 / Chapter 4 --- Symbolic Dynamics of β-expansion --- p.40 / Chapter 4.1 --- The symbolic dynamical system Sβ --- p.40 / Chapter 4.2 --- Classification of β and properties of Sβ --- p.42 / Chapter 5 --- Sizes of the classes --- p.49 / Chapter 5.1 --- Sizes of C1 and C2 --- p.49 / Chapter 5.2 --- "Sizes of C3, C4 and C5" --- p.50 / Bibliography --- p.59