The thesis consists of four papers that address likelihood-based unit root tests for panel data with cross-sectional dependence arising from common factors. In the first three papers, we derive Lagrange multiplier (LM)-type tests for common and idiosyncratic unit roots in the exact factor models based on the likelihood function of the differenced data. Also derived are the asymptotic distributions of these test statistics. The finite sample properties of these tests are compared by simulation with other commonly used unit root tests. The results show that our LM-type tests have better size and local power properties. In the fourth paper, we estimate the spaces spanned by the common factors and the spaces spanned by the idiosyncratic components of the static factor model by using the quasi-maximum likelihood (ML) method and compare it with the widely used method of principal components (PC). Next, by simulation, we compare the size and power properties of established tests for idiosyncratic unit roots, using both the ML and PC methods. Simulation results show that the idiosyncratic unit root tests based on the likelihood-based residuals generally have better size and higher size-adjusted power, especially when the cross-sectional dimension is small and the time series dimension is large.

The main purpose of this dissertation is to investigate necessary optimality conditions for a class of very general nonsmooth optimization problems called the mathematical program with geometric constraints (MPGC). The geometric constraint means that the image of certain mapping is included in a nonempty and closed set. We first study the conventional nonlinear program with equality, inequality and abstract set constraints as a special case of MPGC. We derive the enhanced Fritz John condition and from which, we obtain the enhanced Karush-Kuhn-Tucker (KKT) condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity implies the existence of a local error bound. We also give a tighter upper estimate for the Fr\'chet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. We then consider a more general MPGC where the image of the mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. One of the technical difficulties in obtaining such a result in an infinite dimensional space is that no compactness result can be used to show the existence of local minimizers of a perturbed problem. We employ the celebrated Ekeland's variational principle to obtain the results instead. We then apply our results to the study of exact penalty and sensitivity analysis. We also study a special class of MPCG named mathematical programs with equilibrium constraints (MPECs). We argue that the MPEC-linear independence constraint qualification is not a constraint qualification for the strong (S-) stationary condition when the objective function is nonsmooth. We derive the enhanced Fritz John Mordukhovich (M-) stationary condition for MPECs. From this enhanced Fritz John M-stationary condition we introduce the associated MPEC generalized pseudonormality and quasinormality condition and build the relations between them and some other widely used MPEC constraint qualifications. We give upper estimates for the subdifferential of the value function in terms of the enhanced M- and C-multipliers respectively. Besides, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian-Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the existence of local error bounds. We further extend the new result to the MPECs. / Graduate / 0405

Research Doctorate - Doctor of Philosophy (PhD) / (**Note: this abstract is a plain text version of the author's abstract, the original of which contains characters and symbols which cannot be accurately represented in this format. The properly formatted abstract can be viewed in the Abstract and Thesis files above.**) Let (G,G+) be a quasi-lattice-ordered group with positive cone G+ Laca and Raeburn have shown that the universal C*-algebra C*(G,G+)introduced by Nica is a crossed product BG+ Xɑ G+ by a semigroup of endomorphisms. Subsequent research centered on totally ordered abelian groups. We generalize the results in [2], [3] and [5] to extend it to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G+ we introduce a closed ideal IH+ of the C*-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly a-invariant. It follows that there is an isomorphism between C*-crossed products (BG+/IH+) XɑG+ and B(G/H)+ XβG+. This leads to one of our main results that B(G/H)+ XβG+ is realized as an induced C*-algebra IndG-H (B(G/H+ Xt(G/H)+). Then we use this result to show the existence of the following short exact sequence of C*-algebras 0-IH+ XɑG+ → BG+ XɑG+ → IndG-H (B(G/H+ Xt(G/H)+) → 0. This leads to show that the ideal IH+ XɑG+ is generated by {iBG+(1-1u):u∊H+} and therefore contained in the commutator ideal CG of the C*-algebra BG+ XɑG+. Moreover, we use our short exact sequence to study the primitive ideals of the C* algebra BG+ XɑG+ which is isomorphic to the Toeplitz albebra T(G) of G.

Research Doctorate - Doctor of Philosophy (PhD) / (**Note: this abstract is a plain text version of the author's abstract, the original of which contains characters and symbols which cannot be accurately represented in this format. The properly formatted abstract can be viewed in the Abstract and Thesis files above.**) Let (G,G+) be a quasi-lattice-ordered group with positive cone G+ Laca and Raeburn have shown that the universal C*-algebra C*(G,G+)introduced by Nica is a crossed product BG+ Xɑ G+ by a semigroup of endomorphisms. Subsequent research centered on totally ordered abelian groups. We generalize the results in [2], [3] and [5] to extend it to the case of discrete lattice-ordered abelian groups. In particular given a hereditary subsemigroup H+ of G+ we introduce a closed ideal IH+ of the C*-algebra BG+. We construct an approximate identity for this ideal and show that IH+ is extendibly a-invariant. It follows that there is an isomorphism between C*-crossed products (BG+/IH+) XɑG+ and B(G/H)+ XβG+. This leads to one of our main results that B(G/H)+ XβG+ is realized as an induced C*-algebra IndG-H (B(G/H+ Xt(G/H)+). Then we use this result to show the existence of the following short exact sequence of C*-algebras 0-IH+ XɑG+ → BG+ XɑG+ → IndG-H (B(G/H+ Xt(G/H)+) → 0. This leads to show that the ideal IH+ XɑG+ is generated by {iBG+(1-1u):u∊H+} and therefore contained in the commutator ideal CG of the C*-algebra BG+ XɑG+. Moreover, we use our short exact sequence to study the primitive ideals of the C* algebra BG+ XɑG+ which is isomorphic to the Toeplitz albebra T(G) of G.

In this work we investigate the use of perfect sampling methods within the context of Bayesian linear regression. We focus on inference problems related to the marginal posterior model probabilities. Model averaged inference for the response and Bayesian variable selection are considered. Perfect sampling is an alternate form of Markov chain Monte Carlo that generates exact sample points from the posterior of interest. This approach removes the need for burn-in assessment faced by traditional MCMC methods. For model averaged inference, we find the monotone Gibbs coupling from the past (CFTP) algorithm is the preferred choice. This requires the predictor matrix be orthogonal, preventing variable selection, but allowing model averaging for prediction of the response. Exploring choices of priors for the parameters in the Bayesian linear model, we investigate sufficiency for monotonicity assuming Gaussian errors. We discover that a number of other sufficient conditions exist, besides an orthogonal predictor matrix, for the construction of a monotone Gibbs Markov chain. Requiring an orthogonal predictor matrix, we investigate new methods of orthogonalizing the original predictor matrix. We find that a new method using the modified Gram-Schmidt orthogonalization procedure performs comparably with existing transformation methods, such as generalized principal components. Accounting for the effect of using an orthogonal predictor matrix, we discover that inference using model averaging for in-sample prediction of the response is comparable between the original and orthogonal predictor matrix. The Gibbs sampler is then investigated for sampling when using the original predictor matrix and the orthogonal predictor matrix. We find that a hybrid method, using a standard Gibbs sampler on the orthogonal space in conjunction with the monotone CFTP Gibbs sampler, provides the fastest computation and convergence to the posterior distribution. We conclude the hybrid approach should be used when the monotone Gibbs CFTP sampler becomes impractical, due to large backwards coupling times. We demonstrate large backwards coupling times occur when the sample size is close to the number of predictors, or when hyper-parameter choices increase model competition. The monotone Gibbs CFTP sampler should be taken advantage of when the backwards coupling time is small. For the problem of variable selection we turn to the exact version of the independent Metropolis-Hastings (IMH) algorithm. We reiterate the notion that the exact IMH sampler is redundant, being a needlessly complicated rejection sampler. We then determine a rejection sampler is feasible for variable selection when the sample size is close to the number of predictors and using Zellner’s prior with a small value for the hyper-parameter c. Finally, we use the example of simulating from the posterior of c conditional on a model to demonstrate how the use of an exact IMH view-point clarifies how the rejection sampler can be adapted to improve efficiency.

Orientador: José Francisco Gomes / Banca: Galen Mihaylov Sotkov / Banca: Abraham Hirsz Zimerman / Banca: Paulo Teotônio Sobrinho / Banca: Márcio José Martins / Resumo: Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do modelo WZNW mediante a calibração da ação Swznw e corresponde ao primeiro membro de grau negativo q = -1 de uma hierarquia de modelos cKP do tipo dyon. O modelo mais simples não relativístico dentro desta hierarquia corresponde ao grau q = 2 positivo. As soluções de 1-sóliton para ambos modelos foram construídas e relações explícitas entre ambas soluções (assim como entre as cargas conservadas) foram encontradas. Outro modelo integrável com simetrias não abelianas locais SL(2) X U(1) é introduzido. Numa aproximação à integrabilidade em espaços não-comutativos estudamos generalizações não comutativas no plano dos modelos integráveis bidimensionais sine-, sinh-Gordon e U(N) Quiral Principal. Calculando a amplitude de espalhamento à nível de árvore de um processo de produção de partículas provamos que a versão não-comutativa do modelo de sinh-Gordon que se obtém mediante a deformação Moyal da respectiva ação não é integrável. Por outro lado, a incorporação de vínculos adicionais que são obtidos a partir da generalização da condição de curvatura nula, tornam o modelo integrável. O modelo Quiral Principal generalizado a partir da deformação Moyal da ação, preserva a sua integrabilidade, ao contrário dos modelos sinh-Gordon e sine-Gordon. / Abstract: In this thesis we have constructed and studied a new class of two-dimensional integrable models (relativistic and nonrelativistic), related to the affine algebra 'A IND.3 POT.(1)'. These models admit U(1) X U(1) charged topological solitons. The affine Toda relativistic model is constructed from the gauged WZNW action and corresponds to the first negative grade q = -1 member of a dyonic hierarchy of cKP models. The simplest nonrelativistic model corresponds to the positive grade q = 2 of this hierarchy. The 1-soliton solutions for both models were constructed and explicit relations between them (and the conserved charges as well) were found. Another integrable model with local nonabelian SL(2) X U(1) simetries is introduced. In the context of integrability on noncommutative spaces, we have studied noncommutative generalizations on the plane of the two-dimensional integrable models sine-, sinh-Gordon and U(N) Principal Quiral. By computing for the sinh-Gordon model, the tree-level amplitude of a process of production of particles, we proved that the noncommutative generalization of this model that it is obtained by the Moyal deformation of the corresponding action is not integrable. On the other hand, the addition of extra constraints, obtained by the generalization of the zero-curvature method, renders the integrability of the model. The generalization of the Principal Quiral model by the Moyal deformation of the action preserves the integrability, contrary to the previous case / Doutor

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

COSTA, Emilia Lima da. A formação de conceitos científicos para sujeitos com deficiência visual: sequência Fedathi como aporte metodológico no ensino de química. 2016. 78f. – Dissertação (Mestrado) – Universidade Federal do Ceará, Programa de Pós-graduação em Educação Brasileira, Fortaleza (CE), 2016. / Submitted by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2016-06-14T16:33:08Z No. of bitstreams: 1 2016_dis_elcosta.pdf: 1819665 bytes, checksum: 24a1f8101f4ee34c10ff32eca3aa56f2 (MD5) / Approved for entry into archive by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2016-06-14T16:53:23Z (GMT) No. of bitstreams: 1 2016_dis_elcosta.pdf: 1819665 bytes, checksum: 24a1f8101f4ee34c10ff32eca3aa56f2 (MD5) / Made available in DSpace on 2016-06-14T16:53:23Z (GMT). No. of bitstreams: 1 2016_dis_elcosta.pdf: 1819665 bytes, checksum: 24a1f8101f4ee34c10ff32eca3aa56f2 (MD5) Previous issue date: 2016 / Chemistry for the visually impaired has been presenting difficulties. Regarding the difficulties we include: new methodologies covering their needs, instructional teaching / stimulus response, lack of inclusion, the own teacher training, language - Braille Chemical spelling for use in Brazil. It is noticed that there is a lack of preparation of some teachers in working with this population and difficulty in addressing the content linked to the concepts of mass, volume and density. Given these data and aiming to contribute to the teaching of chemistry for the visually impaired, this research has the general objective to observe the formation of scientific concepts for visually impaired subjects and use the Fedathi sequence as methodological support for Chemistry Teaching, aspirating changes in the way teachers conduct their classes, the Fedathi sequence was created by Professor Dr. Herminio Borges Neto from Universidade Federal do Ceará (UFC). Initial work report to Mathematics Teaching and is based on four sequential and interdependent steps: taking position, maturity, solution and proof. Although Fedathi sequence has been developed with emphasis on Mathematics, it can be used in any subject. So for the research we adopted as theoretical frame the authors Borges Neto et. al. (2013), Brandão (2004, 2009), Juca (2011), Magalhães (2015), Mól et. al. (2012), Nuñez Ramalho (2004), Perrenoud (2003), Pozo and Crespo (2009), Freire (1996). The research aimed to investigate and experience Fedathi sequence at regular schools, the subject of chemistry, the high school first and second year, with visually impaired students. The results show a student avid for knowledge and unfortunately , by not having adequate teaching their needs have hampered his training process. Therefore, lies with the student the "burden" of being formed into a traditional stimulus-response system, which somehow comes to prejudice the participation of the same in the classroom, further undermining the teaching and learning process. With the experience of Fedathi sequence it was possible to observe another posture from the student even insisting on questions. Making them critical in order to seek and have their participation. / A Química para o deficiente visual tem se apresentando com indicativos de dificuldades. Com relação as dificuldades destacamos: novas metodologias que abrange as suas necessidades, ensino instrucionista /estímulo-resposta, a falta de inclusão, a própria formação do professor, a linguagem – Grafia Química Braille para uso no Brasil. Percebe-se que há falta de preparo de alguns docentes em trabalhar com esse público e dificuldade na abordagem dos conteúdos atrelados aos conceitos de massa, volume e densidade. Diante desses dados e com intuito de contribuir com o ensino da Química para o deficiente visual, a presente pesquisa trouxe como objetivo geral observar a formação de conceitos científicos para sujeitos com deficiência visual e utilizar a Sequência Fedathi como aporte metodológico para o Ensino da Química, aspirando mudanças na forma como os professores conduzem suas aulas, a Sequência Fedathi foi criada pelo professor Dr. Hermínio Borges Neto da Universidade Federal do Ceará (UFC). Os trabalhos iniciais reportam ao Ensino da Matemática e tem por base quatro etapas sequenciais e interdependentes: tomada de posição, maturação, solução e prova. Embora a Sequência Fedathi tenha sido desenvolvida com ênfase na Matemática, a mesma pode ser usada em qualquer outra disciplina. Portanto, para a realização da pesquisa adotamos como referencial teórico autores como Borges Neto et. al. (2013), Brandão (2004, 2009), Jucá (2011), Magalhães (2015), Mól et. al.(2012), Nuñez Ramalho (2004), Perrenoud (2003), Pozo e Crespo (2009), Freire (1996). A pesquisa se propôs investigar e vivenciar a Sequência Fedathi em escolas regulares, na disciplina de Química, do Ensino Médio do primeiro e segundo ano, com alunos deficientes visuais. Os resultados encontrados mostram um aluno ávido por conhecimento e que, por não possuir um ensino adequado as suas necessidades têm seu processo de formação prejudicado. Assim sendo, recai sobre o discente o “peso” de ser formado em um sistema tradicional estímulo-resposta, o que de certa forma vem prejudicar a participação do mesmo em sala de aula, minando ainda mais o processo de ensino aprendizagem. Com a vivência da Sequência Fedathi foi possível observar outra postura do aluno mesmo insistindo nas perguntas. Tornando-o crítico para buscar e ter a sua participação

Virtualização permite o compartilhamento de uma rede física entre uma ou mais redes virtuais. O Problema de Mapeamento de Redes Virtuais é um dos principais desafios na virtualização de redes. Esse problema consiste em mapear uma rede virtual em uma rede física, respeitando restrições de capacidade. O presente trabalho mostra que encontrar uma solução factível para esse problema é NP-Difícil. Mesmo assim, muitas instâncias podem ser pode ser resolvidas na prática através da exploração de sua estrutura. Nós apresentamos um algoritmo de Branch & Price aplicado a instâncias de diferentes topologias e tamanhos. Os experimentos realizados sugerem que o algoritmo proposto é superior ao modelo de programação linear resolvido com CPLEX. / Virtualization allows one or more virtual networks to share physical infrastructures. The Virtual Network Embedding problem (VNEP) is one of the main challenges in the virtualization of physical networks. This problem consists in mapping a virtual network into a physical network while respecting capacity constraints. This work shows that finding a feasible solution for this problem is NP-Hard. However, many instances can be solved up to optimality in practice by exploiting the problem structure. We present a Branch & Price algorithm applied to instances of different topologies and sizes. The experimental results suggest that the proposed algorithm is superior to the Integer Linear Programming model solved by CPLEX.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta dissertação, procuramos soluções exatas das equações de campo de Einstein em Relatividade Geral que descrevem um fluido perfeito em um espaço-tempo estático com simetria esférica. A técnica utilizada para encontrar essas soluções é o algoritmo de Kovacic, que pode ser aplicado a equações diferenciais ordinárias lineares e homogêneas de segunda ordem com coeficientes racionais. Esse algoritmo é capaz de nos dar soluções fechadas em termos de funções liouvillianas, se tal equação tiver esse tipo de solução. Para esse fim, vários sistemas de coordenadas foram investigados até encontrar o que fosse mais adequado à aplicação do algoritmo. Impondo que a função da métrica 11 g seja racional, ficamos com uma equação diferencial linear e homogênea de segunda ordem que tem coeficientes racionais. Nesse trabalho, as formas arbitradas foram: g11=-A/4x x-z1/x-Z1, g11=-A/4x x-z1/(x-Z1)(x-Z2), g11=-A/4x (x-z1) (x-z2)/x-Z1 e g11= -A/4x (x-z1) (x-z2)/ 4x(x-Z1) (x-Z2) onde x é uma coordenada espacial da métrica e Α, z1 , z2 , Z1 e Z2 são parâmetros dos modelos. Depois de obter soluções analíticas, verificamos se elas satisfazem determinadas condições físicas e, então, poderiam ser utilizadas como modelos de estrelas de nêutrons sem rotação (estrelas de alta densidade).