Stochastic control problems that arise in sequential decision making applications typically assume that information used for decision-making is obtained according to a predetermined sampling schedule. In many real applications however, there is a high sampling cost associated with collecting such data. It is therefore of equal importance to determine when information should be collected as it is to decide how this information should be utilized for optimal decision-making. This type of joint optimization has been a long-standing problem in the operations research literature, and very few results regarding the structure of the optimal sampling and control policy have been published. In this thesis, the joint optimization of sampling and control is studied in the context of maintenance optimization. New theoretical results characterizing the structure of the optimal policy are established, which have practical interpretation and give new insight into the value of condition-based maintenance programs in life-cycle asset management. Applications in other areas such as healthcare decision-making and statistical process control are discussed. Statistical parameter estimation results are also developed with illustrative real-world numerical examples.

Made available in DSpace on 2014-12-17T15:43:56Z (GMT). No. of bitstreams: 1 AnaCSPT_DISSERT.pdf: 2140417 bytes, checksum: 8ecf2918cdf8a508e2b68c89eeb3e3ea (MD5) Previous issue date: 2014-03-11 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Aim: To determine the frequency and type of complications related to removable partial denture (RPD) less, Kennedy Class I, over time . Materials and Methods: This observational study consisted of a sample of 65 users PPR lower arches in Kennedy Class I and dentures, rehabilitated in the Department of Dentistry, Federal University of Rio Grande do Norte (UFRN). Patients were followed through periodic controls during periods of 60 days, 6 months and 1 year from installation. After the first year of control had other returns annually. The occurrence of complications or prosthetic failure was observed and recorded in a specific clinical record over 39 months. The patterns of failures observed were classified in the following situations: occurrence of traumatic ulcers after 2 months of installation, lack of retention, fracture or caries in the rest, fracture or dislocation of the artificial teeth, the larger connector fracture, fracture clip fracture support, poor support (need to reline the denture) and prosthesis fracture. Results: The incidence of complications was low frequency, being higher in the second year of use of the prosthesis. Among the complications that occurred more is the loss of retention (31.57%). Failures more severe and difficult to solve as the fracture elements of the metal structure of the PPR had low occurrence and were represented by only one case of the larger connector (5.3%) fractures. Conclusion: Removable partial dentures mandibular free end opposing of the conventional dentures have a low complication rate after 39 months of use when subjected to periodic controls / Objetivo: Verificar a frequ?ncia e tipo de complica??es relacionadas ? pr?tese parcial remov?vel (PPR) inferior, classe I de Kennedy, ao longo do tempo. Materiais e M?todos: Este estudo observacional foi composto por uma amostra de 65 usu?rios de PPR inferior em arcos Classe I de Kennedy e pr?tese total superior, reabilitados no Departamento de Odontologia da Universidade Federal do Rio Grande do Norte (UFRN). Os pacientes foram acompanhados por meio de controles peri?dicos nos per?odos de 60 dias, 6 meses e 1 ano desde a instala??o. Ap?s o primeiro ano de controle os demais retornos tiveram periodicidade anual. A ocorr?ncia de complica??es ou falhas prot?ticas foi observada e registrada em ficha cl?nica espec?fica ao longo de 39 meses. Os padr?es de falhas observados foram enquadrados nas seguintes situa??es: ocorr?ncia de ?lceras traum?ticas depois de 2 meses de instala??o, aus?ncia de reten??o, fratura de nicho ou c?rie sob o nicho, fratura ou descolamento dos dentes artificiais, fratura do conector maior, fratura de grampo, fratura do apoio, suporte deficiente (necessidade de reembasamento da pr?tese) e fratura da pr?tese. Resultados: A ocorr?ncia de complica??es apresentou baixa frequ?ncia, sendo maior a partir do segundo ano de uso da pr?tese. Dentre as complica??es que mais aconteceram est? a perda de reten??o (31,57%). Falhas de maior gravidade e de dif?cil resolu??o como a fratura de elementos da estrutura met?lica da PPR tiveram baixa ocorr?ncia e foram representadas por apenas um caso de fratura do conector maior (5,3%). Conclus?o: Pr?teses parciais remov?veis de extremidade livre mandibulares opostas a pr?teses totais convencionais apresentam baixo ?ndice de complica??es ap?s 39 meses de uso quando submetidas a controles peri?dicos

L’instruction des ADV (Aveugles et Déficients visuels) sous-tend leur apprentissage et leur intégration aussi bien scolaire que sociale, et est fondée sur des politiques mises en œuvre dans divers pays. En France et dans d’autres pays, sont conçues au profit des ADV des politiques d’intégration dont celles en milieu ouvert et en milieu spécialisé. Les études de terrain en France et en Tunisie montrent, qu’avec de supports et de matériels spécifiques, les ADV ont pu apprendre les mathématiques en concrétisation de ces politiques d’intégration. / Teaching the BVI (Blind and Visually Impaired) is the foundation of their learning and integration in both school and society, and is based on policies implemented in various countries. In France and in other countries, integration policies, in an open and specialized setting, are formed for the BVI. Field studies in France and in Tunisia show that with specific media and materials, the BVI were able to learn Math, thus concretizing these integration policies.

To quench a thermal runaway reaction in a chemical rector, an efficient approach is the introduction of a small quantity of a liquid inhibiting agent, named a “killer”, into the mixing vessel. In this thesis, an experimental approach has been coupled tightly with numerical modelling using Computational Fluid Dynamics (CFD). The first part of this thesis is devoted to a study of the hydrodynamics of partially-baffled mixing vessels, including the free-surface deformation caused by the central vortex. The use of an inhomogeneous, multiphase approach allowed simulation of the free-surface deformation. The capability of this novel method was demonstrated by very good agreement between the numerical predictions and experimental data. In the second part, liquid jet injection at the free-surface was coupled with the vessel hydrodynamics. Numerical results, obtained using an Eulerian-Lagrangian approach, have again shown good agreement with experimental data. These results allowed the jet trajectory to be modelled and its penetration into the agitated vessel was quantified. New mixing criteria were introduced that are specific to this application. Finally, the numerical methods validated at the pilot scale were applied at the industrial scale and allowed the proposal of practical improvements to the safety of the synthesis reactors studied

As we navigate the world, for example when driving a car from our home to the work place, we continuously perceive the 3D structure of our surroundings and intuitively recognise the objects we see. Such capabilities help us in our everyday lives and enable free and accurate movement even in completely unfamiliar places. We largely take these abilities for granted, but for robots, the task of understanding large outdoor scenes remains extremely challenging. In this thesis, I develop novel algorithms for (near) real-time dense 3D reconstruction and semantic segmentation of large-scale outdoor scenes from passive cameras. Motivated by "smart glasses" for partially sighted users, I show how such modeling can be integrated into an interactive augmented reality system which puts the user in the loop and allows her to physically interact with the world to learn personalized semantically segmented dense 3D models. In the next part, I show how sparse but very accurate 3D measurements can be incorporated directly into the dense depth estimation process and propose a probabilistic model for incremental dense scene reconstruction. To relax the assumption of a stereo camera, I address dense 3D reconstruction in its monocular form and show how the local model can be improved by joint optimization over depth and pose. The world around us is not stationary. However, reconstructing dynamically moving and potentially non-rigidly deforming texture-less objects typically require "contour correspondences" for shape-from-silhouettes. Hence, I propose a video segmentation model which encodes a single object instance as a closed curve, maintains correspondences across time and provide very accurate segmentation close to object boundaries. Finally, instead of evaluating the performance in an isolated setup (IoU scores) which does not measure the impact on decision-making, I show how semantic 3D reconstruction can be incorporated into standard Deep Q-learning to improve decision-making of agents navigating complex 3D environments.

Au cours des conflits récents, les véhicules ont été sujet à des attaques impliquant une grande quantité d'explosif enterré. En général, les planchers sont visés, et leurs déformations absorbent une partie de l'énergie. Le véhicule subit également une impulsion, transmise par la détonation, qui peut blesser gravement les occupants. L'intensité de l'impulsion dépend principalement de trois paramètres: le degré de saturation du sol, la nature du sol dans lequel l'explosif est enterré, et la profondeur d'enfouissement de la charge. Les simulations numériques doivent reproduire le processus intégral de l'explosion, incluant l'initiale interaction entre la charge et le sol, l'expansion des produits de détonation, la propagation de l'onde de choc jusqu'au plancher du véhicule, et la grande déformation des projections de sol. L'information mécanique transmise jusqu'au niveau du plancher doit être suffisamment précise car les effets sur le véhicule constituent l'objectif des simulations. Développer un modèle constitutif de sol est par conséquent délicat.%délicat. un défi. tâche difficile. Le modèle de sol est visco-plastique avec un cap écrouissable, une surface de rupture pour limiter les contraintes de cisaillement et un cut off contre les contraintes excessives de tension. La surface de charge est entièrement lisse afin que les incréments de déformation plastique soient continus. Un mécanisme de rigidification est présenté pour tenir compte de la compression de l'air et des très grandes contraintes dans l'environnement immédiat de la charge. Le taux d'humidité du sol est également pris en compte. Deux séries d'essais ont été réalisés à DGA TT pour servir de référence pour les simulations numériques. Une première campagne a mis en jeu de petites quantités d'explosif à plusieurs profondeurs d'enfouissement. Les pressions aériennes ont été mesurées à plusieurs hauteurs et comparées aux simulations. Un moyen d'essai a été utilisé lors de la seconde campagne d'essais pour mesurer à la fois la déformation d'une plaque représentant un plancher de véhicule, mais aussi l'impulsion transmise par l'explosion enfouie. Un certain nombre de taux d'humidité, profondeurs d'enfouissement, épaisseurs de plaques et gardes au sol a été étudié. Au cours des essais, le sol STANAG, composé de sable et de graviers, défini dans l'AEP 55 relatif au STANAG 4569, a été utilisé. Des simulations Eulériennes ont été réalisées et sont en accord avec les résultats d'essais. Le rôle des trois parties de la surface de charge, des mécanismes de rigidification élastique et d'écrouissage plastique a été évalué. La masse volumique initiale du sol et la position initiale du cap sont les paramètres ayant la plus grande influence sur les pressions aériennes. Quant à l'impulsion, elle est principalement contrôlée par le degré de saturation du sol. / In recent conflicts, vehicles have been facing underbelly attacks involving a large quantity of buried explosive. A part of the energy is absorbed by the deformation of the belly. Still the vehicle is subjected to the impulse transmitted by the detonation which may severely injure occupants. The intensity of the impulse is highly dependent on three main parameters which are the degree of saturation of the soil, the nature of the soil in which the explosive is buried and the depth of burial of the charge. Computer simulations should follow the complete process of the explosion, including the early interaction of the charge with the soil, the expansion of the detonation products, the propagation of the shock wave up to the vehicle floor, and the large deformation of the soil projections. The mechanical information transmitted up to the floor level should be sufficiently accurate because the impact on the vehicle is the key target of the simulations. Developing a constitutive soil model is therefore a challenging task. The soil model is visco-plastic with a hardening cap surface, a failure surface to limit shear stresses and a cut off surface against excessive tension. The entire yield surface is smooth so that the plastic strain increments are continuous. A stiffening mechanism is introduced to account for air compression and accommodate the huge stresses in the immediate neighborhood of the charge. The water content of the soil is also taken into account. Two sets of experiments were carried out at DGA TT to serve as a reference for computer simulations. A first campaign involved small quantity of explosive at several depths of burial. The aerial pressures were measured at various heights and compared to simulations. The second set of experiments used a test rig to measure both the deformation of a floor simulating plate and the impulse transmitted by the buried explosion. A range of soil water contents, depths of burial of the explosive, plate thicknesses and stand off distances has been explored. For all the experiments, the sandy gravel STANAG soil defined in AEP 55 of STANAG 4569 has been used. Eulerian simulations were run and fit with these experiments. The roles of the three parts of the yield surface, of the elastic stiffening and plastic hardening mechanisms could be assessed. The initial soil density and the initial cap position were found to have the largest influence on aerial pressures. As for the impulse transmitted to the metallic plate, it was observed to be mostly controlled by the degree of saturation of the soil.

Depuis Ruelle, puis Rugh, Baladi, Tsujii, Liverani et d'autres, on sait que la fuite vers l'équilibre statistique dans de nombreux systèmes dynamiques chaotiques est gouvernée par le spectre de résonances de Ruelle de l'opérateur de transfert. A la suite de récents travaux de Faure, Sjöstrand et Roy, cette thèse propose une approche semiclassique de systèmes dynamiques chaotiques de type partiellement expansifs. Une partie du mémoire est consacrée aux extensions d'applications expansives vers des groupes de Lie compacts, en se reistreignant essentiellement aux extensions vers le groupe spécial unitaire SU(2). On se sert de la théorie des états cohérents pour les groupes de Lie, développée dans les années 70 par Perelomov et Gilmore, pour mettre en oeuvre les outils semiclassiques et la théorie des résonances de Helfer et Sjöstrand. On en déduira une estimation de Weyl et un gap spectral pour les résonances de Ruelle prouvant que la fuite vers l'équilibre statistique dans ces modèles est gouvernée par un opérateur de rang fini (en accord avec les résultats obtenus par Tsujii pour les semi-flots partiellement expansifs). On étend ensuite cette approche aux modèles "ouverts" pour lesquels la dynamique présente un ensemble captif de Cantor. On montrera l'existence d'un spectre discret de résonances de Ruelle et on prouve une loi de Weyl fractale, analogue classique du théorème de Lin-Guillopé-Zworski pour les résonances du laplacien hyperbolique sur les surfaces à courbure négative constante. On montre aussi un gap spectral asymptotique. On expliquera pourquoi ces modèles semblent être des objets d'étude adaptés pour approcher des questions importantes et difficiles du chaos classique ou quantique. On pense en particulier au problème de la minoration du nombre de résonances, étudié dans le contexte des applications quantiques par Nonnenmacher et Zworski. / Since the work of Ruelle, then Rugh, Baladi, Tsujii, Liverani and others, it is kown that the convergence towards statistical equilibrium in many chaotic dynamical systems is gouverned by the Ruelle spectrum of resonances of the so-called transfer operator. Following recent works from Faure, Sjöstrand and Roy, this thesis gives a semiclassical approach for partially expanding chaotic dynamical systems. The first part of the thesis is devoted to compact Lie groups extenstions of expanding maps, essentially restricting to SU(2) extensions. Using Perlomov's coherent state theory for Lie groups, we apply the semiclassical theory of resonances of Helfer and Sjöstrand. We deduce Weyl type estimations and a spectral gap for the Ruelle resonances, showing that the convergence towards equilibrium is controled by a finite rank operator (as Tsujii already showed for partially expanding semi-flows). We then extend this approach to "open" models, for which the dynamics exhibits a fractal invariant reppeler. We show the existence of a discrete spectrum of resonances and we prove a fractal Weyl law, the classical analogue of Lin-Guillopé-Zworski's theorem on resonances of non-compact hyperbolic surfaces. We also show an asymptotic spectral gap. Finally we breifly explain why these models are interseting "toy models" to explore important questions of classical and quantum chaos. In particular, we have in mind the problem of proving lower bounds on the number of resonances, studied in the context of open quantum maps by Nonnenmacher and Zworski.

On étudie une sous-classe des suites b-multiplicatives rarefiées avec un pas de raréfaction p premier, et on trouve une structure asymptotique avec un exposant alphain]0,1[ et une fonction de raréfaction continue périodique. Cette structure vaut pour les suites qui contiennent des nombres complexes du disque unité (section 1.1), et aussi pour des systèmes de numération avec b chiffres successifs positifs et négatifs (section 1.2). Ce formalisme est analogue à celui décrit (pour le cas particuler de la suite de Thue-Morse) par Gelfond; Dekking; Goldstein, Kelly, Speer; Grabner; Drmota, Skalba et autres. Dans la deuxième partie, largement indépendante, on étudie la raréfaction dans les suites composées de -1,0 et +1. On se restreint davantage au cas où b engendre le groupe multiplicatif modulo p. Cette hypothèse est conjecturée (Artin) d'être vraie pour une infinité de nombres premiers. Les constantes qui apparaissent s'expriment alors comme polynômes symétriques des P(zeta^j) où P est un polynôme à coefficients entiers, zeta est une racine primitive p-ième de l'unité, $j$ parcourt les entiers de 1 à p-1 (ce lien est explicité dans la section 1.3). On définit une méthode pour étudier les valeurs de ces polynômes symétriques, basée sur la combinatoire, notamment sur le problème de comptage des solutions des congruences et des systèmes linéaires modulo p avec deux conditions supplémentaires: les résidus modulo p utilisés doivent être non nuls et différents deux à deux. L'importance est donnée à la différence entre les nombres de soluions de deux congruences qui ne diffèrent que du terme sans variable. Le cas des congruences de la forme $x_1+x_2+...+x_n=i mod p$ équivaut à un résultat connu. Le mémoire (section 2.2) lui donne une nouvelle preuve qui en fait une application originale de la formule d'inversion de Möbius dans le p.o.set des partitions d'un ensemble fini. Si au moins deux coefficients distincts sont présents, on peut classer les réponses associées à toutes les congruences possibles qui ont un ensemble fixe de coefficients (de taille d), dans un tableau qu'on va appeler un "simplexe de Pascal fini". Ce tableau est une fonction delta:N^d->Z restreinte aux points de somme des coordonnées inférieure à p (un simplexe), avec deux propriétés: l'équation récursive de Pascal y est vérifiée partout sauf les points où la somme des coefficients est multiple de p (qui seront appelés les "sources" et forment un sous-réseau de l'ensemble des points entiers), et les valeurs en-dehors du simplexe induites par l'équation sont nulles (c'est démontré, en réutilisant la méthode précédente, dans la section 2.3 et en partie 2.4). On décrit un algorithme (section 2.4) qui consiste en applications successives de l'équation dans un ordre précis, qui permet de trouver l'unique fonction delta qui vérifie les deux conditions. On applique ces résultats aux suites b-multiplicatives (dans la section 2.5). On montre aussi que le nombre de sources ne dépend que de la dimension du simplexe d et de la longueur de son côté p. On formule la conjecture (partie 2.6) qu'il serait le plus petit possible parmi les tableaux de forme d'un simplexe de la dimention fixe et taille fixe qui vérifient les mêmes conditions. On montre un premier résultat sur les systèmes de deux congruences linéaires (section 2.5.4), et on montre (section 1.4) un lien avec une méthode de Drmota et Skalba pour prouver l'absence de phénomène de Newman (dans un sens précis), décrit initialement pour la suite de Thue-Morse et tout p tel que b engendre le groupe multiplicatif modulo p, et généralisé (section 1.4) à la suite (-1)^{nombre de chiffres 2 dans l'écriture en base 3 de n} appelée "++-". Cette problématique est riche en problèmes d'algorithmique et de programmation. Différentes sections du mémoire sont illustrées dans l'Annexe. La plupart de ces figures sont inédites. / The primary object of study is a subclass of b-multiplicative sequences, p-rarefied which means that the subsequence of terms of index multiple of a prime number p is taken. The sums of their initial terms have an asymptotic structure described by an exponent alphain]0,1[ and a contnous periodic "rarefaction function". This structure is valid for sequences with complex values in the unit disc, in both cases of the usual numerating system (section 1.1) and one with b successive digits among which there are positive and negative (section 1.2). This formalism is analogous to the formalism for the Thue-Morse sequence in texts by Gelfond; Dekking; Goldstein, Kelly, Speer; Grabner; Drmota, Skalba and others. The second, largely independent, part concerns rarefaction in sequences with terms in -1,0 or 1. Most results concern the case where b is a generator of the multiplicative group modulo p. This condition has been conjectured to be valid for infinity of primes, by Artin. The constants which are important, can be written as symmetric polynomials of P(zeta^j) where zeta is a primitive p-th root of unity, P is a polynomial with integer coefficients and j runs through the numbers from 1 to p-1 (section 1.3). The text describes a combinatorics-based method to study the values of these symmetric polynomials, where the combinatorial problem is as follows. Count the solutions of a linear congruence or a system modulo p, which satisfy a condition: the values of variables must be different from each other and from zero. Importance is attached to the difference between the numbers of solutions of two congruences that differ only in the free term. For the congruences of the form $x_1+x_2+...+x_n=i mod p$ this problem reduces to a well-known result. The text (section 2.2) gives an original proof of it, using the Möbius inversion formula in the p.o.set of partitions of a finite set. If at least two distinct coefficients are present, we can fix a set of coefficients (of size d) and put the answers corresponding to all possible linear congruences into an array that will be called "finite Pascal's triangle". It is a function delta:N^d->Z restricted to inputs with the sum of coordinates smaler than p (a simplex), and it has two properties. A recursive equation similar to the equation of Pascal holds everywhere except the points where the sum of coefficients is a multiple of p (a sublattice of Z^d the points of which are called "sources"); the values induced by this equation beyond the simplex are zeroes (section 2.3 and part of 2.4). An algorithm that finds the unique function delta satisfying these condiditions is described (section 2.4). It consists in successive applications of the equation in a precise order. These results are then applied to the b-multiplicative sequences (section 2.5). We also prove that the number of sources depends only on the dimention d and the size p of the simplex. We conjecture (section 2.6) that this number is the smallest possible for all numerical arrays of the same dimention and size that satisfy the same conditions. A first result about the systems of two linear congruences is proved (section 2.5.4). It is shown how these systems are related to a method by Drmota and Skalba of proving the absence of Newman's phenomenon (in a precise sence) initially described for the Thue-Morse sequence and for a prime p such that 2 is a generator of the multiplicative group modulo p, then extended to the sequence (-1)^{number of digits 2 in the ternary extension of n} called "++-". These questions generate many algorithmic and programming problems. Several sections link to illustration situated in the Annexe. Most of these figures are published for the first time.

Submitted by Maike Costa (maiksebas@gmail.com) on 2017-09-20T12:52:54Z No. of bitstreams: 1 arquivototal.pdf: 1155001 bytes, checksum: c813651173e6bf037a98328b32bc7d5a (MD5) / Made available in DSpace on 2017-09-20T12:52:54Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1155001 bytes, checksum: c813651173e6bf037a98328b32bc7d5a (MD5) Previous issue date: 2016-10-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the thirties of the last century, several formal versions for the intuitive notion of algorithmic function were offered. Among them, the version of the recursive functions and the version of the Turing-computable functions. Posteriorly, such versions were extended in order to also include the partial algorithmic functions, giving rise, in this way, to the version of the partial recursive functions and to the version of the partially Turing-computable functions. In this context, this research, located into Computability Theory domain and built in the light of theoretical assumptions of Davis (1982), Mendelson (2009), Dias & Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), among others, is intended to rebuild the proof that the given formal versions referred to the intuitive notion of partial algorithmic function, despite being conceptually distinct, they are extensionally equivalents in the sense that they determine the same set of theoretical-numerical functions. As a part of this rebuilding, we shall prove, in na unprecedented way, using quintuples, that every partial recursive function is partially Turing-computable. In the literature, this theorem is proved by means of a set of quadruples. However, defining a lower cardinality set constructed by quintuples, it is possible to prove it in a smaller time interval, which representes a gain from the computational point of view. Besides presenting this alternative proof, posed by the Church-Turing thesis that the set of partial recursive functions includes all the partial algorithmic functions, we shall investigate if this set itself and its infinite subsets are or are not algorithmic. In this survey, we shall demonstrate, in arithmetical terms, with the aid of Rice‟s theorem, that although the set of partial recursive functions is algorithmic, all its subsets which are different from the empty set are not, among which are the set of recursive functions and the set of primitive recursive functions. / Na década de 30 do século passado, foram oferecidas várias versões formais para a noção intuitiva de função algorítmica. Dentre elas, a versão das funções recursivas e a versão das funções Turing-computáveis. Posteriormente, tais versões foram estendidas a fim de abranger também as funções parciais algorítmicas, dando origem, deste modo, à versão das funções parciais recursivas e à versão das funções parcialmente Turing-computáveis. Nesse contexto, esta pesquisa, situada dentro do domínio da Teoria da Computabilidade e construída à luz dos pressupostos teóricos de Davis (1982), Mendelson (2009), Dias e Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), entre outros, destina-se a reconstruir a prova de que as referidas versões formais dadas para a noção intuitiva de função parcial algorítmica, apesar de conceitualmente distintas, são extensionalmente equivalentes no sentido de que elas determinam o mesmo conjunto de funções numéricas. Como parte desta reconstrução, provaremos, de modo inédito, mediante o uso de quíntuplas, que toda função parcial recursiva é parcialmente Turing-computável. Na literatura especializada, esse teorema é provado por meio de um conjunto de quádruplas. Porém, definindo um conjunto de menor cardinalidade constituído por quíntuplas, é possível prová-lo em um intervalo menor de tempo, o que representa um ganho do ponto de vista computacional. Além de apresentar essa prova alternativa, posto pela Tese de Church-Turing que o conjunto das funções parciais recursivas contém todas as funções parciais algorítmicas, investigaremos se ele próprio e os seus infinitos subconjuntos são ou não algorítmicos. Nesta investigação, demonstraremos, em termos aritméticos, com o auxílio do Teorema de Rice, que embora o conjunto das funções parciais recursivas seja algorítmico, todos os seus subconjuntos diferentes do conjunto vazio não o são, dentre os quais estão o conjunto das funções recursivas e o conjunto das funções recursivas primitivas.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2018-06-29T19:22:20Z No. of bitstreams: 2 Tese- Alaciy José Gomes - 2016.pdf: 5745946 bytes, checksum: d980380f3722151dde3e85c3a179ecf8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-07-03T15:20:24Z (GMT) No. of bitstreams: 2 Tese- Alaciy José Gomes - 2016.pdf: 5745946 bytes, checksum: d980380f3722151dde3e85c3a179ecf8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-07-03T15:20:24Z (GMT). No. of bitstreams: 2 Tese- Alaciy José Gomes - 2016.pdf: 5745946 bytes, checksum: d980380f3722151dde3e85c3a179ecf8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-13 / In this work we first consider regular vector fields : R3 􀀀! R3 and its orthogonal distribution of planes. We present a characterization of the normal curvature associated to and the system of implicit differential equations 2(D (dr); dr; ) + h rot( ); i hdr; dri = 0; hdr; i = 0; which define two one-dimensional singular and orthogonal foliations, which we call by principal foliations and whose leaves are the principal lines of the distribution . Next we describe the configurations of the principal foliations in a neighborhood of the generic singular points that constitutes a regular curve in R3, which are denoted by Darbouxian umbilic partially points and semi-Darbouxian. We proceed by studying the stability of the closed principal lines and we also present a Kupka- Smale genericity result. To conclude, we study the structure of the singularities of the principal foliations in a neighborhood of a singular hyperbolic point of the vector field . / Neste trabalho consideramos inicialmente campos de vetores regulares : R3 􀀀! R3 e sua distribuições ortogonais de planos . Apresentamos uma caracterização da curvatura normal associada a e do sistema de equações diferenciais implícitas, 2(D (dr); dr; ) + h rot( ); i hdr; dri = 0; hdr; i = 0; que definem duas folheações unidimensionais singulares e ortogonais, denominadas de folheações principais e cujas folhas são as linhas principais da distribuição . A seguir descrevemos as configurações das folheações principais, numa vizinhança dos pontos singulares genéricos que constituem uma curva regular em R3, denominados de pontos parcialmente umbílicos Darbouxianos e semi-Darbouxianos. Depois estudamos a estabilidade das linhas principais fechadas e apresentamos também um resultado de genericidade do tipo Kupka-Smale. Na parte final, estudamos a estrutura dos pontos singulares das folheações principais na vizinhança de um ponto singular hiperbólico do campo de vetores .