Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2018-03-01T13:44:47Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Andrés Fernando Montenegro.pdf: 11976346 bytes, checksum: fa909dec838336e8c5a4ed73180bb65b (MD5) / Made available in DSpace on 2018-03-01T13:44:47Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Andrés Fernando Montenegro.pdf: 11976346 bytes, checksum: fa909dec838336e8c5a4ed73180bb65b (MD5) Previous issue date: 2017-10-16 / O objetivo deste estudo foi verificar o efeito da densidade de energia e o tempo de exposição de fotopolimerizadores LED de terceira geração em uma resina ortodôntica disponível comercialmente nos valores de microdureza, cisalhamento, índice de remanescente de resina e grau de conversão. Para tanto, foram realizados 3 experimentos: Experimento 1, o objetivo foi avaliar o grau de conversão (DC) e microdureza vickers (MHV) da resina ortodôntica utilizando dois LEDs de terceira geração, assim como, protocolos de fotoativação diferentes. Foram necessários 80 brackets cerâmicos e 80 brackets metálicos, sendo divididos em 16 grupos experimentais (n=10) tendo os seguintes grupos para cada LED: um grupo controle, diminuição da metade do tempo de exposição do grupo controle, um quarto do tempo do grupo controle, função turbo ou plasma para os LEDs Bluephase e Valo, respetivamente. Imediatamente após a polimerização, foram realizados os ensaios de DC e MHV. O experimento 2, objetivou verificar a influência de diferentes densidades de energia emitidas por dois fotoativadores LED de alta potência nas propriedades físicas e mecânicas de uma resina ortodôntica em brackets metálicos. Foram necessários 80 pré-molares superiores, sendo usadas as superfícies vestibulares dos dentes para a colagem dos 80 brackets metálicos. Os dentes foram divididos aleatoriamente em 8 grupos experimentais (n=10), sendo: um grupo controle, redução da metade do tempo de exposição do grupo controle, um quarto do tempo do grupo controle, função plasma ou turbo para cada LED estudado, sendo Valo e Bluephase. Após 24 horas da polimerização, foram realizados os testes de cisalhamento (SBS), índice remanescente de resina (ARI) e MHV. O objetivo do experimento 3 foi verificar a influência de diferentes densidades de energia depositadas por dois fotoativadores LED diferentes de alta potência nas propriedades físicas e mecânicas de uma resina ortodôntica em brackets cerâmicos. Foram necessários 80 dentes pré-molares superiores hígidos, sendo utilizadas as superfícies linguais ou palatinas dos dentes para colagem dos 80 brackets cerâmicos. Os dentes foram divididos aleatoriamente em 8 grupos experimentais (n=10), foram formados grupos iguais para cada LED Valo e Bluephase: um grupo controle, diminuição da metade do tempo de exposição do grupo controle, um quarto do tempo do grupo controle, função turbo do LED Bluephase ou plasma do LED Valo. Após 24 horas da polimerização, foram realizados os testes de SBS, ARI e MHV. Os resultados de cada experimento foram analisados através de testes estatísticos específicos, para determinar se houve ou não diferença estatisticamente significativa. Para o experimento 1 foram realizados ANOVA de duas vias e teste de Tukey (α=0,05), para o experimento 2 e 3 foram realizados Anova de duas vias com testes de Tukey (α=0,05). O experimento 1 mostrou que os grupos dos brackets cerâmicos tem baixa variação, porém pequenas mudanças no aumento dos valores da energia aplicada em Joules totais aumentam os valores de DC e MHV, nos brackets metálicos pelo fato de impedir a passagem da luz o DC e HVK diminuem significativamente, permanecendo dentro dos parâmetros considerados normais. O experimento 2 mostrou que ambos LED utilizados foram efetivos tanto na função standard como na turbo ou plasma, sendo que as funções turbo ou plasma ofereceram resultados similares aos do controle, efetivando mesmo com a redução do tempo para a polimerização dos brackets metálicos. No experimento 3 não houve diferença estatisticamente significativa nos grupos analisados. Os LEDs estudados proporcionaram valores suficientes de Joules em alguns grupos experimentais sendo este suficiente para atingir bons valores no DC, SBS e MHV. O uso de LEDs com uma potência adequada, sendo o mínimo de 1200 mW/cm2, ou o uso de uma potência elevada de entre 2400 a 3200 mW/cm2 e um curto período de tempo de exposição entre 3 a 6 segundos, são efetivos para a colagem de acessórios ortodônticos. / The objective of this study was to verify the effect of energy density and the time of exposure of third generation LED light curing agents on a commercially available orthodontic resin in the values of microhardness, shear, resin remaining index and degree of conversion. Three experiments were carried out: Experiment 1, the objective was to evaluate the degree of conversion (DC) and microhardness vickers (MHV) of the orthodontic resin using two third generation LEDs, as well as different photoactivation protocols. 80 ceramic brackets and 80 metallic brackets were required and divided into 16 experimental groups (n=10), with the following groups for each LED: control group, one half, one quarter of the control group time, turbo or plasma function for the Bluephase and Valo LEDs, respectively. Immediately after the polymerization, the DC and MHV assays of the specimens were performed. The experiment 2, aimed to verify the influence of different energy densities emitted by two high power LED photoactivators on the physical and mechanical properties of an orthodontic resin in metallic brackets. For this experiment, 80 carious cavity-free, superior human premolar teeth were used, and the buccal surfaces of the teeth were used for the bonding of the 80 metal brackets. The teeth were randomly divided into 8 experimental groups (n=10), with the following groups being a control group, half the time of exposure of the control group, one quarter of the time in the control group, plasma or turbo function for each LED studied, being Valo and Bluephase. After polymerization, the teeth and specimens were stored 24h at 37°C to perform the shear tests (SBS), resin remaining index (ARI) and MHV. The objective of experiment 3 was to verify the influence of different energy densities deposited by two different LED light-curing on the physical and mechanical properties of an orthodontic resin in ceramic brackets. For this experiment, it was necessary to have 80 carious free upper premolar human teeth, using the lingual or palatine surfaces of the teeth for bonding the 80 ceramic brackets. The teeth were randomly divided into 8 experimental groups (n=10), equal groups were formed for each Valo and Bluephase LEDs: one control group, one half-time control group exposure time, one-fourth time control group, function LED Bluephase turbo or LED Valo Plasma. After polymerization, the teeth and specimens were stored 24 hours at 37°C to perform the SBS, ARI and MHV tests. The results of each experiment were analyzed by specific statistical tests to determine whether or not there was a statistically significant difference. For experiment 1, 2 and two-way ANOVA and Tukey's test (α=0.05) were performed. Experiment 1 showed that the groups of ceramic brackets have low variation, but small changes in the increase of the values of the applied energy in total Joules increase the values of DC and MHV in the metallic brackets because it prevents the passage of light the DC and HVK decrease significantly, remaining within the parameters considered normal. Experiment 2 showed that both LEDs were effective both in the standard function and in the turbo or plasma, and the turbo or plasma functions gave similar results to the control, even effecting with the reduction of the time for the polymerization of the metal brackets. In the experiment 3 there was no statistically significant difference in the analyzed groups. The studied LEDs provided sufficient values of Joules in some experimental groups being sufficient to reach good values in DC, SBS and HVK. The use of LEDs with adequate power, being at least 1000 mW/cm2, or the use of a high power of between 2400 and 3200 mW/cm2 and a short period of exposure of between 3 to 6 seconds, are sufficient for the bonding of orthodontic accessories.

Cette thèse étudie deux problèmes de nature géométrique et topologique associés au crochet de Poisson sur les variétés symplectiques. Le premier problème porte sur la notion de submersion symplectique que nous introduisons dans le présent texte et qui généralise la notion de symplectomorphisme. Il s'avère qu'une submersion symplectique est un morphisme de Poisson : il s'agit d'une application entre variétés symplectiques qui préserve le crochet de Poisson. Notre intérêt pour ces fonctions réside dans le fait que le théorème de non-tassement de Gromov porte sur l'aire minimale possible pour les images des submersions symplectiques (allant d'une boule symplectique vers le plan symplectique) obtenues comme compositions d'un plongement symplectique dans l'espace symplectique euclidien de dimension 2n et de la projection standard vers le plan de coordonnées conjuguées (p_1, q_1). Nous investiguons le problème inverse dit « de représentabilité » : nous obtenons des conditions nécessaires et suffisantes pour qu'une submersion symplectique comme ci-dessus se factorise comme précédemment à travers un plongement ou une immersion symplectique dans l'espace euclidien. Nous montrons par ailleurs qu'il existe une submersion symplectique qui ne se factorise pas de la sorte à travers une immersion et qu'il existe aussi une submersion symplectique qui se factorise de la sorte à travers une immersion, mais pas à travers un plongement. Le deuxième problème porte sur la conjecture du crochet de Poisson de Polterovich. Étant donné une variété symplectique (M, omega) et un recouvrement U de M, nous pouvons définir l'invariant pb(F) associé à une partition de l'unité F subordonnée à U, qui est une sorte de norme sur les crochets de Poisson entre les paires de fonctions de la partition. En dénotant e(U) l'énergie de disjonction de Hofer maximale d'un ouvert du recouvrement U, la conjecture demande s'il existe une constante positive C indépendante de U et de F telle que le produit de pb(F) et de e(U) soit supérieur à C. Cette conjecture a été établie récemment par Buhovski-Logunov-Tanny dans le cas des surfaces ; en nous inspirant de travaux antérieurs de Buhovski-Tanny, nous avons aussi démontré la conjecture pour les surfaces de genre plus grand que 1. Nous exposons notre approche dans le second chapitre de cette thèse. À l'aide des submersions symplectiques, nous généralisons nos méthodes afin d'attaquer la conjecture en dimensions supérieures ; nous obtenons ainsi une nouvelle preuve d'un théorème de Polterovich et de Buhovski-Tanny concernant l'invariant pb pour des recouvrements formés de petits ouverts. Afin de rendre cette thèse aussi accessible et auto-suffisante que possible, nous débutons par une introduction à la topologie symplectique. Des annexes recueillent les faits plus particuliers que nous utilisons tout au long de ce travail. / This thesis studies two problems of geometric and topological nature associated to the Poisson bracket on symplectic manifolds. The first problem concerns the notion of "symplectic submersion" that we introduce here and which generalizes the concept of symplectomorphism. A symplectic submersion turns out to be a Poisson morphism, namely a map between symplectic manifolds which preserves the Poisson bracket. Our interest in those maps stems from the fact that Gromov's nonsqueezing theorem is a statement about the minimal area possible for the images of the symplectic submersions (going from a symplectic ball to a symplectic plane) which are compositions of a symplectic embedding into the Euclidean symplectic space and of the standard projection onto the plane of conjugated variables (p_1, q_1). We investigate the inverse "representability" problem: we give necessary and sufficient conditions for a symplectic submersionas above to factorize in the previous way either through a symplectic embedding or through a symplectic immersion into Euclidean space. We show moreover that there exists a symplectic submersion which does not factorize in this way through an immersion, and also that there exists a symplectic submersion which does factorize in this way through an immersion, but not through an embedding. The second problem concerns Polterovich's Poisson bracket conjecture. Given a symplectic manifold (M, omega) and an open cover U of M, we can define the invariantpb(F) of a partition of unity F subordinated to U, which is a sort of norm on the pairwise Poisson brackets of the functions in F. Denoting e(U) the maximal Hofer displacement energy of a set in U, the conjecture asks whether there exists a positive constant C independent of U and F such that the product of pb(F) and e(U) is greater than C. This conjecture was proved recently by Buhovsky-Logunov-Tanny in the case of surfaces; based on earlier work of Buhovsky-Tanny , we also proved the conjecture for surfaces of genus one and above. We present our approach in the second chapter of this thesis. Using symplectic submersions, we generalize our methods in order to tackle the conjecture in higher dimensions; in particular, we obtain a new proof of a theorem of Polterovich and Buhovsky-Tanny about the pb invariant of covers made up of small open sets. In order to make this thesis as accessible and self-contained as possible, we first give an introduction to symplectic topology. The appendices also collect the more specialized facts we use throughout this work.

This thesis deals with the theory of geometric control of the trident robot. The thesis describes the basic concepts of differential geometry and control theory, which are subsequently used for describing various mechanisms. Finally, the thesis proposes the management using inferred results.

The theme of the master’s thesis is to design steel structures sports hall. The proposal is developed in three variants according to ČSN EN. The work addresses the static effect of the steel structure and design of parts and materials design. Plan dimensions are 60x38m, max. internal height is 9,3m. The structure is designed for ultimate limit states and serviceability. The supporting structure is designed as roof arches surround an elliptical girder. In both gable walls are designed steel columns. The work also details and solution design. Sports hall was solved in Scia Engineer 2011 and includes a drawing documentation.

O objetivo principal do estudo é comparar o teste em 3 pontos com braquetes com o teste de resistência ao deslizamento utilizando um novo dispositivo que realiza a mensuração simultânea do coeficiente de atrito, das forças e dos momentos nos braquetes de ancoragem e da força de desativação no braquete desalinhado, exercidos por fios ortodônticos. Os objetivos secundários foram desenvolver o dispositivo e comparar, no teste em 3 pontos: (i) a influência, nas grandezas e no coeficiente de atrito cinético, da variação da simetria nas distâncias inter-braquetes, do tipo de braquete de ancoragem (canino ou 2º pré-molar), do deslocamento (3 ou 5mm) do braquete central, do sentido do desalinhamento (vestibular ou lingual) do braquete central e da marca de fio-braquete; (ii) as 3 formas de cálculo do coeficiente de atrito cinético; (iii) os 10 ciclos, para vestibular ou lingual, para verificar se eles são semelhantes ou não entre si. Foram utilizados braquetes autoligáveis (dentes 13, 14 e 15) e fios 0.014\'\' NiTi e CuNiTi das marcas Aditek e Ormco. O teste de resistência ao deslizamento foi realizado no desalinhamento lingual, nos dois deslocamentos e na configuração simétrica. O teste em 3 pontos com braquetes foi realizado no desalinhamento lingual e vestibular, nos dois deslocamentos e na configuração simétrica e assimétrica. Por meio da ANOVA, foram comparados, entre os dois tipos de teste: (A) as grandezas e o coeficiente de atrito e (B) o coeficiente de atrito gerado apenas no braquete de 2º pré-molar. Utilizando-se do mesmo teste estatístico foram comparados, no teste em 3 pontos com braquetes: (A) na configuração simétrica, algumas grandezas e o coeficiente de atrito advindos da variação da marca de fio-braquete, do deslocamento, do desalinhamento e do tipo de braquete; (B) algumas grandezas e o coeficiente de atrito gerados na configuração simétrica e assimétrica; (C) os valores das 3 formas de cálculo do coeficiente de atrito na configuração simétrica; e (D) algumas grandezas e o coeficiente de atrito encontrados nos 10 ciclos. Resultados: (A) a maioria dos valores das grandezas e do coeficiente de atrito gerados pelos dois tipos de teste foram diferentes estatisticamente; (B) o braquete de 2º pré-molar apresentou valores de coeficiente de atrito diferentes entre os dois tipos de teste; (C) na configuração simétrica, as variáveis foram estatisticamente significantes na maioria dos casos para as grandezas analisadas e para o coeficiente de atrito; (D) houve diferença entre a configuração simétrica e assimétrica; (E) o coeficiente de atrito baseado nas duas normais e na força de atrito se aproximou mais da realidade clínica e foi sensível à variação da geometria da relação fio-braquete; e (F) os 10 ciclos para lingual foram semelhantes entre si em 70% dos casos e os 10 ciclos para vestibular foram diferentes em 57% dos casos. Conclusões: o teste em 3 pontos com braquetes é diferente do teste de resistência ao deslizamento; a variação das configurações geométricas e da marca de fio-braquete pode influenciar nos valores das grandezas e do coeficiente de atrito cinético; os 10 ciclos para lingual foram mais semelhantes entre si que os 10 ciclos para vestibular. / The main objective of the study is to compare the three-bracket bending test with the resistance to sliding test using a new device that performs simultaneous measurement of coefficient of friction, the forces and moments on the anchor brackets and deactivation force in misaligned bracket, exercised by orthodontic wires. Secondary objectives were to develop the device and compare, in the three-bracket bending test: (i) the influence, on the physical quantities and on the kinetic friction coefficient, of the variation of the symmetry in the inter-bracket distance, of the type of anchor bracket (canine or 2nd premolar), of displacement (3 or 5mm) and misalignment (buccal or lingual) of the central bracket, and of the wire and bracket brand; (ii) the three ways to calculate the coefficient of kinetic friction; (iii) the 10 cycles, for buccal or lingual, to see if they are similar or not. Self-ligating brackets were used (teeth 13, 14 and 15) and wires 0.014 \'\' NiTi and CuNiTi of Aditek and Ormco brands. The resistance to sliding test was conducted on the lingual misalignment, on both displacements and on symmetrical configuration. The three-bracket bending test was held at the lingual and vestibular misalignment, at both displacements and at the symmetrical and asymmetrical configuration. Through ANOVA, were compared, between the two types of tests: (A) the quantities and the coefficient of friction and (B) the coefficient of friction generated only in the second premolar bracket. Using the same statistical test were compared, in three-bracket bending test: (A) in symmetrical configuration, the quantities and the coefficient of friction arising from the variation in the wire and bracket brands, displacement, misalignment and the type of bracket; (B) the quantities and the coefficient of friction generated by the symmetric and asymmetric configuration; (C) the values of the three ways of calculating friction coefficient; and (D) the quantities and the coefficient of friction encountered in 10 cycles. Results: (A) most of the values of the quantities and the coefficient of friction generated by the two types of test were statistically different; (B) the 2nd premolar bracket showed different friction coefficient values between the two types of test; (C) in the symmetrical configuration, the variables were statistically significant in the most of cases for quantities and the friction coefficient; (D) was found difference between symmetric and asymmetric configuration; (E) the friction coefficient based on both normal forces and frictional force was closer to the clinical reality and was sensitive to variations in the geometry of the wire-bracket relationship; and (F) the 10 cycles for lingual were similar in 70% of cases and the 10 cycles for buccal desalignment were different in 57% of cases. Conclusions: The three-bracket bending test is different from the resistance to sliding test; the variation of geometric configurations and wire and bracket brands may influence the values of the quantities and the coefficient of kinetic friction; the 10 cycles for lingual were more similar to each other than the 10 cycles for buccal.

O objetivo principal do estudo é comparar o teste em 3 pontos com braquetes com o teste de resistência ao deslizamento utilizando um novo dispositivo que realiza a mensuração simultânea do coeficiente de atrito, das forças e dos momentos nos braquetes de ancoragem e da força de desativação no braquete desalinhado, exercidos por fios ortodônticos. Os objetivos secundários foram desenvolver o dispositivo e comparar, no teste em 3 pontos: (i) a influência, nas grandezas e no coeficiente de atrito cinético, da variação da simetria nas distâncias inter-braquetes, do tipo de braquete de ancoragem (canino ou 2º pré-molar), do deslocamento (3 ou 5mm) do braquete central, do sentido do desalinhamento (vestibular ou lingual) do braquete central e da marca de fio-braquete; (ii) as 3 formas de cálculo do coeficiente de atrito cinético; (iii) os 10 ciclos, para vestibular ou lingual, para verificar se eles são semelhantes ou não entre si. Foram utilizados braquetes autoligáveis (dentes 13, 14 e 15) e fios 0.014\'\' NiTi e CuNiTi das marcas Aditek e Ormco. O teste de resistência ao deslizamento foi realizado no desalinhamento lingual, nos dois deslocamentos e na configuração simétrica. O teste em 3 pontos com braquetes foi realizado no desalinhamento lingual e vestibular, nos dois deslocamentos e na configuração simétrica e assimétrica. Por meio da ANOVA, foram comparados, entre os dois tipos de teste: (A) as grandezas e o coeficiente de atrito e (B) o coeficiente de atrito gerado apenas no braquete de 2º pré-molar. Utilizando-se do mesmo teste estatístico foram comparados, no teste em 3 pontos com braquetes: (A) na configuração simétrica, algumas grandezas e o coeficiente de atrito advindos da variação da marca de fio-braquete, do deslocamento, do desalinhamento e do tipo de braquete; (B) algumas grandezas e o coeficiente de atrito gerados na configuração simétrica e assimétrica; (C) os valores das 3 formas de cálculo do coeficiente de atrito na configuração simétrica; e (D) algumas grandezas e o coeficiente de atrito encontrados nos 10 ciclos. Resultados: (A) a maioria dos valores das grandezas e do coeficiente de atrito gerados pelos dois tipos de teste foram diferentes estatisticamente; (B) o braquete de 2º pré-molar apresentou valores de coeficiente de atrito diferentes entre os dois tipos de teste; (C) na configuração simétrica, as variáveis foram estatisticamente significantes na maioria dos casos para as grandezas analisadas e para o coeficiente de atrito; (D) houve diferença entre a configuração simétrica e assimétrica; (E) o coeficiente de atrito baseado nas duas normais e na força de atrito se aproximou mais da realidade clínica e foi sensível à variação da geometria da relação fio-braquete; e (F) os 10 ciclos para lingual foram semelhantes entre si em 70% dos casos e os 10 ciclos para vestibular foram diferentes em 57% dos casos. Conclusões: o teste em 3 pontos com braquetes é diferente do teste de resistência ao deslizamento; a variação das configurações geométricas e da marca de fio-braquete pode influenciar nos valores das grandezas e do coeficiente de atrito cinético; os 10 ciclos para lingual foram mais semelhantes entre si que os 10 ciclos para vestibular. / The main objective of the study is to compare the three-bracket bending test with the resistance to sliding test using a new device that performs simultaneous measurement of coefficient of friction, the forces and moments on the anchor brackets and deactivation force in misaligned bracket, exercised by orthodontic wires. Secondary objectives were to develop the device and compare, in the three-bracket bending test: (i) the influence, on the physical quantities and on the kinetic friction coefficient, of the variation of the symmetry in the inter-bracket distance, of the type of anchor bracket (canine or 2nd premolar), of displacement (3 or 5mm) and misalignment (buccal or lingual) of the central bracket, and of the wire and bracket brand; (ii) the three ways to calculate the coefficient of kinetic friction; (iii) the 10 cycles, for buccal or lingual, to see if they are similar or not. Self-ligating brackets were used (teeth 13, 14 and 15) and wires 0.014 \'\' NiTi and CuNiTi of Aditek and Ormco brands. The resistance to sliding test was conducted on the lingual misalignment, on both displacements and on symmetrical configuration. The three-bracket bending test was held at the lingual and vestibular misalignment, at both displacements and at the symmetrical and asymmetrical configuration. Through ANOVA, were compared, between the two types of tests: (A) the quantities and the coefficient of friction and (B) the coefficient of friction generated only in the second premolar bracket. Using the same statistical test were compared, in three-bracket bending test: (A) in symmetrical configuration, the quantities and the coefficient of friction arising from the variation in the wire and bracket brands, displacement, misalignment and the type of bracket; (B) the quantities and the coefficient of friction generated by the symmetric and asymmetric configuration; (C) the values of the three ways of calculating friction coefficient; and (D) the quantities and the coefficient of friction encountered in 10 cycles. Results: (A) most of the values of the quantities and the coefficient of friction generated by the two types of test were statistically different; (B) the 2nd premolar bracket showed different friction coefficient values between the two types of test; (C) in the symmetrical configuration, the variables were statistically significant in the most of cases for quantities and the friction coefficient; (D) was found difference between symmetric and asymmetric configuration; (E) the friction coefficient based on both normal forces and frictional force was closer to the clinical reality and was sensitive to variations in the geometry of the wire-bracket relationship; and (F) the 10 cycles for lingual were similar in 70% of cases and the 10 cycles for buccal desalignment were different in 57% of cases. Conclusions: The three-bracket bending test is different from the resistance to sliding test; the variation of geometric configurations and wire and bracket brands may influence the values of the quantities and the coefficient of kinetic friction; the 10 cycles for lingual were more similar to each other than the 10 cycles for buccal.

No description available.

Cette thèse se divise en trois parties qui peuvent être toutes regroupées autour d'une même bannière : l'étude de structures algébriques reliées aux algèbres de type Askey–Wilson. Alors que dans la première partie on s'efforce d'obtenir des interprétations duales (au sens de Howe) de ces algèbres, dans les autres parties on étudie des généralisations de ces algèbres. Des dégénérations de l'algèbre de Sklyanin, générées par des blocs plus fondamentaux que ceux générant les algèbres de type Askey–Wilson, sont étudiées dans la deuxième partie et des généralisations de plus haut rang des algèbres de type Askey–Wilson sont étudiées dans la troisième partie. Dans la première partie, en invoquant la dualité de Howe, deux interprétations duales sont obtenues pour les algèbres de Racah, Bannai–Ito, Askey–Wilson, Higgs, Hahn, \(q\)-Hahn et dual \(-1\) Hahn. La façon dont la dualité de Howe opère est rendue explicite par l'examen de processus de réduction dimensionnelle. Un modèle superintégrable 2D de mécanique quantique superconforme dont l'algèbre de symétrie est celle de type dual \(-1\) Hahn est également introduit et solutionné. Dans la deuxième partie, des algèbres générées par des opérateurs de contiguïté et d'échelle encodant des propriétés de familles de polynômes sont étudiées. Ces opérateurs appartiennent à la classe des opérateurs de Sklyanin–Heun, qui peuvent être définis sur plusieurs grilles diverses. On découvre qu'ils génèrent des dégénérations de l'algèbre de Sklyanin. On démontre que les représentations irréductibles de dimension finie de ces algèbres ont pour base des familles de para-polynômes. Les grilles linéaires, quadratiques, exponentielles et d'Askey–Wilson sont étudiées et mènent respectivement aux polynômes orthogonaux des familles de para-Krawtchouk, para-Racah, \(q\)-para-Krawtchouk et \(q\)-para-Racah. Enfin, la façon dont les polynômes de para-Krawtchouk et d'autres familles de polynômes orthogonaux sont reliées aux représentations tridiagonales du plan de Jordan déformé est présentée. Dans la dernière partie, on explore des généralisations à plus haut rang pour les algèbres de Racah et Askey–Wilson. Pour ce faire, on étudie les réalisations de ces algèbres en termes de Casimirs intermédiaires. Le rôle de la matrice \(R\) tressée est élucidé : celle-ci permet de relier divers Casimirs intermédiaires entre eux par conjugaison. Un isomorphisme entre l'algèbre de skein du crochet de Kauffman de la sphère à 4 trous et l'algèbre engendrée par les Casimir intermédiaires dans \(U_q(\mathfrak{sl}_2)^{\otimes 3}\) est présenté et permet d'interpréter de façon diagrammatique la conjugaison par la matrice \(R\) tressée mentionnée ci-haut. Finalement, une présentation du centralisateur \(Z_n(\mathfrak{sl}_2)\) de \(U(\mathfrak{sl}_2)\) dans \(U(\mathfrak{sl}_2)^{\otimes n}\) par générateurs et relations est obtenue et on montre que ce centralisateur est isomorphe à un quotient (obtenu explicitement) de l'algèbre de Racah de plus haut rang \(R(n)\). / This thesis is divided in three parts which all orbit around the same theme: the study of algebraic structures related to the algebras of Askey–Wilson type. In the first part we obtain two interpretations that are dual in the sense of Howe for the algebras of Askey–Wilson type. Meanwhile, the other two parts are concerned with generalizations of these algebras. In the second part, we study degenerations of the Sklyanin algebra, which are built out of generators that are more fundamental than those of the Askey–Wilson algebra. In the last part, generalizations of the Askey–Wilson type algebras to higher rank are studied. In the first part, dual interpretations are obtained for the Racah, Bannai–Ito, Askey–Wilson, Higgs, Hahn, \(q\)-Higgs and dual \(-1\) Hahn algebras by invoking Howe duality. The way that this Howe duality operates is made explicit through the examination of a dimensional reduction procedure. A 2D superintegrable superconformal quantum mechanics model, whose symmetry algebra is the one of dual \(-1\) Hahn type, is also introduced and solved. In the second part, we study algebras that are generated by contiguity and ladder operators that encode properties of families of orthogonal polynomials. We show that these operators belong to the Sklyanin–Heun class of operators, which can be defined for various grids. We also show how their algebraic relations correspond to those of degenerations of the Sklyanin algebra. Then, we show how various families of para-polynomials support finite-dimensional irreducible representations of these degenerate algebras. From the linear, quadratic, exponential and Askey–Wilson grids, we are respectively led to the para-Krawtchouk, para-Racah, \(q\)-para-Krawtchouk and \(q\)-para-Racah polynomials. Later, we connect the para-Krawtchouk polynomials (and other families of orthogonal polynomials) to tridiagonal representations of the deformed Jordan plane. In the final part, we explore higher rank generalizations of the Racah and Askey–Wilson algebras. To that end, their realizations in terms of intermediate Casimir elements are studied. The role of the braided \(R\)-matrix is understood as follows: it connects various intermediate Casimir elements through conjugation. We obtain an isomorphism between the Kauffman bracket skein algebra of the four-punctured sphere and the algebra generated by the intermediate Casimir elements in \(U_q(\mathfrak{sl}_2)^{\otimes3}\). This leads to a diagrammatic interpretation of the conjugation by the braided \(R\)-matrix mentioned in the above. Lastly, a presentation of the centralizer \(Z_n(\mathfrak{sl}_2)\) of \(U(\mathfrak{sl}_2)\) in \(U(\mathfrak{sl}_2)^{\otimes n}\) by generators and relations is obtained and we show that this centralizer is isomorphic to a quotient (which we provide explicitly) of the higher rank Racah algebra \(R(n)\).

L'article "A systematic search for nonrelativistic systems with dynamical symetries, Part I" publié il y a à peu près 50 ans a commencé une classification de ce qui est maintenant appelé les systèmes superintégrables. Il était dévoué aux systèmes dans l'espace Euclidien ayant plus d'intégrales de mouvement que de degrés de liberté. Les intégrales étaient toutes supposées de second ordre en quantité de mouvement. Dans ce mémoire, sont présentés de nouveaux résultats sur la superintégrabilité de second ordre qui sont pertinents à l'étude de la superintégrabilité d'ordre supérieur et de la superintégrabilité de systèmes ayant des potentiels vecteurs ou des particules avec spin. / The article "A systematic search for nonrelativistic systems with dynamical symetries, Part I" published about 50 years ago started the classification of what is now called superintegrable systems. It was devoted to systems in Euclidean space with more integrals of motion than degrees of freedom. The integrals were all assumed to be second order polynomials in the particle momentum. Here we present some further results on second order superintegrability that are relevant for studies of higher order superintegrability and for superintegrability for systems with vector potentials or for particles with spin.

本文以符合時代潮流之免稅額制度為主，重新探討改革單一稅率所得稅制至兩課稅級距稅制後，整體社會福利與所得分配情形之變化，並將所得結果與負所得稅制下之結論作一比較，最後，再將稅制改革下社會福利變動數額與稅制改革造成租稅管理成本增加之數額兩相比較，作為政府選擇稅制時之參考。 本文主要擴展Kemper(1992)建立的具免稅額單一稅率模型，建構本研究具免稅額的兩課稅級距理論模型，並針對各種租稅改革方案詳加分類，以釐清各方案對個人效用與勞動供給產生之影響；模擬分析方法係採用Yitzhaki(1982)提出之”Tax Programming Model”（租稅程式設計模型），假設社會有100人，工資率分配型態以平均數=-1；變異數=0.39的Lognormal Distribution近似之，再配合不同社會風險趨避係數、人民勞動替代彈性及政府所需稅收等模型參數設定，求出精密度為百分之一的最適解。 藉由模擬分析結果，本研究得到以下結論： 一、 單一稅率改制為兩課稅級距稅制確有提升整體社會福利與改善所得分配公平的效果，而當社會重視效用分配公平的程度愈強烈，兩課稅級距稅制較單一稅率為優的特性愈明顯。 二、 單一稅率改制為兩課稅級距稅制之改革方案共有六種，每種方案對個人效用及勞動供給造成之影響各不相同，而最適改革方案之選擇，決定於人民勞動替代彈性的大小、社會重視效用分配公平的程度與政府所需稅收的多寡。不過，當社會較重視效用分配公平、人民勞動替代彈性愈小與政府所需稅收增加時，型一改革方案成為最適改革方案的可能性愈大。 三、 本研究提及六種租稅改革方案中以型一方案為最佳，這是因為勞動替代彈性愈小，邊際稅率上升帶來的效率損失也愈小，使得稅制雖具有邊際稅率遞增之特性，其效率損失亦不如邊際稅率遞增改善所得重分配的優點來得大；再者，由第三章比較靜態的分析可知免稅額下降有刺激勞動供給增加的效果，可以抵消一部份稅率上升帶來的效率損失，故型一改革方案（降低免稅額、第一級距邊際稅率及增加第二級距邊際稅率）在同時考量效率與公平之後，仍能被選為最佳稅制改革方案。 四、 兩課稅級距稅制之最適稅率結構，不限於邊際稅率遞增或遞減之型態，但仍必須具有平均稅率累進之特性。 五、 人民勞動替代彈性改變對最適兩課稅級距稅制之影響，是當勞動彈性愈大時，無論第一或第二級距邊際稅率均應下降，且免稅額亦減少；若由人民稅負變化而言，此時決定之稅制使中、低所得者之稅負較重，高所得者的稅負減輕。 六、 社會重視效用分配公平程度改變對最適兩課稅級距稅制之影響，是當社會重視效用分配公平的程度愈強時，免稅額下降、第一級邊際稅率愈輕而第二級邊際稅率會愈重，且兩邊際稅率間之差距隨社會重視效用分配公平程度提高而加大；若由人民稅負變化而言，此時決定之稅制使中、低所得者稅負減輕，高所得者稅負加重。 七、 政府所需稅收改變對最適兩課稅級距稅制之影響，是當所需稅收愈多時，免稅額就愈低，至於邊際稅率結構之變化，則無明顯特徵；若由人民稅負變化而言，此時決定之稅制會使全體人民稅負均加重。