Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-03T11:30:54Z No. of bitstreams: 2 Dissertação - Ulisses Fernandes Motta - 2015.pdf: 4145018 bytes, checksum: 5f3e3b801fb14d3f7d6deb192d982ac8 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-03T11:33:57Z (GMT) No. of bitstreams: 2 Dissertação - Ulisses Fernandes Motta - 2015.pdf: 4145018 bytes, checksum: 5f3e3b801fb14d3f7d6deb192d982ac8 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-11-03T11:33:57Z (GMT). No. of bitstreams: 2 Dissertação - Ulisses Fernandes Motta - 2015.pdf: 4145018 bytes, checksum: 5f3e3b801fb14d3f7d6deb192d982ac8 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-07 / This study is about a proposal of using the GeoGebra software in the geometry course to rst year high school students. The reason for the choice of this software is due to its didactic characteristics which make the studied concepts more accessible to the students. The software was applied, as a suggestion, in the study of angles, triangles, polygons and circumferences mentioning some historical facts and relating the subjects, as far as possible, to other knowledge areas. Parallel to the writing of this work, many of the suggested proposals were worked in class and the nal results were satisfactory. We hope that the reading of this material produces among teachers the will to create new ideas for the use of this and other softwares in class as well as placing the math teaching in a more current perspective through the use of technological tools which are familiar to the students everyday activities. / Este trabalho é uma proposta de uso do software GeoGebra no curso de geometria plana para alunos de 1o ano do ensino médio. A escolha deste software se deu pelas suas características didáticas, que tornam a compreensão dos conceitos trabalhados mais acessíveis aos alunos. O software foi aplicado, como sugestão, no estudo dos ângulos, triângulos, polígonos e circunferência, citando alguns fatos históricos e relacionando os assuntos, quando possível, com outras áreas do conhecimento. Paralelamente à escrita deste trabalho, muitas das propostas sugeridas foram trabalhadas em sala de aula, e os resultados obtidos foram satisfatórios. Espero que a leitura deste material suscite nos professores o desejo de criação de novas ideias para uso deste software e de outros em suas aulas, inserindo o ensino da matemática em uma perspectiva mais atual, utilizando ferramentas tecnológicas que são comuns ao cotidiano dos alunos.

Os métodos, mais divulgados na literatura, para a avaliação da relação ânteroposterior entre a maxila e a mandíbula, receberam considerações. Alguns utilizavam pontos cefalométricos em estruturas anatômicas longe da região avaliada (ângulo ANB), outros como a avaliação Wits apresentavam instabilidade e variação do plano oclusal e, o plano MM° Bisector ou a avaliação ProjUSP que utilizavam muitos pontos cefalométricos e uma complexa técnica de traçado cefalométrico. Para facilitar esta avaliação, propusemos a utilização do plano PmA, com projeção ortogonal apenas do ponto B, para que somente com 3 pontos fosse possível alcançar uma confiável avaliação da relação ântero-posterior entre a maxila e a mandíbula. Para tanto a correlação entre a avaliação (PlanUSP) e os ângulos ANB e FABA e as avaliações Wits e Tpi foi pesquisada em uma amostra com 85 indivíduos, sendo 47 Classe I e 38 Classe II de Angle. Com a análise estatística obtivemos significativa correlação entre a avaliação PlanUSP e as outras medidas e avaliações pesquisadas, tanto para indivíduos Classe I como Classe II de Angle. Conclusão: a avaliação PlanUSP mostrou ser um método com significativa correlação e homogeneidade com as medidas dos ângulos ANB e FABA e com os métodos Wits e TPi, na avaliação da relação ântero-posterior entre a maxila e a mandíbula. / The most published methods, for the anteroposterior jaw relationship appraisal, have got consideration. Some of them used cephalometric points in the anatomical structures far from the evaluated area (ANB angle), others as the Wits appraisal got instability and alteration of the occlusal plane and some others like MMº Bisector plane and ProjUSP evaluation used many cephalometric points and a complex cephalometric tracing technique. The aim of this paper is making easier the assessment of the anteroposterior jaw relationship by using the PmA plane with perpendicular drawing from just point B, with only a 3 point way, that may get possible a reliable anteroposterior jaw relationship assessment. The correlation among the PlanUSP appraisal and the ANB and FABA angles and the Wits and TPi appraisals was researched with a sample of 85 subjects (47 Class I and 38 Class II). The statistical analysis showed a significant correlation between the PlanUSP appraisal and the others measurements and evaluations researched, as if Class I or Class II subjects. Conclusion: The PlanUSP appraisal showed to be a method with a significant correlation and homogeneity with the ANB and FABA angles measurements and the Wits and TPi methods for the anteroposterior jaw relationship assessments.

Objetivo: avaliar a relação entre o tipo facial e as variações da inclinação do Plano Oclusal e do ângulo ANB em indivíduos com oclusão normal. Material e Método: a amostra foi composta por 98 telerradiografias em norma lateral de 98 indivíduos (47 homens e 51 mulheres) com idade média de 15,2 anos (desvio padrão de 1,4 anos), com oclusão normal e perfil harmonioso. As radiografias foram digitalizadas em escala 1:1 eo programa Nemoceph (Nemotec® - Espanha), foi usado para a análise cefalométrica, que incluiu as cinco variáveis que segundo Ricketts definem o padrão facial, a relação sagital (SNA, SNB, ANB, N.S.Ba, SN.Go-Me, ANB individualizado, AP-BP e Wits)e ainclinação do Plano Oclusal (PLO.Linha S-N, PLO.PF, PLO.PP, PLO.XiPm e PLO.PM). Os dados foram analisados estatisticamente com um nível de significância de 5%. Resultados: acomposição dos tipos faciais foi: 11% dólicofaciais, 39% mesofaciais e 50% braquifaciais. Os valores médios e intervalo de confiança de 95% das variáveis que avaliaram a inclinação do plano oclusal, para os tipos faciais dólico, meso e braqui foramrespectivamente: PLO.SN: 21,7° (± 2,14°), 17,0° (± 1,10°) e 15,1° (± 1,43°); PLO.PF: 13,5° (±1,77)°, 10° (SD 1,01°) and 8,1° (± 1,25°); PLO.PP: 12,2° (±1,99°), 9.1° (± 1,31°) e 8,1° (± 1,21°); PLO.Xi-Pm: 20,5° (± 1,76°), 19,2° (± 0,96°) e 16,4° (± 1,12°); PLO.PM: 17,5° (± 2,02°), 15,3° (± 1,27°) e 12,1° (± 1,19°). Os valores médios das variáveis que avaliam a relação sagital maxilomandibular respectivamente foram: ANB: 3,8° (± 0,98°), 2,5° (± 0,62°) e1,3° (± 0,53°); distância AP-BP: 7,3mm (± 2,19mm), 3,4mm (± 0,94mm) e 1,9mm (± 0,78mm); ANB Individualizado: 4,7° (± 0,70°), 4,4° (± 0,43°) e 3,7° (± 0,39°); Wits: 1,8mm (± 1,27mm), -2,4mm (± 0,83mm) e -3,5mm (± 0,92mm). Conclusões: Tanto as variáveis que avaliam a inclinação do Plano Oclusal como as variáveis que avaliam a relação sagital maxilo-mandibular ANB e AP-BP, caracterizam-se diferencialmente segundo o tipo facial, observando-se um decréscimo dos valores do tipo dólicofacial para o braquifacial. / Objective: evaluate the relation between the facialtype and the inclination of the occlusal plane and ANB angle in individuals with normal occlusion.Material and Methods: the sample was composed of 98 radiographs, in lateral norm, of 98 individuals (47 men, 51 women), with an average age of 15.2 years (standard deviation of 1.4 years), normal occlusion and harmonic profile.The radiographs were digitalized in a 1:1 scale and the software Nemoceph (Nemotec® - Spain) was used for the cephalometric analysis, which included Rickettsfive variables thatdetermine the facial type, the saggital relation (SNA, SNB, ANB, N.S.Ba, SN.Go-Me, ANB individualized, AP-BP and Wits) and theinclination of the occlusal plane (OPL.S-N, OPL.PF, OPL.PP, OPL.XiPmand OPL.PM). The data was analyzed statistically with a significance level of 5%.Results: the composition of the sample by facial type was: 11% dolichofacial, 39% mesofacial e 50% braquifacial. The averagevalues and 95% confidence interval of the variables that measured the inclination of the occlusal plane, for the dolichofacial, mesofacial and braquifacialgroups were,respectively: OPL.SN: 21.7° (± 2.14°), 17.0° (± 1.10°) and 15.1° (± 1.43°); OPL.PF: 13.5° (±1.77)°, 10° (SD 1.01°) and 8.1° (± 1.25°); OPL.PP: 12.2° (± 1.99°), 9.1° (± 1.31°) and 8.1° (± 1.21°); OPL.Xi-Pm: 20.5° (± 1.76°), 19.2° (± 0.96°) and 16.4° (± 1.12°); OPL.PM: 17.5° (± 2.02°), 15.3° (± 1.27°) and 12.1° (± 1.19°). The average values and 95% confidence interval of the variables that measure the maxilar-mandibular saggital relation were respectively: ANB: 3.8° (± 0.98°), 2.5° (± 0.62°) and1.3° (± 0.53°);distance AP-BP: 7.3mm (± 2.19mm), 3.4mm (± 0.94mm)and 1.9mm (± 0.78mm); ANB Individualized: 4,7° (± 0.70°), 4.4° (± 0.43°) and 3.7° (± 0.39°); Wits: 1.8mm (± 1.27mm), -2.4mm (± 0.83mm)and -3.5mm (± 0.92mm). Conclusion: Both variables that measure the inclination of the occlusal plane and the variables that measure the ANB and AP-BP maxillomandibularsaggital relation have different characteristics according to the facial type, being observed a decrease in values from the dolichofacial type to the brachifacial type.

The aim of orthodontic treatment is to provide the patient with a good static and functional occlusion. During research that was conducted to complete a seminar on the static and functional aspects of occlusion, the author discovered that there might be a discrepancy between the goals of an ideal static occlusion, and the goals of an ideal functional occlusion. An ideal static occlusion seemed to require a flat mandibular plane and a minimal amount of overbite after active orthodontic treatment, whereas an ideal functional occlusion required a curved mandibular plane and an overbite of 4 mm to prevent cusp interferences during functional mandibular movements. The rationale behind the excessively flat mandibular plane and minimal overbite after orthodontic treatment is to compensate for the tendency of the bite to deepen during the period following orthodontic treatment. This tendency to relapse causes uncertainty about the stability of orthodontic treatment. Little research has been dedicated to examining the long-term stability of the leveled curve of Spee. In addition, there seems to be a considerable amount of controversy surrounding the long-term stability of overbite correction after orthodontic treatment. The aim of this study was to evaluate the stability of the curve of Spee and the overbite following orthodontic treatment. In addition, the relationship between the curve of Spee and the presence of anterior guidance after a period of orthodontic retention, was examined. The relationship between the overbite and the presence of anterior guidance was also examined, and the results were used to predict an ideal value for the overbite to avoid possible dental cusp interferences. Standardized digital photographs of the dental casts of 40 subjects were taken at three different stages: before treatment (T1), after orthodontic treatment (T2), and three years (mean) post-treatment. Accurate electronic measurement of the curve of Spee, using computer software, was completed for all three stages. The overbite was measured with a dial caliper. Clinical evaluation of the functional occlusion, with special reference to anterior guidance, was performed on all the subjects. Statistical analysis was carried out in search of statistical significant changes between the various stages, and possible correlations between the different variables. The results indicated that the leveling of the curve of Spee is a stable treatment procedure. The overbite was less stable than the curve of Spee, and nearly half the amount of overbite correction obtained during treatment, relapsed in the three years (mean) post-treatment. No relationship was found between the curve of Spee and the presence of anterior guidance at T3. A highly significant relationship was found between the overbite and the presence of anterior guidance. Subjects with a small overbite seemed to be predisposed to posterior interferences during mandibular protrusion. An overbite of not less than 3mm was found to be a desirable feature after orthodontic retention in order to reduce potentially interfering contacts. More research is necessary to clarify the relationship between dental interferences and temporomandibular disorders (TMD). / Dissertation (MChD (Orthodontics))--University of Pretoria, 2004. / Orthodontics / unrestricted

Let k be a field of characteristic zero and q ∈ kx not a root of unity. We may obtain non-commutative counterparts of various commutative algebras by twisting the multiplication using the scalar q: one example of this is the quantum plane kq[x; y], which can be viewed informally as the set of polynomials in two variables subject to the relation xy = qyx. We may also consider the full localization of kq[x; y], which we denote by kq(x; y) or D and view as the non-commutative analogue of k(x; y), and also the quantization Oq(Mn) of the coordinate ring of n x n matrices over k. Our aim in this thesis will be to use the language of deformation-quantization to understand the quantized algebras by looking at certain properties of the commutative ones, and conversely to obtain results about the commutative algebras (upon which a Poisson structure is induced) using existing results for the non-commutative ones. The q-division ring kq(x; y) is of particular interest to us, being one of the easiest infinite-dimensional division rings to define over k. Very little is known about such rings: in particular, it is not known whether its fixed ring under a finite group of automorphisms should always be isomorphic to another q-division ring (possibly for a different value of q) nor whether the left and right indexes of a subring E ? D should always coincide. We define an action of SL2(Z) by k-algebra automorphisms on D and show that the fixed ring of D under any finite group of such automorphisms is isomorphic to D. We also show that D is a deformation of the commutative field k(x; y) with respect to the Poisson bracket fy; xg = yx and that for any finite subgroup G of SL2(Z) the xed ring DG is in turn a deformation of k(x; y)G. Finally, we describe the Poisson structure of the fixed rings k(x; y)G, thus answering the Poisson-Noether question in this case. A number of interesting results can be obtained as a consequence of this: in particular, we are able to answer several open questions posed by Artamonov and Cohn concerning the structure of the automorphism group Aut(D). They ask whether it is possible to define a conjugation automorphism by an element z 2 LnD, where L is a certain overring of D, and whether D admits any endomorphisms which are not bijective. We answer both questions in the affirmative, and show that up to a change of variables these endomorphisms can be represented as non-bijective conjugation maps. We also consider Poisson-prime and Poisson-primitive ideals of the coordinate rings O(GL3) and O(SL3), where the Poisson bracket is induced from the non-commutative multiplication on Oq(GL3) and Oq(SL3) via deformation theory. This relates to one case of a conjecture made by Goodearl, who predicted that there should be a homeomorphism between the primitive (resp. prime) ideals of certain quantum algebras and the Poisson-primitive (resp. Poisson-prime) ideals of their semi-classical limits. We prove that there is a natural bijection from the Poisson-primitive ideals of these rings to the primitive ideals of Oq(GL3) and Oq(SL3), thus laying the groundwork for verifying this conjecture in these cases.

Within Mater’s Thesis a design of the communication module for X-Plane simulator was worked out. It will enable to read data from simulation model or change current flight situation.

The purpose of this dissertation is to address various geometric aspects of second-order scalar hyperbolic partial differential equations in two independent variables and one dependent variable F(x, y, u, u_x, u_y, u_xx, u_xy, u_yy )= 0 (1) We find a characterization of hyperbolic Darboux integrable equations at level k (1) in terms of the vanishing of the generalized Laplace invariants and provide an invariant characterization of various cases in the Goursat general classification of hyperbolic Darboux integrable equations (1). In particular we give a contact invariant characterization of equations integrable by the methods of general and intermediate integrals. New relative invariants that control the existence of the first integrals of the characteristic Pfaffian systems are found and used to obtain an invariant characterization for the class of -Gordon equations. A notion of a hyperbolic Darboux system is introduced and we show by examples that the classical Laplace transformation is just a special case of a diffeomorphism of hyperbolic Darboux systems. We also construct new examples of homomorphisms between certain hyperbolic systems. We characterize Monge-Ampere equations and explicitly exhibit two invariants whose vanishing is a necessary and sufficient condition for the equation to be of the Monge-Ampere type. The solution to the inverse problem of the calculus of variations for hyperbolic equations (1) in terms of the generalized Laplace invariants is presented. We also obtain some partial results on symplectic conservation laws. We characterize, up to contact equivalence, some classical equations using the generalized Laplace invariants. These results contain characterizations of the wave, Liouville, Klein-Gordon, and certain types of Euler-Poisson equations.

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This master thesis deals with conics in the real projective plane. The goal was to com- prehensibly introduce conics in the projective plane to high-school students and teachers. In order to fulfill this goal, the projective plane and homogenous coordinates were intro- duced, and harmonic set and priniple of duality were studied closely. The conics in the projective plane were approached from the perspective of history, and various definitions. Well-motivated introduction of a pole and a polar was emphasized.

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