[pt] O objetivo deste trabalho é o de estudar propriedades geométricas de curvas poligonais genéricas. Inicialmente abordamos resultados clássicos para curvas quanto à sua curvatura total no caso discreto e discutimos aqueles pertinentes a nós poligonais. Também é feito o estudo do Grafo de Maxwel para poligonais. No caso, temos uma interessante relação entre a natureza do grafo quanto ao seu número de componentes e à condição de a poligonal ser ou não convexa. / [en] The aim of this work is to study geometrical properties of generic polygonal lines. We begin with some classical results for curves with respect to total curvature, in the discrete case, and discuss results related to polygonal knots. Maxwell graphs are also considered for polygonal lines: We study the relation between the number of components of the graph and the convexity of the polygonal line.

This study investigates the first-order mechanics of polygonal fault networks in Utopia Planitia, Mars and whether terrestrial sedimentary basin polygonal terrains are an analog for giant Martian polygons since there is an overlap in scale between the 3 km terrestrial polygons and the 1-40 km giant polygons of Mars. Volumetric contraction accommodates the extensional faulting observed in both cases. Boundary Element Method numerical models are used to simulate the first-order-mechanics of the faulting process. Models use material properties for wet, fine sediment, and apply an extensional strain to produce volumetric contraction. Fracture seeds that simulate the buried topography beneath the basin are placed at the base of the model. MOLA tracks from the Highlands are used to create the uneven topography beneath the basin since the underlying topography of the Northern Lowlands is thought to be similar to the topography of the older, Southern Highlands. The model investigates whether 1 & 2 km layer of wet, fine sediments will produce the fracture spacing observed within the polygonal terrains in Utopia (~5 – 6.5 km). A fracture network that is similar to the scale of the polygonal terrain in the Utopia Basin is established within the model at low strain, supporting the idea that buried topography could be the primary scaling factor for the polygon grabens. The results do not constrain an upper limit for strain; the observed trough widths in Utopia suggest that further strain was expressed by the widening of the troughs. Material properties for wet, fine sediments, analogous to the terrestrial counterpart, are appropriate for the model to match what is observed in Utopia. The power-law scale of Highlands topography controls the scale of the surface fracture spacing in the models. Measurements of running average of trough spacing along radial transects with respect to the center of the basin did not yield a monotonic decrease in trough spacing as would be expected for a smooth basement with no buried topography. Study results support the case for buried topography controlling the scale of the giant polygons of Utopia Planitia.

Converging cylindrical shock waves have been studied experimentally. Numericalcalculations based on the Euler equations and analytical comparisons basedon the approximate theory of geometrical shock dynamics have been made tocomplement the study.Shock waves with circular or polygonal shock front shapes have been createdand focused in a shock tube. With initial Mach numbers ranging from 2 to4, the shock fronts accelerate as they converge. The shocked gas at the centreof convergence attains temperatures high enough to emit radiation which isvisible to the human eye. The strength and duration of the light pulse due toshock implosion depends on the medium. In this study, shock waves convergingin air and argon have been studied. In the latter case, the implosion lightpulse has a duration of roughly 10 μs. This enables non-intrusive spectrometricmeasurements on the gas conditions.Circular shock waves are very sensitive to disturbances which deform theshock front, decreasing repeatability. Shocks consisting of plane sides makingup a symmetrical polygon have a more stable behaviour during focusing,which provides less run-to-run variance in light strength. The radiation fromthe gas at the implosion centre has been studied photometrically and spectrometrically.Polygonal shocks were used to provide better repeatability. Thefull visible spectrum of the light pulse created by a shock wave in argon hasbeen recorded, showing the gas behaving as a blackbody radiator with apparenttemperatures up to 6000 K. This value is interpreted as a modest estimation ofthe temperatures actually achieved at the centre as the light has been collectedfrom an area larger than the bright gas core.As apparent from experimental data real gas effects must be taken intoconsideration for calculations at the implosion focal point. Ideal gas numericaland analytical solutions show temperatures and pressures approaching infinity,which is clearly not physical. Real gas effects due to ionisation of theargon atoms have been considered in the numerical work and its effect on thetemperature has been calculated.The propagation of circular and polygonal have also been experimentallystudied and compared to the self-similar theory and geometrical shock dynamics,showing good agreement. / QC 20110502

No description available.

The determination of an aircraft's mass properties is critical during its conceptual design phase. Obtaining reliable mass property information early in the design of an aircraft can prevent design mistakes that can be extremely costly further along in the development process. In this thesis, several methods are presented in order to automatically calculate the mass properties of aircraft structural components and fuel stored in tanks. The first method set forth calculates the mass properties of homogenous solids represented by polyhedral surface geometry. A newly developed method for calculating the mass properties of thin shell objects, given the same type of geometric representation, is derived and explained. A methodology for characterizing the mass properties of fuel in tanks has also been developed. While the concepts therein are not completely original, the synthesis of past research from diverse sources has yielded a new comprehensive approach to fuel mass property analysis during conceptual design. All three of these methods apply to polyhedral geometry, which in many cases is used to approximate NURBS (Non-Uniform Rational B-Spline) surface geometry. This type of approximate representation is typically available in design software since this geometric format is conducive to graphically rendering three-dimensional geometry. The accuracy of each method is within 10% of analytical values. The methods are highly precise (only affected by floating point error) and therefore can reliably predict relative differences between models, which is much more important during conceptual design than accuracy. Several relevant and useful applications of the presented methods are explored, including a methodology for creating a CG (Center of Gravity) envelope graph. / Master of Science

In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter partial-estimator polygonal line processes. We derive asymptotic results for these processes in Holder spaces. The behavior of test statistics under the null hypothesis of no change and alternative is provided. Empirical power analysis has shown that tests are more powerful when absolute values of model parameter are quite large or autoregressive process changes from a stationary state to a nonstationary one. We prove the consistency of the least square changed-segment estimators and provide their convergence rates. / Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų įvertinių dalinių sumų ir modelio parametro dalinių įvertinių laužčių procesais. Šiems procesams gautos ribinės teoremos Hiolderio erdvėse. Nurodomas testų statistikų ribinis elgesys esant teisingai nulinei ir alternatyviajai hipotezėms. Iš empirinio kriterijų galios tyrimo rezultatų matyti, kad pasiūlytų testų galia didžiausia aptinkant pasikeitimus iš stacionarios būklės į nestacionarią arba esant artimoms vienetui modelio parametro reikšmėms. Taip pat įrodoma, kad mažiausių kvadratų metodu gauti pasikeitusio segmento pradžios ir ilgio įverčiai bei autoregresinio modelio su pasikeitusiu segmentu parametrų įverčiai yra suderintieji bei pateikiamas jų konvergavimo greitis.

Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų įvertinių dalinių sumų ir modelio parametro dalinių įvertinių laužčių procesais. Šiems procesams gautos ribinės teoremos Hiolderio erdvėse. Nurodomas testų statistikų ribinis elgesys esant teisingai nulinei ir alternatyviajai hipotezėms. Iš empirinio kriterijų galios tyrimo rezultatų matyti, kad pasiūlytų testų galia didžiausia aptinkant pasikeitimus iš stacionarios būklės į nestacionarią arba esant artimoms vienetui modelio parametro reikšmėms. Taip pat įrodoma, kad mažiausių kvadratų metodu gauti pasikeitusio segmento pradžios ir ilgio įverčiai bei autoregresinio modelio su pasikeitusiu segmentu parametrų įverčiai yra suderintieji bei pateikiamas jų konvergavimo greitis. / In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter partial-estimator polygonal line processes. We derive asymptotic results for these processes in Holder spaces. The behavior of test statistics under the null hypothesis of no change and alternative is provided. Empirical power analysis has shown that tests are more powerful when absolute values of model parameter are quite large or autoregressive process changes from a stationary state to a nonstationary one. We prove the consistency of the least square changed-segment estimators and provide their convergence rates.

This thesis was elaborated on the topic: Project and realisation of the network for planimetry control points using the methods geodetic and GPS. The aim was carry out the reconnaissance of the terrain, valorize of the current state of the point field in the selected locality, as necessary complete him in the density for the detailed mapping of big ratio scale and locate. All calculations, evaluation of the accuracy and processing of the graphic supplements were a part of this thesis. The point network was built in the cadastral territory Horní Planá in the drainage area of the river Ostřice. Following the geodetic data and the map basis was effected the reconnaissance of the selected locality, the stabilization of the new points PPBP and after that they were positional located. On the whole there were stabilized 14 new points. They were located by using the total station Leica TC407 by the help of double - sided incorporated and double - sided oriented polygonal traverse and by using GPS station Trimble 4600LS for the fast static method.

In this thesis was elaborated the topic: Project and surveying of the network for planimetry and hight points in the area of the river Ostřice using several methods. It{\crq}s purpose was a reconnaissance of the part of a basin of Ostřice, assessment of existing point field, propose and complete the point network for planimetry in sufficient density for further surveying work in the area and survey of location and level by using geodetic methods and GPS. The reconnaissance of the area was conducted due to geodetic and levelling data of the points and maps. A network of 18 points of the detailed point network was built. I located nine of them by using a GPS method and a method of polygonal traverse. The electronic total station Leica TC 407 was used for the point survey by the method of polygonal traverse, for the GPS method was used a GPS apparatus Trimble 4600LS. Altitude of the points was determined by the method of technical levelling. For the altitude determination was used a Topcon AT {--} 24A levelling device.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-10-27T14:48:51Z No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-27T14:53:07Z (GMT) No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-27T14:53:07Z (GMT). No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-07-06 / Our work had as main objective to study the intersection of integer sequences, denominated polygonal numbers, through Pell's equation. In this context, the solution of two equations will be treated: x2 􀀀 Dy2 = 1 and x2 􀀀 Dy2 = N, jNj > 1. For the rst one we have used results from the theory of continued fractions. For the last one, we have used the method of solution delineated in literature. Besides, propositions referring to the intersection of polygonal numbers for some particular cases are presented and demonstrated. Also, the proposition of the general case is presented and demonstrated. Finally, we have performed the solution of some of Pell's equations in order to determine the intersection of some polygonal numbers. / Nosso trabalho teve como objetivo central estudar a interseção de sequências de inteiros, denominadas números geométricos, através da equação de Pell. Neste contexto, a resolução de duas equações serão tratadas: x2 􀀀 Dy2 = 1 e x2 􀀀 Dy2 = N com jNj > 1. Para a primeira utilizamos importantes resultados presentes na teoria das frações contínuas. Para última, utilizamos o método de resolução delineado na literatura. Além disso, proposições referentes a interseção de números geométricos para alguns casos particulares são apresentadas e demonstradas. Também a proposição do caso geral é apresentada e demonstrada. Por m, realizamos a resolução de algumas equações de Pell para determinarmos a interseção de alguns números geométricos.