This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = &plusmn / L. General expressions for this problem are obtained by solving Navier equations using Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approaches the radius of the cylinder, the ends at z = &plusmn / L become cut and subject to uniformly distributed tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

傘型迴歸函數是類似傘的形狀的迴歸函數，只要符合先上升後下降的趨勢皆為傘型迴歸函數。無母數迴歸函數中最常見的方法之一是樣條(Splines)迴歸函數。樣條為充分平滑分段多項式函數，而節點(knots)為平滑多項式函數連接的地方。在本論文中，將節點以等距離擺放並以AIC(Akaike information criterion)值得到合理的節點數。用三種方法的樣條迴歸函數去估計傘型函數。第一種為RSPL(restrictted spline regression)，也就是有形狀限制時的樣條迴歸函數。第二種是CSPL(concave spline regression)，是參考Meyer寫的樣條迴歸函數，此樣條迴歸函數為凹函數(concave function)。最後一種則稱SPL(spline regression)，為沒有形狀限制也不是凹函數的樣條函數。以IMSE為評估標準，IMSE越小，則代表此方法估計的越好。由模擬結果，在估計先上升後下降的函數時，用RSPL的方法去估計會得到最小的IMSE；而在估計凹函數時，則是CSPL會得到最小的IMSE。利用RSPL和SPL兩個方法估計由中央氣象局蒐集最近13年(1998-2010)的月均溫資料並探討最近幾年的月均溫資料趨勢是否有改變。未來假如需要估計傘型函數時，則可利用本篇所述的方法去估計。 / In this thesis, we consider the problem of estimating a regression function assuming the regression function is unimodal. The proposed method is to model the regression function as linear combination of B-spline basis functions with equally spaced knots, and the number of knots is determined using AIC (Akaike information criterion). Specific constraints are placed on the coefficients of basis functions to ensure that estimated regression function is unimodal. The coefficients are estimated using least square method. The proposed method is refered as RSPL and is compared with two other methods: SPL and CSPL, where SPL is similar to RSPL except that the coefficients of basis functions are estimated without any constraints, and CSPL gives concave regression function estimates. Simulation results show that RSPL outperforms SPL and CSPL when the true regression function is unimodal but not concave, and CSPL outperforms RSPL and SPL when the true regression function is concave. Also, RSPL is applied to temperature data to estimate temperature trend within one year.

Early this century "S-shaped" curves, sigmoids, gained popularity among demographers. However, by 1940, the approach had "fallen out of favour", being criticised for giving poor results and having no theoretical validity. It was also considered that models of total population were of little practical interest, the main forecasting procedure currently adopted being the bottom-up "cohort-component" method. In the light of poor forecasting performance from component methods, a re-assessment is given in this thesis of the use of simple trend models. A suitable means of fitting these models to census data is developed, using a non-linear least squares algorithm based on minimisation of a proportionately weighted residual sum of squares. It is demonstrated that useful models can be obtained from which, by using a top-down methodology, component populations and vital components can be derived. When these models are recast in a recursive parameterisation, it is shown that forecasts can be obtained which, it is argued, are superior to existing official projections. Regarding theoretical validity, it is argued that sigmoid models relate closely to Malthusian theory and give a mathematical statement of the demographic transition. In order to judge the suitability of extrapolating from sigmoid models, a framework using Catastrophe Theory is developed. It is found that such a framework allows one qualitatively to model population changes resulting from subtle changes in influencing variables. The use of Catastrophe Theory has advantages over conventional demographic models as it allows a more holistic approach to population modelling.

Neste trabalho é realizada a otimização de antena de microfita banda larga usando o método de Diferenças Finitas no Domínio do Tempo (FDTD) e software comercial de onda completa. Inicialmente é feita uma introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer uma revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. A seguir, discorre-se sobre a teoria eletromagnética aplicada a antenas planares. O tópico de base é concluído com síntese dos métodos de simulação usados na análise de antenas de microfita, enfatizando o de FDTD. O próximo item revisa fundamentos teóricos e técnicas aplicadas na obtenção de banda larga em antenas de microfita. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho e da eficiência da antena E e de geometria inovadora aplicando técnica de alimentação capacitiva à antena E. A seguir, o algoritmo genético é apresentado e utilizado na otimização do plano de terra de antena de microfita com alimentação por sonda coaxial e também com alimentação capacitiva, para aplicações em banda larga. Resultados simulados e medidos são apresentados e boa concordância entre eles é obtida. Obteve-se 88% de largura de banda para PIFA com alimentação capacitiva e plano de terra otimizado. A tese é concluída com observações sobre os resultados apresentados e sugestões para prosseguimento e aperfeiçoamento das investigações realizadas. / In the present work, the optimization of broadband microstrip antenna employing the Finite Difference Time Domain (FDTD) and full wave commercial software are presented. First, an introduction on the subject considering main issues in communications and microstrip antennas are described, also a bibliographical review and the state of the art are presented. A review of electromagnetic theory applied to microstrip antenna is presented at the following topic, with emphasis on the FDTD method. The next step is a review of theory and techniques on bandwidth optimization of microstrip antennas. The work follows with numeric simulations and measurements on bandwidth, gain, efficiency of E shapped antenna and with a novel design procedure employing capacitive feeding on the E shapped antenna. The work follows with genetic algorithm being presented and utilized to the optimization of ground plane shape microstrip antenna with coaxial feeding and also with capacitive feeding, aiming to broadband applications. Simulated and measured results are presented. Good agreement is observed. Relative bandwidth of 88% was found for PIFA with capacitive feeding and optimized ground plane. The thesis is concluded with some comments and observations on the results obtained and suggestions for the continuation of the work.

Neste trabalho é realizada a otimização de antena de microfita banda larga usando o método de Diferenças Finitas no Domínio do Tempo (FDTD) e software comercial de onda completa. Inicialmente é feita uma introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer uma revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. A seguir, discorre-se sobre a teoria eletromagnética aplicada a antenas planares. O tópico de base é concluído com síntese dos métodos de simulação usados na análise de antenas de microfita, enfatizando o de FDTD. O próximo item revisa fundamentos teóricos e técnicas aplicadas na obtenção de banda larga em antenas de microfita. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho e da eficiência da antena E e de geometria inovadora aplicando técnica de alimentação capacitiva à antena E. A seguir, o algoritmo genético é apresentado e utilizado na otimização do plano de terra de antena de microfita com alimentação por sonda coaxial e também com alimentação capacitiva, para aplicações em banda larga. Resultados simulados e medidos são apresentados e boa concordância entre eles é obtida. Obteve-se 88% de largura de banda para PIFA com alimentação capacitiva e plano de terra otimizado. A tese é concluída com observações sobre os resultados apresentados e sugestões para prosseguimento e aperfeiçoamento das investigações realizadas. / In the present work, the optimization of broadband microstrip antenna employing the Finite Difference Time Domain (FDTD) and full wave commercial software are presented. First, an introduction on the subject considering main issues in communications and microstrip antennas are described, also a bibliographical review and the state of the art are presented. A review of electromagnetic theory applied to microstrip antenna is presented at the following topic, with emphasis on the FDTD method. The next step is a review of theory and techniques on bandwidth optimization of microstrip antennas. The work follows with numeric simulations and measurements on bandwidth, gain, efficiency of E shapped antenna and with a novel design procedure employing capacitive feeding on the E shapped antenna. The work follows with genetic algorithm being presented and utilized to the optimization of ground plane shape microstrip antenna with coaxial feeding and also with capacitive feeding, aiming to broadband applications. Simulated and measured results are presented. Good agreement is observed. Relative bandwidth of 88% was found for PIFA with capacitive feeding and optimized ground plane. The thesis is concluded with some comments and observations on the results obtained and suggestions for the continuation of the work.

About 15 kilometers north-east of the Turkish city of Şanliurfa lies the mound of Göbekli Tepe with its Stone Age Sanctuaries. Its enormous deposit layers, up to 15 meters high, have accumulated over several millennia on an area of about 9 hectares. Excavations done by the German Archaeological Institute with the Archaeological Museum of Şanliurfa, which have been carried out since 1995, found a very important site, which contributes to a completely new understanding of the process of sedentism and the beginning of agriculture. Amazingly, no residential buildings have been discovered up to now. However, at least two phases of monumental religious architecture have been uncovered. Of these, the oldest layer, with its richly adorned monolithic T-shaped pillars, is the most impressive. The buildings on this layer are circular, with a diameter of over 20 meters, and constructed from quarry stone. There are the enclosures A-D on the southern slope and enclosure E at the western plateau. Their age is impressive, having been dated to the 10th millennium BC, a time when men still lived as hunter-gatherers. This opened up a layer of the Stone Age, in which the so-called Neolithic Revolution took place. Overlying layer III is layer II, which has been dated to the 9th millennium BC. During this latter period there is a certain reduction both in the size of the structures and in the numbers of pillars. The uppermost layer I is represented by the surface debris including enormous deposits of Hangfußsedimente, accumulations of eroded sediments from layers II and III. There is no occupation from periods younger than the Pre-Pottery Neolithic at the site. The sanctuaries of Göbekli Tepe were completely filled in during the Stone Age. The old surfaces that can be observed in the excavations and the processes that occurred in the sediment have been subjected to pedological analyses and allow the act of filling to be dated into the late 9th millennium BC. / El montículo de Göbekli Tepe, con sus santuarios de la Edad de Piedra, se ubica a unos 15 kilómetros al noreste de la ciudad de Şanliurfa, en Turquía. Sus enormes capas de sedimentos, que alcanzan más de 15 metros de espesor, se acumularon en una superficie de alrededor de 9 hectáreas durante varios milenios. En las excavaciones realizadas desde 1995 por el Deutsches Archäologisches Institut (DAI), en cooperación con el Archaeological Museum of Şanliurfa, se descubrió un sitio muy importante que ofrece una comprensión totalmente nueva del proceso de la sedentarización y del inicio de la agricultura. Resulta sorprendente que no se hayan descubierto construcciones residenciales hasta el momento. En vez de ello, se han ubicado, al menos, dos fases de arquitectura monumental, de las que la más temprana es la más espectacular por sus grandes pilares ricamente adornados. Las construcciones de este nivel, hechas de piedras canteadas, son de planta circular y tienen un diámetro de más de 20 metros. Los denominados recintos A a D se encuentran en la pendiente sur, mientras que el Recinto E se ubica en la meseta occidental. Su edad es impresionante, ya que data del décimo milenio a.C., en una época en que el hombre aún vivía de la caza y la recolección; es, por lo tanto, un grado de la Edad de Piedra en el que ocurrió la Revolución Neolítica. La capa II cubre la III y fue fechada en el noveno milenio a.C. En este tiempo se advierte una cierta reducción en el tamaño de las estructuras y en la cantidad de los pilares. La capa I es superficial, con derrumbes e importantes depósitos de sedimentos de piedemonte, como acumulaciones de sedimentos erosionados procedentes de las capas II y III. No existen vestigios más recientes que el PPN (Pre-Pottery Neolithic o Neolítico Precerámico) en el sitio: los santuarios de Göbekli Tepe fueron rellenados completamente durante la Edad de Piedra. Las superficies antiguas se observan en la excavación y los procesos que ocurrieron en el sedimento fueron sometidos a análisis pedológicos que permitieron determinar la edad del relleno en la parte tardía del noveno milenio a.C.

An Approach to the Formative Period in the Chillón ValleyThe author describes 29 Formative sites in the Chillon Valley subdivided into monumental architecture (U-shaped buildings, pyramid with circular sunken courts and simple pyramids) and 17 domestic sites. A typology of the recollected ceramics is given as well as comparisons with other sites and chronological proposals. U-shaped complexes are concentrated in the lower valley but located up to km 59. Huacoy is the largest one of them, communicated with Ancon and related with 8000 has of arable land. Chocas is probably a minor copy of Huacoy and part of the system, while Pucara integrates the middle valley. / El autor describe 29 sitios del Formativo en el valle de Chillón. Los subdivide en arquitectura monumental: edificios en forma de U, pirámide y recinto circular hundido y pirámides simples además de 17 sitios domésticos. Se presenta una tipología cerámica con propuestas anteriores. La distribución de los complejos en U se percibe hasta el kilómetro 59 pero se concentra en la parte baja; Huacoy es el mayor de ellos, comunicado con Ancón y relacionado con 8000 hectáreas de tierra cultivable. Chocas probablemente es una copia menor de Huacoy y parte del sistema, mientras que Pucara integra el valle medio.

Neste trabalho é realizada a otimização de antena de microfita banda larga usando o método de Diferenças Finitas no Domínio do Tempo (FDTD) e software comercial de onda completa. Inicialmente é feita uma introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer uma revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. A seguir, discorre-se sobre a teoria eletromagnética aplicada a antenas planares. O tópico de base é concluído com síntese dos métodos de simulação usados na análise de antenas de microfita, enfatizando o de FDTD. O próximo item revisa fundamentos teóricos e técnicas aplicadas na obtenção de banda larga em antenas de microfita. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho e da eficiência da antena E e de geometria inovadora aplicando técnica de alimentação capacitiva à antena E. A seguir, o algoritmo genético é apresentado e utilizado na otimização do plano de terra de antena de microfita com alimentação por sonda coaxial e também com alimentação capacitiva, para aplicações em banda larga. Resultados simulados e medidos são apresentados e boa concordância entre eles é obtida. Obteve-se 88% de largura de banda para PIFA com alimentação capacitiva e plano de terra otimizado. A tese é concluída com observações sobre os resultados apresentados e sugestões para prosseguimento e aperfeiçoamento das investigações realizadas. / In the present work, the optimization of broadband microstrip antenna employing the Finite Difference Time Domain (FDTD) and full wave commercial software are presented. First, an introduction on the subject considering main issues in communications and microstrip antennas are described, also a bibliographical review and the state of the art are presented. A review of electromagnetic theory applied to microstrip antenna is presented at the following topic, with emphasis on the FDTD method. The next step is a review of theory and techniques on bandwidth optimization of microstrip antennas. The work follows with numeric simulations and measurements on bandwidth, gain, efficiency of E shapped antenna and with a novel design procedure employing capacitive feeding on the E shapped antenna. The work follows with genetic algorithm being presented and utilized to the optimization of ground plane shape microstrip antenna with coaxial feeding and also with capacitive feeding, aiming to broadband applications. Simulated and measured results are presented. Good agreement is observed. Relative bandwidth of 88% was found for PIFA with capacitive feeding and optimized ground plane. The thesis is concluded with some comments and observations on the results obtained and suggestions for the continuation of the work.

O Grupo Corumbá, SW Brasil, documenta uma etapa importante na evolução da vida por causa de seu registro fóssil de microbialitos, microfósseis, e organismos multicelulares indicativos da complexidade cada vez maior da biosfera no final do período Ediacarano. A importância paleobiológica da Formação Bocaina, inserido no meio do Grupo Corumbá, e datado em cerca de 560 Ma, é embasada em sua diversidade de microbialitos e registro de significativo evento fosfogenético, associados a supostos \"microfósseis em forma de vaso\", semelhantes à tecamebas, interpretadas como os primeiros protistas heterótrofos. Estes fósseis, bem como formas semelhantes reconhecidos em outras unidades geológicas do mundo, precedem o registro da explosão de organismos multicelulares macroscópicos esqueléticos (Cloudina, Corumbella) na formação sobrejacente Tamengo (543 Ma). A morfologia do microbialitos fornece evidências de variação local do nível do mar durante a deposição da Form ação Bocaina. As análises morfológicas e químicas dos microfósseis usando microscopia óptica e eletrônica de varredura, EDS e espectroscopia Raman ajudaram a esclarecer a natureza biológica desses objetos e, assim, contribuir para a compreensão da importância da evolução da vida no Ediacarano, na Formação Bocaina, Grupo Corumbá. / The Corumbá Group, SW Brazil, documents an important stage in the evolution of life because of its fossil record of microbialites, microfossils, and early multicellular organisms indicative of the rapidly increasing complexity of the biosphere at the very end of the Ediacaran period. The paleobiological importance of the Bocaina Formation, in middle of the Corumbá Group and dated at about 560 Ma, lies in its diversity of microbialites and its record of a significant phosphogenesis event with associated putative \"vase-shaped microfossils\", similar to testate amoebae, interpreted as early protistan heterotrophs. Th ese fossils, as well as similar forms recognized in other geologic units in the world precede the record of the explosion of macroscopic multicellular skeletal organisms (Cloudina, Corumbella) in the overlying Tamengo Formation (543 Ma). The morphology of microbialites provides evidence of local sea level variation during deposition of the Bocaina Formation. Morphological and chemical analyses of the microfossils using optical and scanning electron microscopy, EDS and Raman spectroscopy helped clarify the biological nature of these objects and thereby contribute to the understanding of the importance of the Bocaina Formation the evolution of late Ediacaran life in the Corumbá Group.

Geometries of sills intruded into the lava pile of the Faroe Island Basalt Group (FIBG), which were targeted in this study, were mostly recorded by conventional mapping methods where measured distances and positions were plotted onto accurate topographic maps aided by the use of high-quality photos of relevant outcrops. These data were subsequently used to manually plot 2D profiles along selected tracks and to produce electronic 3D maps using ArcGIS software. The general geometries of the investigated sills, measured at lateral scales ranging from a few metres to a few kilometres and at vertical scales ranging from a few metres to a few hundred metres, differ somewhat from typical sill geometries reported previously for sills intruded into sedimentary successions. The ubiquitous saucer-shapes of the sills from this study, which generally curve upwards in a gradual manner from inner sub-horizontal sections to steeper outer margins, contrast with the common angular transitions from inner sub-horizontal to outer steeper sections of sills reported from sedimentary host-rocks. In this thesis we explore possible alternatives to already existing theories on sill emplacement in sedimentary successions. Major and trace element compositions for samples representing most of the sills exposed in the Faroe Islands have been determined by means of XRF and ICP-MS analyses. Geochemically most of these sills can be grouped into two main categories characterised either by high or by low TiO2 contents. Different sorts/types of metasomatism of source rocks to high-TiO2 versus low-TiO2 sills are indicated by different Nb and Ta anomalies. Modelling by means of REE and other trace elements suggest that much of the compositional differences between these two main categories can be explained by various degrees of partial melting of broadly similar mantle sources. Additional fractionation and accumulation of plagioclase modified some of the melts that gave rise to the actual sills. The initial partial melting event probably occurred at depths slightly shallower than the lower limit of the garnet stability field at ~85 km while plagioclase crystallisation/accumulation most likely occurred at depths shallower than ~18 km. Isotopic compositions may point to very slight contamination of some sills with crustal material.