The concepts of continuity for set-valued mappings were introduced by G. Bouligand and K. Kuratowski. There are two ways defining differentiability of set-valued mapping. One is defined by classical differentiability theorem and another is defined by normal cone which was introduced by B.S. Mordukhovich. In this thesis, we survey various definitions of continuity and differentiability for set-valued mapping.

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / O objetivo desta dissertaÃÃo e dar uma exposiÃÃo da teoria das extensÃes Lipschitz absolutamente minimizantes, baseada no trabalho de Gunnar Aronsson, Michael G.Crandall e Petri Juutinen em [1], apresentando vÃrios detalhes em uma forma acessÃvel aos leitores sem qualquer conhecimento prÃvio do assunto. Em particular, refazemos resultados melhorados relativos a existÃncia atravÃs de argumentos que sÃo mais simples do que aqueles que podem ser encontrados na literatura. NÃs apresentamos uma prova do conhecido resultado de unicidade, o qual nÃo se baseia na teoria de soluÃÃes de viscosidade. Em nossa nossa abordagem, mostraremos que as funÃÃes absolutamente minimizantes sÃo as funÃÃes que satisfazem uma condiÃÃo geomÃtrica a qual chamaremos de gozar de comparaÃÃo com cones. Este elementar dispositivo geomÃtrico torna a teoria versÃtil e transparente. Aqui, encontraremos por exemplo, estimativas de continuidade a priori, desigualdade de Harnack, o mÃtodo de Perron para comprovar os resultados de existÃncia, questÃes de unicidade e regularidade, e algumas ferramentas bÃsicas da teoria de soluÃÃes de viscosidade. NÃs acreditamos que a nossa apresentaÃÃo fornece um resumo unificado da teoria unificada existente, assim como alguns resultados de interesse para os peritos e pesquisadores e, ao mesmo tempo, uma fonte que possa ser utilizada para introduzir estudantes a algumas significantes ferramentas analÃticas. / The objective of this dissertation is to give an exposition of the theory of absolutely minimizing Lipschitz extensions, based on the work of Gunnar Aronsson, Michael G. Crandall and Petri Juutinen in [1], showing various details in a form accessible to readers without any prior knowledge of the subject. In particular, we retrace the improved results on the existence through arguments that are simpler than those that can be found in literature. We present a proof of the known uniqueness result, which is not based on the theory of viscosity solutions. In our approach we will show that the absolutely minimizing functions are the functions that satisfy a geometric condition which we will call to enjoy comparison with cones. This elementary geometric device renders the theory versatile and transparent. Here we will nd a priori continuity estimates, Harnack inequality, Perron's method for proving existence results, uniqueness and regularity questions, and some basic tools of viscosity solution theory. We believe that our presentation provides a unied sum-mary of the existing theory as well as some results of interest to experts and researchers and, at the same time, a source which can be used for introducing students to some signicant analytical tools.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Our aim in this work is threefold. First, we get an extension, to the spherical case, of a theorem due to J. Simons, which concerns unstability of minimal cones constructed over a certain class of minimal submanifolds of the Euclidean sphere. Second, we classify the quasi-Einstein structures of the Riemannian product Hn x R. Third, we get a rigidity theorem for complete hypersurfaces into the De Sitter space, under certain conditions on the mean and scalar curvatures. / Este trabalho aborda trÃs problemas em Geometria Diferencial. Primeiro, obtemos uma extensÃo, para o caso esfÃrico, de um teorema devido a J. Simons sobre instabilidade de cones mÃnimos construÃdos sobre uma certa classe de subvariedades mÃnimas da esfera Euclidiana. Depois, classificamos as estruturas quasi-Einstein existentes sobre o produto Riemanniano Hn X R. Por fim, obtemos um teorema de rigidez para hipersuperfÃcies tipo-espaÃo completas do espaÃo de De Sitter, sob certas condiÃÃes sobre as curvaturas mÃdia e escalar, alÃm de uma condiÃÃo de integrabilidade.

A visãao é o sentido humano mais complexo e importante para os processos de cognição e de interação de um indivíduo com o mundo. Neurofiisiologistas buscam identificar e compreender como funcionam os mecanismos celulares envolvidos neste processo. O sistema visual recebe os sinais de imagens captadas pelos olhos e, por meio de transformações e processamento diversos, integra esses sinais em representações de objetos internos perceptuais. O projeto Olho Virtual consegue reconstruir, em três dimensões, modelos de olhos utilizando córneas reais ou simuladas em computador, reproduzindo suas propriedades ópticas captando imagens de maneira satisfatória. Este trabalho introduz, no projeto Olho Virtual, um modelo computacional de retina baseado no modelo biológico, capaz de reproduzir as propriedades das células cones e bastonetes em suas distribuições radiais e também em suas funcionalidades em particular. Além dessa, é apresentado uma modelagem para reprodução dos campos receptivos das células ganglionares presentes na retina, gerando sinais de saída nos sistemas parvo e magno. Por fim são feitas simulações de experimentos psicofísicos com propósito de verificar a validade da modelagem proposta / The vision is the human sense more complex and important in cognitive processes and the interaction of an individual with the world. Neurophysiologists seek to identify and understand how the cellular mechanisms involved in this process work. The visual system receives the image signals captured by the eyes and, through several transformations and processing, integrate those signals into internal representations of perceptual objects. The project Virtual Eye can reconstruct three-dimensional models of eye corneas using real or simulated on the computer, playing their optical properties capturing images satisfactorily. This work introduces the Virtual Eye project, a computational model of retina-based biological model, able to reproduce the properties of rod and cone cells in their radial distributions and also in its functionality in particular. Besides this, a model is presented for reproduction of the receptive fields of ganglion cells present in the retina, generating output signals in the parvo and magno systems. Finally, simulations are made with psychophysical experiments in order to verify the accuracy of the proposed model

Estudos prévios do nosso laboratório têm mostrado a presença e importância das GTPases Rho, proteínas de baixo peso molecular que são ativadas por diversos sinais extracelulares, em neurônios da retina adulta, durante o desenvolvimento e na degeneração induzida por luz. O objetivo deste trabalho foi determinar por meio de imunocitoquímica a distribuição de alguns membros desta família (RhoA, Rac1 e Cdc42) nos fotorreceptores da retina de camundongos BalbC em situações normais e de adaptação ao claro e ao escuro. Os resultados mostraram que Rac1, Cdc42 e RhoA são expressos principalmente no segmento interno e nas possíveis terminações de cones e bastonetes na camada plexiforme externa. Em condições diferentes de estimulação não ocorreu translocação das GTPases, como ocorre com outras proteínas envolvidas na fototransdução. Os resultados sugerem que elas possam desempenhar papéis importantes na reorganização do citoesqueleto ou no processo de fototransdução, regulando outras proteínas e/ou protegendo contra danos induzidos pela luz. / Previous studies from our laboratory have shown the presence and importance of the Rho family of small GTPases, proteins that are activated by different extracellular signals, in neurons of the adult retina, during development and light-induce degeneration. The aim of the present work was to determine by immunocytochemistry the distribution of RhoA, Rac1 and Cdc42 in photoreceptors of the BalbC mice retina in different conditions of light/dark adaptation. Our results showed that Rac1, RhoA and Cdc42 are mainly expressed in the inner segments and presumptive axon terminals of cones and rods in the outer plexiform layer. In addition, there was no evidence of Rho GTPases translocation under different conditions of stimulation, as shown for some phototransduction proteins. The results suggest that Rho GTPases may play important roles in the reorganization of the cytoskeleton or in the phototransduction process, regulating other proteins and/ or protecting against light-induced damage.

[pt] O presente estudo tem como objetivo mostrar a existência de cones de assimetria e curtose no mercado brasileiro de opções. Além disso, os coeficientes de assimetria e curtose são de suma importância para a aplicação do modelo de Corrado e Su (1996). As volatilidades implícitas calculadas pelo método inverso deste modelo serão sobrepostas aos cones de volatilidade, buscando oportunidades de compra ou de venda de volatilidade. Para efeito de comparação, o modelo de Black e Scholes também será utilizado para a extração de tais medidas de volatilidade implícita. Outra contribuição deste trabalho é mostrar se os efeitos do sorriso de volatilidade e da estrutura a termo da volatilidade são amenizados diante de operações realizadas com os cones de volatilidade, levando-se em consideração a volatilidade implícita calculada pelos diferentes modelos. Para isto, foram realizados testes estatísticos de eficiência, além de uma análise descritiva das variáveis mais importantes para uma correta análise do mercado de opções, em momentos de estabilidade e baixa volatilidade como o verificado no ano de 2010. O estudo mostra a existência de cones de assimetria e curtose no mercado brasileiro de opções e possibilidades de ganhos com as operações feitas através dos cones de volatilidade, porém os resultados obtidos pelos dois modelos não apresentaram diferenças estatisticamente significantes. / [en] The present study aims to show the existence of skewness and kurtosis cones in the Brazilian market. In addition, the coefficients of skewness and kurtosis are of paramount importance for the application of the model of Corrado and Su (1996). The implied volatilities calculated by the inverse of this template will be superimposed to the cones of volatility, seeking opportunities to acquire or dispose of volatility. Comparison of Black and Scholes model will also be used for the extraction of such measures of implied volatility. Another contribution of this paper is to show the effects of the volatility smile and term structure of volatility are amenable before operations performed with the cones of volatility, taking into account the implied volatility calculated by different models. For this, statistical tests were performed, efficiency and a descriptive analysis of the most important variables for a correct analysis of the options market, in times of stability and low volatility as the year of 2010. The study showed the existence of skewness and kurtosis cones in the Brazilian market and gains possibilities with volatility cones operations, but the results obtained with the two models didn´t have significative statistics differences.

Cinder Cone is the most recent cinder cone eruption in the continental United States at ~350 years old. This study examines the physical characteristics of the explosive deposit of the volcano in order to infer eruption timing, style, and mechanisms. Building on previous work and using spatial extent, field relationships, and grain size, componentry, and textural data of ten samples from one column, this study demonstrates that Cinder Cone erupted in at least two distinct phases with at least two distinct eruption styles. This speaks to the changing magma supply and transport processes occurring beneath the volcano. Curiosities about the eruption include the extensive degree of contamination that contributed abundant quartz xenocrysts to all the deposits. Future work includes determining the extent and mechanism/s of contamination and tephra component creation. These data are important for informing hazard assessments of areas with abundant cinder cone volcanoes.

The western spruce budworm, Choristoneura occidentalis Freeman (Lepidoptera: Tortricidae), is a serious defoliator of conifers in the western U.S. and western Canada. In 1985 epidemic levels of the budworm caused average tree defoliation in west-central Idaho to increase to 83%, up substantially from the 35% average tree defoliation of 1984. Associated with this increase in defoliation was a change in the relative stand defolation ranking between the two years. found to damage all types and In 1985 the budworm was developmental stages of reproductive structures of Douglas- fir, including: seedcone buds, pollen-cones buds, maturing cones, and seeds. Differential selection of feeding sites was observed, with a significantly higher proportion of larvae found in seedcone buds than in pollen-cone buds. Shortly after larval emergence, 25% of the total number of seed-cones buds were infested. A subsample of 171 branch tips indicated that only 9% of pollen-cones, while less than 2% of the vegetative buds contained larvae. A total of 640 cones from 21 trees were examined. Of these cones, 76% were infested with larvae, however not all of the seeds were destroyed. The average percent of destroyed seeds per tree was found to be exponentially related to the average current defoliation of the tree.

Six species of insects were found attacking limber pine cones from July 26, 1968, through October 4, 1969, in Cache National Forest. The three species considered of major importance are: Conophthorus flexilis Hopkins, Dioryctria abietella (D. & S.), and D. sp. near or disclusa Heinrich. The three minor species encountered are; Bradysia sp., Trogoderma parabile Beal, and Asynapta keeni (Foote). In addition to the major and minor cone pests three parasites, Apanteles sp . prob. starki Mason, Elacherus sp., and Hypopteromalus percussor Girault were found associated with the cone pests. C. flexilis, which completely destroys the cone, was ranked as the number one pest on the basis of numbers present plus severity of damage. During 1968 and 1969 C.flexilis destroyed 11.47 percent of the 1500 cones examined, with a mean of 5.87 larvae per infested cone. The cone moths, D. abietella and D. sp. near or disclusa, were ranked second and third in importance respectively. D. sp . near or disclusa was potentially the more important cone moth, as it caused a total destruction of the seed bearing portion of the cones. However, D. abietella infested 15.40 percent of the cones, in contrast to 2.00 percent by D. sp. near or disclusa. There were no significant statistical differences in insect populations between 1968 and 1969, although the percent infestation of C. flexilis and D. sp. near or disclusa increased slightly and D. abietella decreased.

Free space is represented as a union of (possibly overlapping) generalized cones. An algorithm is presented which efficiently finds good collision free paths for convex polygonal bodies through space littered with obstacle polygons. The paths are good in the sense that the distance of closest approach to an obstacle over the path is usually far from minimal over the class of topologically equivalent collision free paths. The algorithm is based on characterizing the volume swept by a body as it is translated and rotated as a generalized cone and determining under what conditions generalized cone is a subset of another.