Neste trabalho apresentamos uma demonstração detalhada para um conhecido teorema de I. J. Schoenberg que caracteriza certas funções positivas definidas em esferas. Analisamos ainda um critério para a obtenção de positividade definida de uma função a partir de condições de suavidade e convexidade dela, em uma tentativa de ratificar alguns resultados da literatura conhecidos como critérios de Pólya. / In this work we present a proof for a famous theorem of Schoenberg on positive definite functions on spheres. We analyze some results that deduce positive definiteness from diferentiability and convexity assumption on the function, an attempt to ratify some Pólya type conjectures found in the literature.

Este trabalho envolve dois diferentes aspectos da estimação de espectros direcionais de onda a partir de movimentos de 1a ordem da embarcação. Sendo a estimação do espectro de ondas feita por meio de um método Bayesiano, existe a necessidade da calibração dos hiperparâmetros derivados da modelagem Bayesiana. O primeiro assunto abordado é a determinação de uma metodologia de calibração dos hiperparâmetros necessários à estimação do espectro direcional de ondas. Desenvolve-se ao longo deste uma primeira análise de um método aplicável a qualquer embarcação do tipo FPSO para a determinação a priori de valores de dois hiperparâmetros de controle da suavização da estimativa. Obtém-se resultados indicativos de que é possível definir valores destes hiperparâmetros dependentes de quantidades observáveis como calado da embarcação e período das ondas, de modo que os erros de estimação ainda se mantém muito próximos aos encontrados por valores ótimos dos hiperparâmetros. Isto leva à conclusão de que na abordagem atual, com valores fixos a cada calado, erros excessivos e desnecessários podem ocorrer no processo de estimação. O segundo tema trata da estimação paramétrica de espectros, utilizando modelos paramétricos de descrição de espectros como forma de obtenção de estatísticas de mar. Abordam-se também os assuntos de mares cruzados, donde se faz necessária a identificação da bimodalidade dos espectros para a estimação correta das estatísticas de mar. / In this work, two differents aspects of directional wave spectra estimation from 1st order ship motions are presented. As the estimation of wave spectrum is made by means of a Bayesian method, it is necessary to calibrate the hyperparameters derived from Bayesian modeling. The first addressed subject is the determination of a calibration methodology of the hyperparameters needed for the directional wave spectrum estimation. It is developed through this work a first analysis of an applicable method to any vessel of FPSO type for the prior determination of values for this two hyperparameters depending on observable quantities, such as draft of the vessel and wave period, in such a way that the estimation errors are still very close to those found by optimum values of the hyperparameters. This leads to the conclusion that in the current approach excessive and unnecessary errors can occur on the estimation process. The second subject addresses the parametric estimation of spectra, using parametric models of spectrum description to acquire the sea statistics. For this purpose, it became necessary the study of crossed-sea states, which was employed in the bimodal spectrum identification for the correct estimation of sea statistics.

O modelo misto é comumente utilizado em dados de medidas repetidas devido a sua flexibilidade de incorporar no modelo a correlação existente entre as observações medidas no mesmo indivíduo e a heterogeneidade de variâncias das observações feitas ao longo do tempo. Este modelo é composto de efeitos fixos, efeitos aleatórios e o erro aleatório e com isso na seleção do modelo misto muitas vezes é necessário selecionar os melhores componentes do modelo misto de tal forma que represente bem os dados. Os critérios de informação são ferramentas muito utilizadas na seleção de modelos, mas não há muitos estudos que indiquem como os critérios de informação se desempenham na seleção dos efeitos fixos, efeitos aleatórios e da estrutura de covariância que compõe o erro aleatório. Diante disso, neste trabalho realizou-se um estudo de simulação para avaliar o desempenho dos critérios de informação AIC, BIC e KIC na seleção dos componentes do modelo misto, medido pela taxa TP (Taxa de verdadeiro positivo). De modo geral, os critérios de informação se desempenharam bem, ou seja, tiveram altos valores de taxa TP em situações em que o tamanho da amostra é maior. Na seleção de efeitos fixos e na seleção da estrutura de covariância, em quase todas as situações, o critério BIC teve um desempenho melhor em relação aos critérios AIC e KIC. Na seleção de efeitos aleatórios nenhum critério teve um bom desempenho, exceto na seleção de efeitos aleatórios em que considera a estrutura de simetria composta, situação em que BIC teve o melhor desempenho. / The mixed model is commonly used in data of repeated measurements because of its flexibility to incorporate in the model the correlation existing between the observations measured in the same individual and the heterogeneity of variances of observations made over time. This model is composed of fixed effects, random effects and random error and with this in the selection of the mixed model it is often necessary to select the best components of the mixed model in such a way that it represents the data well. Information criteria are tools widely used in model selection, but there are not many studies that indicate how information criteria play out in the selection of fixed effects, random effects, and the covariance structure that makes up the random error. In this work, a simulation study was performed to evaluate the performance of the AIC, BIC and KIC information criteria in the selection of the components of the mixed model, measured by the TP (True positive Rate). In general, the information criteria performed well, that is, they had high TP rate in situations where the sample size is larger. In the selection of fixed effects and in the selection of the covariance structure, in almost all situations, the BIC criterion had a better performance in relation to the AIC and KIC criteria. In the selection of random effects no criterion had a good performance, except in the selection of Random effects in which it considers the compound symmetric structure, situation in which BIC had the best performance.

" Sample cutting is an important minimally invasive medical procedure. Currently there are several types of medical devices used to cut a distal biological sample, for example, a video endoscope and TurboHawk Plaque Excision Systems. Directional Atherectomy (DA) with the TurboHawk Plaque Excision Systems is a catheter-based, minimally invasive treatment method for peripheral arterial disease (PAD). During a procedure, a catheter is directed toward an area of plaque buildup to remove the plaque from the body, restoring blood flow (Covidien, 2013). Endoscopy is an important procedure used in the medical field to study and diagnose different parts of a body without the need to undergo a major surgery. The major devices are a video endoscope with a flexible or rigid insertion tube and endoscopic therapy devices. Arrays of the devices, through the instrument channel in the insertion tube of endoscopes, to perform a variety of functions are offered. The biological sample cut is one of the important endoscopic therapies. Both of Directional Atherectomy and endoscopy procedures require a power transmission from the proximal tip of device to the distal end, where the cutter is located, for cutting a sample. However, the working length is up to meters, and the diameter of the devices is in millimeter scale in the minimally invasive surgery. Thus enough power transmitting to the distal end of the device for the biological sample cutting is crucial. This research presents the effort toward the investigation of the potential power mechanisms from the proximal tip to the cutter at the distal end of the device for rapid rotational cutting motion to improve the cutting efficiency and accuracy. In this thesis, the potential powering mechanisms including fluid, electrical, and torque coils are investigated. Since the transmission power is used for a rotational cutting action, and the cutting geometry has influence on the cutting power, thus this research also focuses on the analysis of the cutting geometry for the rotational sample cutting. The Hertz contact theory and von Mises yield criterion are used to find the influence of tool geometry on the material removing process, as well as Abaqus, a commercial FEM software, is used for the finite element analysis. Fiber-reinforced composite structures are the main characteristic of the representative biological sample, and their mechanical behavior is strongly influenced by the concentration and structural arrangement of constitute such as collagen and elastin. Researches show that the biological sample, for example, a soft biological sample, has hyperelastic properties and behave anisotropically, and there are a few publications about the plastic properties and cutting mechanics. Thus a linear elastic and linear plastic material model is defined for the finite element analysis of material removal. The analytical results and finite element results both show that as the tool rake angle increases or the tool angle decreases, the magnitude of cutting force decreases. A preliminary representative sample cutting experiment was conducted, and standard cutters with different cutting geometries were tested in order to find the characteristic of the biological sample cutting and the influence of tool geometry on the required cutting power. The experiments reveal the same conclusions as the analytical and finite element results. "

La nitruration gazeuse est un traitement thermochimique permettant une meilleure résistance à la fatigue grâce à l’apport de propriétés mécaniques importantes telles que l’augmentation de la dureté et les contraintes résiduelles de compressions. Cette étude est réalisée sur un acier 33CrMoV12-9 utilisé dans l’industrie aéronautique. Un modèle complet adapté à cette nuance permet de quantifier les profils de contraintes résiduelles et de dureté en fonction des paramètres de nitruration. La prise en compte de l’apport de ces propriétés mécaniques est possible grâce à l’utilisation de critère de fatigue de type Crossland. Ce type de critère est intégré dans une méthodologie, afin de calculer la limite en fatigue dans une couche nitrurée et prédire la résistance de la pièce, ainsi que la potentielle zone d’initiation de rupture en fonction d’un chargement, d’une durée de vie et d’une probabilité à rupture donnés. L’utilisation combinée du modèle de calcul des propriétés mécaniques (dureté et contraintes résiduelles) et de la prédiction de l’initiation de rupture dans un matériau nitruré, rend possible une méthode inverse permettant de calculer les paramètres de nitruration adaptés à un chargement subi. Cette approche se justifie dans le cas de nitruration gazeuse, car il a été démontré lors de cette étude, que ce traitement reste robuste face au chargement subi par la pièce. / Gaseous nitriding is a thermochemical treatment that improves fatigue strength by providing important mechanical properties such as increased hardness and residual compressive stresses. This study is carried out on a 33CrMoV12-9 steel used in the aeronautical industry. A complete model adapted to this grade allows to quantify the residual stress and hardness profiles as a function of the nitriding parameters. Taking into account the contribution of these mechanical properties is possible thanks to the use of fatigue criterion such as Crossland. This type of criterion is integrated in a methodology in order to calculate the fatigue limit in a nitrided layer and to predict the resistance of the workpiece, as well as the potential initiation zone of rupture according to a load, a lifetime And a given break probability. The combination of the model for the calculation of mechanical properties (hardness and residual stresses) and the prediction of the initiation of rupture in a nitrided material, makes possible an inverse method allowing to calculate the nitriding parameters adapted to a load suffered. This approach is justified in the case of gaseous nitriding because it has been demonstrated in this study that this treatment remains robust against the loading undergone by the workpiece.

O objetivo desta pesquisa é apresentar o modelo racional jurídico elaborado por Hart e o modelo racional jurídico elaborado por Dworkin, assim como a crítica realizada por Dworkin em face do Conceito de Direito oferecido por Hart. O positivista, Herbert Hart, propõe que o direito é formado por um sistema de regras primárias e regras secundárias, sendo que uma regra de reconhecimento é responsável por identificar quais regras estão ou não incluídas em tal sistema. Caso seja apresentado um problema que não é resolvido por uma regra reconhecida pelo critério, deverá o julgador apelar para a discricionariedade. Dworkin, em um primeiro momento, criticará o conceito de Hart, alegando que o seu critério de demarcação entre o que é direito e o que não é direito é insatisfatório, por deixar de reconhecer vários elementos como jurídicos, uma vez que a regra de reconhecimento, sendo um teste de pedigree, não à capaz de captar princípios de direito não legislados e direitos e deveres controversos. Ademais, há um erro na teoria positivista de Hart, ao afirmar que os casos não claramente resolvidos por uma regra serão resolvidos a partir da arbitrariedade da autoridade estatal. Posteriormente, Dworkin oferecerá um modelo de direito que dê conta da realidade jurídica, em seu entendimento. Um modelo em que o jurista, a partir do equilíbrio reflexivo e do axioma da equidade poderá deduzir teorias possíveis para responder problemas do direito, identificando, dentre estas teorias, qual é a melhor resposta, sendo portanto a resposta exigível para a solução da lide concreta. / The objective of this research is to present the rational legal model presented by Hart and rational legal model presented by Dworkin as well as criticism made by Dworkin in the face of the Concept of Law offered by Hart. The positivist, Herbert Hart, proposes that the right is formed by a system of primary rules and secondary rules, and a rule of recognition is responsible for identifying what rules are or are not included in this system. If presented with a problem that is not resolved by a rule recognized by the criterion, the judge should resort to discretion. Dworkin, at first, criticize the concept of Hart, claiming that his criterion of demarcation between what is right and what is not right is unsatisfactory, for failing to recognize various elements such as legal, as a rule of recognition , being a test of pedigree, not able to capture the principles of law and not legislated rights and duties controversial. Furthermore, there is an error in the positivist theory of Hart, asserting that the cases do not clearly resolved by a rule will be resolved from the arbitrariness of state authority. Later, Dworkin offer a model law that embraces the legal reality in his mind. A model in which the lawyer from the reflective equilibrium and the axiom of justice may deduct possible theories to address problems of law, identifying, among these theories, what is the best answer, the answer is therefore required for the solution of the dispute concrete.

The study examines the role of different types of value of the material in selecting documents for digitization at Swedish humanities special libraries. The main goals of the study were to find out, which types of value are most and least important in the selection process at these libraries, to aid on the identification of general tendencies in attributing values to analogue material for digitization and to provide an overall depiction of significance of different value types for the digitization at the humanities special libraries in Sweden. The two research questions of the study are: 1) Which aspects of value of the material are most important for the Swedish humanities special libraries in their decisions for selecting documents for digitization? and 2) Is there any agreement about the concept of value of the material for digitization among these special libraries? The empirical data has been gathered by means of an extensive self-completion questionnaire which was constructed on the basis of the analysis of previous research literature on selection of material for digitization. The analysis of the findings demonstrates that the intrinsic (intellectual content) value types and use value types are the most important ones for the Swedish humanities special libraries in selecting documents for digitization. Even though the respondent libraries appear to be in accordance in perceiving and assessing significance of many value categories, several of them generate discrepancies and confusion within the informant library group. Therefore, there isn't any general agreement about the concept of value of the material for digitization among the respondent libraries.

Neste trabalho apresentamos uma demonstração detalhada para um conhecido teorema de I. J. Schoenberg que caracteriza certas funções positivas definidas em esferas. Analisamos ainda um critério para a obtenção de positividade definida de uma função a partir de condições de suavidade e convexidade dela, em uma tentativa de ratificar alguns resultados da literatura conhecidos como critérios de Pólya. / In this work we present a proof for a famous theorem of Schoenberg on positive definite functions on spheres. We analyze some results that deduce positive definiteness from diferentiability and convexity assumption on the function, an attempt to ratify some Pólya type conjectures found in the literature.

The Borg Ratings of Perceived Exertion (RPE) Scale has proven to be a highly popular instrument in measuring the subjective responses of individuals to a given work or exercise task. Historically, the instrument was designed to correlate highly with the heart rates in young-to-middle-aged men performing various tasks. The body of literature, however, has revealed inconsistencies in the extent of just how strong the relationship is between ratings of perceived exertion and various physiological criterion variables, most notably, heart rate. In addition, most studies have invoked the question of whether the criterion-related validity coefficients derived from the relationship between ratings of perceived exertion and a specified physiological criterion variable are just as valid as those for which the Borg RPE Scale was originally performed. A meta-analysis, therefore, was undertaken to determine the magnitude of the relationship between ratings of perceived exertion scores and each of three commonly used physiological measures or criterion variables: heart rate, blood lactate, and oxygen uptake. Results show that by using Tests of Homogeneity for each physiological criterion variable, the observed sample size-weighted validity coefficients are heterogeneous. The median of the mean sample size-weighted validity coefficients is .574 for heart rate, .561 for blood lactate, and .480 for oxygen uptake. Each study in the meta-analysis was grouped by the study characteristics of subject gender, fitness level, RPE Scale, exercise type, exercise protocol, and study quality. For heart rate, the highest validity coefficients are those in which the subjects are highly fit, the exercise type is fairly unusual, such as swimming, and the subjects are required to maximally exert themselves. For blood lactate, the highest validity coefficients are for females, healthy-inactive subjects, the 15-point RPE Scale, treadmill use, and swimming. For oxygen uptake, the highest validity coefficients between ratings of perceived exertion and oxygen uptake are for swimming. In a meta-analysis of study effects, when the validity coefficients are analyzed by study, the resultant mean validity coefficients are only somewhat higher (ratings of perceived exertion and heart rate, .657; ratings of perceived exertion and blood lactate, .642; ratings of perceived exertion and oxygen uptake, .609) than those obtained using sample size-weighted validity coefficients. Finally, corrections for bias generally resulted in increased validity coefficients and decreased variances.

We investigate local properties of the Green function of the complement of a compact set E. First we consider the case E ⊂ [0, 1] in the extended complex plane. We extend a result of V. Andrievskii which claims that if the Green function satisfies the Hölder1/2 condition locally at the origin, then the density of E at 0, in terms of logarithmic capacity, is the same as that of the whole interval [0, 1]. We give an integral estimate on the density in terms of the Green function, which also provides a necessary condition for the optimal smoothness. Then we extend the results to the case E ⊂ [−1, 1]. In this case the maximal smoothness of the Green function is H¨older-1 and a similar integral estimate and necessary condition hold as well. In the second part of the paper we consider the case when E is a compact set in Rd , d > 2. We give a Wiener type characterization for the Hölder continuity of the Green function, thus extending a result of L. Carleson and V. Totik. The obtained density condition is necessary, and it is sufficient as well, provided E satisfies the cone condition. It is also shown that the Hölder condition for the Green function at a boundary point can be equivalently stated in terms of the equilibrium measure and the solution to the corresponding Dirichlet problem. The results solve a long standing open problem - raised by Maz’ja in the 1960’s - under the simple cone condition.