Title: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight...

[pt] Este trabalho teve como objetivo avaliar a qualidade de amostras intactas da Argila do Sarapuí II extraídas com amostradores tubulares de pistão estacionário Geonor/NGI 76 mm. Este amostrador possui comprimento útil de 800 mm e diâmetro interno de 76,2 mm sem folga interna, dispondo de um pistão estacionário com ponta cônica, não sendo necessária a execução de pré-furo para a sua cravação. Duas amostras foram extraídas entre as profundidades de 3,50 e 4,30 m, sendo que um dos tubos de amostragem teve a sua superfície interna revestida com um polímero de baixo coeficiente de atrito, com o intuito de reduzir a tensão cisalhante entre a amostra e o amostrador durante a manobra de cravação do tubo no solo e, assim, avaliar a influência dessa redução na qualidade das amostras. As qualidades das amostras foram avaliadas com base nos resultados de ensaios de adensamento edométrico de carga incremental realizados em corpos de prova moldados com diâmetros de cerca de 50 mm e de 70 mm e altura de 20 mm, o que possibilitou também a avaliação da influência do diâmetro do corpo de prova na qualidade. Todos os corpos de prova foram classificados como de qualidade excelente a muito boa segundo o critério de Lunne et al. (1997), não tendo sido observada influência do diâmetro do corpo de prova nos resultados. Da mesma forma, a aplicação do polímero na superfície interna do tubo de amostragem parece não ter exercido influência nas qualidades dos corpos de prova. / [en] The aim of this work is to evaluate the quality of intact Sarapuí II clay samples taken with stationary piston tube samplers Geonor/NGI 76 mm. This sampler has a net tube length of 800 mm and an inner diameter of 76,2 mm with no inside clearance. It has a cone ended stationary piston, and pre-drilled boreholes are not required when driving the sampler. Two samples were taken from a depth l of 3.50 m to 4.30 m. One of the sampler tubes was coated on the inside with a low friction polymer in order to try to reduce the shearing stress between the sample and the sampler tube when pushing the tube during sampling, as to evaluate the influence of such reduction on the quality of the samples. The sample s quality was evaluated based on the results of incremental-loading one-dimensional consolidation tests carried out on specimens trimmed with diameters of about 50 mm and 70 mm, and a height of 20 mm. This also allowed the evaluation of the influence of the specimen s diameter on quality. All specimens were classified as excellent to very good according to Lunne et al s (1997) criterion. Moreover, no influence of the specimen diameter on the results was observed. Furthermore, the use of the polymer on the inner surface of the sampler tube seems to have had no influence on the quality of the specimens.

Detta arbete behandlar undersökningen och valideringen av kylförlustmodellen i det nyligen framtagna programmet för endimensionell turbindesign, Mean Line Tool (MLT), skapat av Siemens Industrial Turbomachinery AB (SIT). Huvudsyftet är att undersöka med vilken noggrannhet MLT kan prediktera de extra aerodynamiska förluster som uppstår vid injektion av kylluft i en turbinpassage. För att validera kylförlustmodellen i MLT, har tidigare resultat från en testrigg på KTH används, där de extra förlusterna på grund av kylinjektion har mätts för ett flertal kylpositioner på en turbinledskena. Lokala flödes- och geometriska parametrar från testriggen ansattes i MLT för att möjliggöra en korrekt jämförelse. Ytterligare validering utfördes mot en testbaserad Siemens-korrelation, som är en sammanställning av ett flertal test från olika turbinkomponenter av SIT. I denna korrelation undersöktes kylning på en ledskenas bladprofil och plattform, samt på skovelns bladprofil, där en ökning av kylmassflöde relaterades till en förändring i stegverkningsgrad. Resultaten, från jämförelsen mellan data från testriggen på KTH samt beräkningar i MLT, visade att MLT predikterar extraförlusterna på grund av kylning på bladprofilen av en ledskena med bra noggrannhet. Däremot visar jämförelsen att MLT beräknar en lägre förlust för bakkantskylning. Således har en modifierad förlustkorrelation för bakkantskylning presenterats, som ger mer överensstämmande resultat mot testriggen. Jämförelsen mellan MLT beräkningar och den testbaserade Siemens-korrelationen visar att MLT inte predikterar förändringen i stegverkningsgrad, på grund av extra kylmassflöde, med bra noggrannhet. På grund av ett flertal osäkerheter har denna jämförelse endast användas för att kvalitativt belysa brister i kylförlustmodellen av MLT. Med detta i åtanke har det fastställts att plattformskylning vid främre delen av en turbinpassage skulle kunna vara mycket överpredikterad av MLT. Den övergripande slutsatsen är att MLT predikterar förändringen i gitterverkningsgrad på grund av kylning på en ledskenas bladprofil med bra noggrannhet, förutom bakkantskylning. Ytterligare jämförelser visar att MLT inte kan prediktera förändringen i stegverkningsgrad, på grund av extra kylmassflöde, med bra noggrannhet för olika kylda komponenter från gasturbinsportfolion av SIT. Således behövs vidare validering av MLT innan programmet kan implementeras i turbindesignsystemet av SIT. / This thesis concerns the investigation and validation of the cooling loss model in newly developed one-dimensional turbine design tool, Mean Line Tool (MLT), of Siemens Industrial Turbomachinery AB (SIT). The main objective is to investigate how accurately MLT can predict the additional aerodynamic losses due to cooling ejection in a turbine blade passage. To validate the cooling loss model of MLT, existing results from an annular sector cascade rig at KTH were used, where the additional losses due to cooling ejection were presented for several cooling locations on a stator vane profile. Local flow- and geometrical parameters from the cascade rig were set in MLT to enable a fair comparison. Moreover, a Siemens test based correlation was used, which is a data collection based on tests using various cooled components of SIT. Cooling ejection on a stator vane profile, stator vane platform and rotor blade profile was investigated, where an increase in coolant mass-flow was related to a change in stage efficiency. The results, when comparing data from the KTH cascade rig against calculations of MLT, show that MLT is able to accurately predict the additional loss due to cooling ejection on a stator vane profile. However, the comparison presents that the calculated loss for trailing edge cooling by MLT is lower than the results from the cascade rig. Therefore, a modified trailing edge cooling correlation is presented, which predicts the results from the cascade rig with better accuracy. Furthermore, comparisons between MLT calculations and the Siemens correlation present that MLT cannot predict the change in stage efficiency, due to added coolant mass-flow, accurately. However, due to several uncertainties, these results are qualitatively used to understand sources of prediction error in the cooling loss model of MLT. Having this in mind, it is established that hub platform cooling at the front part of a blade passage might be greatly overpredicted by MLT. The general conclusion is that MLT predicts the change in cascade efficiency due to coolant ejection with good accuracy for a stator vane profile, except for cooling at the trailing edge. However, MLT is not able to predict the change in stage efficiency, due to added coolant mass-flow, with good accuracy for various cooled components from the SIT gas turbine product portfolio. Thus, MLT needs further validation before it can be implemented into the SIT design system.

This paper considers the way Herbert Marcuse’s re-formulation of the instrumental reason as a technical reason can be understood as an intensification or acceleration of some of the themes presented by Theodor W. Adorno and Max Horkheimer in The Dialectics of Enlightenment. By reading Marcuse´s The One-Dimensional Man in dialogue with Martin Heidegger’s The Question Concerning Technology, the paper explores a thesis that Marcuse draws on concepts from Heidegger, especially Ge-stell and Bestand, in his notion of the “technical reason” and “technological rationality” to think and think beyond modern technology. By positing modern technology as the focal point of the instrumentalization of reason, Marcuse sheds light of historical and contemporary problems with human thinking. The staging of this conversation with Marcuse and Heidegger that never really took place allows the paper to fully explore and understand Marcuse’s invoking of the aesthetical dimension, as well as his re-appropriation of Freudian terminology, as a model to re-establish negative thinking as a necessary counteraction to the one-dimensional positive thinking that is dominating private and public sphere.

The Cone Calorimeter has been used widely for various purposes as a bench - scale apparatus. Originally the retainer frame (edge frame) was designed to reduce unrepresentative edge burning of specimens. In general, the frame has been used in most Cone tests without enough understanding of its effect. It is very important to have one - dimensional (1D) conditions in order to estimate thermal properties of materials. It has been implicitly assumed that the heat conduction in the Cone Calorimeter is 1D using the current specimen preparation. However, the assumption has not been corroborated explicitly to date. The first objective of this study was to evaluate the heat transfer behavior of a Cone specimen by examining its three - dimensional (3D) heat conduction. It is essential to understand the role of wall lining materials when they are exposed to a fire from an ignition source. Full - scale test methods permit an assessment of the performance of a wall lining material. Fire growth models have been developed due to the costly expense associated with full - scale testing. The models require heat flux maps from the ignition burner flame as input data. Work to date was impeded by a lack of detailed spatial characterization of the heat flux maps due to the use of limited instrumentation. To increase the power of fire modeling, accurate and detailed heat flux maps from the ignition burner are essential. High level spatial resolution for surface temperature can be provided from an infrared camera. The second objective of this study was to develop a heat flux mapping procedure for a room test burner flame to a wall configuration with surface temperature information taken from an infrared camera. A prototype experiment is performed using the ISO 9705 test burner to demonstrate the developed heat flux mapping procedure. The results of the experiment allow the heat flux and spatial resolutions of the method to be determined and compared to the methods currently available.

Nous avons étudiés des fils quantiques dopés de semi-conducteurs gravés par spectroscopie de diffusion Raman. Nous avons observés les excitations du gaz d'électrons. Celles-ci présentent des règles de sélection différentes de celles établies pour les systèmes bi-dimensionnels. Nous avons montré théoriquement qu'elles proviennent de la modification de la structure du champ électromagnétique local provoquée par la géométrie particulière des fils gravés. Pour cela nous avons dû calculer le champ local et l'introduire dans la section efficace de diffusion Raman pour en déduire les règles de sélection de toutes les excitations. Cela a permis de déterminer sans équivoque la nature des excitations qui sont des plasmons. Aucune excitations à une particule ni fluctuations de densité de spin n'a été observées. Nous avons étudié l'évolution continue des dispersions de ces plasmons lorsque la largeur du fil est réduite de 1 micromètre à 30 nm. Jusqu'à 60 nm, celles-ci sont en très bon accord avec les résultats d'un modèle hydrodynamique. Au dessous de 60 nm, la comparaison avec un modèle RPA s'impose. Le plasmon intra-bande dispersif est observé jusqu'à 45 nm, largeur en dessous de laquelle les spectres Raman sont dominés par des excitations localisées qui nécessitent une analyse ultérieure pour en déterminer clairement leur nature. Nous montrons à l'aide du modèle RPA que nous avons atteint la limite quantique pour un fil de largeur 55 nm. Une gamme étroite de fils dont les largeurs sont comprises entre 55 nm à 45 nm permet donc l'étude de gaz strictement unidimensionnel.<br />Nous avons cherché à déterminer la contribution de la forte illumination dans les conclusions précédentes. Nous avons utilisé pour cela la spectroscopie de magnéto-transmission infra-rouge qui ne modifie pas les conditions d'équilibre du gaz d'électrons. Une largeur critique de 130 nm a été extraite, en dessous de laquelle nous n'avons plus aucun signe de la présence d'électrons libres. La comparaison des mesures Raman et infra-rouge a permis l'établissement et la validation d'un modèle microscopique du potentiel de confinement présent dans les fils. Enfin nous avons fabriqués des échantillons de géométries plus complexes. L'observation et l'analyse par diffusion Raman des plasmons dans ces fils a montré que nous pouvions contrôler la géométrie du potentiel confinant les électrons et a mis en évidence des effets nouveaux tels que le repliement et le confinement de plasmons unidimensionnels.

The aim of this diploma thesis is the application of vibrational spectroscopy in pharmaceutical analysis in studying solid pharmaceutical forms. The surface of tablet samples containing the active substance from the group of statins has been studied especially by the methods infrared microscopy. Spectral maps of samples were collected thanks to the techniques of specular reflection, attenuated total reflection (ATR) and "inverse" ATR after determining optimal conditions for measurements. In order to evaluate these measured maps, one-dimensional analysis and principal component analysis were used. As the same samples of tablets were also measured by Raman microscopy, the comparison has been provided. The measured distribution maps enable both a determination of substances in the sample and conclusion concerned a method of tablets' preparation. The method in this case is a granulation, which has been found out from a comparison of maps of generic and original medicament. The specular reflection method was selected to be the most appropriate technique for obtaining the maps of the surface of a tablet, via confrontation of particular methods consequently with consideration of their advantages and disadvantages in the measurement and data processing.

In this manuscript we study the action of one-dimensional integral operators on rearrangement-invariant Banach function spaces. Our principal goal is to characterize optimal target and optimal domain spaces corresponding to given spaces within the category of rearrangement-invariant Banach function spaces as well as to establish pointwise estimates of the non-increasing rearrangement of a given operator applied on a given function. We apply these general results to proving optimality relations between special rearrangement-invariant spaces. We pay special attention to the Laplace transform, which is a pivotal example of the operators in question. Powered by TCPDF (www.tcpdf.org)

Escoamentos bifásicos estão presentes em diversos processos naturais e industriais, como na indústria de petróleo. Podem apresentar-se em diferentes configurações topológicas, ou, padrões de escoamento, entre eles o escoamento estratificado ondulado e o estratificado com mistura na interface. Os escoamentos bifásicos estratificados óleo-água têm sido utilizados como uma forma conveniente de evitar a formação de emulsões de água em óleo em oleodutos e possuem uma ocorrência comum em poços de petróleo direcionais. Quando a onda interfacial ultrapassa determinado limite geométrico e cinemático, surge o fenômeno do entranhamento de gotas, representado por misturas entre as fases junto à interface que promovem um aumento na queda de pressão. Modelos têm sido apresentados pela literatura na tentativa de descrever o fenômeno do entranhamento de gotas. Neste trabalho é apresentada uma nova proposta de modelagem matemática unidimensional para o entranhamento de gotas com o objetivo de melhorar a previsão dos parâmetros envolvidos, em especial, da fração volumétrica de óleo e da queda de pressão bifásica. Também foi utilizada simulação numérica computacional, CFD (Computational Fluid Dynamics), com o uso de software comercial para obtenção dos valores dos parâmetros do escoamento estratificado ondulado óleo-água (fração volumétrica de óleo, queda de pressão, amplitude e comprimento da onda interfacial). Os resultados da modelagem fenomenológica para entranhamento e os de CFD foram comparados com bancos de dados experimentais. Os resultados em CFD mostram concordância com os resultados experimentais, tanto na análise qualitativa das propriedades geométricas das ondas interfaciais, quanto na comparação direta com os dados para fração volumétrica e queda de pressão. Os resultados numéricos da modelagem fenomenológica para fatores de entranhamento apresentam boa concordância com dados da literatura. / Two-phase flows are present in many natural and industrial processes, such as in the oil industry. They may be found arranged in several flow patterns, including the wavy stratified flow and the stratified with mixing at the interface. The stratified oil-water flow has been used as a convenient way to avoid the formation of emulsions of water in oil and have a common occurrence in directional oil wells. When the interfacial wave exceeds a certain geometric and kinematic limit the phenomenon of drop entrainment arises at the interface, causing an increase of pressure drop. Models have been presented in the literature in an attempt to describe the phenomenon of drop entrainment. In this work, we present a new method for the one-dimensional mathematical modeling of entrainment in order to improve the prediction of oil volume fraction and pressure drop. It was also used a commercial computational fluid dynamics tool (CFD) to obtain the values of flow parameters of wavy stratified oil-water flow, such as oil volume fraction, pressure drop, amplitude and length of the interfacial waves. The results of the phenomenological modeling for entrainment and CFD were compared with experimental databases. The CFD results are in agreement with the experimental results in both the qualitative analysis of the geometric properties of the interfacial waves and in direct comparison with oil-volumetric-fraction and pressure-drop data. The numerical results of the phenomenological model for entrainment factors are in agreement with data from the literature.

Foram medidas funções de excitação para a fusão completa dos sistemas 16O+46,50Ti em energias abaixo e em torno da barreira Coulombiana. A seção de choque de fusão foi obtida utilizando-se os métodos da espectroscopia em linha e fora da linha através da soma das seções de choque dos canais de decaimento do núcleo composto formado, observados experimen- talmente. As vantagens e limitações do método são discutidas em detalhes. As funções de excitação da fusão dos sistemas citados foram analisados utilizando-se modelos semiclássicos de penetração de barreira. Através desta análise determinamos o raio e a altura da barreira de fusão para estes sistemas. Os valores obtidos concordam com valores da literatura na mesma região de massa. A seção de choque de fusão calculada pelo modelo de penetração de barreira unidimensional utilizando potenciais que descrevem a interação entre íons pesados, é subestimada em energias abaixo da barreira Coulombiana. A introdução da vibração de ponto zero da superfície dos núcleos interagentes, apesar de produzir um aumento da seção de choque em energias sub- Coulombianas, não consegue reproduzir os dados de maneira satisfatória, pois prevê uma diferença isotópica nas funções de excitação que não e observada experimentalmente. As previsões do modelo estatístico para o decaimento do núcleo composto (programa CASCA- DE) apresentam uma concordância satisfatória para os canais de decaimento mais intensos. / Excitation functions for complete fusion of the systems 16O + 46,50Ti, with energies near and below the Coulomb barrier, were measured. With the use of the in-beam and out of beam spectroscopy, the formation of the compound nucleus was experimentally detected. The fusi- on cross section was then attained by the sum of all observed compound nucleus decay chan- nels. The limitation and advantages of measurements methods are discussed. Theoretical analysis of the experimental results using the semi-classical barrier penetration model allowed us to obtain the fusion barrier height and radius for the studied systems. These values are in good agreement with others reported for this mass range. Using the unidimensionaL barrier penetration model with different nuclear potentials, descri- bing the heavy ion interactions gave theoretical fusion cross section values systematically smaller than our measured values in the energy region below the Coulomb barrier. The introduction of the nuclear surface zero point vibrations enhances the theoreticaL fusion cross sections in the sub-Coulomb region, but simultaneously introduces an isotopic difference in the fusion excitation functions that is not observed experimentally. The statistical model predictions for the compound nucleus decay (calculated by the CASCADE program) show reasonable agreement for the more intense decay channels.