In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these two fields in abstract terms. Then we expand on this initial concept, using it to devise visualisation methods and a wide variety of solvers for flutter problems. We assess these solvers, applying them to real-life aeroelastic systems and measuring their performance. We then discuss and devise methods for improving these solvers. All our conclusions are supported by a variety of evidence from numerical experiments. Finally, we assess all of our methods, providing recommendations as to their use and future development. We do achieve several things in this thesis which have not been achieved before. Firstly, we solved a non-trivial flutter problem with a direct solver. The only direct solvers that have previously been presented are those that arise from classical flutter analysis, which applies only to very simple systems. Secondly, and as an extension of this first point, we solved a system with Theodorsen aerodynamics (approximated by a highly accurately) with a direct solver. This was achieved in an industrially competitive time (0.2s). This has never before been achieved. Thirdly, we solved an unstructured multiparameter eigenvalue problem. Unstructured problems have not been considered before, even in theoretical literature. This result is thus of significance both for multiparameter spectral theory and aeroelasticity. However, the single most important contribution of this thesis is the opening of a whole new field of study which stretches beyond aeroelasticity and into other industries: the treatment of instability problems using multiparameter methods. This field of research is wide and untrodden, and has the potential to change the way we analyse instability across many industries.

In der molekularen Diagnostik besteht ein Bedarf an schnellen und spezifischen Testsystemen, die entweder für die Labordiagnostik oder in Point of Care-Umgebungen eingesetzt werden können. Um dieses Ziel zu erreichen, stehen die Miniaturisierung und Parallelisierung im Mittelpunkt des Forschungsinteresses. Die führende Methode im Bereich der DNA-Analytik ist derzeit die Realtime-PCR. Dieser Technologie sind hinsichtlich der Multiplexfähigkeit technologischen Hürden gesetzt, da derzeit nur eine Analyse von maximal vier Parametern parallel in einem Versuchsansatz erfolgen kann. Microarrays stellen hingegen die benötigten Voraussetzungen zur Verfügung, um als Werkzeuge für die Multiparameteranalyse in verschiedensten Anwendungsbereichen zu dienen. Ein Schwerpunkt dieser Arbeit war es, Multiplex-PCRs und diagnostische Microarrays zu entwickeln, die für analytische Fragestellungen eine schnelle und zuverlässige Multiparameteranalytik ermöglichen, um die bisherigen Einschränkungen aktueller Nachweisverfahren zu vermeiden. Als Anwendungen wurden zum einen ein Nachweissystem für acht relevante Geflügelpathogene zur Überwachung in der Geflügelzucht, zum anderen ein Nachweissystem zur Identifikation potentiell allergener Lebensmittelinhaltstoffe entwickelt. Neben der Entwicklung geeigneter PCR und Multiplex-PCR-Verfahren sowie spezifischer Microarrays für die Detektion der gesuchten Zielsequenzen stand auch die weiterführende Integration von DNA-Amplifikation und Microarray-Technologie im Fokus dieser Arbeit. Die OnChip-Amplifikation stellt eine Möglichkeit dar, um DNA-Analytik und Detektion in einem Reaktionsschritt zu integrieren. Entsprechend wurden die in der Arbeit entwickelten PCR- und Multiplex-PCR-Verfahren zum Nachweis potentieller allergener Lebensmittelinhaltsstoffe für die OnChip-Amplifikation adaptiert und Reaktionsbedingungen getestet, die eine Multiparameteranalyse auf dem Chip ermöglichen. Die entwickelten OnChip-PCR-Verfahren zeigten eine hohe Spezifität sowohl in Single- als auch in der Multiplex-OnChip-PCR. Eine Sensitivität von 10 Kopien bzw. <10ppm konnte in Single-OnChip-PCRs für den Nachweis allergener Lebensmittelinhaltsstoffe gezeigt werden. In Multiplex-OnChip-PCRs konnten 10-100ppm allergene Verunreinigungen spezifisch in unterschiedlichen Lebensmitteln nachgewiesen werden. Ein weiterer Schritt in Richtung einer möglichen Verwendung im Point of Care-Bereich stellt der Einsatz eines isothermalen Amplifikationsverfahrens dar. Vorteil eines solchen Verfahrens ist die Möglichkeit, auf das ansonsten benötigte Thermocycling zu verzichten. Dies vereinfacht eine Integration der OnChip-Amplifikation in mobile Analysegeräte oder Lab on Chip-Systeme und qualifiziert das Verfahren für den Einsatz in Point of Care-Umgebungen. In dieser Arbeit wurde eine noch junge isothermale Amplifikationsmethode, die helikase-abhängige Amplifikation (HDA), hinsichtlich ihrer Eignung für die Integration auf einem Microarray getestet. Hierfür konnte die bislang erste OnChip-HDA für Einzel- und Duplex-Nachweise von Pathogenen entwickelt werden. / In molecular diagnostics there is a need for fast and specific assay systems that could be used in the clinics and in point of care settings alike. Therefore miniaturisation and parallelisation are in the main focus of current assay development researches. The current gold standard for DNA analytics is the realtime PCR. However, this technology has its restraints in context to multiplex analysis. With the currently available technology an efficient multiplexing is only possible for four different targets per analysed sample. Microarrays in contrast offer the needed multiplex capabilities and have advanced to capable tools used in multiple fields of application. One focus of this work was the integration of Multiplex PCR and microarray technology, developing a microarray capable of analysing multiple parameters in one given sample, circumventing the problems and restraints of the exsisting technologies. As an example microarray assays for two different application fields were developed. One microarray assay for the detection of pathogens in poultry and another microarray assay for the detection of potentially allergenic food ingredients. Single- and Multiplex OnChip-PCR assays for both applications were developed and tested. OnChip-PCRs developed in this work showed high specificity in Single- and Multiplex-OnChip amplifications. The sensitivity was in the range of 10 DNA copies or 10ppm respectively for Single-OnChip-PCR in experiments for the detection of allergenic food contaminations. In Multiplex-OnChip-PCR experiments 100 DNA copies or 100ppm of food contaminents could be detected in different food matrices. A further focus of this work was the adaption of the OnChip amplification for the use in Point of Care settings. Isothermal amplification is a promising approach having the advantage of avoiding the thermocycling needed in the PCR. This opens up certain opportunities for the development of smaller, more flexible mobile diagnostic analysis devices. In this work we have evaluated the helicase dependent amplification (HDA) in terms of usability in OnChip amplification. In this work it was shown for the first time that HDA could be used for the detection of different pathogens in an Duplex-OnChip-PCR, showing the potential of this technology for integration in Point of Care settings.

Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers fortunes and survival analysis, Just as commutative integration theory may be realised as a special case of the more general non-commutative theory for integrals, so too, we find classical probability may be realised as a limiting, special case of quantum probability theory. In this thesis we are concerned with the development of multiparameter quantum stochastic integrals extending non-commutative constructions to the general n parameter case, these being multiparameter quantum stochastic integrals over the positive n - dimensional plane, employing martingales as integrator. The thesis extends previous analogues of type one, and type two stochastic integrals, for both Clifford and quasi free representations. As with one and two dimensional parameter sets, the stochastic integrals constructed form orthogonal, centred L2 - martingales, obeying isometry properties. We further explore analogues for weakly adapted processes, properties relating to the resulting quantum stochastic integrals, develop analogues to Fubini’s theorem, and explore applications for quantum stochastic integrals in a security setting.

Die Dissertation widmet sich dem inversen Problem der Bestimmung der fünf Parameter eines Jump-Diffusions-Prozesses aus einer Preistrajektorie. Numerische Rechnungen zu statistischen Standardverfahren haben gezeigt, dass Stabilitätsprobleme insbesondere dann auftreten, wenn die Parameter aus einer relativ kleinen Zahl beobachteter Assetpreise bestimmt werden. Daher untersuchen wir das Problem der Parameterschätzung in dieser Arbeit unter Einbeziehung von Methoden aus der Theorie inverser Probleme, da deren zentrales Anliegen die Analyse und Regularisierung inkorrekter und instabiler inverser Aufgaben ist. In dieser Arbeit werden Phänomene der Instabilität der Parameterbestimmung herausgearbeitet und analysiert. Hierfür leiten wir eine entsprechende nichtlineare Operatorgleichung her, die den Zusammenhang zwischen einer von den Parametern abhängigen Trajektorie des Jump-Diffusions-Prozesses und der Dichtefunktion der Returns beschreibt. Diese Operatorgleichung untersuchen wir bezüglich ihrer Korrektheit. Wir zeigen anhand einer Fallstudie mit simulierten Daten, dass bei der numerischen Lösung Inkorrektheitsphänomene auftreten, sobald die Daten mit kleinen Datenfehlern behaftet sind. Um diese Stabilitätsprobleme zu überwinden, diskutieren wir einen Multiparameter-Regularisierungszugang, bei dem zusätzlich zur Least-Squares Anpassung der empirischen Dichtefunktion die Semiinvarianten berücksichtigt werden. / This thesis deals with the inverse problem of estimating simultaneously the five parameters of a jump diffusion process based on return observations of a price trajectory. It is well known that there occur instability effects using conventional statistical methods, particularly if only a small number of data are available. Therefore we apply the theory of inverse problems for parameter estimation. We analyse the forward operator mapping the parameters to the density function of the returns with respect to well-posedness and ill-posedness of the problem. We show that there occur some ill-posedness phenomena in the parameter estimation problem in case of noisy data and illustrate the instability effect by a numerical case study. To obtain stable approximate solutions of the estimation problem, we use a multi-parameter regularization approach, where a least-squares fitting of empirical densities is superposed by a quadratic penalty term of fitted semi-invariants with weights.

Random field models have provided a flexible environment in which the properties of the term structure of interest rates are captured almost as observed. In this study we provide an overview of the forward rate random fiield models and propose an extension in which the forward rates fluctuate along with a two parameter process represented by a random field. We then provide a mathematical expression of the yield curve under this model and sketch the prospective utilities and applications of this model for interest rate management.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Concern over water quality in Brazil is being hotly debated currently. In order to obtain information about the water quality at the national level, it was created the National Program for Assessment of Water Quality (PNQA). This program is the main axis of the National Network for Water Quality Monitoring (RNQA). To obtain water quality data and to create a standardized procedure, multiparameter probes were delivered to the federations, which allow determining the quality in real time through a few parameters. The multiparameter probes are presented in the market to supply the basics requirements to determine water quality with standardization, and the cost for the adoption of these probes will depend on the parameters. The more parameters evaluated, the higher its cost and it can derail monitoring. The basic probes simultaneously evaluate parameters such as dissolved oxygen, conductivity, total suspended solids, redox potential, temperature, pH and turbidity. These parameters allow inferences about the water quality and it has the advantage of providing results within minutes. However, the results are reliable? In this context, the aim of this thesis was to evaluate the reliability of the data presented by the multiparameter probe for monitoring of surface water, which was determined and compared to the results presented by multiparameter probe mark Aquaread AP 1000 with used equipment and methodologies by traditional laboratories. The time of immersion of the probe was determined for all its parameters were stabilized, the transport time so that did not occur changes in the sample values determined in field, we compared their readings with traditional methods and created a protocol probe operation. The results presented in research showed that the average time recommended for stabilization of parameters is 20 minutes. Regarding the conservation of water samples collected in the field, there was no significant difference in the readings over time. The multiparameter probe showed no reliable values in order to assert the water quality due to a high discrepancy between individual equipment, laboratory analysis regarding the probe, being a correction of each parameter required. / A preocupação com a qualidade da água no território brasileiro está sendo muito debatida atualmente. Com o objetivo de obter informações sobre a qualidade da água no âmbito nacional, criou-se o Programa Nacional de Avaliação da Qualidade das Águas (PNQA). Esse programa é o principal eixo da Rede Nacional de Monitoramento de Qualidade das Águas (RNQA). Para obter os dados da qualidade da água e para que houvesse uma padronização metodológica, foram entregues às federações sondas multiparâmetros, as quais permitem determinar a qualidade da água em tempo real através da leitura de alguns parâmetros. As sondas multiparâmetros apresentam-se no mercado para suprir as exigências básicas para a determinação da qualidade da água, com uma padronização, sendo que o custo para a adoção dessas sondas dependerá dos parâmetros a serem lidos. Quanto mais parâmetros avaliados, maior será seu custo, podendo inviabilizar o monitoramento. As sondas básicas avaliam ao mesmo tempo parâmetros como: oxigênio dissolvido, condutividade elétrica, sólidos totais em suspensão, potencial redox, temperatura, pH e turbidez. Esses parâmetros permitem inferir sobre a qualidade da água tendo como vantagem disponibilizar os resultados em alguns minutos. Porém, os resultados apresentados são confiáveis? Neste contexto, objetivou-se com esta dissertação avaliar a confiabilidade dos dados apresentados pela sonda multiparâmetros para o monitoramento de águas superficiais, determinou-se e comparou-se estatisticamente os resultados apresentados pela sonda multiparâmetros da marca Aquaread AP 1000 com equipamentos e metodologias utilizados por laboratórios tradicionais. Foram determinados: o tempo de submersão da sonda para que todos os seus parâmetros fossem estabilizados e ainda o tempo de transporte para que não ocorresse alteração dos valores das amostras determinadas a campo, compararam-se suas leituras com os métodos tradicionais e criou-se um protocolo de operação da sonda. Os resultados apresentados na pesquisa mostraram que o tempo médio indicado para a estabilização dos parâmetros é de 20 minutos. Em relação à conservação das amostras de águas coletadas a campo, não se observou diferença significativa com as leituras no decorrer do tempo. A sonda multiparâmetros não apresentou valores confiáveis a fim de afirmar a qualidade da água, pois ocorreu uma alta discrepância entre os equipamentos individuais, análise de laboratório em relação à sonda, sendo necessária uma correção de cada parâmetro.

Regenerative medicine and cell therapies hold great potential to treat a variety of medical conditions. Product characterisation of these therapies is particularly difficult as they pose regulatory challenges due to donor heterogeneity and the lack of standardised lot release tests that can reliably predict in vivo function. Human mesenchymal stem cells (hMSCs), also called multipotent stem cells or mesenchymal stromal cells, are a viable option in cell therapies due to their immunosuppressive and pro-angiogenic functions. Currently there are no standardised methods or potency assays to quantify these properties. To address this, five individual hMSCs lines from different donors were created and characterised based upon growth rate, differentiation capability and extracellular surface protein expression. A novel multiparameter flow cytometry method to characterise the cells based upon extracellular surface markers was developed that supports high-throughput and high-content analyses. Three candidate lines were taken forward and assessed in multiple in vitro bioassays that examined the hMSC immunosuppressive response to a defined inflammatory environment, effect on T-cell proliferation, and effect on a mixed lymphocyte population. Next, the angiogenic properties were assessed using human umbilical vein endothelial cells (HUVECs) tube formation as a model for cardiac regeneration. This involved utilising automated time lapse microscopy techniques coupled with image analysis software to quantify endothelial to tube formation. Further analysis of the hMSC secretome revealed differences in the levels of pro-angiogenic cytokines such as vascular endothelial growth factor, hepatocyte growth factor and IL-8. Significant differences in angiogenic potency were found between the hMSC lines. This thesis highlights the need to develop specific assays that reflect the intended clinical action. Taken together, these quantitative approaches provide valuable tools to measure hMSC quality and potency, and supports continued efforts to improve characterisation strategies for cellular therapies.

Die Dissertation widmet sich dem inversen Problem der Bestimmung der fünf Parameter eines Jump-Diffusions-Prozesses aus einer Preistrajektorie. Numerische Rechnungen zu statistischen Standardverfahren haben gezeigt, dass Stabilitätsprobleme insbesondere dann auftreten, wenn die Parameter aus einer relativ kleinen Zahl beobachteter Assetpreise bestimmt werden. Daher untersuchen wir das Problem der Parameterschätzung in dieser Arbeit unter Einbeziehung von Methoden aus der Theorie inverser Probleme, da deren zentrales Anliegen die Analyse und Regularisierung inkorrekter und instabiler inverser Aufgaben ist. In dieser Arbeit werden Phänomene der Instabilität der Parameterbestimmung herausgearbeitet und analysiert. Hierfür leiten wir eine entsprechende nichtlineare Operatorgleichung her, die den Zusammenhang zwischen einer von den Parametern abhängigen Trajektorie des Jump-Diffusions-Prozesses und der Dichtefunktion der Returns beschreibt. Diese Operatorgleichung untersuchen wir bezüglich ihrer Korrektheit. Wir zeigen anhand einer Fallstudie mit simulierten Daten, dass bei der numerischen Lösung Inkorrektheitsphänomene auftreten, sobald die Daten mit kleinen Datenfehlern behaftet sind. Um diese Stabilitätsprobleme zu überwinden, diskutieren wir einen Multiparameter-Regularisierungszugang, bei dem zusätzlich zur Least-Squares Anpassung der empirischen Dichtefunktion die Semiinvarianten berücksichtigt werden. / This thesis deals with the inverse problem of estimating simultaneously the five parameters of a jump diffusion process based on return observations of a price trajectory. It is well known that there occur instability effects using conventional statistical methods, particularly if only a small number of data are available. Therefore we apply the theory of inverse problems for parameter estimation. We analyse the forward operator mapping the parameters to the density function of the returns with respect to well-posedness and ill-posedness of the problem. We show that there occur some ill-posedness phenomena in the parameter estimation problem in case of noisy data and illustrate the instability effect by a numerical case study. To obtain stable approximate solutions of the estimation problem, we use a multi-parameter regularization approach, where a least-squares fitting of empirical densities is superposed by a quadratic penalty term of fitted semi-invariants with weights.

New catalyst development for the hydrotreating process, employing functionalized mesoporous carbon (mC) support is studied. mC support was prepared by the volume templating of alkali modified SBA-15 using sucrose as the carbon source and then functionalized using nitric acid of various concentrations (upto 8M HNO3). A series of NiMo catalysts (12% Mo and 2.4% Ni) were prepared using these functionalized mC supports. The supports and catalysts were characterized by N2 physisorption, SAXS, XRD, FTIR, TGA, SEM, TEM, H2-TPR and HRTEM. SAXS results indicated mild reduction in ordered structure of mesoporous carbons after functionalization. N2 physisorption analysis indicated progressive reduction in surface area and pore volume with the increase in nitric acid concentration. Enhancement of surface functional groups and acidity after functionalization were observed through FTIR spectroscopy and Boehm titration. SEM images showed the retention of needle like morphology in all functionalized carbon supports. TEM images showed that the increase in nitric acid concentration causes excessive etching, resulting in the reduction of ordered structure of functionalized mesoporous carbons. Hydrotreating study of these NiMo/mC catalysts were carried out under industrial operating conditions in a laboratory scale trickle bed reactor using coker light gas oil derived from Athabasca bitumen as feedstock. NiMo catalyst supported on 6M acid treated mC (i.e. NiMo/mC-6M) showed the highest activity due to higher surface functional groups, higher acidity and better textural properties. The HDS and HDN activities of NiMo/mC-6M catalyst were higher than that of NiMo/ã-Al2O3 catalyst owing to lower support metal interaction (SMI), higher surface area and effective functionalization. Using the mC-6M support, NiMo catalysts with different metal loading (12 27% Mo, 2.4 to 5.4% Ni) were prepared and characterized. Hydrotreating activity study of these catalysts indicated that the catalyst with 22% Mo and 2.9% Ni loading was the optimum catalyst on 6M functionalized mC support. Higher metal loading (>22%Mo) led to excessive pore blockage and improper metal dispersion resulting in decreased activity. Kinetic study of the optimum catalyst was carried out by varying temperature (330°C to 370°C), gas-to-oil ratio (400 1000 Nm3/m3), LHSV (1.0 to 2.5 hr-1) and pressure (7.8 to 9.8 MPa) and the data was fitted by non-linear regression method using power law model. The calculated reaction orders and activation energies were 2.8, 1.5 and 189 KJ/mol, 98.9 KJ/mol for HDS and HDN, respectively. The results of HRTEM and H2-TPR indicated lower SMI in mC supported catalyst resulting in the generation of qualitatively Type-II like NiMoS phase on functionalized mC supports, which is considered to be very active for hydrotreating. The hydrotreating activity of the optimum catalyst was higher than that of commercial catalyst (supported on ã-Al2O3). Long term deactivation experiment carried out over a total period of 10 weeks confirmed the durability of NiMo/mC catalyst for the duration of operation. This study reveals the immense capability of functionalized mC supports to become the potential alternative catalyst support to conventional ã-Al2O3 for the hydrotreating of gas oil feedstocks.

New catalyst development for the hydrotreating process, employing functionalized mesoporous carbon (mC) support is studied. mC support was prepared by the volume templating of alkali modified SBA-15 using sucrose as the carbon source and then functionalized using nitric acid of various concentrations (upto 8M HNO3). A series of NiMo catalysts (12% Mo and 2.4% Ni) were prepared using these functionalized mC supports. The supports and catalysts were characterized by N2 physisorption, SAXS, XRD, FTIR, TGA, SEM, TEM, H2-TPR and HRTEM. SAXS results indicated mild reduction in ordered structure of mesoporous carbons after functionalization. N2 physisorption analysis indicated progressive reduction in surface area and pore volume with the increase in nitric acid concentration. Enhancement of surface functional groups and acidity after functionalization were observed through FTIR spectroscopy and Boehm titration. SEM images showed the retention of needle like morphology in all functionalized carbon supports. TEM images showed that the increase in nitric acid concentration causes excessive etching, resulting in the reduction of ordered structure of functionalized mesoporous carbons. Hydrotreating study of these NiMo/mC catalysts were carried out under industrial operating conditions in a laboratory scale trickle bed reactor using coker light gas oil derived from Athabasca bitumen as feedstock. NiMo catalyst supported on 6M acid treated mC (i.e. NiMo/mC-6M) showed the highest activity due to higher surface functional groups, higher acidity and better textural properties. The HDS and HDN activities of NiMo/mC-6M catalyst were higher than that of NiMo/ã-Al2O3 catalyst owing to lower support metal interaction (SMI), higher surface area and effective functionalization. Using the mC-6M support, NiMo catalysts with different metal loading (12 27% Mo, 2.4 to 5.4% Ni) were prepared and characterized. Hydrotreating activity study of these catalysts indicated that the catalyst with 22% Mo and 2.9% Ni loading was the optimum catalyst on 6M functionalized mC support. Higher metal loading (>22%Mo) led to excessive pore blockage and improper metal dispersion resulting in decreased activity. Kinetic study of the optimum catalyst was carried out by varying temperature (330°C to 370°C), gas-to-oil ratio (400 1000 Nm3/m3), LHSV (1.0 to 2.5 hr-1) and pressure (7.8 to 9.8 MPa) and the data was fitted by non-linear regression method using power law model. The calculated reaction orders and activation energies were 2.8, 1.5 and 189 KJ/mol, 98.9 KJ/mol for HDS and HDN, respectively. The results of HRTEM and H2-TPR indicated lower SMI in mC supported catalyst resulting in the generation of qualitatively Type-II like NiMoS phase on functionalized mC supports, which is considered to be very active for hydrotreating. The hydrotreating activity of the optimum catalyst was higher than that of commercial catalyst (supported on ã-Al2O3). Long term deactivation experiment carried out over a total period of 10 weeks confirmed the durability of NiMo/mC catalyst for the duration of operation. This study reveals the immense capability of functionalized mC supports to become the potential alternative catalyst support to conventional ã-Al2O3 for the hydrotreating of gas oil feedstocks.