In this work we have developed the method of back-transfoprmation within the Douglas-Kroll-Hess (DKH) framework, which has simplified the picture-change consistent transformation of first-order property operators in the DKH approach, making the implementation feasible. This has enabled us to implement the first all-electron scalar relativistic calculations of hyperfine coupling tensors at DKH2 level. Furthemore we have presented a general, relativistic two-component DFT approach for the unrestricted calculations of electronic g-tensors, based on DKH Hamiltonian. Additionally we have derived the expressions for the evaluation of hyperfine structurs and two-component unrestricted treatment of g-tensor within the Resolution of Identity Dirac Kohn Sham method developed by Stanoslav Komorovsky and Michal Repisky in collaboration with other members of the group of V. G. Malkin. All these approaches have been extensively validated. / In dieser Arbeit entwickelten wir ein Rücktransformations-Verfahren, das im Rahmen der relativistischen Douglas-Kroll-Hess (DKH) Methode die Picture-Change-konsistente Transformation von Eigenschaftsoperatoren erster Ordnung vereinfacht. Dies ermöglichte uns, die ersten skalar-relativistischen Allelektronen-Berechnungen von Hyperfinekopplungskonstanten auf DKH2-Niveau zu implementieren. Darüber hinaus entwickelten wir eine allgemeine relativistische zweikomponentige Methode für spin-polarisierte Berechnungen von elektronischen g-Tensoren. Zusätzlich leiteten wir die Gleichungen für die Berechnungen der von Stanislav Komorovsky und Michal Repisky entwickelten Resolution-of-Identity-Dirac-Kohn-Sham-Methode her. Alle diese Verfahren wurden in umfangreichen Studien validiert.

A general class of fluctuation tests for parameter instability in an M-estimation framework is suggested. The tests are based on partial sum processes of M-estimation scores for which functional central limit theorems are derived under the null hypothesis of parameter stability and local alternatives. Special emphasis is given to parameter instability in (generalized) linear regression models and it is shown that the introduced M-fluctuation tests contain a large number of parameter instability or structural change tests known from the statistics and econometrics literature. The usefulness of the procedures is illustrated using artificial data and data for the German M1 money demand, historical demographic time series from Großarl, Austria, and youth homicides in Boston. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Es werden die Parameter Summe-G2/GF und G0/G1 der hochauflösenden, zweiparametrigen Zellzyklusanalyse von Lymphozyten bei Fanconi-Anämie-Patienten, bei denen mehrere Meßwerte vorliegen, im Hinblick auf Schwankungen untersucht. Nach Auswertung der Daten stellen die Werte keine konstanten Parameter für den einzelnen Patienten dar. Die Langzeitanalyse des Zellzyklusverhaltens peripherer Blutlymphozyten reflektiert jedoch weitgehend die klinische Situation der Patienten. / Two Parameter - Sum of G2/GF and G0/G1 - of twoparametric, high definition Cellcycle Analyses from Lymphocytes of Fanconi-Anemia-Patients were examined over the time. After Evaluation of Data it became clear, that Sum G2/GF and G0/G1-Parameter are not constant for each Patient over the time. But the longtime Analyses of peripheric Lymphocytes showed that they almost represent the clinical Situation of a Patient.

Freiburg i. Br., Univ., Diss., 2007.

The purpose of this study is to investigate forced convection of air through open cell foams. It can be numerically investigated either by implementing the time efficient macroscopic models or computationally expensive microscopic models. However, during the course of this study, it was observed that the macroscopic models are not sufficient for determining the desired key parameters. Nevertheless, it is still possible that these macroscopic models can be used to design an application accurately with minimum time efforts if the concerned key parameters are already known through other means. Accordingly, in this work, a methodology is developed to determine the desired key parameters by implementing the microscopic models, which are further used into the macroscopic models for designing different applications. To validate the proposed methodology, a set of steady state and transient forced convection experiments were performed for a set of ceramic foams having different pore diameter (10−30 PPI) and porosity (0.79−0.87) for a superficial velocity in the range of 0.5−10 m/s.

The purpose of this study is to investigate forced convection of air through open cell foams. It can be numerically investigated either by implementing the time efficient macroscopic models or computationally expensive microscopic models. However, during the course of this study, it was observed that the macroscopic models are not sufficient for determining the desired key parameters. Nevertheless, it is still possible that these macroscopic models can be used to design an application accurately with minimum time efforts if the concerned key parameters are already known through other means. Accordingly, in this work, a methodology is developed to determine the desired key parameters by implementing the microscopic models, which are further used into the macroscopic models for designing different applications. To validate the proposed methodology, a set of steady state and transient forced convection experiments were performed for a set of ceramic foams having different pore diameter (10−30 PPI) and porosity (0.79−0.87) for a superficial velocity in the range of 0.5−10 m/s.

To meet the global hydrocarbon energy demand, it is imperative either to enhance the production from existing fields by applying innovative engineering solutions or discovering new field /resource areas. Both of these options are investigated by petroleum engineers intensively to tackle the challenges of meeting the ever-increasing demand. Meeting the energy demand as, like any other developing country, Jordan is facing a formidable challenge and requires exploration for conventional and unconventional hydrocarbon resources. As Jordan has a long exploration history for conventional reservoirs, Unconventional resource exploration and production seems to be the way to find new energy sources. Different exploration wells were drilled to evaluate the hydrocarbon potential. This research work is focusing on an experimental investigation to evaluate Jordanian hydrocarbon potential as well as to provide recommendations for future exploration activities in shale resources. The Evaluations were performed through comprehensive laboratory experiments that include measurements of Total Organic Content, Grain density, Pore Size Distribution, Specific Surface Area (BET), Mineralogy, Thermogravimetry Analysis, and Rock-Eval pyrolysis. The petrophysical properties (TOC, grain density, pore size distribution) of Jordanian shale (nine different wells) are investigated. The TOC and grain density are in an inversely proportional relationship. The TOC results show a gradual increment with the depth. All the samples have higher porosity dominated by macro pores. Fourteen (14) samples were selected primarily based on TOC (above 1.5%) for further analysis. The specific surface area results show a proportional relationship with the TOC content. Considering the petrophysical properties and mineralogy, these Jordanian shales broadly can be considered as high porosity clay and mudstone type of shale. Thermogravimetry analysis (TG/DTG) results indicate quantitative information related to organic and inorganic matter. Detection of thermos-reactive minerals, especially clay, carbonate, muscovite, pyrite is possible due to the combination of TG/DTG/DSC. The samples are examined under three different procedures which includes different heating programs. The oxidizing and inert atmospheric conditions (procedure i & ii) have the same heating program whereas procedure iii (inert atmospheric condition) has a heating program similar to the Rock-Eval pyrolysis program. The results of these samples show the complex nature of shale as well as organic matter by reacting in different stages (two or, three stages). Depending of the maturity of organic matter, the reaction occurring temperature range varies. Maximum oxidization reaction peaks happen between 479°C to 502°C. The maximum pyrolysis reaction peaks between 498°C to 521°C. Compared with complex heating (procedure iii) and rock Eval pyrolysis, S2 results indicate a high amount of inorganic compounds. Considering TGA reaction peaks and rock Eval pyrolysis results, these Jordanian shales indicate immature with low hydrocarbon generation potential. The Jordanian shale samples are analyzed by using Rock-Eval pyrolysis. Analysis results are used to interpret petroleum potential in rocks. The most important information includes organic matter types (also connected with the depositional settings), organic matter thermal maturity, and the remaining hydrocarbon generation potential in the current form. The organic geochemical analysis results indicate mostly poor to no source rock potential except JF2-760 samples. The hydrogen index (HI) and oxygen index (OI) result suggests that type iii kerogen and type iii/ iv kerogen are most likely from terrestrial and varied settings origin. The low hydrogen, as well as, low S2 value indicate very little hydrocarbon generation potential. Similarly, The Tmax and PI data indicate immature to early mature source rock status and low conversion scenario. Furthermore, the supercritical CO2 is injected into the samples, which is similar to gas flooding experiments to understand the recovery process. Hydrocarbon recovery or, CO2-shale interaction is determined by comparing three different properties (TOC, SSA, and TGA) pre-and-post supercritical CO2 injection. Supercritical CO2 injection in immature shale shows very limited property changes (TOC, SSA, and TGA) to the samples. However, in presence of hydrocarbon the pre-and post-injection property changes TOC, TGA, and SSA (BET) are noticeable enough to conclude HC recovery. Although in the case of immature shale with no hydrocarbon potential the kerogen or bitumen extraction has not been detected, which can be significant in the case of greenhouse gas storage, especially CCUS. This could reduce the risk of Organic Matter (OM) migration possibility in case immature shale formation is present in a suitable geological location.

This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.

This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identification of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial differential equation. The option prices are only available as discrete noisy observations so that the main difficulty is the ill-posedness of the numerical differentiation. Finite difference schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these difficulties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial differential equation and evaluate the performance of the finite difference schemes and the new algorithm for synthetic and real option prices.