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Deligne-Lusztig theory allows the parametrization of generic character tables of finite groups of Lie type in terms of families of conjugacy classes and families of irreducible characters "independently" of \(q\).
Only in small cases the theory also gives all the values of the table.
For most of the groups the completion of the table must be carried out with ad-hoc methods.
The aim of the present work is to describe one possible computation which avoids Lusztig's theory of "character sheaves".
In particular, the theory of Gel'fand-Graev characters and Clifford theory is used to complete the generic character table of \(G={\rm Spin}_8^+(q)\) for \(q\) odd.
As an example of the computations, we also determine the character table of \({\rm SL}_4(q)\), for \(q\) odd.
In the process of finding character values, the following tools are developed.
By explicit use of the Bruhat decomposition of elements, the fusion of the unipotent classes of \(G\) is determined.
Among others, this is used to compute the 2-parameter Green functions of every Levi subgroup with disconnected centre of \(G\).
Furthermore, thanks to a certain action of the centre \(Z(G)\) on the characters of \(G\), it is shown how, in principle, the values of any character depend on its values at the unipotent elements.
It is important to consider \({\rm Spin}_8^+(q)\) as it is one of the "smallest" interesting examples for which Deligne--Lusztig theory is not sufficient to construct the whole character table.
The reasons is related to the structure of \({\mathbf G}={\rm Spin}_8\), from which \(G\) is constructed.
Firstly, \({\mathbf G}\) has disconnected centre.
Secondly, \({\mathbf G}\) is the only simple algebraic group which has an outer group automorphism of order 3.
And finally, \(G\) can be realized as a subgroup of bigger groups, like \(E_6(q)\), \(E_7(q)\) or \(E_8(q)\).
The computation on \({\rm Spin}_8^+(q)\) serves as preparation for those cases.

Mussel-inspired catechol-containing polymers provide a promising basis for developing strong biogenic adhesives (see chapter 1). In order to develop a biomimetic adhesive, solvent stable laccases were investigated for their application as biochemical catalyst for the functionalization of natural polymers (see chapter 2), such as chitosan and lignin, with catechols. Investigation of the laccase-catalysed C–N bond formation between primary amines and catechols, such as protocatechuic acid (PCA) and dihydrocaffeic acid (DHC), suggest that the reaction is promoted by a low pKa value of the primary amine used and a neutral or mildly acidic reaction pH. Since the pKa of chitosan’s amine groups is below 7, spontaneous reactions with catechols were possible, resulting in a PCA-functionalized chitosan, which achieved a tensile strength of 4.56 MPa ± 0.54 MPa on aluminum surfaces blasted with corundum (see chapter 3). For the functionalization of lignin, which was extracted with the Organosolv (OS) process, a two-step concept was required, where first L-lysine and subsequently DHC and PCA were grafted onto lignin. For DHC-lignin, a tensile strength of 169.3 kPa ± 130.6 kPa was measured (see chapter 4). Since the functionalization and curing processes use naturally occurring substances exclusively and are free of toxic chemicals, novel and sustainable bioadhesives were developed.
Moreover, differential scanning calorimetry (DSC) analysis was used to characterize the mussel-inspired chitosan adhesive (see chapter 5). Furthermore, DSC measurements were validated for monitoring biodegradation quantitatively using small sample quantities and simple sample preprocessing. Using only DSC measurements, quantifiable detection of degradation progress was possible, while at the same time qualitative assessment of changes in crystallinity (indicating incomplete biodegradation) was obtained. The implemented method is recommended for the quantification of the biodegradability of the PCA-chitosan adhesive.
This work introduces novel bio-based adhesives, as well as a new measuring technique for measuring biodegradability of various material.

We present a study of optoelectronically active Ga(As)As quantum dots (QDs) on Al-rich AlxGa1-xAs layers with Al concentrations
up to x=90%. So far, however, it has not been possible to grow optoelectronically active Ga(As)As QDs epitaxially
directly on and in between Al-rich barrier layers in the AlGaInAsSb material system. A QD morphology might appear on the
growth front, but the QD-like entities will not luminesce. Here, we use photoluminescence (PL) measurements to show that thin
Al-free capsule layers between Al-rich barrier layers and the QD layers can solve this problem; this way, the QDs become
optoelectronically active; that is, the dots become QDs. We consider antimonide QDs, that is, Ga(As)Sb QDs, either on GaAs for
comparison or on AlxGa1-xAs barriers (x >10%) with GaAs capsule layers in between. We also discuss the influence of QD
coupling both due to stress/strain from neighboring QDs and quantum-mechanically on the wavelength of the photoluminescence
peak. Due to their mere existence, the capsule layers alter the barriers by becoming part of them. Quantum dots
applications such as QD semiconductor lasers for spectroscopy or QDs as binary storage cells will profit from this additional
degree of design freedom.

Reflectance anisotropy spectroscopy (RAS), which was originally invented to monitor
epitaxial growth, can—as we have previously shown—also be used to monitor the reactive ion
etching of III/V semiconductor samples in situ and in real time, as long as the etching rate is not
too high and the abrasion at the etch front is not totally chaotic. Moreover, we have proven that—
using RAS equipment and optical Fabry-Perot oscillations due to the ever-shrinking thickness of the
uppermost etched layer—the in situ etch-depth resolution can be as good as +/-0.8 nm, employing a
Vernier-scale type measurement and evaluation procedure. Nominally, this amounts to +/-1.3 lattice
constants in our exemplary material system, AlGaAsSb, on a GaAs or GaSb substrate. In this
contribution, we show that resolutions of about +/-5.6 nm can be reliably achieved without a Vernier
scale protocol by employing thin doped layers or sharp interfaces between differently doped layers
or quantum-dot (QD) layers as etch-stop indicators. These indicator layers can either be added
to the device layer design on purpose or be part of it incidentally due to the functionality of the
device. For typical etch rates in the range of 0.7 to 1.3 nm/s (that is, about 40 to 80 nm/min), the RAS
spectrum will show a distinct change even for very thin indicator layers, which allows for the precise
termination of the etch run.

The present study deals with the cause of head-curve instability and the influence of impeller-outlet and diffuser-inlet width on pump performances. Experiments and Computational Fluid Dynamics (CFD) simulations were carried out on a 4-stage model pump. Three impellers and diffusers with different meridional-widths were designed for a specific speed around 30 [m\(^3\)/s, m, rpm]. Overall-performance curves, stage-head curves, inlet recirculation in the 1\(^{st}\) stage, internal-head curves in the 2\(^{nd}\) stage and pressure profiles in the impeller side room were measured with 29 pressure sensors. Pressure pulsations were recorded at various positions in the multistage pump.
When the pump ran at the onset of the instability, an excessive head-loss was detected in the inlet triangular section of the diffuser. The pressure profiles in the side room and flow patterns in the impeller showed a sudden shift of flow recirculation at the impeller outlet across the span. According to [1, 2], this flow phenomenon is called flow pattern switching. The abrupt movement of outlet recirculation across the span produced a large momentum-exchange between streamlines and a massive mixing-loss in the inlet triangular section. This was considered the main cause of the instability.
As the meridional-width increased, flow recirculation at the impeller outlet was intensified, giving a higher head and power at shut-off. In contrast, the onset of the instability did not vary systematically with the meridional width. Diffuser rotating-stall was detected at \(f/f_n\) = 0.029 when the pump with the largest width ran at the onset of the instability. Even though all three designs generated a head-curve instability, the rotating stall appeared only in the largest meridional-width.
The uncertainty in the CFD prediction of pressure pulsations was evaluated. The discrepancy between measured and calculated values was largely dependent on the sampling location and operating points.

The present work investigates the role of higher education experience in the process of students’ adult identity formation. In the broadest sense, adult identity is “seeing oneself as an adult” (Macmillan, 2007: 20), and it lays in the core of intensive processes of personal identity formation in the years following adolescence, which are for an increasing number of youth over the past decades spent in higher education. Approaches to adulthood in prior studies reveal ongoing discussions and attempts at re-conceptualisation against changing conditions and regimes of transition to adulthood. Traditionally, the so-called “objective markers” of adulthood have dominated the discourses for a long time, emphasising role transitions and demographic features as criteria for adulthood. The new research venues adding biographical approaches and subjective experiences reveal significance of inner, psychological processes of becoming an adult. However, the problem of the role of higher education in the process of students’ adult identity has not been fully illuminated thus far. The reason for this might be sought within the domain of disciplinary orientation of the field of higher education and Educational Sciences.
Higher education research focuses on the overall, “grand” effects of education, while traditional Educational Sciences have not been showing much interest in higher education topics. Substantial work has been produced from developmental sciences, psychology in particular, which has revealed an intricate forest of today’s adulthood and conditions for its attainment, leaving open a whole set of educational, social, economic, cultural antecedents, correlates and experiences affecting transition to adulthood. Besides, as analyses presented in Chapter 2 show, students’ position in dominant discourses marked by political and economic imperatives is marginal. Their experiences and voices are in a sense excluded, making it almost impossible to infer on actual students’ personal benefits of the higher education process.
The theoretical framework for this research consists of Erikson’s (Erikson, 1959; 1963; 1968) positions on human development in post-adolescent years, and McAdams’s model of narrative identity (1988; 2011; 2018), which also arose from Eriksonian tradition. Psychosocial theory (Erikson, 1959; 1963; 1968) assumes that social institutions provide structure and guidance to personal development, whereby they create a niche for psychosocial moratorium enabling youth a period of “identity work” before taking on long-term adult commitments. Research over recent decades reporting that higher education provides opportunities for students’ self-growth, exploration and resolving key identity questions in a variety of fields (e.g., Adams and Fitch, 1983; Arnett, 2004a; Berman, Kennerley, Kennerley, 2008; Mayhew, Rockenbach, Bowman, Seifert, Wolniak, Pascarella, Terenzin, 2016) supports such theoretical stances. The present research intends to extend existing knowledge raising the central question: What role of higher education experience students perceive in their adult identity formation?
The empirical part reports on biographical research into senior year students’ lived experiences of their developmental path and their meaning to the higher education process. Students’ experiences are approached using the qualitative technique of problem-centred interviewing (PCI), which helps focus participants’ narration on the researcher’s interest and subsequent in-depth analysis of collected experiences. In total, 40 senior year students coming from diverse backgrounds were interviewed. Data were analysed in Atlas.ti software, which enabled the coding system’s better organization and browsing through transcripts. The qualitative analysis process consisted of both inductive and deductive approaches, wherein open and thematic coding techniques were performed interchangeably.
Research findings indicate that in certain groups of students – but not in all – higher education experience facilitates and enriches the process of adult identity formation granting orientation and guidelines. Students identify experiences with the highest adult identity formational potential organised in the four broad categories: relationships with teachers and peers, respectively, teaching approach and study material, and extra-curricular activities. Based on the obtained findings, four patterns of thinking about the role of higher education in students’ adult identity formation have been identified: generator of adult identity formation, a safe-zone for exploration processes, interim phase leading to adulthood, and higher education suspending adult identity formation. This formed the basis for constructing the four student types; proactive, explorer, comfort-zone and atypical student. Research findings give the rationale for rethinking the educative potential of higher education in terms of its relevance for diverse students personally – for their self-growth and forming their personal identities, in addition to the professional ones.

Estimation and Portfolio Optimization with Expert Opinions in Discrete-time Financial Markets
(2021)

In this thesis, we mainly discuss the problem of parameter estimation and
portfolio optimization with partial information in discrete-time. In the portfolio optimization problem, we specifically aim at maximizing the utility of
terminal wealth. We focus on the logarithmic and power utility functions. We consider expert opinions as another observation in addition to stock returns to improve estimation of drift and volatility parameters at different times and for the purpose of asset optimization.
In the first part, we assume that the drift term has a fixed distribution, and
the volatility term is constant. We use the Kalman filter to combine the two
types of observations. Moreover, we discuss how to transform this problem
into a non-linear problem of Gaussian noise when the expert opinion is uniformly distributed. The generalized Kalman filter is used to estimate the parameters in this problem.
In the second part, we assume that drift and volatility of asset returns are both driven by a Markov chain. We mainly use the change-of-measure technique to estimate various values required by the EM algorithm. In addition,
we focus on different ways to combine the two observations, expert opinions and asset returns. First, we use the linear combination method. At the same time, we discuss how to use a logistic regression model to quantify expert
opinions. Second, we consider that expert opinions follow a mixed Dirichlet distribution. Under this assumption, we use another probability measure to
estimate the unnormalized filters, needed for the EM algorithm.
In the third part, we assume that expert opinions follow a mixed Dirichlet distribution and focus on how we can obtain approximate optimal portfolio
strategies in different observation settings. We claim the approximate strategies from the dynamic programming equations in different settings and analyze the dependence on the discretization step. Finally we compute different
observation settings in a simulation study.

The subject of this thesis is the probabilistic reliability assessment of notched metallic components under periodic constant-amplitude loads with respect to the failure mode of high-cycle fatigue. The latter refers to the crack initiation within the considered component caused by a high number, typically millions, of load cycles characterized by their small magnitude in terms of the material's static strength. In order to estimate the probability of failure due to high-cycle fatigue for a specified component under given loads, a new empirical model based on weakest-link theory is developed which describes a probabilistic and component specific constant-life diagram with respect to the anticipated design life. A conventional, non-probabilistic constant-life diagram reflects a discrete design boundary in terms of mean stress and stress amplitude, typically based on test results with respect to unnotched coupons made from the material of interest. Its application to the design of a notched component is established by identifying the stress conditions at the component's hot spot with those acting in the smooth coupons during the tests, and comparing those hot-spot conditions with the design boundary described in the constant-life diagram. Disregarded influences, such as notch and statistical size effect have to be incorporated by respective correction factors. The proposed probabilistic model on the other hand describes a continuous field of failure probabilities in the design stress plane, taking into account not only the hot-spot stresses, but the entire cyclic stress field acting throughout the component. In this way, the methodology directly accounts for notch and statistical size effects. Responsible for providing this greater scope is the weakest-link concept, which represents a non-local stochastic approach for quantifying the failure probability of loaded solids. The four model parameters can be calibrated with fatigue test data sets containing entirely unrelated test results on arbitrary specimen geometries, obliterating the constraining need for test data following staircase or probit schemes. This work contains the formulation, analysis, validation and application of the proposed model. After its introduction and a comparison with existing methods, it is analyzed in terms of its numerical properties when applied to finite element models, its efficient calibration and the corresponding model uncertainty. The validation is split into two parts. In a first analysis, the model is fitted to test data, containing results on several types of notched specimens, reflecting predominantly elastic material behavior. In a second step, this restriction is lifted and the model is used in order to predict the failure behavior of notched test specimens experiencing notch root plasticity due to high mean stresses. In both validation studies, the derived model predictions are, for the most part, well in line with the experimentally observed failure behavior of the test specimens. Finally, the applicability of the proposed probabilistic methodology in a design context is demonstrated on the example of a gas turbine compressor blade and the corresponding compressor stage.

Synaptic transmission is controlled by re-uptake systems that reduce transmitter concentrations in the synaptic cleft and recycle the transmitter into presynaptic terminals. The re-uptake systems are thought to ensure cytosolic concentrations in the terminals that are sufficient for reloading empty synaptic vesicles (SVs). Genetic deletion of glycine transporter 2 (GlyT2) results in severely disrupted inhibitory neurotransmission and ultimately to death. Here we investigated the role of GlyT2 at inhibitory glycinergic synapses in the mammalian auditory brainstem. These synapses are tuned for resilience, reliability, and precision, even during sustained high-frequency stimulation when endocytosis and refilling of SVs probably contribute substantially to efficient replenishment of the readily releasable pool (RRP). Such robust synapses are formed between MNTB and LSO neurons (medial nucleus of the trapezoid body, lateral superior olive). By means of patch-clamp recordings, we assessed the synaptic performance in controls, in GlyT2 knockout mice (KOs), and upon acute pharmacological GlyT2 blockade. Via computational modeling, we calculated the reoccupation rate of empty release sites and RRP replenishment kinetics during 60-s challenge and 60-s recovery periods. Control MNTB-LSO inputs maintained high fidelity neurotransmission at 50 Hz for 60 s and recovered very efficiently from synaptic depression. During 'marathon-experiments' (30,600 stimuli in 20 min), RRP replenishment accumulated to 1,260-fold. In contrast, KO inputs featured severe impairments. For example, the input number was reduced to ~1 (vs. ~4 in controls), implying massive functional degeneration of the MNTB-LSO microcircuit and a role of GlyT2 during synapse maturation. Surprisingly, neurotransmission did not collapse completely in KOs as inputs still replenished their small RRP 80-fold upon 50 Hz | 60 s challenge. However, they totally failed to do so for extended periods. Upon acute pharmacological GlyT2 inactivation, synaptic performance remained robust, in stark contrast to KOs. RRP replenishment was 865-fold in marathon-experiments, only ~1/3 lower than in controls. Collectively, our empirical and modeling results demonstrate that GlyT2 re-uptake activity is not the dominant factor in the SV recycling pathway that imparts indefatigability to MNTB-LSO synapses. We postulate that additional glycine sources, possibly the antiporter Asc-1, contribute to RRP replenishment at these high-fidelity brainstem synapses.

Laser-induced interstitial thermotherapy (LITT) is a minimally invasive procedure to destroy liver
tumors through thermal ablation. Mathematical models are the basis for computer simulations
of LITT, which support the practitioner in planning and monitoring the therapy.
In this thesis, we propose three potential extensions of an established mathematical model of
LITT, which is based on two nonlinearly coupled partial differential equations (PDEs) modeling
the distribution of the temperature and the laser radiation in the liver.
First, we introduce the Cattaneo–LITT model for delayed heat transfer in this context, prove its
well-posedness and study the effect of an inherent delay parameter numerically.
Second, we model the influence of large blood vessels in the heat-transfer model by means
of a spatially varying blood-perfusion rate. This parameter is unknown at the beginning of
each therapy because it depends on the individual patient and the placement of the LITT
applicator relative to the liver. We propose a PDE-constrained optimal-control problem for the
identification of the blood-perfusion rate, prove the existence of an optimal control and prove
necessary first-order optimality conditions. Furthermore, we introduce a numerical example
based on which we demonstrate the algorithmic solution of this problem.
Third, we propose a reformulation of the well-known PN model hierarchy with Marshak
boundary conditions as a coupled system of second-order PDEs to approximate the radiative-transfer
equation. The new model hierarchy is derived in a general context and is applicable
to a wide range of applications other than LITT. It can be generated in an automated way by
means of algebraic transformations and allows the solution with standard finite-element tools.
We validate our formulation in a general context by means of various numerical experiments.
Finally, we investigate the coupling of this new model hierarchy with the LITT model numerically.