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This dissertation investigates corporate acquisition decisions that represent important corporate development activities for family and non-family firms. The main research objective of this dissertation is to generate insights into the subjective decision-making behavior of corporate decision-makers from family and non-family firms and their weighting of M&A decision-criteria during the early pre-acquisition target screening and selection process. The main methodology chosen for the investigation of M&A decision-making preferences and the weighting of M&A decision criteria is a choice-based conjoint analysis. The overall sample of this dissertation consists of 304 decision-makers from 264 private and public family and non-family firms from mainly Germany and the DACH-region. In the first empirical part of the dissertation, the relative importance of strategic, organizational and financial M&A decision-criteria for corporate acquirers in acquisition target screening is investigated. In addition, the author uses a cluster analysis to explore whether distinct decision-making patterns exist in acquisition target screening. In the second empirical part, the dissertation explores whether there are differences in investment preferences in acquisition target screening between family and non-family firms and within the group of family firms. With regards to the heterogeneity of family firms, the dissertation generated insights into how family-firm specific characteristics like family management, the generational stage of the firm and non-economic goals such as transgenerational control intention influences the weighting of different M&A decision criteria in acquisition target screening. The dissertation contributes to strategic management research, in specific to M&A literature, and to family business research. The results of this dissertation generate insights into the weighting of M&A decision-making criteria and facilitate a better understanding of corporate M&A decisions in family and non-family firms. The findings show that decision-making preferences (hence the weighting of M&A decision criteria) are influenced by characteristics of the individual decision-maker, the firm and the environment in which the firm operates.
The harmonic Faber operator
(2018)
P. K. Suetin points out in the beginning of his monograph "Faber Polynomials and Faber Series" that Faber polynomials play an important role in modern approximation theory of a complex variable as they are used in representing analytic functions in simply connected domains, and many theorems on approximation of analytic functions are proved with their help [50]. In 1903, the Faber polynomials were firstly discovered by G. Faber. It was Faber's aim to find a generalisation of Taylor series of holomorphic functions in the open unit disc D in the following way. As any holomorphic function in D has a Taylor series representation f(z)=\sum_{\nu=0}^{\infty}a_{\nu}z^{\nu} (z\in\D) converging locally uniformly inside D, for a simply connected domain G, Faber wanted to determine a system of polynomials (Q_n) such that each function f being holomorphic in G can be expanded into a series
f=\sum_{\nu=0}^{\infty}b_{\nu}Q_{\nu} converging locally uniformly inside G. Having this goal in mind, Faber considered simply connected domains bounded by an analytic Jordan curve. He constructed a system of polynomials (F_n) with this property. These polynomials F_n were named after him as Faber polynomials. In the preface of [50], a detailed summary of results concerning Faber polynomials and results obtained by the aid of them is given. An important application of Faber polynomials is e.g. the transfer of known assertions concerning polynomial approximation of functions belonging to the disc algebra to results of the approximation of functions being continuous on a compact continuum K which contains at least two points and has a connected complement and being holomorphic in the interior of K. In this field, the Faber operator denoted by T turns out to be a powerful tool (for an introduction, see e.g. D. Gaier's monograph). It
assigns a polynomial of degree at most n given in the monomial basis \sum_{\nu=0}^{n}a_{\nu}z^{\nu} with a polynomial of degree at most n given in the basis of Faber polynomials \sum_{\nu=0}^{n}a_{\nu}F_{\nu}. If the Faber operator is continuous with respect to the uniform norms, it has a unique continuous extension to an operator mapping the disc algebra onto the space of functions being continuous on the whole compact continuum and holomorphic in its interior. For all f being element of the disc algebra and all polynomials P, via the obvious estimate for the uniform norms ||T(f)-T(P)||<= ||T|| ||f-P||, it can be seen that the original task of approximating F=T(f) by polynomials is reduced to the polynomial approximation of the function f. Therefore, the question arises under which conditions the Faber operator is continuous and surjective. A fundamental result in this regard was established by J. M. Anderson and J. Clunie who showed that if the compact continuum is bounded by a rectifiable Jordan curve with bounded boundary rotation and free from cusps, then the Faber operator with respect to the uniform norms is a topological isomorphism. Now, let f be a harmonic function in D. Similar as above, we find that f has a uniquely determined representation f=\sum_{\nu=-\infty}^{\infty}a_{\nu}p_{\nu}
converging locally uniformly inside D where p_{n}(z)=z^{n} for n\in\N_{0} and p_{-n}(z)=\overline{z}^{n} for n\in\N}. One may ask whether there is an analogue for harmonic functions on simply connected domains G. Indeed, for a domain G bounded by an analytic Jordan curve, the conjecture that each function f being harmonic in G has a uniquely determined representation f=\sum_{\nu= \infty}^{\infty}b_{\nu}F_{\nu} where F_{-n}(z)=\overline{F_{n}(z\)} for n\inN, converging locally uniformly inside G, holds true. Let now K be a compact continuum containing at least two points and having a connected complement. A main component of this thesis will be the examination of the harmonic Faber operator mapping a harmonic polynomial given in the basis of the harmonic monomials \sum_{\nu=-n}^{n}a_{\nu}p_{\nu} to a harmonic polynomial given as \sum_{\nu=-n}^{n}a_{\nu}F_{\nu}.
If this operator, which is based on an idea of J. Müller, is continuous with respect to the uniform norms, it has a unique continuous extension to an operator mapping the functions being continuous on \partial\D onto the continuous functions on K being
harmonic in the interior of K. Harmonic Faber polynomials and the harmonic Faber operator will be the objects accompanying us throughout
our whole discussion. After having given an overview about notations and certain tools we will use in our consideration in the first chapter, we begin our studies with an introduction to the Faber operator and the harmonic Faber operator. We start modestly and consider domains bounded by an analytic Jordan curve. In Section 2, as a first result, we will show that, for such a domain G, the harmonic Faber operator has a unique continuous extension to an operator mapping the space of the harmonic functions in D onto the space
of the harmonic functions in G, and moreover, the harmonic Faber
operator is an isomorphism with respect to the topologies of locally
uniform convergence. In the further sections of this chapter, we illumine the behaviour of the (harmonic) Faber operator on certain function spaces. In the third chapter, we leave the situation of compact continua bounded by an analytic Jordan curve. Instead we consider closures of domains bounded by Jordan curves having a Dini continuous curvature. With the aid of the concept of compact operators and the Fredholm alternative, we are able to show that the harmonic Faber operator is a topological isomorphism. Since, in particular, the main result of the third chapter holds true for closures K of domains bounded by analytic Jordan curves, we can make use of it to obtain new results concerning the approximation of functions being continuous on K and harmonic in the interior of K by harmonic polynomials. To do so, we develop techniques applied by L. Frerick and J. Müller in [11] and adjust them to our setting. So, we can transfer results about the classic Faber operator to the harmonic Faber operator. In the last chapter, we will use the theory of harmonic Faber polynomials
to solve certain Dirichlet problems in the complex plane. We pursue
two different approaches: First, with a similar philosophy as in [50],
we develop a procedure to compute the coefficients of a series \sum_{\nu=-\infty}^{\infty}c_{\nu}F_{\nu} converging uniformly to the solution of a given Dirichlet problem. Later, we will point out how semi-infinite programming with harmonic Faber polynomials as ansatz functions can be used to get an approximate solution of a given Dirichlet problem. We cover both approaches first from a theoretical point of view before we have a focus on the numerical implementation of concrete examples. As application of the numerical computations, we considerably obtain visualisations of the concerned Dirichlet problems rounding out our discussion about the harmonic Faber polynomials and the harmonic Faber operator.
The formerly communist countries in Central and Eastern Europe (transitional economies in Europe and the Soviet Union – for example, East Germany, Czech Republic, Hungary, Lithuania, Poland, Russia) and transitional economies in Asia – for example, China, Vietnam had centrally planned economies, which did not allow entrepreneurship activities. Despite the political-socioeconomic transformations in transitional economies around 1989, they still had an institutional heritage that affects individuals’ values and attitudes, which, in turn, influence intentions, behaviors, and actions, including entrepreneurship.
While prior studies on the long-lasting effects of socialist legacy on entrepreneurship have focused on limited geographical regions (e.g., East-West Germany, and East-West Europe), this dissertation focuses on the Vietnamese context, which offers a unique quasi-experimental setting. In 1954, Vietnam was divided into the socialist North and the non-socialist South, and it was then reunified under socialist rule in 1975. Thus, the intensity of differences in socialist treatment in North-South Vietnam (about 21 years) is much shorter than that in East-West Germany (about 40 years) and East-West Europe (about 70 years when considering former Soviet Union countries).
To assess the relationship between socialist history and entrepreneurship in this unique setting, we survey more than 3,000 Vietnamese individuals. This thesis finds that individuals from North Vietnam have lower entrepreneurship intentions, are less likely to enroll in entrepreneurship education programs, and display lower likelihood to take over an existing business, compared to those from the South of Vietnam. The long-lasting effect of formerly socialist institutions on entrepreneurship is apparently deeper than previously discovered in the prominent case of East-West Germany and East-West Europe as well.
In the second empirical investigation, this dissertation focuses on how succession intentions differ from others (e.g., founding, and employee intentions) regarding career choice motivation, and the effect of three main elements of the theory of planned behavior (e.g., entrepreneurial attitude, subjective norms, and perceived behavioral control) in transition economy – Vietnam context. The findings of this thesis suggest that an intentional founder is labeled with innovation, an intentional successor is labeled with roles motivation, and an intentional employee is labeled with social mission. Additionally, this thesis reveals that entrepreneurial attitude and perceived behavioral control are positively associated with the founding intention, whereas there is no difference in this effect between succession and employee intentions.
Many NP-hard optimization problems that originate from classical graph theory, such as the maximum stable set problem and the maximum clique problem, have been extensively studied over the past decades and involve the choice of a subset of edges or vertices. There usually exist combinatorial methods that can be applied to solve them directly in the graph.
The most simple method is to enumerate feasible solutions and select the best. It is not surprising that this method is very slow oftentimes, so the task is to cleverly discard fruitless search space during the search. An alternative method to solve graph problems is to formulate integer linear programs, such that their solution yields an optimal solution to the original optimization problem in the graph. In order to solve integer linear programs, one can start with relaxing the integer constraints and then try to find inequalities for cutting off fractional extreme points. In the best case, it would be possible to describe the convex hull of the feasible region of the integer linear program with a set of inequalities. In general, giving a complete description of this convex hull is out of reach, even if it has a polynomial number of facets. Thus, one tries to strengthen the (weak) relaxation of the integer linear program best possible via strong inequalities that are valid for the convex hull of feasible integer points.
Many classes of valid inequalities are of exponential size. For instance, a graph can have exponentially many odd cycles in general and therefore the number of odd cycle inequalities for the maximum stable set problem is exponential. It is sometimes possible to check in polynomial time if some given point violates any of the exponentially many inequalities. This is indeed the case for the odd cycle inequalities for the maximum stable set problem. If a polynomial time separation algorithm is known, there exists a formulation of polynomial size that contains a given point if and only if it does not violate one of the (potentially exponentially many) inequalities. This thesis can be divided into two parts. The first part is the main part and it contains various new results. We present new extended formulations for several optimization problems, i.e. the maximum stable set problem, the nonconvex quadratic program with box
constraints and the p-median problem. In the second part we modify a very fast algorithm for finding a maximum clique in very large sparse graphs. We suggest and compare three alternative versions of this algorithm to the original version and compare their strengths and weaknesses.
This thesis sheds light on the heterogeneous hedging behavior of airlines. The focus lies on financial hedging, operational hedging and selective hedging. The unbalanced panel data set includes 74 airlines from 39 countries. The period of analysis is 2005 until 2014, resulting in 621 firm years. The random effects probit and fixed effects OLS models provide strong evidence of a convex relation between derivative usage and a firm’s leverage, opposing the existing financial distress theory. Airlines with lower leverage had higher hedge ratios. In addition, the results show that airlines with interest rate and currency derivatives were more likely to engage in fuel price hedging. Moreover, the study results support the argument that operational hedging is a complement to financial hedging. Airlines with more heterogeneous fleet structures exhibited higher hedge ratios.
Also, airlines which were members of a strategic alliance were more likely to be hedging airlines. As alliance airlines are rather financially sound airlines, the positive relation between alliance membership and hedging reflects the negative results on the leverage
ratio. Lastly, the study presents determinants of an airlines’ selective hedging behavior. Airlines with prior-period derivative losses, recognized in income, changed their hedge portfolios more frequently. Moreover, the sample airlines acted in accordance with herd behavior theory. Changes in the regional hedge portfolios influenced the hedge portfolio of the individual airline in the same direction.
Entrepreneurship has become an essential phenomenon all over the world because it is a major driving force behind the economic growth and development of a country. It is widely accepted that entrepreneurship development in a country creates new jobs, pro-motes healthy competition through innovation, and benefits the social well being of individuals and societies. The policymakers in both developed and developing countries focus on entrepreneurship because it helps to alleviate impediments to economic development and social welfare. Therefore, policymakers and academic researchers consider the promotion of entrepreneurship as essential for the economy and research-based support is needed for further development of entrepreneurship activities.
The impact of entrepreneurial activities on economic and social development also varies from country to country. The effect of entrepreneurial activities on economic and social development also varies from country to country because the level of entrepreneur-ship activities also varies from one region to another or one country to another. To under-stand these variations, policymakers have investigated the determinants of entrepreneur-ship at different levels, such as the individual, industry, and country levels. Moreover, entrepreneurship behavior is influenced by various personal and environmental level factors. However, these personal-level factors cannot be separated from the surrounding environment.
The link between religion and entrepreneurship is well established and can be traced back to Weber (1930). Researchers have analyzed the relationship between religion and entrepreneurship from various perspectives, and the research related to religion and entrepreneurship is diversified and scattered across disciplines. This dissertation tries to explain the link between religion and entrepreneurship, specifically Islamic religion and entrepreneurship. Technically this dissertation comprises three parts. The first part of this dissertation consists of two chapters that discuss the definition and theories of entrepreneurship (Chapter 2) and the theoretical relationship between religion and entrepreneur-ship (Chapter 3).
The second part of this dissertation (Chapter 4) provides an overview of the field with a purpose to gain a better understanding of the field’s current state of knowledge to bridge the different views and perspectives. In order to provide an overview of the field, a systematic literature search leading to a descriptive overview of the field based on 270 articles published in 163 journals Subsequently, bibliometric methods are used to identify thematic clusters, the most influential authors and articles, and how they are connected.
The third part of this dissertation (Chapter 5) empirically evaluates the influence of Islamic values and Islamic religious practices on entrepreneurship intentions within the Islamic community. Using the theory of planned behavior as a theoretical lens, we also take into account that the relationship between religion and entrepreneurial intentions can be mediated by individual’s attitude towards entrepreneurship. A self-administrative questionnaire was used to collect the responses from a sample of 1895 Pakistani university students. A structured equation modeling was adopted to perform a nuanced assessment of the relationship between Islamic values and practices and entrepreneurship intentions and to account for mediating effect of attitude towards entrepreneurship.
The research on religion and entrepreneurship has increased sharply during the last years and is scattered across various academic disciplines and fields. The analysis identifies and characterize the most important publications, journals, and authors in the area and map the analyzed religions and regions. The comprehensive overview of previous studies allows us to identify research gaps and derive avenues for future research in a substantiated way. Moreover, this dissertation helps the research scholars to understand the field in its entirety, identify relevant articles, and to uncover parallels and differences across religions and regions. Besides, the study reveals a lack of empirical research related to specific religions and specific regions. Therefore, scholars can take these regions and religions into consideration when conducting empirical research.
Furthermore, the empirical analysis about the influence of Islamic religious values and Islamic religious practices show that Islamic values served as a guiding principle in shaping people’s attitudes towards entrepreneurship in an Islamic community; they had an indirect influence on entrepreneurship intention through attitude. Similarly, the relationship between Islamic religious practices and the entrepreneurship intentions of students was fully mediated by the attitude towards entrepreneurship. Furthermore, this dissertation contributes to prior research on entrepreneurship in Islamic communities by applying a more fine-grained approach to capture the link between religion and entrepreneurship. Moreover, it contributes to the literature on entrepreneurship intentions by showing that the influence of religion on entrepreneurship intentions is mainly due to religious values and practices, which shape the attitude towards entrepreneurship and thereby influence entrepreneurship intentions in religious communities. The entrepreneur-ship research has put a higher emphasis on assessing the influence of a diverse set of con-textual factors. This dissertation introduces Islamic values and Islamic religious practices as critical contextual factors that shape entrepreneurship in countries that are characterized by the Islamic religion.
In vielen Branchen und vor allem in großen Unternehmen gehört eine Unterstützung von Geschäftsprozessen durch Workflow-Management-Systeme zum gelebten Alltag. Im Zentrum steht dabei die Steuerung kontrollflussorientierter Abläufe, während Prozesse mit einem Schwerpunkt auf Daten, Informationen und Wissen meist außen vor bleiben. Solche wissensintensive Prozesse (engl.: knowledge intensive processes) (KiPs) sind Untersuchungsgegenstand in vielen aktuellen Studien, welche ein derzeit aktives Forschungsgebiet formen.
Im Vordergrund solcher KiPs steht dabei das durch die mitwirkenden Personen eingebrachte Wissen, welches in einem wesentlichen Maß die Prozessausführung beeinflusst, hierdurch jedoch die Bearbeitung komplexer und meist hoch volatiler Prozesse ermöglicht. Hierbei handelt es sich zumeist um entscheidungsintensive Prozesse, Prozesse zur Wissensakquisition oder Prozesse, die zu einer Vielzahl unterschiedlicher Prozessabläufe führen können.
Im Rahmen dieser Arbeit wird ein Ansatz entwickelt und vorgestellt, der sich der Modellierung, Visualisierung und Ausführung wissensintensiver Prozesse unter Verwendung Semantischer Technologien widmet. Hierzu werden als die zentralen Anforderungen zur Ausführung von KiPs Flexibilität, Adaptivität und Zielorientierung definiert. Daran anknüpfend werden drei zentrale Grundprinzipien der Prozessmodellierung identifiziert, welche in der ersten Forschungsfrage aufgegriffen werden: „Können die drei Grundprinzipien in einem einheitlichen datenzentrierten, deklarativen, semantischen Ansatz (welcher mit ODD-BP bezeichnet wird) kombiniert werden und können damit die zentralen Anforderungen von KiPs erfüllt werden?”
Die Grundlage für ODD-BP bildet ein Metamodell, welches als Sprachkonstrukt fungiert und die Definition der angestrebten Prozessmodelle erlaubt. Darauf aufbauend wird mit Hilfe von Inferenzierungsregeln ein Verfahren entwickelt, welches das Schlussfolgern von Prozesszuständen ermöglicht und somit eine klassische Workflow-Engine überflüssig macht. Zudem wird eine Methodik eingeführt, die für jede in einem Prozess mitwirkende Person eine maßgeschneiderte, adaptive Prozessvisualisierung ermöglicht, um neben dem Freiheitsgrad der Flexibilität auch eine fundierte Prozessunterstützung bei der Ausführung von KiPs leisten zu können. All dies erfolgt innerhalb einer einheitlichen Wissensbasis, die zum einen die Grundlage für eine vollständige semantische Prozessmodellierung bildet und zum anderen die Möglichkeit zur Integration von Expertenwissen eröffnet. Dieses Expertenwissen kann einen expliziten Beitrag bei der Ausführung wissensintensiver Prozesse leisten und somit die Kollaboration von Mensch und Maschine durch Technologien der symbolischen KI ermöglichen. Die zweite Forschungsfrage greift diesen Aspekt auf: „Kann in dem ODD-BP Ansatz ontologisches Wissen so integriert werden, dass dieses in einer Prozessausführung einen Beitrag leistet?”
Das Metamodell sowie die entwickelten Methoden und Verfahren werden in einem prototypischen, generischen System realisiert, welches grundsätzlich für alle Anwendungsgebiete mit KiPs geeignet ist. Zur Validierung des ODD-BP Ansatzes erfolgt eine Ausrichtung auf den Anwendungsfall einer Notrufabfrage aus dem Leitstellenumfeld. Im Zuge der Evaluation wird gezeigt, wie dieser wissensintensive Ablauf von einer flexiblen, adaptiven und zielorientierten Prozessausführung profitiert. Darüber hinaus wird medizinisches Expertenwissen in den Prozessablauf integriert und es wird nachgewiesen, wie dieses zu verbesserten Prozessergebnissen beiträgt.
Wissensintensive Prozesse stellen Unternehmen und Organisationen in allen Branchen und Anwendungsfällen derzeit vor große Herausforderungen und die Wissenschaft und Forschung widmet sich der Suche nach praxistauglichen Lösungen. Diese Arbeit präsentiert mit ODD-BP einen vielversprechenden Ansatz, indem die Möglichkeiten Semantischer Technologien dazu genutzt werden, eine eng verzahnte Zusammenarbeit zwischen Mensch und Maschine bei der Ausführung von KiPs zu ermöglichen. Die zur Evaluation fokussierte Notrufabfrage innerhalb von Leitstellen stellt zudem einen höchst relevanten Anwendungsfall dar, da in einem akuten Notfall in kürzester Zeit Entscheidungen getroffen werden müssen, um weitreichenden Schaden abwenden und Leben retten zu können. Durch die Berücksichtigung umfassender Datenmengen und das Ausnutzen verfügbaren Expertenwissens kann so eine schnelle Lagebewertung mit Hilfe der maschinellen Unterstützung erreicht und der Mensch beim Treffen von richtigen Entscheidungen unterstützt werden.
The dissertation deals with methods to improve design-based and model-assisted estimation techniques for surveys in a finite population framework. The focus is on the development of the statistical methodology as well as their implementation by means of tailor-made numerical optimization strategies. In that regard, the developed methods aim at computing statistics for several potentially conflicting variables of interest at aggregated and disaggregated levels of the population on the basis of one single survey. The work can be divided into two main research questions, which are briefly explained in the following sections.
First, an optimal multivariate allocation method is developed taking into account several stratification levels. This approach results in a multi-objective optimization problem due to the simultaneous consideration of several variables of interest. In preparation for the numerical solution, several scalarization and standardization techniques are presented, which represent the different preferences of potential users. In addition, it is shown that by solving the problem scalarized with a weighted sum for all combinations of weights, the entire Pareto frontier of the original problem can be generated. By exploiting the special structure of the problem, the scalarized problems can be efficiently solved by a semismooth Newton method. In order to apply this numerical method to other scalarization techniques as well, an alternative approach is suggested, which traces the problem back to the weighted sum case. To address regional estimation quality requirements at multiple stratification levels, the potential use of upper bounds for regional variances is integrated into the method. In addition to restrictions on regional estimates, the method enables the consideration of box-constraints for the stratum-specific sample sizes, allowing minimum and maximum stratum-specific sampling fractions to be defined.
In addition to the allocation method, a generalized calibration method is developed, which is supposed to achieve coherent and efficient estimates at different stratification levels. The developed calibration method takes into account a very large number of benchmarks at different stratification levels, which may be obtained from different sources such as registers, paradata or other surveys using different estimation techniques. In order to incorporate the heterogeneous quality and the multitude of benchmarks, a relaxation of selected benchmarks is proposed. In that regard, predefined tolerances are assigned to problematic benchmarks at low aggregation levels in order to avoid an exact fulfillment. In addition, the generalized calibration method allows the use of box-constraints for the correction weights in order to avoid an extremely high variation of the weights. Furthermore, a variance estimation by means of a rescaling bootstrap is presented.
Both developed methods are analyzed and compared with existing methods in extensive simulation studies on the basis of a realistic synthetic data set of all households in Germany. Due to the similar requirements and objectives, both methods can be successively applied to a single survey in order to combine their efficiency advantages. In addition, both methods can be solved in a time-efficient manner using very comparable optimization approaches. These are based on transformations of the optimality conditions. The dimension of the resulting system of equations is ultimately independent of the dimension of the original problem, which enables the application even for very large problem instances.
Coastal erosion describes the displacement of land caused by destructive sea waves,
currents or tides. Due to the global climate change and associated phenomena such as
melting polar ice caps and changing current patterns of the oceans, which result in rising
sea levels or increased current velocities, the need for countermeasures is continuously
increasing. Today, major efforts have been made to mitigate these effects using groins,
breakwaters and various other structures.
This thesis will find a novel approach to address this problem by applying shape optimization
on the obstacles. Due to this reason, results of this thesis always contain the
following three distinct aspects:
The selected wave propagation model, i.e. the modeling of wave propagation towards
the coastline, using various wave formulations, ranging from steady to unsteady descriptions,
described from the Lagrangian or Eulerian viewpoint with all its specialties. More
precisely, in the Eulerian setting is first a steady Helmholtz equation in the form of a
scattering problem investigated and followed subsequently by shallow water equations,
in classical form, equipped with porosity, sediment portability and further subtleties.
Secondly, in a Lagrangian framework the Lagrangian shallow water equations form the
center of interest.
The chosen discretization, i.e. dependent on the nature and peculiarity of the constraining
partial differential equation, we choose between finite elements in conjunction
with a continuous Galerkin and discontinuous Galerkin method for investigations in the
Eulerian description. In addition, the Lagrangian viewpoint offers itself for mesh-free,
particle-based discretizations, where smoothed particle hydrodynamics are used.
The method for shape optimization w.r.t. the obstacle’s shape over an appropriate
cost function, constrained by the solution of the selected wave-propagation model. In
this sense, we rely on a differentiate-then-discretize approach for free-form shape optimization
in the Eulerian set-up, and reverse the order in Lagrangian computations.
In order to classify smooth foliated manifolds, which are smooth maifolds equipped with a smooth foliation, we introduce the de Rham cohomologies of smooth foliated manifolds. These cohomologies are build in a similar way as the de Rham cohomologies of smooth manifolds. We develop some tools to compute these cohomologies. For example we proof a Mayer Vietoris theorem for foliated de Rham cohomology and show that these cohomologys are invariant under integrable homotopy. A generalization of a known Künneth formula, which relates the cohomologies of a product foliation with its factors, is discussed. In particular, this envolves a splitting theory of sequences between Frechet spaces and a theory of projective spectrums. We also prove, that the foliated de Rham cohomology is isomorphic to the Cech-de Rham cohomology and the Cech cohomology of leafwise constant functions of an underlying so called good cover.