@phdthesis{Moeller2009,
  author    = {M{\"o}ller, Florian},
  title     = {Exceptional polynomials and monodromy groups in positive characteristic},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-34871},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {We discuss exceptional polynomials, i.e. polynomials over a finite field \$k\$ that induce bijections over infinitely many finite extensions of \$k\$. In the first chapters we give the theoretical background to characterize this class of polynomials with Galois theoretic means. This leads to the notion of arithmetic resp. geometric monodromy groups. In the remaining chapters we restrict our attention to polynomials with primitive affine arithmetic monodromy group. We first classify all exceptional polynomials with the fixed field of the affine kernel of the arithmetic monodromy group being of genus less or equal to 2. Next we show that every full affine group can be realized as the monodromy group of a polynomial. In the remaining chapters we classify affine polynomials of a given degree.},
  subject      = {Algebraischer Funktionenk{\"o}rper},
  language  = {en}
}
@phdthesis{Winkler2008,
  author    = {Winkler, Ralf},
  title     = {Schwache Randwertprobleme von Systemen elliptischen Charakters auf konischen Gebieten},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-34544},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {In der vorliegenden Arbeit werden lineare Systeme elliptischer partieller Differentialgleichungen in schwacher Formulierung auf konischen Gebieten untersucht. Auf einem zun{\"a}chst unbeschr{\"a}nkten Kegelgebiet betrachten wir den Fall beschr{\"a}nkter und nur von den Winkelvariablen abh{\"a}ngiger Koeffizientenfunktionen. Die durch selbige definierte Bilinearform gen{\"u}ge einer G{\aa}rdingschen Ungleichung. In gewichteten Sobolevr{\"a}umen werden Existenz- und Eindeutigkeitsfragen gekl{\"a}rt, wobei das Problem mittels Fouriertransformation auf eine von einem komplexen Parameter abh{\"a}ngige Familie T(·) von Fredholmoperatoren zur{\"u}ckgef{\"u}hrt wird. Unter Anwendung des Residuenkalk{\"u}ls gewinnen wir eine Darstellung der L{\"o}sung in Form einer Zerlegung in einen glatten Anteil einerseits sowie eine endliche Summe von Singul{\"a}rfunktionen andererseits. Durch Abschneidetechniken werden die gewonnenen Erkenntnisse auf den Fall schwach formulierter elliptischer Systeme auf beschr{\"a}nkten Kegelgebieten unter Formulierung in gew{\"o}hnlichen, nicht-gewichteten Sobolevr{\"a}umen angewendet. Die f{\"u}r Regularit{\"a}tsfragen maßgeblichen Eigenwerte der Operatorfunktion T mit minimalem positiven Imagin{\"a}rteil werden im letzten Kapitel der Arbeit am Beispiel der ebenen elastischen Gleichungen numerisch bestimmt.},
  subject      = {Elliptische Differentialgleichung},
  language  = {de}
}
@phdthesis{Baumann2008,
  author    = {Baumann, Markus},
  title     = {Newton's Method for Path-Following Problems on Manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28099},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {Many optimization problems for a smooth cost function f on a manifold M can be solved by determining the zeros of a vector field F; such as e.g. the gradient F of the cost function f. If F does not depend on additional parameters, numerous zero-finding techniques are available for this purpose. It is a natural generalization however, to consider time-dependent optimization problems that require the computation of time-varying zeros of time-dependent vector fields F(x,t). Such parametric optimization problems arise in many fields of applied mathematics, in particular path-following problems in robotics, recursive eigenvalue and singular value estimation in signal processing, as well as numerical linear algebra and inverse eigenvalue problems in control theory. In the literature, there are already some tracking algorithms for these tasks, but these do not always adequately respect the manifold structure. Hence, available tracking results can often be improved by implementing methods working directly on the manifold. Thus, intrinsic methods are of interests that evolve during the entire computation on the manifold. It is the task of this thesis, to develop such intrinsic zero finding methods. The main results of this thesis are as follows: - A new class of continuous and discrete tracking algorithms is proposed for computing zeros of time-varying vector fields on Riemannian manifolds. This was achieved by studying the newly introduced time-varying Newton Flow and the time-varying Newton Algorithm on Riemannian manifolds. - Convergence analysis is performed on arbitrary Riemannian manifolds. - Concretization of these results on submanifolds, including for a new class of algorithms via local parameterizations. - More specific results in Euclidean space are obtained by considering inexact and underdetermined time-varying Newton Flows. - Illustration of these newly introduced algorithms by examining time-varying tracking tasks in three application areas: Subspace analysis, matrix decompositions (in particular EVD and SVD) and computer vision.},
  subject      = {Dynamische Optimierung},
  language  = {en}
}
@phdthesis{Pechmann2008,
  author    = {Pechmann, Patrick R.},
  title     = {Penalized Least Squares Methoden mit st{\"u}ckweise polynomialen Funktionen zur L{\"o}sung von partiellen Differentialgleichungen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28136},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {Das Hauptgebiet der Arbeit stellt die Approximation der L{\"o}sungen partieller Differentialgleichungen mit Dirichlet-Randbedingungen durch Splinefunktionen dar. Partielle Differentialgleichungen finden ihre Anwendung beispielsweise in Bereichen der Elektrostatik, der Elastizit{\"a}tstheorie, der Str{\"o}mungslehre sowie bei der Untersuchung der Ausbreitung von W{\"a}rme und Schall. Manche Approximationsaufgaben besitzen keine eindeutige L{\"o}sung. Durch Anwendung der Penalized Least Squares Methode wurde gezeigt, dass die Eindeutigkeit der gesuchten L{\"o}sung von gewissen Minimierungsaufgaben sichergestellt werden kann. Unter Umst{\"a}nden l{\"a}sst sich sogar eine h{\"o}here Stabilit{\"a}t des numerischen Verfahrens gewinnen. F{\"u}r die numerischen Betrachtungen wurde ein umfangreiches, effizientes C-Programm erstellt, welches die Grundlage zur Best{\"a}tigung der theoretischen Voraussagen mit den praktischen Anwendungen bildete.},
  subject      = {Approximationstheorie},
  language  = {de}
}
@phdthesis{Gregor2008,
  author    = {Gregor, Thomas},
  title     = {{0,1}-Matrices with Rectangular Rule},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28389},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {The incidence matrices of many combinatorial structures satisfy the so called rectangular rule, i.e., the scalar product of any two lines of the matrix is at most 1. We study a class of matrices with rectangular rule, the regular block matrices. Some regular block matrices are submatrices of incidence matrices of finite projective planes. Necessary and sufficient conditions are given for regular block matrices, to be submatrices of projective planes. Moreover, regular block matrices are related to another combinatorial structure, the symmetric configurations. In particular, it turns out, that we may conclude the existence of several symmetric configurations from the existence of a projective plane, using this relationship.},
  subject      = {Projektive Ebene},
  language  = {en}
}
@phdthesis{Jordan2008,
  author    = {Jordan, Jens},
  title     = {Reachable sets of numerical iteration schemes : a system semigroup approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-28416},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {We investigate iterative numerical algorithms with shifts as nonlinear discrete-time control systems. Our approach is based on the interpretation of reachable sets as orbits of the system semigroup. In the first part we develop tools for the systematic analysis of the structure of reachable sets of general invertible discrete-time control systems. Therefore we merge classical concepts, such as geometric control theory, semigroup actions and semialgebraic geometry. Moreover, we introduce new concepts such as right divisible systems and the repelling phenomenon. In the second part we apply the semigroup approach to the investigation of concrete numerical iteration schemes. We extend the known results about the reachable sets of classical inverse iteration. Moreover, we investigate the structure of reachable sets and systemgroup orbits of inverse iteration on flag manifolds and Hessenberg varieties, rational iteration schemes, Richardson's method and linear control schemes. In particular we obtain necessary and sufficient conditions for controllability and the appearance of repelling phenomena. Furthermore, a new algorithm for solving linear equations (LQRES) is derived.},
  subject      = {Nichtlineare Kontrolltheorie},
  language  = {en}
}
@misc{Proell2013,
  type      = {Master Thesis},
  author    = {Pr{\"o}ll, Sebastian},
  title     = {Stability of Switched Epidemiological Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-108573},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {In this thesis it is shown how the spread of infectious diseases can be described via mathematical models that show the dynamic behavior of epidemics. Ordinary differential equations are used for the modeling process. SIR and SIRS models are distinguished, depending on whether a disease confers immunity to individuals after recovery or not. There are characteristic parameters for each disease like the infection rate or the recovery rate. These parameters indicate how aggressive a disease acts and how long it takes for an individual to recover, respectively. In general the parameters are time-varying and depend on population groups. For this reason, models with multiple subgroups are introduced, and switched systems are used to carry out time-variant parameters. When investigating such models, the so called disease-free equilibrium is of interest, where no infectives appear within the population. The question is whether there are conditions, under which this equilibrium is stable. Necessary mathematical tools for the stability analysis are presented. The theory of ordinary differential equations, including Lyapunov stability theory, is fundamental. Moreover, convex and nonsmooth analysis, positive systems and differential inclusions are introduced. With these tools, sufficient conditions are given for the disease-free equilibrium of SIS, SIR and SIRS systems to be asymptotically stable.},
  subject      = {Gew{\"o}hnliche Differentialgleichung},
  language  = {en}
}
@phdthesis{Harms2014,
  author    = {Harms, Nadja},
  title     = {Primal and Dual Gap Functions for Generalized Nash Equilibrium Problems and Quasi-Variational Inequalities},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-106027},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {In this thesis we study smoothness properties of primal and dual gap functions for generalized Nash equilibrium problems (GNEPs) and finite-dimensional quasi-variational inequalities (QVIs). These gap functions are optimal value functions of primal and dual reformulations of a corresponding GNEP or QVI as a constrained or unconstrained optimization problem. Depending on the problem type, the primal reformulation uses regularized Nikaido-Isoda or regularized gap function approaches. For player convex GNEPs and QVIs of the so-called generalized `moving set' type the respective primal gap functions are continuously differentiable. In general, however, these primal gap functions are nonsmooth for both problems. Hence, we investigate their continuity and differentiability properties under suitable assumptions. Here, our main result states that, apart from special cases, all locally minimal points of the primal reformulations are points of differentiability of the corresponding primal gap function. Furthermore, we develop dual gap functions for a class of GNEPs and QVIs and ensuing unconstrained optimization reformulations of these problems based on an idea by Dietrich (``A smooth dual gap function solution to a class of quasivariational inequalities'', Journal of Mathematical Analysis and Applications 235, 1999, pp. 380--393). For this purpose we rewrite the primal gap functions as a difference of two strongly convex functions and employ the Toland-Singer duality theory. The resulting dual gap functions are continuously differentiable and, under suitable assumptions, have piecewise smooth gradients. Our theoretical analysis is complemented by numerical experiments. The solution methods employed make use of the first-order information established by the aforementioned theoretical investigations.},
  subject      = {Nash-Gleichgewicht},
  language  = {en}
}
@phdthesis{Oswald2014,
  author    = {Oswald, Nicola},
  title     = {Hurwitz's Complex Continued Fractions - A Historical Approach and Modern Perspectives},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-106040},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {The thesis 'Hurwitz's Complex Continued Fractions - A Historical Approach and Modern Perspectives.' deals with two branches of mathematics: Number Theory and History of Mathematics. On the first glimpse this might be unexpected, however, on the second view this is a very fruitful combination. Doing research in mathematics, it turns out to be very helpful to be aware of the beginnings and development of the corresponding subject. In the case of Complex Continued Fractions the origins can easily be traced back to the end of the 19th century (see [Perron, 1954, vl. 1, Ch. 46]). One of their godfathers had been the famous mathematician Adolf Hurwitz. During the study of his transformation from real to complex continued fraction theory [Hurwitz, 1888], our attention was arrested by the article 'Ueber eine besondere Art der Kettenbruch-Entwicklung complexer Gr{\"o}ssen' [Hurwitz, 1895] from 1895 of an author called J. Hurwitz. We were not only surprised when we found out that he was the elder unknown brother Julius, furthermore, Julius Hurwitz introduced a complex continued fraction that also appeared (unmentioned) in an ergodic theoretical work from 1985 [Tanaka, 1985]. Those observations formed the Basis of our main research questions: What is the historical background of Adolf and Julius Hurwitz and their mathematical studies? and What modern perspectives are provided by their complex continued fraction expansions? In this work we examine complex continued fractions from various viewpoints. After a brief introduction on real continued fractions, we firstly devote ourselves to the lives of the brothers Adolf and Julius Hurwitz. Two excursions on selected historical aspects in respect to their work complete this historical chapter. In the sequel we shed light on Hurwitz's, Adolf's as well as Julius', approaches to complex continued fraction expansions. Correspondingly, in the following chapter we take a more modern perspective. Highlights are an ergodic theoretical result, namely a variation on the D{\"o}blin-Lenstra Conjecture [Bosma et al., 1983], as well as a result on transcendental numbers in tradition of Roth's theorem [Roth, 1955]. In two subsequent chapters we are concernced with arithmetical properties of complex continued fractions. Firstly, an analogue to Marshall Hall's Theorem from 1947 [Hall, 1947] on sums of continued fractions is derived. Secondly, a general approach on new types of continued fractions is presented building on the structural properties of lattices. Finally, in the last chapter we take up this approach and obtain an upper bound for the approximation quality of diophantine approximations by quotients of lattice points in the complex plane generalizing a method of Hermann Minkowski, improved by Hilde Gintner [Gintner, 1936], based on ideas from geometry of numbers.},
  subject      = {Kettenbruch},
  language  = {en}
}
@phdthesis{Staab2002,
  author    = {Staab, Patricia},
  title     = {Geometrische Eigenschaften von Spiraltypfl{\"a}chen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-3727},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {Spiraltypfl{\"a}chen sind Minimalfl{\"a}chen des dreidimensionalen euklidischen Raums, die sich durch hohe Symmetrie gegen{\"u}ber komplexen {\"A}hnlichkeitsabbildungen der Minimalkurve auszeichnen. Ihren Namen verdanken Sie folgender Eigenschaft: Sie und ihre komplex Homothetischen sind die einzigen auf Spiralfl{\"a}chen abwickelbaren Minimalfl{\"a}chen. Bekannte Spiraltypfl{\"a}chen sind die Spiralminimalfl{\"a}chen (zugleich Minimal- und Spiralfl{\"a}chen) und die Bourfl{\"a}chen (auf Rotationsfl{\"a}chen abwickelbare Minimalfl{\"a}chen). Das Katenoid und die Enneperfl{\"a}che sind spezielle Bourfl{\"a}chen. In dieser Arbeit werden die Spiraltypfl{\"a}chen auf ihre geometrischen Eigenschaften untersucht. Wir stellen ihre Periodizit{\"a}ten und Symmetrien fest und versuchen, ausgezeichnete Fl{\"a}chenkurven auf ihnen zu finden. Wir verwenden eine globale Weierstraß-Darstellung der Spiraltypfl{\"a}chen. In dieser Darstellung ergeben die Fl{\"a}chen eine Schar mit einem komplexen Scharparameter. Anhand dieser Darstellung leiten wir s{\"a}mtliche Symmetrien der Spiraltypfl{\"a}chen zu linearen {\"A}hnlichkeitsabbildungen der Minimalkurve her. Als Spezialf{\"a}lle erhalten wir die Symmetrien unter Assoziationen und Derivationen (Drehung der Minimalkurve um einen imagin{\"a}ren Drehwinkel), sowie die reellen Symmetrien (Dreh-, Spiegel- und Strecksymmetrien). Unter den Spiraltypfl{\"a}chen gibt es nur zwei translationssymmetrische Fl{\"a}chen. Die Umorientierung einer Spiraltypfl{\"a}che entspricht (bis auf komplexe Homothetie) dem Vorzeichenwechsel des Fl{\"a}chenparameters. Im {\"U}brigen kann durch einfache Spiegelungen an den Koordinatenebenen beziehungsweise Drehungen um die Koordinatenachsen das Vorzeichen von Real- beziehungsweise Imagin{\"a}rteil des Fl{\"a}chenparameters umgekehrt werden. Schließlich stellen wir noch ausgezeichnete Fl{\"a}chenkurven auf den Spiraltypfl{\"a}chen vor: Kr{\"u}mmungslinien, Asymptotenlinien und Geod{\"a}tische, sowie als deren Verallgemeinerungen die Pseudokr{\"u}mmungslinien und Pseudogeod{\"a}tischen.},
  subject      = {Spiraltypfl{\"a}che},
  language  = {de}
}