@techreport{NedrencoBeck2016,
  author    = {Nedrenco, Dmitri and Beck, Johannes},
  title     = {Flachfaltbarkeit: Mathematik mit eigenen H{\"a}nden schaffen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-133647},
  pages     = {11},
  year      = {2016},
  abstract  = {Die Arbeit besch{\"a}ftigt sich mit dem Einsatz von Origami im Schulunterricht. Genauer beschreibt sie eine Unterrichtssequenz zur Flachfaltbarkeit, einem Teilgebiet des mathematischen Papierfaltens, f{\"u}r den Mathematikunterricht in der Oberstufe an Gymnasien und h{\"o}heren Schulen. Es werden konkrete Handlungsanweisungen sowie Alternativen ausgef{\"u}hrt und begr{\"u}ndet und mit vielen Grafiken erl{\"a}utert. Ferner werden Ziele dieser Unterrichtssequenz gem{\"a}ß KMK-Bildungsstandards dargelegt. Anschließend wird ein mathematischer Blick auf die Besch{\"a}ftigung mit der Flachfaltbarkeit sowie eine Einordnung in die aktuelle Forschungslage gegeben.},
  subject      = {Origami},
  language  = {de}
}
@phdthesis{Boehm2015,
  author    = {B{\"o}hm, Christoph},
  title     = {Loewner equations in multiply connected domains},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-129903},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {The first goal of this thesis is to generalize Loewner's famous differential equation to multiply connected domains. The resulting differential equations are known as Komatu--Loewner differential equations. We discuss Komatu--Loewner equations for canonical domains (circular slit disks, circular slit annuli and parallel slit half-planes). Additionally, we give a generalisation to several slits and discuss parametrisations that lead to constant coefficients. Moreover, we compare Komatu--Loewner equations with several slits to single slit Loewner equations. Finally we generalise Komatu--Loewner equations to hulls satisfying a local growth property.},
  subject      = {Biholomorphe Abbildung},
  language  = {en}
}
@phdthesis{Solak2007,
  author    = {Solak, Ebru},
  title     = {Almost Completely Decomposable Groups of Type (1,2)},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-24794},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {A torsion free abelian group of finite rank is called almost completely decomposable if it has a completely decomposable subgroup of finite index. A p-local, p-reduced almost completely decomposable group of type (1,2) is briefly called a (1,2)-group. Almost completely decomposable groups can be represented by matrices over the ring Z/hZ, where h is the exponent of the regulator quotient. This particular choice of representation allows for a better investigation of the decomposability of the group. Arnold and Dugas showed in several of their works that (1,2)-groups with regulator quotient of exponent at least p^7 allow infinitely many isomorphism types of indecomposable groups. It is not known if the exponent 7 is minimal. In this dissertation, this problem is addressed.},
  language  = {en}
}
@phdthesis{Teichert2009,
  author    = {Teichert, Christian},
  title     = {Globale Minimierung von Linearen Programmen mit Gleichgewichtsrestriktionen und globale Konvergenz eines Filter-SQPEC-Verfahrens f{\"u}r Mathematische Programme mit Gleichgewichtsrestriktionen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-38700},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Mathematische Programme mit Gleichgewichtsrestriktionen (oder Komplementarit{\"a}tsbedingungen), kurz MPECs, sind als {\"a}ußerst schwere Optimierungsprobleme bekannt. Lokale Minima oder geeignete station{\"a}re Punkte zu finden, ist ein nichttriviales Problem. Diese Arbeit beschreibt, wie man dennoch die spezielle Struktur von MPECs ausnutzen kann und mittels eines Branch-and-Bound-Verfahrens ein globales Minimum von Linearen Programmen mit Gleichgewichtsrestriktionen, kurz LPECs, bekommt. Des Weiteren wird dieser Branch-and-Bound-Algorithmus innerhalb eines Filter-SQPEC-Verfahrens genutzt, um allgemeine MPECs zu l{\"o}sen. F{\"u}r das Filter-SQPEC Verfahren wird ein globaler Konvergenzsatz bewiesen. Außerdem werden f{\"u}r beide Verfahren numerische Resultate angegeben.},
  subject      = {Nichtlineare Optimierung},
  language  = {de}
}
@article{Zillober1993,
  author    = {Zillober, Christian},
  title     = {A globally convergent version of the method of moving asymptotes},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-31984},
  year      = {1993},
  abstract  = {No abstract available},
  language  = {en}
}
@article{KredlerZilloberJohannesetal.1993,
  author    = {Kredler, Christian and Zillober, Christian and Johannes, Frank and Sigl, Georg},
  title     = {An application of preconditioned conjugate gradients to relative placement in chip design},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-31996},
  year      = {1993},
  abstract  = {In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.},
  language  = {en}
}
@inproceedings{Zillober1993,
  author    = {Zillober, Christian},
  title     = {Sequential convex programming in theory and praxis},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-35513},
  year      = {1993},
  abstract  = {In this paper, convex approximation methods, suclt as CONLIN, the method of moving asymptotes (MMA) and a stabilized version of MMA (Sequential Convex Programming), are discussed with respect to their convergence behaviour. In an extensive numerical study they are :finally compared with other well-known optimization methods at 72 examples of sizing problems.},
  language  = {en}
}
@phdthesis{Even2009,
  author    = {Even, Nadine},
  title     = {On Hydrodynamic Limits and Conservation Laws},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-38374},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {No abstract available},
  language  = {en}
}
@phdthesis{Wissel2009,
  author    = {Wissel, Julia},
  title     = {A new biased estimator for multivariate regression models with highly collinear variables},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-36383},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Es ist wohlbekannt, dass der Kleinste-Quadrate-Sch{\"a}tzer im Falle vorhandener Multikollinearit{\"a}t eine große Varianz besitzt. Eine M{\"o}glichkeit dieses Problem zu umgehen, besteht in der Verwendung von verzerrten Sch{\"a}tzern, z.B den Ridge-Sch{\"a}tzer. In dieser Arbeit wird ein neues Sch{\"a}tzverfahren vorgestellt, dass auf Addition einer kleinen Konstanten omega auf die Regressoren beruht. Der dadurch erzeugte Sch{\"a}tzer wird in Abh{\"a}ngigkeit von omega beschrieben und es wird gezeigt, dass dessen Mean Squared Error kleiner ist als der des Kleinste-Quadrate-Sch{\"a}tzers im Falle von stark korrelierten Regressoren.},
  subject      = {Starke Kopplung},
  language  = {en}
}
@phdthesis{Wurst2015,
  author    = {Wurst, Jan-Eric},
  title     = {Hp-Finite Elements for PDE-Constrained Optimization},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-024-5 (print)},
  doi       = {10.25972/WUP-978-3-95826-025-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-115027},
  school      = {W{\"u}rzburg University Press},
  pages     = {188},
  year      = {2015},
  abstract  = {Diese Arbeit behandelt die hp-Finite Elemente Methode (FEM) f{\"u}r linear quadratische Optimal-steuerungsprobleme. Dabei soll ein Zielfunktional, welches die Entfernung zu einem angestrebten Zustand und hohe Steuerungskosten (als Regularisierung) bestraft, unter der Nebenbedingung einer elliptischen partiellen Differentialgleichung minimiert werden. Bei der Anwesenheit von Steuerungsbeschr{\"a}nkungen k{\"o}nnen die notwendigen Bedingungen erster Ordnung, die typischerweise f{\"u}r numerische L{\"o}sungsverfahren genutzt werden, als halbglatte Projektionsformel formuliert werden. Folglich sind optimale L{\"o}sungen oftmals auch nicht-glatt. Die Technik der hp-Diskretisierung ber{\"u}cksichtigt diese Tatsache und approximiert raue Funktionen auf feinen Gittern, w{\"a}hrend Elemente h{\"o}herer Ordnung auf Gebieten verwendet werden, auf denen die L{\"o}sung glatt ist. Die erste Leistung dieser Arbeit ist die erfolgreiche Anwendung der hp-FEM auf zwei verwandte Problemklassen: Neumann- und Interface-Steuerungsprobleme. Diese werden zun{\"a}chst mit entsprechenden a-priori Verfeinerungsstrategien gel{\"o}st, mit der randkonzentrierten (bc) FEM oder interface konzentrierten (ic) FEM. Diese Strategien generieren Gitter, die stark in Richtung des Randes beziehungsweise des Interfaces verfeinert werden. Um f{\"u}r beide Techniken eine algebraische Reduktion des Approximationsfehlers zu beweisen, wird eine elementweise interpolierende Funktion konstruiert. Außerdem werden die lokale und globale Regularit{\"a}t von L{\"o}sungen behandelt, weil sie entscheidend f{\"u}r die Konvergenzgeschwindigkeit ist. Da die bc- und ic- FEM kleine Polynomgrade f{\"u}r Elemente verwenden, die den Rand beziehungsweise das Interface ber{\"u}hren, k{\"o}nnen eine neue L2- und L∞-Fehlerabsch{\"a}tzung hergeleitet werden. Letztere bildet die Grundlage f{\"u}r eine a-priori Strategie zum Aufdatieren des Regularisierungsparameters im Zielfunktional, um Probleme mit bang-bang Charakter zu l{\"o}sen. Zudem wird die herk{\"o}mmliche hp-Idee, die daraus besteht das Gitter geometrisch in Richtung der Ecken des Gebiets abzustufen, auf die L{\"o}sung von Optimalsteuerungsproblemen {\"u}bertragen (vc-FEM). Es gelingt, Regularit{\"a}t in abz{\"a}hlbar normierten R{\"a}umen f{\"u}r die Variablen des gekoppelten Optimalit{\"a}tssystems zu zeigen. Hieraus resultiert die exponentielle Konvergenz im Bezug auf die Anzahl der Freiheitsgrade. Die zweite Leistung dieser Arbeit ist die Entwicklung einer v{\"o}llig adaptiven hp-Innere-Punkte-Methode, die Probleme mit verteilter oder Neumann Steuerung l{\"o}sen kann. Das zugrundeliegende Barriereproblem besitzt ein nichtlineares Optimilit{\"a}tssystem, das eine numerische Herausforderung beinhaltet: die stabile Berechnung von Integralen {\"u}ber Funktionen mit m{\"o}glichen Singularit{\"a}ten in Elementen h{\"o}herer Ordnung. Dieses Problem wird dadurch gel{\"o}st, dass die Steuerung an den Integrationspunkten {\"u}berwacht wird. Die Zul{\"a}ssigkeit an diesen Punkten wird durch einen Gl{\"a}ttungsschritt garantiert. In dieser Arbeit werden sowohl die Konvergenz eines Innere-Punkte-Verfahrens mit Gl{\"a}ttungsschritt als auch a-posteriori Schranken f{\"u}r den Diskretisierungsfehler gezeigt. Dies f{\"u}hrt zu einem adaptiven L{\"o}sungsalgorithmus, dessen Gitterverfeinerung auf der Entwicklung der L{\"o}sung in eine Legendre Reihe basiert. Hierbei dient das Abklingverhalten der Koeffizienten als Glattheitsindikator und wird f{\"u}r die Entscheidung zwischen h- und p-Verfeinerung herangezogen.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@phdthesis{Karl2015,
  author    = {Karl, Sabine},
  title     = {Firm Values and Systemic Stability in Financial Networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-115739},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Based on the work of Eisenberg and Noe [2001], Suzuki [2002], Elsinger [2009] and Fischer [2014], we consider a generalization of Merton's asset valuation approach where n firms are linked by cross-ownership of equities and liabilities. Each firm is assumed to have a single outstanding liability, whereas its assets consist of one system-exogenous asset, as well as system-endogenous assets comprising some fraction of other firms' equity and liability, respectively. Following Fischer [2014], one can obtain no-arbitrage prices of equity and the recovery claims of liabilities as solutions of a fixed point problem, and hence obtain no-arbitrage prices of the `firm value' of each firm, which is the value of the firm's liability plus the firm's equity. In a first step, we consider the two-firm case where explicit formulae for the no-arbitrage prices of the firm values are available (cf. Suzuki [2002]). Since firm values are derivatives of exogenous asset values, the distribution of firm values at maturity can be determined from the distribution of exogenous asset values. The Merton model and most of its known extensions do not account for the cross-ownership structure of the assets owned by the firm. Therefore the assumption of lognormally distributed exogenous assets leads to lognormally distributed firm values in such models, as the values of the liability and the equity add up to the exogenous asset's value (which has lognormal distribution by assumption). Our work therefore starts from lognormally distributed exogenous assets and reveals how cross-ownership, when correctly accounted for in the valuation process, affects the distribution of the firm value, which is not lognormal anymore. In a simulation study we examine the impact of several parameters (amount of cross-ownership of debt and equity, ratio of liabilities to expected exogenous assets value) on the differences between the distribution of firm values obtained from our model and correspondingly matched lognormal distributions. It becomes clear that the assumption of lognormally distributed firm values may lead to both over- and underestimation of the "true" firm values (within the cross-ownership model) and consequently of bankruptcy risk, too. In a second step, the bankruptcy risk of one firm within the system is analyzed in more detail in a further simulation study, revealing that the correct incorporation of cross-ownership in the valuation procedure is the more important, the tighter the cross-ownership structure between the two firms. Furthermore, depending on the considered type of cross-ownership (debt or equity), the assumption of lognormally distributed firm values is likely to result in an over- resp. underestimation of the actual probability of default. In a similar vein, we consider the Value-at-Risk (VaR) of a firm in the system, which we calculate as the negative α-quantile of the firm value at maturity minus the firm's risk neutral price in t=0, i.e. we consider the (1-α)100\%-VaR of the change in firm value. If we let the cross-ownership fractions (i.e. the fraction that one firm holds of another firm's debt or equity) converge to 1 (which is the supremum of the possible values that cross-ownership fractions can take), we can prove that in a system of two firms, the lognormal model will over- resp. underestimate both univariate and bivariate probabilities of default under cross-ownership of debt only resp. cross-ownership of equity only. Furthermore, we provide a formula that allows us to check for an arbitrary scenario of cross-ownership and any non-negative distribution of exogenous assets whether the approximating lognormal model will over- or underestimate the related probability of default of a firm. In particular, any given non-negative distribution of exogenous asset values (non-degenerate in a certain sense) can be transformed into a new, "extreme" distribution of exogenous assets yielding such a low or high actual probability of default that the approximating lognormal model will over- and underestimate this risk, respectively. After this analysis of the univariate distribution of firm values under cross-ownership in a system of two firms with bivariately lognormally distributed exogenous asset values, we consider the copula of these firm values as a distribution-free measure of the dependency between these firm values. Without cross-ownership, this copula would be the Gaussian copula. Under cross-ownership, we especially consider the behaviour of the copula of firm values in the lower left and upper right corner of the unit square, and depending on the type of cross-ownership and the considered corner, we either obtain error bounds as to how good the copula of firm values under cross-ownership can be approximated with the Gaussian copula, or we see that the copula of firm values can be written as the copula of two linear combinations of exogenous asset values (note that these linear combinations are not lognormally distributed). These insights serve as a basis for our analysis of the tail dependence coefficient of firm values under cross-ownership. Under cross-ownership of debt only, firm values remain upper tail independent, whereas they become perfectly lower tail dependent if the correlation between exogenous asset values exceeds a certain positive threshold, which does not depend on the exact level of cross-ownership. Under cross-ownership of equity only, the situation is reverse in that firm values always remain lower tail independent, but upper tail independence is preserved if and only if the right tail behaviour of both firms' values is determined by the right tail behaviour of the firms' own exogenous asset value instead of the respective other firm's exogenous asset value. Next, we return to systems of n≥2 firms and analyze sensitivities of no-arbitrage prices of equity and the recovery claims of liabilities with respect to the model parameters. In the literature, such sensitivities are provided with respect to exogenous asset values by Gouri{\´e}roux et al. [2012], and we extend the existing results by considering how these no-arbitrage prices depend on the cross-ownership fractions and the level of liabilities. For the former, we can show that all prices are non-decreasing in any cross-ownership fraction in the model, and by use of a version of the Implicit Function Theorem we can also determine exact derivatives. For the latter, we show that the recovery value of debt and the equity value of a firm are non-decreasing and non-increasing in the firm's nominal level of liabilities, respectively, but the firm value is in general not monotone in the firm's level of liabilities. Furthermore, no-arbitrage prices of equity and the recovery claims of liabilities of a firm are in general non-monotone in the nominal level of liabilities of other firms in the system. If we confine ourselves to one type of cross-ownership (i.e. debt or equity), we can derive more precise relationships. All the results can be transferred to risk-neutral prices before maturity. Finally, following Gouri{\´e}roux et al. [2012] and as a kind of extension to the above sensitivity results, we consider how immediate changes in exogenous asset values of one or more firms at maturity affect the financial health of a system of n initially solvent firms. We start with some theoretical considerations on what we call the contagion effect, namely the change in the endogenous asset value of a firm caused by shocks on the exogenous assets of firms within the system. For the two-firm case, an explicit formula is available, making clear that in general (and in particular under cross-ownership of equity only), the effect of contagion can be positive as well as negative, i.e. it can both, mitigate and exacerbate the change in the exogenous asset value of a firm. On the other hand, we cannot generally say that a tighter cross-ownership structure leads to bigger absolute contagion effects. Under cross-ownership of debt only, firms cannot profit from positive shocks beyond the direct effect on exogenous assets, as the contagion effect is always non-positive. Next, we are concerned with spillover effects of negative shocks on a subset of firms to other firms in the system (experiencing non-negative shocks themselves), driving them into default due to large losses in their endogenous asset values. Extending the results of Glasserman and Young [2015], we provide a necessary condition for the shock to cause such an event. This also yields an upper bound for the probability of such an event. We further investigate how the stability of a system of firms exposed to multiple shocks depends on the model parameters in a simulation study. In doing so, we consider three network types (incomplete, core-periphery and ring network) with simultaneous shocks on some of the firms and wiping out a certain percentage of their exogenous assets. Then we analyze for all three types of cross-ownership (debt only, equity only, both debt and equity) how the shock intensity, the shock size, and network parameters as the number of links in the network and the proportion of a firm's debt or equity held within the system of firms influences several output parameters, comprising the total number of defaults and the relative loss in the sum of firm values, among others. Comparing our results to the studies of Nier et al. [2007], Gai and Kapadia [2010] and Elliott et al. [2014], we can only partly confirm their results with respect to the number of defaults. We conclude our work with a theoretical comparison of the complete network (where each firm holds a part of any other firm) and the ring network with respect to the number of defaults caused by a shock on a single firm, as it is done by Allen and Gale [2000]. In line with the literature, we find that under cross-ownership of debt only, complete networks are "robust yet fragile" [Gai and Kapadia, 2010] in that moderate shocks can be completely withstood or drive the firm directly hit by the shock in default, but as soon as the shock exceeds a certain size, all firms are simultaneously in default. In contrast to that, firms default one by one in the ring network, with the first "contagious default" (i.e. a default of a firm not directly hit by the shock) already occurs for smaller shock sizes than under the complete network.},
  subject      = {Finanzmathematik},
  language  = {en}
}
@article{LuKlingenbergRendonetal.2014,
  author    = {Lu, Yun-guang and Klingenberg, Christian and Rendon, Leonardo and Zheng, De-Yin},
  title     = {Global Solutions for a Simplified Shallow Elastic Fluids Model},
  series = {Abstract and Applied Analytics},
  journal   = {Abstract and Applied Analytics},
  number    = {920248},
  issn      = {1687-0409},
  doi       = {10.1155/2014/920248},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-117978},
  year      = {2014},
  abstract  = {The Cauchy problem for a simplified shallow elastic fluids model, one 3 x 3 system of Temple's type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth (rho - 0). This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), which provided the global existence of weak solutions for 2 x 2 strictly hyperbolic system and (Heibig, 1994) for n x n strictly hyperbolic system with smooth Riemann invariants.},
  language  = {en}
}
@phdthesis{Geiselhart2015,
  author    = {Geiselhart, Roman},
  title     = {Advances in the stability analysis of large-scale discrete-time systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-112963},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Several aspects of the stability analysis of large-scale discrete-time systems are considered. An important feature is that the right-hand side does not have have to be continuous. In particular, constructive approaches to compute Lyapunov functions are derived and applied to several system classes. For large-scale systems, which are considered as an interconnection of smaller subsystems, we derive a new class of small-gain results, which do not require the subsystems to be robust in some sense. Moreover, we do not only study sufficiency of the conditions, but rather state an assumption under which these conditions are also necessary. Moreover, gain construction methods are derived for several types of aggregation, quantifying how large a prescribed set of interconnection gains can be in order that a small-gain condition holds.},
  subject      = {Ljapunov-Funktion},
  language  = {en}
}
@article{RudelPrustySiegletal.2013,
  author    = {Rudel, Thomas and Prusty, Bhupesh K. and Siegl, Christine and Hauck, Petra and Hain, Johannes and Korhonen, Suvi J. and Hiltunen-Back, Eija and Poulakkainen, Mirja},
  title     = {Chlamydia trachomatis Infection Induces Replication of Latent HHV-6},
  series = {PLoS ONE},
  journal   = {PLoS ONE},
  doi       = {10.1371/journal.pone.0061400},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96731},
  year      = {2013},
  abstract  = {Human herpesvirus-6 (HHV-6) exists in latent form either as a nuclear episome or integrated into human chromosomes in more than 90\% of healthy individuals without causing clinical symptoms. Immunosuppression and stress conditions can reactivate HHV-6 replication, associated with clinical complications and even death. We have previously shown that co-infection of Chlamydia trachomatis and HHV-6 promotes chlamydial persistence and increases viral uptake in an in vitro cell culture model. Here we investigated C. trachomatis-induced HHV-6 activation in cell lines and fresh blood samples from patients having Chromosomally integrated HHV-6 (CiHHV-6). We observed activation of latent HHV-6 DNA replication in CiHHV-6 cell lines and fresh blood cells without formation of viral particles. Interestingly, we detected HHV-6 DNA in blood as well as cervical swabs from C. trachomatis-infected women. Low virus titers correlated with high C. trachomatis load and vice versa, demonstrating a potentially significant interaction of these pathogens in blood cells and in the cervix of infected patients. Our data suggest a thus far underestimated interference of HHV-6 and C. trachomatis with a likely impact on the disease outcome as consequence of co-infection.},
  language  = {en}
}
@phdthesis{Schleissinger2013,
  author    = {Schleißinger, Sebastian},
  title     = {Embedding Problems in Loewner Theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96782},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {The work at hand studies problems from Loewner theory and is divided into two parts: In part 1 (chapter 2) we present the basic notions of Loewner theory. Here we use a modern form which was developed by F. Bracci, M. Contreras, S. D{\´i}az-Madrigal et al. and which can be applied to certain higher dimensional complex manifolds. We look at two domains in more detail: the Euclidean unit ball and the polydisc. Here we consider two classes of biholomorphic mappings which were introduced by T. Poreda and G. Kohr as generalizations of the class S. We prove a conjecture of G. Kohr about support points of these classes. The proof relies on the observation that the classes describe so called Runge domains, which follows from a result by L. Arosio, F. Bracci and E. F. Wold. Furthermore, we prove a conjecture of G. Kohr about support points of a class of biholomorphic mappings that comes from applying the Roper-Suffridge extension operator to the class S. In part 2 (chapter 3) we consider one special Loewner equation: the chordal multiple-slit equation in the upper half-plane. After describing basic properties of this equation we look at the problem, whether one can choose the coefficient functions in this equation to be constant. D. Prokhorov proved this statement under the assumption that the slits are piecewise analytic. We use a completely different idea to solve the problem in its general form. As the Loewner equation with constant coefficients holds everywhere (and not just almost everywhere), this result generalizes Loewner's original idea to the multiple-slit case. Moreover, we consider the following problems: • The "simple-curve problem" asks which driving functions describe the growth of simple curves (in contrast to curves that touch itself). We discuss necessary and sufficient conditions, generalize a theorem of J. Lind, D. Marshall and S. Rohde to the multiple-slit equation and we give an example of a set of driving functions which generate simple curves because of a certain self-similarity property. • We discuss properties of driving functions that generate slits which enclose a given angle with the real axis. • A theorem by O. Roth gives an explicit description of the reachable set of one point in the radial Loewner equation. We prove the analog for the chordal equation.},
  subject      = {Biholomorphe Abbildung},
  language  = {en}
}
@article{StoevesandtHofmannHainetal.2013,
  author    = {Stoevesandt, Johanna and Hofmann, Bernd and Hain, Johannes and Kerstan, Andreas and Trautmann, Axel},
  title     = {Single venom-based immunotherapy effectively protects patients with double positive tests to honey bee and Vespula venom},
  series = {Allergy, Asthma \& Clinical Immunology},
  journal   = {Allergy, Asthma \& Clinical Immunology},
  doi       = {10.1186/1710-1492-9-33},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96808},
  year      = {2013},
  abstract  = {Background Referring to individuals with reactivity to honey bee and Vespula venom in diagnostic tests, the umbrella terms "double sensitization" or "double positivity" cover patients with true clinical double allergy and those allergic to a single venom with asymptomatic sensitization to the other. There is no international consensus on whether immunotherapy regimens should generally include both venoms in double sensitized patients. Objective We investigated the long-term outcome of single venom-based immunotherapy with regard to potential risk factors for treatment failure and specifically compared the risk of relapse in mono sensitized and double sensitized patients. Methods Re-sting data were obtained from 635 patients who had completed at least 3 years of immunotherapy between 1988 and 2008. The adequate venom for immunotherapy was selected using an algorithm based on clinical details and the results of diagnostic tests. Results Of 635 patients, 351 (55.3\%) were double sensitized to both venoms. The overall re-exposure rate to Hymenoptera stings during and after immunotherapy was 62.4\%; the relapse rate was 7.1\% (6.0\% in mono sensitized, 7.8\% in double sensitized patients). Recurring anaphylaxis was statistically less severe than the index sting reaction (P = 0.004). Double sensitization was not significantly related to relapsing anaphylaxis (P = 0.56), but there was a tendency towards an increased risk of relapse in a subgroup of patients with equal reactivity to both venoms in diagnostic tests (P = 0.15). Conclusions Single venom-based immunotherapy over 3 to 5 years effectively and long-lastingly protects the vast majority of both mono sensitized and double sensitized Hymenoptera venom allergic patients. Double venom immunotherapy is indicated in clinically double allergic patients reporting systemic reactions to stings of both Hymenoptera and in those with equal reactivity to both venoms in diagnostic tests who have not reliably identified the culprit stinging insect.},
  language  = {en}
}
@article{FreibergMatlachGrehnetal.2013,
  author    = {Freiberg, Florentina Joyce and Matlach, Juliane and Grehn, Franz and Karl, Sabine and Klink, Thomas},
  title     = {Postoperative subconjunctival bevacizumab injection as an adjunct to 5-fluorouracil in the management of scarring after trabeculectomy},
  series = {Clinical Ophthalmology},
  journal   = {Clinical Ophthalmology},
  doi       = {10.2147/OPTH.S41750},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96546},
  year      = {2013},
  abstract  = {Purpose: Scarring after glaucoma filtering surgery remains the most frequent cause for bleb failure. The aim of this study was to assess if the postoperative injection of bevacizumab reduces the number of postoperative subconjunctival 5-fluorouracil (5-FU) injections. Further, the effect of bevacizumab as an adjunct to 5-FU on the intraocular pressure (IOP) outcome, bleb morphology, postoperative medications, and complications was evaluated. Methods: Glaucoma patients (N = 61) who underwent trabeculectomy with mitomycin C were analyzed retrospectively (follow-up period of 25 ± 19 months). Surgery was performed exclusively by one experienced glaucoma specialist using a standardized technique. Patients in group 1 received subconjunctival applications of 5-FU postoperatively. Patients in group 2 received 5-FU and subconjunctival injection of bevacizumab. Results: Group 1 had 6.4 ± 3.3 (0-15) (mean ± standard deviation and range, respectively) 5-FU injections. Group 2 had 4.0 ± 2.8 (0-12) (mean ± standard deviation and range, respectively) 5-FU injections. The added injection of bevacizumab significantly reduced the mean number of 5-FU injections by 2.4 ± 3.08 (P ≤ 0.005). There was no significantly lower IOP in group 2 when compared to group 1. A significant reduction in vascularization and in cork screw vessels could be found in both groups (P < 0.0001, 7 days to last 5-FU), yet there was no difference between the two groups at the last follow-up. Postoperative complications were significantly higher for both groups when more 5-FU injections were applied. (P = 0.008). No significant difference in best corrected visual acuity (P = 0.852) and visual field testing (P = 0.610) between preoperative to last follow-up could be found between the two groups. Conclusion: The postoperative injection of bevacizumab reduced the number of subconjunctival 5-FU injections significantly by 2.4 injections. A significant difference in postoperative IOP reduction, bleb morphology, and postoperative medication was not detected.},
  language  = {en}
}
@article{TrautmannSeitzBrockowetal.2014,
  author    = {Trautmann, Axel and Seitz, Cornelia S. and Brockow, Knut and Hain, Johannes},
  title     = {Non-steroidal anti-inflammatory drug hypersensitivity: association with elevated basal serum tryptase?},
  doi       = {10.1186/1710-1492-10-19},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-110399},
  year      = {2014},
  abstract  = {Background It is hypothesized that because of higher mast cell numbers and mediator release, mastocytosis predisposes patients for systemic immediate-type hypersensitivity reactions to certain drugs including non-steroidal anti-inflammatory drugs (NSAID). Objective To clarify whether patients with NSAID hypersensitivity show increased basal serum tryptase levels as sign for underlying mast cell disease. Methods As part of our allergy work-up, basal serum tryptase levels were determined in all patients with a diagnosis of NSAID hypersensitivity and the severity of the reaction was graded. Patients with confirmed IgE-mediated hymenoptera venom allergy served as a comparison group. Results Out of 284 patients with NSAID hypersensitivity, 26 were identified with basal serum tryptase > 10.0 ng/mL (9.2\%). In contrast, significantly (P = .004) more hymenoptera venom allergic patients had elevated tryptase > 10.0 ng/mL (83 out of 484; 17.1\%). Basal tryptase > 20.0 ng/mL was indicative for severe anaphylaxis only in venom allergic subjects (29 patients; 4x grade 2 and 25x grade 3 anaphylaxis), but not in NSAID hypersensitive patients (6 patients; 4x grade 1, 2x grade 2). Conclusions In contrast to hymenoptera venom allergy, NSAID hypersensitivity do not seem to be associated with elevated basal serum tryptase levels and levels > 20 ng/mL were not related to increased severity of the clinical reaction. This suggests that mastocytosis patients may be treated with NSAID without special precautions.},
  language  = {en}
}
@phdthesis{Reinwand2021,
  author    = {Reinwand, Simon},
  title     = {Functions of Bounded Variation: Theory, Methods, Applications},
  publisher = {Cuvillier-Verlag, G{\"o}ttingen},
  isbn      = {9783736974036},
  doi       = {10.25972/OPUS-23515},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-235153},
  school      = {Universit{\"a}t W{\"u}rzburg},
  pages     = {326},
  year      = {2021},
  abstract  = {Functions of bounded variation are most important in many fields of mathematics. This thesis investigates spaces of functions of bounded variation with one variable of various types, compares them to other classical function spaces and reveals natural "habitats" of BV-functions. New and almost comprehensive results concerning mapping properties like surjectivity and injectivity, several kinds of continuity and compactness of both linear and nonlinear operators between such spaces are given. A new theory about different types of convergence of sequences of such operators is presented in full detail and applied to a new proof for the continuity of the composition operator in the classical BV-space. The abstract results serve as ingredients to solve Hammerstein and Volterra integral equations using fixed point theory. Many criteria guaranteeing the existence and uniqueness of solutions in BV-type spaces are given and later applied to solve boundary and initial value problems in a nonclassical setting. A big emphasis is put on a clear and detailed discussion. Many pictures and synoptic tables help to visualize and summarize the most important ideas. Over 160 examples and counterexamples illustrate the many abstract results and how delicate some of them are.},
  subject      = {Funktion von beschr{\"a}nkter Variation},
  language  = {en}
}
@phdthesis{Nguyen2012,
  author    = {Nguyen, Danh Nam},
  title     = {Understanding the development of the proving process within a dynamic geometry environment},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-71754},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Argumentation and proof have played a fundamental role in mathematics education in recent years. The author of this dissertation would like to investigate the development of the proving process within a dynamic geometry system in order to support tertiary students understanding the proving process. The strengths of this dynamic system stimulate students to formulate conjectures and produce arguments during the proving process. Through empirical research, we classified different levels of proving and proposed a methodological model for proving. This methodological model makes a contribution to improve students' levels of proving and develop their dynamic visual thinking. We used Toulmin model of argumentation as a theoretical model to analyze the relationship between argumentation and proof. This research also offers some possible explanation so as to why students have cognitive difficulties in constructing proofs and provides mathematics educators with a deeper understanding on the proving process within a dynamic geometry system.},
  subject      = {Argumentation},
  language  = {en}
}
@article{SchaeffnerSchloemerkemper2018,
  author    = {Sch{\"a}ffner, M. and Schl{\"o}merkemper, A.},
  title     = {On Lennard-Jones systems with finite range interactions and their asymptotic analysis},
  series = {Networks and Heterogeneous Media},
  volume    = {13},
  journal   = {Networks and Heterogeneous Media},
  number    = {1},
  doi       = {10.3934/nhm.2018005},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-228428},
  pages     = {95-118},
  year      = {2018},
  abstract  = {The aim of this work is to provide further insight into the qualitative behavior of mechanical systems that are well described by Lennard-Jones type interactions on an atomistic scale. By means of Gamma-convergence techniques, we study the continuum limit of one-dimensional chains of atoms with finite range interactions of Lennard-Jones type, including the classical Lennard-Jones potentials. So far, explicit formula for the continuum limit were only available for the case of nearest and next-to-nearest neighbour interactions. In this work, we provide an explicit expression for the continuum limit in the case of finite range interactions. The obtained homogenization formula is given by the convexification of a Cauchy-Born energy density. Furthermore, we study rescaled energies in which bulk and surface contributions scale in the same way. The related discrete-to-continuum limit yields a rigorous derivation of a one-dimensional version of Griffith' fracture energy and thus generalizes earlier derivations for nearest and next-to-nearest neighbors to the case of finite range interactions. A crucial ingredient to our proofs is a novel decomposition of the energy that allows for re fined estimates.},
  language  = {en}
}
@phdthesis{Dirr2001,
  author    = {Dirr, Gunther},
  title     = {Differentialgleichungen in Fr{\´e}chetr{\"a}umen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-1180417},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {Teil 1 der Arbeit beinhaltet eine Zusammenfassung grundlegender funktionalanalytischer Ergebnisse sowie eine Einf{\"u}hrung in die Integral- und Differentialrechnung in Fr{\´e}chetr{\"a}umen. Insbesondere wird in Kapitel 2 eine ausf{\"u}hrliche Darstellung des Lebesgue-Bochner-Integrals auf Fr{\´e}chetr{\"a}umen geliefert. Teil 2 behandelt die Theorie der linearen Differentialgleichungen auf Fr{\´e}chetr{\"a}umen. Dazu werden in Kapitel 3 stark differenzierbare Halbgruppen und deren infinitesimale Generatoren charakterisiert. In Kapitel 4 werden diese Ergebnisse benutzt, um lineare Evolutionsgleichungen (von hyperbolischem oder parabolischem Typ) zu untersuchen. Teil 3 enth{\"a}lt die zentralen Resultate der Arbeit. In Kapitel 5 werden zwei Existenz- und Eindeutigkeitss{\"a}tze f{\"u}r nichtlineare gew{\"o}hnliche Differentialgleichungen in zahmen Fr{\´e}chetr{\"a}umen bewiesen. Kapitel 6 liefert eine Anwendung der Ergebnisse aus Kapitel 5 auf nichtlineare partielle Differentialgleichungen erster Ordnung.},
  subject      = {Differentialgleichung},
  language  = {de}
}
@phdthesis{Dittmann2001,
  author    = {Dittmann, Ulrich},
  title     = {Coset Types and Tight Subgroups of Almost Completely Decomposable Groups},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2762},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {A completely decomposable group is a direct sum of subgroups of the rationals. An almost completely decomposable group is a torsion free abelian group that contains a completely decomposable group as subgroup of finite index. Tight subgroups are maximal subgroups (with respect to set inclusion) among the completely decomposable subgroups of an almost completely decomposable group. In this dissertation we show an extended version of the theorem of Bezout, give a new criterion for the tightness of a completely decomposable subgroup, derive some conditions under which a tight subgroup is regulating and generalize a theorem of Campagna. We give an example of an almost completely decomposable group, all of whose regulating subgroups do not have a quotient with minimal exponent. We show that among the types of elements of a coset modulo a completely decomposable group there exists a unique maximal type and define this type to be -the- coset type. We give criteria for tightness and regulating in term of coset types as well as a representation of the type subgroups using coset types. We introduce the notion of reducible cosets and show their key role for transitions from one completely decomposable subgroup up to another one containing the first one as a proper subgroup. We give an example of a tight, but not regulating subgroup which contains the regulator. We develop the notion of a fully single covered subset of a lattice, show that V-free implies fully single covered, but not necessarily vice versa, and we define an equivalence relation on the set of all finite subsets of a given lattice. We develop some extension of ordinary Hasse diagrams, and apply the lattice theoretic results on the lattice of types and almost completely decomposable groups.},
  subject      = {Torsionsfreie Abelsche Gruppe},
  language  = {en}
}
@phdthesis{Keilbach2000,
  author    = {Keilbach, Rupert},
  title     = {Minimalfl{\"a}chen und Bj{\"o}rlingsches Problem in der Relativgeometrie},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2782},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2000},
  abstract  = {In dieser Arbeit besch{\"a}ftigen wir uns mit Themen aus der affinen Hyperfl{\"a}chentheorie. Nachdem wir die euklidische Normale, die Blaschkesche Affinnormale, eine gewisse Einparameterfamilie von Relativnormalen und die zentroaffine Normale besprochen und eine neue Einparameterfamilie von Relativnormalen definiert haben, behandeln wir die folgenden drei Schwerpunkte: Zuerst befassen wir uns mit Minimalfl{\"a}chen bez{\"u}glich verschiedener Volumina und der Rolle der jeweiligen Mittleren Kr{\"u}mmung. Wir berechnen die erste und zweite Variation der Volumina, die von den Normalen der erw{\"a}hnten Familien induziert werden. Hierbei stellen wir fest, daß die Mittlere Kr{\"u}mmung nicht immer das Verschwinden der ersten Variation des Volumens anzeigt. Anschließend {\"u}bertragen wir die Begriffe Adjungierte und Assoziierte bei euklidischen Minimalfl{\"a}chen auf Affinminimalfl{\"a}chen: Analog zum euklidischen Fall kann man die Konormale einer Affinminimalfl{\"a}che durch bestimmte ,,harmonische'' Abbildungen darstellen. Wir geben eine Methode an, wie man aus einer gegebenen Affinminimalfl{\"a}che weitere gewinnt, indem man diese Abbildungen entsprechend modifiziert. Schließlich l{\"o}sen wir eine Verallgemeinerung des Bj{\"o}rlingschen Problems f{\"u}r Normalen der oben erw{\"a}hnten Familien: Bei Vorgabe einer Kurve mit zwei Vektorfeldern und der Art der Normalisierung existiert - mit Ausnahmen - je genau eine elliptische und eine hyperbolische Fl{\"a}che in (pseudo-)isothermen Parametern mit folgenden Eigenschaften: Die Kurve ist eine Parameterlinie, die Normale l{\"a}ngs der Kurve stimmt mit dem einen Vektorfeld {\"u}berein, die Konormale mit dem anderen und die Mittlere und Gaußsche Kr{\"u}mmung erf{\"u}llen eine vorgegebene Bedingung.},
  subject      = {Minimalfl{\"a}che},
  language  = {de}
}
@phdthesis{Kessler2000,
  author    = {Keßler, Manuel},
  title     = {Die Ladyzhenskaya-Konstante in der numerischen Behandlung von Str{\"o}mungsproblemen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2791},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2000},
  abstract  = {Charakteristisch f{\"u}r die L{\"o}sbarkeit von elliptischen partiellen Differentialgleichungssystemen mit Nebenbedingungen ist das Auftreten einer inf-sup-Bedingung. Im prototypischen Fall der Stokes-Gleichungen ist diese auch als Ladyzhenskaya-Bedingung bekannt. Die G{\"u}ltigkeit dieser Bedingung, bzw. die Existenz der zugeh{\"o}rigen Konstante ist eine Eigenschaft des Gebietes, innerhalb dessen die Differentialgleichung gel{\"o}st werden soll. W{\"a}hrend die Existenz schon die L{\"o}sbarkeit garantiert, ist beispielsweise f{\"u}r Fehleraussagen bei der numerischen Approximation auch die Gr{\"o}ße der Konstanten sehr wichtig. Insbesondere auch deshalb, weil eine {\"a}hnliche inf-sup-Bedingung auch bei der Diskretisierung mittel Finiter-Elemente-Methoden auftaucht, die hier Babuska-Brezzi-Bedingung heißt. Die Arbeit befaßt sich auf der einen Seite mit einer analytischen Absch{\"a}tzung der Ladyzhenskaya-Konstante f{\"u}r verschiedene Gebiete, wobei {\"A}quivalenzen mit verwandten Problemen aus der komplexen Analysis (Friedrichs-Ungleichung) und der Strukturmechanik (Kornsche Ungleichung) benutzt werden. Ein weiterer Teil befaßt sich mit dem Zusammenhang zwischen kontinuierlicher Ladyzhenskaya- Konstante und diskreter Babuska-Brezzi-Konstante. Die dabei gefundenen Ergebnisse werden mit Hilfe eines dazu entwickelten leistungsf{\"a}higen Finite-Elemente-Programmsystems numerisch verifiziert. Damit k{\"o}nnen erstmals genaue Absch{\"a}tzungen der Konstanten in zwei und drei Dimensionen gefunden werden. Aufbauend auf diesen Resultaten wird ein schneller L{\"o}sungsalgorithmus f{\"u}r die Stokes-Gleichungen vorgeschlagen und anhand von problematischen Gebieten dessen {\"U}berlegenheit gegen{\"u}ber klassischen Verfahren wie beispielsweise der Uzawa-Iteration demonstriert. W{\"a}hrend selbst bei einfachen Geometrien eine Konvergenzbeschleunigung um einen Faktor 5 erwartet werden kann, sind in kritischen F{\"a}llen Faktoren bis zu 1000 m{\"o}glich.},
  subject      = {Stokes-Gleichung},
  language  = {de}
}
@phdthesis{Nahler2001,
  author    = {Nahler, Michael},
  title     = {Isomorphism classes of almost completely decomposable groups},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2817},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {In this thesis we investigate near-isomorphism classes and isomorphism classes of almost completely decomposable groups. In Chapter 2 we introduce the concept of almost completely decomposable groups and sum up their most important facts. A local group is an almost completely decomposable group with a primary regulator quotient. A uniform group is a rigid local group with a homocyclic regulator quotient. In Chapter 3 a weakening of isomorphism, called type-isomorphism, appears. It is shown that type-isomorphism agrees with Lady's near-isomorphism. By the Main Decomposition Theorem and the Primary Reduction Theorem we are allowed to restrict ourselves on clipped local groups, namely groups without a direct rank-one summand. In Chapter 4 we collect facts of matrices over commutative rings with an identity element. Matrices over the local ring (Z / p^e Z) of residue classes of the rational integers modulo a prime power play an important role. In Chapter 5 we introduce representing matrices of finite essential extensions. Here a normal form for local groups is found by the Gauß algorithm. Uniform groups have representing matrices in Hermite normal form. The classification problems for almost completely decomposable groups up to isomorphism and up to near-isomorphism can be rephrased as equivalence problems for the representing matrices. In Chapter 6 we derive a criterion for the representing matrices of local groups in Gauß normal form. In Chapter 7 we formulate the matrix criterion for uniform groups. Two representing matrices in Hermite normal form describe isomorphic groups if and only if the rest blocks of the representing matrices are T-diagonally equivalent. Starting from a fixed near-isomorphism class in Chapter 8 we investigate isomorphism classes of uniform groups. We count groups and isomorphism classes. In Chapter 9 we specialize on uniform groups of rank 2r with a regulator quotient of rank r such that the rest block of the representing matrix is invertible and normed.},
  subject      = {Fast vollst{\"a}ndig zerlegbare Gruppe},
  language  = {en}
}
@phdthesis{Kramer2004,
  author    = {Kramer, Helmut},
  title     = {Inzidenzmatrizen endlicher projektiver Ebenen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-11215},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {Ziel dieser Arbeit ist eine computerunterst{\"u}tzte Suche nach, bis auf Isomorphie, allen projektiven Ebenen zu einer gegebenen Ordnung durch Berechnung ihrer Inzidenzmatrix. Dies gelingt durch geeignete Vorstrukturierung der Matrix mit Hilfe der Doppelordnung bis Ordnung 9 auf einem aktuellen PC. In diesem Zusammenhang ist insbesondere durch einen gen{\"u}gend schnellen Algorithmus das Problem zu l{\"o}sen, ob zwei Inzidenzmatrizen zu derselben projektiven Ebene geh{\"o}ren. Die besondere Struktur, die die berechneten Beispiele von doppelgeordneten Inzidenzmatrizen der desarguesschen Ebenen aufzeigen, wird zudem durch theoretische {\"U}berlegungen untermauert. In einem letzten Kapitel wird noch eine Verbindung der projektiven Ebenen zu besonderen Blockpl{\"a}nen geschaffen.},
  subject      = {Projektive Ebene},
  language  = {de}
}
@phdthesis{Flegel2005,
  author    = {Flegel, Michael L.},
  title     = {Constraint qualifications and stationarity concepts for mathematical programs with equilibrium constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-12453},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {An exhaustive discussion of constraint qualifications (CQ) and stationarity concepts for mathematical programs with equilibrium constraints (MPEC) is presented. It is demonstrated that all but the weakest CQ, Guignard CQ, are too strong for a discussion of MPECs. Therefore, MPEC variants of all the standard CQs are introduced and investigated. A strongly stationary point (which is simply a KKT-point) is seen to be a necessary first order optimality condition only under the strongest CQs, MPEC-LICQ, MPEC-SMFCQ and Guignard CQ. Therefore a whole set of KKT-type conditions is investigated. A simple approach is given to acquire A-stationarity to be a necessary first order condition under MPEC-Guiganrd CQ. Finally, a whole chapter is devoted to investigating M-stationary, among the strongest stationarity concepts, second only to strong stationarity. It is shown to be a necessary first order condition under MPEC-Guignard CQ, the weakest known CQ for MPECs.},
  subject      = {Nichtlineare Optimierung},
  language  = {en}
}
@book{FalkMarohnMicheletal.2005,
  author    = {Falk, Michael and Marohn, Frank and Michel, Ren{\´e} and Hofmann, Daniel and Macke, Maria and Tewes, Bernward and Dinges, Peter},
  title     = {A First Course on Time Series Analysis : Examples with SAS},
  organization    = {Universit{\"a}t W{\"u}rzburg / Lehrstuhl f{\"u}r Statistik , Universit{\"a}t Eichst{\"a}tt/Rechenzentrum},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-12593},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License.},
  subject      = {Zeitreihenanalyse},
  language  = {en}
}
@phdthesis{Trumpf2002,
  author    = {Trumpf, Jochen},
  title     = {On the geometry and parametrization of almost invariant subspaces and observer theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-5034},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {In my Ph.D. thesis "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned invariant subspaces were introduced by Willems. They generalize the concept of a conditioned invariant subspace requiring the invariance condition to hold only up to an arbitrarily small deviation in the metric of the state space. One of the goals of the theory of almost conditioned invariant subspaces was to identify the subspaces appearing as limits of sequences of conditioned invariant subspaces. An example due to {\"O}zveren, Verghese and Willsky, however, shows that the set of almost conditioned invariant subspaces is not big enough. I address this question in a joint paper with Helmke and Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003). Antoulas derived a description of conditioned invariant subspaces as kernels of permuted and truncated reachability matrices of controllable pairs of the appropriate size. This description was used by Helmke and Fuhrmann to construct a diffeomorphism from the set of similarity classes of certain controllable pairs onto the set of tight conditioned invariant subspaces. In my thesis I generalize this result to almost conditioned invariant subspaces describing them in terms of restricted system equivalence classes of controllable triples. Furthermore, I identify the controllable pairs appearing in the kernel representations of conditioned invariant subspaces as being induced by corestrictions of the original system to the subspace. Conditioned invariant subspaces are known to be closely related to partial observers. In fact, a tracking observer for a linear function of the state of the observed system exists if and only if the kernel of that function is conditioned invariant. In my thesis I show that the system matrices of the observers are in fact the corestrictions of the observed system to the kernels of the observed functions. They in turn are closely related to partial realizations. Exploring this connection further, I prove that the set of tracking observer parameters of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections making the subspaces invariant, over that manifold. Willems and Trentelman generalized the concept of a tracking observer by including derivatives of the output of the observed system in the observer equations (PID-observers). They showed that a PID-observer for a linear function of the state of the observed system exists if and only if the kernel of that function is almost conditioned invariant. In my thesis I replace PID-observers by singular systems, which has the advantage that the system matrices of the observers coincide with the matrices appearing in the kernel representations of the subspaces. In a second approach to the parametrization of conditioned invariant subspaces Hinrichsen, M{\"u}nzner and Pr{\"a}tzel-Wolters, Fuhrmann and Helmke and Ferrer, F. Puerta, X. Puerta and Zaballa derived a description of conditioned invariant subspaces in terms of images of block Toeplitz type matrices. They used this description to construct a stratification of the set of conditioned invariant subspaces of fixed dimension into smooth manifolds. These so called Brunovsky strata consist of all the subspaces with fixed restriction indices. They constructed a cell decomposition of the Brunovsky strata into so called Kronecker cells. In my thesis I show that in the tight case this cell decomposition is induced by a Bruhat decomposition of a generalized flag manifold. I identify the adherence order of the cell decomposition as being induced by the reverse Bruhat order.},
  subject      = {Invarianter Unterraum},
  language  = {en}
}
@phdthesis{Vodopivec2005,
  author    = {Vodopivec, Andrija},
  title     = {Quasibasen abelscher, nichtseparabler p-Gruppen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-15359},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {In dieser Arbeit wird der Bau der (abz{\"a}hlbaren) abelschen p-Gruppen untersucht, durch die Betrachtung der dazugeh{\"o}rigen Quasibasen, die als bestimmte erzeugende Systeme der gegebenen p-Gruppe definiert sind. Die Untersuchung wird insbesondere auf die nichtseparablen p-Gruppen und ihre induktiven Quasibasen bezogen.},
  subject      = {Abelsche p-Gruppe},
  language  = {de}
}
@misc{Forster2013,
  type      = {Master Thesis},
  author    = {Forster, Johannes},
  title     = {Mathematical Modeling of Complex Fluids},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83533},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {This thesis gives an overview over mathematical modeling of complex fluids with the discussion of underlying mechanical principles, the introduction of the energetic variational framework, and examples and applications. The purpose is to present a formal energetic variational treatment of energies corresponding to the models of physical phenomena and to derive PDEs for the complex fluid systems. The advantages of this approach over force-based modeling are, e.g., that for complex systems energy terms can be established in a relatively easy way, that force components within a system are not counted twice, and that this approach can naturally combine effects on different scales. We follow a lecture of Professor Dr. Chun Liu from Penn State University, USA, on complex fluids which he gave at the University of Wuerzburg during his Giovanni Prodi professorship in summer 2012. We elaborate on this lecture and consider also parts of his work and publications, and substantially extend the lecture by own calculations and arguments (for papers including an overview over the energetic variational treatment see [HKL10], [Liu11] and references therein).},
  subject      = {Variationsrechnung},
  language  = {en}
}
@phdthesis{Klug2006,
  author    = {Klug, Andreas},
  title     = {Affine-Scaling Methods for Nonlinear Minimization Problems and Nonlinear Systems of Equations with Bound Constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18851},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {In this thesis affine-scaling-methods for two different types of mathematical problems are considered. The first type of problems are nonlinear optimization problems subject to bound constraints. A class of new affine-scaling Newton-type methods is introduced. The methods are shown to be locally quadratically convergent without assuming strict complementarity of the solution. The new methods differ from previous ones mainly in the choice of the scaling matrix. The second type of problems are semismooth system of equations with bound constraints. A new affine-scaling trust-region method for these problems is developed. The method is shown to have strong global and local convergence properties under suitable assumptions. Numerical results are presented for a number of problems arising from different areas.},
  subject      = {Skalierungsfunktion},
  language  = {en}
}
@phdthesis{Michel2006,
  author    = {Michel, Ren{\´e}},
  title     = {Simulation and Estimation in Multivariate Generalized Pareto Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18489},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {The investigation of multivariate generalized Pareto distributions (GPDs) in the framework of extreme value theory has begun only lately. Recent results show that they can, as in the univariate case, be used in Peaks over Threshold approaches. In this manuscript we investigate the definition of GPDs from Section 5.1 of Falk et al. (2004), which does not differ in the area of interest from those of other authors. We first show some theoretical properties and introduce important examples of GPDs. For the further investigation of these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. This algorithm is based on the Shi transformation, which was introduced by Shi (1995) and was used in Stephenson (2003) for the simulation of multivariate extreme value distributions of logistic type. We also present nonparametric and parametric estimation methods in GPD models. We estimate the angular density nonparametrically in arbitrary dimension, where the bivariate case turns out to be a special case. The asymptotic normality of the corresponding estimators is shown. Also in the parametric estimations, which are mainly based on maximum likelihood methods, the asymptotic normality of the estimators is shown under certain regularity conditions. Finally the methods are applied to a real hydrological data set containing water discharges of the rivers Altm{\"u}hl and Danube in southern Bavaria.},
  subject      = {Pareto-Verteilung},
  language  = {en}
}
@phdthesis{Petra2006,
  author    = {Petra, Stefania},
  title     = {Semismooth least squares methods for complementarity problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18660},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {This thesis is concerned with numerical methods for solving nonlinear and mixed complementarity problems. Such problems arise from a variety of applications such as equilibria models of economics, contact and structural mechanics problems, obstacle problems, discrete-time optimal control problems etc. In this thesis we present a new formulation of nonlinear and mixed complementarity problems based on the Fischer-Burmeister function approach. Unlike traditional reformulations, our approach leads to an over-determined system of nonlinear equations. This has the advantage that certain drawbacks of the Fischer-Burmeister approach are avoided. Among other favorable properties of the new formulation, the natural merit function turns out to be differentiable. To solve the arising over-determined system we use a nonsmooth damped Levenberg-Marquardt-type method and investigate its convergence properties. Under mild assumptions, it can be shown that the global and local fast convergence results are similar to some of the better equation-based method. Moreover, the new method turns out to be significantly more robust than the corresponding equation-based method. For the case of large complementarity problems, however, the performance of this method suffers from the need for solving the arising linear least squares problem exactly at each iteration. Therefore, we suggest a modified version which allows inexact solutions of the least squares problems by using an appropriate iterative solver. Under certain assumptions, the favorable convergence properties of the original method are preserved. As an alternative method for mixed complementarity problems, we consider a box constrained least squares formulation along with a projected Levenberg-Marquardt-type method. To globalize this method, trust region strategies are proposed. Several ingredients are used to improve this approach: affine scaling matrices and multi-dimensional filter techniques. Global convergence results as well as local superlinear/quadratic convergence are shown under appropriate assumptions. Combining the advantages of the new methods, a new software for solving mixed complementarity problems is presented.},
  subject      = {Komplementarit{\"a}tsproblem},
  language  = {en}
}
@phdthesis{Kraus2004,
  author    = {Kraus, Christiane},
  title     = {On some maximal convergence theorems for real analytic functions in R^N},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-9795},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {Ausgangspunkt dieser Arbeit war eine Publikation von D. Braess [Bra01], in der die Approximationsg{\"u}te der Funktionen \$\$ \frac{1}{((x-x_0)^2 + (y-y_0)^2)^s}, \qquad x_0^2 + y_0^2 \ge 1, \quad s \in (0,\infty),\$\$ auf der Einheitskreisscheibe \$x^2+y^2 \le 1\$ durch reelle Polynome untersucht wurde. Braess's Ergebnisse und insbesondere die von ihm angesprochenen offenen Probleme waren von besonderem Interesse, da sie Anlaß zu der Vermutung gaben, dass die klassische Theorie der ``Maximalen Konvergenz'' in Sinne von Walsh auf (zun{\"a}chst) die oben erw{\"a}hnten reell analytischen Funktionen erweitert werden kann. (Die Theorie der Maximalen Konvergenz bringt die Approximationsg{\"u}te einer Funktion auf einer kompakten Menge durch Polynome mit der Analyzit{\"a}t dieser Funktion in Verbindung.) \\ Hauptgegenstand der Arbeit ist die Erweiterung des klassischen ``Maximalen Konvergenz''--Konzeptes auf reell analytische Funktionen in h{\"o}heren Dimensionen. Es werden verschiedene maximale Konvergenzs{\"a}tze sowohl in einer als auch in mehreren Ver{\"a}nderlichen bewiesen. \\ Die Arbeit gliedert sich in drei Hauptteile. \\[2mm] Im ersten Teil wird der theoretische Hintergrund der ``Maximalen Konvergenz'' mit dem Problemkreis von Braess in Zusammenhang gebracht. Es wird gezeigt, dass f{\"u}r betrags-quadratisch holomorphe Funktionen folgender Satz gilt: \\ { \bf {Satz 1}}: Es sei \$g\$ eine holomorphe Funktion auf der abgeschlossenen Einheitskreisscheibe \$\overline{\mathbb{D}}:=\{ z \in \mathbb{C} : |z| \le 1\}\$ und \$F(x,y):= |g(x+iy)|^2\$, \$x,y \in \mathbb{R}\$. Dann gilt: \$\$ \limsup_{n \to \infty} \sqrt[n]{E_n ( \overline{\mathbb{D}},F)} = \frac{1}{\rho}\$\$ genau dann, wenn \$g\$ auf \$ \{ z \in \mathbb{C} : |z| < \rho \}\$ holomorph ist, aber auf keiner echt gr\"o\3eren Kreisscheibe, wobei \$\$ E_n ( \overline{\mathbb{D}},F)= \inf \{ ||F -P_n||_{\overline{\mathbb{D}}}, \, P_n: \mathbb{R}^2 \to \mathbb{R} \mbox{ Polynom vom Grad } \le n \}.\$\$ Dieser Satz beinhaltet nicht nur die Ergebnisse von Braess [Bra01], sondern erweitert ihn, und beantwortet die von Braess aufgeworfenen Fragen vollst{\"a}ndig. Zudem zeigt der Satz die genaue Analogie des klassischen ``Maximalen Konvergenz''--Konzeptes f{\"u}r die Funktionenklasse der betrag--quadratisch holomorphen Funktionen im \$\mathbb{R}^2\$. \\[2mm] In der Literatur gibt es viele Verallgemeinerungen des ``Maximalen Konvergenz''--Begriffes f{\"u}r mehrere komplexe Ver{\"a}nderlichen. Im Hinblick auf die vorliegende Arbeit sind besonders die Artikel [Sic62] und [Sic81] zu erw{\"a}hnen. Diese bereits bekannten Ergebnisse werden im zweiten Teil der Arbeit herangezogen, um den ``Maximalen Konvergenz''--Begriff auf mehrere reelle Ver{\"a}nderlichen zu erweitern. Man beachte, dass der entscheidende Unterschied hier in der polynomialen Approximationsklasse liegt. \\[2mm] Der dritte Teil befaßt sich mit der Verallgemeinerung des Satzes 1 in mehreren Ver{\"a}nderlichen. Eng verbunden mit diesem Problemkreis ist die Charakterisierung einer gewissen Extremalfunktion. Diese Funktion wird zur Bestimmung des Analyzit{\"a}tsbereichs der zu approximierenden Funktion ben{\"o}tigt. Mittels geeigneter Darstellung der Extremalfunktion und Charakterisierung des Analyzit{\"a}tsbereichs gelingt es schließlich, den folgenden Hauptsatz der vorliegenden Arbeit zu beweisen:\\ { \bf { Satz 2}}: Es seien \$g,h\$ holomorphe Funktionen auf der abgeschlossenen Einheitskugel \$\overline{\mathbb{D}}_N:=\{ z \in \mathbb{C}^N : |z| \le 1\}\$ und \$F(x,y):= g(x+iy) \overline{h(x+iy)}\$, \$x,y \in \mathbb{R}^N\$. Dann gilt: \$\$ \limsup_{n \to \infty} \sqrt[n]{E_n ( \overline{\mathbb{D}}_N,F)} = \frac{1}{\rho}\$\$ genau dann, wenn \$g,h\$ auf \${\mathbb{D}}_{N,\rho}:= \{ z \in \mathbb{C}^N : |z| < \rho \}\$ holomorph sind, und mindestens eine der zwei Funktionen \$g,h\$ auf keinem echt gr\"o\3eren Ball als \$\mathbb{D}_{N,\rho}\$ holomorph fortsetzbar ist. Hierbei bezeichnet \$\$ E_n ( \overline{\mathbb{D}}_N,F)= \inf \{ ||F -P_n||_{\overline{\mathbb{D}}_N}, \, P_n: \mathbb{R}^{2N} \to \mathbb{C} \mbox{ Polynom vom Grad } \le n \}.\$\$ \$[\$Bra01\$]\$ Braess, D., {\it Note on the Approximation of Powers of the Distance in Two-Dimensional Domains}, Constructive Approximation (2001), {\bf 17} No. 1, 147-151. \\ \$[\$Sic62\$]\$ Siciak, J., {\it On some extremal functions and their applications in the theory of analytic functions of several complex variables}, Trans. Amer. Math. Soc. (1962), {\bf 105}, 322--357. \\ \$[\$Sic81\$]\$ Siciak, J., {\it Extremal plurisubharmonic functions in \$\mathbb{C}^N\$}, Ann. Pol. Math. (1981), {\bf 39}, 175--211.},
  subject      = {Reelle Funktion},
  language  = {de}
}
@phdthesis{Seider2004,
  author    = {Seider, David},
  title     = {Solving an eigenvalue problem in laser simulation},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-10057},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {In this thesis a new and powerful approach for modeling laser cavity eigenmodes is presented. This approach is based on an eigenvalue problem for singularly perturbed partial differential operators with complex coefficients; such operators have not been investigated in detail until now. The eigenvalue problem is discretized by finite elements, and convergence of the approximate solution is proved by using an abstract convergence theory also developed in this dissertation. This theory for the convergence of an approximate solution of a (quadratic) eigenvalue problem, which particularly can be applied to a finite element discretization, is interesting on its own, since the ideas can conceivably be used to handle equations with a more complex nonlinearity. The discretized eigenvalue problem essentially is solved by preconditioned GMRES, where the preconditioner is constructed according to the underlying physics of the problem. The power and correctness of the new approach for computing laser cavity eigenmodes is clearly demonstrated by successfully simulating a variety of different cavity configurations. The thesis is organized as follows: Chapter 1 contains a short overview on solving the so-called Helmholtz equation with the help of finite elements. The main part of Chapter 2 is dedicated to the analysis of a one-dimensional model problem containing the main idea of a new model for laser cavity eigenmodes which is derived in detail in Chapter 3. Chapter 4 comprises a convergence theory for the approximate solution of quadratic eigenvalue problems. In Chapter 5, a stabilized finite element discretization of the new model is described and its convergence is proved by applying the theory of Chapter 4. Chapter 6 contains computational aspects of solving the resulting system of equations and, finally, Chapter 7 presents numerical results for various configurations, demonstrating the practical relevance of our new approach.},
  subject      = {Laser},
  language  = {en}
}
@phdthesis{Kleinsteuber2005,
  author    = {Kleinsteuber, Martin},
  title     = {Jacobi-type methods on semisimple Lie algebras : a Lie algebraic approach to numerical linear algebra},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-16454},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {Es wird eine Lie-algebraische Verallgemeinerung sowohl des klassischen als auch des Sortier-Jacobi-Verfahrens f{\"u}r das symmetrische Eigenwertproblem behandelt. Der koordinatenfreie Zugang erm{\"o}glicht durch eine neue Betrachtungsweise die Vereinheitlichung strukturierter Eigen- und Singul{\"a}rwertprobleme, darunter bis dato noch nicht betrachtete F{\"a}lle. F{\"u}r beide Verfahren wird lokal quadratische Konvergenz, sowohl f{\"u}r den regul{\"a}ren als auch f{\"u}r den irregul{\"a}ren Fall, gezeigt. Die Analyse und Verallgemeinerung der sog. speziellen Sweeps f{\"u}r das symmetrische Eigenwertproblem f{\"u}hrt zu neuen Sweep-Methoden f{\"u}r strukturierte Eigen- und Singul{\"a}rwertprobleme, die ein besseres Konvergenzverhalten als die bisher bekannten aufweisen.},
  subject      = {Eigenwert},
  language  = {en}
}
@book{FalkMarohnMicheletal.2006,
  author    = {Falk, Michael and Marohn, Frank and Michel, Ren{\´e} and Hofmann, Daniel and Macke, Maria and Tewes, Bernward and Dinges, Peter},
  title     = {A First Course on Time Series Analysis : Examples with SAS},
  organization    = {Universit{\"a}t W{\"u}rzburg / Lehrstuhl f{\"u}r Statistik},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-16919},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License.},
  subject      = {Zeitreihenanalyse},
  language  = {en}
}
@phdthesis{Lageman2007,
  author    = {Lageman, Christian},
  title     = {Convergence of gradient-like dynamical systems and optimization algorithms},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-23948},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {This work studies the convergence of trajectories of gradient-like systems. In the first part of this work continuous-time gradient-like systems are examined. Results on the convergence of integral curves of gradient systems to single points of Lojasiewicz and Kurdyka are extended to a class of gradient-like vector fields and gradient-like differential inclusions. In the second part of this work discrete-time gradient-like optimization methods on manifolds are studied. Methods for smooth and for nonsmooth optimization problems are considered. For these methods some convergence results are proven. Additionally the optimization methods for nonsmooth cost functions are applied to sphere packing problems on adjoint orbits.},
  subject      = {Dynamisches System},
  language  = {en}
}
@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}
}