@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}
}