@book{FalkMarohnMicheletal.2011,
  author    = {Falk, Michael and Marohn, Frank and Michel, Ren{\´e} and Hofmann, Daniel and Macke, Maria and Tewes, Bernward and Dinges, Peter and Spachmann, Christoph and Englert, Stefan},
  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-56489},
  publisher      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2011},
  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. 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 three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 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. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License.},
  subject      = {Zeitreihenanalyse},
  language  = {en}
}
@phdthesis{Buchholzer2011,
  author    = {Buchholzer, Hannes},
  title     = {The Semismooth Newton Method for the Solution of Reactive Transport Problems Including Mineral Precipitation-Dissolution Reactions},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-65342},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2011},
  abstract  = {In dieser Arbeit befassen wir uns mit einem reaktiven Transportmodell mit Niederschlags-Aufl{\"o}sung Reaktionen das aus den Geowissenschaften stammt. Es besteht aus PDGs, gew{\"o}hnlichen Differentialgleichungen, algebraischen Gleichungen und Komplementarit{\"a}tsbedingungen. Nach Diskretisation dieses Modells erhalten wir eine großes nichtlineares und nichtglattes Gleichungssystem. Wir l{\"o}sen dieses System mit der semismoothen Newtonverfahren, das von Qi und Sun eingef{\"u}hrt wurde. Der Fokus dieser Arbeit ist in der Anwendung und Konvergenz dieses Algorithmus. Wir zeigen, dass dieser Algorithmus f{\"u}r dieses Problem wohldefiniert ist und sogar lokal quadratisch konvergiert gegen eine BD-regul{\"a}re L{\"o}sung. Wir befassen uns auch mit den dabei entstehenden linearen Gleichungssystemen, die sehr groß und d{\"u}nn besetzt sind, und wie sie effizient gel{\"o}st werden k{\"o}nnen. Ein wichtiger Bestandteil dieser Untersuchung ist die Beschr{\"a}nktheit einer gewissen matrixwertigen Funktion, die in einem eigenen Kapitel gezeigt wird. Als Seitenbetrachtung untersuchen wir wie die extremalen Eigenwerte (und Singul{\"a}rwerte) von gewissen PDE-Operatoren, welche in unserem diskretisierten Modell vorkommen, genau abgesch{\"a}tzt werden k{\"o}nnen.},
  subject      = {Komplementarit{\"a}tsproblem},
  language  = {en}
}
@phdthesis{Schwartz2011,
  author    = {Schwartz, Alexandra},
  title     = {Mathematical Programs with Complementarity Constraints: Theory, Methods and Applications},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-64891},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2011},
  abstract  = {The subject of this thesis are mathematical programs with complementarity conditions (MPCC). At first, an economic example of this problem class is analyzed, the problem of effort maximization in asymmetric n-person contest games. While an analytical solution for this special problem could be derived, this is not possible in general for MPCCs. Therefore, optimality conditions which might be used for numerical approaches where considered next. More precisely, a Fritz-John result for MPCCs with stronger properties than those known so far was derived together with some new constraint qualifications and subsequently used to prove an exact penalty result. Finally, to solve MPCCs numerically, the so called relaxation approach was used. Besides improving the results for existing relaxation methods, a new relaxation with strong convergence properties was suggested and a numerical comparison of all methods based on the MacMPEC collection conducted.},
  subject      = {Zwei-Ebenen-Optimierung},
  language  = {en}
}
@article{BallesterBolinchesBeidlemanHeinekenetal.2010,
  author    = {Ballester-Bolinches, A. and Beidleman, J. C. and Heineken, H. and Pedraza-Aguilera, M. C.},
  title     = {Local Classes and Pairwise Mutually Permutable Products of Finite Groups},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68062},
  year      = {2010},
  abstract  = {The main aim of the paper is to present some results about products of pairwise mutually permutable subgroups and local classes.},
  subject      = {Mathematik},
  language  = {en}
}
@article{FerranteWimmer2010,
  author    = {Ferrante, Augusto and Wimmer, Harald K.},
  title     = {Reachability matrices and cyclic matrices},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68074},
  year      = {2010},
  abstract  = {We study reachability matrices R(A, b) = [b,Ab, . . . ,An-1b], where A is an n × n matrix over a field K and b is in Kn. We characterize those matrices that are reachability matrices for some pair (A, b). In the case of a cyclic matrix A and an n-vector of indeterminates x, we derive a factorization of the polynomial det(R(A, x)).},
  subject      = {Mathematik},
  language  = {en}
}
@phdthesis{Zhai2010,
  author    = {Zhai, Xiaomin},
  title     = {Design, Development and Evaluation of a Virtual Classroom and Teaching Contents for Bernoulli Stochastics},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-56106},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {This thesis is devoted to Bernoulli Stochastics, which was initiated by Jakob Bernoulli more than 300 years ago by his master piece 'Ars conjectandi', which can be translated as 'Science of Prediction'. Thus, Jakob Bernoulli's Stochastics focus on prediction in contrast to the later emerging disciplines probability theory, statistics and mathematical statistics. Only recently Jakob Bernoulli's focus was taken up von Collani, who developed a unified theory of uncertainty aiming at making reliable and accurate predictions. In this thesis, teaching material as well as a virtual classroom are developed for fostering ideas and techniques initiated by Jakob Bernoulli and elaborated by Elart von Collani. The thesis is part of an extensively construed project called 'Stochastikon' aiming at introducing Bernoulli Stochastics as a unified science of prediction and measurement under uncertainty. This ambitious aim shall be reached by the development of an internet-based comprehensive system offering the science of Bernoulli Stochastics on any level of application. So far it is planned that the 'Stochastikon' system (http://www.stochastikon.com/) will consist of five subsystems. Two of them are developed and introduced in this thesis. The first one is the e-learning programme 'Stochastikon Magister' and the second one 'Stochastikon Graphics' that provides the entire Stochastikon system with graphical illustrations. E-learning is the outcome of merging education and internet techniques. E-learning is characterized by the facts that teaching and learning are independent of place and time and of the availability of specially trained teachers. Knowledge offering as well as knowledge transferring are realized by using modern information technologies. Nowadays more and more e-learning environments are based on the internet as the primary tool for communication and presentation. E-learning presentation tools are for instance text-files, pictures, graphics, audio and videos, which can be networked with each other. There could be no limit as to the access to teaching contents. Moreover, the students can adapt the speed of learning to their individual abilities. E-learning is particularly appropriate for newly arising scientific and technical disciplines, which generally cannot be presented by traditional learning methods sufficiently well, because neither trained teachers nor textbooks are available. The first part of this dissertation introduces the state of the art of e-learning in statistics, since statistics and Bernoulli Stochastics are both based on probability theory and exhibit many similar features. Since Stochastikon Magister is the first e-learning programme for Bernoulli Stochastics, the educational statistics systems is selected for the purpose of comparison and evaluation. This makes sense as both disciplines are an attempt to handle uncertainty and use methods that often can be directly compared. The second part of this dissertation is devoted to Bernoulli Stochastics. This part aims at outlining the content of two courses, which have been developed for the anticipated e-learning programme Stochastikon Magister in order to show the difficulties in teaching, understanding and applying Bernoulli Stochastics. The third part discusses the realization of the e-learning programme Stochastikon Magister, its design and implementation, which aims at offering a systematic learning of principles and techniques developed in Bernoulli Stochastics. The resulting e-learning programme differs from the commonly developed e-learning programmes as it is an attempt to provide a virtual classroom that simulates all the functions of real classroom teaching. This is in general not necessary, since most of the e-learning programmes aim at supporting existing classroom teaching. The forth part presents two empirical evaluations of Stochastikon Magister. The evaluations are performed by means of comparisons between traditional classroom learning in statistics and e-learning of Bernoulli Stochastics. The aim is to assess the usability and learnability of Stochastikon Magister. Finally, the fifth part of this dissertation is added as an appendix. It refers to Stochastikon Graphics, the fifth component of the entire Stochastikon system. Stochastikon Graphics provides the other components with graphical representations of concepts, procedures and results obtained or used in the framework of Bernoulli Stochastics. The primary aim of this thesis is the development of an appropriate software for the anticipated e-learning environment meant for Bernoulli Stochastics, while the preparation of the necessary teaching material constitutes only a secondary aim used for demonstrating the functionality of the e-learning platform and the scientific novelty of Bernoulli Stochastics. To this end, a first version of two teaching courses are developed, implemented and offered on-line in order to collect practical experiences. The two courses, which were developed as part of this projects are submitted as a supplement to this dissertation. For the time being the first experience with the e-learning programme Stochastikon Magister has been made. Students of different faculties of the University of W{\"u}rzburg, as well as researchers and engineers, who are involved in the Stochastikon project have obtained access to Stochastikon Magister via internet. They have registered for Stochastikon Magister and participated in the course programme. This thesis reports on two assessments of these first experiences and the results will lead to further improvements with respect to content and organization of Stochastikon Magister.},
  subject      = {Moment <Stochastik>},
  language  = {en}
}
@techreport{Englert2009,
  author    = {Englert, Stefan},
  title     = {Mathematica in 15 Minuten (Mathematica Version 6.0)},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-70275},
  year      = {2009},
  abstract  = {Mathematica ist ein hervorragendes Programm um mathematische Berechnungen - auch sehr komplexe - auf relativ einfache Art und Weise durchf{\"u}hren zu lassen. Dieses Skript soll eine wirklich kurze Einf{\"u}hrung in Mathematica geben und als Nachschlagewerk einiger g{\"a}ngiger Anwendungen von Mathematica dienen. Dabei wird folgende Grobgliederung verwendet: - Grundlagen: Graphische Oberfl{\"a}che, einfache Berechnungen, Formeleingabe - Bedienung: Vorstellung einiger Kommandos und Einblick in die Funktionsweise - Praxis: Beispielhafte Berechnung einiger Abitur- und {\"U}bungsaufgaben},
  subject      = {Anwendungssoftware},
  language  = {de}
}
@misc{Englert2009,
  type      = {Master Thesis},
  author    = {Englert, Stefan},
  title     = {Sch{\"a}tzer des Artenreichtums bei speziellen Erscheinungsh{\"a}ufigkeiten},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-71362},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {Bei vielen Fragestellungen, in denen sich eine Grundgesamtheit in verschiedene Klassen unterteilt, ist weniger die relative Klassengr{\"o}ße als vielmehr die Anzahl der Klassen von Bedeutung. So interessiert sich beispielsweise der Biologe daf{\"u}r, wie viele Spezien einer Gattung es gibt, der Numismatiker daf{\"u}r, wie viele M{\"u}nzen oder M{\"u}nzpr{\"a}gest{\"a}tten es in einer Epoche gab, der Informatiker daf{\"u}r, wie viele unterschiedlichen Eintr{\"a}ge es in einer sehr großen Datenbank gibt, der Programmierer daf{\"u}r, wie viele Fehler eine Software enth{\"a}lt oder der Germanist daf{\"u}r, wie groß der Wortschatz eines Autors war oder ist. Dieser Artenreichtum ist die einfachste und intuitivste Art und Weise eine Population oder Grundgesamtheit zu charakterisieren. Jedoch kann nur in Kollektiven, in denen die Gesamtanzahl der Bestandteile bekannt und relativ klein ist, die Anzahl der verschiedenen Spezien durch Erfassung aller bestimmt werden. In allen anderen F{\"a}llen ist es notwendig die Spezienanzahl durch Sch{\"a}tzungen zu bestimmen.},
  subject      = {Statistik},
  language  = {de}
}
@phdthesis{Hofmann2009,
  author    = {Hofmann, Daniel},
  title     = {Characterization of the D-Norm Corresponding to a Multivariate Extreme Value Distribution},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-41347},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {It is well-known that a multivariate extreme value distribution can be represented via the D-Norm. However not every norm yields a D-Norm. In this thesis a necessary and sufficient condition is given for a norm to define an extreme value distribution. Applications of this theorem includes a new proof for the bivariate case, the Pickands dependence function and the nested logistic model. Furthermore the GPD-Flow is introduced and first insights were given such that if it converges it converges against the copula of complete dependence.},
  subject      = {Kopula <Mathematik>},
  language  = {en}
}
@phdthesis{Hoheisel2009,
  author    = {Hoheisel, Tim},
  title     = {Mathematical Programs with Vanishing Constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-40790},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {A new class of optimization problems name 'mathematical programs with vanishing constraints (MPVCs)' is considered. MPVCs are on the one hand very challenging from a theoretical viewpoint, since standard constraint qualifications such as LICQ, MFCQ, or ACQ are most often violated, and hence, the Karush-Kuhn-Tucker conditions do not provide necessary optimality conditions off-hand. Thus, new CQs and the corresponding optimality conditions are investigated. On the other hand, MPVCs have important applications, e.g., in the field of topology optimization. Therefore, numerical algorithms for the solution of MPVCs are designed, investigated and tested for certain problems from truss-topology-optimization.},
  subject      = {Nichtlineare Optimierung},
  language  = {en}
}
@phdthesis{vonHeusinger2009,
  author    = {von Heusinger, Anna},
  title     = {Numerical Methods for the Solution of the Generalized Nash Equilibrium Problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47662},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {In the generalized Nash equilibrium problem not only the cost function of a player depends on the rival players' decisions, but also his constraints. This thesis presents different iterative methods for the numerical computation of a generalized Nash equilibrium, some of them globally, others locally superlinearly convergent. These methods are based on either reformulations of the generalized Nash equilibrium problem as an optimization problem, or on a fixed point formulation. The key tool for these reformulations is the Nikaido-Isoda function. Numerical results for various problem from the literature are given.},
  subject      = {Spieltheorie},
  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}
}
@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{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{Kurniawan2009,
  author    = {Kurniawan, Indra},
  title     = {Controllability Aspects of the Lindblad-Kossakowski Master Equation : A Lie-Theoretical Approach},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-48815},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {One main task, which is considerably important in many applications in quantum control, is to explore the possibilities of steering a quantum system from an initial state to a target state. This thesis focuses on fundamental control-theoretical issues of quantum dynamics described by the Lindblad-Kossakowski master equation which arises as a bilinear control system on some underlying real vector spaces, e.g controllability aspects and the structure of reachable sets. Based on Lie-algebraic methods from nonlinear control theory, the thesis presents a unified approach to control problems of finite dimensional closed and open quantum systems. In particular, a simplified treatment for controllability of closed quantum systems as well as new accessibility results for open quantum systems are obtained. The main tools to derive the results are the well-known classifications of all matrix Lie groups which act transitively on Grassmann manifolds, and respectively, on real vector spaces without the origin. It is also shown in this thesis that accessibiity of the Lindblad-Kossakowski master equation is a generic property. Moreover, based on the theoretical accessibility results, an algorithm is developed to decide when the Lindblad-Kossakowski master equation is accessible.},
  subject      = {Kontrolltheorie},
  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}
}