@book{Marohn1990, author = {Marohn, Frank}, title = {On statistical information of extreme order statistics}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47866}, publisher = {Universit{\"a}t W{\"u}rzburg}, year = {1990}, abstract = {No abstract available}, subject = {Rangstatistik}, language = {en} } @article{Marohn1991, author = {Marohn, Frank}, title = {Global sufficiency of extreme order statistics in location models of Weibull type}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47874}, year = {1991}, abstract = {In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter -1 < a < 1 the k(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.}, subject = {Extremwertstatistik}, language = {de} } @incollection{FalkMarohn1992, author = {Falk, Michael and Marohn, Frank}, title = {Laws of small numbers : Some applications to conditional curve estimation}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45841}, publisher = {Universit{\"a}t W{\"u}rzburg}, year = {1992}, abstract = {No abstract available}, subject = {Gesetz der kleinen Zahlen}, language = {en} } @article{FalkMarohn1993, author = {Falk, Michael and Marohn, Frank}, title = {Von Mises condition revisited}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45790}, year = {1993}, abstract = {It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.}, language = {en} } @article{FalkMarohn1993, author = {Falk, Michael and Marohn, Frank}, title = {Asymptotically optimal tests for conditional distributions}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45823}, year = {1993}, abstract = {No abstract available}, language = {en} } @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} } @article{JanssenMarohn1994, author = {Janssen, A. and Marohn, Frank}, title = {On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45816}, year = {1994}, abstract = {The aim of the present paper is to clarify the role of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCam's sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is asymptotically Gaussian if, and only if, a fixed number of extremes asymptotically does not contain any information. In other words: A fixed number of extremes asymptotically contains information iff the Poisson part of the limit experiment is non-trivial. Suggested by this result, we propose a new extreme value model given by local alternatives. The local structure is described by introducing the space of extreme value tangents. It turns out that under local alternatives a new class of extreme value distributions appears as limit distributions. Moreover, explicit representations of the Poisson limit experiments via Poisson point processes are found. As a concrete example nonparametric tests for Frechet type distributions against stochastically larger alternatives are treated. We find asymptotically optimal tests within certain threshold models.}, language = {en} } @inproceedings{Marohn1994, author = {Marohn, Frank}, title = {On testing the exponential and Gumbel distribution}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45804}, year = {1994}, abstract = {No abstract available}, subject = {Gumbel-Verteilung}, language = {en} } @article{Marohn1994, author = {Marohn, Frank}, title = {Asymptotic sufficiency of order statistics for almost regular Weibull type densities}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45837}, year = {1994}, abstract = {Consider a location family which is defined via a Weibull type density having shape parameter a = 1. We treat the problem, which portion of the order statistics is asymptotically sufficient. It turns out that the intermediate order statistics are relevant.}, 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{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{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{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{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} } @phdthesis{Preiss2002, author = {Preiß, Martin}, title = {Analytizit{\"a}tseigenschaften gewichteter zentraler Pfade bei monotonen Komplementarit{\"a}tsproblemen und ihre Ausnutzung}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-3969}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2002}, abstract = {Die vorliegende Arbeit untersucht die Analytizit{\"a}tseigenschaften unzul{\"a}ssiger Innerer-Punkte Pfade bei monotonen Komplementarit{\"a}tsproblemen und diskutiert m{\"o}gliche algorithmische Anwendungen. In Kapitel 2 werden einige matrixanalytische Konzepte und Resultate zusammengestellt, die f{\"u}r die Beweisf{\"u}hrung in den folgenden Kapiteln ben{\"o}tigt werden. Kapitel 3 gibt eine genaue Definition der Begriffe "monotones lineares Komplementarit{\"a}tsproblem" (LCP) bzw. "semidefinites monotones lineares Komplementarit{\"a}tsproblem" (SDLCP) und zeigt die Grundidee hinter den Innere-Punkte-Verfahren zur L{\"o}sung solcher Probleme. Kapitel 4 beinhaltet die analytischen Hauptresultate f{\"u}r monotone Komplementarit{\"a}tsprobleme. In Abschnitt 4.1 werden einige wohlbekannte Resultate {\"u}ber die Analytizit{\"a}tseigenschaften unzul{\"a}ssiger Innerer-Punkte-Pfade f{\"u}r LCP's wiedergegeben. Diese werden in Abschnitt 4.2 auf den semidefiniten Fall {\"u}bertragen. Unter der Annahme, dass das zugrundeliegende SDLCP eine strikt komplement{\"a}re L{\"o}sung besitzt, wird gezeigt, dass die Inneren-Punkte-Pfade sogar noch im Randpunkt analytisch sind. Kapitel 5 benutzt die Resultate aus Kapitel 4, um die lokal hohe Konvergenzordnung einer Langschrittmethode zur L{\"o}sung von SDLCP's zu zeigen. Kapitel 6 f{\"u}hrt eine neue Methode zur L{\"o}sung von LCP's und SDLCP's mit Hilfe von Inneren-Punkte-Techniken ein. Dabei werden die Pfadfunktionen derart gew{\"a}hlt, dass alle Iterierten auf unzul{\"a}ssigen zentralen Pfaden liegen. Es wird globale und lokale Konvergenz des Verfahrens bewiesen.}, subject = {Innere-Punkte-Methode}, language = {de} } @phdthesis{BletzSiebert2002, author = {Bletz-Siebert, Oliver}, title = {Homogeneous spaces with the cohomology of sphere products and compact quadrangles}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-3994}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2002}, abstract = {We consider homogeneous spaces G/H with the same rational homotopy as a product of a 1-sphere and a (m+1)-sphere. We show that these spaces have also the rational cohomology of such a sphere product if H is connected and if the quotient has dimension m+2. Furthermore, we prove that if additionally the fundamental group of G/H is cyclic, then G/H is locally a product of a 1-torus and ofA/H, where A/H is a simply connected rational cohomology (m+1)-sphere (and hence classified). If H fails to be connected, then with U as the connected component of H the G-action on the covering space G/U of G/H has connected stabilizers, and the results apply to G/U. To show that under the assumptions above every natural number may be realized as the order of the group of connected components of H we calculate the cohomology of certain homogeneous spaces. We also determine the rational cohomology of the fibre bundle U-->G-->G/U if G/H meets the assumptions above. This is done by considering the respective Leray-Serre spectral sequence. The structure of the cohomology of U-->G-->G/U then gives a second proof for the structure of compact connected Lie groups acting transitively on spaces with the rational homotopy of a product of a 1-sphere and a (m+1)-sphere. Since a quotient of a homogeneous space with the same rational homotopy or cohomology as a product of a 1-sphere and a (m+1)-sphere is not simply connected, there often arises the question whether or not a considered fibre bundle or fibration is orientable. A large amount of space will therefore be given to the problem of showing that certain fibrations are orientable. For compact connected (m+2)-manifolds with cyclic fundamental groups and with the rational homotopy of a product of a 1-sphere and a (m+1)-sphere we show the following: if a connected Lie group acts transitively on the manifold, then the maximal compact subgroups are either transitive, or their orbits are simply connected rational cohomology spheres of codimension 1. Homogeneous spaces with the same rational cohomology or homotopy as a a product of a 1-sphere and a (m+1)-sphere play a role in the study of different types of geometrical objects. They appear for example as focal manifolds of isoparametric hypersurfaces with four distinct principal curvatures. Further examples of such spaces are the point spaces and the line spaces of compact connected generalized quadrangles. We determine the isometry groups of isoparametric hypersurfaces with 4 principal curvatures of multiplicities 1 and m which are transitive on the focal manifold with non-trivial fundamental group. Buildings were introduced by Jacques Tits to give interpretations of simple groups of Lie type. They are a far-reaching generalization of projective spaces, in particular a generalization of projective planes. There is another generalization of projective planes called generalized polygons. A projective plane is the same as a generalized triangle. The generalized polygons are also contained in the class of buildings: they are the buildings of rank 2. To compact quadrangles one can assign a pair of natural numbers called the topological parameters of the quadrangles. We treat the case k=1. It turns out that there are no other point-transitive compact connected Lie groups for (1,m)-quadrangles than the ones for the real orthogonal quadrangles. Furthermore, we solve the problem of three infinite series of group actions which Kramer left as open problems; there are no quadrangles with the homogeneous spaces in question as point spaces (up to maybe a finite number of small parameters in one of the three series).}, subject = {Homogener Raum}, language = {en} }