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Showing 1 to 20 of 23 for “"510 Mathematik"”.
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Correlated trajectories in semiclassical approaches to quantum chaos
This thesis is concerned with the application and extension of semiclassical methods, involving correlated trajectories, that were recently developed to explain the observed universal statistics of classically chaotic quantum systems. First we consider systems that depend on an external parameter …
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Konstruktion rationaler Darstellungen endlicher Gruppen
This work developes a new method to construct integral representaions of a finite group G. Starting point are the modular constituents of this representations for a prime p. An algorithm described in this work will construct an approximative representation over the p-adic integers. The construction …
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Some results on degenerate parabolic equations not in divergence form
The present work deals with initial-boundary value problems for second-order quasilinear degenerate parabolic equations not in divergence form. After establishing existence and uniqueness results in the first chapter, in Chapters 2 through 6 more special problems of the above type are investigated …
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Eindeutige Faktoren von Graphen - maximale Kantenzahlen und Extremalgraphen
We are given a set V of vertices and a class of graphs on V. In this paper we examine the following question: What is the maximum number of edges in a graph on V, which contains exactly one graph of the class as a subgraph? What can we say about the corresponding extremal graphs? In this thesis we …
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Numerical schemes and well-posedness in nonlinear aeroelasticity
The panel-flutter-problem is considered to study issues of numerical schemes and well-posedness that appear in aeroelastic models. The question of well-posedness is addressed by a uniqueness theorem. Here the flow is modelled by the compressible Navier-Stokes-equations in Lagrangian coordinates and …
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Functional spaces : a direct approach
In this thesis I define the notion of a functional tensor space, and derive the specific form of the Lie derivative (w.r.t. generalized vector fields) on the constructed spaces, giving them a Lie module structure over the Lie algebra of generalized vector fields. I also construct the Euler complex …
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Homeomorphisms on edges of the Mandelbrot set
Consider the iteration of complex quadratic polynomials. They form a one-parameter family, and the Mandelbrot set is defined as a subset of the parameter plane: it contains those parameters, such that the Julia set of the corresponding polynomial is connected. Homeomorphisms of subsets of the …
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Modular forms for the orthogonal group O(2,5)
This thesis deals with modular forms for orthogonal groups of signature (2,n), n>2, with particular emphasis on the case n=5. First we determine suitable generators and the abelian characters of some orthogonal groups. Then we present a few methods for constructing orthogonal modular forms: by …
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Untersuchungen zu Donovans Vermutung für klassische Gruppen
In 1980, Donovan conjectured that the number of Morita equivalence classes ofblocks of finite groups with prescribed defect group is finite. In this thesisDonovan's conjecture is investigated for classical groups. First, a recenttheorem of Bonnafe and Rouquier is used to reduce Donovan'sconjecture …
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Regular factors in graphs
The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the …
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Unipotente Charaktere und Zerlegungszahlen der endlichen Chevalleygruppen vom Typ F 4
This thesis contributes to the representation theory of finite Chevalleygroups. First we describe algorithms for explicit computation in connected reductive algebraic groups. These algorithms are well adapted to the computation in some finite subgroups, i.e., the finite groups of Lie type and their …
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Antriebs- und Meßtechniken für die Qualifizierung von Teilchenbeschleunigermagneten
Metrology and mechatronics for automated probes used in particle accelerator magnets have to cope with unusual environmental conditions: High magnetic fields, casual vacuum and narrow space. This document discusses instrumentation solutions suited for use in magnetic fields of 8,5 Tesla by the …
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Infinite graphs generated by tree rewriting
Finite graphs and algorithms on finite graphs are an important tool for the verification of finite-state systems. To transfer the methods for finite systems, at least partially, to infinite systems a theory of infinite graphs with finite representations is needed. In this thesis the class of the …
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Charaktertafeln parabolischer Untergruppen der Steinbergschen Trialitätsgruppen und Anwendungen auf deren Darstellungstheorie
The first part of this thesis deals with the character tables of the maximal parabolic subgroups of Steinberg's triality groups. First, an algorithm is presented, based on the Steinberg presentation, for generic computations in finite groups of Lie type and connected reductive algebraic groups. …
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Elementare Wege zur mathematischen Modellbildung : Fallbeispiele aus Biowissenschaften und Chemie
The role of mathematical models in high school education is often restricted to the application of model equations, or to fitting parameters. The modelling process is usually not a focus topic, and rarely the derivation of a model is discussed extensively. In the present thesis, using examples from …
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Die Struktur rotationsinvarianter Paley-Wiener-Räume : mit einer Anwendung auf Abtastprobleme
The Paley-Wiener classes belong to the classical function spaces, which are used to model one and multi-dimensional signals. They consist of functions which are defined on some finite-dimensional real Euclidean space and whose Fourier transforms are supported in a fixed and in general compact …
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Formal computational methods for control theory
This thesis treats structural properties of control systems, e.g. controllability and parametrizability of their behavior, from an algebraic point of view. It contributes the following formal computational methods. Janet's algorithm is extended to Ore algebras which are relevant for system …
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Untersuchungen zu James' Vermutung über Iwahori-Hecke-Algebren vom Typ A
This thesis deals with a conjecture by Gordon James from 1990 and a variant by Meinolf Geck about decomposition maps of the generic Iwahori-Hecke algebra H of the symmetric group on n points arising from specialization to characteristic l>0. If the parameter of the algebra is specialized to an …
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Stabilizability, controllability and optimal strategies of linear and nonlinear dynamical games
In this work we investigate besides the optimal control theory, also dynamic game theory in case of linear and nonlinear differential systems. In Chapter 1 the most important results of the linear control theory are presented, whereby also for some classical statements modified proof and resuming …
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