Mathematisch-Naturwissenschaftliche Fakultät: Suche
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Three models of ordinal computability
(2013-05-07)
In this thesis we expand the scope of ordinal computability, i.e., the study of models of computation that are generalized to infinite domains. The discipline sets itself apart from classical work on generalized recursion ...
Energieskalierung, Gebietsverzweigung und SO(2)-Invarianz in einem fest-fest Phasenübergangsproblem
(2013-10-28)
In den frühen 90er Jahren haben Robert Kohn und Stefan Müller ein Modell entwickelt, das Musterbildung in martensitischen Formgedächtnismetallen erklären konnte. In dieser Arbeit wird eine vektorwertige Verallgemeinerung ...
Analytische und p−adische Aspekte von klassischen und Mock-Modulformen
(2013-10-17)
Ausgangsfrage dieser Doktorarbeit war die Gleichverteilung von geschlossenen Geodaetischen im Fundamentalbereich der Modulgruppe in der hyperbolischen Geometrie. Das fuehrt auf das Studium der Eigenfunktionen des ...
Independence in Algebraic Complexity Theory
(2013-12-16)
This thesis examines the concepts of linear and algebraic independence in algebraic complexity theory. Arithmetic circuits, computing multivariate polynomials over a field, form the framework of our complexity considerations. ...
Algebraic Multigrid (AMG) for Saddle Point Systems
(2013-10-11)
We introduce an algebraic multigrid method for the solution of matrices with saddle point structure. Such matrices e.g. arise after discretization of a second order partial differential equation (PDE) subject to linear ...
On the Classification of Cohomology Bott Manifolds
(2013-11-07)
We study cohomology Bott manifolds by means of modified surgery theory. Cohomology Bott manifolds admit a ring isomorphism to the cohomology ring of a Bott manifold which preserves the Pontrjagin and Stiefel-Whitney classes. ...
Proof-checking mathematical texts in controlled natural language
(2013-10-30)
The research conducted for this thesis has been guided by the vision of a computer program that could check the correctness of mathematical proofs written in the language found in mathematical textbooks. Given that reliable ...
Relative singularity categories
(2013-12-05)
In this thesis, we study a new class of triangulated categories associated with singularities of algebraic varieties. For Gorenstein rings, triangulated singularity categories were introduced by Buchweitz. In 2006 Orlov ...
Geometric Structures arising from Partial Differential Equations
(2014-01-14)
We study several geometric problems arising from partial differential equations: (1) the geometry of Laplacian Eigenfunctions on smooth, compact manifolds without boundary (2) the energy landscape of the conservation laws ...
Global Existence Without Decay
(2013-12-05)
We treat some problems related to the small data global existence theory of some dispersive PDEs. That is, we try to abstractly construct solutions which exist globally in time and have “good” properties, under a smallness ...