Mathematisch-Naturwissenschaftliche Fakultät: Suche
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The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation
(2015-03-12)
In this thesis, we discuss numerical methods for the solution of the high-dimensional backward Kolmogorov equation, which arises in the pricing of options on multi-dimensional jump-diffusion processes.
First, we apply ...
First, we apply ...
Untersuchung der Primzahlzählfunktion und verwandter Funktionen
(2015-04-22)
Die Verteilung der Primzahlen ist bekanntlich eng mit den Nullstellen der Riemannschen Zetafunktion verbunden. Insbesondere hat die Riemannsche Vermutung, nach welcher alle nichttrivialen Nullstellen den Realteil 1/2 ...
Counting classes of special polynomials
(2015-04-20)
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gauß count the remaining ones, approximately and exactly.
In two or ...
In two or ...
VLSI Routing for Advanced Technology
(2015-05-05)
Routing is a major step in VLSI design, the design process of complex integrated circuits (commonly known as chips). The basic task in routing is to connect predetermined locations on a chip (pins) with wires which serve ...
Local Smoothing and Well-Posedness Results for KP-II Type Equations
(2015-04-22)
We study two equations of KP-II type: the Kadomtsev-Petviashvili II equation and its cubical generalization (gKP-II)$_{3}$.
In Chapter 3, we discuss the qualitative properties of the Kadomtsev-Petviashvili II equation ...
In Chapter 3, we discuss the qualitative properties of the Kadomtsev-Petviashvili II equation ...
On arithmetic properties of Fuchsian groups and Riemann surfaces
(2015-02-11)
In this thesis, Riemann surfaces and their fundamental groups are studied from an arithmetic point of view. First the image of the absolute Galois group of a number field under Grothendieck's representation with values in ...
Numerical Simulation of Droplets with Dynamic Contact Angles
(2015-02-04)
The numerical simulation of droplet impact is of interest for a vast variety of industrialprocesses, where practical experiments are costly and time-consuming. In these simulations, the dynamic contact angle is a key ...
Homotopy-Theoretic Studies of Khovanov-Rozansky Homology
(2015-07-29)
This dissertation applies homotopy-theoretic methods to the study of Khovanov-Rozansky homology, a generalization of Khovanov homology (which in turn categorifies the Jones polynomial) that is constructed using categories ......
In dieser Dissertation widme ich mich der homotopietheoretischen Untersuchung der Khovanov-Rozansky Homologie, einer 2004 gefundenen Invariante von Knoten und Verschlingungen im Raum. Sie ist eine Verallgemeinerung der ......
In dieser Dissertation widme ich mich der homotopietheoretischen Untersuchung der Khovanov-Rozansky Homologie, einer 2004 gefundenen Invariante von Knoten und Verschlingungen im Raum. Sie ist eine Verallgemeinerung der ......
Linear Inviscid Damping for Monotone Shear Flows, Boundary Effects and Sharp Sobolev Regularity
(2015-07-23)
In this thesis, we study the linear stability and long-time asymptotic behavior of solutions to the 2D incompressible Euler equations, which model the evolution of an inviscid, incompressible fluid.
The Euler equations ...
The Euler equations ...
Stable maps and singular curves on K3 surfaces
(2015-08-05)
This thesis develops and applies the theory of arbitrary genus stable maps to K3 surfaces. In the first application of the theory, we study the loci of smooth curves of genus p-n admitting n-nodal models on K3 surfaces. ...