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Now showing items 211-220 of 221
Dissertation
Lösungen linearer Polynomgleichungen in Funktionenkörpern und Uniformisierbarkeit von t-Moduln
(2018)
Bei abelschen t-Moduln über Funktionenkörpern, denen der Ring F_q[t] zugrunde liegt, spielt die Frage der Uniformisierbarkeit eine wichtige Rolle. In dieser Arbeit werden t-Moduln betrachtet, die durch
t = τ^2 + A τ+ θ
gegeben sind, wobei τ den q-Frobenius-Endomorphismus bezeichnet, A eine (d x d)-Matrix mit d = 2 ist und θ eine Unbestimmte über F_q ist, die als Skalar (der t entspricht) im Funktionenkörper F_q(( 1/θ )) aufgefasst wird.
Nach einem Satz von Anderson aus der grundlegenden Arbeit “t-motives” (1986) ...
Dissertation
Symmetrien von Differentialgleichungen via Vessiot-Theorie
(2021-04)
Die übliche Definition des Symmetriebegriffs einer Differentialgleichung lautet wie folgt: Symmetrien sind Transformationen, die Lösungen wieder in Lösungen überführen. Modelliert man Differentialgleichungen als Untermannigfaltigkeiten eines Jetbündels, so lassen sich zwei Arten von Symmetrien unterscheiden: innere und äußere. Der erste Fall entspricht einer Transformation, die ausschließlich auf der Differentialgleichung definiert ist. Im zweiten Fall ist die betrachtete Transformation auf dem gesamten umgebenden ...
Preprint
Numerical Methods for Non-Stationary Stokes Flow
(2008)
We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, ...
Dissertation
Root parametrized differential equations
(2012-10-17)
The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.
In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear ...
Dissertation
On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials
(2014-07-16)
In this work, we have mainly achieved the following:
1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved;
2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization ...
Dissertation
Positive und konservative Verfahren höherer Ordnung
(2010-03-17)
In der Anwendung treten häufig Differentialgleichungssysteme auf, deren Komponenten über das Lösen mit einer vorgegeben Genauigkeit hinaus Anforderungen an die, zur Näherung verwendeten, numerischen Verfahren stellen. Die Arbeit widmet sich hierbei den beiden Forderungen
1. Erhaltung der Positivität aller positiven Größen (z.B. Massen, Konzentrationen, Energie) und
2. Erhaltung der Masse in abgeschlossenen Systemen.
Ausgehend von einem komplexen ökologischen 2D Modell zur Beschreibung von Algendynamiken in flachen ...
Dissertation
Generation Human Body Motion by the Centralized Networks
(2023)
The main goal of the thesis is to describe and study reduced models for efficient simulations of human body motions (HBM). To this end, we propose new coupled oscillator models, which are networks of dynamically coupled elements. These networks consist of a few of centers and many satellites. The centers evolve in time as periodical oscillators with different frequencies. The satellite states are defined via center states by a radial basis function (RBF) networks. To simulate different motions we adjust the parameter ...
Dissertation
On the analysis of path-dependent functionals of stochastic PDEs
(2023)
Weak approximation methods for stochastic partial differential equations (SPDEs) are concerned with approximating the probability distribution of the solution process rather than the realizations of the solution process itself. In this thesis, we provide new results and methods concerning the weak error analysis of numerical approximations of path-dependent functionals of solution processes of SPDEs. Two separate approaches to analyzing weak approximation errors are considered: the Itô calculus approach and the ...
Dissertation
Existence and Asymptotic Behavior of Solutions to the Time-Periodic Navier-Stokes Equations in a Layer Domain with Nonhomogeneous Boundary Data
(2024)
This dissertation is dedicated to the analysis of the Navier-Stokes equations in a timeperiodic framework in the so-called layer domain Π = R2 × (0, 1), described by:
∂tu − νΔu + (u · ∇)u + ∇p = f in [0, T] × Π,
div u = 0 in [0, T] × Π,
u|∂Π = a for all t ∈ [0, T] ,
u|t=0 = u|t=T in Π.
The velocity field u and the pressure p are unknowns, while the external force f is prescribed. Challenges arise due to unboundedness of the layer Π and from introduction of a nonhomogeneous boundary condition a. The investigated ...
Habilitation
Twin Basic Quantum Calculus and its Applications
(2024)
We give in this work some results on twin basic quantum calculus. The (p,q)-derivative, the (p,q)-integral and some (p,q)-Taylor formula are discussed. Next, we introduce and provide several results about (p,q)-Gamma and (p,q)-Beta functions. Some (p,q)-Sturm Liouville problems are introduced and some (p,q)-hypergeometric solutions are obtained. The work ends with the introduction (p,q)-Appell polynomials and some (p,q)-Laplace transforms.