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Dissertation
Adsorption kinetic investigations of phthalocyanine derivatives self assembled monolayers (SAMs) on gold: Temperature influence on the SAM formation process and quality
(2015-08-12)
The ordered nano-structured surfaces, like self-assembled monolayers (SAMs) are of a great scientific interest, due to the low cost, simplicity, and versatility of this method. SAMs found numerous of applications in molecular electronics, biochemistry and optical devices. Phthalocyanine (Pc) complexes are of particular interest for the SAM preparation. These molecules exhibit fascinating physical properties and are chemically and thermally stable. Moreover their complex structure is advantageous for the fabrication ...
Dissertation
Elimination in Operator Algebras
(2014-08-08)
A large class of special functions are solutions of systems of linear difference and differential equations with polynomial coefficients. For a given function, these equations considered as operator polynomials generate a left ideal in a noncommutative algebra called Ore algebra. This ideal with finitely many conditions characterizes the function uniquely so that Gröbner basis techniques can be applied.
Many problems related to special functions which can be described by such ideals can be solved by performing ...
Dissertation
Ein Algorithmus zur numerischen Verifikation der äquivarianten Tamagawazahlvermutung für eine Familie von Zahlkörpererweiterungen
(2011-04-07)
Sei $N/K$ eine galoissche Zahlkörpererweiterung mit Galoisgruppe $G$, so dass es in $N$ eine Stelle mit voller
Zerlegungsgruppe gibt. Die vorliegende Arbeit beschäftigt sich mit Algorithmen, die für das gegebene Fallbeispiel $N/K$, die äquivariante Tamagawazahlvermutung
von Burns und Flach für das Paar $(h^0(Spec(N), \mathbb{Z}[G]))$ (numerisch) verifizieren.
Grob gesprochen stellt die äquivariante Tamagawazahlvermutung (im Folgenden ETNC) in diesem Spezialfall einen Zusammenhang her zwischen Werten von
Artinschen ...
Preprint
Convergence analysis of time-discretization schemes for rate-independent systems
(2017-12-21)
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is ...
Preprint
Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads
(2019-09-25)
We study a rate-independent system with non-convex energy and in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized BV-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.
Preprint
On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices
(2010)
The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation ...
Preprint
Balanced Viscosity solutions to a rate-independent system for damage
(2017-05-02)
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the ...
Dissertation
Strukturelle und funktionelle Charakterisierung des Dnmt2-Homologs DnmA von Dictyostelium discoideum
(2016-04-08)
In dieser Arbeit wurde die DNA Methyltransferase 2 aus Dictyostelium discoideum strukturell und funktionell untersucht. Sie vermittelt die Methylierung des Cytosin an Position 38 nahe des Anticodons der tRNAAsp (Goll et al., 2006; Müller et al., 2013). Jedoch ist die biologische Funktion dieser Methylierung bis heute nicht hinreichend geklärt.
In der Vergangenheit konnten erhebliche Unterschiede in der in vivo- und in vitro-Methylierungsaktivität von DnmA, dem Dnmt2-Homolog aus D. discoideum, beobachtet werden. So ...
Aufsatz
Controlling the transport of an ion: classical and quantum mechanical solutions
(IOP, 2014)
The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant ...
Aufsatz
A simple retroelement based knock-down system in Dictyostelium
(PLoS, 2015)
Characteristics of DIRS-1 Mediated Knock-Downs __ We have previously shown that the most abundant Dictyostelium discoideum retroelement DIRS-1 is suppressed by RNAi mechanisms. Here we provide evidence that both inverted terminal repeats have strong promoter activity and that bidirectional expression apparently generates a substrate for Dicer. A cassette containing the inverted terminal repeats and a fragment of a gene of interest was sufficient to activate the RNAi response, resulting in the generation of ~21 nt ...