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Dissertation
Free Resolutions from Involutive Bases
(2016-11-02)
We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the ...
Dissertation
1.55 μm Quantum Dot Lasers for Telecommunication
(2019)
The thesis at hand investigates the suitability of quantum dot (QD) material for use in long-distance coherent communication. The thesis was written in the frame of the SASER project MONOLOP that is aiming for a compact, monolithically integrated light source with a tunable wavelength covering the C+-band and narrow spectral linewidth below 500 kHz.
The thesis reviews the theoretical background of quantum dot material based on the InP material system and distributed feedback (DFB) lasers with lateral gratings as ...
Dissertation
Optimal Control of Quantum Information Tasks in Open Quantum Systems
(2020-07-30)
Every quantum system inevitably interacts with its environment. This is a fundamental requirement that allows us to control, measure and, in general, interact with quantum systems. In that respect, a quantum system's openness can be interpreted as prerequisite that enables quantum technologies in the first place. The latter are built to harness the intrinsic quantum mechanical behavior of quantum devices in order to build new, powerful technologies. However, a quantum system's openness also causes it to interact ...
Dissertation
Rethinking the genus Hyphodontia s.l. (Hymenochaetales, Basidiomycota) – investigations on a worldwide scope including new taxonomy, phylogeny, and identification keys
(2018-12)
The dissertation “Rethinking the genus Hyphodontia s.l. (Hymenochaetales, Basidiomycota) – investigations on a worldwide scope including new taxonomy, phylogeny, and identification keys” was elaborated by Janett Riebesehl in the Department of Ecology at the University of Kassel.
Changing the classification system of the fungal genus Hyphodontia s.l. to treat the species from the broad Hyphodontia s.l. concept by a division into other genera was continued. Hjortstam and Ryvarden (2002, 2009) began the concept, but ...
Dissertation
Development of Carrier-Envelope-Phase-Stabilized, mJ-Class Laser Sources Generating Intense, Few-Cycle Laser Pulses
(2020-05-19)
Over a decade ago the frontiers of ultrashort physics and nonlinear optics have reached the attosecond timescale ($1 as = 10 ^ {-18} s$) . Currently, in order to generate isolated attosecond pulses, an intense femtosecond pulse is focused in a jet of a noble gas. Given the sufficient intensity, this leads to high harmonic generation (HHG), which can be filtered (gated) to create a single isolated attosecond pulse. The laser source for the driver pulses has to fulfill two requirements: the pulses need to be limited ...
Dissertation
Ferrocen-basierte N-heterocyclische Tetrylene mit tertiären Alkylsubstituenten an den Stickstoff-Atomen
(2020)
In 2009, our group published two stable N-heterocyclic carbenes (NHCs) with a 1,1'-ferrocenediyl backbone (fc), which formally exhibit a six-membered FeIIC2N2CII-heterocycle. The stabilization of the fcNHCs is favored by bulky N-substituents. So far neopentyl and 2-adamantyl have been used for this purpose - a bulky primary and secondary alkyl substituent. In contrast to other cyclic diaminocarbenes, the fcNHCs are capable of activating small molecules such as NH3 or CO. The reason for this remarkable ability is the ...
Dissertation
Power Series Representations of Hypergeometric Type and Non-Holonomic Functions in Computer Algebra
(2020-06-10)
A Laurent-Puiseux series
$$ \sum\limits_{n = n_0}^{\infty }{a_n (z - z_0)^{n/k} (a_n \in K, k \in ℕ, n_0 \in ℤ ) } \quad (1) $$
where $ k $ denotes the corresponding Puiseux number and $ K $ an infinite computable field - mostly $ K= ℚ(α_1,\ldots,α_n) $ : a field of rational functions in several variables, is mainly characterized by the general coefficient. We consider the case where an is a term of an m-fold hypergeometric sequence.
That is $ a_{n+m} = r(n) a_n $ for all sufficiently large integers $ n, r(n) $ ...
Dissertation
Berücksichtigung von Studierendenvorstellungen zum Thema Gehirn und Lernen in der Lehrkräfteausbildung Biologie
(2019-11)
Lehrer*innenbildung hat das Ziel, Studierende zu Fachleuten für das Lehren und Lernen auszubilden. Zahlreiche empirische Studien zeigen jedoch sowohl bei angehenden als auch praktizierenden Lehrkräften eine hohe Verbreitung von Fehlvorstellungen zum Thema Gehirn und Lernen – sogenannte Neuromythen. Für Biologielehrkräfte ist das Thema Gehirn und Lernen auch als Unterrichtsinhalt relevant. Sie unterrichten Themen wie Bau und Funktion des Gehirns oder Langzeitpotenzierung. Demnach ist es besonders wichtig, dass sie ...
Dissertation
Quantum optimal control theory of photoelectron spectroscopy
(2018)
The object of this doctoral thesis is two-fold and can be classified into two, but intrinsically related categories: (i) development of theoretical models for the simulation of electron dynamics and in parallel to this, (ii) method development of efficient numerical algorithms for ad hoc control of photoelectron and photoion-related observables. The first category primarily focuses on the development of a variety of theoretical models describing the interaction of light and matter for the extraction and control of ...
Dissertation
Automatic computation of continued fraction representations as solutions of explicit differential equations
(2019)
The main focus of this thesis is to present a variation of an algorithm first presented by Maulat and Salvy, with which it is possible to algorithmically guess as well as prove continued fraction expansions of analytical expressions with the help of ordinary differential equations.