Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Title
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The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions.
(20120621)This dissertation is devoted to the study of certain analytic problems inspired by recent results in the theory of Toeplitz operators on the Bergman spaces. We attack the problem of commuting Toeplitz operators with ... 
The BarbanDavenportHalberstam for tuples of kfree numbers
(20201023)An asymptotic formula for variance of tuples of kfree numbers in arithmetic progressions 
The Capitulation Problem in Class Field Theory
(20120410)We develop Chevalley's Theorem and interesting implications. Revisiting Galois Cohomology we analyse the structure of the capitulation kernel. Moreover investigate the growth of ideal classes and consequences of a ... 
The contact process in an evolving random environment
(20211126)Recently, there has been an increasing interest in interacting particle systems on evolving random graphs, respectively in time evolving random environments. In this thesis a contact process in a time evolving edge random ... 
The distribution of rational points on some projective varieties
(20200109)This thesis is concerned with establishing Manin's conjecture on the distribution of ratinal points for a certain class of bihomogeneous varieties. It generalizes work of Vaughan on the representation of integers as sum ... 
The Empirical Hierarchical Bayes Approach for Pathway Integration and GeneEnvironment Interactions in GenomeWide Association Studies
(20121024)Complex diseases such as cancer result from a complicated interplay of multiple genetic and environmental factors. To unveil their genetic component, the simple analysis of singlenucleotide polymorphisms (SNP) as done in ... 
The Generalized Operator Based Prony Method
(20190510)The well known Prony method was introduced to reconstruct finite linear combinations of complex exponentials. A first approach towards generalizing this method to more arbitrary expansions was made by Peter & Plonka in ... 
The Geometry of the Milnor Number
(20120612)In the first part of this thesis we derive a volumepreserving normal form for function germs in n complex variables which are right equivalent to the product of all coordinates. In the second part of the thesis we discuss ... 
The Index Bundle for GapContinuous Families, MorseType Index Theorems and Bifurcation
(20111121)We generalise the well known index bundle construction of Atiyah and Jänich to families of (generally unbounded) Fredholm operators which are assumed to be continuous with respect to the ... 
The integration of different functional and structural plant models
(20190709)Plant scientists use Functional and Structural Plant (FSP) Models to model the interactions between the biological functions and physical structures within a limited spacetime range. To break through the limitation, an ... 
The Integration of the Brain Bank Imaging Workflow into the Infrastructure of the Multiple Sclerosis Research Network
(20190326)Digital pathology (DP) provides powerful tools for the acquisition, management, storage, viewing, and analysis of highresolution digital microscope images. During the last decade, DP tools were increasingly used for a ... 
The InterDomain Key Exchange Protocol
(20060227)This thesis introduces, specifies and evaluates a novel key establishment mechanism to enable seamless authenticated handovers in IP networks called InterDomain Key Exchange Protocol (IDKE). ... 
The Likelihood Ratio Test for Order Restricted Hypotheses in NonInferiority Trials
(20031016)In clinical investigations with the goal to evaluate new therapies, the efficacy of a new therapy is usually declared by its superiority over a palcebo or standard. In the last decade new approaches became popular focussing ... 
The M2X Economy – Concepts for Business Interactions, Transactions and Collaborations Among Autonomous Smart Devices
(20200107)Nowadays, business transactions almost exclusively focus on humantohuman transactions. The persistent growth and expansion of the Internet of Things, the ubiquitousness of so called smart devices, as well as progressing ... 
The MinkowskiSiegel Formula for quadratic bundles on curves
(20070926)The subject of this thesis is the arithmetic theory of quadratic forms in the language of algebraic geometry. The main goal is to formulate and prove the MinkowskiSiegel formula for definite ... 
The Optimization of the 3d Structure of Plants, Using FunctionalStructural Plant Models
(20151203)One component of the performance of plants is their capability to intercept light. By using a functionalstructural modelling approach, an optimization model of the 3d aboveground structure of plants is constructed, ... 
The Quintic Gauss Sums
(20040914)We investigate the possibility of generalization of the CasselMcGettrick formula for the quintic Gauss sums. We construct a fundamental region for the fifth cyclotomic field. we describe ... 
The shifted convolution of generalized divisor functions
(20170418)We prove an asymptotic formula for the shifted convolution of the divisor functions \(d_k(n)\) and \(d(n)\) with \(k \geq 3\), which is uniform in the shift parameter and which has a power saving error term. Along the way, ... 
The Spectra on Lie Groups and Its Application to twisted L2Invariants
(20240229)We computed spectra of various $G$invariant differential operators on the universal cover of 2x2 unimodular groups. This was achieved by applying tools from harmonic analysis/representation theory to corresponding groups. ... 
The split prime μconjecture and further topics in Iwasawa theory
(20190325)The thesis is divided in three independent chapters, each focused on a different problem in Iwasawa theory. In Chapter 1 we prove the split prime μconjecture for abelian extensions of imaginary quadratic fields. In Chapter ...