Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Title
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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 ... 
Theory and Numerics for Shape Optimization in Superconductivity
(20060918)We consider a mathematical model for a thin superconducting film which is magnetically shielded by permanent magnets in order to improve the current carrying capability of the film. In a ... 
Thetafunktionen und konjugationsinvariante Funktionen auf Paaren von Matrizen
(20090116)We express conjugationinvariant functions on the space of equivalence classes of pairs of kxk matrices via theta functions. Our approach is based on the wellknown interplay between algebraic ... 
Topological construction of C*correspondences for groupoid C*algebras
(20150909)Let G and H be locally compact, Hausdor groupoids with Haar systems. We de fine a topological correspondence from G to H to be a GH bispace X carrying a Gquasi invariant and Hinvariant family of measures. We show that ... 
Topological Invariants for NonArchimedean Bornological Algebras
(20201013)In this thesis, we define a cyclic homology theory for nonarchimedean bornological algebras, which we call analytic cyclic homology. Let V be a complete, discrete valuation ring with uniformiser p, residue field k, and ... 
Toward Trustworthiness of Deep Learning Models for 12Lead ECGs
(20240131)A 12lead electrocardiogram (ECG), a common examination tool in cardiology, represents the electrical activity of the heart as waveforms. Predictions and classifications with deep learning (DL) algorithms show great potential ... 
Towards a Lightweight, Secure, and Untraceable RFID Authentication Protocol
(20150911)This dissertation tackles the problem of user privacy and security of transactions in the authentication protocols of the technology of Radiofrequency identification (RFID). Radiofrequency identification is ubiquitously ... 
Towards a Robust and Secure Decentralized Online Social Network
(20150115)The virtually unlimited growth of popular Online Social Networks (OSNs) is often accompanied by severe violations of their users' privacy and intellectual property rights. Both problems are rooted in the centralized ... 
Towards Personalized Cardiac Modeling of Failing Heart with Engineered Heart Muscle
(20240528)This dissertation investigates the biomechanics of the left ventricle across multiple geometric levels toward personalized cardiac modeling with engineered heart muscle. Firstly, a physicsbased model for the EDPVR and ... 
Towards Rigorous AgentBased Modelling
(20150107)Agent or individualbased modelling is a modelling approach where the heterogeneity of entities, i.e. agents, matters. In the past ten to twenty years agentbased models became increasingly popular and were applied in ... 
Tracking and Fusion Methods for Extended Targets Parameterized by Center, Orientation, and Semiaxes
(20220114)The improvements in sensor technology, e.g., the development of automotive Radio Detection and Ranging (RADAR) or Light Detection and Ranging (LIDAR), which are able to provide a higher detail of the sensor’s environment, ... 
Triadic Closure and Its Influence in Social Networks
(20160912)Social triad—a group of three people—is one of the simplest and most fundamental social groups, which serves as the basis of social network analysis. Triadic closure, a closing process of an open triad, is a useful ... 
Twisted equivariant Ktheory and equivariant Tduality
(20230918)This thesis is about two things: twisted equivariant Ktheory and equivariant topological Tduality. First, we prove a fixed point decomposition theorem for twisted equivariant Ktheory, generalising a result of Atiyah and ... 
Twisted Ktheory with coefficients in a C*algebra and obstructions against positive scalar curvature metrics
(20100317)We introduce the notion of twisted Hilbert Amodule bundles to construct a geometric realization of twisted Ktheory with coefficients in a C*algebra A. Like ordinary bundles of Hilbert ... 
Twisted Kloosterman sums and cubic exponential sums
(20091215)In this thesis work, we study the problem of the distribution of cubic exponential sums. Using the theory of of automorphic forms, we are able to determine the asymptotic behavior of these ...