Mathematics - General

This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can...

The Navier-Stokes equations are the fundamental model for the mathematical analysis of incompressible viscous fluids. In this text, a modification of this system of partial differential equations representing the situation of geophysical flows is investigated. An important mathematical model of geophysical boundary layers is...

B-Spline and NURBS techniques have already been successfully used in Isogeometric Analysis which is a method for directly integrating CAD models in numerical simulations. Our purpose is to improve existing techniques to enhance the efficiency. First, we use local B-Spline subdivisions and knot insertions...

In recent years, Dellnitz, Junge and co-workers developed a subdivision algorithm for the approximation of invariant measures in discrete dynamical systems based on the so-called Ulam's approach. In high dimensions, this adaptive invariant measure (AIM) algorithm suffers from the "curse of dimension" even when...

This thesis contributes to the field of inverse problems with sparsity constraints. In recent years this has been a rapidly developing field within the theory of inverse and ill-posed problems. It turned out that solutions of many inverse problems have a sparse structure, which...

European freight railway companies face cost pressure and need to increase efficiency in order to keep pace with the competition. A large share of the total costs is due to crews that are required to operate trains. Crew scheduling aims at operating a given...

In this paper we study a famous conjecture which relates the leading terms at zero of Artin L-functions attached to a finite Galois extension L/K of number fields to natural arithmetic invariants. This conjecture is called the Lifted Root Number Conjecture (LRNC) and has...

Whether the results of statistical procedures are accepted or not is strongly influenced by the way how they are interpreted. Effects based on data encodings and the order in which the data occurs in the learning sample are particularly problematic. Modern data collections often...

Thema der vorliegenden Arbeit ist die Entwicklung und Realisierung einer neuen Methode zur Gitterdeformation im Hinblick auf die Anwendung in r- und rh-adaptiven Verfahren. Das neu entwickelte Verfahren wird sowohl numerisch als auchtheoretisch analysiert. Die vorliegende Arbeit ist in sechs Kapitel gegliedert.Das erste Kapitel...

In this work we identify the main concepts of Aspect Orientation (AO), namely message filters and an aspect weaver. In doing so, we substantiate these notions by defining a composition model based on the formal language FOCUS and a model of composition filters designed...

Almost any kind of application requires the analysis of functions or data. In order to analyze them, they are decomposed into simple building blocks. Such methods are not only used in mathematics, but also in physics, eletrical engeneering, seismic geology, wireless communication, target detection,...

Author: Boris RankovISBN-10: 3832517448ISBN-13: 9783832517441Publisher: Logos Verlag BerlinLanguage: EnglishPublished: 11/30/2007Pages: 214Format: Paperback

Die vorliegende Dissertation behandelt grundlegende inverse Probleme der diskreten Tomographie im Fall von gewissen Delone Mengen, die, wie beispielsweise Gitter, eine weitreichende Ordnungsstruktur aufweisen. Als wichtigste Klasse wird die diskreteTomographie von Systemen aperiodischer Ordnung, genauer, von Streifenprojektionsmengen (auch Quasigitter oder mathematischeQuasikristalle genannt), studiert. Wir...

The Jak/Stat1 signalling pathway is a prototypical example of a direct signal transduction system which relays external signals directly from the receptor located at the cellular membrane to its nuclear target genes. This work seeks to acquire a comprehensive theoretical understanding of the quantitative...

The focus of the thesis is placed on macroscopic traffic flow models on networks and corresponding optimal control problems. We present a multi-class traffic model on traffic flow networks that respects driver's destination preferences, i.e., everyone arrives at their desired destination. The result is...

The minimum graph bisection problem is a special kind of a graph partitioning problem, where the nodes of a weighted graph are divided into two subsets with prescribed capacity, and the weighted sum of edges joining nodes in different subsets is minimized. Due to...

This book evolved over a period of years as the author taught classes in numerical analysis, optimization theory and optimal control to graduate students in mathematics and engineering. The material presented in this monograph is the result of author's work at the E.M.A. University...

This thesis is concerned with the application of wavelet methods to the adaptive numerical solutionof elliptic and parabolic operator equations over a polygonal domain. Driven by the insight that the construction of wavelet bases on more general domains is complicated and may pose stability...

The origins of von Neumann-regular rings and *-regular rings are the works of John von Neumann and F. J. Murray during the 30ies of the last century. They constitute a connection of the areas of operator theory, ring theory and lattice theory. Starting from...

Within the last two decades, wavelet analysis has become a very powerful tool in applied mathematics. Wavelet algorithms have been successfully applied in signal analysis and compression as well as in numerical analysis, geophysics, meteorology and in many other fields. Usually, wavelets are constructed...

his book systematically discusses a basic problem in combinatorics on words: the ambiguity of morphisms, i. e. the question of whether, for any finite string s and any given morphism h, there is another morphism g satisfying g(s)=h(s). These studies yield a characterisation of...

Mutual Information belongs to the most popular and powerful tools for multi-modal image registration. Nevertheless, its handling is involved, and despite a wide spread use in a large number of applications no standard treatment exists. Here, we present both theory and numerics for non-linear...

Combining different methodologies in the field of soft computing as rule based fuzzy classification systems, fuzzy clustering methods and neural networks like multilayer perceptrons, enables us to combine their advantages. As this work shows that the well known and commonly used fuzzy max-min classification...

Modelling electrical circuits leads to differential algebraic equations (DAEs) having a properly stated leading term. These equations need to be solved numerically, e.g. in case of a transient analysis of the given circuit. Classical methods such as linear multistep methods or Runge-Kutta schemes suffer...

his thesis is concerned with the finite element analysis and the a posteriori error estimation for eigenvalue problems for general operator pencils on two-dimensional manifolds. A specific application of the presented theory is the computation of corner singularities. Engineers use the knowledge of the...

This thesis presents new models and estimation techniques based on the generalized linear model framework. In Chapter 1 the GAMBoost procedure for estimation of generalized additive models is developed. Based on boosting and gradient descent in function space it generalizes the notion of repeated...

Survival analysis is concerned with the analysis of events occuring over time. Many regression models have been suggested to describe the relation of covariates to these events. Model checks can be used to determine whether a certain model is not suitable for a given...

Biological invasions are a severe ecological problem threatening biodiversity and causing substantial economic damages. Mathematical models of spatiotemporal spread have proven to be powerful tools in identifying the underlying mechanisms, thus contributing to the understanding of the factors that determine invasion processes and to...

Die vorliegende Dissertation beschaftigt sich mit der Formulierung und Losung eines mathematischen Modells zur integrierten Optimierung der Schulanfangszeiten und des Nahverkehrsangebots, kurz: IOSANA. Ziel ist es, die Schulanfangszeiten in die Optimierung der Abfahrtszeiten und derUmlaufe von Bussen des offentlichen Personennahverkehrs (OPNV) einzubeziehen, um auf...

Nonconvex variational problems are of importance in modeling problems of microstructures and elasticity. In this book, we consider a $1$-d nonconvex problem and we prove existence of solutions of the corresponding non-elliptic Euler-Lagrange equation by considering the Euler-Lagrange equation of the singular perturbed variational...

The holomorphic functional calculus for sectorial unbounded operators is an extension of the classical Dunford calculus for bounded operators. The interest in this calculus is motivated by the Kato square root problem and applications to the operator-sum method introduced by DaPrato and Grisvard to...

This work describes the development of the new discrete ordinate scattering algorithm, which is a part of the Atmospheric Radiative Transfer Simulator (ARTS). Furthermore, applications of the algorithm, which was implemented to study for example the influence of cirrus clouds on microwave limb sounding,...

Automatic fact retrieval from text documents is becoming one of the key technologies for the Information Age. One category of Intelligent Information Systems aims at supporting the user in search and retrieval of precious information from data resources like intranets or the World Wide...

Variational problems involving nonlocal terms are of growing importance in the mathematical modeling of microstructures that occur in solid-solid phase transitions. For a model describing an austenite / twinned martensite interface, it is conjectured that the minimizers are highly oscillating near-periodic functions. The nonlocality,...

Traffic flow has been a continuous source of challenging mathematical problems. The following work is dedicated to recent questions in modeling, simulation and optimization of traffic flow networks. Mathematics can help to solve traffic problems in different ways. Modelling provides fundamental understanding of traffic...

This dissertation describes the design, implementation, and evaluation of an audio watermarking algorithm on the basis of a statistical mathematical model. The design of the basic audio watermarking method, relying on hypothesis testing, is motivated by a discussion of possible application scenarios determining algorithmic...

In dieser Dissertation werden katalytisch interagierende Fellersche Diffusionen untersucht. Der betrachtete Prozess ist ein katalytisches Zweitypenmodell; er wird definiert als Losung eines abzahlbaren Systems stochastischer Differentialgleichungen.Die Betrachtungen umfassen folgende Punkte:1. Zunachst wird das Langzeitverhaltens auf den unendlichen Gittern analysiert. Hier ist insbesondere der sogenannte...

The volume includes the proceedings from the conference FOL75 -- 75 Years of First-Order Logic held at Humboldt University, Berlin, September 18 - 21, 2003 on the occasion of the anniversary of the publication of Hilbert's and Ackermann's Grundzuge der theoretischen Logik. The papers...

The group of parallel displacements, the so-called holonomy group, is an important tool in order tostudy geometric structures on a smooth manifold. It describes parallel objects in tensor bundles as well as in other geometric vector bundles, such as the spinor bundle. The question:...

Certain classes of partial differential equations generically give rise to solutions with strong directional features, e.g. with boundary layers. Such solutions are called anisotropic. Their discretization by means of the finite element method (for example) can favourably employ so-called anisotropic meshes. These meshes are...

In this thesis we see deductive systems for classical propositionaland predicate logic which use deep inference, i.e. inference rules apply arbitrarily deep inside formulas, and a certain symmetry, which provides an involution on derivations. Like sequent systems, they have a cut rule which is...

This dissertation shows that information assurance properties can be both specified within a formal model of systems to which the properties are applied using the same formal theory for modeling, specification, and reasoning and enforced in such a way that enforcement is performed consistently...

This volume contains the papers on optimization presented to the 11th conference on Methods and Techniques of Mathematical Physics , held on December 1-7, 1985 at the Mathematisches Forschungsinstitut Oberwolfach.Author: Bruno BrosowskiISBN-10: 382049894XISBN-13: 9783820498943Publisher: Peter Lang Gmbh, Internationaler Verlag Der WLanguage: EnglishPublished: 12/31/1987Pages: 194Format:...

A representation in terms of explicitly given generalized eigenfunctions is obtained for the semigroup S(t) = exp(-ixt) solving the Cauchy problem for the time-dependent Maxwell equations in the case of two distinct media filling the upper and lower half spaces of R3, whereby the...

This volume contains the papers on problems of applied analysis presented to the 11th conference on Methods and Techniques of Mathematical Physics , held on December 1-7, 1985 at the Mathematisches Forschungsinstitut Oberwolfach.Author: Bruno BrosowskiISBN-10: 3820498389ISBN-13: 9783820498387Publisher: Peter Lang Gmbh, Internationaler Verlag Der WLanguage:...

This volume contains the papers on dynamical problems im mathematical physics presented to the 10th Conference on Methoden und Verfahren der Mathematischen Physik , held on February 21-27, 1982 at the Mathematisches Forschungsinstitut Oberwolfach .Author: Bruno BrosowskiISBN-10: 3820476288ISBN-13: 9783820476286Publisher: Peter Lang Gmbh, Internationaler Verlag...

This volume contains the papers on approximation and optimization in mathematical physics presented to the 10th Conference on Methoden und Verfahren der Mathematischen Physik , held on February 21-27, 1982 at the Mathematisches Forschungsinstitut Oberwolfach .Author: Bruno BrosowskiISBN-10: 3820476318ISBN-13: 9783820476316Publisher: Peter Lang Gmbh, Internationaler...

Representation of analytical and numerical methods for the treatment of special fluid mechanical problems. Further, some contributions to the foundations of the Navier-Stokes-equations and some important experimental results. Vorwiegend analytische und numerische Verfahren zur Behandlung von speziellen strömungsmechanischen Problemen, aber auch Beiträge zu Grundlagenfragen...

The kinetic theory of gases is a most fruitful field for mathematical research. This is evident from the multiplicity of mathematical methods used, the originality of the questions posed and the large number of hitherto unsolved fundamental problems. For example, the question of existence...

At the Conference in Oberwolfach organized by Prof. R. Kress and Prof. J. Wick questions on mathematical methods of plasmaphysics were being dealt with. This book contains the papers presented at this Conference by the following mathematicians and physicists: Klaus Elsässer, K. Graf Finck...