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Tue, 01 Aug 2017 14:57:12 +0200Tue, 01 Aug 2017 14:57:12 +0200Bulk-boundary correspondence in non-equilibrium dynamics of one-dimensional topological insulators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4702
Dynamical phase transitions (DPT) are receiving a rising interest. They are known to behave analogously to
equilibrium phase transitions (EPT) to a large extend. However, it is easy to see that DPT can occur in finite
systems, while EPT are only possible in the thermodynamic limit. So far it is not clear how far the analogy of
DPT and EPT goes. It was suggested, that there is a relation between topological phase transitions (TPT)
and DPT, but many open questions remain.
Typically, to study DPT, the Loschmidt echo (LE) after a quench is investigated, where DPT are visible as
singularities. For one-dimensional systems, each singularity is connected to a certain critical time scale, which
is given by the dispersion in the chain.
In topological free-fermion models with winding numbers 0 or 1, only the LE in periodic boundary conditions
(PBC) has been investigated. In open boundary conditions (OBC), these models are characterized by symmetry
protected edge modes in the topologically non-trivial phase. It is completely unclear how these modes affect
DPT. We investigate systems with PBC governed by multiple time scales with a Z topological invariant. In
OBC, we provide numerical evidence for the presence of bulk-boundary correspondence in DPT in quenches
across a TPT.Philipp Jaegerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4702Tue, 01 Aug 2017 14:57:12 +0200Untersuchung des Migrationsverhaltens von Fibroblasten auf dreidimensionalen Mikrostrukturen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4209
Zur Untersuchung der Zell-Topographie-Interaktionen werden im Rahmen dieser Arbeit zwei Arten von Mikrostrukturen mittels Direktem Laser Schreiben erzeugt, einerseits Pfosten unterschiedlicher Abstände und andererseits Pfosten-Steg-Strukturen mit unterschiedlicher Steghöhe. Auf diesen Topographien werden die untersuchten Zellen ausgesät und ihr Verhalten mit Zeitrafferaufnahmen über einen Zeitraum von 24 h beobachtet. Aus den Zellkoordinaten und den daraus erhaltenen Zellpfaden wird das Migrationsverhalten der Zellen im Hinblick auf den lenkenden Einfluss der betrachteten Topographie analysiert.Mona Kirstin Fehlingdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4209Tue, 03 Nov 2015 14:49:55 +0100Treiber für nachhaltiges unternehmerisches Handeln: Bedeutung von Spiritualität für Unternehmensgründer
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4124
Konzeptionelle Studien der letzten Jahre deuten darauf hin, dass für eine Verwurzelung von Nachhaltigkeit in modernen Unternehmen eine Veränderung der Denkweise der Unternehmensentscheidungsträger notwendig ist. Dabei werden Verantwortung und nachhaltiges Handeln nicht ausschließlich als Instrumente zur Erreichung ökonomischer Ziele eingesetzt, sondern bilden, verankert in der persönlichen Spiritualität, fundamentale Prinzipien und eigenständige Werte. Ziel der vorliegenden Arbeit ist es deshalb, die Zusammenhänge zwischen Spiritualität und unternehmerischer Nachhaltigkeit zu beleuchten. Mit Hilfe von sechs halbstrukturierten Interviews mit GründerInnen und Un-ternehmensführerInnen kleiner und mittlerer Unternehmen des Dienstleistungssektors untersuchte die Autorin, inwiefern die Spiritualität der UnternehmerInnen einen Einfluss auf nachhaltige Entscheidungen in ihren Unternehmen hat. Sie konnte herausfinden, dass Werte und Ansichten, die die individuelle Spiritualität der UnternehmerInnen ausdrücken, als Motivation für nachhaltiges unternehmerisches Handeln dienen können. Überdies identifizierte sie einzelne Werte und Ansichten, die als Treiber für einzelne Dimensionen der Nachhaltigkeit fungieren. Weiterhin entwickelte sie ein Modell, das sowohl persönliche Werte und Ansichten als Teil der Spiritualität, als auch die in der Literatur diskutierten Konzepte Spiritualität am Arbeitsplatz und spirituelle Führung integriert. Dieses Modell kann als Grundlage für weitere Forschung im Kontext von Spiritualität und unternehmerische Nachhaltigkeit dienen. Die Ergebnisse implizieren, dass in Bildung und Gesellschaft verankerte Aktivitäten zur Unterstützung von Spiritualität eine nachhaltige Entwicklung innerhalb und außerhalb von Unternehmen vorantreiben können.Julia Hufnageldiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4124Thu, 23 Jul 2015 10:35:49 +0200European Groupings of Territorial Cooperation (EGTCs): Applicability in the Transnational and Interregional Cooperation – The Example of Network-EGTCs –
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4047
This diploma thesis sets out to analyse the applicability of the instrument ’European Grouping of
Territorial Cooperation (EGTC)’ in the transnational and interregional non-contiguous cooperation.
EGTCs that are applied in spatially non-contiguous cooperations are called ’Network-EGTCs’. As
no scientific research about network-EGTCs has been made so far, this diploma thesis fills this
research gap.
As a basis for the analysis, a literature review on the instrument EGTC in general and its historic
background was conducted. In addition the scientific literature has been searched for characteristics
of non-contiguous cooperations and different stakeholders were interviewed for their
estimations about network-EGTCs. The so far existing and planned network-EGTCs have been
explored. Out of these network-EGTCs two case studies – the E.G.T.C. Amphictyony and the
planned CETC-EGTC – have been examined in depth. Their characteristics have further been
compared with the information about EGTCs and non contiguous-cooperations in general.
It was found out that network-EGTCs show advantages from ordinary non-contiguous cooperations.
Additionally, it was discovered that network-EGTCs do not differ in their character as much
as it had been expected from EGTCs established in the cross-border cooperation. This applies
also to the establishment process as well as to the fulfilment of the instrument’s potentials. In
general all EGTCs show discrepancies between planning and practice. Only a few differences
have been discovered. Contrary to expectation network-EGTCs show only certain disadvantages
but also advantages compared to EGTCs in the cross-border cooperation.
This thesis delivers evidence that EGTCs are applicable in the transnational and interregional
cooperation when certain preconditions are fulfilled. Then they can contribute to a successful
transnational and interregional cooperation.
Recommendations were given to territorial non-contiguous cooperations that are considering to
establish an EGTC.
It is expected that more network-EGTCs will be established in the future due to the higher experience
and knowledge about network-EGTCs.Beate Caesardiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4047Tue, 07 Apr 2015 10:58:04 +0200Vector bundles on elliptic curves and factors of automorphy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3387
The Atiyah’s results on classification of vector
bundles on elliptic curves are translated to the language of factors of automorphy.Oleksandr Ienadiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3387Wed, 16 Jan 2013 16:52:18 +0100Intersection Theory of the Tropical Moduli Spaces of Curves
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3276
Tropical geometry is a very new mathematical domain. The appearance of
tropical geometry was motivated by its deep relations to other mathematical
branches. These include algebraic geometry, symplectic geometry, complex
analysis, combinatorics and mathematical biology.
In this work we see some more relations between algebraic geometry and
tropical geometry. Our aim is to prove a one-to-one correspondence between
the divisor classes on the moduli space of n-pointed rational stable curves
and the divisors of the moduli space of n-pointed abstract tropical curves.
Thus we state some results of the algebraic case first. In algebraic geometry
these moduli spaces are well understood. In particular, the group of divisor
classes is calculated by S. Keel. We recall the needed results in chapter one.
For the proof of the correspondence we use some results of toric geometry.
Further we want to show an equality of the Chow groups of a special toric
variety and the algebraic moduli space. Thus we state some results of the
toric geometry as well.
This thesis tries to discover some connection between algebraic and tropical
geometry. Thus we also need the corresponding tropical objects to the
algebraic objects. Therefore we give some necessary definitions such as fan,
tropical fan, morphisms between tropical fans, divisors or the topical moduli
space of all n-marked tropical curves. Since we need it, we show that the
tropical moduli space can be embedded as a tropical fan.
After this preparatory work we prove that the group of divisor classes in
v
classical algebraic geometry has it equivalence in tropical geometry. For this
it is useful to give a map from the group of divisor classes of the algebraic
moduli space to the group of divisors of the tropical moduli space. Our aim is
to prove the bijectivity of this map in chapter three. On the way we discover
a deep connection between the algebraic moduli space and the toric variety
given by the tropical fan of the tropical moduli space.Matthias Herolddiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3276Mon, 01 Oct 2012 16:25:45 +0200Asymptotics for a thin elastic fiber in contact with a rigid body
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2828
In this work a 3-dimensional contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin-condition (by meaning of the penalized and linearized non-penetration and friction conditions).
The dimension of the problem is reduced by an asymptotic approach. Scaling the Robin parameters appropriately we obtain a recurrent chain of Neumann type boundary value problems which are considered only in the microscopic scale. The problem for the leading term is a homogeneous Neumann problem, hence the leading term depends only on the slow variable. This motivates the choice of a multiplicative ansatz in the asymptotic expansion.
The theoretical results are illustrated with numerical examples performed with a commercial finite-element software-tool.Daniel Zoufiné Baré Contrerasdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2828Fri, 16 Dec 2011 02:31:20 +0000Computation of the central elements and centralizers of sets of elements in non-commutative polynomial algebras
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2308
In this thesis we present the implementation of libraries center.lib and perron.lib for the non-commutative extension Plural of the Computer Algebra System Singular. The library center.lib was designed for the computation of elements of the centralizer of a set of elements and the center of a non-commutative polynomial algebra. It also provides solutions to related problems. The library perron.lib contains a procedure for the computation of relations between a set of pairwise commuting polynomials. The thesis comprises the theory behind the libraries, aspects of the implementation and some applications of the developed algorithms. Moreover, we provide extensive benchmarks for the computation of elements of the center. Some of our examples were never computed before.Oleksandr Motsakdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2308Mon, 11 Apr 2011 10:14:50 +0200Four Generations of Asset Pricing Models and Volatility Dynamics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2248
The scope of this diploma thesis is to examine the four generations of asset pricing models and the corresponding volatility dynamics which have been devepoled so far. We proceed as follows: In chapter 1 we give a short repetition of the Black-Scholes first generation model which assumes a constant volatility and we show that volatility should not be modeled as constant by examining statistical data and introducing the notion of implied volatility. In chapter 2, we examine the simplest models that are able to produce smiles or skews - local volatility models. These are called second generation models. Local volatility models model the volatility as a function of the stock price and time. We start with the work of Dupire, show how local volatility models can be calibrated and end with a detailed discussion of the constant elasticity of volatility model. Chapter 3 focuses on the Heston model which represents the class of the stochastic volatility models, which assume that the volatility itself is driven by a stochastic process. These are called third generation models. We introduce the model structure, derive a partial differential pricing equation, give a closed-form solution for European calls by solving this equation and explain how the model is calibrated. The last part of chapter 3 then deals with the limits and the mis-specifications of the Heston model, in particular for recent exotic options like reverse cliquets, Accumulators or Napoleons. In chapter 4 we then introduce the Bergomi forward variance model which is called fourth generation model as a consequence of the limits of the Heston model explained in chapter 3. The Bergomi model is a stochastic local volatility model - the spot price is modeled as a constant elasticity of volatility diffusion and its volatility parameters are functions of the so called forward variances which are specified as stochastic processes. We start with the model specification, derive a partial differential pricing equation, show how the model has to be calibrated and end with pricing examples and a concluding discussion.Sascha Desmettrediplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2248Mon, 24 Jan 2011 09:08:01 +0100A Survey of Earliest Arrival Flows and a Study of the Series-Parallel Case
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2175
This work is concerned with dynamic flow problems, especially maximal dynamic flows and earliest arrival flows - also called universally maximal flows. First of all, a survey of known results about existence, computation and approximation of earliest arrival flows is given. For the special case of series-parallel graphs a polynomial algorithm for computing maximal dynamic flows is presented and this maximal dynamic flow is proven to be an earliest arrival flow.Mechthild Steinerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2175Wed, 21 Jul 2010 13:20:49 +0200Weight-Constrained Minimum Spanning Tree Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1873
In an undirected graph G we associate costs and weights to each edge. The weight-constrained minimum spanning tree problem is to find a spanning tree of total edge weight at most a given value W and minimum total costs under this restriction. In this thesis a literature overview on this NP-hard problem, theoretical properties concerning the convex hull and the Lagrangian relaxation are given. We present also some in- and exclusion-test for this problem. We apply a ranking algorithm and the method of approximation through decomposition to our problem and design also a new branch and bound scheme. The numerical results show that this new solution approach performs better than the existing algorithms.Sebastian Tobias Henndiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1873Thu, 21 Jun 2007 22:56:38 +0200Polyhedral Analysis of Hub Center Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1851
A hub location problem consists of locating p hubs in a network in order to collect and consolidate flow between node pairs. This thesis deals with the uncapacitated single allocation p-hub center problem (USApHCP) as a special type of hub location problem with min max objective function. Using the so-called radius formulation of the problem, the dimension of the polyhedron of USApHCP is derived. The formulation constraints are investigated to find out which of these define facets. Then, three new classes of facet-defining inequalities are derived. Finally, efficient procedures to separate facets in a branch-and-cut algorithm are proposed. The polyhedral analysis of USApHCP is based on a tight relation to the uncapacitated facility location problem (UFL). Hence, many results stated in this thesis also hold for UFL.Silke Baumgartnerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1851Wed, 11 Apr 2007 10:46:01 +0200Wavelet-based Adaptive Multiresolution Tools Applied to Speech Recognition
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1785
* naive examples which show drawbacks of discrete wavelet transform and windowed Fourier transform; * adaptive partition (with a 'best basis' approach) of speech-like signals by means of local trigonometric bases with orthonormal windows. * extraction of formant-like features from the cosine transform; * further proceedingings for classification of vowels or voiced speech are suggested at the end.Andreas Simondiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1785Tue, 17 Oct 2006 14:15:45 +0200Das Verhalten ausgewählter technischer Indikatoren bei simulierten Finanzzeitreihen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1718
In der Arbeit sollen ausgewählte technische Indikatoren und deren Handelsstrategien hinsichtlich ihres Verhaltens bzw. ihrer Profitabilität in verschiedenen Marktphasen untersucht werden. Um das Argument, dass die Indikatoren selbst erfüllend sind, zu entkräften, werden Finanzzeitreihen simuliert und die Indikatoren auf diese angewendet und ausgewertet. Zu diesem Zweck wird zu gegebenen echten Kursdaten ein finanzzeitreihenanalytisches Modell angepasst. Dieses wird zur Simulation von Finanzzeitreihen und damit zur Auswertung der Indikatoren verwendet werden. Durch geeignete Auswahlverfahren sollen verschiedene Handelsstrategien zu Strategien kombiniert werden, um ein besseres Ertrag/Risikoverhältnis zu erreichen als dies bei einzelnen Strategien der Fall wäre.Carsten Zimmerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1718Fri, 24 Mar 2006 13:41:17 +0100Hub Cover and Hub Center Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1692
Using covering problems (CoP) combined with binary search is a well-known and successful solution approach for solving continuous center problems. In this thesis, we show that this is also true for center hub location problems in networks. We introduce and compare various formulations for hub covering problems (HCoP) and analyse the feasibility polyhedron of the most promising one. Computational results using benchmark instances are presented. These results show that the new solution approach performs better in most examples.Tanja Meyerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1692Thu, 05 Jan 2006 20:04:45 +0100Minimum Fundamental Cut Basis Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1675
Any tree in an undirected graph defines a fundamental cut basis. The minimum fundamental cut basis problem is to find a tree minimizing the weight of the corresponding basis. This problem is NP, in the thesis heuristics, relaxations, and numerical results are presented.Anne Schwahndiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1675Wed, 26 Oct 2005 16:08:26 +0200Aggregation of Large-Scale Network Flow Problems with Application to Evacuation Planning at SAP
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1652
Our initial situation is as follows: The blueprint of the ground floor of SAP’s main building the EVZ is given and the open question on how mathematic can support the evacuation’s planning process ? To model evacuation processes in advance as well as for existing buildings two models can be considered: macro- and microscopic models. Microscopic models emphasize the individual movement of evacuees. These models consider individual parameters such as walking speed, reaction time or physical abilities as well as the interaction of evacuees during the evacuation process. Because of the fact that the microscopic model requires lots of data, simulations are taken for implementation. Most of the current approaches concerning simulation are based on cellular automats. In contrast to microscopic models, macroscopic models do not consider individual parameters such as the physical abilities of the evacuees. This means that the evacuees are treated as a homogenous group for which only common characteristics are considered; an average human being is assumed. We do not have that much data as in the case of the microscopic models. Therefore, the macroscopic models are mainly based on optimization approaches. In most cases, a building or any other evacuation object is represented through a static network. A time horizon T is added, in order to be able to describe the evolution of the evacuation process over time. Connecting these two components we finally get a dynamic network. Based on this network, dynamic network flow problems are formulated, which can map evacuation processes. We focused on the macroscopic model in our thesis. Our main focus concerning the transfer from the real world problem (e.g. supporting the evacuation planning) will be the modeling of the blueprint as a dynamic network. After modeling the blueprint as a dynamic network, it will be no problem to give a formulation of a dynamic network flow problem, the so-called evacuation problem, which seeks for an optimal evacuation time. However, we have to solve a static large-scale network flow problem to derive a solution for this formulation. In order to reduce the network size, we will examine the possibility of applying aggregation to the evacuation problem. Aggregation (lat. aggregare = piling, affiliate; lat. aggregatio = accumulation, union; the act of gathering something together) was basically used to reduce the size of general large-scale linear or integer programs. The results gained for the general problem definitions were then applied to the transportation problem and the minimum cost network flow problem. We review this theory in detail and look on how results derived there can be used for the evacuation problem, too.Florian Dreifusdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1652Tue, 09 Aug 2005 20:16:37 +0200Crane Scheduling in Container Terminals
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1650
This diploma thesis examines logistic problems occurring in a container terminal. The thesis focuses on the scheduling of cranes handling containers in a port. Two problems are discussed in detail: the yard crane scheduling of rubber-tired gantry cranes (RMGC) which move freely among the container blocks, and the scheduling of rail-mounted gantry cranes (RMGC) which can only move within a yard zone. The problems are formulated as integer programs. For each of the two problems discussed, two models are presented: In one model, the crane tasks are interpreted as jobs with release times and processing times while in the other model, it is assumed that the tasks can be modeled as generic workload measured in crane minutes. It is shown that the problems are NP-hard in the strong sense. Heuristic solution procedures are developed and evaluated by numerical results. Further ideas which could lead to other solution procedures are presented and some interesting special cases are discussed.Peter Bohrerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1650Mon, 08 Aug 2005 15:05:24 +0200Über die Asymptotik des Bayesrisikos bei Diffusionsmodellen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1562
Diese Diplomarbeit gibt eine kurze Einführung in das Gebiet der Diffusionsprozesse (beschrieben als Lösungen stochastischer Differentialgleichungen) und der großen Abweichungen. Mit Methoden aus dem Gebiet der großen Abweichungen wird dann das asymptotische Verhalten des Bayesrisikos für die unterscheidung zweier Diffusionsprozesse untersucht.Jochen Voßdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1562Wed, 11 Aug 2004 16:18:46 +0200Regularization of Inverse Problems in Satellite Geodesy by Wavelet Methods with Orbital Data Given on Closed Surfaces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1399
Satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG), respectively, are two measurement principles in modern satellite geodesy which yield knowledge of the first and second order radial derivative of the earth's gravitational potential at satellite altitude, respectively. A numerical method to compute the gravitational potential on the earth's surface from those observations should be capable of processing huge amounts of observational data. Moreover, it should yield a reconstruction of the gravitational potential at different levels of detail, and it should be possible to reconstruct the gravitational potential from only locally given data. SST and SGG are modeled as ill-posed linear pseudodifferential operator equations with an injective but non-surjective compact operator, which operates between Sobolev spaces of harmonic functions and such ones consisting of their first and second order radial derivatives, respectively. An immediate discretization of the operator equation is obtained by replacing the signal on its right-hand-side either by an interpolating or a smoothing spline which approximates the observational data. Here the noise level and the spatial distribution of the data determine whether spline-interpolation or spline-smoothing is appropriate. The large full linear equation system with positive definite matrix which occurs in the spline-interplation and spline-smoothing problem, respectively, is efficiently solved with the help of the Schwarz alternating algorithm, a domain decomposition method which allows it to split the large linear equation system into several smaller ones which are then solved alernatingly in an iterative procedure. Strongly space-localizing regularization scaling functions and wavelets are used to obtain a multiscale reconstruction of the gravitational potential on the earth's surface. In a numerical experiment the advocated method is successfully applied to reconstruct the earth's gravitational potential from simulated 'exact' and 'error-affected' SGG data on a spherical orbit, using Tikhonov regularization. The applicability of the numerical method is, however, not restricted to data given on a closed orbit but it can also cope with realistic satellite data.Petra Baumanndiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1399Mon, 02 Jun 2003 14:58:23 +0200Nichtparametrische Trend- und Volatilitätsschätzer für Finanzzeitreihen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1382
Zuerst einmal werden die Grundlagen der nichtparametrischen Regression sowie die der Kleinste-Quadrate-Schätzer behandelt und unser verwendetes Modell hergeleitet. Kapitel 3 führt dann in die Theorie der gewichteten Kernschätzer ein, wobei auch das asymptotische Verhalten genauer untersucht wird. Des Weiteren wird ein numerischer Algorithmus zur Berechnung der Kernschätzer angegeben. Die Simulationsstudie der gewichteten Kernschätzer anhand von Regressionsdaten und Zeitreihendaten sowie die praktische Beurteilung erfolgen in Kapitel 4 und 5. Reale Zeitreihendaten bilden danach im sechsten Kapitel die Grundlage für die praktische Betrachtung der neuen Schätzer. Im letzten Kapitel folgt dann ein Resümee und ein kleiner Ausblick auf die gewichteten Kernschätzer für allgemeinere Modelle.Daniel Kopfdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1382Wed, 19 Mar 2003 13:31:45 +0100Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1368
While there exist closed-form solutions for vanilla options in the presence of stochastic volatility for nearly a decade, practitioners still depend on numerical methods - in particular the Finite Difference and Monte Carlo methods - in the case of double barrier options. It was only recently that Lipton proposed (semi-)analytical solutions for this special class of path-dependent options. Although he presents two different approaches to derive these solutions, he restricts himself in both cases to a less general model, namely one where the correlation and the interest rate differential are assumed to be zero. Naturally the question arises, if these methods are still applicable for the general stochastic volatility model without these restrictions. In this paper we show that such a generalization fails for both methods. We will explain why this is the case and discuss the consequences of our results.Oliver Faulhaberdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1368Mon, 20 Jan 2003 16:00:03 +0100The genealogy of branching processes with continuous state space
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1362
The thesis presents the construction of the so called height processes to code the genealogy of continuous state branching processes, due to Le Gall. A generalized Ray-Knight is dirived and conditions for the finite biodiversity of continuous state branching process are given.Pascal Vogtdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1362Fri, 13 Dec 2002 11:21:58 +0100Numerical Simulation of a Channel Inflow with Moving Contact Lines
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1269
The flow of a liquid into an empty channel is simulated. The simulation is based on a recently published model for general fluid/liquid/solid systems which eliminates the shear stress singularity at the moving contact line between the liquid/fluid interface and the solid. This model is carefully analyzed for low Reynolds and Capillary numbers, adapted to the channel inflow problem, and implemented. Very convincing numerical results are presented.Dirk Kehrwalddiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1269Mon, 10 Dec 2001 00:00:00 +0100Matrices with the consecutive ones property, interval graphs and their applications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1253
Matrices with the consecutive ones property and interval graphs are important notations in the field of applied mathematics. We give a theoretical picture of them in first part. We present the earliest work in interval graphs and matrices with the consecutive ones property pointing out the close relation between them. We pay attention to Tucker's structure theorem on matrices with the consecutive ones property as an essential step that requires a deep considerations. Later on we concentrate on some recent work characterizing the matrices with the consecutive ones property and matrices related to them in the terms of interval digraphs as the latest and most interesting outlook on our topic. Within this framework we introduce a classiffcation of matrices with consecutive ones property and matrices related to them. We describe the applications of matrices with the consecutive ones property and interval graphs in different fields. We make sure to give a general view of application and their close relation to our studying phenomena. Sometimes we mention algorithms that work in certain fields. In the third part we give a polyhedral approach to matrices with the consecutive ones property. We present the weighted consecutive ones problem and its relation to Tucker's matrices. The constraints of the weighted consecutive ones problem are improved by introducing stronger inequalities, based on the latest theorems on polyhedral aspect of consecutive ones property. Finally we implement a separation algorithm of Oswald and Reinhelt on matrices with the consecutive ones property. We would like to mention that we give a complete proof to the theorems when we consider important within our framework. We prove theorems partially when it is worthwhile to have a closer look, and we omit the proof when there are is only an intersection with our studying phenomena.Dritan Osmanidiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1253Thu, 28 Jun 2001 00:00:00 +0200