Kaiserslautern - Fachbereich Mathematik
Refine
Year of publication
- 2003 (37) (remove)
Document Type
- Preprint (17)
- Doctoral Thesis (13)
- Report (5)
- Diploma Thesis (2)
Has Fulltext
- yes (37) (remove)
Keywords
- Lineare Algebra (4)
- Mathematikunterricht (4)
- Modellierung (4)
- linear algebra (4)
- modelling (4)
- praxisorientiert (4)
- Wavelet (3)
- mathematical education (3)
- Inverses Problem (2)
- Lineare Optimierung (2)
- Mehrskalenanalyse (2)
- Navier-Stokes-Gleichung (2)
- Simplex (2)
- Stücklisten (2)
- Up Functions (2)
- linear optimization (2)
- praxis orientated (2)
- simplex (2)
- time series (2)
- Abel integral equations (1)
- Algebraische Geometrie (1)
- Approximation (1)
- Archimedische Kopula (1)
- Asiatische Option (1)
- Basket Option (1)
- Bessel functions (1)
- Biot-Savart Operator (1)
- Biot-Savart operator (1)
- Brownian motion (1)
- Brownsche Bewegung (1)
- CHAMP (1)
- Cauchy-Navier-Equation (1)
- Cauchy-Navier-Gleichung (1)
- Chi-Quadrat-Test (1)
- Cholesky-Verfahren (1)
- Decomposition and Reconstruction Schemes (1)
- Deformationstheorie (1)
- Druckkorrektur (1)
- Dynamic cut (1)
- Earliest arrival augmenting path (1)
- Elastische Deformation (1)
- Elliptische Verteilung (1)
- Erdmagnetismus (1)
- Euler's equation of motion (1)
- Expected shortfall (1)
- Extreme value theory (1)
- Filtergesetz (1)
- Finite-Volumen-Methode (1)
- Flachwasser (1)
- Flachwassergleichungen (1)
- Fourier-Transformation (1)
- Garbentheorie (1)
- Gewichtung (1)
- Glättung (1)
- Glättungsparameterwahl (1)
- Gravitationsfeld (1)
- Gruppenoperation (1)
- Harmonische Spline-Funktion (1)
- Heavy-tailed Verteilung (1)
- Hochschild homology (1)
- Hochschild-Homologie (1)
- Homologietheorie (1)
- Hub-and-Spoke-System (1)
- Hydrostatischer Druck (1)
- Immobilienaktie (1)
- Inverse problems in Banach spaces (1)
- Kernschätzer (1)
- Kopula <Mathematik> (1)
- Kreditrisiko (1)
- L-curve Methode (1)
- Label correcting algorithm (1)
- Label setting algorithm (1)
- Lagrangian relaxation (1)
- Lavrentiev regularization for equations with monotone operators (1)
- Lineare Elastizitätstheorie (1)
- Locally Supported Radial Basis Functions (1)
- Marktrisiko (1)
- Martingaloptimalitätsprinzip (1)
- Mehrkriterielle Optimierung (1)
- Modellbildung (1)
- Modulraum (1)
- Multiple criteria analysis (1)
- Multiresolution Analysis (1)
- Multisresolution Analysis (1)
- Multivariate Wahrscheinlichkeitsverteilung (1)
- Network flows (1)
- Nichtparametrische Regression (1)
- Nonparametric time series (1)
- Numerische Strömungssimulation (1)
- Oberflächenmaße (1)
- Optimierung (1)
- Optionsbewertung (1)
- Optionspreistheorie (1)
- Polyhedron (1)
- Portfolio-Optimierung (1)
- Poröser Stoff (1)
- Quantile autoregression (1)
- Quasi-identities (1)
- Reflection (1)
- Regularisierung (1)
- Riemannian manifolds (1)
- Riemannsche Mannigfaltigkeiten (1)
- Risikomanagement (1)
- SWARM (1)
- Scale function (1)
- Shallow Water Equations (1)
- Spherical (1)
- Spherical Wavelets (1)
- Stochastische Processe (1)
- Stratifaltigkeiten (1)
- Tail Dependence Koeffizient (1)
- Value at Risk (1)
- Vektorkugelfunktionen (1)
- Vektorwavelets (1)
- Wavelet-Theorie (1)
- Wavelet-Theory (1)
- Wirbelabtrennung (1)
- Wirbelströmung (1)
- Zeitreihen (1)
- Zyklische Homologie (1)
- abgeleitete Kategorie (1)
- algebraic geometry (1)
- archimedean copula (1)
- asian option (1)
- associated Legendre functions (1)
- basket option (1)
- bills of material (1)
- bills of materials (1)
- conditional quantiles (1)
- consecutive ones property (1)
- cyclic homology (1)
- derived category (1)
- elasticity problem (1)
- elliptical distribution (1)
- estimate (1)
- estimator (1)
- flood risk (1)
- geomagnetism (1)
- group action (1)
- hyper-quasi-identities (1)
- hypergeometric functions (1)
- hyperquasivarieties (1)
- incident wave (1)
- integer programming (1)
- kernel estimate (1)
- martingale optimality principle (1)
- mathematica education (1)
- moduli space (1)
- multileaf collimator (1)
- multivariate chi-square-test (1)
- nichtparametrisch (1)
- non-commutative geometry (1)
- non-parametric regression (1)
- nonlinear term structure dependence (1)
- nonparametric (1)
- option pricing (1)
- parameter choice (1)
- portfolio-optimization (1)
- pressure correction (1)
- quantile autoregression (1)
- quasi-P (1)
- quasi-SH (1)
- quasi-SV (1)
- quasivarieties (1)
- radiation therapy (1)
- refraction (1)
- set covering (1)
- sheaf theory (1)
- singular spaces (1)
- singuläre Räume (1)
- stochastic processes (1)
- stop location (1)
- subgradient (1)
- surface measures (1)
- tail dependence coefficient (1)
- toric geometry (1)
- torische Geometrie (1)
- triclinic medium (1)
- uniform consistency (1)
- value-at-risk (1)
- vector spherical harmonics (1)
- vectorial wavelets (1)
- vertical velocity (1)
- vertikale Geschwindigkeiten (1)
- vortex seperation (1)
- Überflutung (1)
- Überflutungsrisiko (1)
Faculty / Organisational entity
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.
In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.
The present thesis deals with coupled steady state laminar flows of isothermal incompressible viscous Newtonian fluids in plain and in porous media. The flow in the pure fluid region is usually described by the (Navier-)Stokes system of equations. The most popular models for the flow in the porous media are those suggested by Darcy and by Brinkman. Interface conditions, proposed in the mathematical literature for coupling Darcy and Navier-Stokes equations, are shortly reviewed in the thesis. The coupling of Navier-Stokes and Brinkman equations in the literature is based on the so called continuous stress tensor interface conditions. One of the main tasks of this thesis is to investigate another type of interface conditions, namely, the recently suggested stress tensor jump interface conditions. The mathematical models based on these interface conditions were not carefully investigated from the mathematical point of view, and also their validity was a subject of discussions. The considerations within this thesis are a step toward better understanding of these interface conditions. Several aspects of the numerical simulations of such coupled flows are considered: -the choice of proper interface conditions between the plain and porous media -analysis of the well-posedness of the arising systems of partial differential equations; -developing numerical algorithm for the stress tensor jump interface conditions, coupling Navier-Stokes equations in the pure liquid media with the Navier-Stokes-Brinkman equations in the porous media; -validation of the macroscale mathematical models on the base of a comparison with the results from a direct numerical simulation of model representative problems, allowing for grid resolution of the pore level geometry; -developing software and performing numerical simulation of 3-D industrial flows, namely of oil flows through car filters.
The question of how to model dependence structures between financial assets was revolutionized since the last decade when the copula concept was introduced in financial research. Even though the concept of splitting marginal behavior and dependence structure (described by a copula) of multidimensional distributions already goes back to Sklar (1955) and Hoeffding (1940), there were very little empirical efforts done to check out the potentials of this approach. The aim of this thesis is to figure out the possibilities of copulas for modelling, estimating and validating purposes. Therefore we extend the class of Archimedean Copulas via a transformation rule to new classes and come up with an explicit suggestion covering the Frank and Gumbel family. We introduce a copula based mapping rule leading to joint independence and as results of this mapping we present an easy method of multidimensional chi²-testing and a new estimate for high dimensional parametric distributions functions. Different ways of estimating the tail dependence coefficient, describing the asymptotic probability of joint extremes, are compared and improved. The limitations of elliptical distributions are carried out and a generalized form of them, preserving their applicability, is developed. We state a method to split a (generalized) elliptical distribution into its radial and angular part. This leads to a positive definite robust estimate of the dispersion matrix (here only given as a theoretical outlook). The impact of our findings is stated by modelling and testing the return distributions of stock- and currency portfolios furthermore of oil related commodities- and LME metal baskets. In addition we show the crash stability of real estate based firms and the existence of nonlinear dependence in between the yield curve.
We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t-1. We discuss an estimate which we get by inverting a kernel estimate of the conditional distribution function, and prove its asymptotic normality and uniform strong consistency. We illustrate the good performance of the estimate for light and heavy-tailed distributions of the innovations with a small simulation study.
We generalize the classical shortest path problem in two ways. We consider two - in general contradicting - objective functions and introduce a time dependency of the cost which is caused by a traversal time on each arc. The resulting problem, called time-dependent bicriteria shortest path problem (TdBiSP) has several interesting practical applications, but has not attained much attention in the literature.
In this paper we discuss an earliest arrival flow problem of a network having arc travel times and capacities that vary with time over a finite time horizon T. We also consider the possibility to wait (or park) at a node before departingon outgoing arc. This waiting is bounded by the value of maximum waiting time and the node capacity which also vary with time.
In this paper we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in many rows of the coefficient matrix, the ones appear consecutively. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecutive ones structure to develop bounds and a branching scheme. Our approach has been tested on real-world data as well as on theoretical problem instances.
The Earth's surface is an almost perfect sphere. Deviations from its spherical shape are less than 0,4% of its radius and essentially arise from its rotation. All equipotential surfaces are nearly spherical, too. In consequence, multiscale modelling of geoscientifically relevant data on the sphere involving rotational symmetry of the trial functions used for the approximation plays an important role. In this paper we deal with isotropic kernel functions showing local support and (one-dimensional) polynomial structure (briefly called isotropic finite elements) for reconstructing square--integrable functions on the sphere. Essential tool is the concept of multiresolution analysis by virtue of the spherical up function. The main result is a tree algorithm in terms of (low--order) isotropic finite elements.