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Wed, 11 Apr 2007 10:46:01 +0200Wed, 11 Apr 2007 10:46:01 +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 +0200Functions preserving 2-series strict orders
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1737
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.Rainer Lenzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1737Tue, 16 May 2006 13:08:47 +0200Numerical solution of coupled flow in plain and porous media
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1531
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.Vsevolod Laptevdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1531Tue, 20 Apr 2004 10:18:53 +0200Modelling, Estimating and Validating Multidimensional Distribution Functions -With Applications to Risk Management-
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1516
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.Markus Junkerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1516Fri, 13 Feb 2004 11:10:18 +0100Multiscale Modeling of CHAMP-Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1457
The following three papers present recent developments in multiscale gravitational field modeling by the use of CHAMP or CHAMP-related data. Part A - The Model SWITCH-03: Observed orbit perturbations of the near-Earth orbiting satellite CHAMP are analyzed to recover the long-wavelength features of the Earth's gravitational potential. More precisely, by tracking the low-flying satellite CHAMP by the high-flying satellites of the Global Positioning System (GPS) a kinematic orbit of CHAMP is obtainable from GPS tracking observations, i.e. the ephemeris in cartesian coordinates in an Earth-fixed coordinate frame (WGS84) becomes available. In this study we are concerned with two tasks: First we present new methods for preprocessing, modelling and analyzing the emerging tracking data. Then, in a first step we demonstrate the strength of our approach by applying it to simulated CHAMP orbit data. In a second step we present results obtained by operating on a data set derived from real CHAMP data. The modelling is mainly based on a connection between non-bandlimited spherical splines and least square adjustment techniques to take into account the non-sphericity of the trajectory. Furthermore, harmonic regularization wavelets for solving the underlying Satellite-to-Satellite Tracking (SST) problem are used within the framework of multiscale recovery of the Earth's gravitational potential leading to SWITCH-03 (Spline and Wavelet Inverse Tikhonov regularized CHamp data). Further it is shown how regularization parameters can be adapted adequately to a specific region improving a globally resolved model. Finally we give a comparison of the developed model to the EGM96 model, the model UCPH2002_02_0.5 from the University of Copenhagen and the GFZ models EIGEN-1s and EIGEN-2. Part B - Multiscale Solutions from CHAMP: CHAMP orbits and accelerometer data are used to recover the long- to medium- wavelength features of the Earth's gravitational potential. In this study we are concerned with analyzing preprocessed data in a framework of multiscale recovery of the Earth's gravitational potential, allowing both global and regional solutions. The energy conservation approach has been used to convert orbits and accelerometer data into in-situ potential. Our modelling is spacewise, based on (1) non-bandlimited least square adjustment splines to take into account the true (non-spherical) shape of the trajectory (2) harmonic regularization wavelets for solving the underlying inverse problem of downward continuation. Furthermore we can show that by adapting regularization parameters to specific regions local solutions can improve considerably on global ones. We apply this concept to kinematic CHAMP orbits, and, for test purposes, to dynamic orbits. Finally we compare our recovered model to the EGM96 model, and the GFZ models EIGEN-2 and EIGEN-GRACE01s. Part C - Multiscale Modeling from EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, UCPH2002_0.5, EGM96: Spherical wavelets have been developed by the Geomathematics Group Kaiserslautern for several years and have been successfully applied to georelevant problems. Wavelets can be considered as consecutive band-pass filters and allow local approximations. The wavelet transform can also be applied to spherical harmonic models of the Earth's gravitational field like the most up-to-date EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, UCPH2002_0.5, and the well-known EGM96. Thereby, wavelet coefficients arise and these shall be made available to other interested groups. These wavelet coefficients allow the reconstruction of the wavelet approximations. Different types of wavelets are considered: bandlimited wavelets (here: Shannon and Cubic Polynomial (CP)) as well as non-bandlimited ones (in our case: Abel-Poisson). For these types wavelet coefficients are computed and wavelet variances are given. The data format of the wavelet coefficients is also included.W. Freeden; V. Michelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1457Mon, 08 Dec 2003 11:25:15 +0100Nonparametric Estimates for Conditional Quantiles of Time Series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1454
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.Jürgen Franke; Peter Mwitapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1454Wed, 19 Nov 2003 16:26:59 +0100A Survey of Approximation Methods in Multiobjective Programming
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1451
Approaches to approximate the efficient and Pareto sets of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers 48 articles published since 1975.Stefan Ruzika; Margaret M. Wiecekpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1451Thu, 13 Nov 2003 11:18:57 +0100Algorithms for Time Dependent Bicriteria Shortest Path Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1450
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.Horst W. Hamacher; Stevanus A. Tjandrapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1450Wed, 12 Nov 2003 14:23:26 +0100Earliest Arrival Flows with Time-Dependent Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1449
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.Horst W. Hamacher; Stevanus A. Tjandrapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1449Wed, 12 Nov 2003 12:49:13 +0100Set Covering With Almost Consecutive Ones Property
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1448
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.Nikolaus Ruf; Anita Schöbelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1448Tue, 11 Nov 2003 14:13:43 +0100A Tree Algorithm for Isotropic Finite Elements on the Sphere
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1447
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.Frank Bauer; Willi Freeden; Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1447Mon, 10 Nov 2003 10:47:32 +0100Multiresolution Analysis by Spherical Up Functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1446
A new class of locally supported radial basis functions on the (unit) sphere is introduced by forming an infinite number of convolutions of ''isotropic finite elements''. The resulting up functions show useful properties: They are locally supported and are infinitely often differentiable. The main properties of these kernels are studied in detail. In particular, the development of a multiresolution analysis within the reference space of square--integrable functions over the sphere is given. Altogether, the paper presents a mathematically significant and numerically efficient introduction to multiscale approximation by locally supported radial basis functions on the sphere.Willi Freeden; Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1446Mon, 10 Nov 2003 10:42:17 +0100On the adaptive selection of the parameter in regularization of ill-posed problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1445
We study a possiblity to use the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme proposed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for non-linear ill-posed problems and an inverse problem of the two-dimensional profile reconstruction.Sergei Pereverzev; Eberhard Schockpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1445Mon, 10 Nov 2003 10:38:04 +0100Maximal Cohen-Macaulay Modules over a Non-Isolated Hypersurface Singularity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1444
Corina Baciupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1444Mon, 03 Nov 2003 14:50:59 +0100Resolutions and Moduli for Equivariant Sheaves over Toric Varieties
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1440
In this thesis the combinatorial framework of toric geometry is extended to equivariant sheaves over toric varieties. The central questions are how to extract combinatorial information from the so developed description and whether equivariant sheaves can, like toric varieties, be considered as purely combinatorial objects. The thesis consists of three main parts. In the first part, by systematically extending the framework of toric geometry, a formalism is developed for describing equivariant sheaves by certain configurations of vector spaces. In the second part, homological properties of a certain class of equivariant sheaves are investigated, namely that of reflexive equivariant sheaves. Several kinds of resolutions for these sheaves are constructed which depend only on the configuration of their associated vector spaces. Thus a partially positive answer to the question of combinatorial representability is given. As a particular result, a new way for computing minimal resolutions for Z^n - graded modules over polynomial rings is obtained. In the third part a complete classification of the simplest nontrivial sheaves, equivariant vector bundles of rank two over smooth toric surfaces, is given. A combinatorial characterization is given and parameter spaces (moduli spaces) are constructed which depend only on this characterization. In appendices a outlook on equivariant sheaves and the relation of Chern classes to their combinatorial classification is given, particularly focussing on the case of the projective plane. A classification of equivariant vector bundles of rank three over the projective plane is given.Markus Perlingdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1440Wed, 08 Oct 2003 09:46:42 +0200Surface Measures on Paths in an Embedded Riemannian Manifold
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1439
We construct and study two surface measures on the space C([0,1],M) of paths in a compact Riemannian manifold M embedded into the Euclidean space R^n. The first one is induced by conditioning the usual Wiener measure on C([0,T],R^n) to the event that the Brownian particle does not leave the tubular epsilon-neighborhood of M up to time T, and passing to the limit. The second one is defined as the limit of the laws of reflected Brownian motions with reflection on the boundaries of the tubular epsilon-neighborhoods of M. We prove that the both surface measures exist and compare them with the Wiener measure W_M on C([0,T],M). We show that the first one is equivalent to W_M and compute the corresponding density explicitly in terms of the scalar curvature and the mean curvature vector of M. Further, we show that the second surface measure coincides with W_M. Finally, we study the limit behavior of the both surface measures as T tends to infinity.Nadja Sidorovadoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1439Mon, 29 Sep 2003 15:47:12 +0200Wavelet Modelling of Ionospheric Currents and Induced Magnetic Fields From Satellite Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1437
The thesis is concerned with the modelling of ionospheric current systems and induced magnetic fields in a multiscale framework. Scaling functions and wavelets are used to realize a multiscale analysis of the function spaces under consideration and to establish a multiscale regularization procedure for the inversion of the considered operator equation. First of all a general multiscale concept for vectorial operator equations between two separable Hilbert spaces is developed in terms of vector kernel functions. The equivalence to the canonical tensorial ansatz is proven and the theory is transferred to the case of multiscale regularization of vectorial inverse problems. As a first application, a special multiresolution analysis of the space of square-integrable vector fields on the sphere, e.g. the Earth’s magnetic field measured on a spherical satellite’s orbit, is presented. By this, a multiscale separation of spherical vector-valued functions with respect to their sources can be established. The vector field is split up into a part induced by sources inside the sphere, a part which is due to sources outside the sphere and a part which is generated by sources on the sphere, i.e. currents crossing the sphere. The multiscale technqiue is tested on a magnetic field data set of the satellite CHAMP and it is shown that crustal field determination can be improved by previously applying our method. In order to reconstruct ionspheric current systems from magnetic field data, an inversion of the Biot-Savart’s law in terms of multiscale regularization is defined. The corresponding operator is formulated and the singular values are calculated. Based on the konwledge of the singular system a regularzation technique in terms of certain product kernels and correponding convolutions can be formed. The method is tested on different simulations and on real magnetic field data of the satellite CHAMP and the proposed satellite mission SWARM.Carsten Mayerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1437Fri, 26 Sep 2003 10:35:10 +0200Subgradient Optimization Methods in Integer Programming with an Application to a Radiation Therapy Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1436
The thesis deals with the subgradient optimization methods which are serving to solve nonsmooth optimization problems. We are particularly concerned with solving large-scale integer programming problems using the methodology of Lagrangian relaxation and dualization. The goal is to employ the subgradient optimization techniques to solve large-scale optimization problems that originated from radiation therapy planning problem. In the thesis, different kinds of zigzagging phenomena which hamper the speed of the subgradient procedures have been investigated and identified. Moreover, we have established a new procedure which can completely eliminate the zigzagging phenomena of subgradient methods. Procedures used to construct both primal and dual solutions within the subgradient schemes have been also described. We applied the subgradient optimization methods to solve the problem of minimizing total treatment time of radiation therapy. The problem is NP-hard and thus far there exists no method for solving the problem to optimality. We present a new, efficient, and fast algorithm which combines exact and heuristic procedures to solve the problem.Berhanu Gutadoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1436Fri, 26 Sep 2003 10:18:18 +0200Mathematical Methods for the efficient Assessment of Market and Credit Risk
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1435
The central theme in this thesis concerns the development of enhanced methods and algorithms for appraising market and credit risks and their application within the context of standard and more advanced market models. Generally, methods and algorithms for analysing market risk of complex portfolios involve detailed knowledge of option sensitivities, the so-called "Greeks". Based on an analysis of symmetries in financial market models, relations between option sensitivities are obtained, which can be used for the efficient valuation of the Greeks. Mainly, the relations are derived within the Black Scholes model, however, some relations are also valid for more general models, for instance the Heston model. Portfolios are usually influenced by lots of underlyings, so it is necessary to characterise the dependencies of these basic instruments. It is usual to describe such dependencies by correlation matrices. However, estimations of correlation matrices in practice are disturbed by statistical noise and usually have the problem of rank deficiency due to missing data. A fast algorithm is presented which performs a generalized Cholesky decomposition of a perturbed correlation matrix. In contrast to the standard Cholesky algorithm, an advantage of the generalized method is that it works for semi-positive, rank deficient matrices as well. Moreover, it gives an approximative decomposition when the input matrix is indefinite. A comparison with known algorithms with similar features is performed and it turns out, that the new algorithm can be recommended in situations where computation time is the critical issue. The determination of a profit and loss distribution by Fourier inversion of its characteristic function is a powerful tool, but it can break down when the characteristic function is not integrable. In this thesis, methods for Fourier inversion of non-integrable characteristic functions are studied. In this respect, two theorems are obtained which are based on a suitable approximation of the unknown distribution with known density and characteristic function. Further it will be shown, that straightforward Fast Fourier inversion works, when the according density lives on a bounded interval. The above techniques are of crucial importance to determine the profit and loss distribution (P&L) of large portfolios efficiently. The so-called Delta Gamma normal approach has become industrial standard for the estimation of market risk. It is shown, that the performance of the Delta Gamma normal approach can be improved substantially by application of the developed methods. The same optimization procedure also applies to the Delta Gamma Student model. A standard tool for computing the P&L distribution of a loan portfolio is the CreditRisk+ model. Basically, the CreditRisk+ distribution is a discrete distribution which can be computed from its probability generating function. For this a numerically stable method is presented and as an alternative, a new algorithm based on Fourier inversion is proposed. Finally, an extension of the CreditRisk+ model to market risk is developed, which distribution can be obtained efficiently by the presented Fourier inversion methods as well.Oliver Reißdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1435Tue, 16 Sep 2003 15:37:01 +0200Abgeleitete Kategorien und Matrixprobleme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1434
Diese Arbeit gehört in die algebraische Geometrie und die Darstellungstheorie und stellt eine Beziehung zwischen beiden Gebieten dar. Man beschäftigt sich mit den abgeleiteten Kategorien auf flachen Entartungen projektiver Geraden und elliptischer Kurven. Als Mittel benutzt man die Technik der Matrixprobleme. Das Hauptergebnis dieser Dissertation ist der folgende Satz: SATZ. Sei X ein Zykel projektiver Geraden. Dann gibt es drei Typen unzerlegbarer Objekte in D^-(Coh_X): - Shifts von Wolkenkratzergarben in einem regulären Punkt; - Bänder B(w,m,lambda), - Saiten S(w). Ganz analog beweist man die Zahmheit der abgeleiteten Kategorien vieler assoziativer Algebren.Igor Burbandoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1434Tue, 16 Sep 2003 11:33:00 +0200Optimizacíon lineal en las clases de matemáticas
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1431
Las matemáticas son atribuidas en general a algo no claro y sólo para matemáticos. La imagen de las matemáticas para los escolares, es la de una ciencia, la cual se sirve sólo de si misma. Es importante hacer frente al prejuicio de que las matemáticas distan lejos de toda utilidad práctica. La matemática es una ciencia al servicio de todas las dem´as ciencias, de cuya ayuda se necesita en casi todos los campos de la vida. La matemática de la escuela debería despertar en cualquier ámbito de la vida de los escolares el interés sobre ...Horst W. Hamacher; Stefanie Müllerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1431Sat, 13 Sep 2003 10:49:54 +0200Linear Optimization in School Mathematics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1430
Linear Optimization is an important area from applied mathematics. A lot of practical problems can be modelled and solved with this technique. This publication shall help to introduce this topic to pupils. The process of modelling, the reduction of problems to their significant attributes shall be described. The linear programms will be solved by using the simplex method. Many examples illustrate the topic.Horst W. Hamacher; Stefanie Müllerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1430Sat, 13 Sep 2003 10:47:10 +0200Lista de productos y álgebra lineal
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1429
A mediados del año 1997 la publicación de los denominados TIMMS-Estudios (Third International Mathematics and Science Study) causó un importante impacto en el público alemán. El motivo de esto fue el rendimiento escolar conseguido en la rama de matemáticas y ciencias naturales del octavo curso, el cual estaba situado en un campo internacional, donde particularmente en el ámbito matemático el conjunto de los estados del norte-, oeste-, y del este de Europa que forman parte del TIMSS - sin mencionar a la mayoría de los paises asiáticos - habían conseguido claramente mejores rendimiento. En definitiva mostraban un peor rendimiento los escolares alemanes con respecto a los paises vecinos y con los ....Florentine Bunke; Horst W. Hamacher; Andreas Maurer; Stefanie Müllerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1429Sat, 13 Sep 2003 10:41:07 +0200Bills of material and linear algebra
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1428
This publication tries to develop mathematical subjects for school from realistic problems. The center of this report are business planning and decision problems which occur in almost all companies. The main topics are: Calculation of raw material demand for given orders, consumption of existing stock and the lot sizing.Florentine Bunke; Horst W. Hamacher; Andreas Maurer; Stefanie Müllerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1428Sat, 13 Sep 2003 10:33:05 +0200Cauchy-Navier Wavelet Solvers and Their Application in Deformation Analysis
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1432
The focus of this work has been to develop two families of wavelet solvers for the inner displacement boundary-value problem of elastostatics. Our methods are particularly suitable for the deformation analysis corresponding to geoscientifically relevant (regular) boundaries like sphere, ellipsoid or the actual Earth's surface. The first method, a spatial approach to wavelets on a regular (boundary) surface, is established for the classical (inner) displacement problem. Starting from the limit and jump relations of elastostatics we formulate scaling functions and wavelets within the framework of the Cauchy-Navier equation. Based on numerical integration rules a tree algorithm is constructed for fast wavelet computation. This method can be viewed as a first attempt to "short-wavelength modelling", i.e. high resolution of the fine structure of displacement fields. The second technique aims at a suitable wavelet approximation associated to Green's integral representation for the displacement boundary-value problem of elastostatics. The starting points are tensor product kernels defined on Cauchy-Navier vector fields. We come to scaling functions and a spectral approach to wavelets for the boundary-value problems of elastostatics associated to spherical boundaries. Again a tree algorithm which uses a numerical integration rule on bandlimited functions is established to reduce the computational effort. For numerical realization for both methods, multiscale deformation analysis is investigated for the geoscientifically relevant case of a spherical boundary using test examples. Finally, the applicability of our wavelet concepts is shown by considering the deformation analysis of a particular region of the Earth, viz. Nevada, using surface displacements provided by satellite observations. This represents the first step towards practical applications.Madalagama Karawitage Abeyratnedoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1432Sat, 13 Sep 2003 09:34:52 +0200