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Fri, 12 May 2000 00:00:00 +0100Fri, 12 May 2000 00:00:00 +0100Das dynamische Travelling-Salesman Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1144
Das TSP wird auf zeitabhängige Kosten und Wegelängen verallgemeinert, der Komplexitätstatus untersucht, verschiedene Formulierungen verglichen, Spezialfälle untersucht und ein auf Lagrange-Relaxation und Branch&Bound beruhendes exaktes Lösungsverfahren von Lucena erweitert, implementiert und getestet. Für das TDTSP wird die Dimension des ganzzahligen Polyeders bestimmt.Martin C. Müllerdiplomhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1144Tue, 05 Dec 2000 00:00:00 +0100The C Programmes for "Numerical Methods (Programmes and Implementation)"
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/594
Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/594Fri, 23 Jun 2000 00:00:00 +0200Multidimensionale Systemtheorie
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/598
Die Theorie der mehrdimensionalen Systeme ist ein relativ junges Forschungsgebiet innerhalb der Systemtheorie, erste Arbeiten stammen aus den 70er Jahren. Hauptmotiv für das Studium multidimensionaler Systeme war die Notwendigkeit einer Erweiterung der Theorie der digitalen Filter, die in der klassischen, eindimensionalen Signalverarbeitung (zeitabhängige Signale) Anwendung finden, auf den Bereich der Bildverarbeitung, also auf zweidimensionale Signale.; Die Vorlesung beschäftigt sich daher in ihrem ersten Teil mit skalaren zweidimensionalen Systemen und beschränkt sich im wesentlichen auf den linearen Fall. Untersucht werden zweidimensionale Filter, ihre wichtigsten Eigenschaften, Kausalität und Stabilität, sowie ihre Zustandsraum- realisierungen, etwa die Modelle von Roesser und Fornasini-Marchesini. Parallelen und Unterschiede zur eindimensionalen Systemtheorie werden betont.; Im zweiten Teil der Vorlesung werden allgemeine höherdimensionale und multivariable Systeme behandelt. Für diese Systeme erweist sich der von Jan Willems begründete Zugang zur Systemtheorie, der sogenannte behavioral approach, als zweckmäßig. Grundlegende Ideen dieses Ansatzes sowie eine der wichtigsten Methoden zum Rechnen mit Polynomen in mehreren Variablen, die Theorie der Gröbnerbasen, werden vorgestellt.E. Zerzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/598Fri, 23 Jun 2000 00:00:00 +0200Asymptotic Behaviour of Self-Organizing Maps with Non-Uniform Stimuli Distribution
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/600
Here the almost sure convergence of one dimensional Kohonen" s algorithm in its general form, namely, 2k point neightbour setting with a non-uniform stimuli distribution is proved. We show that the asymptotic behaviour of the algorithm is governed by a cooperative system of differential equations which in general is irreducible. The system of differential equation has an asymptotically stable fixed point which a compact subset of its domain of attraction will be visited by the state variable Xn infinitely often.Ali A. Sadeghipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/600Fri, 23 Jun 2000 00:00:00 +0200Singular Optimal Control - The State of the Art
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/603
The purpose of this paper is to present the state of the art in singular optimal control. If the Hamiltonian in an interval \([t_1,t_2]\) is independent of the control we call the control in this interval singular. Singular optimal controls appear in many applications so that research has been motivated since the 1950s. Often optimal controls consist of nonsingular and singular parts where the junctions between these parts are mostly very difficult to find. One section of this work shows the actual knowledge about the location of the junctions and the behaviour of the control at the junctions. The definition and the properties of the orders (problem order and arc order), which are important in this context, are given, too. Another chapter considers multidimensional controls and how they can be treated. An alternate definition of the orders in the multidimensional case is proposed and a counterexample, which confirms a remark given in the 1960s, is given. A voluminous list of optimality conditions, which can be found in several publications, is added. A strategy for solving optimal control problems numerically is given, and the existing algorithms are compared with each other. Finally conclusions and an outlook on the future research is given.Volker Michelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/603Fri, 23 Jun 2000 00:00:00 +0200On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/753
Bernd Kreußlerarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/753Mon, 03 Apr 2000 00:00:00 +0200On strategies and implementations for computations of free resolutions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/477
Thomas Siebertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/477Mon, 03 Apr 2000 00:00:00 +0200Introducing Reduction to Polycyclic Group Rings - A Comparison of Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/478
t is well-known that for the integral group ring of a polycyclic group several decision problems are decidable. In this paper a technique to solve themembership problem for right ideals originating from Baumslag, Cannonito and Miller and studied by Sims is outlined. We want to analyze, how thesedecision methods are related to Gröbner bases. Therefore, we define effective reduction for group rings over Abelian groups, nilpotent groups and moregeneral polycyclic groups. Using these reductions we present generalizations of Buchberger's Gröbner basis method by giving an appropriate definition of"Gröbner bases" in the respective setting and by characterizing them using concepts of saturation and s-polynomials.Birgit Reinertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/478Mon, 03 Apr 2000 00:00:00 +0200Structure and Construction of Instanton Bundles on P3
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/481
Thomas Nüßlerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/481Mon, 03 Apr 2000 00:00:00 +0200Heuristics for the K-Cardinality Tree and Subgraph Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/524
In this paper we consider the problem of finding in a given graph a minimal weight subtree of connected subgraph, which has a given number of edges. These NP-hard combinatorial optimization problems have various applications in the oil industry, in facility layout and graph partitioning. We will present different heuristic approaches based on spanning tree and shortest path methods and on an exact algorithm solving the problem in polynomial time if the underlying graph is a tree. Both the edge- and node weighted case are investigated and extensive numerical results on the behaviour of the heuristics compared to optimal solutions are presented. The best heuristic yielded results within an error margin of less than one percent from optimality for most cases. In a large percentage of tests even optimal solutions have been found.Matthias Ehrgott; Horst. W. Hamacher; J. Freitag; F. Maffiolipreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/524Mon, 03 Apr 2000 00:00:00 +0200Spherical Wavelet Transform and its Discretization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/555
A continuous version of spherical multiresolution is described, starting from continuous wavelet transform on the sphere. Scale discretization enables us to construct spherical counterparts to Daubechies wavelets and wavelet packets (known from Euclidean theory). Essential tool is the theory of singular integrals on the sphere. It is shown that singular integral operators forming a semigroup of contraction operators of class (Co) (like Abel-Poisson or Gauß-Weierstraß operators) lead in canonical way to (pyramidal) algorithms.Willi Freeden; U. Windheuserpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/555Mon, 03 Apr 2000 00:00:00 +0200An Adaptive Hierarchical Approximation Method on the Sphere Using Axisymmetric Locally Supported Basis Functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/561
The paper discusses the approximation of scattered data on the sphere which is one of the major tasks in geomathematics. Starting from the discretization of singular integrals on the sphere the authors devise a simple approximation method that employs locally supported spherical polynomials and does not require equidistributed grids. It is the basis for a hierarchical approximation algorithm using differently scaled basis functions, adaptivity and error control. The method is applied to two examples one of which is a digital terrain model of Australia.Willi Freeden; J. Fröhhlich; R. Brandpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/561Mon, 03 Apr 2000 00:00:00 +0200Deformation Analysis Using Navier Spline Interpolation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/567
The static deformation of the surface of the earth caused by surface pressure like the water load of an ocean or an artificial lake is discussed. First a brief mention is made on the solution of the Boussenesq problem for an infinite halfspace with the elastic medium to be assumed as homogeneous and isotropic. Then the elastic response for realistic earth models is determinied by spline interpolation using Navier splines. Major emphasis is on the derteminination of the elastic field caused by water loads from surface tractions on the (real) earth" s surface. Finally the elastic deflection of an artificial lake assuming a homogeneous isotropic crust is compared for both evaluation methods.Willi Freeden; E. Groten; Michael Schreiner; W. Söhhne; M. Tücckspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/567Mon, 03 Apr 2000 00:00:00 +0200Gradiometry - an Inverse Problem in Modern Satellite Geodesy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/595
Satellite gradiometry and its instrumentation is an ultra-sensitive detection technique of the space gravitational gradient (i.e. the Hesse tensor of the gravitational potential). Gradeometry will be of great significance in inertial navigation, gravity survey, geodynamics and earthquake prediction research. In this paper, satellite gradiometry formulated as an inverse problem of satellite geodesy is discussed from two mathematical aspects: Firstly, satellite gradiometry is considered as a continuous problem of harmonic downward continuation. The space-borne gravity gradients are assumed to be known continuously over the satellite (orbit) surface. Our purpose is to specify sufficient conditions under which uniqueness and existence can be guaranteed. It is shown that, in a spherical context, uniqueness results are obtainable by decomposition of the Hesse matrix in terms of tensor spherical harmonics. In particular, the gravitational potential is proved to be uniquely determined if second order radial derivatives are prescribed at satellite height. This information leads us to a reformulation of satellite gradiometry as a (Fredholm) pseudodifferential equation of first kind. Secondly, for a numerical realization, we assume the gravitational gradients to be known for a finite number of discrete points. The discrete problem is dealt with classical regularization methods, based on filtering techniques by means of spherical wavelets. A spherical singular integral-like approach to regularization methods is established, regularization wavelets are developed which allow the regularization in form of a multiresolution analysis. Moreover, a combined spherical harmonic and spherical regularization wavelet solution is derived as an appropriate tool in future (global and local) high-presision resolution of the earth" s gravitational potential.Willi Freeden; F. Schneider; Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/595Mon, 03 Apr 2000 00:00:00 +0200Enskog-like kinetic models for vehicular traffic
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/596
In the present paper a general criticism of kinetic equations for vehicular traffic is given. The necessity of introducing an Enskog-type correction into these equations is shown. An Enskog-line kinetic traffic flow equation is presented and fluid dynamic equations are derived. This derivation yields new coefficients for the standard fluid dynamic equations of vehicular traffic. Numerical simulations for inhomogeneous traffic flow situations are shown together with a comparison between kinetic and fluid dynamic models.Axel Klar; R. Wegenerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/596Mon, 03 Apr 2000 00:00:00 +0200Orthogonal and non-orthogonal multiresolution analysis, scale discrete and exact fully discrete wavelet transform on the sphere
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/597
Based on a new definition of delation a scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen. In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully discrete wavelet approximation is discussed in case of band-limited wavelets.Willi Freeden; Michael Schreinerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/597Mon, 03 Apr 2000 00:00:00 +0200Some Estimates on the Boltzmann Collision Operator
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/599
The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L -norm of the gain term can be bounded in terms of the L1 and L -norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L -norm of the density function and the loss term of the Boltzmann collision operator.Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/599Mon, 03 Apr 2000 00:00:00 +0200Adaptive Load Balance Techniques in Parallel Rarefied Gas Simulations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/601
The paper presents some adaptive load balance techniques for the simulation of rarefied gas flows on parallel computers. It is shown that a static load balance is insufficient to obtain a scalable parallel efficiency. Hence, two adaptive techniques are investigated which are based on simple algorithms. Numerical results show that using heuristic techniques one can achieve a sufficiently high efficiency over a wide range of different hardware platforms.S. Antonov; Franz-Josef Pfreundt; Jens Struckmeierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/601Mon, 03 Apr 2000 00:00:00 +0200Particle Methods for Evolution Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/602
Michael Junk; Axel Klar; Jens Struckmeier; Sudarshan Tiwaripreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/602Mon, 03 Apr 2000 00:00:00 +0200Some formulae with logarithmic derivatives related to a quantization of some infinite-dimensional Hamiltonian
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/768
Some formulae, containing logarithmic derivatives of (smooth) measures on infinitedimensional spaces, arise in quite different situations. In particular, logarithmic derivatives of a measure are inserted in the Schr"odinger equastion in the space consisting of functions that are square integrable with respect to this measure, what allows us to describe very simply a procedure of (canonical) quantization of infinite-dimensional Hamiltonian systems with the linear phase space. Further, the problem of reconstructing of a measure by its logarithmic derivative (that was posed in [1] independently of any applications) can be equivalent either to the problem of finding the "ground state" (considered as some measure) for infinite-dimensional Schr"odinger equation, or to the problem of finding an invariant measure for a stochastic differential equation (that is a central question of so-called stochastic quantization), or to the problem of recenstruc ting "Gibbsian measure by its specification" (i.e. by a collection of finite-dimensional conditional distributions). Logarithmic derivatives of some measure appear in Cameron-Martin-Girsanov-Maruyama formulae and in its generalizations related to arbitrary smooth measures; they allow also to connect these formulae and the Feynman-Kac formulae. This note discusses all these topics. Of course due to its shortness the presentation is formal in main, and precise analitical assumptions are usually absent. Actually only a list of formulae with small comments is given. Let us mention also that we do not consider at all so-called Dirichlet forms to which a great deal of literature is devoted (cf. [3] and references therein to the works of S. Alberion and others).O.G. Smolyanov; Heinrich von Weizsäckerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/768Mon, 03 Apr 2000 00:00:00 +0200Toying with Jordan matrices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/788
It is shown that an important resolvent estimate is unstable under small perturbations.Eberhard Schockpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/788Mon, 03 Apr 2000 00:00:00 +0200Deformationen isolierter Kurvensingularitäten mit eingebetteten Komponenten
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/802
Christian Brücker; Gert-Martin Greuelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/802Mon, 03 Apr 2000 00:00:00 +0200On moduli spaces of semiquasihomogeneous singularities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/805
Gert-Martin Greuel; Gerhard Pfisterpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/805Mon, 03 Apr 2000 00:00:00 +0200Semicontinuity for representations of Cohen-Macaulay rings
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/807
Yurij Drozd; Gert-Martin Greuelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/807Mon, 03 Apr 2000 00:00:00 +0200Equianalytic and equisingular families of curves on surfaces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/808
Gert-Martin Greuel; Christoph Lossenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/808Mon, 03 Apr 2000 00:00:00 +0200