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Sun, 17 Dec 2006 20:46:17 +0100Sun, 17 Dec 2006 20:46:17 +0100Mathematik für Physiker ... und Mathematiker
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1824
Eine Vorlesung für Studenten der Physik oder Mathematik im ersten Studienjahr: lineare Algebra und Analysis in einer und mehreren Veränderlichen.Klaus Wirthmüllerlecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1824Sun, 17 Dec 2006 20:46:17 +0100On Simpson Moduli Spaces of Stable Sheaves on P_2 with Linear Hilbert Polynomial
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1280
In this short note we prove some general results on semi-stable sheaves on P_2 and P_3 with arbitrary linear Hilbert polynomial. Using Beilinson's spectral sequence, we compute free resolutions for this class of semi-stable sheaves and deduce that the smooth moduli spaces M_{r m + s}(P_2) and M_{r m + r - s}(P_2) are birationally equivalent if r and s are coprime.Hans Georg Freiermuthpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1280Tue, 08 Jan 2002 00:00:00 +0100Homological Mirror Symmetry in Dimension One
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1254
In this paper we complete the proof began by A. Polishchuk and E. Zaslow of a weak version of Kontsevich's symmetry conjecture for elliptic curves.Bernd Kreusslerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1254Fri, 07 Sep 2001 00:00:00 +0200Presentation of power-ordered sets
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1259
Power-ordered sets are not always lattices. In the case of distributive lattices we give a description by disjoint of chains. Finite power-ordered sets have a polarity. We introduct the leveled lattices and show examples with trivial tolerance. Finally we give a list of Hasse diagrams of power-ordered sets.Dietmar Schweigertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1259Fri, 07 Sep 2001 00:00:00 +0200Kryptanalyse der Verschlüsselungsalgorithmen der Microsoft Word Versionen 2.0-7.0
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1258
Roland Fiat; Andreas Guthmann; Georg Kuxpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1258Thu, 31 May 2001 00:00:00 +0200A stochastic control approach to portfolio problems with stochastic interest rates
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1142
We consider investment problems where an investor can invest in a savings account, stocks and bonds and tries to maximize her utility from terminal wealth. In contrast to the classical Merton problem we assume a stochastic interest rate. To solve the corresponding control problems it is necessary to prove averi cation theorem without the usual Lipschitz assumptions.Ralf Korn; Holger Kraftpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1142Mon, 18 Sep 2000 00:00:00 +0200A martingale method of portfolio optimization for unobservable mean rate of return
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1141
In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.Juri Hinz; Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1141Mon, 11 Sep 2000 00:00:00 +0200Orthogonal non-bandlimited wavelets on the sphere
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1138
W. Freeden; V. Michelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1138Thu, 07 Sep 2000 00:00:00 +0200On the Connectedness of Efficient Solutions in Combinatorial Optimization Problems and Ordered Graphs - Matching and Partial Orders -
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1139
In multicriteria optimization problems the connectedness of the set of efficient solutions (pareto set) is of special interest since it would allow the determination of the efficient solutions without considering non-efficient solutions in the process. In the case of the multicriteria problem to minimize matchings the set of efficient solutions is not connected. The set of minimal solutions E pot with respect to the power ordered set contains the pareto set. In this work theorems about connectedness of E pot are given. These lead to an automated process to detect all efficient solutions.Ulrike Bossongpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1139Thu, 07 Sep 2000 00:00:00 +0200Some Complexity Results for k-Cardinality Minimum Cut Problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1140
Many polynomially solvable combinatorial optimization problems (COP) become NP when we require solutions to satisfy an additional cardinality constraint. This family of problems has been considered only recently. We study a newproblem of this family: the k-cardinality minimum cut problem. Given an undirected edge-weighted graph the k-cardinality minimum cut problem is to find a partition of the vertex set V in two sets V 1 , V 2 such that the number of the edges between V 1 and V 2 is exactly k and the sum of the weights of these edges is minimal. A variant of this problem is the k-cardinality minimum s-t cut problem where s and t are fixed vertices and we have the additional request that s belongs to V 1 and t belongs to V 2 . We also consider other variants where the number of edges of the cut is constrained to be either less or greater than k. For all these problems we show complexity results in the most significant graph classes.Maurizio Bruglieri; Matthias Ehrgott; Horst W. Hamacherpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1140Thu, 07 Sep 2000 00:00:00 +0200Performance of some preconditioners for the p - and hp -version of the finite element method in 3D
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1137
Willy Dörfler; Chr. Badurapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1137Thu, 31 Aug 2000 00:00:00 +0200Lineare Algebra I & II
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1135
Inhalte der Grundvorlesungen Lineare Algebra I und II im Winter- und Sommersemester 1999/2000: Gruppen, Ringe, Körper, Vektorräume, lineare Abbildungen, Determinanten, lineare Gleichungssysteme, Polynomring, Eigenwerte, Jordansche Normalform, endlich-dimensionale Hilberträume, Hauptachsentransformation, multilineare Algebra, Dualraum, Tensorprodukt, äußeres Produkt, Einführung in Singular.Gert-Martin Greuellecturehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1135Wed, 30 Aug 2000 00:00:00 +0200Geometrical properties of generalized single facility location problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1125
In this paper we deal with single facility location problems in a general normed space where the existing facilities are represented by sets. The criterion to be satis ed by the service facility is the minimization of an increasing function of the distances from the service to the closest point ofeach demand set. We obtain a geometrical characterization of the set of optimal solutions for this problem. Two remarkable cases - the classical Weber problem and the minmax problem with demand sets - are studied as particular instances of our problem. Finally, for the planar polyhedral case we give an algorithmic description of the solution set of the considered problems.Stefan Nickel; Justo Puerto; Antonio M. Rodriguez-Chiapreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1125Tue, 29 Aug 2000 00:00:00 +0200The Balance Space Approach to Multicriteria Decision Making - Involving the Decision Maker
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1127
The balance space approach (introduced by Galperin in 1990) provides a new view on multicriteria optimization. Looking at deviations from global optimality of the different objectives, balance points and balance numbers are defined when either different or equal deviations for each objective are allowed. Apportioned balance numbers allow the specification of proportions among the deviations. Through this concept the decision maker can be involved in the decision process. In this paper we prove that the apportioned balance number can be formulated by a min-max operator. Furthermore we prove some relations between apportioned balance numbers and the balance set, and see the representation of balance numbers in the balance set. The main results are necessary and sufficient conditions for the balance set to be exhaustive, which means that by multiplying a vector of weights (proportions of deviation) with its corresponding apportioned balance number a balance point is attained. The results are used to formulate an interactive procedure for multicriteria optimization. All results are illustrated by examples.Matthias Ehrgottpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1127Tue, 29 Aug 2000 00:00:00 +0200Nadir Values: Computation and Use in Compromise Programming
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1128
In this paper we investigate the problem offending the Nadir point for multicriteria optimization problems (MOP). The Nadir point is characterized by the component wise maximal values of efficient points for (MOP). It can be easily computed in the bicriteria case. However, in general this problem is very difficult. We review some existing methods and heuristics and propose some new ones. We propose a general method to compute Nadir values for the case of three objectives, based on theoretical results valid for any number of criteria. We also investigate the use of the Nadir point for compromise programming, when the goal is to be as far away as possible from the worst outcomes. We prove some results about (weak) Pareto optimality of the resulting solutions. The results are illustrated by examples.Matthias Ehrgott; Dagmar Tenfelde-Podehlpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1128Tue, 29 Aug 2000 00:00:00 +0200On the Number of Criteria Needed to Decide Pareto Optimality
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1129
In this paper we address the question of how many objective functions are needed to decide whether a given point is a Pareto optimal solution for a multicriteria optimization problem. We extend earlier results showing that the set of weakly Pareto optimal points is the union of Pareto optimal sets of subproblems and show their limitations. We prove that for strictly quasi-convex problems in two variables Pareto optimality can be decided by consideration of at most three objectives at a time. Our results are based on a geometric characterization of Pareto, strict Pareto and weak Pareto solutions and Helly's Theorem. We also show that a generalization to quasi-convex objectives is not possible, and state a weaker result for this case. Furthermore, we show that a generalization to strictly Pareto optimal solutions is impossible, even in the convex case.Matthias Ehrgott; Stefan Nickelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1129Tue, 29 Aug 2000 00:00:00 +0200An Annotated Bibliography of Multiobjective Combinatorial Optimization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1130
This paper provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO problems, and review the main properties and theoretical results for these problems. One section is devoted to a brief description of the available solution methodology, both exact and heuristic. The main part of the paper is devoted to an annotation of the existing literature in the field organized problem by problem. We conclude the paper by stating open questions and areas of future research. The list of references comprises more than 350 entries.Matthias Ehrgott; Xavier Gandibleuxpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1130Tue, 29 Aug 2000 00:00:00 +0200Linear Facility Location in Three Dimensions - Models and Solution Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1131
We consider the problem of locating a line or a line segment in three- dimensional space, such that the sum of distances from the linear facility to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and effcient solution methods are given.Jack Brimberg; Henrik Juel; Anita Schöbelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1131Tue, 29 Aug 2000 00:00:00 +0200Polyhedral Properties of the Uncapacitated Multiple Allocation Hub Location Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1132
We examine the feasibility polyhedron of the uncapacitated hub location problem (UHL) with multiple allocation, which has applications in the fields of air passenger and cargo transportation, telecommunication and postal delivery services. In particular we determine the dimension and derive some classes of facets of this polyhedron. We develop some general rules about lifting facets from the uncapacitated facility location (UFL) for UHL and projecting facets from UHL to UFL. By applying these rules we get a new class of facets for UHL which dominates the inequalities in the original formulation. Thus we get a new formulation of UHL whose constraints are all facet defining. We show its superior computational performance by benchmarking it on a well known data set.Horst W. Hamacher; Martine Labbé; Stefan Nickel; Tim Sonnebornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1132Tue, 29 Aug 2000 00:00:00 +0200Optimal portfolios under the threat of a crash
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1122
We consider the determination of optimal portfolios under the threat of a crash. Our main assumption is that upper bounds for both the crash size and the number of crashes occurring before the time horizon are given. We make no probabilistic assumption on the crash size or the crash time distribution. The optimal strategies in the presence of a crash possibility are characterized by a balance problem between insurance against the crash and good performance in the crash-free situation. Explicit solutions for the log-utility case are given. Our main finding is that constant portfolios are no longer optimal ones.Ralf Korn; Paul Wilmottpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1122Mon, 28 Aug 2000 00:00:00 +0200Optimal portfolios with bounded Capital-at-Risk
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1123
We consider some continuous-time Markowitz type portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the Capital-at-Risk. In a Black-Scholes setting we obtain closed form explicit solutions and compare their form and implications to those of the classical continuous-time mean-variance problem. We also consider more general price processes which allow for larger uctuations in the returns.Susanne Emmer; Claudia Klüppelberg; Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1123Mon, 28 Aug 2000 00:00:00 +0200A spectrum preserving collocation scheme for Slender-Body Approximations to Stokes Flow
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1118
Linearized flows past slender bodies can be asymptotically described by a linear Fredholm integral equation. A collocation method to solve this equation is presented. In cases where the spectral representation of the integral operator is explicitly known, the collocation method recovers the spectrum of the continuous operator. The approximation error is estimated for two discretizations of the integral operator and the convergence is proved. The collocation scheme is validated in several test cases and extended to situations where the spectrum is not explicit.Thomas Götzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1118Tue, 22 Aug 2000 00:00:00 +0200On the Multiscale Solution of Satellite Problems by Use of Locally Supported Kernel Functions Corresponding to Equidistributed Data on Spherical Orbits
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1117
Being interested in (rotation-)invariant pseudodi erential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i. e. in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical di erence wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).Willi Freeden; Kerstin Hessepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1117Mon, 21 Aug 2000 00:00:00 +0200Basic Aspects of Geopotential Field Approximation From Satellite-to-Satellite Tracking Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1116
The satellite-to-satellite tracking (SST) problems are characterized from mathematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth's gravitational potential by "scalar basis systems" and (vectorial) approximation of the gravitational eld by "vectorial basis systems". Finally, the mathematical justication is given for approximating the external geopotential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi-poles) consistent to a given set of SST data.Willi Freeden; Volker Michelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1116Mon, 21 Aug 2000 00:00:00 +0200On the approximation of kinetic equations by moment systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1115
The aim of this article is to show that moment approximations of kinetic equations based on a Maximum Entropy approach can suffer from severe drawbacks if the kinetic velocity space is unbounded. As example, we study the Fokker Planck equation where explicit expressions for the moments of solutions to Riemann problems can be derived. The quality of the closure relation obtained from the Maximum Entropy approach as well as the Hermite/Grad approach is studied in the case of five moments. It turns out that the Maximum Entropy closure is even singular in equilibrium states while the Hermite/Grad closure behaves reasonably. In particular, the admissible moments may lead to arbitrary large speeds of propagation, even for initial data arbitrary close to global eqilibrium.Wolfgang Dreyer; Michael Junk; Matthias Kunikpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1115Thu, 17 Aug 2000 00:00:00 +0200