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Fri, 10 Nov 2017 10:53:46 +0100Fri, 10 Nov 2017 10:53:46 +0100Information Complexity of Multivariate Fredholm Equations in Sobolev Classes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5062
In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.Karin Frank; Stefan Heinrich; Sergei Pereverzevreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5062Fri, 10 Nov 2017 10:53:46 +0100An improved asymptotic analysis of the expected number of pivot steps required by the simplex algorithm
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5049
Let \(a_1,\dots,a_m\) be i.i .d. vectors uniform on the unit sphere in \(\mathbb{R}^n\), \(m\ge n\ge3\) and let \(X\):= {\(x \in \mathbb{R}^n \mid a ^T_i x\leq 1\)} be the random polyhedron generated by. Furthermore, for linearly independent vectors \(u\), \(\bar u\) in \(\mathbb{R}^n\), let \(S_{u, \bar u}(X)\) be the number of shadow vertices of \(X\) in \(span (u, \bar u\)). The paper provides an asymptotic expansion of the expectation value \(E (S_{u, \bar u})\) for fixed \(n\) and \(m\to\infty\). The first terms of the expansion are given explicitly. Our investigation of \(E (S_{u, \bar u})\) is closely connected to Borgwardt's probabilistic analysis of the shadow vertex algorithm - a parametric variant of the simplex algorithm. We obtain an improved asymptotic upper bound for the number of pivot steps required by the shadow vertex algorithm for uniformly on the sphere distributed data.Karl-Heinz Küferreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5049Wed, 08 Nov 2017 16:03:14 +0100A Note on Approximation Algorithms for the Multicriteria \(\Delta\)-TSP
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5031
The Tree and Christofides heuristic are weil known 1- and \(\frac{1} {2}\)- approximate algorithms for the \(\Delta\)-TSP. In this note their performance for the multicriteria case is described, depending on the norm in \(\mathbb{R}^Q\) in case of \(Q\) criteria.Matthias Ehrgott; Alexander Feldmannreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5031Mon, 06 Nov 2017 11:45:28 +0100Ähnlichkeit von Prozeßmodellen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5013
Die Sichten von Projektmitgliedern auf Prozesse von Software-Entwicklungen sollen in der Prozeßmodellierungssprache MVP-L formuliert und anschließend in ein Umfassendes Prozeßmodell integriert werden. Dabei ist die Identifikation ähnlicher Informationen in verschiedenen Sichten von Bedeutung. In dieser Arbeit berichten
wir über die Adaption und Synthese verschiedener Ansätze zum Thema Ähnlichkeit aus unterschiedlichen Domänen (Schema-Integration beim Datenbank-Entwurf, Analoges und Fallbasiertes Schließen, Wiederverwendung und System-Spezifikation). Das Ergebnis, die Ähnlichkeitsfunktion vsim, wird anhand eines Referenzbeispiels illustriert. Dabei gehen wir insbesondere auf die Eigenschaft der Funktion vsim ein und berichten über Erfahrungen im Umgang mit dieser Funktion zur Berechnung der Ähnlichkeit zwischen Prozeßmodellen.Martin Verlage; Horst Hientzreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5013Thu, 02 Nov 2017 14:00:48 +0100Evaluation of a BRDF using BSP Trees
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4957
In this paper an analytic hidden surface removal algorithm is presented which uses a combination
of 2D and 3D BSP trees without involving point sampling or scan conversion. Errors like aliasing
which result from sampling do not occur while using this technique. An application of this
algorithm is outlined which computes the energy locally reflected from a surface having an
arbitrary BRDF. A simplification for diffuse reflectors is described, which has been implemented
to compute analytic form factors from diffuse light sources to differential receivers as they are needed for shading and radiosity algorithms.Philip Jacobreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4957Thu, 26 Oct 2017 12:37:05 +0200Variance reduction for Monte Carlo methods by means of deterministic numerical computation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4954
A new variance reduction technique for the Monte Carlo solution of integral
equations is introduced. It is based on separation of the main part. A neighboring equation with exactly known solution is constructed by the help of a deterministic Galerkin scheme. The variance of the method is analyzed, and an application to the radiosity equation of computer graphics, together with numerical test results is given.Stefan Heinrichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4954Thu, 26 Oct 2017 10:03:58 +0200Efficient algorithms for computing the \(L_2\) discrepancy
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4941
The \(L_2\)-discrepancy is a quantitative measure of precision for multivariate quadrature rules. It can be computed explicitly. Previously known algorithms needed \(O(m^2\)) operations, where \(m\) is the number of nodes. In this paper we present algorithms which require
\(O(m(log m)^d)\) operations.Stefan Heinrichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4941Wed, 25 Oct 2017 09:35:31 +0200Visualization of Unstable Surface Regions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4939
Computer processing of free form surfaces forms the basis of a closed construction process starting with surface design and up to NC-production.
Numerical simulation and visualization allow quality analysis before manufacture. A new aspect in surface analysis is described, the stability
of surfaces versus infinitesimal bendings. The stability concept is derived
from the kinetic meaning of a special vector field which is given by the deformation. Algorithms to calculate this vector field together with an appropriate visualization method give a tool able to analyze surface stability.Stefanie Hahmannreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4939Wed, 25 Oct 2017 08:34:19 +0200Numerical Aspects of Stability Investigations on Surfaces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4937
The CAD/CAM-based design of free-form surfaces is the beginning of a chain of operations, which ends with the numerically controlled (NC-) production of the designed object. During this process the shape control is an important step to amount efficiency. Several surface interrogation methods already exist to analyze curvature and continuity behaviour of the shape. This paper deals with a new aspect of shape control: the stability of surfaces with respect to infnitesimal bendings. Each inEnitesimal bending of a surface determines a so called instability surface, which is used for the stability investigations. The kinematic meaning of this instability surface will be discussed and we present algorithms to calculate it.Stefanie Hahmann; Hans Hagenreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4937Wed, 25 Oct 2017 08:26:12 +0200Complexity of Multivariate Integral Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4926
The problem of full solution of Fredholm integral equations of the second kind with data from Sobolev spaces with dominating mixed derivative is studied. Existing estimates for the univariate case are extended to arbitrary dimension.Karin Frankreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4926Tue, 24 Oct 2017 09:24:12 +0200An Optimal Algorithm for the Local Solution of Integral Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4923
The local solution problem of multivariate Fredholm integral equations is studied. Recent research proved that for several function classes the complexity of this problem is closely related to the Gelfand numbers of some characterizing operators. The generalization of this approach to the situation of arbitrary Banach spaces is the subject of the present paper.
Furthermore, an iterative algorithm is described which - under some additional conditions - realizes the optimal error rate. The way these general theorems work is demonstrated by applying them to integral equations in a Sobolev space of periodic functions with dominating mixed derivative of various order.Karin Frankreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4923Tue, 24 Oct 2017 08:45:17 +0200The geometry of optimal degree reduction of Bezier curves
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4910
Optimal degree reductions, i.e. best approximations of \(n\)-th degree Bezier curves
by Bezier curves of degree \(n\) - 1, with respect to different norms are studied. It
is shown that for any \(L_p\)-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree \(n\) - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for \(p\) = 1 and \(p\) = 2 and in the constrained case for \(p\) = 2.Guido Brunnett; Thomas Schreiber; Jörg Braunreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4910Mon, 23 Oct 2017 09:06:07 +0200MVP-L Language Report Version 2
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4908
Intellectual control over software development projects requires the existence of an integrated set of explicit models of the products to be developed, the processes used to develop them, the resources needed, and the productivity and quality aspects involved. In recent years the development of languages, methods and tools for modeling software processes, analyzing and enacting them has become a major emphasis of software engineering research. The majority of current process research concentrates on prescriptive modeling of small, completely formalizable processes and their execution entirely on computers. This research direction has produced process modeling languages suitable for machine rather than human consumption. The MVP project, launched at the University of Maryland and continued at Universität Kaiserslautern, emphasizes building descriptive models of large, real-world processes and their use by humans and computers for the purpose of understanding, analyzing, guiding and improving software development projects. The language MVP-L has been developed with these purposes in mind. In this paper, we
motivate the need for MVP-L, introduce the prototype language, and demonstrate its uses. We assume that further improvements to our language will be triggered by lessons learned from applications and experiments.Alfred Bröckers; Christopher M. Lott; H. Dieter Rombach; Martin Verlagereporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4908Fri, 20 Oct 2017 14:27:14 +0200A graphical representation schema for the software process modeling language MVP-L
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4906
Experience gathered from applying the software process modeling language MVP-L in software development organizations has shown the need for graphical representations of process models. Project members (i.e„ non MVP-L specialists) review models much more easily by using graphical representations. Although several various graphical notations were developed for individual projects in which MVP-L was applied, there was previously no consistent definition of a mapping between textual MVP-L models and graphical representations. This report defines a graphical representation schema for MVP-L
descriptions and combines previous results in a unified form. A basic set of building blocks (i.e., graphical symbols and text fragments) is defined, but because we must first gain experience with the new symbols, only rudimentary guidelines are given for composing basic
symbols into a graphical representation of a model.Alfred Bröckers; Christiane Differding; Barbara Hoisl; Frank Kollnischko; Christopher M. Lott; Jürgen Münch; Martin Verlage; Stefan Vorwiegerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4906Fri, 20 Oct 2017 13:22:09 +0200Data-procedural Languages for FPL-based Machines
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4899
This paper introduces a new high Level programming language for a novel
class of computational devices namely data-procedural machines. These machines are by up to several orders of magnitude more efficient than the von Neumann paradigm of computers and are as flexible and as universal as computers. Their efficiency and flexibility is achieved by using field-programmable logic as the essential technology platform. The paper briefly summarizes and illustrates the essential new features of this language by means of two example programs.Andreas Ast; J. Becker; Reiner W. Hartenstein; R. Kress; H. Reinig; K. Schmidtreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4899Fri, 20 Oct 2017 11:32:19 +0200Mathematik als Vehikel der Philosophie und Weltanschauung
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4887
Knut Radbruchreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4887Thu, 19 Oct 2017 10:05:34 +0200On Matroids with Multiple Objectives
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4850
In this paper we investigate two optimization problems for matroids with multiple objective functions, namely finding the pareto set and the max-ordering problem which conists in finding a basis such that the largest objective value is minimal. We prove that the decision versions of both problems are NP-complete. A solution procedure for the max-ordering problem is presented and a result on the relation of the solution sets of the two problems is given. The main results are a characterization of pareto bases by a basis exchange property and finally a connectivity result for proper pareto solutions.Matthias Ehrgottreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4850Mon, 16 Oct 2017 09:14:56 +0200Lexicographic Max-Ordering - A Solution Concept for Multicriteria Combinatorial Optimization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4849
In this paper we will introduce the concept of lexicographic max-ordering solutions for multicriteria combinatorial optimization problems. Section 1 provides the basic notions of
multicriteria combinatorial optimization and the definition of lexicographic max-ordering solutions. In Section 2 we will show that lexicographic max-ordering solutions are pareto optimal as well as max-ordering optimal solutions. Furthermore lexicographic max-ordering solutions can be used to characterize the set of pareto solutions. Further properties of lexicographic max-ordering solutions are given. Section 3 will be devoted to algorithms. We give a polynomial time algorithm for the two criteria case where one criterion is a sum and one is a bottleneck objective function, provided that the one criterion sum problem is solvable in polynomial time. For bottleneck functions an algorithm for the general case of Q criteria is presented.Matthias Ehrgottreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4849Mon, 16 Oct 2017 08:57:51 +0200Connectedness of Efficient Solutions in Multiple Criteria Combinatorial Optimization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4844
In multiple criteria optimization an important research topic is the topological structure of the set \( X_e \) of efficient solutions. Of major interest is the connectedness of \( X_e \), since it would allow the determination of \( X_e \) without considering non-efficient solutions in the
process. We review general results on the subject,including the connectedness result for efficient solutions in multiple criteria linear programming. This result can be used to derive a definition of connectedness for discrete optimization problems. We present a counterexample to a previously stated result in this area, namely that the set of efficient solutions of the shortest path problem is connected. We will also show that connectedness does not hold for another important problem in discrete multiple criteria optimization: the spanning tree problem.Matthias Ehrgott; Kathrin Klamrothreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4844Mon, 16 Oct 2017 08:41:05 +0200Velocitiy-resolved recombination dynamics in a laser-produced Ta plasma
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1921
Ion energy spectra of a laser-produced Ta plasma have been investigated as a function of the flight distance from the focus. The laser (Nd:YAG, 20 ns, 210 mJ) is incident obliquely (45°) and focused to an intensity of about 10^11 W cm-2. The changes in the ion distributions have been analysed for the Ta+ to Ta6+ ions in an expansion range 64 - 220 cm. With increasing distance from the target, a weak but monotonic decrease is observed for the total number of ions, which is essentially due to the decrease in the number of the more highly charged species. For the Ta+ and Ta2+ ions the net changes approximately cancel. A more sophisticated picture of the recombination dynamics is obtained, however, if the changes within individual groups of ions expanding with different velocities are compared. Here, in the same spectrum, both increasing and decreasing ion numbers can be observed. This can be interpreted as direct evidence of recombination and its dependence on temperature, density and charge.Axel Rupp; Klaus Rohrworkingpaperhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1921Sat, 29 Dec 2007 13:22:37 +0100Clifford's Legacy to Mathematics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1306
Heinz Krügerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1306Tue, 03 Jul 2001 00:00:00 +0200Nonvacuum pseudoparticles, quantum tuneling and metastability
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1189
Abstract: It is shown that nonvacuum pseudoparticles can account forquantum tunneling and metastability. In particular the saddle-point nature of the pseudoparticles is demonstrated, and the evaluation of path-integrals in their neighbourhood. Finally the relation between instantons and bounces is used to derive a result conjectured by Bogomolny andFateyev.Jiu-Qing Liang; H.J.W. Müller-Kirstenpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1189Thu, 05 Apr 2001 00:00:00 +0200An Overview of the Method of Smoothed Particle Hydrodynamics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/585
This report is intended to provide an introduction to the method of SmoothedParticle Hydrodynamics or SPH. SPH is a very versatile, fully Lagrangian, particle based code for solving fluid dynamical problems. Many technical aspects of the method are explained which can then be employed to extend the application of SPH to new problems.J.P. Morrispreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/585Fri, 23 Jun 2000 00:00:00 +0200A Model for the Cloudiness of Fabrics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562
Cloudy inhomogenities in artificial fabrics are graded by a fast method which is based on a Laplacian pyramid decomposition of the fabric image. This band-pass representation takes into account the scale character of the cloudiness. A quality measure of the entire cloudiness is obtained as a weighted mean over the variances of all scales.Joachim Weickertarticlehttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/562Wed, 07 Jun 2000 00:00:00 +0200Direct Coupling of Fluid and Kinetic Equations: I
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/556
J. Schneiderpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/556Wed, 07 Jun 2000 00:00:00 +0200