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Fri, 10 Nov 2017 09:47:24 +0100Fri, 10 Nov 2017 09:47:24 +0100Polynomial functions of modular lattices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5060
A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (for every \(x \in L\)), \(a \in L\) by applying the operations \(\land, \lor\) finitely often. Every polynomial function in one or also in several variables is a monotone function of \(\mathcal{L}\).
If every monotone function of \(\mathcal{L}\)is a polynomial function then \(\mathcal{L}\) is called orderpolynomially complete. In this paper we give a new characterization of finite order-polynomially lattices. We consider doubly irreducible monotone functions and point out their relation to tolerances, especially to central relations. We introduce chain-compatible lattices
and show that they have a non-trivial congruence if they contain a finite interval and an infinite chain. The consequences are two new results. A modular lattice \(\mathcal{L}\) with a finite interval is order-polynomially complete if and only if \(\mathcal{L}\) is finite projective geometry. If \(\mathcal{L}\) is simple modular lattice of infinite length then every nontrivial interval is of infinite length and has the same cardinality as any other nontrivial interval of \(\mathcal{L}\). In the last sections we show the descriptive power of polynomial functions of
lattices and present several applications in geometry.Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5060Fri, 10 Nov 2017 09:47:24 +0100On derived varieties
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5059
Derived varieties play an essential role in the theory of hyperidentities. In [11] we have shown that derivation diagrams are a useful tool in the analysis of derived algebras and varieties. In this paper this tool is developed further in order to use it for algebraic constructions of derived algebras. Especially the operator \(S\) of subalgebras, \(H\) of homomorphic irnages and \(P\) of direct products are studied. Derived groupoids from the groupoid \(N or (x,y)\) = \(x'\wedge y'\) and from abelian groups are considered. The latter class serves as an example for fluid algebras and varieties. A fluid variety \(V\) has no derived variety as a subvariety and is introduced as a counterpart for solid varieties. Finally we use a property of the commutator of derived algebras in order to show that solvability and nilpotency are preserved under derivation.Dietmar Schweigertreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5059Fri, 10 Nov 2017 09:22:23 +0100Error estimates for Tikhonov regularization with unbounded regularizing operators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5056
It is shown that Tikhonov regularization for ill- posed operator equation
\(Kx = y\) using a possibly unbounded regularizing operator \(L\) yields an orderoptimal algorithm with respect to certain stability set when the regularization parameter is chosen according to the Morozov's discrepancy principle. A more realistic error estimate is derived when the operators \(K\) and \(L\) are related to a Hilbert scale in a suitable manner. The result includes known error estimates for ordininary Tikhonov regularization and also the estimates available under the Hilbert scale approach.M. Thamban Nairreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5056Thu, 09 Nov 2017 12:01:16 +0100On the expected number of shadow vertices of the convex hull of random points
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5051
Let \(a_1,\dots,a_m\) be independent random points in \(\mathbb{R}^n\) that are independent and identically distributed spherically symmetrical in \(\mathbb{R}^n\). Moreover, let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_m\) and let \(L_k\) be an arbitrary \(k\)-dimensional
subspace of \(\mathbb{R}^n\) with \(2\le k\le n-1\). Let \(X_k\) be the orthogonal projection image of \(X\) in \(L_k\). We call those vertices of \(X\), whose projection images in \(L_k\) are vertices of \(X_k\)as well shadow vertices of \(X\) with respect to the subspace \(L_k\) . We derive a distribution independent sharp upper bound for the expected number of shadow vertices of \(X\) in \(L_k\).Karl-Heinz Küferreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5051Thu, 09 Nov 2017 10:49:33 +0100A comparison method for expectations of a class of continuous polytope functionals
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5047
Let \(a_1,\dots,a_n\) be independent random points in \(\mathbb{R}^d\) spherically symmetrically but not necessarily identically distributed. Let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_n\) and for any \(k\)-dimensional subspace \(L\subseteq \mathbb{R}^d\) let \(Vol_L(X) :=\lambda_k(L\cap X)\) be the volume of \(X\cap L\) with respect to the \(k\)-dimensional Lebesgue measure \(\lambda_k, k=1,\dots,d\). Furthermore, let \(F^{(i)}\)(t):= \(\bf{Pr}\) \(\)(\(\Vert a_i \|_2\leq t\)),
\(t \in \mathbb{R}^+_0\) , be the radial distribution function of \(a_i\). We prove that the expectation
functional \(\Phi_L\)(\(F^{(1)}, F^{(2)},\dots, F^{(n)})\) := \(E(Vol_L(X)\)) is strictly decreasing in
each argument, i.e. if \(F^{(i)}(t) \le G^{(i)}(t)t\), \(t \in {R}^+_0\), but \(F^{(i)} \not\equiv G^{(i)}\), we show \(\Phi\) \((\dots, F^{(i)}, \dots\)) > \(\Phi(\dots,G^{(i)},\dots\)). The proof is clone in the more general framework
of continuous and \(f\)- additive polytope functionals.Karl-Heinz Küferreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5047Wed, 08 Nov 2017 13:33:06 +0100New Integrals for \(\zeta(s)\zeta(s+1)\)
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5038
Andreas Guthmannreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5038Tue, 07 Nov 2017 11:46:13 +0100Measurement-Based Feedback in a Process-Centered Software Engineering Environment
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5026
Software development organizations measure their real-world processes, products, and resources to achieve the goal of improving their practices. Accurate and useful measurement relies on explicit models of the real-world processes, products, and resources. These explicit models assist with planning measurement, interpreting data, and assisting developers with their work. However, little work has been done on the joint use of measurem(int and process technologies. We hypothesize that it is possible to integrate measurement and process technologies in a way that supports automation of measurement-based feedback. Automated support for measurementbased feedback means that software developers and maintainers are provided with on-line, detailed information about their work. This type of automated support is expected to help software professionals gain intellectual control over their software projects. The dissertation offers three major contributions. First, an integrated measurement and
process modeling framework was constructed. This framework establishes the necessary foundation for integrating measurement and process technologies in a way that will permit automation. Second, a process-centered software engineering environment was developed to support measurement-based feedback. This system provides personnel with information about the tasks expected of them based on an integrated set of measurement and process views. Third, a set of assumptions and requirements about that system were examined in a controlled experiment. The experiment compared the use of different levels of automation to evaluate the acceptance and effectiveness of measurement-based feedback.Christopher M. Lottreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5026Fri, 03 Nov 2017 13:25:02 +0100Partikelgestützte Triangulierung skelettbasierter impliziter Flächen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5000
Skelettbasierte implizite Flächen haben aufgrund ihrer Fähigkeit, durch automatisches Verschmelzen aus wenigen, einfachen Primitiven komplexe Strukturen zu formen, für Modellierung, Visualisierung und Animation zunehmend an Bedeutung gewonnen. Eine wesentliche Schwierigkeit beim Einsatz impliziter Flächen ist nach wie vor eine effiziente Visualisierung der resultierenden Objekte. In der vorliegenden
Arbeit werden die grundlegenden Ideen einer Methode zur partikelgestützten Triangulierung skelettbasierter impliziter Flächen beschrieben, die die Vorteile einer partikelgestützten Abtastung
impliziter Flächen mit der polygonalen Darstellung durch Dreiecke kombiniert. Der Algorithmus ist in der Lage, effizient auf dynamische Veränderungen der Gestalt sowie das Auseinanderreißen nicht allzu
komplexer implizit gegebener Objekte zu reagieren. Zusätzlich besteht die Möglichkeit, die Triangulierung krümmungsadaptiv zu gestalten, um bei gleichbleibender Darstellungsqualität eine Reduktion der Dreiecksanzahl zu erreichen.Hans-Christian Rodrian; Peter Schüller; Hardy Moockreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5000Mon, 30 Oct 2017 15:25:21 +0100The fast Calculation of Form Factors using Low Discrepancy Sequences
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4971
The calculation of form factors is an important problem in computing the global illumination in the radiosity setting. Closed form solutions often are only available for objects without obstruction and are very hard to calculate. Using Monte Carlo integration and ray tracing provides a fast and elegant tool for the estimation of the form factors. In this paper we show, that using deterministic low discrepancy sample points is superior to random sampling, resulting in an acceleration of more than half an order of magnitude.Alexander Kellerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4971Thu, 26 Oct 2017 16:15:25 +0200Quasi-Monte Carlo Radiosity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4968
The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating
solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-rondom walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks also is applicable to transport problems in settings other
than computer graphics.Alexander Kellerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4968Thu, 26 Oct 2017 14:53:33 +0200Variance reduction by means of deterministic computation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4953
We study the collision estimate of Monte Carlo methods for the solution of integral equations. A new variance technique is proposed and analyzed. It
consists in the separation of the main part by constructing a neighboring equation based on deterministic numerical methods.Stefan Heinrichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4953Thu, 26 Oct 2017 09:50:51 +0200Computing Discrepancies Related to Spaces of Smooth Periodic Functions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4928
A notion of discrepancy is introduced, which represents the integration error on spaces of \(r\)-smooth periodic functions. It generalizes the diaphony and constitutes a periodic counterpart to the classical \(L_2\)-discrepancy as weil as \(r\)-smooth versions of it introduced recently by Paskov [Pas93]. Based on previous work [FH96], we develop an efficient algorithm for computing periodic discrepancies for quadrature formulas possessing certain tensor product structures, in particular, for Smolyak quadrature rules (also called sparse grid methods). Furthermore, fast algorithms of computing periodic discrepancies for lattice rules can easily be derived from well-known properties of lattices. On this basis we carry out numerical comparisons of discrepancies between Smolyak and lattice rules.Karin Frank; Stefan Heinrichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4928Tue, 24 Oct 2017 09:52:59 +0200Computing Discrepancies of Smolyak Quadrature Rules
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4927
In recent years, Smolyak quadrature rules (also called hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadrature formulas
consists in computing their \(L_2\)-discrepancy. Especially for larger dimensions, such computations are a highly complex task. In this paper we develop a fast recursive algorithm for computing the \(L_2\)-discrepancy (and related quality measures) of general Smolyak quadratures. We carry out numerical comparisons between the discrepancies of certain Smolyak rules, Hammersley and Monte Carlo sequences.Karin Frank; Stefan Heinrichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4927Tue, 24 Oct 2017 09:36:20 +0200Technology Package for the Goal Question Metric Paradigm
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4916
This document offers a concise introduction to the Goal Question Metric Paradigm (GQM Paradigm), and surveys research on applying and extending the GQM Paradigm. We describe the GQM Paradigm in terms of its basic principles, techniques for structuring GQM-related documents, and methods for performing tasks of planning and implementing a measurement program based on GQM. We also survey prototype software tools that support applying the GQM Paradigm in various ways. An annotated bibliography lists sources that document experience gained while using the GQM Paradigm and offer in-depth information about the GQM Paradigm.Christiane Differding; Barbara Hoisl; Christopher M. Lottreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4916Mon, 23 Oct 2017 11:05:51 +0200Kontinuierliche Software-Qualitätsverbesserung in der industriellen Praxis
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4914
In der industriellen Praxis werden immer häufiger Verbesserungs- und Meßansätze zur Steigerung der Qualität von Software-Produkten und -Projektdurchführungen diskutiert. Dieser Artikel gibt eine Übersicht über potentielle Ansätze zur kontinuierliche Software-Qualitätsverbesserung:
QIP, CMM und AMI. Aus dem Vergleich der Verbesserungsansätze geht hervor, daß u.a. zielorientiertes Messen eine integrale Technologie zur Verbesserung ist. Deshalb wird in diesem Artikel ein Ansatz für zielorientiertes Messen, der GQM-Ansatz, detaillierter diskutiert. Insbesondere wird auf die Anwendung in der Praxis eingegangen, wobei die Erfahrungen aus realen Projekten in Form von Richtlinien vorgestellt werden. Der Artikel will Praktikern einen Einstieg in die Software Qualitätsverbesserung mittels Messen vermittlen.Christiane Differding; Dieter Rombachreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4914Mon, 23 Oct 2017 10:13:49 +0200Derived Varieties of Semigroups and Groupoids
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4889
Dietmar Schweigert; S.L. Wismathreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4889Thu, 19 Oct 2017 11:35:28 +0200Determinantal Rational Surface Singularities
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4866
In this paper we give explicit equations for determinantal rational surface singularities and prove dimension formulas for the \(T^1\) and \(T^2\) for those singularities.Theo de Jongreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4866Tue, 17 Oct 2017 11:38:01 +0200Superlinear convergence rates for the Lanczos method applied to elliptic operators
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4864
This paper investigates the convergence of the Lanczos method for computing the smallest eigenpair of a selfadjoint elliptic differential operator via inverse iteration (without shifts).
Superlinear convergence rates are established, and their sharpness is investigated for a simple model problem. These results are illustrated numerically for a more difficult problem.Martin Hankereporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4864Tue, 17 Oct 2017 09:10:44 +0200Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4863
This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration.
These assumptions are fulfilled , e.g., for the inverse problem of identifying the diffusion coefficient in a parabolic differential equation from distributed data.Martin Hankereporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4863Tue, 17 Oct 2017 08:51:54 +0200Nonstationary lterated Tikhonov Regularization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4862
A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. lt is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number.Martin Hanke; C.W. Groetschreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4862Mon, 16 Oct 2017 16:20:02 +0200A regularization Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4861
The first part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fréchet derivative of the nonlinear operator at the exact solution, the new Levenberg-Marquardt scheme is suitable for ill-posed problems as long as the Taylor remainder is of second order in the interpolating metric between the range and dornain
topologies. Estimates of this type are established in the second part of the paper for ill-posed parameter identification problems arising in inverse groundwater hydrology. Both, transient and steady state data are investigated. Finally, the numerical performance of the new Levenberg-Marquardt scheme is
studied and compared to a usual implementation on a realistic but synthetic 2D model problem from the engineering literature.Martin Hankereporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4861Mon, 16 Oct 2017 15:27:12 +0200Infinitesimal module deformations in the Thom-Sebastiani Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4851
Florian Enescu; Gerhard Pfister; Dorin Popescureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4851Mon, 16 Oct 2017 09:24:50 +0200On the Solution Region for Certain Scheduling Problems with Preemption
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4839
The paper deals with parallel-machine and open-shop scheduling problems with preemptions and arbitrary nondecreasing objective function. An approach to describe
the solution region for these problems and to reduce them to minimization problems on polytopes is proposed. Properties of the solution regions for certain problems are investigated. lt is proved that open-shop problems with unit processing times are equivalent to certain parallel-machine problems, where preemption is allowed at arbitrary time. A polynomial algorithm is presented transforming a schedule of one type into a schedule of the other type.Heidemarie Bräsel; Natalia Shakhlevichreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4839Fri, 13 Oct 2017 14:01:28 +0200Industrieversicherungen als Element des modernen Risikomanagements - Ergebnisse einer empirischen Untersuchung
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4280
Industrieversicherungen als Element des modernen Risikomanagements - Ergebnisse einer empirischen UntersuchungReinhold Hölscher; Markus Kremers; Uwe-Christian Rückerworkingpaperhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4280Wed, 20 Jan 2016 11:41:14 +0100The Roughening Transition of the 3D Ising Interface: A Monte Carlo Study
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1313
Abstract: We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature K_R = 0.40754(5) is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer [9].M. Hasenbusch; S. Meyer; M. Pützpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1313Tue, 03 Jul 2001 00:00:00 +0200