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    <title>OPUS 4 Latest Documents RSS Feed</title>
    <description>Latest documents</description>
    <link>http://opus4.kobv.de/opus4-ubbayreuth/index/index/</link>
    <pubDate>Thu, 15 Nov 2012 13:23:46 +0100</pubDate>
    <lastBuildDate>Thu, 15 Nov 2012 13:23:46 +0100</lastBuildDate>
    <item>
      <title>The Integrated Size and Price Optimization problem</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886</link>
      <description> We present the Integrated Size and Price Optimization Problem (ISPO)&#13;
  for a fashion discounter with many branches.  Based on a two-stage&#13;
  stochastic programming model with recourse, we develop an exact&#13;
  algorithm and a production-compliant heuristic that produces small&#13;
  optimality gaps.  In a field study we show that a distribution of&#13;
  supply over branches and sizes based on ISPO solutions is&#13;
  significantly better than a one-stage optimization of the&#13;
  distribution ignoring the possibility of optimal pricing.&#13;
  </description>
      <author>Miriam  Kießling; Sascha Kurz; Jörg  Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/886</guid>
      <pubDate>Thu, 15 Nov 2012 13:23:46 +0100</pubDate>
    </item>
    <item>
      <title>Das Optimierungslabor – ein Erfahrungsbericht</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/838</link>
      <description>Seit mehreren Jahren besuchen uns Schülerinnen und Schüler an der&#13;
Universität zu Anlässen wie dem Tag der Mathematik, dem Girls’ Day,&#13;
der MINT-Universität oder einfach auf Initiative ihrer&#13;
Klassenleitungen. Sie möchten einen Einblick in die Welt der&#13;
Mathematik über die Schulmathematik hinaus bekommen. Doch wie lässt&#13;
sich die Brücke vom Schulstoff zu den Inhalten der&#13;
Universitätsmathematik schlagen? Und: findet man einen&#13;
Themenschwerpunkt, bei dem ein aktives Mitmachen trotz fehlender&#13;
Vorkenntnisse in Anbetracht begrenzter Zeit möglich wird?&#13;
&#13;
In der diskreten Optimierung lassen sich Problem-Modellierung und&#13;
Problem-Lösung sehr gut trennen. Selbst forschungsnahe Modelle der&#13;
ganzzahligen linearen Optimierung (MILP-Modelle) basieren auf sehr&#13;
elementaren Überlegungen, wie die Entscheidungsmöglichkeiten, Ziele&#13;
und Restriktionen eines Alltagsproblems in Variablen,&#13;
Bewertungsfunktionen, Gleichungen und Ungleichungen ausgedrückt werden&#13;
können. Wie dann optimale Lösungen gefunden werden, erfordert zwar&#13;
tiefergehende Mathematik, es gibt aber Software dafür, in der das&#13;
Wissen aus Teilen des Mathematik-Studiums und der mathematischen&#13;
Forschung kondensiert vorliegt.&#13;
&#13;
Unser Vermittlungsziel: Schülerinnen und Schüler wissen nach dem&#13;
Besuch, dass man verschiedenste Probleme angreifen kann, indem man sie&#13;
in die Sprache der Mathematik übersetzt, denn in Software gegossenes&#13;
mathematisches Know-How kann dann diese Probleme lösen, ohne etwas&#13;
über die Probleme selbst zu wissen. Unsere Idee für eine Maßnahme:&#13;
Ein Optimierungslabor. Die Schülerinnen und Schüler isolieren in&#13;
Teamarbeit die wesentlichen logischen Merkmale von Sudokulösen,&#13;
Rucksackpacken, Routenplanung u.v.a.m. Dann übersetzen sie die&#13;
Problemstellungen in die Sprache der Mathematik (hier: MILP-Modelle)&#13;
und lassen sie (unterstützt durch unser Team) von Computerprogrammen&#13;
lösen (MILP-Löser), die nichts anderes als diese Sprache verstehen.&#13;
Schließlich übersetzen sie die mathematischen Lösungen wieder in die&#13;
Sprache der Problemstellung. Erfahrungen mit der Modellierung auf&#13;
Basis linearer Gleichungssysteme können dabei aus dem Schulunterricht&#13;
eingebracht werden.&#13;
&#13;
In diesem Bericht wollen wir unsere Erfahrungen mit konkreten Details&#13;
der Umsetzung schildern.</description>
      <author>Miriam Kießling; Tobias Kreisel; Sascha Kurz; Jörg Rambau; Konrad Schade; Cornelius Schwarz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/838</guid>
      <pubDate>Thu, 11 Oct 2012 10:27:37 +0200</pubDate>
    </item>
    <item>
      <title>An exact column-generation approach for the lot-type design problem</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877</link>
      <description>We consider a fashion discounter distributing its many branches with&#13;
integral multiples from a set of available lot-types. For the problem of&#13;
approximating the branch and size dependent demand using those lots&#13;
we propose a tailored exact column generation approach assisted by fast&#13;
algorithms for intrinsic subproblems, which turns out to be very efficient&#13;
on our real-world instances.&#13;
</description>
      <author>Sascha Kurz; Miriam Kießling; Jörg Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/877</guid>
      <pubDate>Mon, 20 Aug 2012 10:11:31 +0200</pubDate>
    </item>
    <item>
      <title>A survey of the higher Stasheff-Tamari orders</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/755</link>
      <description>The Tamari lattice, thought as a poset on the set of triangulations of a convex polygon with n vertices, generalizes to the higher Stasheff-Tamari orders on the set of triangulations of a cyclic d-dimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them.</description>
      <author>Jörg Rambau; Victor Reiner</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/755</guid>
      <pubDate>Tue, 13 Mar 2012 08:36:20 +0100</pubDate>
    </item>
    <item>
      <title>The Stochastic Guaranteed Service Model with Recourse for  Multi-Echelon Warehouse Management</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/754</link>
      <description>The Guaranteed Service Model (GSM) computes optimal order-points in multi-echelon inventory control under the assumptions that delivery times can be guaranteed and the demand is bounded. Our new Stochastic Guaranteed Service Model (SGSM) with Recourse covers also scenarios that violate these assumptions. Simulation experiments on real-world data of a large German car manufacturer show that policies based on the SGSM dominate GSM-policies.</description>
      <author>Jörg Rambau; Konrad Schade</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/754</guid>
      <pubDate>Tue, 13 Mar 2012 07:58:08 +0100</pubDate>
    </item>
    <item>
      <title>Stability with uniform bounds for online dial-a-ride problems under reasonable load</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/682</link>
      <description>In continuously running logistic systems (like in-house pallet transportation systems), finite buffer capacities usually require controls achieving uniformly bounded waiting queues (strong stability). Standard stochastic traffic assumptions (arrival rates below service rates) can, in general, not guarantee these strong stability requirements, no matter which control. Therefore, the worst-case traffic notion of reasonable load was introduced, originally for the analysis of the Online-Dial-a-Ride Problem. A set of requests is reasonable if the requests that are presented in a sufficiently large time period can be served in a time period of at most the same length. The rationale behind this concept is that the occurrence of non-reasonable request sets renders the system overloaded, and capacity should be extended. For reasonable load, there are control policies that can guarantee uniformly bounded flow times, leading to strong stability in many cases. Control policies based on naive eoptimization, however, can in general achieve neither bounded flow times nor strong ability. In this chapter, we review the concept and examples for reasonable load. Moreover, we present new control policies achieving strong stability as well as new elementary examples of request sets where naive reoptimization fails.</description>
      <author>Sven O. Krumke; Jörg Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/682</guid>
      <pubDate>Tue, 31 May 2011 13:18:23 +0200</pubDate>
    </item>
    <item>
      <title>Local Approximation of Discounted Markov Decision Problems by Mathematical Programming Methods</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/678</link>
      <description>We develop a method to approximate the value vector of discounted Markov decision problems (MDP) with guaranteed error bounds. It is based on the linear programming characterization of the optimal expected cost. The new idea is to use column generation to dynamically generate only such states that are most relevant for the bounds by incorporating the reduced cost information. The number of states that is sufficient in general and necessary in the worst case to prove such bounds is independent of the cardinality of the state space. Still, in many instances, the column generation algorithm can prove bounds using much fewer states. In this paper, we explain the foundations of the method. Moreover, the method is used to improve the well-known nearest-neighbor policy for the elevator control problem.</description>
      <author>Stefan Heinz; Jörg Rambau; Andreas Tuchscherer</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/678</guid>
      <pubDate>Tue, 24 May 2011 11:15:59 +0200</pubDate>
    </item>
    <item>
      <title>A generalized job-shop problem with more than one resource demand per task</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/661</link>
      <description>We study a generalized job-shop problem called the Laser Sharing Problem with fixed tours (LSP-T) where the tasks may need more than one resource simultaneously. This fact will be used to model possible collisions between industrial robots. For three robots we will show that the special case where only one resource is used by more than one robot is already NP-hard. This also implies that one machine scheduling with chained min delay precedence constraints is NP-hard for at least three chains. On the positive side, we present a polynomial algorithm for the two robot case and a pseudo-polynomial algorithm together with an FPTAS for an arbitrary but constant number of robots. This gives a sharp boundary of the complexity status for a constant number of robots.</description>
      <author>Joachim Schauer; Cornelius Schwarz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/661</guid>
      <pubDate>Mon, 04 Apr 2011 09:21:55 +0200</pubDate>
    </item>
    <item>
      <title>How to avoid collisions in scheduling industrial robots?</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/583</link>
      <description>In modern production facilities industrial robots play an important role. When two ore more of them are moving in the same area, care must be taken to avoid collisions between them. Due to expensive equipment costs our approach to handle this is very conservative: Each critical area is modeled as a shared resource where only one robot is allowed to use it at a time. We studied collision avoidance in the context of arc welding robots in car manufacture industry. Here another shared resource comes into place. When using laser welding technology every robot needs to be connected to a laser source supplying it with the necessary energy. Each laser source can be connected to up to six robots but serve only one at a time. An instance of the problem consists of a set of robots, a set of welding task, a number of laser sources, a distance table, collision information and a production cycle time. The goal is to design robot tours covering all task and schedule them resource conflict free such that the makespan does not exceed the cycle time. We propose a general model for integrated routing and scheduling including collision avoidance as well as a branch-and-bound algorithm for it. Computational results on data generated with the robot simulation software KuKa Sim Pro are also provided showing that our algorithm outperforms standard mixed-integer models for our application.</description>
      <author>Jörg Rambau; Cornelius Schwarz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/583</guid>
      <pubDate>Tue, 05 Oct 2010 09:18:51 +0200</pubDate>
    </item>
    <item>
      <title>Bounds for the minimum oriented diameter</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378</link>
      <description>We consider the problem of finding an orientation with minimum diameter of a connected bridgeless graph. Fomin et. al. discovered a relation between the minimum oriented diameter an the size of a minimal dominating set. We improve their upper bound.</description>
      <author>Sascha Kurz; Martin Lätsch</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/378</guid>
      <pubDate>Tue, 15 Apr 2008 11:09:47 +0200</pubDate>
    </item>
    <item>
      <title>Integral point sets over Z_n^m</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377</link>
      <description>There are many papers studying properties of point sets in the Euclidean space or on integer grids, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the point sets which instead of being integers are elements of Z_n, and study the properties of the resulting combinatorial structures.</description>
      <author>Axel Kohnert; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377</guid>
      <pubDate>Tue, 15 Apr 2008 11:07:00 +0200</pubDate>
    </item>
    <item>
      <title>There are integral heptagons, no three points on a line, no four on a circle</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/376</link>
      <description>We give two configurations of seven points in the plane, no three points in a line, no four points on a circle with pairwise integral distances. This answers a famous question of Paul Erdös.</description>
      <author>Tobias Kreisel; Sasch Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/376</guid>
      <pubDate>Tue, 15 Apr 2008 11:04:02 +0200</pubDate>
    </item>
    <item>
      <title>On the minimum diameter of plane integral point sets</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375</link>
      <description>Since ancient times mathematicians consider geometrical objects with integral side lengths. We consider plane integral point sets P, which are sets of n points in the plane with pairwise integral distances where not all the points are collinear. The largest occurring distance is called its diameter. Naturally the question about the minimum possible diameter d(2,n) of a plane integral point set consisting of n points arises. We give some new exact values and describe state-of-the-art algorithms to obtain them. It turns out that plane integral point sets with minimum diameter consist very likely of subsets with many collinear points. For this special kind of point sets we prove a lower bound for d(2,n) achieving the known upper bound n^{c_2loglog n} up to a constant in the exponent.</description>
      <author>Sascha Kurz; Alfred Wassermann</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/375</guid>
      <pubDate>Tue, 15 Apr 2008 11:01:24 +0200</pubDate>
    </item>
    <item>
      <title>The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374</link>
      <description>We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branchs individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.</description>
      <author>Sascha Kurz; Jörg Rambau; Jörg Schlüchtermann; Rainer Wolf</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/374</guid>
      <pubDate>Tue, 15 Apr 2008 10:59:29 +0200</pubDate>
    </item>
    <item>
      <title>Lotsize optimization leading to a p-median problem with cardinalities</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373</link>
      <description>We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programming formulation and a primal heuristic for this problem we also consider a more abstract version which we relate to several other classical optimization problems like the p-median problem, the facility location problem or the matching problem.</description>
      <author>Constantin Gaul; Sascha Kurz; Jörg Rambau</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/373</guid>
      <pubDate>Tue, 15 Apr 2008 10:55:26 +0200</pubDate>
    </item>
    <item>
      <title>Inclusion-maximal integral point sets over finite fields</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372</link>
      <description>We consider integral point sets in affine planes over finite fields. Here an integral point set is a set of points in $GF(q)^2$ where the formally defined Euclidean distance of every pair of points is an element of $GF(q)$. From another point of view we consider point sets over $GF(q)^2$ with few and prescribed directions. So this is related to Redeis work. Another motivation comes from the field of ordinary integral point sets in Euclidean spaces. In this article we study the spectrum of integral point sets over $GF(q)^2$ which are maximal with respect to inclusion. We give some theoretical results, constructions, conjectures, and some numerical data.</description>
      <author>Michael Kiermaier; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/372</guid>
      <pubDate>Tue, 15 Apr 2008 10:52:18 +0200</pubDate>
    </item>
    <item>
      <title>Integral point sets over finite fields</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371</link>
      <description>We consider point sets in the affine plane GF(q)^2 where each Euclidean distance of two points is an element of GF(q). These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces. We determine their maximal cardinality I(GF(q),2). For arbitrary commutative rings R instead of GF(q) or for further restrictions as no three points on a line or no four points on a circle we give partial results. Additionally we study the geometric structure of the examples with maximum cardinality.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/371</guid>
      <pubDate>Tue, 15 Apr 2008 10:50:28 +0200</pubDate>
    </item>
    <item>
      <title>Enumeration of generalized polyominoes</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/370</link>
      <description>Wir verallgemeinern den Begriff von Polyominoes (Tetrisbausteine) und betrachten Seite-an-Seite benachbarte überschneidungsfreie Vereinigungen von regelmäßigen k-Ecken. Für n&lt;=4 geben wir Formeln für die Anzahl a_k(n) von verallgemeinerten Polyominoes, bestehend aus n regelmäßigen k-Ecken, an. Für weitere kleine Werte von k und n tabellieren wir durch computerunterstützte Enumeration gewonnene Anzahlen. Zum Abschluss erwähnen wir ein paar ungelöste Probleme für verallgemeinerte Polyominoes.</description>
      <author>Matthias Koch; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/370</guid>
      <pubDate>Tue, 15 Apr 2008 10:48:06 +0200</pubDate>
    </item>
    <item>
      <title>Maximal integral point sets over Z^2</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369</link>
      <description>Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a set P={p(1),...,p(n)} in Z^2 a maximal integral point set over Z^2 if all pairwise distances are integral and every additional point p(n+1) destroys this property. Here we consider such sets for a given cardinality and with minimum possible diameter. We determine some exact values via exhaustive search and give several constructions for arbitrary cardinalities. Since we cannot guarantee the maximality in these cases we describe an algorithm to prove or disprove the maximality of a given integral point set. We additionally consider restrictions as no three points on a line and no four points on a circle.</description>
      <author>Sascha Kurz; Andrey Radoslavov Antonov</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/369</guid>
      <pubDate>Tue, 15 Apr 2008 10:45:28 +0200</pubDate>
    </item>
    <item>
      <title>Zwei auf einen Streich: Optimierte dynamische Einsatzplanung für Gelbe Engel und Lastenaufzüge</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/278</link>
      <description>Wir modellieren zwei verschiedene dynamische Einsatzplanungsprobleme: die dynamische Einsatzplanung Gelber Engel beim ADAC und die Steuerung von Lastenaufzügen in einem Versandlager der Herlitz PBS AG. Wir benutzen eine Reoptimierungspolitik, die die Steuerung des Systems mit Hilfe der Lösung von statischen Schnappschussproblemen durchführt. Für die auftretenden Schnappschussprobleme vergleichen wir zwei Modellierungsansätze (Flussmodell versus Tourenmodell), von denen nur einer echtzeittauglich ist. Das Verfahren zur dynamischen Einsatzplanung Gelber Engel ist beim ADAC in Betrieb.</description>
      <author>Jörg Rambau; Cornelius Schwarz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/278</guid>
      <pubDate>Tue, 31 Jul 2007 09:25:11 +0200</pubDate>
    </item>
    <item>
      <title>Convex hulls of polyominoes</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245</link>
      <description>In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of $n$ unit hypercubes in $mathbb{R}^d$. For $d=2$ we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each $n$.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/245</guid>
      <pubDate>Thu, 01 Mar 2007 12:38:38 +0100</pubDate>
    </item>
    <item>
      <title>A homotopy argument and its applications to the transformation rule for bi-Lipschitz mappings, the Brouwer fixed point theorem and the Brouwer degree</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222</link>
      <description>The main purpose of the paper is to present an elementary self-contained proof of the change of variables formula for injective, locally bi-Lipschitz mappings. The proof is based on a homotopy argument. Various properties of bi-Lipschitz mappings are studied. As a by-product Lipschitz variants of the classical implicit function theorem and the local diffeomorphism theorem are proved. With the help of the homotopy argument a simple proof is given of Brouwer’s fixed point theorem and the main properties of Brouwer’s degree of mapping.</description>
      <author>Christian G. Simader</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222</guid>
      <pubDate>Thu, 07 Sep 2006 11:25:42 +0200</pubDate>
    </item>
    <item>
      <title>A note on Erdös-Diophantine graphs and Diophantine carpets</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</link>
      <description>A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in $\mathbb{Z}^{2}$ (the coordinates)and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diophantine graphs are equivalent if they only differ by translation or rotation of vertices. Due to a famous theorem of Erdös and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdös-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdös-Diophantine graphs and characterize the chromatic number of Diophantine carpets.</description>
      <author>Axel Kohnert; Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177</guid>
      <pubDate>Wed, 07 Dec 2005 14:56:57 +0100</pubDate>
    </item>
    <item>
      <title>On the characteristic of integral point sets in $\mathbb{E}^m$</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175</link>
      <description>We generalise the definition of the characteristic of an integral triangle to integral simplices and prove that each simplex in an integral point set has the same characteristic. This theorem is used for an efficient construction algorithm for integral point sets. Using this algorithm we are able to provide new exact values for the minimum diameter of integral point sets.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/175</guid>
      <pubDate>Mon, 05 Dec 2005 10:33:52 +0100</pubDate>
    </item>
    <item>
      <title>Counting polyominoes with minimum perimeter</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/142</link>
      <description>Es wird die Anzahl der wesentlich verschiedenen Polyominoes der Ordnung n mit minimalem Umfang p(n) bestimmt.</description>
      <author>Sascha Kurz</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/142</guid>
      <pubDate>Mon, 27 Jun 2005 13:48:50 +0200</pubDate>
    </item>
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