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Termination of Rewriting
(1994)
More and more, term rewriting systems are applied in computer science aswell as in mathematics. They are based on directed equations which may be used as non-deterministic functional programs. Termination is a key property for computing with termrewriting systems.In this thesis, we deal with different classes of so-called simplification orderings which areable to prove the termination of term rewriting systems. Above all, we focus on the problemof applying these termination methods to examples occurring in practice. We introduce aformalism that allows clear representations of orderings. The power of classical simplifica-tion orderings - namely recursive path orderings, path and decomposition orderings, Knuth-Bendix orderings and polynomial orderings - is improved. Further, we restrict these orderingssuch that they are compatible with underlying AC-theories by extending well-known methodsas well as by developing new techniques. For automatically generating all these orderings,heuristic-based algorithms are given. A comparison of these orderings with respect to theirpowers and their time complexities concludes the theoretical part of this thesis. Finally, notonly a detailed statistical evaluation of examples but also a brief introduction into the designof a software tool representing the integration of the specified approaches is given.
In dieser Dissertation wird das Konzept der Gröbnerbasen für endlich erzeugte Monoid-und Gruppenringe verallgemeinert. Dabei werden Reduktionsmethoden sowohl zurDarstellung der Monoid- beziehungsweise Gruppenelemente, als auch zur Beschreibungder Rechtsidealkongruenz in den entsprechenden Monoid- beziehungsweise Gruppenrin-gen benutzt. Da im allgemeinen Monoide und insbesondere Gruppen keine zulässigenOrdnungen mehr erlauben, treten bei der Definition einer geeigneten Reduktionsrela-tion wesentliche Probleme auf: Zum einen ist es schwierig, die Terminierung einer Re-duktionsrelation zu garantieren, zum anderen sind Reduktionsschritte nicht mehr mitMultiplikationen verträglich und daher beschreiben Reduktionen nicht mehr unbedingteine Rechtsidealkongruenz. In dieser Arbeit werden verschiedene Möglichkeiten Reduk-tionsrelationen zu definieren aufgezeigt und im Hinblick auf die beschriebenen Problemeuntersucht. Dabei wird das Konzept der Saturierung, d.h. eine Polynommenge so zu er-weitern, daß man die von ihr erzeugte Rechtsidealkongruenz durch Reduktion erfassenkann, benutzt, um Charakterisierungen von Gröbnerbasen bezüglich der verschiedenenReduktionen durch s-Polynome zu geben. Mithilfe dieser Konzepte ist es gelungenfür spezielle Klassen von Monoiden, wie z.B. endliche, kommutative oder freie, undverschiedene Klassen von Gruppen, wie z.B. endliche, freie, plain, kontext-freie odernilpotente, unter Ausnutzung struktureller Eigenschaften spezielle Reduktionsrelatio-nen zu definieren und terminierende Algorithmen zur Berechnung von Gröbnerbasenbezüglich dieser Reduktionsrelationen zu entwickeln.
Structure and Construction of Instanton Bundles on P3
At present the standardization of third generation (3G) mobile radio systems is the subject of worldwide research activities. These systems will cope with the market demand for high data rate services and the system requirement for exibility concerning the offered services and the transmission qualities. However, there will be de ciencies with respect to high capacity, if 3G mobile radio systems exclusively use single antennas. Very promising technique developed for increasing the capacity of 3G mobile radio systems the application is adaptive antennas. In this thesis, the benefits of using adaptive antennas are investigated for 3G mobile radio systems based on Time Division CDMA (TD-CDMA), which forms part of the European 3G mobile radio air interface standard adopted by the ETSI, and is intensively studied within the standardization activities towards a worldwide 3G air interface standard directed by the 3GPP (3rd Generation Partnership Project). One of the most important issues related to adaptive antennas is the analysis of the benefits of using adaptive antennas compared to single antennas. In this thesis, these bene ts are explained theoretically and illustrated by computer simulation results for both data detection, which is performed according to the joint detection principle, and channel estimation, which is applied according to the Steiner estimator, in the TD-CDMA uplink. The theoretical explanations are based on well-known solved mathematical problems. The simulation results illustrating the benefits of adaptive antennas are produced by employing a novel simulation concept, which offers a considerable reduction of the simulation time and complexity, as well as increased exibility concerning the use of different system parameters, compared to the existing simulation concepts for TD-CDMA. Furthermore, three novel techniques are presented which can be used in systems with adaptive antennas for additionally improving the system performance compared to single antennas. These techniques concern the problems of code-channel mismatch, of user separation in the spatial domain, and of intercell interference, which, as it is shown in the thesis, play a critical role on the performance of TD-CDMA with adaptive antennas. Finally, a novel approach for illustrating the performance differences between the uplink and downlink of TD-CDMA based mobile radio systems in a straightforward manner is presented. Since a cellular mobile radio system with adaptive antennas is considered, the ultimate goal is the investigation of the overall system efficiency rather than the efficiency of a single link. In this thesis, the efficiency of TD-CDMA is evaluated through its spectrum efficiency and capacity, which are two closely related performance measures for cellular mobile radio systems. Compared to the use of single antennas, the use of adaptive antennas allows impressive improvements of both spectrum efficiency and capacity. Depending on the mobile radio channel model and the user velocity, improvement factors range from six to 10.7 for the spectrum efficiency, and from 6.7 to 12.6 for the spectrum capacity of TD-CDMA. Thus, adaptive antennas constitute a promising technique for capacity increase of future mobile communications systems.
In this thesis a new family of codes for the use in optical high bit rate transmission systems with a direct sequence code division multiple access scheme component was developed and its performance examined. These codes were then used as orthogonal sequences for the coding of the different wavelength channels in a hybrid OCDMA/WDMA system. The overall performance was finally compared to a pure WDMA system. The common codes known up to date have the problem of needing very long sequence lengths in order to accommodate an adequate number of users. Thus, code sequence lengths of 1000 or more were necessary to reach bit error ratios of with only about 10 simultaneous users. However, these sequence lengths are unacceptable if signals with data rates higher than 100 MBit/s are to be transmitted, not to speak about the number of simultaneous users. Starting from the well known optical orthogonal codes (OOC) and under the assumption of synchronization among the participating transmitters - justified for high bit rate WDM transmission systems -, a new code family called ?modified optical orthogonal codes? (MOOC) was developed by minimizing the crosscorrelation products of each two sequences. By this, the number of simultaneous users could be increased by several orders of magnitude compared to the known codes so far. The obtained code sequences were then introduced in numerical simulations of a 80 GBit/s DWDM transmission system with 8 channels, each carrying a 10 GBit/s payload. Usual DWDM systems are featured by enormous efforts to minimize the spectral spacing between the various wavelength channels. These small spacings in combination with the high bit rates lead to very strict demands on the system components like laser diode, filters, multiplexers etc. Continuous channel monitoring and temperature regulations of sensitive components are inevitable, but often cannot prevent drop downs of the bit error ratio due to aging effects or outer influences like mechanical stress. The obtained results show that - very different to the pure WDM system - by orthogonally coding adjacent wavelength channels with the proposed MOOC, the overall system performance gets widely independent from system parameters like input powers, channel spacings and link lengths. Nonlinear effects like XPM that insert interchannel crosstalk are effectively fought. Furthermore, one can entirely dispense with the bandpass filters, thus simplifying the receiver structure, which is especially interesting for broadcast networks. A DWDM system upgraded with the OCDMA subsystem shows a very robust behavior against a variety of influences.
Abstract
The main theme of this thesis is about Graph Coloring Applications and Defining Sets in Graph Theory.
As in the case of block designs, finding defining sets seems to be difficult problem, and there is not a general conclusion. Hence we confine us here to some special types of graphs like bipartite graphs, complete graphs, etc.
In this work, four new concepts of defining sets are introduced:
• Defining sets for perfect (maximum) matchings
• Defining sets for independent sets
• Defining sets for edge colorings
• Defining set for maximal (maximum) clique
Furthermore, some algorithms to find and construct the defining sets are introduced. A review on some known kinds of defining sets in graph theory is also incorporated, in chapter 2 the basic definitions and some relevant notations used in this work are introduced.
chapter 3 discusses the maximum and perfect matchings and a new concept for a defining set for perfect matching.
Different kinds of graph colorings and their applications are the subject of chapter 4.
Chapter 5 deals with defining sets in graph coloring. New results are discussed along with already existing research results, an algorithm is introduced, which enables to determine a defining set of a graph coloring.
In chapter 6, cliques are discussed. An algorithm for the determination of cliques using their defining sets. Several examples are included.
Urban Design Guidelines have been used in Jakarta for controlling the form of the built environment. This planning instrument has been implemented in several central city redevelopment projects particularly in superblock areas. The instrument has gained popularity and implemented in new development and conservation areas as well. Despite its popularity, there is no formal literature on the Indonesian Urban Design Guideline that systematically explain its contents, structure and the formulation process. This dissertation attempts to explain the substantive of urban design guideline and the way to control its implementation. Various streams of urban design theories are presented and evaluated in term of their suitability for attaining a high urbanistic quality in major Indonesian cities. The explanation on the form and the practical application of this planning instrument is elaborated in a comparative investigation of similar instrument in other countries; namely the USA, Britain and Germany. A case study of a superblock development in Jakarta demonstrates the application of the urban design theories and guideline. Currently, the role of computer in the process of formulating the urban design guideline in Indonesia is merely as a replacement of the manual method, particularly in areas of worksheet calculation and design presentation. Further support of computer for urban planning and design tasks has been researched in developed countries, which shows its potential in supporting decision-making process, enabling public participation, team collaboration, documentation and publication of urban design decisions and so on. It is hoped that the computer usage in Indonesian urban design process can catch up with the global trend of multimedia, networking (Internet/Intranet) and interactive functions that is presented with examples from developed countries.
The study of families of curves with prescribed singularities has a long tradition. Its foundations were laid by Plücker, Severi, Segre, and Zariski at the beginning of the 20th century. Leading to interesting results with applications in singularity theory and in the topology of complex algebraic curves and surfaces it has attained the continuous attraction of algebraic geometers since then. Throughout this thesis we examine the varieties V(D,S1,...,Sr) of irreducible reduced curves in a fixed linear system |D| on a smooth projective surface S over the complex numbers having precisely r singular points of types S1,...,Sr. We are mainly interested in the following three questions: 1) Is V(D,S1,...,Sr) non-empty? 2) Is V(D,S1,...,Sr) T-smooth, that is smooth of the expected dimension? 3) Is V(D,S1,...Sr) irreducible? We would like to answer the questions in such a way that we present numerical conditions depending on invariants of the divisor D and of the singularity types S1,...,Sr, which ensure a positive answer. The main conditions which we derive will be of the type inv(S1)+...+inv(Sr) < aD^2+bD.K+c, where inv is some invariant of singularity types, a, b and c are some constants, and K is some fixed divisor. The case that S is the projective plane has been very well studied by many authors, and on other surfaces some results for curves with nodes and cusps have been derived in the past. We, however, consider arbitrary singularity types, and the results which we derive apply to large classes of surfaces, including surfaces in projective three-space, K3-surfaces, products of curves and geometrically ruled surfaces.
In der vorliegenden Arbeit wird das Verhalten von thermoplastischen
Verbundwerkstoffen mittels experimentellen und numerischen Untersuchungen
betrachtet. Das Ziel dieser Untersuchungen ist die Identifikation und Quantifikation
des Versagensverhaltens und der Energieabsorptionsmechanismen von geschichteten,
quasi-isotropen thermoplastischen Faser-Kunststoff-Verbunden und die Umsetzung
der gewonnenen Einsichten in Eigenschaften und Verhalten eines Materialmodells zur
Vorhersage des Crash-Verhaltens dieser Werkstoffe in transienten Analysen.
Vertreter der untersuchten Klassen sind un- und mittel-vertreckte Rundgestricke und
glasfaserverstärkte Thermoplaste (GMT). Die Untersuchungen an rundgestrickten
glasfaser-(GF)-verstärktem Polyethylentherephthalat (PET) waren Teil eines
Forschungsprojektes zur Charakterisierung sowohl der Verarbeitbarkeit als auch des
mechanischen Verhaltens. Experimente an GMT und Schnittfaser-GMT wurden
ebenfalls zum Vergleich mit dem Gestrick durchgeführt und dienen als Bestätigung
des beobachteten Verhaltens des Gestrickes.
Besonderer Aufmerksamkeit wird der Einfluß der Probengeometrie auf die Resultate
gewidmet, weil die Crash-Charakteristiken wesentlich von der Geometrie des
getesteten Probekörpers abhängen. Hierzu wurde ein Rundhutprofil zur Untersuchung
dieses Einflußes definiert. Diese spezielle Geometrie hat insbesondere Vorteile
hinsichtlich Energieabsorptionsvermögen sowie Herstellbarkeit von thermoplastischen
Verbundwerkstoffen (TPCs). Es wurden Impakt- und Perforationsversuche zur
Untersuchung der Schädigungsausbreitung und zur Charakterisierung der Zähigkeit
der untersuchten Materialien durchgeführt.
Geschichtete TPCs versagen hauptsächlich in einem Laminat-Biegemodus mit
kombiniertem intra- und interlaminaren Schub (transversaler Schub zwischen Lagen und teilweise mit transversalen Schubbrüchen in einzelnen Lagen). Durch eine
Kopplung der aktuellen Versagensmodi und Crash-Kennwerten wie der mittleren
Crash-Spannung, konnten Indikationen über die Relation zwischen Materialparameter
und absoluter Energieabsorption gewonnen werden.
Numerische Untersuchungen wurden mit einem expliziten Finiten Elemente-
Programm zur Simulation von dreidimensionalen, großen Verformungen durchgeführt.
Das Modell besteht bezüglich des Querschnittaufbaus aus einer mesoskopischen
Darstellung, die zwischen Matrix-zwischenlagen und mesoskopischen Verbundwerkstofflagen unterscheidet. Die Modellgeometrie stellt einen vereinfachten
Längsquerschnitt durch den Probekörper dar. Dabei wurden Einflüsse der Reibung
zwischen Impaktor und Material sowie zwischen einzelnen Lagen berücksichtigt.
Auch die lokal herrschende Dehnrate, Energie und Spannungs-Dehnungsverteilung
über die mesoskopischen Phasen konnten beobachtet werden. Dieses Modell zeigt
deutlich die verschiedenen Effekte, die durch den heterogenen Charakter des Laminats
entstehen, und gibt auch Hinweise für einige Erklärungen dieser Effekte.
Basierend auf den Resultaten der obengenannten Untersuchungen wurde ein
phänomenologisches Modell mit a-priori Information des inherenten
Materialverhaltens vorgeschlagen. Daher, daß das Crashverhalten vom heterogenen
Charakter des Werkstoffes dominiert wird, werden im Modell die Phasen separat
betrachtet. Eine einfache Methode zur Bestimmung der mesoskopischen Eigenschaften
wird diskutiert.
Zur Beschreibung des Verhaltens vom thermoplastischen Matrixsystem während
„Crushing“ würde ein dehnraten- und temperaturabhängiges Plastizitätsgesetz
ausreichen. Für die Beschreibung des Verhaltens der Verbundwerkstoffschichten wird
eine gekoppelte Plastizitäts- und Schädigungsformulierung vorgeschlagen. Ein solches
Modell kann sowohl den plastischen Anteil des Matrixsystems als auch das
„Softening“ - verursacht durch Faser-Matrix-Grenzflächenversagen und Faserbrüche -
beschreiben. Das vorgeschlagene Modell unterscheidet zwischen Belastungsfällen für
axiales „Crushing“ und Versagen ohne „Crushing“. Diese Unterteilung ermöglicht
eine explizite Modellierung des Werkstoffes unter Berücksichtigung des spezifischen
Materialzustandes und der Geometrie für den außerordentlichen Belastungsfall, der
zum progressiven Versagen führt.