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Partitioned chain grammars
(1979)
This paper introduces a new class of grammars, the partitioned chain grammars, for which efficient parsers can be automatically generated. Besides being efficiently parsable these grammars possess a number of other properties, which make them very attractive for the use in parser-generators. They for instance form a large grammarclass and describe all deterministic context-free languages. Main advantage of the partitioned chain grammars however is, that given a language it is usually easier to describe it by a partitioned chain grammar than to construct a grammar of some other type commonly used in parser-generators for it.
In this paper we continue the study of p - groups G of square order \(p^{2n}\) and investigate the existence of partial congruence partitions (sets of mutually disjoint subgroups of order \(p^n\)) in G. Partial congruence partitions are used to construct translation nets and partial difference sets, two objects studied extensively in finite geometries and combinatorics. We prove that the maximal number of mutually disjoint subgroups of order \(p^n\) in a group G of order \(p^{2n}\) cannot be more than \((p^{n-1}-1)(p-1)^{-1}\) provided that \(n\ge4\)and that G is not elementary abelian. This improves a result in [6] and as we do not distinguish the cases p=2 and p odd in the present paper, we also have a generalization of D. FROHARDT' s theorem on 2 - groups in [4]. Furthermore we study groups of order \(p^6\). We can show that for each odd prime number, there exist exactly four nonisomorphic groups which contain at least p+2 mutually disjoint subgroups of order \(p^3\). Again, as we do not distinguish between the even and the odd case in advance, we in particular obtain
D. GLUCK' s and A. P. SPRAGUE' s classification of groups of order 64 which contain at least 4 mutually disjoint subgroups of order 8 in [5] and [13] respectively.
In this paper the existence of translation transversal designs which is equivalent to the existence of certain particular partitions in finite groups is studied. All considerations are based on the fact that the particular component of such a partition (the component representing the point classes of the corresponding design) is a normal subgroup of the translation group. With regard to groups admitting an (s,k,\(\lambda\))-partiton, on one hand the already known families of such groups are determined without using R. BAER's, 0.H.KEGEL's and M. SUZUKI' s classification of finite groups with partition and on the other hand some new results on the special structure of p - groups are proved. Furthermore, the existence of a series of nonabelian p - groups of odd order which can be represented as translation groups of certain (s,k,1) - translation transversal designs is shown; moreover, the translation groups are normal subgroups of collineation groups acting regularly on the set of flags of the same designs.
Moduli for singularities
(1991)
The aim of this article is to give a survey on recent results about moduli spaces for curve singularities and for modules over the local ring of a fixed curve singularity. We emphasize especially the general concept which lies behind these constructions.
Therefore, the article might be useful to the reader who wishes to have the leading ideas and the main steps of the proofs explained without going into all the details. We also calculate explicit examples (for singularities and for modules) which illustrate
the general theorems.
Limits of instantons
(1991)
Das sind die Texte der Vorlesungen, die ich im Dezember 1988 - März 1989 an der Universität Kaiserslautern hielt. Die Sektionen 1-4 enthalten Materialien, die in Russisch im Buch [33] und in früheren Arbeiten [27,28] [30-33] publiziert sind.
Sektion 5 enthält neue Ergebnisse, die wir während meines Aufenthaltes in Kaiserslautern in Zusammenarbeit mit Herrn Robert Plato
(TU Berlin) ausarbeiteten (siehe [21,22]). Sektion 6 ist eine Erweiterung der Arbeit [31].
The notion of Q-Gorenstein smoothings has been introduced by Kollar. ([KoJ], 6.2.3). This notion is essential for formulating Kollar's conjectures on smoothing components for rational surface singularities. He conjectures, loosely speaking, that every smoothing of a rational surface singularity can be obtained by blowing down a deformation of a partial resolution, this partial resolution having the property (among others) that the singularities occuring on it all have qG-smoothings. (For more details and precise statements see [Ko], ch. 6.). It is therefore of interest to construct singularities having qG-smoothings.
In Laufe der letzten Jahrzehnte ist der Prozeß der Softwareentwicklung methodisiert und zum Teil auch formalisiert worden. I.a. unterteilt man den Vorgang in grobe Stufen, Entwicklungsphasen genannt. Jede dieser Phasen betrachtet den entstehenden Entwurf des Projekts aus verschiedenen Sichtweisen. Aus dieser Sichtweise resultieren etliche Modelle und Darstellungsformen und mit ihnen auch verschiedene rechnergestützte Entwicklungswerkzeuge. In frühen Phasen sind beispielsweise Datenflußdiagramme eine nützliche Darstellungsform, in späteren konkrete Algorithmenbeschreibungen. Entwurfsänderungen im Laufe der Entwicklungszeit müssen in allen betroffenen Ebenen neu formuliert werden, eine automatisierte phasenübergreifende Behandlung ist
daher i.a. nicht oder nur teilweise möglich. Um effizienter und weniger fehleranfällig arbeiten zu können, wurden aus diesem Grund in letzter Zeit Ansätze gemacht, den gesamten Softwareentwicklungsprozeß von der ·Anforderungsanalyse bis hin zur Wartungsphase einem einheitlichen Konzept und einer einheitlichen Darstellungsform zu unterwerfen, die sich darüberhinaus zur Realisation auf Rechnersystemen eignen. Der vorliegende Bericht entstand im Rahmen eines solchen Projekts. Es wurden eine allumfassende Systementwurfssprache und die dazugehörigen Konzepte entwickelt, die sämtliche Entwurfsphasen und die wichtigsten -prinzipien zu unterstützen vermögen. Es liegen bereits zwei Arbeiten zu diesem Projekt vor. Sie stellen im wesentlichen neben der eigentlichen Definition der Systementwurfssprache zwei Entwicklungswerkzeuge vor, die auf einer einheitlichen Datenbasis operieren [GK-91, Kel-90]. Ein Bereich innerhalb der Forschungen ist die Wiederverwendung von Softwareentwürfen. Schon existierende Lösungen sollen bei der Entwicklung eines neuen Entwurfs durch Vergleich und Bewertung des Grades der Ähnlichkeit ausgewählt und dem Entwickler nutzbar gemacht werden. Dieser Bericht beschäftigt sich mit einem Kernpunkt der Wiederverwendung, dem Vergleich zweier Softwareentwürfe. Es werden zunächst grundsätzliche Konzepte ausgearbeitet, die den Ähnlichkeitsaspekt unter verschiedenen Gesichtspunkten charakterisieren. Daraufhin werden Algorithmen konstruiert, die verschiedenartige Vergleichsfunktionen realisieren und zu einer Gesamtfunktion kombinieren. Um zu einem späteren Zeitpunkt die Leistungsfähigkeit dieser
Funktionen in der Praxis untersuchen zu können, liegt darüberhinaus ein lauffähiges
Programm vor.
Trimming of surfaces and volumes, curve and surface modeling via Bézier's idea of destortion, segmentation, reparametrization, geometric continuity are examples of applications of functional composition. This paper shows how to
compose polynomial and rational tensor product Bézier representations. The problem of composing Bezier splines and B-spline representations will also be addressed in this paper.
The use of non-volatile semiconductor memory within an extended storage hierarchy promises significant performance improvements for transaction processing. Although page-addressable semiconductor memories like extended memory, solid-state disks and disk caches are commercially available since several years, no detailed investigation of their use for transaction processing has been performed so far. We present a comprehensive simulation study that compares the performance of these storage types and of different usage forms. The following usage forms are considered: allocation of entire log and database files in non-volatile semiconductor memory, using a so-called write buffer to perform disk writes asynchronously, and caching of database pages at intermediate storage levels (in addition to main memory caching). Our simulations are conducted with both synthetically generated workloads and traces from real-life database applications. In particular, simulation results will be presented for the debit-credit workload frequently used in transaction processing benchmarks. As expected, the greatest performance improvements (but at the highest cost) can be achieved by storing log and database files completely in non-volatile semiconductor memory. For update-intensive
workloads, a limited amount of non-volatile memory used as a write buffer also proved to be very effective. To reduce the number of disk reads; caching of database pages in addition to main memory is best supported by an extended memory buffer. In this respect, disk caches are found to be less effective as they are designed for one-level caching. Different storage costs suggest that it may be cost-effective to use two or even three of the intermediate storage types together. The performance improvements obtainable by the use of non-volatile semiconductor memory is also found to reduce the need for sophisticated DBMS buffer management in order to achieve high transaction processing performance.
Hyperidentities
(1992)
The concept of a free algebra plays an essential role in universal algebra and in computer science. Manipulation of terms, calculations and the derivation of identities are performed in free algebras. Word problems, normal forms, system of reductions, unification and finite bases of identities are topics in algebra and logic as well as in computer science. A very fruitful point of view is to consider structural properties of free algebras. A.I. Malcev initiated a thorough research of the congruences of free algebras. Henceforth congruence permutable, congruence distributive and congruence modular varieties are
intensively studied. A lot of Malcev type theorems are connected to the congruence lattice of free algebras. Here we consider free algebras as semigroups of compositions of terms and more specific as clones of terms. The properties of these semigroups and clones are adequately described by hyperidentities. Naturally a lot of theorems of "semigroup" or "clone" type can be derived. This topic of research is still in its beginning and therefore a lot öf concepts and results cannot be presented in a final and polished form. Furthermore a lot of problems and questions are open which are of importance for the further development of the theory of hyperidentities.
We present a generalization of Proth's theorem for testing certain large integers for primality. The use of Gauß sums leads to a much simpler approach to these primality criteria as compared to the earlier tests. The running time of the algorithms is bounded by a polynomial in the length of the input string. The applicability of our algorithms is linked to certain diophantine approximations of \(l\)-adic roots of unity.
A Remark on Primes of the Form \(2^{3n}a + 2^{2n}b+2^nc+1\). Necessary and sufficient conditions for the numbers in the title to be prime are given. The tests are well suited for practical purposes.
In der CAGD Literatur werden häufig Ableitungen und Graderhöhungen von Bezierkurven und -flächen wiederum in Bezierform angegeben [1][2][3][6]. Meistens werden diese Darstellungen nur für theoretische Betrachtungen verwendet, z.B. geometrischer Deutung von Stetigkeiten zwischen angrenzenden Flächenstücken. Für praktische Anwendungen reicht die Menge der Operationen jedoch nicht aus. Farouki und Rajan [4] zeigten, daß die Resultate arithmetischer Operationen, wie Addition und Multiplikation auf Bezierkurven auch als Bezierkurven darstellbar sind. Hier werden wir die Operationen auf polynomiale und rationale Tensorprodukt Bezierflächen und Flächen über Dreiecken ausdehnen. Eine Erweiterung auf rationale Flächen ermöglicht insbesondere die Ausführung einer Division, wie sie für viele Anwendungen benötigt wird. Das Rechnen mit Flächen hat im Gegensatz zu punktweisen Auswertungen den Vorteil gleichzeitig mit Hilfe von notwendigen Bedingungen an das entstandene Beziernetz sichere Ergebnisabschätungen angeben zu können. Diese lassen sich für adaptive Verfahren nutzen und sind insbesondere dort wichtig, wo es auf exakte Aussagen über das Verhalten von Flächen ankommt, wie z.B. bei der Qualitätsanalyse von Freiformflächen [5]. Mit Hilfe der hier vorgestellten Operationen läßt sich u.a. an Vorzeichenwechseln erkennen, ob eine zu untersuchende Bezierfläche konvex ist oder nicht (siehe Kapitel 4). Außerdem können Fehler, die bei punktweisen Auswertungen auf Gittern mit großer Maschenweite entstehen, vermieden werden. Nachdem in Kapitel 2 die zum Verständnis nötigen Definitionen und Schreibweisen erläutert wurden, werden in Kapitel 3 die grundlegenden Operationen für eine Arithmetik
auf Bezierflächen beschrieben. Dabei werden Formeln angegeben, die die Bezierpunkte und Gewichte der Ergebnisfläche aus denen der Operandenflächen bestimmen. Durch Aneinanderreihung und Verkettung einzelner Operationen lassen sich dann komplexe Berechnungen mit der gesamten Fläche ausführen. Zum Schluß werden in Kapitel 4 einige Beispiele aus dem Bereich der Qualitätsanalyse von Freiformflächen angegeben.
Let \(a_i i:= 1,\dots,m.\) be an i.i.d. sequence taking values in \(\mathbb{R}^n\). Whose convex hull is interpreted as a stochastic polyhedron \(P\). For a special class of random variables which decompose additively relative to their boundary simplices, eg. the volume of \(P\), integral representations of their first two moments are given which lead to asymptotic estimations of variances for special "additive variables" known from stochastic approximation theory in case of rotationally symmetric distributions.
We show that the different module structures of GF(\(q^m\)) arising from the intermediate fields of GF(\(q^m\))and GF(q) can be studied simultaneously with the help of some basic properties of cyclotomic polynomials. We use this ideas to give a detailed and constructive proof of the most difficult part of a Theorem of D. Blessenohl and K. Johnsen (1986), i.e., the existence of elements v in GF(\(q^m\)) over GF(q) which generate normal bases over any intermediate field of GF(\(q^m\)) and GF(q), provided that m is a prime power. Such elements are called completely free in GF(\(q^m\)) over GF(q). We develop a recursive formula for the number of completely free elements in GF(\(q^m\)) over GF(q) in the case where m is a prime power. Some of the results can be generalized to finite cyclic Galois extensions
over arbitrary fields.
Let \(a_1, i:=1,\dots,m\), be an i.i.d. sequence taking values in \(\mathbb{R}^n\), whose convex hull is interpreted as a stochastic polyhedron \(P\). For a special class of random variables, which decompose additively relative to their boundary simplices, eg. the volume of \(P\), simple integral representations of its first two moments are given in case of rotationally symmetric distributions in order to facilitate estimations of variances or to quantify large deviations from the mean.
We are concerned with a parameter choice strategy for the Tikhonov regularization \((\tilde{A}+\alpha I)\tilde{x}\) = T* \(\tilde{y}\)+ w where \(\tilde{A}\) is a (not necessarily selfadjoint) approximation of T*T and T*\(\tilde y\)+ w is a perturbed form of the (not exactly computed) term T*y. We give conditions for convergence and optimal convergence rates.
Weighted k-cardinality trees
(1992)
We consider the k -CARD TREE problem, i.e., the problem of finding in a given undirected graph G a subtree with k edges, having minimum weight. Applications of this problem arise in oil-field leasing and facility layout. While the general problem is shown to be strongly NP hard, it can be solved in polynomial time if G is itself a tree. We give an integer programming formulation of k-CARD TREE, and an efficient exact separation routine for a set of generalized subtour elimination constraints. The polyhedral structure of the convex huLl of the integer solutions is studied.
Jede Wissenschaft entfaltet sich in einem Spannungsverhältnis zu ihren Nachbardisziplinen. In diesem Beitrag wird insbesondere das Disziplinenpaar Mathematik-Philosophie in den Blick genommen. Dies geschieht entlang der Leitfrage, ob und gegebenenfalls wie Philosophie auf die Entwicklung und Ausformung der Mathematik Einfluß genommen hat. Dazu wird nach philosophischen Spuren in der Mathematik gefragt, wobei jene historischen Konstellationen bevorzugt betrachtet werden, die eine grundlegende Änderung im Mathematikverständnis erbracht haben. Deshalb gilt das Hauptinteresse dieser Untersuchung dem Verhältnis von Philosophie und Mathematik in der klassischen Antike, bei Kant und in der Gegenwart.
Facility location problems in the plane are among the most widely used tools of Mathematical Programming in modeling real-world problems. In many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden. We consider center and median problems where the forbidden set is
a union of pairwise disjoint convex sets. As applications we discuss the assembly of printed circuit boards, obnoxious facility location and the location of emergency facilities.
Gauss Frame Offsets
(1992)
Virtual Reality (VR) is to be seen as the superset of simulation and animation. Visualization is done by rendering. The fundamental model of VR accounts for all phenomenons to be modelled with help of a computer. Examples range from simple dragging actions with a mouse device to the complex simulation of physically based animation.
Der ProLan-X - Sprachreport
(1992)
Bei der Realisierung großer Software-Projekte treten immer wieder Probleme auf, was die
Koordination der Mitarbeiter, die Ausnutzung der vorhandenen Ressourcen und nicht zuletzt die
Qualität der erzeugten Produkte angeht. Um die Vorgänge bei der Produktion von Software
durchschaubarer und verständlicher zu machen, versucht man, diese aus der Sicht von Meta-Modellen zu beschreiben. Dabei fließen die individuellen Rahmenbedingungen einer jeden
Entwicklungsumgebung ein; die vorhandenen Ressourcen werden ebenso modellien wie die
durchzuführenden Tätigkeiten und ihre Abhängigkeiten. Die Beschreibungssprache für den Software-Prozeß ProLan-X dient der (konkreten) Beschreibung der Bestandteile des Meta-Modells MoMo, das ebenfalls in dieser Arbeitsgruppe entwickelt wurde [Schramm]. Die am Projekt beteiligten Personen, Hardware- und Software-Ressourcen und ihre Aufgaben werden in möglichst natürlicher Weise verhaltensorientien beschrieben. Aus dieser Beschreibung kann eine Ablaufumgebung generien werden, die die Durchführung des Projekts unterstützt und protokolliert. Der vorliegende Bericht faßt die Eigenschaften der Sprache ProLan-X zusammen und erläuten ihre Verwendung. Er setzt das MoMo-Modell als bekannt voraus.
User interfaces for large distributed applications have to handle specific problems: the complexity of the application itself and the integration of online-data into the user interface. A main task of the user interface architecture is to provide powerful tools to design and augment the end-user system easily, hence giving the designer more time to focus on user requirements. Our experiences developing a user interface system for a process control room showed that a lot of time during the development process is wasted for the integration of online-data residing anywhere but not in the user interface itself. Furtheron external data may be kept by different kinds of programs, e.g. C-programs running
a numerical process model or PROLOG-programs running a diagnosis system, both in parallel to the process and in parallel to the user interface. Facing these specific requirements, we developed a user interface architecture following two main goals: 1. integration of external information into high-level graphical objects and 2. the system should be open for any program running as a separate process using its own problem-oriented language. The architecture is based on two approaches: an asynchronous, distributed and language independent communication model and an object model describing the problem domain and the interface using object-oriented techniques. Other areas like rule-based programming are involved, too. With this paper, we will present the XAVIA user interface architecture, the (as far as we know) first user inteface architecture, which is consequently based on a distributed object model.
Vorliegender Bericht ist eine Studie für einen möglichen Immissionsdatenverbund in Österreich. Die Grundlage dieser ersten Version der Studie sind Gespräche, welche Anfang Januar 1992 im Forschungszentrum Seibersdorf und im Umweltbundesamt in Wien stattfanden. Seit einigen Jahren beschäftigt sich die von mir geleitete Gruppe Umweltinformatik an der Universität Kaiserslautern mit den besonderen Schwierigkeiten bei der Vernetzung und Integration heterogener Systeme, welche darüberhinaus unter unterschiedlichen Vollzugshoheiten stehen können. Wir haben diese Problemstellung bei der Führung verfahrenstechnischer Anlagen weitestgehend gelöst und beschäftigen uns, zum Teil in Zusammenarbeit mit Kollegen aus anderen Institutionen, nun hauptsächlich mit der Umsetzung dieser Lösungen in verteilten Systemen im Umweltschutz. Unsere derzeitigen Arbeiten haben zum Ziel, möglichst allgemeine Ansätze für die Integration in verteilten, offenen Umweltinformationssystemen (UIS) zu entwickeln. Dabei sind wir uns darüber bewußt, daß diese allgemeinen Ansätze nur aus den konkreten Gegebenheiten, Zielen und Vorstellungen abgeleitet werden können. Diese Studie soll zwei Dinge bezwecken: einerseits will ich versuchen, den Blick dafür zu öffnen, wie ein Immissionsdatenverbund aussehen könnte, welcher allen Betreibern eine hohe Funktionalität und großen Komfort bietet. Es soll auch diskutiert werden, welcher technischer und organisatorischer Aufwand unter Verwendung welcher Konzepte entsteht. Auch wenn man sich in naher Zukunft nicht dazu entschließen sollte, die von mir vorgeschlagenen oder ähnliche Wege zu gehen, so könnte man doch bei der Realisierung auf
niedrigerem funktionalen Niveau zukünftige Möglichkeiten schon heute berücksichtigen und damit zukünftige Entwicklungen begünstigen. Ich hoffe, daß die Leser dieser Studie in dieser Hinsicht von meinen Erfahrungen profitieren. Zum zweiten ist diese Studie für meine Arbeitsgruppe ein Einstieg in die konkreten Problemstellungen großer verteilter UIS. Meßnetze sind inhärente Komponenten solcher UIS und weisen aufgrund ihrer technischen Orientierung interessante Merkmale auf. Daher erhoffen wir uns, hier wichtige Erkenntnisse auch für unsere Arbeiten zu gewinnen. Im Prinzip weiß heute noch niemand, wie man einen großen Umweltdatenverbund organisieren könnte. Ein Teil eines solchen Verbundes sind die Meßnetze. Die damit verbundenen Probleme alleine technischer Art sind riesig und es gibt bisher nur wenige Personen, die in der Umweltinformatik sich überhaupt mit diesen Themen beschäftigen. Diese Studie versteht sich daher hochgradig als Diskussionpapier. Jegliche geäußerten Ideen und Konzepte sollen von Lesern kritisch bewertet, notfalls angegriffen und vernichtend geschlagen werden - sofern sie dies verdienen. Diese Diskussion ist notwendig, damit wir überhaupt einmal eine Ahnung davon bekommen, wohin die Umweltinformatik der verteilten Systeme gehen kann.