Grenzleistungsgesetze für Verzweigungs- und Zusammenführungselemente

Zusammenfassung Verzweigungen und Zusammenführungen sind leistungsbestimmende Elemente von Transportsystemen. Für diese speziellen Transportknoten werden Grenzleistungsgesetze hergeleitet, die es erlauben, den Einfluß der Transportströme, der maßgebenden technischen Kenngrößen sowie der möglichen Betriebsstrategien auf die Leistungsfähigkeit zu quantifizieren. Für mehrere Beispiele durchgeführte Simulationsrechnungen bestätigen die analytischen Grenzleistungsgesetze. Die Ergebnisse enthalten unter anderem auch für die Verkehrstheorie neue Aussagen und sind sehr vielseitig anwendbar.

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Summary Branching and merging elements critically determine the performance of transport systems. For the performance of these special junction elements, analytical formulas are derived which allow the influence of the current structure, the technical parameters and the possible operation strategies to be quantified. For several examples simulated experiments confirm the analytical predictions. Some of the results are interesting, in particular for the traffic theory.

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Der Verfasser dankt HerrnH. Utter für die programmtechnische Durchführung der Simulationen auf der Rechenanlage der DEMAG Fördertechnik sowie HerrnB. Forwick für verschiedene nützliche Diskussionen.     

Zur Existenz optimaler Quadraturformeln mit freien Knoten bei Integration analytischer Funktionen

Summary In the present paper we discuss the optimal quadrature rules for integration with positive continuous weight function in Hardy space H₂ of functions analytic in a circle of the complex plane. The new representations of the optimal weights and the norm of the error functional as functions of the nodes are obtained. On this basis we give an elementary proof for the existence of the optimal quadrature formula with free nodes.     

S-Stability properties for generalized Runge-Kutta methods

Summary A class of generalized Runge-Kutta methods is considered for the numerical integration of stiff systems of ordinary differential equations. These methods are characterized by the fact that the coefficients of the integration formulas are matrices depending on the Jacobian, or on an approximation to the Jacobian. Special attention is paid to stability aspects. In particular, theS-stability properties of the method are investigated. The concept of internal stability is discussed. Internal stability imposes conditions on intermediate results in the Runge-Kutta scheme. Some numerical examples are discussed.     

Eine gemeinsame Basis für die Theorie der Eulerschen Graphen und den Satz von Petersen

The main result states: Lete ₁,e ₂,e ₃ be three lines incident to the pointv (degv4) of the connected bridgeless graphG such thate ₁ ande ₃ belong to different blocks ifv is a cutpoint. Split the pointv in two ways: Lete ₁,e _j ,j=2, 3, be incident to a new pointv _1j and leave the remainder ofG unchanged, thus obtainingG _1j . Then at least one of the two graphsG ₁₂,G ₁₃ is connected and bridgeless. — A classical result ofFrink follows from this theorem which is the key to a simple proof of Petersen's theorem. Moreover, the above result can be used to prove practically all classical results on Eulerian graphs, including best upper and lower bounds for the number of Eulerian trails in a connected Eulerian graph. In the theory of Eulerian graphs, it can be viewed as the basis for good algorithms checking on several properties of this class of graphs.

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Herrn Prof. Dr. H. Hornich zum 70. Geburtstag gewidmet     

Two questions in diophantine approximation

The first question is about a possible variation on Dirichlet's approximation theorem for linear forms x+y+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t ^–1)) by solutions of first order linear differential equationsx+y+z=0, wherex,y,z are polynomials int. Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday     

The method of Iterated Defect-Correction and its application to two-point boundary value problems

Summary In Part II of this paper we present a rigorous analysis of the Iterated Defect-Correction — applied to two-point boundary value problems — which was introduced in Part I of this paper [1]. A complete proof of Theorem 5. 1 of [1] is given.     

Die Verteilung der schlichten Funktionen in einem Funktionenraum

We consider the set of regular functions . We construct a Borel measure and a class of outer measures _h onH. With these and _h we show that: (HS)=0 and _h (HS)=0, (S is the set of normed univalent functions). From _h (HS)=0 follows—forh=t —that the Hausdorff—Billingsley-dimension ofHS is zero.     

Krull-Schmidt fails for serial modules

We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold for serial modules, as we show via an example. Nevertheless we prove a weak form of the Krull-Schmidt Theorem for serial modules (Theorem 1.9). And we show that the Grothendieck group of the class of serial modules of finite Goldie dimension over a fixed ring is a free abelian group.

     

Surgery on 3-manifolds with \mathbb{S} 1-actions

We study the topological structure of all 3-manifolds obtained by surgery along principal fibers of a closed orientable -manifold. As a consequence, we give alternative proofs of some classical results due to W. Heil and L. Moser. Moreover, we completely specify the Seifert invariants for the considered manifolds. Finally we classify the manifolds obtained by surgery along certain Seifert links and determine geometric presentations of their fundamental groups.Work performed under the auspices of C.N.R. (National Research Council) of Italy and partially supported by Ministero della Ricerca Scientifica e Tecnologica within the projects Geometria Reale e Complessa and Topologia.     

Strongly prime alternative pairs with minimal inner ideals

In this paper, we use the known classification of the finite capacity simple alternative pairs and the version of the Litoff Theorem for Jordan pairs to describe all the strongly prime alternative pairs with nonzero socle. We study the inheritance of some properties (primeness, nondegenerancy,…) when passing from the original alternative pair to the symmetrized pair. Thus, we can apply Jordan theoretical results to the alternative case. This work has been partially supported by 1) the “Plan Andaluz de Investigación y Desarrollo Tecnológico” with project no. 1027 and 2) the DGICYT with project no. PB93-0990