Eine spezielle Vorgangsdauerverteilung zur Netzplananalyse durch Simulation

Zusammenfassung Es wird eineC genannte Verteilung bereitgestellt, die sich zur Erfassung von Vorgangsdauern bei Netzplanproblemen eignet und durch besondere Wirtschaftlichkeit bei Simulationsmethoden auszeichnet.

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Summary In this paper a distributionC will be presented for the activity duration times in network problems which from the economical point of view is fit for the solution to network problems via Monte Carlo simulation.

     

Zur Entscheidungstheorie bei mehrfacher Zielsetzung

Zusammenfassung Der Begriff eines rationalen Lösunxgsprinzips für Entscheidungsprobleme mit mehrfacher Zielsetzung wird definitorisch eingeführt. Anhand der definierenden Bedingungen werden die neueren Lösungsansätze auf Rationalität untersucht. Zusätzlich wird besonderes Gewicht auf die kritische Untersuchung der den einzelnen Verfahren zugrundeliegenden Informationsannahmen gelegt. Dabei zeigt sich, wie auch aus empirischen Untersuchungen abgeleitet wird, daß es bei der Formulierung von Lösungsansätzen auf eine präzise Darstellung des Lösungsprinzips und der damit im Zusammenhang stehenden Informationsannahme ankommt; erst auf dieser Grundlage kann die entscheidungspraktische Relevanz solcher Verfahren überprüft werden.

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Summary For multiobjective decision problems a notion of a rational solution principle is introduced by definition. The recently suggested solution approaches are tested for rationality under the defining conditions. Additionally, great importance is attached to the critical analysis of the information requirements underlying the different methods. It turns out, as well as it will be derived from empirical investigations, that a precise presentation of the solution principle and of the corresponding information requirements is indispensable formulating such approaches; first on this basis the practical relevance of solution procedures can be examined.

     

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     

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.     

The exponent of convergence of poincaré series

This paper continues the systematic study of the exponent of convergence (G) of a Fuchsian groupG begun byA. F. Beardon. The object is to show that in various senses (G) is a continuous function ofG. In view of the incompleteness of our knowledge about (G) considerable attention is paid to illustrative examples.     

Three theorems on σ-m-expandable spaces

Results concerning the connections between -m-expandability and compact-m-expandability, as well as the connections between -m-normality and compact-m-normality. Two problems are proposed.     

First observation of the P-wave spin-singlet bottomonium states hb(1P) and hb(2P)

We report the first observations of the spin-singlet bottomonium states h(b)(1P) and h(b)(2P). The states are produced in the reaction e(+)e(-)→h(b)(nP)π(+)π(-) using a 121.4 fb(-1) data sample collected at energies near the Υ(5S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We determine M[h(b)(1P)]=(9898.2(-1.0-1.1)(+1.1+1.0)) MeV/c(2) and M[h(b)(2P)]=(10,259.8±0.6(-1.0)(+1.4)) MeV/c(2), which correspond to P-wave hyperfine splittings ΔM(HF)=(+1.7±1.5) and (+0.5(-1.2)(+1.6)) MeV/c(2), respectively. The significances of the h(b)(1P) and h(b)(2P) are 5.5σ and 11.2σ, respectively. We find that the production of the h(b)(1P) and h(b)(2P) is not suppressed relative to the production of the Υ(1S), Υ(2S), and Υ(3S).