Konvexität in halbgeordneten Ebenen

Let (E, (ie63-01),) be a halfordered plane and call convex if M contains for any two points a,bM all pointsx between a and b. It is shown that segments [a,b] are convex if and only if (E, (ie63-02)) is the affine plane of order 3, (E, (ie63-03),) is an ordered plane or is near-trivial.

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Herrn Professor Johannes Böhm zum 70. Geburtstag gewidmet     

Two new bounds on the size of binary codes with a minimum distance of three

We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)76 andA(11, 3)152.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For thek _⊥ jet finder withy _cut=0.02, we find as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

Measurement of the hadronic decay current in τ?→π??+vτ

The properties of hadronic Z⁰ decays with final state photons, measured with OPAL at LEP, have been compared with predictions from two different matrix element calculations ofO( _s ). Two calculations, GNJETS and EEPRAD, have been investigated which use different schemes to restrict the phase space around the poles of the cross section. Assuming the E0-JADE jet definition, both calculations describe the data well in large regions of phase space fory _cut values around 0.06. For very large and very small jet-photon masses some deviations from the predictions have been found, indicating the importance of higher order corrections. Significant differences between the calculations are only apparent in the predicted rate of 1-jet plus photon events. The rate is higher in GNJETS which reproduces the data better than EEPRAD.     

On some Λ-analytic pro-p groups

This paper is devoted to the first steps towards a systematic study of pro-p groups which are analytic over a commutative Noetherian local pro-p ring Λ, e.g. Λ= . We restrict our attention to Λ-standard groups, which are pro-p groups arising from a formal group defined over Λ. Under some additional assumptions we show that these groups are of ‘intermediate growth’ in various senses, strictly betweenp-adic analytic pro-p groups and free pro-p groups. This suggests a refinement of Lazard's theory which stresses the dichotomy betweenp-adic analytic pro-p groups and all the others. In the course of the discussion we answer a question posed in [LM1], and settle two conjectures from [Bo].