Finite sphere packing and sphere covering

A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceE ^d , (1) the minimal volume of all convex bodies into which thek balls can be packed and (2) the maximal volume of all convex bodies which can be covered by thek balls. In the sausage conjectures by L. Fejes Tóth and J. M. Wills it is conjectured that, for alld5, linear arrangements of thek balls are best possible. In the paper several partial results are given to support both conjectures. Furthermore, some relations between finite and infinite (space) packing and covering are investigated.This paper was written while the first named author was visiting the Forschungsinstitut für Geistes- und Sozialwissenschaften at the University of Siegen.     

A connection between Fano configurations and Minkowski planes of odd order

It is shown in this paper that a pair of points contained in a Fano configuration in a projective plane of odd order cannot induce a Minkowski plane. From this result we derive that no pair of points in the Hughes plane of order 9 can induce a Minkowski plane.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

Forward-backward multiplicity correlations in σ+ p,K + p andpp collisions at 250 GeV/c

Forward-backward multiplicity correlations in σ⁺,K ⁺ p andpp collisions at 250 GeV/c ( \(\sqrt s \) =22 GeV) are given for all charges and for the different charge combinations. The correlations are found to be caused predominantly by centrally produced particles. It is demonstrated that this result is an agreement with observations at the ISR and the CERNp \(\bar p\) -Collider. The results are compared to expectations from LUND, DPM and FRITIOF Monte Carlo models and a geometrical picture relating correlations in hadron-hadron collisions toe ⁺ e ^? data in terms of impact parameters is tested.     

Peptide labeling using 188Re, 188Re-MAG3 and 153Sm-H1ETA: A comparison on their in vitro lipophilicity

Lanreotide peptide was labeled with ¹⁵³Sm-H₁ETA and ¹⁸⁸Re-MAG₃ in order to evaluate whether or not their conjugation to the peptide produce significant differences of the in vitro lipophilicity with respect to the ¹⁸⁸Re-lanreotide prepared by the direct labeling method (highly lipophilic). The differences of lipophilicity between the complexes, were evaluated using a reverse phase HPLC system. The measured lipophilicity of ¹⁵³Sm-H₁ETA-lanreotide, ¹⁸⁸Re-MAG₃-lanreotide and ¹⁸⁸Re-lanreotide was taken to be the capacity factor [k" = (t _R-t ₀)/t ₀ where t _R is the retention time and t ₀ is the dead time] for each of the complexes under identical chromatography conditions. Results showed that the in vitro lipophilicity decreased in the order ¹⁸⁸Re-lanreotide (direct labeling), ¹⁸⁸Re-MAG₃-lanreotide and ¹⁵³Sm-H₁ETA-lanreotide. Since the last one has a capacity factor (k") similar to that of ¹⁸⁸Re-MAG₃, some renal elimination for ¹⁵³Sm-H₁ETA-lanreotide could be expected, which probably would reduce the unnecessary radiation dose to normal tissues.