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.     

Oxidative dehydrogenation of n-butenes: Product effect in the reactions over tin-antimony mixed oxides

The addition of possible oxidation and/or isomerization products (butadiene, water, isomeric n-butenes) resulted in neither promotion nor inhibition in the oxidative dehydrogenation of n-butenes over tin-antimony mixed oxide catalysts. On the basis of these and other information on the influence of products an interpretation has been given to complete the reaction mechanism more realistic than those based on previous experimental results.

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Dehydrocyclization of 1-heptene-1-14C over chromia on non-acidic alumina

The dehydrocyclization of 1-heptene-1-¹⁴C has been investigated over a chromia on nonacidic alumina catalyst with the aim of determining the¹⁴C distribution in the ring of the toluene product. As high as 80% of the¹⁴C was consistently found in the methyl position as predicted for direct six-carbon ring formation.

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1--1-C¹⁴ , , C¹⁴ . 80%- C¹⁴ , .