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We prove that any simple polytope (and some non-simple polytopes) in R 3 admits an inscribed regular octahedron.
For convex partitions of a convex body B we prove that we can put a homo-thetic copy of B into each set of the partition so that the sum of homothety coefficients is ≥ 1. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition.
Pharmacological investigations showed that benzylic acid ~-diethylaminoethyl ester hydrochloride, amizyl, has cholinolytic and gangliolytic properties . To study the changes in the cholinolytic action of amizyl, when two bromine atoms are introduced into its acid part at the 4,4'-positions of the phenyl groups, and also on altering the aminoalkanol… (More)
Consider a polygon P and all neighboring circles (circles going through three consecutive vertices of P). We say that a neighboring circle is extremal if it is empty (no vertices of P inside) or full (no vertices of P outside). It is well known that for any convex polygon there exist at least two empty and at least two full circles, i.e. at least four… (More)
Earlier we published an article on the synthesis and biological activity of hydrochlorides of ~-phenyl-flamino-(3fluoro-4-methoxy)propiophenones . As a continuation of these investigations and with the purpose of studying the local anesthetic and antiinflammatory activities, we have prepared by the reaction of a-bromoand… (More)