Triangles of Minimal Perimeter Circumscribed about a Convex n-Gon

An algorithm for finding a circumscribed triangle of the minimal perimeter is suggested. Properties of such a triangle are described. Bibliography: 1 title.     

Analysis of the structure of an amorphous sediment obtained upon decomposition of potassium oxofluroniobate in water

An amorphous sediment was prepared by the decomposition of potassium oxofluoroniobate K_{2 ? x} Nb₄O₃(O, F)₃F in water. For this sediment, the atomic radial distribution function was analyzed with the use of a fragment model, which allows one to interpret expanded coordination spheres as being formed by first several strongest diffusion maxima. These spheres carry the most reliable information on the structure. It is shown that the amorphous sediment consists of the randomly packed Nb(O,F)₆-octahedra with interatomic distances close to those observed in the ordered region in the N-Nb₂O₅ structure. During decomposition in water, the initial K_{2 ? x} Nb₄O₃(O, F)₃F phase loses KF-layers, whereas Nb₆ clusters with metal bonds are destroyed.     

Amplified spontaneous emission and its application for population of resonant states of the Xe and Kr atoms

To extend the capabilities of the existing spectroscopic methods of investigation and diagnostics of gaseous media, we consider a macroscopic effect of an increase in the rate of spontaneous emission, which results in the transition of a considerable part of excited molecules to lower-lying optically accessible states with light pulse emission along the direction of propagation of the exciting laser radiation. As an application of the effect of amplified spontaneous emission, we propose the population with its help of optically inaccessible electronic states of atoms and molecules.     

Advances in the chemical synthesis of brassinosteroids

This review generalizes the latest advances in the chemical synthesis of the plant growth regulators brassinosteroids in 1990–1994.Institute of Bioorganic Chemistry, Belarus Academy of Sciences, 220141, Minsk, ul. Zhodinskaya, 5/2. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 507–544, July–August, 1997.     

On complementability of certain generalized hypercenters in Artinian modules

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.