Algebras Generated by Linearly Dependent Elements with Prescribed Spectra

We consider associative algebras presented by a finite set of generators and relations of special form: each generator is annihilated by some polynomial, and the sum of generators is zero. The growth of this algebra in dependence on the degrees of the polynomials annihilating the generators is studied. The tuples of degrees for which the algebras are finite-dimensional, have polynomial growth, or have exponential growth are indicated. To the tuple of degrees, we assign a graph, and the above-mentioned cases correspond to Dynkin diagrams, extended Dynkin diagrams, and the other graphs, respectively. For extended Dynkin diagrams, we indicate the hyperplane in the space of parameters (roots of the polynomials) on which the corresponding algebras satisfy polynomial identities.     

Effect of annealing on the spin density of dangling bonds and the structures of amorphous germanium

Electron paramagnetic resonance was used to study the dependence of the volume spin density of dangling bonds ina-Ge films produced by cathode sputtering in argon on annealing temperature. The structure of the films is determined by x-ray diffraction analysis. Two EPR lines with g=2.019 and g=2.003 are observed whose intensities change nonmonotonically with annealing temperature. The g=2.019 line is characteristic only of the amorphous state of germanium, while the g=2.003 line persists even after crystallization of the films. When the results are compared with structure data, the conclusion may be drawn that the observed lines in the EPR spectrum are related to the dangling bonds in the peripheral regions of two types of clusters. The g=2.003 line is due to dangling bonds in the peripheral region of clusters with the usual cubic packing of atoms, and the g=2.019 line is due to clusters of the hexagonal type, which is not characteristic of the normal structure of crystalline germanium.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 51–57, July, 1989.     

Oleksii Mykolajovych Boholyubov (on His 90th Birthday)

Ukrainian Mathematical Journal -     

Anatolii Vladimirovich Skorokhod (On His 70th Birthday)

Ukrainian Mathematical Journal -     

The Influence of the Composition on the Atomic Structure of Bi1 – xYxFeO3 Ceramics

Technical Physics - The variation of the Bi1 – xYxFeO3 ceramics atomic structure with yttrium concentration x = 0, 0.10, 0.15, and 0.20 has been analyzed. Ceramic samples have been prepared...