Essential spectrum of the Laplacian for the Neumann problem in a model region of complicated structure

A class of regions in which the Laplacian for the Neumann problem has an essential spectrum is considered. The connection between the geometrical characteristics of the region and spectral properties of the Laplacian for the Neumann problem is studied in specific examples.St. Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 1, pp. 3–19, April, 1994.     

Classification of ordered nonsingular configurations of at most seven lines of ℝP 3 up to rigid isotopy

A projective m-configuration is a collection of m nonoriented pairwise disjoint lines in ℝP ³. An isotopy consisting of projective m-configurations is called a rigid isotopy. In the paper, the rigid isotopy classification of ordered projective m-configurations is obtained for m≤7. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 269–285. Translated by V. F. Mazurovskii.     

Crystallization of X-type zeolite from concentrated sodium silicate and aluminate solutions

Crystallization of an X-type zeolite from concentrated solutions of sodium aluminate (Al₂O₃ 90–330 g l^?1) and silicate (SiO₂ 110–180 g l^?1) was studied.     

Quasi-Relativism,the Narrow-Gap Property,and Forced Electron Dynamics in Solids

Narrow-gap semiconductors, used in quantum network engineering, are characterized by small effective electron masses on the Fermi level and hence by high electron mobility in the lattice. We construct an explicitly solvable model that clarifies one possible mechanism for small effective masses to appear. Another mathematical model constructed here describes a possible mechanism for using a traveling wave to control an alternating quantum current in a one-dimensional lattice.     

Exciton absorption and optical-gain bands in the presence of laser radiation

The absorption and gain bands of a weak probe signal in the presence of the Bose-Einstein condensation of excitons, which appears under nonequilibrium conditions in a field of coherent laser radiation, are considered. It is shown that the absorption of light is caused by a quantum transition from the ground state of the crystal to the quasiexciton branch of the spectrum. Amplification of the signal occurs as a result of transitions from the quasiexciton branch of the spectrum to the ground state of the crystal. Fiz. Tverd. Tela (St. Petersburg) 40, 924–927 (May 1998)     

Effect of instability of body shape on magnetoacoustic shock

The formation of magnetoacoustic shock waves excited by an axially symmetric thin body of unstable shape moving in a plasma is investigated.St. Petersburg State University. Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1499–1502, December, 1994.