Proof schemata in Hilbert-type axiomatic theories

A derivation schema in an axiomatic theory is defined as a finite sequence of analysis of applications of rules and axioms. A derivation by a schema U is any derivation whose list of analyses of applications of rules and axioms is precisely U. A derivation schema is admissible if a corresponding derivation can be constructed. Let G be a Hilbert-type axiomatic theory. The following problems are considered: a) to decide whether a given derivation scheme is admissible in G; b) to decide whether a formula is derivable by a given derivation schema in G. In the usual formulations of the predicate calculus without equality, the first problem is shown to be decidable, the second undecidable.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 174, pp. 132–146, 1988.     

Symmetric normal wave spectrum in an orthotropic layer

A solution is constructed for an orthotropic layer with free plane faces, that corresponds to the plane elastic waves symmetric over the thickness. The dynamical reconstruction of the normal wave spectrum during rotation of the wave vector from one to another elastically equivalent direction is investigated on the basis of a numerical analysis of the dispersion equation.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 116–121, 1988.     

Spectral-luminescent properties of water-alcohol solutions of coumarin derivatives with additions of lithium chloride

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 965–969, June, 1991.     

Fully closed mappings and their applications

This survey is devoted to the theory of fully closed mappings and their applications. The theoretical part includes a systematic study of relations between fully closed mappings and fiber products, inverse systems, and resolutions. The projective properties of fully closed mappings are studied. The applications are largely related to dimension and cardinal functions. The results are mainly due to the author and his students. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 4, pp. 105–235, 2003.     

Determination of the similarities between a sample and the likeness of microparticle size distribution in a disperse system

A method is proposed for determining the similarities and differences between the experimental distribution of particles in a disperse system with respect to a significant feature-particle size (sample) and the corresponding distribution (likeness), selected from the diversity of theoretical distributions with positive and negative asymmetry. The aim of the comparison is to extract the necessary information about the nature of the internal processes in the disperse system evolving as a result of the Ostwald reaction coagulation of microparticles. The procedure of comparing the distributions is illustrated on the example of the histogram of disperse Al₃Mg₂ particles of an aluminum-magnesium alloy heated isothermally at 430°C.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 80–84, December, 1991.     

Minimax estimators of spectral intensities of acoustic sources

We investigate some issues of minimax estimation of spectral intensity of acoustic sources in cases when the noise and the spectral amplitudes satisfy quadratic constraints. Recursive minimax filters are obtained.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 116–119, 1986.     

Mobility of electrons on a liquid-helium film with a rough substrate

The origin of the specific activation-type behavior of the mobility of electrons on liquid-helium films with different kinds of substrates is discussed. The characteristic feature of the activation energy E _a observed in the experiment is its dependence on the effective film thickness d in the form E _a∝d _?2. A scenario of this effect is proposed with consideration for the roughness of the substrate underlying the liquid-helium film.     

Density of states for one hole in a half filled infinite U two-dimensional Hubbard model

We investigate this problem by two methods. In the first one the density of states is determined from its moment expansion. In the second approach an imaginary time Green function obtained by a special world line Monte Carlo algorithm is analytically continued to the real frequency axis.