Energetics of an adiabatically-loaded excited anharmonic oscillator

The dependence of the energy characteristics on an adiabatically slowly increasing external force is determined analytically for an anharmonic oscillator. The analytical results are confirmed by a numerical calculation. The nature of the force dependences of the energy characteristics are determined and discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 153–157 (January 1997)     

Shell effects in the symmetric-modal fission of pre-actinide nuclei

Mass distributions of fragments in the low-energy fission of nuclei from ¹⁸⁷Ir to ²¹³At have been analysed. This analysis has shown that shell effects in symmetric-mode fragment mass yields from the fission of pre-actinide nuclei could be described if one assumes the existence of two strongly deformed neutron shells in the arising fragments with neutron numbers N₁ ≈ 52 and N₂ ≈ 68. A new method has been proposed for quantitatively describing the mass distributions of the symmetric fission mode for pre-actinides with A ≈ 180–220.     

Solution of the Problem of Convecitve Heat Exchange for A Two-Dimensional Body in A Low-Prandtl-Number Fluid Flow

It is shown that the exact solution of the problem of convective heat exchange in a low-Prandtl-number fluid flow (Pr ? 1) can be obtained for a two-dimensional body of arbitrary shape provided that the conformal mapping relating the body contour with a circle is known. By way of example, the Joukowsky airfoil is considered.     

Homogeneous Stäckel-type systems

A class of Hamiltonian dynamic systems integrated by the variable separation method is considered. The integration for this class is the inversion of an Abel mapping on hyperelliptic curves. We prove that the derivative of the Abel mapping is the Stäckel matrix, which determines a diagonal Riemannian metric and curvilinear orthogonal coordinate systems in a flat space. Lax representations with the spectral parameter are constructed. The corresponding classicalr-matrices are dynamic. It is shown how the class of pointwise canonical transformations can be naturally generalized using the Abel integral reduction theory.     

Constructing a model transport equation for a massless bose gas and its analytic solution

A model kinetic equation is constructed for the transport of a massless Bose gas. This equation is applied to solve the boundary value problem for the transport of radiation in the half-space occupied by a dispersive medium that is in local thermal equilibrium with the radiation. It is shown that the difference in temperature between the dispersive medium and the incident radiation substantially depends on the character of the scattering properties of the particles in the medium. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 462–472, June, 1997.     

Transfer theorems and the algebra of modal operators

A set theory ZFI′ which does not employ the Law of the Excluded Middle φ ∀ ⊥ φ, for all φ, retians the stock of expressive capacities of the classical set theory ZF, on the one hand, and has many of the features of an effective theory on the other. In the article, a broad class of formulas σ is constructed for which ZF ⊥ σ implies ZFI′ ⊥ σ. This result provides a generalization of Friedman's theorem on AE-arithmetic formulas. Besides, we prove transfer theorems of classical logic for the case of rings; in particular, Hilbert's theorem on zeros and Artin's theorem on ordered fields are extended to the case of regular f-rings, and we bring in appropriate upper bounds for them. Supported by RFFR grant No. 93-012-1027. Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 282–303, May–June, 1997.     

On finite-dimensional approximation of solutions of ill-posed problems

We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first kind presented in this paper is more economical than traditional methods for finite-dimensional approximation. Institute of Mathematies, Ukrainian Academy of Science, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 289–295, February, 1997.