On the integrability of hyperbolic systems of riccati-type equations

We consider equations of the form U_xy = U * U_x, where U(x, y) is a function taking values in an arbitrary finite-dimensional algebra T over the field ℂ. We show that every such equation can be naturally associated with two characteristic Lie algebras, L_x and L_y. We define the notion of a ℤ-graded Lie algebraB corresponding to a given equation. We prove that for every equation under consideration, the corresponding algebraB can be taken as a direct sum of the vector spaces L_x and L_y if we define the commutators of the elements from L_x and L_y by means of the zero-curvature relations. Assuming that the algebra T has no left ideals, we classify the equations of the specified type associated with the finite-dimensional characteristic Lie algebras L_x and L_y. All of these equations are Darboux-integrable. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 2, pp. 261–275, November, 1997.     

The effect of radiofrequency modulation of 57Fe hyperfine interaction by rotating magnetic field

The effect of ⁵⁷Fe hyperfine interaction radiofrequency (rf) modulation by external rotating magnetic field was studied in thin Permalloy foil by means of Mössbauer spectroscopy. The rf effect was investigated as a function of intensity for several rf field frequencies. The experiments show that the external rotating rf field causes considerable changes in the hyperfine pattern. The obtained spectra are in disagreement with those obtained by Perlow [Phys. Rev. 172 (1968) 319]. They also are inconsistent with magnetostriction hypothesis. Proceeding from the Mössbauer spectrum analysis one may conclude that the magnetization of investigated foil changes its direction in a complex manner. However, the undertaken experiments show that the essential number of Mössbauer nuclei experience the rotating magnetic field influence.     

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.     

Strain of an anisotropic monolith during the excavation of minerals

We solve the problem of the normal and transverse shear in an anisotropic monolith during the excavation of a stratum of solid mineral. It is shown that the stress perturbation field in the rock is due to the whole extent of the excavated portion of the stratum. We study way in which the friction that arises between the interacting rock of the roof and the floor influences the strain and stress fields as the front of the excavation evolves, and also the influence of the extent of the excavated portion of the rock stratum on the magnitude of the accumulated tangential displacements. Three figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 62–69.