Experimental check of the dispersion law for ultracold neutrons

An experiment to check the standard dispersion law for ultracold neutrons is described. The experiment is based on searching for a shift of the resonance line of a neutron interference filter as the neutron velocity component parallel to the filter surface is varied. The first results attest to a statistically significant effect. No mimicking effects were found in a control experiment, but their possible existence cannot be completely ruled out at present. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 746–751 (25 May 1998)     

Anharmonicity and the mean square displacement in perovskite-type crystals

The theoretical expression is derived for the free energy (FE) of perovskite- type crystals (PTC) on the basis of the model of the crystal with several anharmoniously vibrating atoms in a unite cell. The expression for the mean square displacement (MSD) of any atom in (PTC) is also obtained as a function of potential coefficients of the Hamiltonian of a crystal.The evaluation of the numerical values of potential coefficients of the Hamiltonians of BaTiO₃ and SrTiO₃ on the basis of the available experimental data is made.     

State of Silicotungstic Acid in Aqueous Solutions in the Presence of Inorganic Salts as Probed by NMR Spectroscopy

The state of silicotungstic acid (STA) in the presence of inorganic salts (Fe₂(SO₄)₃, SnCl₂, and SnSO₄) in aqueous solutions was studied by ¹⁸³W NMR spectroscopy. Silicotungstic acid was found to retain its structure, and no new heteropoly compounds were formed. This finding proves the enhanced stability of STA toward complex formation at high acidities.     

On polyhedral approximations in an <Emphasis Type="Italic">n</Emphasis>-dimensional space

The polyhedral approximation of a positively homogeneous (and, in general, nonconvex) function on a unit sphere is investigated. Such a function is presupporting (i.e., its convex hull is the supporting function) for a convex compact subset of Rⁿ. The considered polyhedral approximation of this function provides a polyhedral approximation of this convex compact set. The best possible estimate for the error of the considered approximation is obtained in terms of the modulus of uniform continuous subdifferentiability in the class of a priori grids of given step in the Hausdorff metric.     

Nature of Equidistant Negative Differential Resonances in Tunneling Spectra of Ultrasmall Nanoparticles

JETP Letters - A model of tunneling multiresonant electronic transitions in nanocontacts containing ultrasmall nanoparticles with adsorbed atoms has been developed. Mechanisms of the formation of...     

RYDMR spectra for reactions of triplet−triplet annihilation and photogeneration of triplet pairs in molecular crystals

The contribution to the RYDMR spectrum from an elementary event of collision of two triplet excitons during their mutual annihilation is calculated, and the reverse process of photogeneration of a pair of triplet excitons in a molecular crystal are considered. The interaction between the excitons in the cell is assumed weak in comparison with the Zeeman splitting and the fine-structure parameters for the triplet state of each of the molecules. For both the annihilation of excitons and the photogeneration of a pair, the RYDMR signal from a single-crystal sample disappears at certain orientations of the crystal relative to the external magnetic field. This effect was previously experimentally observed for the anthracene?tetracyanobenzene crystal and was explained in the case of stationary optical excitation of the molecule. The results obtained in this paper make it possible to consider an arbitrary, not only stationary, mode of irradiation sample. An interval of angles between the static magnetic field and the crystallographic axes of the crystal within which the lines in the spectrum can disappear is determined. The possibility of using the RYDMR method for studying nanosized objects, for which additional peaks in the RYDMR spectrum may arise, is briefly discussed.     

About the Lipschitz property of the metric projection in the Hilbert space

We consider the metric projection operator from the real Hilbert space onto a strongly convex set. We prove that the restriction of this operator on the complement of some neighborhood of the strongly convex set is Lipschitz continuous with the Lipschitz constant strictly less than 1. This property characterizes the class of strongly convex sets and (to a certain degree) the Hilbert space. We apply the results obtained to the question concerning the rate of convergence for the gradient projection algorithm with differentiable convex function and strongly convex set.