On matrix types of prime varieties of associative algebras

Some answer is obtained to the problem by A. R. Kemer: We show that for a given number k and all sufficiently large p every prime variety of associative algebras of matrix type k over a field of characteristic p > 0 is regular.     

An optimal boundary control problem for the motion equations of polymer solutions

We study an optimal boundary control problem for stationary equations of a model of the motion of weakly concentrated water solutions of polymers. Sufficient conditions are obtained for the solvability of the problem. Some properties of the set of optimal solutions are established.     

Coherent effect in the radiation of relativistic electrons in the field of bent atomic crystallographic planes

The effect of the intense monochromatic radiation arising when relativistic electrons intersect periodically bent atomic crystallographic planes in a crystal is predicted. This effect is independent of the channeling of the particles in the crystal and is possible for relativistic positrons and electrons.     

Anomalous proximity effect in superconducting oxide structures with an antiferromagnetic layer

The electrophysical parameters of superconductor/antiferromagnetic insulator structures based on the Nb/Au/Ca_1?x Sr _x CuO₂/YBa₂Cu₃O_7?δ hybrid heterostructure have been examined. YBa₂Cu₃O_7?δ and Ca_1?x Sr _x SuO₂ epitaxial films are grown by the laser ablation method on NdGaO₃ single crystal substrates, the thickness of the Ca_1?x Sr _x CuO₂ layer varies from 20 to 50 nm, and x = 0.15 and 0.5. The superconducting pair potential in the interface between the YBa₂Cu₃O_7?δ superconductor and Ca_1?x Sr _x CuO₂ antiferromagnet is found to penetrate into the antiferromagnet at distances much larger than the coherence length calculated for the ferromagnetic layer. The critical current of the superconducting transition manufactured at such an interface is highly sensitive to the magnetic field.     

An axiomatization for the linear logic of knowledge and time LTK r with intransitive time relation

We study the problem of the axiomatization of the linear multimodal logic of knowledge and time LTK _r with reflexive intransitive time relation. The logic is defined semantically as the set of formulas true on frames of a special kind. The LTK _r -frames are linear chains of clusters connected by a reflexive intransitive relation R _T which simulates time. Elements inside a cluster are connected by several equivalence relations imitating the knowledge of different agents. The main result of the article is the proof of the fact that the finite set of formulas proposed by the authors is an axiomatization of the logic LTK _r with reflexive intransitive time relation.     

Circular dichroism spectra of langasite family crystals in the range of electronic transitions of structure defects

The absorption and circular dichroism spectra of langasite family crystals are studied. Wide bands in the range of 285–500 nm that are related to the structure lattice defects are found. For all the crystals, these bands are in approximately the same spectral region, have identical structures, and can be attributed to one type of defects formed by cation vacancies and excess oxygen atoms in the optically active positions.     

Generalized normal homogeneous Riemannian metrics on spheres and projective spaces

In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres ${S^n}$ . We prove that for any connected (almost effective) transitive on $S^n$ compact Lie group $G$ , the family of $G$ -invariant Riemannian metrics on $S^n$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $n\ge 5$ . Any such family (that exists only for $n=2k+1$ ) contains a metric $g_\mathrm{can}$ of constant sectional curvature $1$ on $S^n$ . We also prove that $(S^{2k+1}, g_\mathrm{can})$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $G$ (except the groups $G={ SU}(k+1)$ with odd $k+1$ ). The space of unit Killing vector fields on $(S^{2k+1}, g_\mathrm{can})$ from Lie algebra $\mathfrak g $ of Lie group $G$ is described as some symmetric space (except the case $G=U(k+1)$ when one obtains the union of all complex Grassmannians in $\mathbb{C }^{k+1}$ ).