Vol. 50 No. 3 (241) (2016)

Within the framework of MIT bag model, properties of hot strange quark matter at zero pressure are investigated. It is shown that the self-boundness property of strange quark matter has a temperature dependent character. With increasing temperature, the strange quark matter which is self-bound at zero temperature, starting with a certain critical temperature becomes not self-bound.

We consider the inflationary regime of the expansion of the Universe within the framework of the modified Jordan theory. In this model, a specific cosmological scalar is an analog of the Einstein cosmological constant L, which is connected with the Hubble parameter by the power-law $\varphi(\Phi) = \alpha H^4$. As a result, a stage of hybrid inflation is obtained, at the end of which the acceleration parameter becomes zero.

We describe the integrals of motion of the high-dimensional Coulomb system with and without the Stark term, perturbed by the Calogero interaction.

Diamagnetic properties of the electron gas in a cylindrical quantum dot with parabolic confinement potential have been investigated. The analytical expressions have been obtained for mean energy, mean magnetization and mean magnetic susceptibility of the electron gas. The diamagnetic character of such system has been shown.

We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank 2 (non-degenerate) contravariant tensor field. We describe the difference between odd Riemannian and odd symplectic structure in terms of the Cartan prolongation of the corresponding Lie algebras, and formulate an analogue of the Levi- Civita theorem for an odd symplectic supermanifold.

We study several aspects of the $N = 1$ super Liouville theory. We show that certain elements of the fusion matrix in the Neveu–Schwarz sector are related to the structure constants according to the same rules, which we observe in rational conformal field theory.

We investigate the vacuum expectation values (VEV) of the electric field squared and of the energy-momentum tensor for the electromagnetic field in anti-de Sitter (AdS) spacetime induced by a plate parallel to the AdS boundary. On the plate the field obeys the boundary condition that generalizes the perfect conductor boundary condition for an arbitrary number of spatial dimensions. We show that the plate-induced contributions in the VEV of the electric field squared and the vacuum energy density are negative, whereas the normal stress is positive. The VEV vanish on the AdS boundary.

We discuss the recently developed energy density functional for hypernuclear matter, which is based on simultaneous calculation of heavy single-$\Lambda$ hypernuclei and compact stars containing hypernuclear core. The nucleonic matter is described in terms of a density-dependent parametrization of nucleon-meson couplings, whereas the hyperonmeson couplings are deduced from the octet model. We identify the parameter space of hyperon-meson couplings for which massive stellar configurations with $M \leq 2.1 M_\odot$ exist and at the same time the laboratory $\Lambda$-hypernuclear data can be described.

The generation of a magnetic field and its distribution inside a rotating strange star are discussed. The difference between the angular velocities of the superfluid and superconducting quark core and of the normal electron plasma increases because of spin-down of the star and this leads to the generation of a magnetic field. The magnetic field distribution in a star is found for a stationary value of difference of angular velocities of these components. In all parts of the star this field is determined entirely by the total magnetic momentMof the star which can vary from 10³¹-10³⁴ G·cm³ for some models of compact stars. Also the maximum possible values of magnetic field on the surface of various models of strange dwarfs have been estimated. Depending on configuration parameters, mass M and radius R of the star, the limit of 10³-10⁵ G has been established. Such values of magnetic field may be an additional condition for identification of strange dwarfs among the large class of observed white dwarfs.

n this paper we consider gap surface plasmon (GSP) propagation properties in slit milled in metal. Developed theoretical model allows to derive equations describing the reflection and transmission of the GSP from the free edge of semi-infinite slit or periodic array of semi-infinite slits in metallic host, analytically. Using these equations we calculate the transmitted power efficiency from the slit and from the array of slits. For the conditions when slit width (d) is very small compared to incident wavelength, the transmitted power efficiency is increased proportional with d^3/2, otherwise the dependence is linear. The relation of transmitted power through periodic array of slits to the transmitted power from single slit depends on slit period for the fixed wavelength. The derived equations give mathematical mechanism to calculate theoretical resonant length, losses and Q-factor of plasmon gap microresonator structures and can be used as a preliminary guideline upon designing plasmon gap microresonator.

In this paper we characterize all semigroups in which the hyperidentity of transitivity $X(X(x, y), X(y, z)) = X(x, z) $ is polynomially satisfied. In particular, we show that every transitive semigroup (that is a semigroup with the identity $xy^2z = xz$ ) is also hypertransitive.

In this paper a proof of a local existence theorem for the equation of motion of viscous liquid in H¨older weight spaces is presented.

This paper studies Noethericity and index in anisotropic weighted Sobolev spaces in R^m. Sufficient conditions are established for Noethericity preservation in weighted spaces. Applying the results obtained for operators acting in weighted Sobolev spaces, sufficient condition for semi-elliptic operator to have zero index is found.

In the article the questions of solvability and construction of the solution of nonlocal mixed value problem for a homogeneous mixed type differential equation are considered. The spectral method based on the separation of variables is used. A criterion for a single-valued solvability of the considered problem is installed. Under this criterion the single-valued solvability of the problem is proved. The existence of problem solutions in the case of uniqueness failure is studied, also.

The question of presence of Stoneley’s surface waves in three-dimensional statement is considered. Conditions are given at the interface of two half-space corresponding to the contact of two half-space without friction. The investigated problems are simplified by the introduction of potential function with analogue of the plane deformation problems. The characteristic equation is obtained concerning the phase speed of the surface wave, for which the special cases are considered.