The reduced anisotropic unitary Whitehead groups of henselian division algebras with unitary involutions are computed in the cases where the centers of residue algebras are of special types. 

 In this paper, the matrix-valued functional integrals generated by the Dirac equation with relativistic Hamiltonian are considered. The Dirac Hamiltonian contains scalar and vector potentials. The sum of the scalar and vector potentials is equal to zero, i.e., the case of pseudospin symmetry is investigated. In this case, a Schrödinger-type equation for the eigenvalues and eigenfunctions of the relativistic Hamiltonian generating the functional integral is constructed. The eigenvalues and eigenfunctions of the Schrödinger-type operator are found using the Sturm sequence method and the reverse iteration method. A method for the evaluation of matrix-valued functional integrals is proposed. This method is based on the relation between the functional integral and the kernel of the evolution operator with the relativistic Hamiltonian and the expansion of the kernel of the evolution operator in terms of the found eigenfunctions of the relativistic Hamiltonian. 

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom of the boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at a point. The smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved, and the conditions under which a piecewise-smooth solution exists are established. The problem with conjugate conditions is considered

In this paper, we obtained the expected constraints on the anomalous CP-even constants of three-boson interactions on the basis of cross-section for the pair production of W⁺ -bosons in proton-proton collisions. The constraints were obtained for luminosity and the kinematic constraints on the final states typical for the CMS experiment at the Large Hadron Collider at √s=13 TeV. One-dimensional and two-dimensional regions of constraints for the anomalous parameters of three-boson interactions were calculated. When calculating the cross-section, the usual approximations of small quark masses and values of the CKM matrix elements were not used. The expected values of the anomalous constants are almost an order of magnitude less than the constraints found at the LEP collider at √s= 200 GeV in the reaction e^–e⁺ → W^–W⁺.

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by 
comparison of the calculation results with the data for the masses of ρ and D mesons. 

In this paper, we considered the radiation instability in a split asymmetric resonator for the relativistic case assuming the space charge of the beam. In the small-signal approximation,  expressions for the energy loss by a particle passing through the resonator and for the beam current modulation are obtained. Based on analytical and numerical calculations, it is shown that the symmetric configuration provides the highest growth rate of instability. It is found that with the increase of the initial electron energy, the modulation of the beam current as well as the efficiency of the energy transfer from particles to the electromagnetic field decrease. The increase of the beam density has a positive effect on the radiation instability. The results obtained have to be taken into account when developing generators of electromagnetic radiation or a system for modulating the beam current based on a split resonator.

In this paper, using the theoretical and numerical investigation of molecular motion, we study heat transfer processes in the gas placed in a Newtonian gravitational field. The influence of gravity on the heat conductivity of the gas is analyzed. The gravity considered is more than 100 000 times higher than that of the Earth. The main differences of the gas heat conductivity under such high gravity from the one detected under normal gravity are demonstrated and explained. It is shown how the thermal equilibrium for the heat conductivity of the gas depends on gravity and the type of gas. The difference between natural gravity and the centrifugal force is discussed. It is shown how the gas density influences the thermal equilibrium for the heat conductivity under a strong centrifugal force. The convective heat transfer in the gas placed into a gravitational or centrifugal field is analyzed. It is shown that the thermal equilibrium of the convective heat transfer under intensive gravity is not the same as under normal gravity. The horizontal convection mechanism is discussed. A technical way of the realization of gravity thermal effects in the gas is represented. All necessary parameters of the experimental setup are given.

 The present-day observational data obtained by satellite  observatories cover seven decades of gamma-ray energy, and there is no universal general model describing the formation of the spectrum. Therefore, it is important to describe the initial stages of radiation propagation in an ultrarelativistically expanding shell. The aim of this study was to obtain equations describing the propagation of radiation in a relativistically expanding shell in the diffusion limit, solve them for natural initial data, and apply the results obtained to the initial radiation of gamma-ray bursts. The following results were obtained: the initial stage of the gamma-ray burst in a photon-thin case can be described by radiation diffusion in an ultrarelativistically expanding shell; the time interval at which it is still possible to use the diffusion approximation increases with increasing the depth inside the shell quadratically; the value of the depth beyond which the diffusion approximation can be used increases, and the value of the radiation intensity decreases in diffusion time approaches; during the main radiation of the photon-thin shell, the diffusion approximation is suitable for most of the jet. The parameters of emission are close to the ones of short gamma-ray bursts.

Herein, the dynamics and mechanisms of induced absorption in thin samples of gallium selenide under various excitation conditions are studied using femtosecond kinetic spectroscopy. We have registered several types of induced changes including induced absorption on free charge carriers (“hot” and thermalized electrons), bleaching and absorption due to the population of near-edge trap or exciton states, as well as rapid changes in the absorption of probing radiation in the region of the overlap of the exciting and probing pulses due to two-quantum two-frequency interband transitions. The time ranges of the relaxation processes are estimated. It is shown that when using relatively low-intensity long-wave excitation (790 nm), the resonant excitation of the near-edge states occurs mainly due to two-quantum two-frequency transitions followed by the formation of the dynamic equilibrium between bound and free electrons in the time range up to 5 ps. When electrons are excited deeply into the conduction band with the formation of hot free electrons and their subsequent thermalization to the bottom of the conduction band in the time range up to 1 ps, the population of the near-edge states and the establishment of the dynamic equilibrium between bound and free electrons is realized in the same time range (5 ps) as when they are excited “from below”.

The periodic switching of fans at certain ambient air temperatures and a constant power is a promising method to enhance the energy operating efficiency of air-cooled heat exchangers. Equipping these heat exchangers with devices increasing the propulsion (for example, an exhaust shaft) facilitates the intensification of heat transfer due to strengthening the free movement of air by lifting forces. Meanwhile, the heat exchanger is used at the mixed convection regime. To make the thermal design of air-cooled heat exchangers with an exhaust shaft, we must have data on the aerodynamic drag of tube beams at small Reynolds numbers (Re < 1000) that permit to calculate the air flow velocity. However, at present, studies on the aerodynamic drag at mixed convection are virtually missing. Moreover, it is necessary to take into account the influence of external air flows on the gravitational pull created by the shaft since air-cooled heat exchangers are designed for outdoor use. Using the results of the experimental investigation, we obtained information about the mass-exchange processes in the finned beam and the exhaust shaft, developed a method for calculating the air velocity in one- and many-row finned beams with the exhaust shaft and determined their aerodynamic drag at small Reynolds numbers. We also established the influence of external air flows on the gravitational pull created by the shaft.

Herein, single crystals of compounds In₂S₃, AgIn₅S₈ and solid solutions (In₂S₃)_х·(AgIn₅S₈)_1–х were grown by directional crystallization. The composition of the obtained single crystals was determined by microprobe X-ray spectral analysis. It is found that the content of the components in the grown single crystals is in satisfactory agreement with the specified composition in the initial charge. The structure of the obtained materials was determined by the X-ray method. It is shown that both the initial compounds and the solid solutions based on them were crystallized in the cubic structure of the spinel. The unit cell parameters of the In₂S₃, AgIn₅S₈ compounds and the solid solutions based on them, which vary linearly with the composition x, were calculated by the least squares method. The density was determined by the pycnometric method, and the microhardness of the In₂S₃ and AgIn₅S₈ compounds and the (In₂S₃)_х·(AgIn₅S₈)_1–х solid solutions was determined by the Knoop method. It is shown that the density, like the unit cell parameter, changes linearly with the composition x, but the dependence of microhardness on the x parameter has a maximum for x = 0.4. Using differential thermal analysis (DTA), the temperatures of phase transformations were determined and the phase diagram of the In₂S₃–AgIn₅S₈ system was constructed, which is characterized by a small crystallization interval and belongs to type III according to the Rosebom classification. The curves of liquidus and solidus are concave to the abscissa axis and have a common point.