Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry

We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for arbitrary $\Omega$. We derive extremals to these problems in general case by using machinery of convex trigonometry, which allows us to do this identically and independently on the shape of $\Omega$. The paper describes geodesics in (i) the Finsler problem on the Lobachevsky hyperbolic plane; (ii) left-invariant sub-Finsler problems on all unimodular 3D Lie groups (SU(2), SL(2), SE(2), SH(2)); (iii) the problem of rolling ball on a plane with distance function given by $\Omega$; (iv) a series of "yacht problems" generalizing Euler's elastic problem, Markov-Dubins problem, Reeds-Shepp problem and a new sub-Riemannian problem on SE(2); and (v) the plane dynamic motion problem.Comment: 50 pages, 56 figure

On one mechanism of light ablation of nanostructures

The mechanism of mechanical ablation of nanoparticles during the interaction with a high-power laser radiation pulse is proposed. A particle is polarized under a laser electric field, and electric forces acting on field-induced oppositesign charges cause rupture stresses. Upon reaching the stresses exceeding the maximum allowable values for a given material, a nanoparticle decays into two ones. This effect can be used for narrowing the size distribution of nanoparticles produced by the laser ablation method

Effect of preparation conditions on physic-chemical properties of tin-doped nanocrystalline indium oxide

In this paper the results of investigation of phase formation and change of concentration of free electrons (Ne) in indium tin oxide system during heat treatment of coprecipitated hydroxides of indium and tin from nitric and hydrochloric solutions and also, for comparison melts of salts nitrates by an alkaline reactant (NH4OH) are considered.The performed investigation allowed to set the optimal condition of preparation of polycrystalline tin-doped indium oxide with maximal electron concentration

The preparation of the Ti-Al alloys based on intermetallic phases

This article deals with a method of obtaining materials in the Ti-Al system. Research was carried out in accordance with the phase diagram of the system state. It was established, that both single-phase and multiphase systems, containing finely dispersed intermetallic compositions of phases Ti3Al, TiAl and TiAl3, are formed. Additionally, it was found that the pure finely dispersed (coherent-scattering region (CSR) up to 100 nm) intermetallic compound TiAl3 is formed at molar ratio of Ti:Al = 1:3. Experimentally proved the possibility of produce the complex composition of alloys and intermetallic compounds and products based on them

The Features of the Presentation of the Topic “Synergetics of the Economics” For Students of Information Technologies

The problems of teaching students the synergistic basis of economy is considered. The scheme of presenting the subject is provided, which is adapted to the aspects of modern students teaching. © 201

Rare earth elements materials production from apatite ores

The paper deals with the study of processing apatite ores with nitric acid and extraction of the rare earth elements. The rare earth elements can be successfully separated and recovered by extraction from the nitrate- phosphate solution, being an tributyl phosphate as extraction agent. The developed scheme of the processing apatite concentrate provides obtaining rare earth concentrates with high qualitative characteristics

Fluoride technology of obtaining REM magnetic alloys and master alloys

Rare earth permanent magnets (REPM) based on neodymium-Fe-boron system are the most promising, since they have the highest magnetic and satisfactory mechanical characteristics. The paper covers physical-chemical principles and shows the results of experimental studies of the process of obtaining REM alloys and master alloys using fundamentally new fluoride technology based on ladle calciothermal REM fluorides and Fe reduction

Development of FEM - Programs for modeling the processes of synthesis by powder metallurgy

The finite element method (FEM) analyzes the features of the spatial distribution of Joule heat in two-phase matrix systems with round inclusions. It was found that in the processes of sintering peaks of heat generation power are formed at certain points of the medium. It is proposed to use the observed phenomenon for the formation of anisotropic and gradient materials. © 2020 American Institute of Physics Inc.. All rights reserved