Numerical methods for construction reachability sets of dynamical systems

The research is devoted to the problem of reachability sets construction and representation in a control problem of a dynamical system. The paper discusses two numerical methods for construction reachability sets of dynamical systems. These methods differ in the way of representations of the reachability sets. The first method is oriented on solution of the control problem on the plane and connected with a representation of sets in the form of polygons. The second one is connected with a pixel representation of sets in the m-dimensional Euclidian space and simplicial complexes. © 2012 American Institute of Physics

CONTROL SYSTEM DEPENDING ON A PARAMETER

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given

Terahertz generation by means of ZnGeP2 large aperture photoconductive antenna

The generation of terahertz (THz) radiation using a ZnGeP2 (ZGP) large-aperture photoconductive antenna (PCA) was demonstrated. The semiconductors were excited above and below the bandgap (400 and 800 nm) by a femtosecond Ti:sapphire laser. The THz pulse waveform generated by the ZGP antenna was measured using a time-domain spectroscopy technique. The antenna’s THz pulse energy dependence on the optical pump energy was measured, and saturation fluence and carrier mobility were estimated. The ZGP and a chemical vapor deposited ZnSe-based PCA were compared

Use finite family of multivalued maps for constructing stable absorption operator

The differential game of pursuit-evasion over a fixed time segment is considered. the problem of construction of the stable absorption operator of control system is investigated. The attainability sets is appointed with the help of the stable absorption operator. The partition of the conjugate space on the finite regions of convexity of Hamiltonian is used for constructing stable absorption operator

Heterocyclization of Bis(2-chloroprop-2-en-1-yl)sulfide in Hydrazine Hydrate–KOH: Synthesis of Thiophene and Pyrrole Derivatives

The article is devoted to heterocyclization of bis(2-chloroprop-2-en-1-yl)sulfide which proceeds in hydrazine hydrate–alkali medium and leads to formation of thiophene and pyrrole derivatives: previously described 4,5,9,10-tetrahydrocycloocta[1,2-c;5,8-c’]dithiophene, as well as unknown hydrazone of 5-methylidene-3-methyldihydrothiophen-2-one and 1-amino-2-(propynylsulfanylpropenylsulfanyl)-3,5-dimethylpyrrole. Tentative mechanisms for the formation of the heterocyclic products are discussed. Obtained hydrazone of 5-methylidene-3-methyldihydrothiophen-2-one was used for the synthesis of a range of azine derivatives and in oxidation process with SeO2. The found reactions open up expedient approaches to the formation of various hardly accessible thiophene and pyrrole compounds from 2,3-dichloropropene and elemental sulfur as starting reagents

Structure, phase composition and mechanical properties of ZrO2 partially stabilized with Y2O3

The structure of PSZ crystals has been studied as a function of the content of the stabilizing impurity (Y2O3) by X-ray diffraction, transmission electron microscopy (TEM) and atomic-force microscope (AFM). The hardness and fracture toughness have been measured by microindentation. The study has shown that PSZ crystals obtained by directional solidification of the melt consist of two tetragonal phases (t and t′) with varying degrees of tetragonality. Increasing the stabilizing impurity concentration leads to an increase in the volume fraction of the “untransformable” t′ phase. Experiments have shown that an increase in the concentration of the stabilizing impurity leads to a growth in the amount of positively charged oxygen vacancies (the F++-centers) which increase the lattice parameter and stabilize the structure. The character of the twinned structure changes depending on the concentration of the stabilizing impurity. In PSZ crystals with Y2O3 concentration from 2.8 to 3.2 mol% twins first, second and third orders as well as large twins consist of smaller twin domains are observed. At high concentrations of stabilizing impurities (3.7–4.0 mol%) the twin structure becomes smaller and more uniform. This suggests that twinning occurs simultaneously and is localized within small volumes. The character of the twinned structure changes depending on the concentration of the stabilizing impurity. This work shows that the quantity of hardening (fracture toughness) is proportional to the content of the transformable t phase

Expedient Strategy for the Synthesis of 5-Acylethynylpyrrole-2-carbaldehydes

<div><p></p><p>5-Acylethynylpyrrole-2-carbaldehydes have been synthesized from the protected pyrrole-2-carbaldehydes by their transition-metal-free topochemical mechanoactivated ethynylation with acylbromoacetylenes in a solid Al₂O₃ medium (room temperature, 6 h, 41–54% yields).</p></div