A guidance problem for a differential inclusion with parameter

A differential inclusion with parameter on a finite time interval is studied. Questions related to determining the solvability set in the problem of guiding a differential inclusion to a compact target set in the phase space are discussed.     

On queue length in a queueing system with Erlang incoming flow

A single-channel queueing system with an Erlang incoming flow and random server unavailability intervals as the system releases is considered. The nonstationary and stationary distributions of queue length are obtained.     

On expansion with respect to Gabor frames generated by the Gaussian function

Mathematical Notes -     

The stereodynamics of 3,5-bis(trifluoromethylsulfonyl)-1,3,5-oxadiazinane and 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane—an experimental and theoretical study

Multinuclear dynamic NMR spectroscopy of 3,5-bis(trifluoromethylsulfonyl)-1,3,5-oxadiazinane (3) revealed the existence of two conformers with differently oriented CF₃ groups with respect to the ring, and two dynamic processes: ring inversion and restricted rotation about the N-S bond. Two transition states connecting the two conformers and corresponding to clockwise and counterclockwise rotations about the N-S bond were found; the calculated activation barriers of about 12 kcal/mol are in excellent agreement with those measured experimentally for the related molecule 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane (1). X-ray analysis proved the existence of the symmetric isomer of 3, which is the minor isomer in solutions but the only one in the crystal due to packing effects. The normal Perlin effect (JCH_ax<JCH_eq) was observed for 2(6)-CH₂ in 3, whereas the reversed Perlin effect was found for the 4-CH₂ group in 3 as well as for all CH₂ groups in 1 both experimentally and theoretically. The latter effect in compounds 1, 3, and 1-(methylsulfonyl)-3,5-bis(trifluoromethylsulfonyl)-1,3,5-triazinane (2) can be considered as a genuine reverse Perlin effect since larger values of ¹J_CH are observed for longer C-H bonds.     

Synthesis,Structure, Spectroscopic Studies,and Complexation of Novel Crown Ether Butadienyl Dyes

Butadienyl dyes of the benzothiazole series with various fragments of benzocrown ethers 1a – c were synthesized for the first time. The structures and spectral properties of crown‐containing butadienyl dyes and their complexes with alkali and alkaline‐earth metal cations were studied by X‐ray diffraction analysis and ¹H‐NMR, UV/VIS, and resonance Raman spectroscopy. To interpret the experimental results, quantum‐chemical calculations were performed. In the case of Sr²⁺ and Ba²⁺ ions, the formation of strong sandwich complexes [M( 1b )₂]²⁺ of an unusual structure involving stacking interactions was established; the dye molecules are arranged one above another in the complex according to the ‘head‐to‐head' pattern.     

Phase composition and the micro- and macrostructures of quasi-crystalline powders obtained by plasma-chemical synthesis

Quasi-crystalline Al₆₅Cu₂₃Fe₁₂ powders have been obtained by the method of plasma-chemical synthesis. Coarse particles have a spherical form and an inhomogeneous structure because of the laminar growth of crystallites toward the surface of the particles. The influence of heat treatment on phase formation and structuring in Al–Cu–Fe alloys has been studied. It has been found that the heat treatment of as-prepared powders changes the phase relationship in the quasi-crystalline alloy.     

One-pot assembly of 4-methylene-3-oxa-1-azabicyclo[3.1.0]hexanes from alkyl aryl(hetaryl) ketoximes, acetylene, and aliphatic ketones: a new three-component reaction

A new three-component reaction between alkyl aryl(hetaryl)ketoximes, acetylene, and aliphatic ketones in the superbasic systems KOH/DMSO and LiOH/CsF/DMSO (70-90 °C, initial acetylene pressure 13-15 atm, 5-60 min) affords novel 4-methylene-3-oxa-1-azabicyclo[3.1.0]hexanes in yields of up to 75%. Using KOH/DMSO, the side products of the reaction are O-vinylketoximes and 2-aryl(hetaryl)pyrroles, while with LiOH/CsF/DMSO, the reaction proves to be selective, only minor amounts of the corresponding alkyl aryl(hetaryl) ketones being detectable.     

Nucleophilic diaddition of secondary phosphine sulfides to acetylene and methylacetylene

Secondary phosphine sulfides react with acetylene and methylacetylene in the system KOH—DMSO (50 °C, 2—3 h) to form the corresponding tertiary bis-phosphine sulfides in high yield (up to 97%). Specific features of the NMR spectra (¹H, ¹³C, and ³¹P) of compounds obtained are discussed.     

On the Acid–Base State of the Surface of Semiconductor Components of the ZnSe–CdS System Exposed to Different Media

Using the methods of hydrolytic adsorption, mechanochemistry, and nonaqueous conductometric titration, the acid–base properties of the surfaces of binary semiconductors and solid solutions of the ZnSe?CdS system are studied. The nature of acid sites, and the extent, character, and mechanism of the surface (absorption) interaction are established. The interrelationships in the changes of the acid–base and bulk physical properties upon changing the chemical composition are determined, which make it possible to draw conclusions that are fundamentally important in scientific and practical aspects.