Numerical algorithm for the Mayer problem for nonlinear dynamic systems

An algorithm is proposed for numerical construction of optimal programmed controls in the Mayer problem for a nonlinear dynamic system. In each step of the optimization process, the algorithm uses the method of successive linearization with subsequent projection of the objective functional gradient on the constraints and recovery of violated boundary conditions and constraints. Solutions of some test problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 107–114, 1985.     

Structure and properties of the Ti-Si-N nanocrystalline coatings synthesized in vacuum by the electroarc method

Phase composition, defect substructure, and mechanical properties of the Ti-Si-N coating deposited on metal and ceramic-metal substrates by electroarc sputtering of the Ti-Si composite cathode in an ionized nitrogen atmosphere are investigated by the methods of modern materials science. It is established that coatings so formed with a thickness of ∼1–3 μm are superhard (H_v ∼ 50 GPa), and have the nanocrystalline structure (with crystalline sizes D = 7 nm) based on titanium nitride δ-TiN. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–51, February, 2007.     

Syntheses and base-pairing properties of locked nucleic acid nucleotides containing hypoxanthine, 2,6-diaminopurine, and 2-aminopurine nucleobases

Second generation 2'-O,4'-C-methylene-linked nucleotides 1-3 containing hypoxanthine, 2,6-diaminopurine, and 2-aminopurine nucleobases were synthesized and incorporated into locked nucleic acid (LNA) oligonucleotides by means of the automated phosphoramidite method. The required phosphoramidite monomeric units were efficiently prepared via convergent synthesis. The glycosyl donor 4 was stereoselectively coupled with hypoxanthine and 6-chloro-2-aminopurine to give the 4'-C-branched nucleosides 5 and 17. The methods for conversion of 5 and 17 into phosphoramidites 11, 25, and 29 were developed and described in full details for the first time. Hybridization properties of LNA octamers containing the new LNA nucleotides were assessed against perfect and singly mismatched DNA. The binding studies revealed that all LNA octamers hybridize very efficiently to DNA following Watson-Crick base-pairing rules with increased binding affinity compared to the DNA analogues. The unique properties of the nucleotides 1-3 make them very useful for further strengthening of the LNA technology.     

Relative viscosity and the solvation number in solutions

It has been shown that part of the free volume of a solvent attaching to the solvation shell must be excluded from the total free volume in the Bachinskii equation. This determines the increase of viscosities of solutions with positive solvation. An equation has been obtained for the inverse relative viscosity of solutions ₀/ = 1-zN₂/(1-N₂), where no and are the dynamic viscosities respectively of the solvent and the solution; z is the solvation number, N₂ is the mole fraction of dissolved material. A method is proposed for determining the solvation number (hydration) from solution viscosity data. Solvation numbers obtained by this method are in good agreement with values of z obtained from the literature and determined by other methods.Translated from Teoreticheskaya i Experimental'naya Khimiya, Vol. 21, No. 5, pp. 627–631, September–October, 1985.The author wish to express their gratitude to professors Yu. Ya. Fialkov and M. A. kvadrigin for fruitful discussions of the result of the current work.     

Computer simulation of the structure and raman spectra of GaAs polytypes

The structure, energy of formation, and Raman spectra of several polytypes (3C, 2H, 4H, and 8H) of gallium arsenide GaAs have been investigated using quantum mechanical calculations based on the local density functional theory. It has been found that the energy of the formation of hexagonal polytypes increases with an increase in the length of the periodicity and approaches the value corresponding to the ground state, i.e., to the structure of the 3C polytype. It has been shown that the calculated frequencies of normal vibrations of different polytypes are consistent, with good accuracy (±6 cm^?1), with the scheme of folding of the phonon branches. In the calculated Raman spectra of the polytypes, there are new lines (forbidden in the spectrum of the 3C polytype) which can serve as characteristic lines of other polytypes. Similar lines can be found in the Raman spectra of GaAs nanowhiskers. This result has opened up new prospects for the application of Raman spectroscopy to the characterization of the structure of these nano-objects.     

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil...