On a Polynomial Fractional Formulation for Independence Number of a Graph

In this paper we characterize the local maxima of a continuous global optimization formulation for finding the independence number of a graph. Classical Karush-Kuhn-Tucker conditions and simple combinatorial arguments are found sufficient to deduce several interesting properties of the local and global maxima. These properties can be utilized in developing new approaches to the maximum independent set problem.     

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.     

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.     

Spatial Focusing of Low-Mode Acoustic Signals in a shallow Sea with Underwater Flow

We analyze the possibilities of increasing noise immunity during observation of low-mode acoustic signals diffracted by a localized inhomogeneity against the noise background in shallow-water oceanic waveguides using vertical transmitting and receiving antenna arrays in the case where their deflections in the vertical direction, arising due to the influence of underwater flows, are assumed known. It is shown that compensation for the array inclination increases significantly the observation-region sizes. UDC 534.231 Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika.     

Synthesis of 4-polyfluoroalkyl-1,3-dithiolanes via [3+2] cycloaddition of thiocarbonyl ylide to polyfluoroalkanethioamides

Chemistry of Heterocyclic Compounds - New 4-polyfluoroalkyl-1,3-dithiolanes were synthesized by reaction of polyfluoroalkanethioamides with thiocarbonyl ylide that was generated in situ by...     

Monogenic functions in the biharmonic boundary value problem

We consider a commutative algebra over the field of complex numbers with a basis {e₁,e₂} satisfying the conditions , . Let D be a bounded domain in the Cartesian plane xOy and D_ζ={xe₁+ye₂:(x,y)∈D}. Components of every monogenic function Φ(xe₁+ye₂) = U₁(x,y)e₁+U₂(x,y)ie₁+U₃(x,y)e₂+U₄(x,y)ie₂ having the classic derivative in D_ζ are biharmonic functions in D, that is, Δ²U_j(x,y) = 0 for j = 1,2,3,4. We consider a Schwarz‐type boundary value problem for monogenic functions in a simply connected domain D_ζ. This problem is associated with the following biharmonic problem: to find a biharmonic function V(x,y) in the domain D when boundary values of its partial derivatives ?V/?x, ?V/?y are given on the boundary ?D. Using a hypercomplex analog of the Cauchy‐type integral, we reduce the mentioned Schwarz‐type boundary value problem to a system of integral equations on the real axes and establish sufficient conditions under which this system has the Fredholm property. Copyright © 2015 John Wiley & Sons, Ltd.     

Homogenization in the Theory of Viscoplasticity

We study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)