Stress relaxation and viscosity of a bulk Pd<Subscript>40</Subscript>Cu<Subscript>30</Subscript>Ni<Subscript>10</Subscript>P<Subscript>20</Subscript> metallic glass under isochronous heating conditions

Isochronous relaxation of tensile stresses is measured in a bulk Pd₄₀Cu₃₀Ni₁₀P₂₀ metallic glass in the initial state and after certain thermal treatments. The results of measurements are used to find the energy spectrum of irreversible structural relaxation, from which the temperature dependence of shear viscosity is then calculated. This dependence is also found independently from measurements of creep in the same glass. The calculated viscosity is shown to agree well with the experimental data.     

Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

Estimates of the singular numbers of a class of integral operators

Let X,Y be smooth compact manifolds in ^m of codimension 1. A pseudodifferential operator of negative order in ^m is contracted to an operator from L₂(Y) to L₂(X). Under the assumption that mes_m–1) (XY)=0, one finds estimates for the singular numbers of the operator.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 95–99, 1981.In conclusion the author expresses his gratitude to M. Z. Solomyak for useful discussions.     

Efficiency of aerosol deposition in gas separators of various designs

Mathematical model of gas treatment to remove a finely dispersed phase, based on the theory of turbulent migration of particles, is discussed. In the approach used, the aerosol separation is considered as a kind of a diffusion process using equations of the mass transfer theory. Expressions are presented for calculating the gas cleaning efficiency in tubular, vortex, and packed gas separators. A specific feature of these expressions is that the calculations can be performed using the hydraulic resistance of the working zone of the apparatus.     

Synthesis of 5,10,15,20-tetra[6' -nitro-1,3,3-trimethylspiro- (indolino-2,2' -2H-chromen-5-yl)]porphyrin and its metal complexes

A new 5,10,15,20-tetrasubstituted porphyrin containing four 6’-nitro-1,3,3-trimethylspiro(indolino-2,2’-2H-chromene) substituents and its complexes with Zn²⁺ and Cu²⁺ ions were prepared and characterized by physicochemical methods of analysis.     

Application of positron spectroscopy for investigation of threshold space of oil-gas rocks

This article considers the possibility of applying the positron annihilation spectroscopy method for investigating the pore space of rocks from oil-gas and methane-coal deposits. The diagnostics of the structure was performed using the method of spectrometry of angular correlation of annihilation rays (ACAR). Using the samples of porous silicon, the authors have shown the applicability of the ACAR method for determination of the average dimensions of spherical and cylindrical nanosized objects and their concentration      

Study of K^ - \to \pi ^0 e^ - \overline \nu _e \gamma decay with ISTRA+ setup

Results of study of the $K^ - \to \pi ^0 e^ - \overline \nu \gamma $ decay at the ISTRA+ setup are presented. We observed 4476 events of this decay. The branching ratio is found to be $R = \frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (1.81±0.03(stat.)±0.07(syst.)) × 10^?2 for E*_γ > 10 MeV and θ*_eγ > 10°. For comparison with the previous experiment the branching ratio with cuts E*_γ > 10 MeV, 0.6 < cos θ*_eγ < 0.9 is calculated: R = $\frac{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e \gamma )}}{{Br(K^ - \to \pi ^0 e^ - \overline \nu _e )}}$ = (0.47±0.02(stat.) ± 0.03(syst.)) × 10^?2. For the cuts E*_γ > 30 MeV and θ*_eγ > 20°, used in most theoretical papers, Br = (3.06 ± 0.09(stat.) ± 0.14(syst.)) × 10^?4. For the asymmetry we get A _ξ = ?0.015 ± 0.021. At present it is the best estimate of this asymmetry.     

Construction and practical use of two-scaled extensions for rapidly oscillating functions

This paper suggests several methods for constructing two-scaled extensions for arbitrary rapidly oscillating functions. Special attention is paid to the continuity (smoothness) of extensions. The author discusses the scheme of applications of extensions to homogenization problems in non-periodic perforated domains and describes the difficulties arising in this case. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 54, Suzdal Conference–2006, Part 2, 2008.