On some properties of solutions of quasilinear degenerate equations

For quasilinear equations div A(x, u, ∇u) = 0 with degeneracy ω(x) of the Muckenhoupt A _p -class, we prove the Harnack inequality, an estimate for the H?lder norm, and a sufficient criterion for the regularity of boundary points of the Wiener type. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 918–936, July, 2008.     

Generation of resin-asphaltene substances in the luminescent concentrate under irradiation

The effect of photoirradiation on the luminescent concentrate of heavy gas oil produced by catalytic cracking (>400°C) was examined.     

Flow and capacity tensor characteristics of anisotropic porous media: Theory and experiment

Tensors determining and describing the main flow and capacity characteristics of anisotropic media are introduced. A system of laboratorymeasurements for the determination of the tensors of areal porosity, permeability, limiting gradients, and characteristic linear dimensions is considered. The pressure dependences of permeability are generalized to take into account the medium anisotropy. The results of an experiment for the determination of the permeability and limiting (initial) gradient tensors in band sandstone with orthotropic flow characteristics are presented. The measurements were carried out on four cores: two along the principal stratification directions, one perpendicular to the stratification, and one inclined at an angle of 45° to the stratification plane. The latter (fourth) specimen was taken for reference: to test the tensor nature of the introduced mathematical objects and formulas. The good agreement of the theoretical and experimental results makes it possible to recommend for engineering calculations both the formulas proposed and the developed method of laboratory investigation of the flow characteristics of anisotropic reservoirs.     

μSR study of the properties of Fe3O4-based nanostructured magnetic systems

A ferrofluid based on Fe₃O₄ nanoparticles dispersed in heavy water D₂O is studied using the μSR method. The experiment has been carried out at temperatures 26–300 K. It is found that the diamagnetic (muon) fraction is formed in the ferrofluid in about the same amount as in D₂O, but the muon-spin relaxation rate in the ferrofluid is much higher than in D₂O. A significant shift of the muon-spin precession frequency in the ferrofluid is observed. It is shown that the shift of the muon precession frequency as a function of the external magnetic field is described by the Langevin function typical of paramagnetic magnetization. The mean magnetic field in the medium due to magnetic-nanoparticle polarization in an external field is experimentally determined. The nanoparticle sizes are estimated.     

3‐(α‐Chlorobenzyl)quinoxalin‐2(1H)‐ones as Versatile Reagents for the Synthesis of 3‐Benzylquinoxalin‐2(1H)‐ones and Thiazolo[3,4‐a]quinoxalin‐4(5H)‐ones

Facile and efficient methods for the synthesis of 3‐benzylquinoxalin‐2(1H)‐ones and thiazolo[3,4‐a]quinoxalin‐4(5H)‐ones by the reaction of the readily available 3‐(α‐chlorobenzyl)quinoxalin‐2(1H)‐ones and thiourea have been developed, with multiple roles of the latter. Possible mechanisms are discussed. These two‐step sequences can be performed in a one‐pot manner to produce the desired products in moderate to high yields.     

Photometric Determination of Tin in Caspian Sea Water

Procedures were developed for the photometric determination of tin(II) with pyrogallol azo compounds, 2,3,4-trihydroxyphenylazo-5-sulfonaphthalene (R₁) and 2,2,3,4-tetrahydroxy-3-sulfo-5-chlorazobenzene (R₂), in the presence of triphenylguanidine and bathophenantroline. The complexation of tin(II) with R₁ and R₂ was studied. It was found that different-ligand complexes formed in the presence of hydrophobic amines. A bathochromic shift in absorption spectra was observed along with shifts of optimum pH formation. The effect of reagent concentration, time, and temperature on the formation of different-ligand complexes was studied, and their stoichiometry was determined by different methods. It was shown that the determination of tin(II) with R₂ in the presence of the third component is highly selective. The developed procedures were used for the photometric determination of tin in Caspian Sea water.__________Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 5, 2005, pp. 468–470.Original Russian Text Copyright © 2005 by Nagiev, Gambarov, Mamedov, Chyragov.