Reduction of operators with almost periodic symbols to operators overC *-Algebras on sections of associated bundles over a torus

A decomposition of any pseudodifferential operator (D) onR ⁿ with almost periodic symbol as 113-1 1 is obtained in the paper, where _A (D) is a pseudodifferential operator over a certainC ^*-algebraA acting on sections of a vector bundle over a torusT ⁿ whose fibre isA. The coincidence of spectra sp (D) = sp _A (D) is proved for all (D) either bounded or elliptic.     

Final results on μe-pair production in neutrino interactions in the SKAT freon bubble chamber experiment

We present the final results from the search for μe pairs produced in neutrino interactions using the freon filled bubble chamber SKAT. The rate of μ^? e ⁺ pairs to charged current events above the charm threshold is \(R_{\mu ^ - e^ + } = (4.8 \pm 1.1)10^{ - 3} \) . Assuming charm particle production to be the origin of the positron we calculate \(R_{\Lambda _c^ + } = (6.2 \pm 3.1)10^{ - 2} \) andR _D =(2.8±0.9)10^?2. We observe no considerable μ^? e ^? pair production above the background. In the regionE _v >3 GeV,p _μ,e >1.0 GeV/c andp _μ>p _e we find with a 90% confidence level the limit \(R_{\mu ^ - e^ - }< 1.7 10^{ - 4} \) .     

Formation of Se0 Nanoparticles in an Aqueous Cationic Polyelectrolyte

The nanostructures formed by reduction of Se(IV) in the selenite-ascorbate redox system in an aqueous solution of supermacromolecular polycation, poly[trimethyl(methacryloyloxyethyl)ammonium] methyl sulfate, were studied by static and dynamic optical scattering and flow birefringence.     

Specific Features of Interaction of Polyacrylic and Polymethacrylic Acids with Nanoparticles of Amorphous Selenium

A study was made of formation of selenium nanoparticles in water from reduction of sodium selenite with ascorbic acid in the presence of polyacrylic and polymethacrylic acids.     

Accessibility of hydroxy groups of pectin substances for deuteration

An apparatus for the deuteration of solid samples and for recording their IR spectra in a current of D₂O vapor, and an IR-spectroscopic method of determining the degree of deuteration (q) of the hydroxy groups of pectin substances (PSs) are described. It has been established that there are no zones of structurally different nature in films of derivatives of PSs at the carboxy group. The rate of deuterium-exchange of the water of hydration of PSs is higher than for the hydroxy groups of the pyranose rings. The rate of deuterium exchange depends on the density of packing of the polymer chains of the pectin derivatives.Center for the Automation of Scientific Investigations and Metrology, Academy of Sciences of the Moldavian SSR, Kishinev. Translated from Khimiya Priorodnykh Soedinenii, No. 3, pp. 343–348, May–June, 1987.     

Rigorous justification of the Friedlander-Keller formulas

In the paper an asymptotic expansion (as , the wave number) is proved for the Green function of the problem of diffraction by a smooth convex body in two cases: when one of the points of the source or observer lies on the boundary while the other is an arbitrary distance from the boundary and also when both points lie off the boundary but not far from it. The two-dimensional Dirichlet problem is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 49–60, 1984.     

Selection of Conditions for the Dynamic Sorption Preconcentration of a 1,1-Dimethylhydrazine Derivative (4-Nitrobenzaldehyde N,N-Dimethylhydrazone) on Hydrophobized Silica

The type of mass transfer in the sorption of 4-nitrobenzaldehyde N,N-dimethylhydrazone (BDH) on silica chemically modified with hexadecyl groups was determined using the linear model of sorption dynamics, and distribution and mass transfer coefficients of hydrazone were calculated. Optimal conditions of the dynamic sorption preconcentration and desorption of BDH and its subsequent determination by reversed-phase high-performance liquid chromatography were proposed. The detection limit of the compound for preconcentration from a sample of 100 mL was 1 g/L.     

On-Line Sorption–Chromatographic Determination of Phenols with Amperometric Detection

Conditions of the preconcentration of phenol on a microcolumn filled with MN-200 hypercrosslinked polystyrene were determined using the linear sorption dynamics model. Conditions of the on-line determination of phenol and its chloro derivatives by reversed-phase high-performance liquid chromatography with amperometric detection were optimized. The detection limit of phenol and chlorophenols for preconcentration from 30 mL of a sample was 3 and 15 ng/L, respectively. The proposed procedure was used for the determination of phenols in tap and river water.     

Unusual cleavage of phenacyl-substituted benzimidazolium salts. Synthesis of 1,4-diarylimidazoles

The action of ammonium acetate in acetic acid on 1-alkyl(aralkyl)-3-phenacylbenzimidazolium bromides leads, in addition to the formation of a new imidazole ring, to cleavage of the benzimidazole fragment of the molecule at the 1,2 bond to give 1-alkyl(aralkyl)aminoaryl-4-arylimidazoles. 1,2-Dimethyl-3-(p-nitrophenacyl)benzimidazolium bromide is converted under similar conditions to the corresponding 2-methylimidazole. 4,4-Dimethyl-2,2-bis(p-nitrophenyl)-1,1-dipyrrolo[1,2-a]benzimidazole was isolated as a side product of this reaction.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 388–392, March, 1982.