On summability of Fourier coefficients of functions from Lebesgue space

In this paper we state new theorems of Hardy–Littlewood type for functions with general monotone Fourier coefficients. Sharpness of stated results is discusses.     

The catalytic efficiency of Fe-containing nanocomposites based on highly dispersed silica in the reaction of CO2 hydrogenation

Research on Chemical Intermediates - Oxide Ni(80)Fe(20)/SiO2, Co(93)Fe(7)/SiO2, and Ni(19)Co(77)Fe(4)/SiO2 nanocomposites (NCs) were prepared using highly dispersed silica. It was modified by...     

A new approach to isochromanes

Some isochromane derivatives exhibit hypotensive,¹ antitumor,² and growth-regulating³ activities; some others have a specific effect on the dopaminergic system.⁴     

Unexpected formation of 4,4,6-trimethyl-2-oxo-1-phenyl-1,2,3,4-tetrahydropyridine-3-carbonitrile via Tandem Knoevenagel condensation-Michael addition-intramolecular cyclization

Knoevenagel condensation (Cope version) of acetone with cyanoacetanilide resulted in the formation of 4,4,6-trimethyl-2-oxo-1-phenyl-1,2,3,4-tetrahydropyridine-3-carbonitrile whose structure was determined by X-ray analysis.     

Synthesis and alkylation of 3-cyano-4-isobutyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-2-thiol

By reaction of isovaleric aldehyde with cyanothioacetamide and cyclohexane-1,3-dione, 3-cyano-4-isobutyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-1-thiol has been obtained, and subsequently used in synthesis of the corresponding substituted 2-alkylthiohexahydroquinolines.Lugansk T. G. Shevchenko State Pedagogical Institute, Lugansk 348011, Ukraine. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913, Russia. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 230–231, February, 1999.     

Two-gap magnetic structure of the two-stack anion-radical salt (N-Me-3,5-Di-Me-Py)(TCNQ)2 (Py is pyridine)

We performed the synthesis of a (N-Me-3,5-di-Me-Py)(TCNQ)2 single crystal and we resolved the crystallic and molecular structure of this salt. Magnetic susceptibility measurements were performed in the temperature range 2-300 K. The results are studied with respect to two energy gaps in the magnetic excitations spectra which could signify that the Peierls dielectric phase forms in two grades.     

Aliphatic aldehydes in synthesis of 4-alkyl-5-carbamoyl-3-cyano-6-methylpyridine-2(1H)-thiones

Condensation of isovaleric or acetic aldehydes with cyanothioacetamide and acetoacetamide leads to formation of 4-isobutyl(methyl)-5-carbamoyl-3-cyano-6-methylpyridine-2(1H)-thiones. By alkylation of 5-carbamoyl-3-cyano-4,6-dimethylpyridine-2(1H)-thione with 4-methoxyphenacyl bromide, 5-carbamoyl-3-cyano-4,6-dimethyl-2-(4-methoxybenzoyl)methylthiopyridine has been obtained.Lugansk T. G. Shevchenko State Pedagogical Institute, Lugansk 348011, Ukraine. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913, Russia. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 228–229, February, 1999.     

On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile

A model spectral problem of the form -i)y+xy= y on the finite interval [-1,1] with the Dirichlet boundary conditions is considered. Here is the spectral parameter and is positive. The behavior of the spectrum of this problem as 0 is completely investigated. The limit curves are found to which the eigenvalues concentrate and the counting eigenvalue functions along these curves are obtained.