Oscillation theorems for differential equations with a nonlinear damping term

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered.     

Photolysis of 2-dialkylamino-3-methyl-1,4-naphthoquinones

The photolysis of 2-dialkylamino-1,4-naphthoquinones is significantly more efficient when a methyl group is at C³. The quantum yields are 2–6 times greater than for 2-dialkylaminonaphthoquinones lacking a methyl group. 2-Monoalkyl-amino-1,4-naphthoquinones also undergo photochemical dealkylation.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2387–2392, October, 1991.     

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.     

Synthesis of partially hydrogenated pyrazolo[3,4-b]quinolinones by condensation of 3-amino-5-methylpyrazole with aromatic aldehydes and dimedone

Cyclocondensation of 3-amino-5-methylpyrazole with 2-arylmethylidene-5,5-dimethylcyclohexane-1,3-diones or 9-aryl-3,3,6,6-tetramethyl-2,3,4,5,6,7,8,9-octahydro-1H-xanthene-1,8-diones, as well as with synthetic precursors of the latter (para-substituted benzaldehydes and dimedone), in dimethylformamide or methanol gives the corresponding 4-aryl-3,7,7-trimethyl-2,4,6,7,8,9-hexahydropyrazolo[3,4-b]quinolin-5-ones. The structure of 4-(4-methoxyphenyl)-3,7,7-trimethyl-2,4,6,7,8,9-hexahydropyrazolo[3,4-b]quinolin-5-one was proved by the X-ray diffraction data.     

4-hydroxy-2-quinolones. 114. Synthesis and structure of 6-R-5-hydroxy-2,4-dioxo-2,3,4,6-tetrahydrobenzo-[<Emphasis Type="Italic">c</Emphasis>][2,7]naphthyridine-1-carbonitriles

Hydration of ethyl 1-R-4-dicyanomethyl-2-oxo-1,2-dihydroquinoline-3-carboxylate gives the corresponding substituted cyanoacetamides which are readily and quantitatively cyclized to 6-R-5-hydroxy-2,4-dioxo-2,3,4,6-tetrahydrobenzo[c][2,7]naphthyridine-1-carbonitriles in the presence of aqueous base. For Communication 113 see [1]. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 726–735, May, 2007.     

Determination of gold in natural waters by neutron activation and γ-spectrometry after preconcentration with tributyl phosphate as solid extractant

A method for the preconcentration of gold in natural waters at the sampling site using tributyl phosphate as a solid extractant [Se(TBP)] was developed as a preliminary step prior to the determination of gold by neutron activation and γ-spectrometry. The SE(TBP) was saturated with gaseous chlorine for extracting all gold species. In batch experiments gold was quantitatively retained on the SE(TBP) in 10 min. After extraction and washing, the SE(TBP) was ashed or back-extracted. Gold was quantitatively eluted with hot, neutral 0.025 M thiourea. The gold content of residues of ashing or eluents after evaporation was determined by neutron activation and γ-spectrometry. The detection limit for the overall procedure was 0.2 ng 1^?1. The efficiency was tested on ‘equilibrated’ solutions prepared from river water and tracer solutions of gold. For comparison, the gold content of natural water samples was determined using preconcentration on activated charcoal.     

X-Ray Investigation of Chiral β-Hydroxyketone Derived From (+)-Isomenthone

X-ray analysis was carried out to study the molecular structure of β-hydroxyketone, which is one of the minor products of selective aldol condensation of (−)-menthone with 4-carbomethoxybenzaldehyde. The cyclohexanone ring of the compound has a practically undistorted chair conformation with an axial orientation of the 1-methyl group and the bulkiest 2-[1′-hydroxy-1′ -(4-carbomethoxyphenyl)]methyl substituent and the equatorial orientation of the isopropyl group in the 4 position. The stereochemical configuration was found to be (1R,2R,4 R, 1′ S), supporting that the compound belongs to the group of (+)-isomenthones; i.e., the starting (-)-menthone undergoes (to a certain extent) epimerization under the reaction conditions used. In crystal, there is intermolecular hydrogen bonding >C=O...HO- (the -O...H- bond length is 2.15 Å). The molecular conformation in hydroxyketone crystals differs from the one which prevails in solutions (according to previous NMR data) and which is characterized by an inverted cyclohexanone ring and intramolecular hydrogen bonding >C=O...HO.Original Russian Text Copyright © 2004 by S. V. Shishkina, T. G. Drushlyak, L. A. Kutulya, N. S. Pivnenko, and O. V. Shishkin__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 933–940, September–October, 2004.     

Cyclocondensation of 2-Aminobenzimidazole with Dimedone and Its Arylidene Derivatives

The reactions of 2-aminobenzimidazole with substituted benzaldehydes and dimedone, 2-arylidene derivatives of dimedone, 9-arylhexahydro-1H-xanthene-1,8(2H)-diones and also with dimedone and DMF have been studied. The direction of formation of the pyrimidine ring has been established and discussed. An X-ray structural investigation of 2,2-dimethyl-2,3-dihydrobenzimidazo[1,2-a]quinazolin-4(1H)-one has been carried out.     

Influence of Z,E-isomerism on the chiral-optical properties of amides

The study of the chiral-optical properties of N-acyl-(–)-1-methyl-1,2,3,4-tetrahydroisoquinolines and their acyclic analogs, the n-acyl-(–)-1-phenylethylamines, with the known ratio of Z- and E-isomers showed that the Z-isomers are characterized by the negative Cotton effect in the region of the absorption band of the amide chromophore. The observed Cotton effects of amides of phenylethylamine, which are higher by comparison with those of amides of tetrahydroisoquinoline, are explained by the interaction of the amide and aromatic chromophores, which are in proximity in certain conformation, possible for acyclic conformationally free phenylethylamides.Chemical Faculty, M. V. Lomonosov Moscow State University, Moscow 119899. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 944–949, July, 1996. Original article submitted May 23, 1996.