Normal and compact solvability of linear operators

Dedicated to Yu. G. Reshetnyak on his sixtieth birthday.     

Mass spectrometric decomposition of Β-phenyloxiranecarboxylic esters

The electron-impact mass spectra of the E- and Z-isomers of the ,-methyl substituted esters of -phenyloxiranecarboxylic acids have been studied.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1310–1314, October, 1986.     

Synthesis of derivatives of pyrrolo[1, 2-α]pyrmidine

Continuing investigations in the field of the synthesis of condensed heterocyclic systems containing pyrrole and indole fragments ¦1–3¦, we have condensed of 2-aminopyrrole derivatives with various 1, 3-dicarbonyl compounds. The reaction took place at the boil in solutions in pyridine or acetic acid, and also without a solvent at 150–160° C, forming in a single stage derivatives of pyrrolo[1, 2-a]pyrimidine (I–III) and pyrrolo[2, 1-b]-tetrahydroquinazoline (IV–VI). The condensation of 2-aminopyrrole with acetoacetic and substituted acetoacetic esters led to 4-oxo derivatives of pyrrolo[1, 2-β]pyrimidine (VII and VIII).     

Functional derivatives of thiophene

A method is proposed for the synthesis of 5-acylamino-2,3-dimethylthiophene-4-carbaldehydes and 5-acylamino-2,3-tetramethylenethiophene-4-carbaldehydes by the formylation of the corresponding thiophenes using the Vilsmeier reaction. From the formyl derivatives obtained, previously unaccessible derivatives of thieno[2,3-b]pyridine, thieno[2,3-d]pyrimidine, and thieno[3′,2′∶5,6]pyrido[2,3-d]-pyrimidine have been synthesized.     

Condensation of 2-(acetamido)cyclohexanone with malononitrile

Depending on the conditions, condensation of 2-(acetamido)-cyclohexanone with malononitrile gives 1-acetyl-2-amino-3-cyano-4,5,6,7-tetrahydroindole or 2-amino-3-cyano-4,5,6,7-tetrahydroindole, from which substituted tetrahydropyrimido[1,2-a]indole and tetrahydropyrimido [4,5-b]indole were synthesized.     

On function spaces for quantum systems with constraints

Various realizations of the Hilbert state space for quantum systems with linear constraints are considered. One of the realizations is the completion of a Schwartz space with inner product differing from L². Another realization is a special class of distributions with inner product. An isomorphism between these realizations is constructed, and the properties of the operators are studied.     

Electrofocusing of inorganic ions

The mechanism of formation of apH gradient along a paper strip is discussed, and an equation has been derived making possible the calculation of thepH along the carrier. An equation is given relating thepH and the place of ion focusing to the stability constant. The distances between the focused zones have been estimated for the system Fe−Sr−Y, and the results are compared with the experimental data.     

1-Acyl-3-arylazoindoles in the synthesis of indolo[1,2-c]quinazolines

Treatment of 1-aeyl-3-arylazoindoles with zinc in acetic acid in the presence of acetic anhydride and sodium acetate leads to 12-acetamidoindolo [1,2-c]quinazolines. 12-Aminoindolo[1,2-c]quinazolines are obtained when the reaction is carried out in the absence of acetic anhydride and sodium acetate.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 377–379, March, 1977.     

Synthesis of derivatives of 2-amino-3-ethoxycarbonylthiophene

A number of alkylidene esters are synthesized from the corresponding ketones and cyanoacetic ester, and treatment of the esters with sulfur in the presence of a catalytic amount of diethylamine gives 2-amino-3-ethoxycarbonylthiophene derivatives.