Research on 2, 1, 3-thia-and selenadiazole

Reductive decomposition followed by hydrolysis of 5-(,-dicarethoxy--acetylamino) ethylbenz-2, 1, 3-selenadiazole gives -(3, 4-diaminophenyl)alanine.For Part XLVII see [1].     

Studies in the field of 2, 1, 3-Thiadiazole and 2,1, 3-Selenadiazole

Benzo-2, 1, 3-thiadiazole (I) undergoes chloromethylation with dichlorodimethyl ether in the presence of anhydrous aluminum chloride with the predominant formation of 4, 7-di(chloromethyl)benzo-2, 1, 3-thiadiazole (II). Bases and pseudobases (paraformaldehyde, hexamethylenetetramine, dimethylformamide) exert an inhibiting influence on this reaction. In the presence of these substances, a mixture of compound II and 4-(chloromethyl)benzo-2, 1, 3-thiadiazole (III) is formed, or else no reaction takes place. The structures of compounds II and III has been shown by their reductive decomposition to o-diamines described in the literature. The high reactivity of the chlorine in the chloromethyl group has enabled various new derivatives of benzo-2, 1, 3-thiadiazole to be obtained by its replacement with hydroxy, thiocyanato, di(-hydroxyethyl)amino, di(-chloroethyl)amino, formyl, and carboxy groups.For communication XLVIII, see [11].     

Investigations on 2, 1, 3-thia- and selenadiazoles

Nitration and nitrosation of 4-hydroxy-5-methyl-benzo-2, 1, 3-thiadiazole gives 4-hydroxy-5-methyl-7-nitro-and 4-hydroxy-5-methyl-7-nitrosobenzo-2, 1, 3-thiadiazoles. Oxidation of the latter, or of 4,7-diamino-5-methylbenzo-2,1,3-thiadiazole gives 5-methyl-4,7-dihydroxy-2, 1, 3-thiadiazole, forming derivatives with sodium bisulfite or hydroxylamine, and reduced by sodium dithionite to 5-methyl-4, 7-dihydroxybenzo-2, 1, 3-thiadiazole. The latter is also obtained by diazotizing 5-methyl-4-hydroxy-7-aminobenzo-2, 1, 3-thiadiazole, and decomposing the diazonium salt. Nitration of 4-ethoxybenzo-2, 1, 3-thiadiazole with sodium ethoxide gives 4-ethoxy-7-aminobenzo-2, 1, 3-thiadiazole, acetylated to 4-ethoxy-7-acetaminobenzo-2, 1, 3-thiadiazole.For Part XXXVII see [1].     

Researches on 2,1,3-thia-and selenadiazole

Chlorination of benzo-2,1,3-thiadiazole (I) in the presence of iron and paraform gives only 4-chlorobenzo-2,1,3-thiazole. Chlorination of 5,6-dimethylbenzo-2,1,3-thiadiazole (II) under exactly the same conditions gives only 5,6-dimethyl-4,7-dichlorobenzo-2,1,2-thiadiazole. Similarly chloromethylation of II in the presence of paraform gives only 5,6-dimethly-4,7-di(chloromethyl)benzo-2,1,3-thiadiazole. Chlorination and chloromethylation of I proceed through the intermediate formation of monosubstituted compounds which change into disubstimted ones.It is known [2,3] that Chlorination of benzo-2,1,3-thiadiazole (I) and its 5,6-dimethyl derivative (II) with chlorine in the presence of iron gives mainly the 4,7-dichloro substitution products III and IV respectively.It was previously shown [4] that chloromethylation of I with dichlorodimethyl ether in the presence of anhydrous aluminum chloride also gives mainly 4,7-di(chloromethyl)benzo-2,1,3-thiadiazole (V). Bases and pseudo-bases (paraform, urotropine. dimethylformamide) have a retarding effect on chloromethylation. When the reaction is run in the presence of these latter the products comprise besides V, 4-chloromethyl-2,1,3-thiadiazole (VI), or else, if enough base is added, there is no reaction.For Part XLII see [1].     

On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions

We consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as Hausdorff dimension, box dimension, etc. We also introduce different ways to define and study the generalized spectrum for dimensions—a one-parameter family of characteristics of dimension type.     

Description of π-partition of a diffeomorphism with invariant measure

For a diffeomorphism of a smooth compact Riemann manifold, retaining a measure equivalent to Riemann volume, a special invariant partition is constructed on a set where at least one value of the characteristic Lyapunov indicators is nonzero. This partition possesses properties analogous to the properties of partition into global condensing sheets for Y-diffeomorphisms while, as the complement to this set, there is partition into points. It is proven that the measurable hull of this partition coincides with the π-partition of a diffeomorphism.