Seminorms and Continuity Modules for Functions Defined on a Segment

We describe in detail fundamental properties of continuity modules of various orders in the spaces L ^p of functions defined on a finite segment. We establish some general estimates of seminorms in terms of continuity modules with the best known constants. An example of application of these results to the best approximations is considered. Bibliography: 32 titles.     

Some inverse problems of internal-diffusion kinetics of adsorption

Methods are proposed for determining the diffusion coefficients of adsorbed molecules and the adsorption isotherms from given concentrations of the solutes in the external solution. The methods are based on a comparison of experimental data with the numerical results produced by a mathematical model of internal-diffusion kinetics of adsorption from a constant bounded volume.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 41–46, 1988.     

Global ecology and the human hair composition

As an example of the mapping of human hair composition, the territory of Uzbekistan was chosen. The data and the maps obtained were compared with the environmental situation and medical statistics. World maps were drawn on the basis of various authors' data. The possibility of using human hair for radioactivity studies is discussed on the basis of data obtained in the Chemobyl area. The proposed scheme of human hair analysis may be used for world mapping for chemical elements, radionuclides, pesticides, dioxines, PCBs, etc., either to picture the global situation or as a health status on the level of populations.Presented at the MTAA-8 Conference, September 16–20, 1991, Vienna, Austria.     

Analogs of pyrimidine mono- and polynucleotides

The corresponding monophosphates, cyclophosphates, and , -diphosphates were obtained by phosphorylation of 1-(1, 4-dihydroxy-2-pentyl) thymine, 1-(1, 3-dihydroxy-2-propyl) uracil, and their derivatives with selective protection of one of the hydroxyl groups. 2-Cyanoethyl phosphate (CEP) in the presence of N, N-dicyclohexylcarbodiimide (DCC), polyphosphoric acid, and pyrophosphoryl chloride were used as phosphorylating agents. The dependence of the yields of the products of phosphorylation of 1-(1, 4-dihydroxy-2-pentyl) thymine with CEP on the ratio of the reacting substances and the reaction time was studied. The monophosphates were cyclized under the influence of DCC. In the case of 1-(1, 3-dihydroxy-2-propyl) uracil 1-phosphate a dimeric phosphate was obtained in addition to a cyclophosphate. The acid hydrolysis of the cyclophosphates was investigated.See [1] for communication V; see [2] for a preliminary communication.Deceased.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 678–683, May, 1978.     

Reaction of succinonitrile with aliphatic amines

Conclusions The reaction of primary amines with succinonitrile leads to the formation of N,N,N,N-tetrasubstituted amidines and the liberation of 2 M of NH₃. The reaction of secondary amines with succinonitrile proceeds as an intramolecular condensation with the liberation of 1 M of NH₃ per mole of the dinitrile and the formation of the ^2,5–, -dialkylaminopyrrolene.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2722–2725, December, 1973.     

Chlorination of tetrahydrofuran-2-carboxylic acid esters

The photochemical chlorinatlon of tetrahydrofuran-2-carboxylic acid esters with chlorine at –15 to –20C leads primarily to the formation of 5-chlorotetrahydrofuran-2-carboxylic acid esters (70–80%). 4,5-Dihydrofuran-2-carboxylic acid and furan-2- carboxylic acid esters are formed as side products. The structures of the principal and side products were investigated by PMR and mass spectroscopy.Deceased.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 166–168, February, 1979.     

Analogs of pyrimidine nucleosides

α-(1-Cytosinyl)-γ-butyrolactone was obtained by condensation of bis(trimethylsilyl)cytosine with α-bromobutyrolactone. The reduction of α-(1-cytosinyl)-γ-butyrolactone with sodium borohydride gave N₁-(1,4-dihydroxy-2-butyl)cytosine, the acylation of which with benzoyl chloride and subsequent partial hydrolysis gave N₁-(1,4-dihydroxy-2-butyl)-N₄-benzoylcytosine.     

Analogs of pyrimidine nucleosides

The reaction of alkoxy bromides with N₁-(-tetrahydrofuryl) derivatives of pyrimidine bases has given a series of 6-alkoxy-5-bromo-1-(-tetrahydrofuryl)-5, 6-dihydrouracils. The hydrogenation of the 1-(-tetrahydrofuryl) derivatives of uracil and of 5-fluorouracil has been studied. It has been shown that in both cases 1-(-tetrahydrofuryl)-5, 6-dihydrouracil is formed.     

Analogs of pyrimidine nucleosides

A number of N₁-(-butyrolactono) derivatives of 5-substituted uracils have been synthesized by condensing the sodium derivatives of the corresponding bases with -bromobutyrolactone or by the halogenation of N₁-(-butyrolactono)uracil.For part I, see [1].