On the univalence of derivatives of functions which are univalent in angular domains

We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f ^(k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane.     

Synthesis of 3,4-di(methylene)tetrahydrothiophene-1,1-dioxide and its use in organic synthesis

A convenient reaction scheme has been developed for obtaining 3,4-di(methylene)tetrahydrothiophene-1,2-dioxide from the readily available 3,4-dimethyl-2,4-dihydrothiophene-1,1-dioxide through 3,4-di(bromomethyl)-2,5-dihydrothiophene-1,1-dioxide. A feasibility study has been made of the use of the butadiene fragment of the heterocycle in a Dieb—Alder reaction with maleic acid derivatives, and the corresponding adducts have been obtained.DeceasedTranslated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 173–175, February, 1992.     

Interaction of 2-bromo-7-methyl-5-oxo-5H-1,3,4-thiadiazolo[3,2-α]pyrimidine with methylene-active compounds and acid hydrolysis of its products

Reactions of 2-bromo-7-methyl-5-oxo-5H-1,3,4-thiadiazolo[3,2-a]pyrimidine with sodium derivatives of pentane-2,4-dione, malonodinitrile, Meldrum acid, acetoacetic, cyanoacetic and malonic esters have been shown to give the respective substituted derivatives. Azinyl-ylidene tautomerism has been found to be characteristic of these compounds, the latter existing mainly in the ylidene form. The acid hydrolysis of pentane-2, 5-dione and cyanoacetic and malonic esters derivatives has been investigated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1957–1961, November, 1993     

Kinetics of solid polypropylene oxidation inhibited by aromatic nitrons

C-phenylcarbamoyl-N-phenylnitron and C(2,4-di-tert-butyl-3-hydroxyphenylcarbamoyl)-N-(p-di-methylaminophenyl) nitron inhibit the oxidation of solid polypropylene. In this case the nitrons studied demonstrate properties of polyfunctional inhibitors: they interrupt oxidation chains by chains by reactions with alkyl and peroxyl radicals.

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C--N- C-(2,4----3-)-N-(-) . , .

     

Kinetic approach to modeling the radical polymerization of styrene in the presence dibenzyl trithiocarbonate

A mathematical model of the kinetics of the radical polymerization of styrene in the presence of dibenzyl trithiocarbonate by the reversible addition-fragmentation chain transfer mechanism with cross-termination of radicals and intermediates and quadratic termination of intermediates is developed. The adequacy of the polymerization mechanism underlying the model and the related mathematical formalism are tested by comparing the calculated and measured values of the average molecular-weight characteristics of resulting polystyrene.     

Variations of Robin capacity and applications

We obtain some estimates for the distortions of the moduli of quadrilaterals, the reduced moduli, and Robin capacities depending on the variation of the boundary of a domain. We show that for sufficiently smooth variations of the boundary the corresponding variations of the moduli and capacities are proportional to the area of the variable part of the domain in some extremal metric. We apply these results to studying the generalized Lavrent’ev problem of finding the shape of an infinitely thin airfoil of given length with the maximal aerodynamical lift under some restriction on the curvature of the airfoil.     

Uniformization of one-parametric families of complex tori

We suggest an approximate method to find an elliptic function uniformizing a compact Riemann surface of genus 1 which is given as a ramified covering of the Riemann sphere. The method is based on including the surface into a smooth one-parametric family. We deduce a system of ordinary differential equations for critical points of elliptic functions uniformizing surfaces of the family.