Solid Echo in Three-Spin Groups with Arbitrary Constants of Dipole–Dipole Interaction

Applied Magnetic Resonance - The suggested approach allowed us to derive analytical expressions for modeling the shape of solid-echo signal and its time evolution for a system of three-spin groups...     

Nonhomogeneous waring equations

It is proved that for an arbitrary positive integer k the equation n=x²+y²+z³+u³+v⁴+w¹⁴+t^4k+1 has a positive integer solution for all sufficiently large n. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 65–68.     

Inverse monodromy problems in mathematical physics

After a short introduction devoted to the origin of the problem considered from the physical problems of quantum field theory and statistical mechanics, the paper considers the mathematical aspects of the Knizhnik-Zamolodchikov equation theory associated with various root systems and the results connected with the inverse monodromy problem for them. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

The chemistry of indole

The opening of the pyrazolidine ring at the nitrogen-nitrogen bond in 1-arylpyrazolidine under the influence of acidic agents which leads to the formation of N-(3-aminoalkyl)indoles is described. The method enables one to obtain indoles with branched aminoalkyl radicals.For part XIII see [1].     

Bromination of 3-acyl-2-aminoindoles

Unlike 3-acylindoles, 3-acyl-2-aminoindoles display high selectivity on being electrophilically attacked in the benzene ring, and are substituted at the 6-position. At the same time, an unco-subsitution of the acyl group takes place (to the greatest extent — the formyl group). Direct bromination of 3-acyl- and 3-cyano-2-aminoindoles provides the 6-bromo- and 6,4-dibromo-2-aminoindoles and their derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 486–490, April, 1990.     

Reactions of Hydroxyazolidines with π-Donor Heterocycles. 3. Reaction of 1-Acetyl-5-hydroxypyrazolidines with Oxindoles

The reaction of oxindoles with 5-hydroxypyrazolidines on the surface of potassium fluoride-modified alumina leads to 3-(5-pyrazolidinyl)oxindoles. The structure of these products was studied.     

Reactions of hydrazine derivatives

Conditions were worked out for the synthesis of a number of 1-arylpyrazolidines with alkyl groups in the 4 and 5 positions of the five-membered ring by reduction of the corresponding 3- or 5-pyrazolidones with lithium aluminum hydride.See [1, 2] for communications XLVI And XLVII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 118–121, January, 1971.     

Synthesis of new functional derivatives of pyrazolidine from 1-acetyl-3-methyl-5-nitromethyl-2-phenylpyrazolidine

3-Nitromethylpyrazolidine reacts with derivatives of unsaturated acids and reducing agents with the formation of polyfunctional compounds of the pyrazolidine nucleus. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1365–1369, September, 2006.     

Asymptotic distribution of integer-valued binary forms of a fixed discriminant

Under the assumption on the boundary of the zeros of the Dirichlet L-functions, one obtains a refinement of the results of Yu. V. Linnik and B. F. Skubenko on the uniformity of the distribution of integral points on the hyperboloids D=b²–ac (D0). As a corollary one obtains the asymptotic behavior of the number of reduced indefinite binary quadratic forms of discriminant 4D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 26–40, 1981.