Preparation of esters of amino acids and of peptides under mild conditions

A new method for obtaining esters of N-protected amino acids and peptides from complexes of their sodium salts with 15-crown-5 that are soluble in organic solvents is proposed.A. V. Bogatskii Physicochemical Institute, Academy of Sciences of the Ukrainian SSR, Odessa. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 224–225, March–April, 1986.     

Effect of obligatory replacement and conformational restriction on psychotropic activity of thyroliberin analogs

Easy lactamization of Gln(Asn)−Pro−NH₂ with the formation of cyclic dipeptides with the diketopiperazine structure (mimetics of the conformational fragments of linear tripeptides with the X−Protrans-bond) was observed in the synthesis of tripeptide Glp−Gln−Pro−NH₂ modified by the replacement of histidine with obligatory similar glutamine in thyroliberin (Glp−His−Pro−NH₂, TRH) and in the synthesis of its structural analog [Asn²]TRH. Ion peaks corresponding to the Glp and Pro amino acid residues were revealed in the mass spectra of the peptides synthesized. The biological properties of the compounds obtained were determined indicating that the obligatory replacement resulted in an increased physiological specificity of [Gln²]TRH. The enhanced activity of conformationally restricted cyclic peptides compared to linear ones suggests that the biologically active conformation responsible for the antidepressant activity of linear TRH analogs is the conformation with X−Protrans-bond. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2015–2020, October, 1998.     

Basic hydrolysis of 3-acetoxy-7-bromo-5-(o-chlorophenyl)-1-ethoxycarbonylmethyl-1,2-dihydro-3H-1,4-benzadiazepin-2-one

The selective basic hydrolysis of 3-acetoxy-7-bromo-5-(o-chlorophenyl)-1-ethoxycarbonylmethyl-1,2-dihydro-3H-1,4-benzdiazepin-2-one has been carried out, resulting in the sequential formation of 3-hydroxy-1-ethoxycarbonylmethyl-, 3-hydroxy-1-methoxycarbonylmethyl-, and 3-hydroxy-1-carboxymethyl derivatives. The structure of the 1-methoxycarbonylmethyl derivatives has been established by x-ray structural analysis.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 685–690, May, 1990.     

The relaxation method for inconsistent systems of linear inequalities (The limit-point set)

The finiteness of the set of limit points obtained by successive projection of an element of Rⁿ on the boundary of the furthest half-space of a finite system of half-spaces with no common points is investigated. Related questions are considered.Translated from Matematicheskie Zametki, Vol. 5, No. 4, pp. 449–456, April, 1969.     

On periodic groups with prescribed orders of elements

This is a survey of results and open problems concerning the structure of periodic group with prescribed orders of their elements. In particular, an outline of a proof of the following recent result is given: every periodic group whose set of element orders coincides with {1,2,3,4,8} is locally finite.     

New periodic solutions of nonautonomous systems of nonlinear differential equations with derivatives multiplied by a small parameter and their stability

Doklady Mathematics -     

Groups containing a strongly embedded subgroup

An involution v of a group G is said to be finite (in G) if vv ^g has finite order for any g ∈ G. A subgroup B of G is called a strongly embedded (in G) subgroup if B and G\B contain involutions, but B ∩ B ^g does not, for any g ∈ G\B. We prove the following results. Let a group G contain a finite involution and an involution whose centralizer in G is periodic. If every finite subgroup of G of even order is contained in a simple subgroup isomorphic, for some m, to L ₂(2 ^m ) or Sz(2 ^m ), then G is isomorphic to L ₂(Q) or Sz(Q) for some locally finite field Q of characteristic two. In particular, G is locally finite (Thm. 1). Let a group G contain a finite involution and a strongly embedded subgroup. If the centralizer of some involution in G is a 2-group, and every finite subgroup of even order in G is contained in a finite non-Abelian simple subgroup of G, then G is isomorphic to L ₂(Q) or Sz(Q) for some locally finite field Q of characteristic two (Thm. 2). Supported by RFBR (project No. 08-01-00322), by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-334.2008.1), and by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project Nos. 2.1.1.419 and 2.1.1./3023). (D. V. Lytkina and V. D. Mazurov) Translated from Algebra i Logika, Vol. 48, No. 2, pp. 190–202, March–April, 2009.