Dibromo[2-(4-methoxyphenyl)cyclopent-1-enyl]phosphine and Its Derivatives

Direct phosphorylation of 4-(1-cyclopent-1-enyl)anisole with PBr₃ was carried out. The resulting compound initially exists in two tautomeric forms. Isolation of the dibromophosphine and its further trans- formations lead to formation of a single tautomer.     

New GMRES(k)-Type Algorithms with Explicit Restarts and the Analysis of Their Convergence Properties Based on Matrix Relations in QR Form

The paper considers the problem of constructing a basic iterative scheme for solving systems of linear algebraic equations with unsymmetric and indefinite coefficient matrices. A new GMRES-type algorithm with explicit restarts is suggested. When restarting, this algorithm takes into account the spectral/singular data transferred using orthogonal matrix relations in the so-called QR form, which arise when performing inner iterations of Arnoldi type. The main idea of the algorithm developed is to organize inner iterations and the filtering of directions before restarting in such a way that, from one restart to another, matrix relations effectively accumulate information concerning the current approximate solution and, simultaneously, spectral/singular data, which allow the algorithm to converge with a rate comparable with that of the GMRES algorithm without restarts. Convergence theory is provided for the case of nonsingular, unsymmetric, and indefinite matrices. A bound for the rate of decrease of the residual in the course of inner Arnoldi-type iterations is obtained. This bound depends on the spectral/singular characterization of the subspace spanned by the directions retained upon filtering and is used in developing efficient filtering procedures. Numerical results are provided. Bibliography: 9 titles.     

Synthesis and Biological Activity of Novel Ethyl Esters of 4‐R‐6,8‐Dimethyl‐1‐oxo‐1,2‐dyhidropyrrolo[1,2‐d][1,2,4]triazine‐7‐carboxylic Acids

The novel heterocyclizations of ethyl 5‐(hydrazinocarbonyl)‐2,4‐dimethyl‐1H‐pyrrole‐3‐carboxylate are developed. New derivatives of ethyl esters of 4‐R‐6,8‐dimethyl‐1‐oxo‐1,2‐dyhidropyrrolo[1,2‐d][1,2,4]triazine‐7‐carboxylic acids were obtained. The in vitro anticancer and antibacterial activities of the synthesized compounds were revealed. The most potent antibacterial compound appeared to be 1.3 inhibiting Staphylococcus aureus. Pyrrolo[1,2‐d][1,2,4]triazine 2.15 showed significant antifungal activity against Candida tenuis. The anticancer activity of the synthesized compounds was determined.     

Corrigendum to “Computing of the number of right coideal subalgebras of Uq(so2n+1)” [J. Algebra 341 (1) (2011) 279–296]

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial construction of the derived set and for the differentiation functor.     

A method of tomographic reconstruction of the three-dimensional velocity distribution function of electrons

An experimental method is proposed for the determination of an arbitrary three-dimensional distribution function for initial energies of electrons emitted by a point source with resolution for two exit direction angles. In a computer experiment, two model distribution functions have been reconstructed using the proposed method.     

Synthesis and reactions of 1-Alkyl-substituted 1,5-diketones with sulfurous reagents

1-Alkyl-substituted 1,5-diketones react with sulfurous reagents (H₂S and P₄S₁₀) to give thiopyrylium salts primarily via a mechanism that is competitive with disproportionation. The reaction depends on the nature of the acidic reagent. Some properties of the compounds obtained are described.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 762–766, June, 1981.     

Preparation and ionic hydrogenation of substituted 4-(3-oxopropyl)-5-pyrazolones

4-(3-Oxopropyl)-5-pyrazolone derivatives were obtained under mild conditions of alkaline catalysis by condensation of 1-phenyl-3-methyl-5-pyrazolone and substituted chalcones. During ionic hydrogenation of the products they undergo heterocyclization with the formation of 5,6-dihydropyrano[3,2-d]pyrazoles.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 245–248, February, 1981.