Hydroamination of 2-vinylpyridine,styrene, and isoprene with pyrrolidine catalyzed by alkali and alkaline-earth metal complexes

The complexes (dpp-bian)Mg(thf)₃, (dpp-bian)Ca(thf)₄ and (dpp-bian)Mg(pyr)₃ (dpp-bian is the 1,2-bis[(2,6-diisopropylphenyl)imino]acenaphthene dianion; pyr is the pyrrolidine) catalyze the addition of pyrrolidine to 2-vinylpyridine at room temperature. The compound (dppbian)Mg[N(SiMe₃)₂] containing a dpp-bian radical anion catalyzes the addition of pyrrolidine to styrene at 60 °C. The dpp-bian radical anion lithium-sodium salt [(dpp-bian)Li{N-(SiMe₃)₂}][Na(C₇H₈)] is an active catalyst of the addition of pyrrolidine to styrene and isoprene at 60 °C. In all the case, the content of the catalyst was from 1 to 2 mol.%. For styrene and 2-vinylpyridine, the reactions proceeded with the formation of anti-Markovnikov addition product, while 1,4-addition product was obtained in the case of isoprene.     

Analysis of the percolation cluster structure

An implementation of algorithms for constructing and analyzing the cluster structure for a square quadruply connected lattice in the uncorrelated percolation problem is considered. Subsets of the complete superior hull and the skeleton of a percolation cluster are singled out using a modification of the Hoshen—Kopelman relabeling algorithm and the Bellman principle of optimality. The critical nature of the percolation process is demonstrated using the method for statistical tests, and the behavior of mass dimension is analyzed for various subsets of a percolation cluster.     

Trifluoroacetylation of 9-methylcarbazole. Example of the formation of a triarylfluoroethane in the heterocyclic series

It is shown that the trifluoroacetylation of 9-methylcarbazole proceeds regio-specifically in the 3 position of the ring. 1,1,1-Tris(9-methyl-3-carbazolyl)-2,2,2-trifluoroethane and 1,1,1,1-tetrakis(9-methyl-3-carbazolyl)-2,2,2,2,2,-2-hexafluorodiethyl ether were also isolated from the reaction mixture. Bis(trifluoroacetyl) derivatives were not detected. Only a 3-trifluoroacetyl derivative is formed when the reaction is carried out by heating in the presence of pyridine.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 640–642, May, 1984.     

A convenient method for obtaining 3-chloro- and 3,6-dichlorocarbazoles

It has been shown that the reaction of carbazole and some of its derivatives with phosphorus pentachloride in 1,2-dichloroethane leads predominantly to 3-chloro- and 3,6-dichlorocarbazoles, depending on the reaction conditions.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 644–645, May, 1985.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Multipath reflection of light from plane-parallel crystalline plates in the presence of additional exciton-polariton waves

The reflectance and transmittance of light by plane-parallel crystal plates were found in the exciton-transition spectral region upon oblique incidence of light with polarization in which two transverse and one longitudinal normal exciton-polariton wave are excited. The reflection spectra calculated for a model crystal with the parameters of the CdSe crystal are analyzed for different thicknesses of the plates, angles of incidence, and damping constants. It is shown that accounting for additional exciton-polariton waves and multiple reflections of light inside the plate results in the possibility of an abrupt change in the phase (by more than 2π) in the vicinity of the exciton transition.     

Trifluoroacetylation of 9-methylcarbazole. 2. Peculiarities of the reaction due to the presence of trifluoroacetic acid

A satisfactory model of the intermediate in the formation of polyaryltrifluoromethylmethanes in the trifluoroacetylation of 9-methylcarbazole is 1,1,1-trifluoro-2,2-bis(9-methyl-3-carbazolyl)-2-hydroxyethane. The kinetic isotope effect of the reaction was evaluated. It is shown that the rate of the reaction is determined by the formation of a complex. The trifluoromethylation of 9-methyl-carbazole at 110C is accompanied by demethylation of the substrate under the influence of trifluoroacetic acid.See [1] for communication 1.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 329–336, March, 1987.     

Synthesis of lactide from lactic acid and its esters in the presence of rare-earth compounds

A procedure is described for the synthesis of lactide by dehydration of L-lactic acid and subsequent depolymerization of its oligomer mixture in the presence of yttrium(III) and praseodymium(III) oxides, as well as of cerium(III) chloride heptahydrate. The catalytic activity of yttrium and praseodymium sesquioxides was determined at different temperatures at the oligomerization and deoligomerization stages. Ethyl lactate was prepared in the presence of Purolite C100 MB cation exchange resin and subjected to oligomerization followed by thermal decomposition of oligoester and oligolactic acid mixture in the presence of yttrium(III) and praseodymium(III) oxides and aqueous cerium(III) chloride.