Generalized Lagrange multiplier technique for nonlinear programming

Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin problem. This transformation is done by using a generalized Lagrange multiplier technique. Such an approach permits us to use Newton's and gradient methods for nonlinear programming. Convergence proofs are provided, and some numerical results are given.     

Research on 1-aza two-ring systems

The catalytic hydrogenation of 5-(3-hydroxypropyl)-1,2-dihydropyrrolizines gave a mixture of stereoisbmers of 3(5)-(3-hydroxypropyl)pyrrolizidines, which was separated successfully. The stereochemistry of the compounds obtained was determined by means of the IR and ¹³C NMR spectra. The presence of strong intramolecular hydrogen bonds was detected. The basicities of the compounds obtained were determined.See [1] for Communication 19.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 63–67, January, 1980.     

Parametric integro-interpolational method of solution of singular integral equations

Use of a parametric intego-interpolational method is proposed for the study of singular integral equations with a singular kernel of Cauchy type; the method involves replacing the regular part of a quadratic formula with subsequent inversion of a singular integral. Justification is given for the computational scheme employed as well as for an estimate of the rate of convergence of the approximate solution, obtained with its aid, to the exact solution.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1614–1617, November, 1992.     

Partial methylation of methyl glycosides

Summary The partial methylation of methyl xylo-, arabino-, lyxo- and rhamnopyranosides by Purdie's method has been studied; it is possible to use the results obtained for the isolation of individual methyl ethers by micro-preparative GLC.Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Scientific Center of the Academy of Sciences of the USSR. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 682–686, November–December, 1975.     

Synthesis of methyl ethers of methyl (methyl α-D-mannopyranosid)-uronate

Methyl (methyl -D-mannopyranosid)uronate (I) has been obtained by the catalytic oxidation of methyl -D-mannopyranoside with oxygen in the presence of platinum carbon with a yield of 20%. The partial methylation of (I) and preparative column chromatography on silica gel has provided a convenient method of obtaining all the methyl ethers of (I) in the individual state.Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Scientific Center, Academy of Sciences of the USSR, Vladivostok. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 203–205, March–April, 1987.     

Polymerization of styrene in the presence of monoesters of aromatic dicarboxylic acids as surfactants

The colloidal properties of monoesters of aromatic dicarboxylic acids and the heterophase polymerization of styrene in their presence have been studied. It has been shown that particles are formed from micro-droplets of the monomer. A high stability of polymer suspensions during the synthesis has been found to be provided by a strong interfacial adsorption layer formed on the surface of particles from the polymer being synthesized and a surfactant.     

New syntheses of methyl ethers from methyl α-L-fucopyranoside

A method for obtaining methyl esters of methyl -L-fucopyranoside based on the partial methylation of methyl -L-fucopyranoside with the subsequent liquid and gasliquid chromatography of the methyl ethers is described. Their properties are given.Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Scientific Center, Academy of Sciences of the USSR, Vladivostok. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 309–312, May–June, 1985.