An easy access to novel steroidal dispiropyrrolidines through 1,3-dipolar cycloaddition of azomethine ylides

A facile one-pot synthesis of novel steroidal dispiropyrrolidines has been accomplished by 1,3-dipolar cycloaddition reaction of various azomethine ylides derived from isatin/acenaphthenequinone/ninhydrin and sarcosine with various estrone derivatives as dipolarophiles, in good yield. The effect of various solvents on the 1,3-dipolar cycloaddition reaction are also studied.     

Triphase catalysis. I. Kinetics and mechanism of alkylation of phenylacetonitrile with alkyl halides catalyzed by aqueous naoh and polymer-supported benzyltriethylammonium chloride

The alkylation and cycloalkylation of phenylacetonitrile (PAN) with excess of 1-bromobutane and 1,4-dibromobutane respectively catalyzed by aqueous NaOH and insoluble polystyrene-bound benzyltriethylammonium chloride were studied and the rates depend upon several experimental parameters. The rate of cycloalkylation of PAN is five times faster than the alkylation and the former proceeds even in the absence of the solid catalyst. Both alkylation and cycloalkylation gave higher rates in reverse addition method than in direct addition. Deprotonation of PAN by hydroxide ion takes place without participation of the polymeric catalyst. The electrostatic force between the positive charge on the nitrogen atom of catalyst and carbanion is responsible for alkylation of active nitrile with polystyrene-bound phase-transfer catalyst. The rates of both the reactions increase with increased stirring speed, ring substitution, hydroxide ion concentration and catalyst amount and decrease with increased particle size and the degree of cross-linking of the polymer. Apparent activation energies for the reactions were calculated. The kinetic results are discussed in terms of mass transfer and a combination of intraparticle diffusion and intrinsic reactivity limitations of the rates.     

η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Activation behavior and dielectric relaxation in polyvinyl alcohol and multiwall carbon nanotube composite films

The dc and ac electrical transport property of Polyvinyl Alcohol-Multiwall Carbon Nanotubes (PVA-MWNT) composites has been investigated within a temperature range and in the frequency range 20Hz-1MHz. The temperature variation of dc conductivity gives the presence of two different activation energies. The dielectric properties of the samples have been explained in terms of electric modulus vector.The dielectric relaxation has been explained in terms of interfacial polarization occurring in between the insulating PVA matrix and MWNT conductive filler. The variation of the relaxation time with temperature also indicates the presence of two different activation energies.     

Almost sure convergence of sums of maxima and minima of positive random variables

For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables.