3-Chloropropyl and 4-chlorobutyl phenyl ethers as sources of 1, 3-dilithiopropane and 1,4-dilithiobutane: sequential reaction with carbonyl compounds

The reaction of 3-chloropropyl and 4-chlorobutyl phenyl ethers (1) with lithium powder and a catalytic amount of DTBB (5% molar) in THF at -78 degrees C followed by successive treatment with a carbonyl compound [R(1)R(2)CO = Bu(t)CHO, Me(2)CO, (CH(2))(5)CO, (-)-menthone] at -78 to 20 degrees C and, after 1.5 h at this temperature, with a second one [R(3)R(4)CO = Bu(t)CHO, PhCHO, Me(2)CO, MeCOPr(n), (CH(2))(5)CO, (-)-menthone] at -78 degrees C leads, after hydrolysis with water, to the corresponding 1,5- and 1, 6-diols (2). Because of the competition of two different reductive cleavages, 1,4- and 1,5-diols 3 were also obtained as side-reaction products.     

An efficient method for the debutylation of o-and p-t-butylphenols and for the hydrolysis of aryl acetates : [Protective group; quinones]

t-Butyl groups can be removed from mono-, di-, or tri-t-butylphenols by refluxing with 70% trifluoroacetic acid. In the same way sterically hindered as well as unhindered aryl acetates can be hydrolysed.     

Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case

For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented.     

Photon statistics of non-stationary gaussian-markovian light

The photon counting distribution due to gaussian-markovian light relaxing from an excited state to equilibrium, is calculated and compared with the distribution due to stationary light having the same average intensity.     

Unique divisibility in Abelian groups

Acta Mathematica Hungarica -     

Tetronamides as latent acyclic vinylogous amides in formal aza-[3 + 3] cycloaddition reactions with alpha,beta-unsaturated iminium salts. An unexpected rearrangement and an approach to synthesis of substituted piperidines

A detailed account regarding formal aza-[3 + 3] cycloaddition reactions of tetronamides with alpha,beta-unsaturated iminium salts is described here. This investigation uncovers regioisomeric cycloadducts that were not found in previous studies involving this formal cycloaddition and an unexpected rearrangement that led to pyridines and dihydropyridines. Both stereochemical and regiochemical issues raised in this study provide further mechanistic insights into this cycloaddition. With careful control of reaction temperatures, the desired formal cycloadducts are obtained. Ensuing transformation of these cycloadducts into functionalized piperidines establishes the concept of employing tetronamides as latent acyclic vinylogous amides for the formal aza-[3 + 3] cycloaddition.     

Isometries of certain operator spaces

Let and be Banach spaces, and be the spaces of bounded linear operators from into In this paper we give full characterization of isometric onto operators of for a certain class of Banach spaces, that includes We also characterize the isometric onto operators of and the compact operators on Furthermore, the multiplicative isometric onto operators of , when multiplication on is taken to be the Schur product, are characterized.

     

Enhancing the axial resolution of quantum optical coherence tomography by chirped quasi-phase matching

We show theoretically that a chirped quasi-phase-matching nonlinear crystal structure can significantly enhance the axial resolution in quantum optical coherence tomography by increasing the spectral width of the generated entangled photon pairs. For pulsed pumps we show how the pump-pulse duration affects the maximum resolution attainable.