A Two-Parameter Deformed N = 2 SUSY Algebra

A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q ₁,q ₂)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made.     

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.     

Indirect spectrophotometric determination of chromium(VI)

A new simple and sensitive spectrophotometric method for the determination of chromium(VI) is established. It relies upon the oxidation of iron(II) with the titled ion, in acidic medium, to form iron(III) which is complexed with tiron to form a stable blue color with maximum absorption at 650 nm. Adherence to Beer's law is observed in the range 10–100 μg of chromium(VI) per 25 ml, with a molar absorptivity of 5.6 × 10³ liters mol^?1 cm^?1, sensitivity index of 0.0093 μg cm^?1, relative error of ?5.0 to +0.3%, and relative standard deviation of 0.3–4.0%, depending on the concentration level. Furthermore, the reaction needs neither temperature control nor an extraction step.     

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.     

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.     

Some Solutions for a Class of Singular Equations

In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients.     

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.