Gallium(III)-catalyzed tandem cycloisomerization/Friedel–Crafts alkylation: a facile synthesis of 2,5-disubstituted furans

A tandem cycloisomerization/Friedel–Crafts alkylation of indoles has been achieved in a one-pot process to produce 2,5-disubstituted furans using gallium-catalyzed sequential nucleophilic addition onto metal-activated 1-alkynyl-2,3-epoxy acetates. The reaction proceeds efficiently under mild conditions with complete regioselectivity to afford the substituted furan derivatives in good yields with high diversity.     

Effect of Fe substitution on the thermal expansion of the highT c superconductor Y1Ba2Cu3O y

Thermal expansion measurements have been carried out on Fe substituted superconducting compounds Y₁Ba₂(Cu_1−x Fe _x )₃O _y (0<x<4%) using a high resolution dilatometer employing the three terminal capacitance technique. The experimental set up is sensitive enough to detect changes in α of less than 10⁻⁸K⁻¹. Results show that the jump Δα in the coefficient of linear thermal expansion at the superconducting transition temperature,T _c, increases almost linearly with Fe concentration. The normal state thermal expansion coefficient α first decreases, attains a minimum value aroundx=1% and then increases for higher Fe concentrations. The oxygen content per unit formula is almost constant up tox=1% and then increases rapidly withx. It has also been observed that the anomalous behaviour of α around 260 K observed by Meingastet al [22] for Fe concentrationx=5% is due to inadequate annealing of the sample.     

An optically-pumped multigas Far-IR laser

We report here the operation of an optically-pumped multigas Far-IR laser. In our experiment, three different gases (CH₃OH, CH₃Br, CH₃I) were simultaneously introduced into the Far-IR cavity. By adjusting the partial pressures of the gases and by tuning the appropriate CO₂ laser pump line, we were able to obtain the laser action for each one of them as efficiently as is observed when the gases are present by themselves.     

Optical absorption spectrum of Ni2+ ion doped in synthetic lecontite

The optical absorption spectrum of Ni²⁺ ion doped in lecontite (sodium ammonium sulphate dihydrate) single crystal has been studied at room and liquid air temperatures. All the bands could be assigned assumingO _h symmetry for the Ni²⁺ ion in the crystal. The splitting of³ T _1g (F) band at liquid air temperature has been attributed to spin-orbit interaction. The crystal field and spin-orbit parameters derived areD _q=1000 cm^?1;B=740 cm^?1;C/B=4.27 and ζ=600 cm^?1. All the bands observed show a blue shift when the crystal was cooled to liquid air temperature.     

Mann-Whitney test for associated sequences

Let {X ₁, ...,X _m } and {Y ₁, ...,Y _n } be two samples independent of each other, but the random variables within each sample are stationary associated with one dimensional marginal distribution functionsF andG, respectively. We study the properties of the classical Wilcoxon-Mann-Whitney statistic for testing for stochastic dominance in the above set up.     

When isf(x1, x2, ..., xn) =u1(x1) +u2(x2) + ... +un(xn)?

We discuss subsetsS of ℝⁿ such that every real valued functionf onS is of the formf(x₁, x₂, ..., x_n) =u ₁(x₁) +u ₂(x₂) +...+u _n(x_n), and the related concepts and situations in analysis.     

Properties of balanced and perfect matrices

In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesA _I,,A _n ofA such thatA is balanced if and only if all the submatricesA ₁,,A _n ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.Partial support under NSF Grants DMS-8606188, ECS-8800281 and DDM-8800281.