Hypervalent iodine-mediated interaction of aldoximes with activated alkenes including Baylis-Hillman adducts: a new and efficient method for the preparation of nitrile oxides from aldoximes

Treatment of aldoximes with activated alkenes in the presence of diacetoxy iodobenzene (DIB) afforded isoxazolines in high yields. The method has been applied for the preparation of polyfunctional isoxazolines from Baylis-Hillman adducts.     

Numerical solutions of coupled Burgers' equation

Two new algorithms based on cubic spline function technique are proposed for solving Burgers' equation in one space variable and coupled Burgers' equation in two space variables. The algorithms have been analysed for their stability and convergence. Two test examples have been solved for illustrating the merits of the proposed numerical method. The method can be extended for solving non-linear problems arising in mechanics and other areas.     

Principal bundles whose restriction to curves are trivial

Let k be an algebraically closed field and X a smooth projective variety defined over k. Let E_G be a principal G–bundle over X, where G is an algebraic group defined over k, with the property that for every smooth curve C in X the restriction of E_G to C is the trivial G–bundle. We prove that the principal G–bundle E_G over X is trivial. We also give examples of nontrivial principal bundle over a quasi-projective variety Y whose restriction to every smooth curve in Y is trivial.     

Poincaré polynomial of the moduli spaces of parabolic bundles

In this paper we use Weil conjectures (Deligne’s theorem) to calculate the Betti numbers of the moduli spaces of semi-stable parabolic bundles on a curve. The quasi parabolic analogue of the Siegel formula, together with the method of HarderNarasimhan filtration gives us a recursive formula for the Poincaré polynomials of the moduli. We solve the recursive formula by the method of Zagier, to give the Poincaré polynomial in a closed form. We also give explicit tables of Betti numbers in small rank, and genera.     

Efficient (bromodimethyl)sulfonium bromide mediated synthesis of benzimidazoles

Benzimidazoles have been efficiently synthesized in high yields by treatment of 1,2-phenylenediamine with aldehydes using (bromodimethyl)sulfonium bromide at room temperature.     

A highly chemoselective Boc protection of amines using sulfonic-acid-functionalized silica as an efficient heterogeneous recyclable catalyst

A facile and versatile method for the chemoselective Boc protection of amines has been developed by a treatment with (Boc)₂O in the presence of sulfonic-acid-functionalized silica as a catalyst. The method is general for the preparation of N-Boc derivatives of aliphatic (acyclic and cyclic), aromatic, and heteroaromatic amines; primary and secondary amines; aminols, amino-esters; and sulfonamides. The catalyst works under heterogeneous conditions and can be recycled.