On numerical evaluation of double integrals of an analytic function of two complex variables

A seventh degree rule of the non-product type has been constructed for numerical evaluation of double integrals of an analytic function of two complex variables by choosing a set of 17 points from the set of 25 points needed in the product Birkhoff-Young rule of fifth degree. An asymptotic error estimate for this rule has been determined and the rule has been numerically tested.     

Schwinger’s action principle,supersymmetry and path integrals

We use Schwinger’s action principle in quantum mechanics to obtain the quantisation from Lagrangian for the fermionic variables, as well as when it contains auxiliary coordinates. We illustrate this with a supersymmetric Lagrangian which naturally includes auxiliary variables. We further show that the action principle also leads to Feynman’s path integral quantisation, which is aesthetically pleasing.     

Kinetics of oxidation of thiohydantoin and rhodanine with vanadium (V)

The oxidation of thiohydantoin and rhodanine by quinquivalent vanadium ion is first order with respect to both vanadium ion and the organic substrate. The rate of oxidation increases with increase in concentration of hydrogen ions. The energy, entropy and free energy of activation have been evaluated. Formation of an intermediate complex between the organic substrate and vanadium (V) is not indicated by kinetic evidence. Some possible steps in the reaction have been proposed.     

Metal-free synthesis of 2-aminothiadiazoles via TBHP-Mediated oxidative C-S bond formation

An efficient one-pot synthesis of 2-amino-1,3,4-thiadiazoles from easily available aldehydes and thiosemicarbazide using TBHP as an oxidant has been described. Notably, these reactions were carried out at room temperature using ethanol as solvent. This is the first example for one-pot synthesis of 2-amino-1,3,4-thiadiazole derivatives from aldehydes. This new synthetic methodology provides a simple procedure utilizing a safer oxidizing system that affords the target products in mild reaction condition with satisfactory yields and wide substrate scope.     

Ultrasound assisted green synthesis of bound type bis-heterocyclic carbazolyl imidazo[1,2-a]pyridines via Groebke-Blackburn-Bienayme reaction

A series of seventeen novel 3-imidazo[1,2-a]pyridine carbazoles bound type bis-heterocycles were synthesized by Ultrasound irradiation (USI) assisted Groebke-Blackburn-Bienaymé reaction (GBBR), by employing ammonium chloride (10?mol%) as a catalyst in excellent yields (90–96%). This new, efficient and mild protocol has silent features such as green inexpensive and easily available catalyst and solvent at room temperature.     

Synthesis of Polyheterocyclic Dimers Containing Restricted and Constrained Peptidomimetics via IMCR-Based Domino/Double CuAAC Click Strategy

A novel strategy via the triple process (multicomponent reactions (MCR)-domino)/tandem was developed for the synthesis of restricted and constrained bis-1,2,3-triazole-linked pyrrolo[3,4-b]pyridine peptidomimetics dimers in overall yields of 20–55%. This strategy allows the construction of six heterocycles in two stages of the reaction.     

Total Synthesis of (E/Z) des-Hydroxy Triticone A and B

The first total synthesis of des-hydroxy triticone A and B was achieved in 12 steps. The highly chemoselective, base mediated iodolactamization of olefins with N-OMe amide motif is a key highlight of the synthesis.