Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples.

Regio- and stereoselective microwave-assisted synthesis of 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin-2-ones

Chiral symmetrical alk-2-yne-1,4-diols have been stereoselectively transformed into 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin- 2-ones, which are precursors of quaternary α-amino β-hydroxy acids. The key step was the cyclization of the bis(tosylcarbamates) of 2- phenylalk-2-yne-1,4-diols, easily obtained from the starting chiral diols. These cyclizations were accomplished with complete regioselectivity and up to 92:8 dr in the presence of catalytic amounts of Ni(0) or Pd (II) derivatives under microwave heating.