Domino 1,3-Dipolar Cycloadditions of N-Alkyl-α-Amino Esters with Paraformaldehyde: A Direct Access to α-Hydroxymethyl α-Amino Acids

N-Alkyl-α-amino esters undergo a domino reaction, based on the iminium cation generation, with paraformaldehyde, followed by a 1,3-dipolar cycloaddition of the stabilized azometh­ine ylide with another equivalent of formaldehyde. The resulting products are oxazolidines, which can be transformed after hydrolysis into α-hydroxymethyl α-amino acid or its derivatives. The diastereoselective 1,3-dipolar cycloaddition was performed using sarcosine (–)-menthyl or (–)-8-phenylmenthyl esters affording the cyclic product with moderate enantiomeric ratio.

The minimal overlap rule: restrictions on mergers for creditors’ consensus

As it is known, there is no rule satisfying additivity in the complete domain of bankruptcy problems. This paper proposes a notion of partial additivity in this context, to be called μ-additivity. We find out that this property, together with two quite compelling axioms, equal treatment of equals and continuity, identify the minimal overlap rule, introduced by O’Neill (Math. Soc. Sci. 2:345–371, 1982).