An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

On the cycle index of point groups

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers of sites of D lying on the symmetry elements for G.     

Synthesis of new pyrazolo[4,3-e]-1,2,4-triazolo[1,5-c]pyrimidines and related heterocycles

The reaction between 5-amino-4-imino-1(2)-substituted-1(2)H-4,5-dihydropyrazolo[3,4-d]pyrimidines and several commercially available reactants afforded new heterocycles with a conserved pyrazolo[3,4-d]pyrimidine nucleus. The key intermediates employed proved to be suitable compounds by virtue of their two vicinal amino and imino groups that were used to obtain five, six and seven-membered rings.