Calculating and interpreting the Mislin genus of a special class of nilpotent spaces

We prove that there is a bijection between the Mislin genus of a circle bundle over a certain nilpotent base space , which is constructed from a nilpotent group of a certain specified type, and the Mislin genus of itself.

     

Unique divisibility in Abelian groups

Acta Mathematica Hungarica -     

Observation of collective-emission-induced cooling of atoms in an optical cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One-third of a falling sample containing 3 x 10(6) cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented, confocal resonator. We observe decelerations up to 1500 m/s(2) and cooling to temperatures as low as 7 microK, well below the free-space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.     

Regiochemical variation in the electrophilic addition of HBr to 1-phenylprop-1-yne

The reaction of aryl alkynes with dilute methylene chloride solutions of quaternary ammonium bromide and 20% trifluoroacetic acid produces primarily the syn Markovnikov adducts of hydrogen bromide. At moderate concentrations of the bromide, the principal product is the Markovnikov anti adduct. At high concentrations of bromide, the anti-Markovnikov anti addition product predominates.