On the Kropholler conjecture

This short note, produced for the volume of conjectures produced on the occasion of Guido Mislin's retirement, describes the status of the Kropholle conjecture which may be viewed as a far reaching generalisation of Stallings' theorem on groups with more than one end

Aerosol particle molecular spectroscopy

The molecular spectroscopy of a solution particle by structure resonance modulation spectroscopy is discussed [S. Arnold and A. B. Pluchino, "Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances," Appl. Opt. 21, 4194 (1982); S. Arnold et al., "Molecular Spectroscopy of a Single Aerosol Particle," Opt. Lett. 9, 4 (1984)]. Analytical equations are derived for time dependence of the particle radius as it interacts with a low intensity IR source (<20 mW/cm^2). This formalism is found to be in good agreement with pulsed experiments. Working equations for the spectroscopy are derived for both constant and periodic IR excitation