Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

In a previous note [Ru] the susceptibility function was analyzed for some examples of maps of the interval. The purpose of the present note is to give a concise treatment of the general unimodal Markovian case (assuming $f$ real analytic). We hope that it will similarly be possible to analyze maps satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru], application of a theorem of Whitney [Wh] should prove differentiability of the map $f\mapsto\rho_f$ restricted to a suitable set.Comment: 8 page

From Elasticity to Hypoplasticity: Dynamics of Granular Solids

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics

Further Studies on Fire Retardant Polystyrene by Friedel–Crafts Chemistry

The combination of a copolymer of 4-vinylbenzyl alcohol and styrene with 2-ethylhexyldiphenylphosphate (DPP) and with metal chlorides has been studied by TGA, radiative gasification, Cone Calorimetry, and oxygen index measurements. Evidence is presented in support of a cross-linking reaction with the additives and the copolymer, which proceeds through a Friedel–Crafts mechanism. This approach reduces the peak heat release rate (HRR) by 60% as measured in the Cone Calorimeter. There is a significant reduction in the mass loss rate during the thermal degradation, and evidence of char formation is observed in the radiative gasification experiments