A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.
The species specific response of photosystem 2 (PS2) efficiency and its thermotolerance to diurnal and seasonal alterations in leaf temperature, irradiance, and water relations were investigated under alpine field conditions (1 950 m) and in response to an in situ long-term heat treatment (+3 K). Three plant species were compared using the naturally occurring microstratification of alpine environments, i.e. under contrasting leaf temperatures but under similar macroclimatic conditions. Thermotolerance of PS2 showed a high variability in all three species of up to 9.6 K. Diumal changes (increases or even decreases) in PS2 thermotolerance occurred frequently with a maximum increase of +4.8 K in Loiseleuria procumbens. Increasing leaf temperatures and photosynthetic photon flux density influenced thermotolerance adjustments. Under long-term heating (+3 K) of L. procumbens canopies with infra-red lamps, the maxima of the critical (Tc) and the lethal (Tp) temperature of PS2 increased by at least 1 K. Thermotolerance of the leaf tissue (LT50) increased significantly by +0.6 K. The effects of slight water stress on thermotolerance of PS2 were species specific. High temperature thresholds for photoinhibition were significantly different between species and increased by 9 K from the species in the coldest microhabitat to the species in the warmest. Experimental heating of L. procumbens canopies by +3 K caused a significant (p>0.01) upward shift of the high temperature threshold for photoinhibition by +3 K. Each species appeared to be very well adapted to the thermal conditions of its microhabitat as under the most frequently experienced daytime leaf temperatures no photoinhibition occurred. The observed fine scale thermal adjustment of PS2 in response to increased leaf temperatures shows the potential to optimise photosynthesis under varying environmental conditions as long as the upper thermal limits are not exceeded. and V. Braun, O. Buchner, G. Neuner.