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We show that computing the lexicographically first four-coloring for planar graphs is Δ p 2 -hard. This result optimally improves upon a result of Khuller and Vazirani who prove this problem NP-hard, and conclude that it is not self-reducible in the sense of Schnorr, assuming P = NP. We discuss this application to non-self-reducibility and provide a general related result. We also discuss when raising a problem's NP-hardness lower bound to Δ p 2 -hardness can be valuable.

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This paper presents the dynamic modelling of a hybrid cascade chiller for solar cooling in industrial applications driven by Fresnel solar thermal collectors. The chiller comprises an adsorption module, which is directly connected to the bottoming vapor compression chiller. This cascade configuration allows enhancing the overall electric COP, since the adsorption module is operated to dissipate the heat rejected by the vapor compression chiller, thus reducing the condensation temperature quite below the ambient temperature. The model was implemented in Dymola/Modelica, allowing describing heat and mass transfer phenomena inside each component. The complete model was then validated against experimental data obtained on a cascade chiller prototype at the CNR ITAE lab. Finally, a reference daily simulation was performed to evaluate the ability of the developed chiller in providing cooling energy to a typical industrial application.

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