Dissolution nature of the lithium hydroxide by water molecules

The structures, stabilities, thermodynamic quantities, dissociation energies, infrared spectra, and electronic properties of LiOH hydrated by up to seven water molecules are investigated by using the density-functional theory and the M?ller-Plesset second-order perturbation theory (MP2). Further accurate analysis based on the coupled-cluster theory with singles, doubles, and perturbative triples excitations agrees with the MP2 results. The Li-OH stretch mode significantly shifts with the increase of water molecules, and it eventually disappears upon dissociation. It is revealed that seven water molecules are needed for the stable dissociation of LiOH (as a completely dissociated conformation), in contrast to the cases of RbOH and CsOH which require four and three water molecules, respectively.     

Differentiable circle maps with a flat interval

We study weakly order preserving circle maps with a flat interval, which are differentiable even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from degenerate geometry to bounded geometry, depending on the degree of the singularities at the boundary of the flat interval.Partially supported by KBN grant Iteracje i Fraktale #210909101.