On geometrically equivalent S-acts

In this paper, considering the geometric equivalence for algebras of a variety $_{S}A$ of S-acts over a monoid S, we obtain representation theorems describing all types of the equivalence classes of geometrically equivalent S-acts of varieties $_{S}A$ over groups S.Comment: 13 pages, some statements were corrected and improve

Phase Separation of Saturated and Mono-unsaturated Lipids as determined from a Microscopic Model

A molecular model is proposed of a bilayer consisting of fully saturated DPPC and mono unsaturated DOPC. The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.Comment: 29 pages, 4 figures, 1 table. revised versio