Surface thermodynamic homeostasis of salivary conditioning films through polar–apolar layering

Salivary conditioning films (SCFs) form on all surfaces exposed to the oral cavity and control diverse oral surface phenomena. Oral chemotherapeutics and dietary components present perturbations to SCFs. Here we determine the surface energetics of SCFs through contact angle measurements with various liquids on SCFs following perturbations with a variety of chemotherapeutics as well as after renewed SCF formation. Sixteen-hour SCFs on polished enamel surfaces were treated with a variety of chemotherapeutics, including toothpastes and mouthrinses. After treatment with chemotherapeutics, a SCF was applied again for 3 h. Contact angles with four different liquids on untreated and treated SCF-coated enamel surfaces were measured and surface free energies were calculated. Perturbations either caused the SCF to become more polar or more apolar, but in all cases, renewed SCF formation compensated these changes. Thus, a polar SCF attracts different salivary proteins or adsorbs proteins in a different conformation to create a more apolar SCF surface after renewed SCF formation and vice versa for apolar SCFs. This polar–apolar layering in SCF formation presents a powerful mechanism in the oral cavity to maintain surface thermodynamic homeostasis—defining oral surface properties within a narrow, biological range and influencing chemotherapeutic strategies. Surface chemical changes brought about by dietary or chemotherapeutic perturbations to SCFs make it more polar or apolar, but new SCFs are rapidly formed compensating for changes in surface energetics

Incomplete Stable Structures In Symmetric Convex Games

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We show that with at most five players the full cooperation structure results according to a subgame perfect Nash equilibrium.Moreover, if the game is strictly convex then every subgame perfect Nash equilibrium results in a structure that is payoff equivalent to the full cooperation structure. Subsequently, we analyze a game with six players that is symmetric and strictly convex.We show that there exists a subgame Nash equilibrium that results in an incomplete structure in which two players are worse off than in the full cooperation structure, whereas four players are better off.Independent of the initial order any pair of players can end up being exploited.

Fuzzy Cores and Fuzzy Balancedness

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it satisfies all (fuzzy) balanced inequalities. We also consider deposit games to illustrate the use of the main result.