Correlated equilibrium and concave games

This paper shows that if a game satisfies the sufficient condition for the existence and uniqueness of a pure-strategy Nash equilibrium provided by Rosen (Econometrica 33:520, 1965), then the game has a unique correlated equilibrium, which places probability one on the unique pure-strategy Nash equilibrium. In addition, it shows that a weaker condition suffices for the uniqueness of a correlated equilibrium. The condition generalizes the sufficient condition for the uniqueness of a correlated equilibrium provided by Neyman (Int J Game Theory 26:223, 1997) for a potential game with a strictly concave potential function. I thank the editor, an associate editor, and an anonymous referee for detailed comments and suggestions, which have substantially improved this paper. Special thanks are due to the referee for pointing out Lemmas 4 and 5. I acknowledge financial support by The Japan Economic Research Foundation and by MEXT, Grant-in-Aid for Scientific Research. All remaining errors are mine.     

Spontaneous formation of a chiral supramolecular superhelix in the crystalline state using a single-stranded tetranuclear metallohelicate

An unprecedented one-handed coiled-coil structure was formed in the crystal of a Zn(3)La tetranuclear metallohelicate, in which the handedness of both the helical component and the helical array was well controlled by the chiral auxiliary of the flexible acyclic ligand.     

Electrochemical activity of nanocrystalline Fe3O4 in aprotic Li and Na salt electrolytes

Fe₃O₄ powders, whose average particle sizes were 400 nm, 100 nm, and 10 nm in diameter, were prepared in order to investigate the effect of particle size on their electrochemical activity. X-ray diffraction and electron microscopy measurements confirmed that all the prepared samples were identified as inverse-spinel type Fe₃O₄, whose crystallite/particle sizes were between 400 nm and 10 nm. We found that the electrochemical activity of Fe₃O₄ in a lithium salt electrolyte was enhanced with a decrease in the particle size from 400 nm to 10 nm. The 10 nm nanocrystalline Fe₃O₄ powder demonstrated the high discharge capacities of about 130 and 160 mAh g⁻¹ with a satisfactory capacity retention as the active cathode material of Li and Na batteries, respectively.     

Facile unidirectional alignment of mesochannels in a mesoporous silica film on a freshly cleaved mica surface

The alignment of mesochannels in a mesoporous silica film on a freshly cleaved mica surface, prepared by an evaporation-induced self-assembly process, is unexpectedly found to be unidirectional with the narrowest directional distribution.     

Manipulation of an intramolecular NH...O hydrogen bond by photoswitching between stable E/Z isomers of the cinnamate framework

Novel carboxylic acid derivatives were synthesized, which allowed switching of the intramolecular distance between amide group and carboxylic oxygen atoms using E to Z photoisomerization of the cinnamate framework. An intramolecular NH...O hydrogen bond was formed in the Z carboxylate compound not only in solution but also in the solid state. The pK(a) value of the carboxylic acid was lowered as a consequence of the E/Z photoisomerization.