The existence of equilibria in certain games,separation for families of convex functions and a theorem of Borsuk-Ulam type

The existence of a Nash equilibrium in the undiscounted repeated two-person game of incomplete information on one side is established. The proof depends on a new topological result resembling in some respect the Borsuk-Ulam theorem.     

Average heat transfer rates measured and numerically analyzed for combined convection of air in an inclined cylindrical enclosure due to both magnetic and gravitational fields

The average heat transfer rates were measured for natural convection of air in a shallow cylindrical enclosure heated from below and cooled from above in a bore space of an inclined super-conducting magnet. Depending on the location of the enclosure in the bore space, the angle of inclination and the strength of magnetic field, the net acceleration force could be arbitrarily varied and in this report, two locations where mostly axial magnetizing force prevails were selected. The average heat transfer rates varied with the angle of inclination due to the change in the total net acceleration of gravitational and magnetizing forces. Numerical computations were also carried out for the similar system under the combined magnetizing and gravitational forces and the computed average Nusselt numbers agreed mostly with the measured results. Detailed flow modes were graphically presented for the computed cases.     

Novel synthesis of macrocycles with 1,1′-binaphthalene-2,2′-diol using intramolecular oxidative coupling

A new series of BINOL-based macrocycles with two phenolic protons have been synthesized via oxidative coupling reaction using CuCl(OH)-TMEDA.     

Laser spectroscopic investigation of salicylic acids hydrogen bonded with water in supersonic jets: Microsolvation effects for excited state proton dislocation

Geometric structures and excited-state proton dislocation of size-selected salicylic acid clusters (salicylic acid and 5-methoxysalicylic acid) with water were studied by using laser spectroscopic techniques. Fluorescence excitation, dispersed fluorescence, and infrared (IR) spectra of those clusters in supersonic jets were examined for both the electronic ground (S0) and first excited (S1) states. The geometric structures of the clusters were determined on the basis of the IR spectra of the OH stretch region with the help of quantum chemical calculations. The hydroxyl group of the water moiety in the clusters forms a ring involving the carboxylic group of the salicylic acid moiety. The IR spectra in S0 show that the intramolecular hydrogen bond in the salicylic acid moiety is still held upon cluster formation, but the phenolic OH stretch band intensity is remarkably weaken in the clusters. The IR spectra in the S1 state and dispersed fluorescence spectra indicated that the intramolecular excited state proton dislocation is hardly affected by the microsolvation with water, in contrast with the strong suppression of the dislocation in the self-solvation.     

An alternate synthesis of 6-substituted-5-deazapteridines

A procedure for synthesis of 2,4-diamino-6-substituted-5-deazapteridines (pyrido[2,3-d]pyrimidines) is described. Condensation of 1-piperidino-1-propene with ethoxymethylenemalononitrile afforded an enamino malononitrile adduct, which when treated with ammonia yielded 2-amino-3-cyano-5-methylpyridine. Cyclization to 2,4-diamino-6-methyl-5-deazapteridine could be effected with guanidine. Similar condensation of piperidinopropene with ethyl methoxymethylenecyanoacetate followed by cyclization with hydroxylamine gave 2-amino-3-carbethoxy-6-methylpyridine 1-oxide. Reduction with phosphorus trichloride afforded the pyridine base, however, attempts to cyclize the amino ester to 2-amino-4-hydroxy-6-methyl-5-deazapteridine were unusccessful.     

Three novel diepoxy tetrahydrochromones from agarwood artificially produced by intentional wounding

Three novel diepoxy tetrahydrochromones, oxidoagarochromones A (1), B (2), and C (3), were isolated from agarwood artificially produced by intentional wounding of Aquilaria crassna. Inductive production of these compounds was also confirmed at the early stage of wounding in A. sinensis and A. crassna. These diepoxy tetrahydrochromones would play an important role in understanding the biosynthesis of chromone derivatives in agarwood.     

Solvent free synthesis of polyaniline-clay nanocomposites from mechanochemically intercalated anilinium fluoride

Nanocomposites consisting of conducting polyaniline and clay minerals were successfully synthesized from mechanochemically intercalated anilinium fluoride; the nanocomposites prepared by the mechanochemical intercalation method contained much more polyaniline in the clay layers than those prepared by a conventional solution method.     

Effects of added metal ions on the interaction between polyvinylpyrrolidone and azo dyes carrying hydroxyl groups

The extent of binding of chrome violet, which is a monoazo dye and involves two hydroxyl groups in o and o′ positions to azo group, by polyvinylpyrrolidone is markedly enhanced in the presence of Co²⁺ ion. The amount of binding in the presence of 1 × 10^?4 mol/L of Co²⁺ ion increases by a factor of about 10 compared to that in the absence of the metal ion. Ni²⁺ and Zn²⁺ ions do not perceptively influence the binding affinity of the dye. Cu²⁺ ion, in contrast, suppresses the binding. To investigate further the action of added metal ions, a cobalt–complex dye was prepared and its binding property for the polymer was compared to that of chrome violet in the presence of metal ions. Some possible mechanisms for the enhancement of chrome violet binding by the addition of Co²⁺ ion are described.