AnN-person noncooperative discounted vector-valued dynamic game with a metric space

AnN-person noncooperative discounted vector-valued game with a metric space is investigated. We define aD-convex equilibrium point and prove that aD-convex equilibrium point exists in this game system. A modified version of the original game system is formulated so that an equilibrium point of the modified version is aD-convex equilibrium point of the original game system. Under appropriate conditions, the converse holds in the sense that aD-convex equilibrium point is also an equilibrium point of the modified game system.     

Synthesis and properties of π‐conjugated dithiafulvene oligomers by addition of a monofunctionalized compound

Dithiafulvene oligomers ( 3 ) were prepared by cycloaddition polymerization of aldothioketenes with their alkynethiol tautomers derived from 1,4‐diethynylbenzene ( 2 ) with the addition of 1‐ethynyl‐4‐methylbenzene ( 1 ) as a monofunctionalized compound. Different feed ratios of 2 / 1 were used to control the molecular weights of 3 . The structures of 3 were confirmed by IR and ¹H NMR spectroscopies in comparison with those of 2‐(4‐tolylidene)‐4‐tolyl‐1,3‐dithiol ( 4 ) as a model compound, which was obtained by the treatment of lithium 2‐tolylethynethiolate with water in Et₂O. The number‐average degree of polymerization (DP) and the number‐average molecular weight were measured by gel permeation chromatographic and ¹H NMR analysis. DP increased with an increasing feed ratio of 2 / 1 . The ultraviolet–visible spectra of 3 in diluted acetonitrile showed that the absorption maxima of 3 increased with an increasing DP of 3 . These redshifts are ascribed to an effective expansion of the π‐conjugation system in 3 . The oligomers exhibited a maximum conjugation length of seven repeating units. The redox properties of 3 were examined by cyclic voltammetry. The oxidation half‐peak potentials (E_p/2) of 3 were slightly cathodically shifted with increasing DP. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 708–715, 2003     

Thickening of crystals during rapid heating. II. Crosslinked polyethylene and methoxymethylated nylon 6

The effect of modification of polymer chains on crystal thickening during heating was investigated with an apparatus devised for rapid measurement of small-angle x-ray diffraction. Thickening of crystals still occurred even at a heating rate of 18°C/min in polyethylene irradiated with gamma ray doses of 30–300 Mrad, and the melting point was depressed. These results showed that the melting point depression due to irradiation is not due to a restriction on crystal thickening but rather to crystal lattice distortion. On the other hand, although methoxymethylation of nylon 6 completely inhibits crystal thickening, the melting point increases or decreases depending on the temperature of annealing preceding methoxymethylation. From these results we are led to conclude that irradiation and methoxymethylation are not effective means of obtaining the relation between melting point and crystal thickness.     

Solvent-induced morphological change of microporous hollow fiber membranes

Microporous polyethylene hollow fiber membranes (EHF-1 and EHF-2) were subjected to solvent treatment, and the effects of this treatment on membrane morphology and permeating properties were studied. Membranes treated with various organic solvents exhibited enhanced permeability, enlarged pore size, and increased shrinkage in the longitudinal direction. These phenomena were found to depend on the surface tension of the solvent: the higher the surface tension of the solvent, the larger the change in morphology and permeation of the membrane. A mechanism to account for the effects of solvent treatment on the morphology of the membrane is proposed taking into consideration the influence of the type of solvent used for treatment. The enhanced morphological and permeation changes are ascribed to the formation of liquid bridges between two microfibrils of the membrane during drying followed by the deformation and adhesion of the adjacent microfibrils based on the surface tension of the solvent.     

Carbon chemical shifts of 1,1-diphenylethylene and α-methylstyrene dimer dianions

The natural abundance C-13 NMR spectra of 1,1-diphenylethylene and α-methylstyrene dimer dianions have been obtained using the proton noise decoupling technique. The extra negative charge distributions in the carbanions have been discussed and compared with those obtained from the proton chemical shifts. The chemical shifts of the two ortho carbons in a phenyl ring are equivalent to each other for the former carbanion but not for the latter.     

Non-cooperative n-person game with a stopped set

A continuous time non-cooperative n-person Markov game with a stopped set is studied in this paper. We prove that, in the game process with or without discount factor, there exists an optimal stationary point of strategies, called the equilibrium point, and each player has his equilibrium stationary strategy, such that the total expected discounted or non-discounted gain are maximums.     

Soft x-ray spectroscopy of Ba24Ge100: electronic phase transition and Ba-atom rattling

The electronic states of Ba24Ge100 are studied by soft x-ray photoelectron spectroscopy (XPS) at a high-energy photon factory. A large reduction in the density of states (DOS) at the Fermi level is clearly shown before and after the electronic phase transition at 200 K. The changes in the spectrum widths and the fine structures of the core-level Ba 4d spectra give a very reasonable indication of the Ba-atom rattlings in the clathrate polyhedra. On-resonance experiments using the excitation from Ba 3d to 4f levels display that the wave functions of Ba 5d and 6s orbitals give only a small contribution to make a Fermi surface through the hybridization with the Ge20 cluster orbitals. Importantly, reliable values of the DOS at the Fermi level NEF are successfully deduced, using two data sets of DOS obtained from high-resolution XPS and the total magnetic susceptibilities by a superconducting quantum interference device, to be 0.149 and 0.0427 states eV(-1) (Ge atom)(-1) for a high-temperature and for a low-temperature phase.     

Biomethylation and biotransformation of arsenic in a freshwater food chain: Green alga (chlorella vulgaris)→shrimp (neocaridina denticulata)→killifish (oryzias iatipes)

Tolerance, bioaccumulation, biotransformation and excretion of arsenic compounds by the fresh–water shrimp (Neocaridina denticulata) and the killifish (Oryzias latipes) (collected from the natural environment) were investigated. Tolerances (LC₅₀) of the shrimp against disodium arsenate [abbreviated as As(V)], methylarsonic acid (MAA), dimethylarsinic acid (DMAA), and arsenobetaine (AB) were 1.5, 10, 40, and 150μg As ml^?1, respectively. N. denticulata accumulated arsenic from an aqueous phase containing 1 μg As ml^?1 of As(V), 10 μg As ml^?1 of MAA, 30 μg As ml^?1 of DMAA or 150 μg As ml^?1 of AB, and biotransformed and excreted part of these species. Both methylation and demethylation of the arsenicals were observed in vivo. When living N. denticulata accumulating arsenic was transferred into an arsenic–free medium, a part of the accumulated arsenic was excreted. The concentration of methylated arsenicals relative to total arsenic was higher in the excrement than in the organism. Total arsenic accumulation in each species via food in the food chain Green algae (Chlorella vulgaris) → shrimp (N. denticulata) → killifish (O. latipes) decreased by one order of magnitude or more, and the concentration of methylated arsenic relative to total arsenic accumulated increased successively with elevation in the trophic level. Only trace amounts of monomethylarsenic species were detected in the shrimp and fish tested. Dimethylarsenic species in alga and shrimp, and trimethylarsenic species in killifish, were the predominant methylated arsenic species, respectively.     

Green polymers from Geobacillus thermodenitrificans DSM465--candidates for molecularly imprinted materials

Novel molecular recognition materials were prepared from water soluble proteins from thermophile G. thermodenitrificans DSM465 by an alternative molecular imprinting method. Water soluble proteins from G. thermodenitrificans DSM465 were converted into the molecularly imprinted materials by adopting 9-EA as a print molecule. The molecularly imprinted protein membranes recognized As in preference to Gs. The adsorption isotherms led to the conclusion that molecular recognition sites toward As were constructed by the presence of 9-EA during the membrane preparation process. The affinity constant between As and the molecular recognition site thus constructed was determined to be 1.75 x 10(5) mol(-1) dm(3). The results obtained in the present study suggest that water soluble proteins from G. thermodenitrificans DSM465 is one of environmentally-friendly 'green' polymers to be converted into molecular recognition materials by applying an alternative molecular imprinting method.     

Lorentz Ricci Solitons on 3-dimensional Lie groups

The three-dimensional Heisenberg group H ₃ has three left-invariant Lorentzian metrics g ₁, g ₂, and g ₃ as in Rahmani (J. Geom. Phys. 9(3), 295–302 (1992)). They are not isometric to each other. In this paper, we characterize the left-invariant Lorentzian metric g ₁ as a Lorentz Ricci Soliton. This Ricci Soliton g ₁ is a shrinking non-gradient Ricci Soliton. We also prove that the group E(2) of rigid motions of Euclidean 2-space and the group E(1, 1) of rigid motions of Minkowski 2-space have Lorentz Ricci Solitons.