Resource pricing games on graphs: existence of Nash equilibria

In this letter, we consider a non-cooperative resource pricing game on a graph where sellers (i.e., players) set the prices for their own resources to maximize the payoffs and buyers migrate to seek the least expensive resources. We present a model for the resource pricing game and prove the existence of Nash equilibria on regular and hierarchical graphs. The results obtained are applicable to the study of market economies, social networks and computer networks where individuals trade resources in a spatially extended environment.     

Effects of polydepsipeptide side‐chain groups on the temperature sensitivity of triblock copolymers composed of polydepsipeptides and poly(ethylene glycol)

To develop new types of biodegradable polymers possessing predictable responses to changes in temperature, ABA‐type and BAB‐type triblock copolymers composed of various polydepsipeptides (PDP) and poly(ethylene glycol) (PEG) (PDP‐PEG‐PDP and PEG‐PDP‐PEG) were synthesized. The specific focus of this study was on the effect of the different side‐chain groups of various amino acids on the temperature‐responsive behavior of the triblock copolymers. An ABA‐type triblock copolymer containing the less hydrophobic glycine (PGG‐PEG‐PGG) did not exhibit any temperature‐responsive behavior; however, ABA‐type triblock copolymers containing the hydrophobic α‐amino acids, L ‐leucine and L ‐phenylalanine (PGL‐PEG‐PGL or PGF‐PEG‐PGF), did exhibit temperature‐responsive behavior. The cloud point of PGF‐PEG‐PGF was 10 °C lower than that of PGL‐PEG‐PGL. It can be possible to control temperature‐sensitivity by changing not only PDP segment length but also kind of α‐amino acid in PDP segment. Moreover, BAB‐type triblock copolymer containing L ‐leucine (PEG‐PGL‐PEG) showed temperature‐responsive sol‐gel transition. Because polydepsipeptides are biodegradable polymers, the information obtained in this study is useful to design biodegradable injectable polymers having controllable temperature‐sensitivity for biomedical use.© 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3892–3903, 2009     

Infrared transmission of (R2O OR R’O)–(TiO2, Nb2O5 OR Ta2O5)-Al2O3 glasses

The new families of aluminate glasses obtained by the present authors from their melts in the systems K₂O–Ta₂O₅–Al₂O₃, Na₂O–K₂O–Ta₂O₅–Al₂O₃, K₂O –Cs₂O– Ta₂O₅–Al₂O₃, K₂O–Nb₂O₅–Al₂O₃, Na₂Oz.sbnd;K₂O–TiO₂–Al₂O₃, BaO–TiO₂–Al₂O₃, BaO–ZrO₂–TiO₂–Al₂O₃ and Na₂O–K₂O–BaO–ZrO₂–Ta₂O₅–TiO₂ –Al₂O₃ showed high transmissions of visible and infrared (IR) radiation ranging from 0.4 to about 6 μm, as well as high refractive indices up to 2.0. Their physical and chemical properties such as glass-forming ability, softening temperature, hardness and hygroscopicity were comparable to conventional silicate glasses. These properties are useful for IR applications. The cause of the high IR transmission of the aluminate glasses was interpreted in terms of the masses of the constituent cations and the single bond strengths of the cations with oxygen ions.     

Quantitative Approximation to the Ordered Dirichlet Distribution under Varying Basic Probability Spaces

An approximate expansion of a sequence of ordered Dirichlet densities is given under the set-up with varying dimensions of the relating basic probability spaces. The problem is handled as the approximation to the joint distribution of an increasing number of selected order statistics based on the random sample drawn from the uniform distribution U(0, 1). Some inverse factorial series to the expansion of logarithmic function enable us to give quantitative error evaluations to our problem. With the help of them the relating modified K-L information number, which is defined on an approximate main domain and different from the usual ones, is accurately evaluated. Further, the proof of the approximate joint normality of the selected order statistics is more systematically presented than those given in existing works. Concerning the approximate normality the modified affinity and the half variation distance are also evaluated.     

The Influence of Defects on the Propagation Light within Polymeric Optical Waveguides Studied by Polarized Near-Field Scanning Optical Microscopy

We have developed a polarization-preserving near-field scanning optical microscopy (NSOM) optical fiber probe and with it observed the influence of defects and weak stresses on a propagation light within polymeric optical waveguides. To characterize the influence, we intentionally printed an indentation in the vicinity of the waveguide and then evaluated the resulting influence using polarized guide-collection-mode NSOM images taken around the indentation. When transverse magnetic polarized light enters a waveguide, the light intensity becomes greater on the near side of the indentation than on the far side, as measured by a linearly polarized component perpendicular to the direction of light propagation. The most probable cause of this phenomenon is microdefects generated by the printing of the indentation. The polarized NSOM technique is useful in searching for small defects or stresses within integrated photonic devices.     

Pervaporation properties of crosslinked poly(dimethylsiloxane) membranes for the removal of hydrocarbons from water

The pervaporation (PV) performance of crosslinked poly(dimethylsiloxane) dimethylmethacrylate (PDMSDMMA) membranes for an aqueous solution of various hydrocarbons was studied using sorption–diffusion theory. Three chlorinated hydrocarbons (chloroform, trichloroethylene, and tetrachloromethane) and three aromatic hydrocarbons (benzene, chlorobenzene, and toluene) were used as the permeants. When aqueous solutions of 0.05 wt % hydrocarbon were permeated through the crosslinked PDMSDMMA membranes, they showed high hydrocarbon/water selectivity and permeability during PV. The hydrocarbon/water selectivity of the crosslinked PDMSDMMA membranes was significantly dependent upon the permeants; in particular, chloroform removed the hydrocarbons most efficiently in this study. The results of the temperature dependence of the PV performance and hydrocarbon absorption into the membrane revealed that the difference in hydrocarbon/water selectivity for various aqueous solutions of hydrocarbons during PV depended significantly on the molar volume and diameter of the hydrocarbons. The permeation and removal mechanism of hydrocarbons from water through crosslinked PDMSDMMA membranes can be explained by a qualitative model based on the diffusion jump model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2079–2090, 2006     

Effect of crosslink on the characteristic length of glass transition of network polymers

The characteristic length of the glass transition temperature was evaluated for crosslinked bulk polystyrenes and poly(methyl methacrylate)s by differential scanning calorimetry. The characteristic length, which corresponds to a length scale of the cooperative rearrangement due to polymer segmental relaxation, was revealed to decrease with increase in the degree of crosslink. The relative values of configurational entropy for crosslinked polymers were evaluated based on a simple polymer network model on a cubic lattice. As a result, the configurational entropy of the smallest cooperatively rearranging region was revealed to decrease with increase in the degree of crosslink, which is responsible for the above behavior of the characteristic length. The effects of crosslink on the characteristic length and the glass transition temperature were found to be stronger for crosslinked poly(methyl methacrylate)s than for crosslinked polystyrenes, which reflects the difference in the structure of crosslink segment. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1958–1966, 2006     

Antithetic function of alcohol in living cationic polymerization: From terminator/inhibitor to useful initiator

We employed alcohols as initiators for living cationic polymerization of vinyl ethers and p‐methoxystyrene, coupled with tolerant Lewis acid, borontrifluoride etherate (BF₃OEt₂), although they were known to be poisonous reagent to bring about chain‐breaking such as chain transfer/termination rather than such beneficial one for propagation and polymerization‐control. As well known, without assistance of additive, ill‐defined polymers with broad molecular weight distributions (MWDs) were produced. Even addition of conventional oxygen‐based bases, for example, ethyl acetate (AcOEt), 1,4‐dioxane (DO), tetrahydrofran (THF), and diethyl ether (Et₂O) was less efficient in this system to control molecular weights and MWDs (M_w/M_n > 2.0). In contrast, by addition of dimethyl sulfide (Me₂S), MWDs of the resultant polymers became much narrower (M_w/M_n < 1.23) and the number‐average molecular weight (M_n) increased in direct proportion to monomer conversion in agreement with the calculated values assuming that one alcohol molecule generates one polymer chain. Studying changed feed‐ratio of alcohol to monomer and structural analyses with NMR and MALDI‐TOF‐MS indicated that quantitative initiation from alcohol giving alkoxide counteranion. This system opens a new way to use a variety of alcohols as initiators, which would allow us to design variety of structures and functions of counteranion. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4194–4201, 2009