Values of games without side payments

A value forn-person games without side payments is given which coincides with theShapley value for games with side payments, and with theNash value for two-person games.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.     

Optimal threat strategies of bimatrix games

A bi-matrix threat game is defined as a triple (A,B,S) whereA andB arem×n payoff matrices, andS is a closed convex subset of the plane, with (a _ij,B _ij) εS for eachi,j. Given (threat) mixed strategiesx andy,Nash's model suggests that the eventual outcome will be that point (u, v) εS which maximizes the product (u ?xAy ^t) (v ?xBy ^t) subject tou ≥xAy ^t,v ≥xBy ^t. Optimality of the threat strategies is then defined in the obvious way. A constructive proof of existence of optimal threat strategies is given; in particular, it is shown that they are optimal strategies for the matrix gameA-kB, wherek is to be determined. In this paper,k is approximated by aNewton-Raphson technique. Two examples are solved in detail.     

Infrared spectra and molecular conformation of butyronitrile and methyl thioacetonitrile

The infrared absorption spectra of two related compounds, butyronitrile (CH₃CH₂-CH₂CN) and methylthioacetonitrile (CH₃SCH₂CN) have been examined in the liquid and solid phases. Vapour phase spectra of butyronitrile have also been recorded. Evidence is given for the existence of two rotational isomers trans and gauche, for both compounds. In both cases the energy difference between the two rotamers appears to be small with the gauche form identified as the low energy conformer for butyronitrile. For methylthioacetonitrile it was not possible to determine the more stable rotational isomer.     

Wall mediated transport in confined spaces: exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.     

Synthesis of highly sulfonated polybenzimidazoles by direct copolymerization and grafting

A series of highly sulfonated, ether‐containing polybenzimidazoles (SOPBI) with controlled sulfonation degrees were synthesized from various stoichiometric ratio mixtures of sodium 6,6'‐oxybis(3‐carboxybenzenesulfonate) (SODBA), 4,4'‐oxydibenzoic acid (ODBA), and 3,3'‐diaminobenzidine (DAB) by solution copolycondensation in poly(phosphoric acid). The resulting sulfonated polymers were further sulfonated by grafting of pendant sulfonic acid chains via a reaction of 1,3‐propane sultone with lithiated‐N of the imidazole rings in the polymer backbone, yielding materials with high, absolute IEC values (3.42–4.15 meq g^?1). Due to self‐neutralization, the solid state polymers possessed “free” acid content of 1.40 to 2.15 meq g^?1, were soluble in organic solvents yet insoluble in aqueous solution, while displaying proton conductivites (11–47 mS cm^?1) at elevated temperatures (80 °C, 95% RH). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3654–3666     

A C2-symmetric analogue of dppf: synthesis and structures of the indenyl-diphosphine complex 1,3-(Ph2PSe)2(C9H6) and the racemic and meso isomers of the heterobimetallic complex Mo(CO)4(1-PPh2-η-C9H6)2Fe

The preparation, isolation and characterisation of 1,3-bis(diphenylphosphino)indene (1) from indene and chlorodiphenylphosphine is described. The reaction of 1 with selenium gives the diselenide adduct 1,3-bis(diphenylselenophosphino)indene (2) which was characterised crystallographically. Deprotonation of 1 and treatment with ferrous chloride gives the unstable tetraphosphine complex bis(1,3-bis(diphenylphosphino)indenyl)iron(II) (3). Complex 3 decomposes to the diphosphine complex bis(1-diphenylphosphinoindenyl)iron(II) (4) via replacement of one diphenylphosphine substituent per indenyl ligand by a hydrogen atom. Complex 4 was also prepared by treatment of two equivalents of 1-diphenylphosphinoindenide with ferrous chloride. The heterobimetallic complex tetracarbonyl(bis(1-diphenylphosphinoindenyl)iron(II))molybdenum(0) (5) was also prepared and crystal structures of both the meso (5a) and C₂-symmetric racemic (5b) isomers are reported.     

Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains

We investigate nodal sets of magnetic Schr?dinger operators with zero magnetic field, acting on a non simply connected domain in ℝ². For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2. Received: 23 July 1998 / Accepted: 17 November 1998