Nash equilibrium based fairness

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ??Nash equilibrium based fair.?? We further define a ??Nash proportionately fair?? Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations.     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

Kinetics of the dehydrochlorination of poly(vinyl chloride) in the presence of NaOH and various diols as solvents

The dehydrochlorination of PVC in the presence of NaOH was investigated in different diols. Diethylene glycol (DEG), triethylene glycol (TEG), and propylene glycol (PG) were found to be effective in accelerating the dechlorination of PVC. The dehydrochlorination was promoted in the order TEG > DEG > PG, which was in agreement with the compatibility between PET and the diol. Compatibility resulted in an improved penetration of the PVC particle by the solvent, leading to the acceleration of the dehydrochlorination. The dehydrochlorination of PVC in NaOH/diol followed first-order kinetics, confirming the progress of the reaction under chemical reaction control. The apparent activation energies were 82 kJ mol⁻¹, 109 kJ mol⁻¹, and 151 kJ mol⁻¹ for TEG, DEG, and PG, respectively. The lower the activation energy became the faster the dehydrochlorination of PVC proceeded.     

Lanthanide-assisted NMR evaluation of a dynamic ensemble of oligosaccharide conformations

A novel methodology is presented for evaluating a dynamic ensemble of oligosaccharide conformations by lanthanide-assisted NMR spectroscopy combined with molecular dynamics (MD) simulations. The results obtained using the GM3 trisaccharide demonstrated that pseudocontact shift measurements offer a valuable experimental tool for the validation of MD simulations of highly flexible biomolecules.     

Conformation of drawn poly(trimethylene terephthalate) studied by solid-state 13C NMR

The change in the conformation of the flexible O-CH2-CH2-CH2-O segment of poly(trimethylene terephthalate) (PTT) monofilament caused by drawing was investigated by means of the gamma-gauche effect on the 13C solid-state NMR chemical shift of the internal methylene carbon, combined with the NMR relaxations. The conformation around the O-CH2 and CH2-O bonds for as-spun fiber was trans/trans. On drawing, followed by heat treatment, the conformation changed to gauche/gauche. The ratio of gauche/gauche to trans/trans for the drawn PTT fiber was determined quantitatively.     

Influence of amino acid side chain packing on Fe-methionine coordination in thermostable cytochrome C

Paramagnetic NMR and optical studies of the oxidized forms of mesophile Pseudomonas aeruginosa cytochrome c(551) and its quintuple mutant (F7A/V13M/F34Y/E43Y/V78I), and thermophile Hydrogenobacter thermophilus cytochrome c(552) demonstrated that the amino acid side chain packings in the protein interior influence the coordination bond between the heme iron and the axial methionine in the proteins. The strength of heme axial coordinations was found to correlate with the overall protein thermostability.     

Kinetic and equilibrium studies of urea adsorption onto activated carbon: Adsorption mechanism

We found that activated carbon effectively removed urea from solution and that urea adsorption onto activated carbon followed a pseudo-second-order kinetic model. We classified the urea adsorption on activated carbon as physical adsorption and found that it was best described by the Halsey adsorption isotherm, suggesting that the multilayer adsorption of urea molecules on the adsorption sites of activated carbon best characterized the adsorption system. The mechanism of adsorption of urea by activated carbon involved two steps. First, an amino (–NH₂) group of urea interacted with a carbonyl (–C?O) group and a hydroxyl (?OH) group on the surface of activated carbon via dipole–dipole interactions. Next, the –C?O group of the urea molecule adsorbed to the activated carbon interacted with another –NH₂ group from a second urea molecule, leading to multilayer adsorption.