Equilibrium In Series Research Articles

How hard is it to find extreme Nash equilibria in network congestion games?

We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series–parallel graphs a worst Nash equilibrium can be found by a Greedy approach while finding a best equilibrium is NP-hard. For a fixed number of users we give a pseudo-polynomial algorithm to find the best equilibrium in series–parallel networks. For general network topologies also finding a worst equilibrium is NP-hard.

MODELING ASYMMETRIES AND MOVING EQUILIBRIA IN UNEMPLOYMENT RATES

The paper discusses a simple univariate nonlinear parametric time-series model for unemployment rates, focusing on the asymmetry observed in many OECD unemployment series. The model is based on a standard logistic smooth transition autoregressive model for the first difference of unemployment, but it also includes a lagged level term. This model allows for asymmetric behavior by permitting “local” nonstationarity in a globally stable model. Linearity tests are performed for a number of quarterly, seasonally unadjusted, unemployment series from OECD countries, and linearity is rejected for a number of them. For a number of series, nonlinearity found by testing can be modeled satisfactorily by use of our smooth transition autoregressive model. The properties of the estimated models, including persistence of the shocks according to them, are illustrated in various ways and discussed. Possible existence of moving equilibria in series not showing asymmetry is investigated and modeled with another smooth transition autoregressive model.

NMR study of proton transfer equilibrium in Schiff bases derived from 2-hydroxy-1-naphthaldehyde and 1-hydroxy-2-acetonaphthone. Deuterium isotope effects on13C and15N chemical shifts

The proton transfer equilibrium in series of Schiff bases derived from 2-hydroxy-1-naphthaldehyde and 1-hydroxy-2-acetonaphthone were measured by means of 1H, 13C and 15N NMR spectra and deuterium isotope effects on 13C and 15N chemical shifts at variable temperature and in different solvents. The latter made it possible to investigate a broad range of equilibrium positions. All compounds exist mainly as the NH tautomer over the full range of temperatures in CDCl3 solution. The position of the equilibrium was estimated using 1J(15N,1H) and 3J(15NH,1H) coupling constants. The correlation between deuterium isotope effects nΔ13C-2(XD) or nΔ15N(XD), where X = O or N, and the mole fraction of the NH form show the characteristic, non-monotonic function as for other intramolecular hydrogen bonded systems. The position of the minimum depends on substituents and the maximal negative values of nΔ13C-2(XD) varies with substituents and solvents. Copyright © 2001 John Wiley & Sons, Ltd.

New Regeneration Process of Heavy-Metal-Loaded Chelating Resins

An alternative to the classical acid-base regeneration of chelating resins loaded with heavy metals is investigated. The new process consists in recovering the heavy metals with recyclable soluble complexing agents. The semiclosed reactor includes a fixed bed and a stirred tank. A three-parameter model, which implies a double equilibrium in series, is introduced. When less than 10 % of the metal is still fixed on the resin at the end of the desorption, a simplified form of the model with two parameters, which describes a quick equilibrium followed by a first-order kinetics reaction, is proposed. Both forms of the model can simulate results for different experimental conditions (polymer and metal types, polymer initial concentration). It was observed for both cases that the first equilibrium constant depends on the polymer type and that the rate constant of desorption depends on the metal type. The scale-up of desorption is then conducted at mini-pilot scale. Scale-up criteria tend to minimize the desorption time and the soluble polymer quantity used.

New Regeneration Process of Heavy-Metal-Loaded Chelating Resins

An alternative to the classical acid-base regeneration of chelating resins loaded with heavy metals is investigated. The new process consists in recovering the heavy metals with recyclable soluble complexing agents. The semiclosed reactor includes a fixed bed and a stirred tank. A three-parameter model, which implies a double equilibrium in series, is introduced. When less than 10 % of the metal is still fixed on the resin at the end of the desorption, a simplified form of the model with two parameters, which describes a quick equilibrium followed by a first-order kinetics reaction, is proposed. Both forms of the model can simulate results for different experimental conditions (polymer and metal types, polymer initial concentration). It was observed for both cases that the first equilibrium constant depends on the polymer type and that the rate constant of desorption depends on the metal type. The scale-up of desorption is then conducted at mini-pilot scale. Scale-up criteria tend to minimize the desorption time and the soluble polymer quantity used.

Proton transfer equilibrium in Schiff bases derived from 5-nitrosalicylaldehyde. a study of deuterium isotope effects on13C NMR chemical shifts

The proton transfer equilibrium in series of Schiff bases derived from 5-nitrosalicylaldehyde and aliphatic amines was investigated by means of variable-temperature NMR spectra and the deuterium isotope effect on 13C NMR chemical shifts. Copyright © 1999 John Wiley & Sons, Ltd.

Parameters of the conformational equilibrium in phenyl formate

The shift of the position of the conformational equilibria in series of formic acid derivatives is determined primarily by steric factors.

Tautomerism of derivatives of azines. 17. Effect of solvents on the position of the azinyl-ylidene tautomeric equilibrium of substitued azinylmethanes

The effect of solvents on the position of the azinyl-ylidene tautomeric equilibrium in series of azinylmethanes was studied. It was shown that an increase in the polarity of the solvent leads to stabilization of the ylidene tautomer; the sensitivity of the tautomeric equilibrium to the effects of the solvent depends on the form of the side fragment that undergoes tautomerization. It was concluded that stabilization of the ylidene tautomeric form by polar solvents is a general tendency in series of prototropic equilibrium of the azinyl-ylidene type as a whole.

Infrared Spectra of Some Substituted Monoazobenzenes, Hydroxyhydrazone Tautomerism in Orthohydroxy, and Orthoaminoazobenzenes

The infrared spectra of substituted monoazobenzenes (O-Cl, m-Cl, p-Cl, p-Br, 2,5-dichloro, O-NO2, m-NO2, p-NO2, and 2,4-dinitro) derived from p-hydroxy, O-aminobenzenes (series A), and of the substituted monoazobenzenes ( O-Cl, m-Cl, p-Cl, 2,5-dichloro, p-Br, and O-NO2) derived from p-amino, O-hydroxybenzene (series B) have been recorded and tentatively assigned. In series A the O-NO2, m-NO2, and 2,4-dinitro compounds and all members of series B show a relatively intense IR band at 1651 ± 17 cm−1. The appearance of this band in the nitrocompounds of series A at 1654 ± 14 cm−1 is interpreted as being probably due to coupling of ΔNH2 and α as NO2. The band at 1642 ± 8 cm−1 in series B is tentatively as signed as a ν C=O absorption. This interpretation is regarded as evidence of tautomeric equilibrium in series B of these azodyes.