Adsorption of 2-naphthalenesulfonic acid/sulfuric acid/sulfurous acid from aqueous solution by iron-impregnated weakly basic resin：Equilibrium and model

Commercial grade weakly basic resin D301 was impregnated with iron through a simple method using ferric chloride. Experiments for single, bisolute and trinary competitive adsorption were carried out to investigate the adsorption behavior of 2-naphthalenesulfonic acid(NSA), sulfuric acid and sulfurous acid from their solution at 298 K onto the novel hybrid iron impregnated D301(Fe-D301). Adsorption affinity of NSA on Fe-D301 was found to be much higher than that of sulfuric acid, while adsorption affinity of sulfuric acid was slightly higher than that of sulfurous acid. The data of single-solute adsorption were fitted to the Langmuir model and the Freundlich adsorption model. The non-ideal competitive adsorbed model coupled with the single-solute adsorption models were used to predict the bisolute and trinary-solute competitive adsorption equilibria. The NICM coupled with the Langmuir model yields the favorable representation of the bisolute and trinary-solute competitive adsorption behavior.

Competitive Communication Spectrum Economy and Equilibrium

Consider a competitive“spectrum economy”in a communication system where multiple users share a common frequency band and each of them,equipped with an endowed“monetary”budget,will“purchase”its own transmit power spectrum(taking others as given)in maximizing its Shannon utility or pay-off function that includes the effects of interference and subjects to its budget constraint.A market equilibrium is a price spectrum and a frequency power allocation that independently and simultaneously maximizes each user’s utility.Furthermore,under an equilibrium the market clears,meaning that the total power demand equals the power supply for every user and every frequency.We prove that such an equilibrium always exists for a discretized version of the problem,and,under a weak-interference condition or the Frequency Division Multiple Access(FMDA)policy,the equilibrium can be computed in polynomial time.This model may lead to an efficient decentralized method for spectrum allocation management and optimization in achieving both higher social utilization and better individual satisfaction.Furthermore,we consider a trading market among individual users to exchange their endowed power spectrum under a price mechanism,and we show that the market price equilibrium also exists and it may lead to a more socially desired spectrum allocation.

Competitive Equilibria and Benefit Distributions of Population Production Economies with External Increasing Returns

Inspired by the work of population games,we establish the model of population production economies with external increasing returns and introduce the notion of competitive equilibria.We first prove the existence of competitive equilibria under some regular assumptions.Furthermore,we assume that there exists the cooperative behavior of different populations.By proving the existence of transferable utility(TU)core,we analyze the benefit distributions of population production economies with external increasing returns.

Core and Equilibrium of a Stock Economy in Incomplete Asset Market

In this paper, we study the core and equilibrium of a stock economy. First, the definition of the core with shareholder vote is given, then an equilibrium model of a production\|exchange economy in incomplete asset markets is established in which the firms′ behavior is involved. Finally, the relation between the Edgeworth equilibrium with shareholder vote and the competitive equilibrium in incomplete asset markets are given.

Comparing Competition Equilibrium with Nash Equilibrium in Electric Power Market

The Nash equilibrium and competition equilibrium have been widely studied in the electric power market up to now.In this paper,it is explained that the Nash equilibrium can be achieved by using marginal cost pricing and the com-petition equilibrium can be performed by using accounting cost pricing based on the model of the power market system.The comparison between the Nash equilibrium and competition equilibrium indicates that surplus and unfair allocation of market benefits may be obtained by the Nash equilibrium,and the competition equilibrium realizes the optimization in economics with maximum market efficiency and fairness for market benefit allocations while the optimization in mathematics is achieved by the Nash equilibrium.There is sameness between the Nash equilibrium and competition equilibrium at the point when the power network characteristics are disregarded.The case study is made on a IEEE 30-bus system,and the calculation results indicate that it is the key issue to perform the competition equilibrium by using accounting cost pricing.

ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.