Papers by Keyword: Equilibrium

Abstract: In this paper, the GFC-KKM mapping is introduced and GFC-KKM theorems are established in GFC-spaces. As applications, a fixed point theorem and maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, equilibrium existence theorems for qualitative games and abstract economies are yielded in GFC-spaces.

Abstract: The solubility of TNT and RDX was measured in supercritical carbon dioxide fluid at 303.0, 308.0, 323.0, 338.0 K, and over the pressure range from 10.0 MPa to 50.0 MPa. This study examined the influences of extraction temperature, extraction pressure and support effect (SE) between molecules of TNT and RDX on their solubility in the TNT/RDX/SC-CO₂ system. The results show that solubility of TNT and RDX in TNT/RDX/SC-CO₂ ternary system is much higher than that in binary system. The values of SE of RDX and TNT increase first and decrease then with the pressure changing. The pressure turning point occurred over the pressure range from 25 MPa to 28 MPa for TNT and from 13 MPa to 20 MPa for RDX.

Abstract: In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

Abstract: Cornstalk, a cellulosic agricultural waste material, was modified by citric acid to improve the adsorption of rhodamine B (RB) and methylene blue (MB) from aqueous media. Characterization of SEM and FTIR spectra confirmed that the surface morphology of adsorbent changed and carboxylic groups were introduced into the raw cornstalk by chemical modification. The effects of pH, contact time, initial concentration and the amount of dried adsorbent were studied in batch experiments. There was no significant difference in the dye concentration remaining when the pH was increased from 4.0 to 10.0. Several models were used to fit experimental data and the results showed that experimental data fitted the Langmuir model and pseudo-second order model best. Compared with 58.71 and 81.71 mg g^-1 obtained by CS (raw cornstalk), the maximum adsorption capacities for RB and MB were 203.0 and 245.6 mg g^-1 by using CCS (cornstalk modified with citric acid), respectively.

Abstract: A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

Abstract: The paper studied the game strategy decisions of alliance leader and members in collaborative information seeking. Based on basic Nash equilibrium model with complete information, it researched Bayesian-Nash equilibrium under incomplete information condition which further implied that the incompleteness of information had effected on the alliance leader’s compensation policy. Furthermore, it revealed a methodology to analyze the stability of Bayesian-Nash equilibrium and gave a detailed algorithm. It provided a framework to systematically explore the relationships between alliance leader and other members while solving work tasks in collaboration.

Abstract: Using the definitions of potential functions and ordinal potential functions of strategic form games, we characterize two classes of potential games and give the solving method of the equilibria of finite potential games by testing and verifying potential games. The main contribution is proving that public goods games and social coordination games based on location strategic interaction with an exogenous network are potential games, and giving the equilibria by the method of solving potential games and ordinal potential games.

Abstract: In this paper, we establish a mathematical model on four-wheel-steering system subjected to white noise excitations and analyze the dynamical behaviors of the system under the sense of mean value. We calculate the Lyapunov exponents and estimate Lyapunov dimensions of the system. The results obtained demonstrate the existence of quasi-periodic orbit, and the simulations certify the conclusion of analysis. All the results showed that the four-wheel-steering system subjected to white noise excitations with weak intensity will move nearly steadily companied with tiny perturbation at not too high driving speeds.

Abstract: The adsorption of acid red G dye onto raw bentonite/cationic starch (RB/CS) and raw bentonite (RB) was investigated in aqueous solution in a bath system with respect to the adsorption kinetics and adsorption isotherms, respectively. For RB and RB/CS composite, the kinetic data showed that the kinetics of adsorption was best described by a pseudo-second-order expression than the pseudo-first-order. Adsorption isotherms of acid red G dye onto RB and RB/CS composite were determined with common isotherm equations such as the Langmuir and Freundlich models. The results showed that for RB/CS composite, the Langmuir model agreed very well with the experimental data, whereas the RB was fitted to both Langmuir and Freundlich models. In summary, the results showed that RB/CS could be employed as low-cost materials for the removal of acid red G dye from effluents compared to RB.

Abstract: Acrylic acid and its derivatives are raw materials for polymeric, paint additives, adhesive, textile and leather treating products. The increasing demand of acrylic acid is great attention for its recovery from dilute aqueous solutions. With this aim, the amine based extraction of acrylic acid from its aqueous solutions in polar diluents was investigated. In the extraction, the tri-n-octylamine in polar diluents was found to provide higher extraction efficiency than that in nonpolar diluents. It was presumed that the acid-amine complex formation is difficult and the low solubility of acid-amine complex is low in nonpolar diluents. Higher extraction efficiency for acrylic acid was obtained with the polarity of active diluents due to higher solubility for acid-amine complex with polarity of diluents.