• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.883-899
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• 2003

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6] , we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.

• Journal of Industrial Technology
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• v.11
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• pp.3-16
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• 1991

The lattice-fluid theory are adopted for modeling the phese equilibria in supercritical fluids, In order to investigate effects of the nonrandom distribution of holes in mixtures on the phase equilibria, the equation of state and the chemical potential of the binary miture are formulated with taking into account nonrandomness of holes distributions in the fluid mixture. The relations of phase equilibria formulated in this work are tested through predictions of solubility of heavy solids in supercritical fluids and predictions of high pressure phase equilibria of binary mixtures. Results obtained exhibit that the lattice fluid model with assumptions of nonrandomness of hole distributions is successful in quantatively mideling the phase equilibria of mixtures of molecules of dissimilar sizes, specifically solids-supercritical fluid mixtures.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.377-385
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• 2000

In this paper we find a sufficient condition to guarantee the existence of pure-strategy equilibria in matrix games. In the process of formulating our condition, the alternative theorem of Farkas is used. The formulated condition is necessary and sufficient to the existence of pure-strategy equilibria in undominated matrix games.

• Journal of Industrial Technology
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• v.18
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• pp.267-275
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• 1998

Continuous thermodynamics has been applied for modeling of phase equilibria in multicomponent mixtures, to avoid disadvantages of the pseudo-component and key-component method. In this paper continuous thermodynamic relations formulated by using the Pate-Teja equation of state were adopted for calculations of phase equilibria in natural gas mixtures, crude oil mixtures and mixtures extracted by supercritical $CO_2$ fluids. Calculations of phase equilibria were performed by two procedures ; a moment method coupled with the beta distribution function and a quadrature method combined with Gaussian-Legendre polynomials. Calculated results were compared with experimental data. It was showed that continuous thermodynamic frameworks considered in this paper were well-matched to experimental data.

• Resources Recycling
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• v.13 no.2
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• pp.24-32
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• 2004

Solvent extraction equilibria of Gd with PC88A from chloride solutions were analyzed by considering chemical equilibria. phase equilibria, mass and charge balance equations. The following solvent extraction reaction and equilibrium constant were evaluated from the experimental data performed in this study. $Gd^{3+}$ $+2H_2$$A_2$,$or=GdA_3$HA.or+3 $H^{+}$ , K=3.3 A procedure was suggested to calculate the initial concentration of chloride ion from initial pH and initial concentration of Gd. By applying ionic equilibria, the distribution of Gd complexes with Gd and HCl concentration was obtained. The predicted distribution coefficients of Gd agreed well with the experimental results.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.1
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• pp.113-120
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• 1994

A duopoly model is developed in order to examine the effect of imperfect competition on the price-setting behavior of competing providers in a congested market. Multiple Nash price equilibria are found and the implications of such multiple price equilibria are discussed.

• Environmental and Resource Economics Review
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• v.18 no.2
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• pp.311-344
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• 2009

The hypothesis that the common market equilibria for housing attributes are attained within distinctive submarkets was tested. Markets for housing attributes with greater supply flexibility, i.e., structural variables, were found to be closer to their common equilibria than markets with less supply flexibility, i.e., neighborhood and distance variables. In addition, submarkets with greater mobility were found to achieve common market equilibria for more housing attributes with greater supply flexibility, but not for housing attributes with lower degree of supply flexibility. Results suggest supply flexibility and occupier mobility are both necessary conditions for achieving common market equilibria for housing attributes.

• Journal of Hydrogen and New Energy
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• v.23 no.6
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• pp.660-669
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• 2012

Gas resources captured in the form of gas hydrates are an order of magnitude larger than the resources available from conventional resources. Focus of this research is to investigate the effect of DME on phase equilibria of methane hydrate, as well as the possibility of the use of the PRO/II computer simulation to estimate the phase equilibria. In systems containing water and a gaseous component like, for instance, methane, ethane, and propane, gas hydrates may occur, if conditions in terms of pressure and temperature are satisfied. Mixtures of gases, e.g. LPG or natural gas, are also able to form gas hydrates in the presence of water. The experiments presented here were performed at temperatures varying between 268.15K and 288.15K and at pressures varying between 1.88 MPa and 10.56 MPa. It was found that the phase equilibria of methane hydrate is influenced by the addition of DME to the system. The pressure for the equilibrium hydrate-liquid water-vapor (H - $L_w$ - V) in the system water + methane is reduced upon addition of DME. The phase equilibria of methane hydrate can be estimated by the PRO/II computer simulation, whereas those of methane hydrate containing DME or LPG can't be estimated properly.

• Progress in Superconductivity and Cryogenics
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• v.14 no.4
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• pp.28-31
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• 2012

We report the solid-liquid phase equilibria on the $GdBa_2Cu_3O_{7-{\delta}}$ (GdBCO) stability phase diagram in low oxygen pressures ($PO_2$) ranging from 1 to 100 mTorr. On the basis of the GdBCO stability phase diagram experimentally determined in low oxygen pressures, the isothermal sections of three different phase fields on log $PO_2$ vs. 1/T diagram were schematically constructed within the $Gd_2O_3-Ba_2CuO_y-Cu_2O$ ternary system, and the solid-liquid phase equilibria in each phase field were described. The invariant points on the phase boundaries include the following three reactions; a pseudobinary peritectic reaction of $GdBCO{\leftrightarrow}Gd_2O_3$ + liquid ($L_1$), a ternary peritectic reaction of $GdBCO{\leftrightarrow}Gd_2O_3+GdBa_6Cu_3O_y$ + liquid ($L_2$), and a monotectic reaction of $L_1{\leftrightarrow}GdBa_6Cu_3O_y+L_2$. A conspicuous feature of the solid-liquid phase equilibria in low $PO_2$ regime (1 - 100 mTorr) is that the GdBCO phase is decomposed into $Gd_2O_3+L_1$ or $Gd_2O_3+GdBa_6Cu_3O_y+L_2$ rather than $Gd_2BaCuO_5+L$ well-known in high $PO_2$ like air.

• Journal of The Korean Astronomical Society
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• v.46 no.6
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• pp.261-268
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• 2013

Magnetohydrostatic equilibria, in which the Lorentz force, the plasma pressure force and the gravitational force balance out to zero, are widely adopted as the zeroth order states of many astrophysical plasma structures. A magnetic flux-current surface is a surface, in which both magnetic field lines and current lines lie. We for the first time derive the necessary and sufficient condition for existence of magnetic flux-current surfaces in magnetohydrostatic equilibria. It is also shown that the existence of flux-current surfaces is a necessary (but not sufficient) condition for the ratio of gravity-aligned components of current density and magnetic field to be constant along each field line. However, its necessary and sufficient condition is found to be very restrictive. This finding gives a significant constraint in modeling solar coronal magnetic fields as force-free fields using photospheric magnetic field observations.