• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.691-698
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• 2010

In this paper, we first introduce a new model of strategic Nash game with insatiability, and next give two social equilibrium existence theorems for general strategic games which are comparable with the previous results due to Arrow and Debreu, Debreu, and Chang in several aspects.

• Journal of Welding and Joining
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• v.16 no.5
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• pp.56-66
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• 1998

During solidification or welding of alloys, the solute redistribution brings out microsegregation. The microsegregation causes the formation of non-equilibrium second phases, shrinkage and porosity degrading mechanical/chemical properties Therefore, it has been required to predict microsegregation quantitatively. To predict the degree of microsegregation, more exact and appropriate computer simulation technique has been actively used during last two decades. To predict the degree of microsegregation in weld metal, an advanced two dimensional model was suggested. In the new model, both primary and secondary arm regions were defined for the analysis region. The growth in the primary arm regina was assumed to be a planar for effective calculation. Especially, for the growth of a secondary arm, a simple and effective mathematical function was established to show the growing pattern, the solute diffusion in the solid phase was calculated by finite difference method (FDM). The solid-liquid interface movement was considered to be in local equilibrium state. The experiments for welding of 310S stainless steel were carried out in order to examined the reasonability and feasibility of this model. The concentration profiles of the solute predicted by this model were compared with those obtained from experimental works.

• Journal of Environmental Science International
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• v.20 no.12
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• pp.1607-1615
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• 2011

The adsorption performance of cupper and zinc ions($Cu^{2+}$ and $Zn^{2+}$) in aqueous solution was investigated by an adsorption process on reagent grade Na-A zeolite(Z-WK) and Na-A zeolite (Z-C1) prepared from coal fly ash. Z-C1 was synthesized by a fusion method with coal fly ash from a thermal power plant. Batch adsorption experiment with Z-C1 was employed to study the kinetics and equilibrium parameters such as initial metal ions concentration and adsorption time of the solution on the adsorption process. Adsorption rate of metal ions occurred rapidly and adsorption equilibrium reached at less than 120 minutes. The kinetics data of $Cu^{2+}$ and $Zn^{2+}$ ions were well fitted by a pseudo-second-order kinetics model more than a pseudo-first-order kinetics model. The equilibrium data were well fitted by a Langmuir model and this result showed $Cu^{2+}$ and $Zn^{2+}$ adsorption on Z-C1 would be occupied by a monolayer adsorption. The maximum adsorption capacity($q_{max}$) by the Langmuir model was determined as $Cu^{2+}$ 99.8 mg/g and $Zn^{2+}$ 108.3 mg/g, respectively. It appeared that the synthetic zeolite, Z-C1, has potential application as absorbents in metal ion recovery and mining wastewater.

• East Asian mathematical journal
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• v.34 no.3
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• pp.317-330
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• 2018

We develop a mathematical model for the obesity dynamics to investigate the long term obesity trend with the consideration of psychological and social factors due to the increasing prevalence of obesity around the world. Many mathematical models for obesity dynamics adopted the modeling idea of infectious disease and treated overweight and obese people infectious and spreading obesity to normal weight. However, this modeling idea is not proper in obesity modeling because obesity is not an infectious disease. In fact, weight gain and loss are related to social interactions among different weight groups not only in the direction from overweight/obese to normal weight but also the other way around. Thus, we consider these aspects in our model and implement personal weight gain feature, a psychological factor such as body image dissatisfaction, and social interactions such as positive support on weight loss and negative criticism on weight status from various weight groups. We show that the equilibrium point with no normal weight population will be unstable and that an equilibrium point with positive normal weight population should have all other components positive. We conduct computer simulations on Korean demography data with our model and demonstrate the long term obesity trend of Korean male as an example of the use of our model.

• Management Science and Financial Engineering
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• v.15 no.1
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• pp.51-69
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• 2009

A network model and a Genetic Algorithm (GA) is proposed to solve the simultaneous estimation of the trip distribution and traffic assignment from traffic counts in the congested networks in a logit-based Stochastic User Equilibrium (SUE). The model is formulated as a problem of minimizing a non-linear objective function with the linear constraints. In the model, the flow-conservation constraints are utilized to restrict the solution space and to force the link flows become consistent to the traffic counts. The objective of the model is to minimize the discrepancies between two sets of link flows. One is the set of link flows satisfying the constraints of flow-conservation, trip production from origin, trip attraction to destination and traffic counts at observed links. The other is the set of link flows those are estimated through the trip distribution and traffic assignment using the path flow estimator in the logit-based SUE. In the proposed GA, a chromosome is defined as a real vector representing a set of Origin-Destination Matrix (ODM), link flows and route-choice dispersion coefficient. Each chromosome is evaluated by the corresponding discrepancies. The population of the chromosome is evolved by the concurrent simplex crossover and random mutation. To maintain the feasibility of solutions, a bounded vector shipment technique is used during the crossover and mutation.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.3 no.2
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• pp.141-145
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• 2002

Successive ion Exchange Column model was developed with the combination of mass action law and mole balance equation. consuming that ions entering the ion exchange bed pass the resin layer via consecutive ion exchange equilibrium. The application of the model to condensate polishing demineralizer in nuclear power plants indicates that the leakage of $Na^+$ and $Cl^-$ depends upon the degree of resin regeneration and that the ratio of specific ion concentration in Influent to in effluent is subject to the characteristics of resin and solution. The model can account for the local in-equilibrium with the correction of resin concentration and also can be applicable to a competitive ion exchange.

• Journal of Korean Society of Transportation
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• v.29 no.2
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• pp.81-89
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• 2011

Trip distribution is the second step of the conventional travel demand estimation process, which connects trips between origin and destination, while transport mode choice is the third step of the process, which chooses transport mode among several modes serving for each origin-destination pair. Although these two steps have closely connected, they have been estimated independently each other in the estimation procedure. This paper presents an integrated model combining trip distribution and transport mode choice, and also presents its solution algorithm. The model integrates gravity model adopted for the trip distribution process with logit model employed for the mode choice process. The model would be expected to cope with the inconsistency issue existing in the conventional travel demand estimation procedure. This paper also presents an equilibrium condition, sensitivity of the model, and compares them with those of existing models.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.6
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• pp.1000-1006
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• 2007

This paper presents a methodology to calculate an optimal solution of equilibrium to differential algebraic equations for power systems. It employs a nonlinear interior point method to solve the optimization formulation which includes dynamic equations representing the two-axis synchronous generator model with AVR and speed governing controls, algebraic equations, and steady-state nonlinear loads. This paper also adopts two algorithms for the improvement of solution convergence. In power system analysis and control, equilibrium optimization (EOPT) is applicable for diverse purposes that need the consideration of dynamic model characteristics at a steady-state condition.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.9
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• pp.461-466
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• 2005

This paper addresses the bidding strategies of a hydro generator in an electricity market, and their effect on the electricity market in accordance with some parameters: the water volume, the demand elasticity, and the hydro unit performance. The competition of a hydro generator is formulated as a hi-level optimization problem, and the solving scheme for the equilibrium condition is proposed as a set of nonlinear simultaneous equations. The equilibrium of the oligopolistic model is evaluated by comparison with that of a perfect competition model from the viewpoint of a market power. Simulation results show some parameters have an influence on the market power of an electricity market including a hydro generator.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1117-1127
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• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.