• 충청수학회지
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• 제23권4호
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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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• 제16권5호
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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.

• 한국환경과학회지
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• 제20권12호
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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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• 제34권3호
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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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• 제15권1호
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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.

• 한국산학기술학회논문지
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• 제3권2호
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• pp.141-145
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• 2002

이온교환수지탑으로 유입된 이온은 연속적인 이온교환 평형을 이루면서 수지층을 통과한다는 가정하에 질량작용법칙과 몰 균형식을 조합하여 연속이은교환평형 칼럼모델을 개발하였다. 연속이온교환평형 칼럼모델을 이용하여 원자력발전소 복수탈염설비 탈염기의 성능을 평가한 결과, Na/sup +/및 Cl/sup -/누출 농도는 수지의 재생효율에 따라 다르며, 특정이온의 유입수 및 유출수에서 농도 비율은 용액 및 수지의 상태에 따라 달라짐을 확인하였다. 본 모델은 수지농도를 보정하여 국부 불완전 평형을 고려할 수 있고, 다성분 존재하의 경쟁적 이온교환을 묘사할 수 있는 장점을 가지고 있다.

• 대한교통학회지
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• 제29권2호
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• pp.81-89
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• 2011

통행분포(trip distribution)는 4단계 통행수요추정의 첫 단계인 통행발생(trip generation)에서 구해진 통행생성(trip production)과 통행 유인(trip attraction)을 연결시키는 작업이다. 즉 하나의 존에서 생성 또는 유인되는 통행량을 다른 존에 분포시키는 과정이다. 이에 반해, 통행수단선택(transport mode choice)은 통행자들이 어떤 교통수단을 선택할 것인지를 결정하는 단계이다. 그러나, 이들 통행분포단계와 통행수단선택단계는 서로 밀접한 관계가 있음에도 불구하고, 서로 독립적으로 수행되어온 경향이 있었다. 본 연구에서는 통행분포단계와 통행수단선택단계를 통합한 모형을 제시하고 이를 풀기 위한 알고리듬도 제시한다. 통합모형의 통행분포모형으로는 중력모형(gravity model)을 적용되며, 수단선택모형으로는 로짓모형(logit model)을 이용한다. 본 연구의 통합모형은 각 단계별로 개별적으로 진행되는 추정단계가 하나의 모형 틀 안에서 통합적으로 이루어져 좀 더 현실적이며, 통행비용의 불일치 문제가 해소될 수 있다. 또한, 통합모형에서도 균형조건(equilibrium condition)이 존재함을 증명하며, 통합모형의 민감도 분석을 통하여 기존 모형과의 차이점을 설명한다.

• 전기학회논문지
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• 제56권6호
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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.

• 대한전기학회논문지:전력기술부문A
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• 제54권9호
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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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• 제29권5_6호
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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.