• 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.

• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.739-756
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• 2005

The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.10 no.2
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• pp.238-250
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• 1998

Vapor-liquid equilibrium apparatus is designed and set up. The vapor-liquid equilibrium data of the binary system HFC125/134a are measured in the range between 268.15 and 283.15K at five compositions. Twenty-five equilibrium data are obtained. To verify consistency of these data, they are tested for thermodynamic consistency. Based upon the present data, the binary interaction parameter for CSD and RKS equation of state is calculated at five isotherms and comparison with the data in the open literatures is made. Results of Nagel and Bier are in very good agreements with those from this study within 0.32∼1.11% for bubble point pressure and －0.66∼0.18% for vapor mole fraction.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.9 no.4
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• pp.527-535
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• 1997

Vapor-liquid equilibrium apparatus is designed and set up. The vapor-liquid equilibrium data of the binary system HFC32/134a are measured in the range between 258.15 and 283.15K at compositions of 0.2, 0.4, 0.6 and 0.8 mole fraction of HFC32. Twenty-two equilibrium data are obtained. Based upon the present data, the binary interaction parameter for Carnahan-Starling-De Santis equation of state is calculated. Temperature range of data is extended to 313.04K using the data in the open literatures. Interaction parameters are determined at nine isotherms.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.1
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• pp.91-99
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• 1999

Vapor-liquid equilibrium apparatus is designed and set up. The equilibrium data of two binary systems, HFC-32/143a and HFC-143a/134a, are measured. Fifteen equilibrium data for HFC-32/143a and HFC-143a/134a systems are measured over the temperature range 263.15~283.15K at 10K interval and the composition range 0.10~0.80, respectively. And vapor-liquid equilibrium data are calculated using equation of state and correlation of activity coefficient and compared with the present data. Equation of state is used CSD and RKS equations and correlation of activity coefficient is used Margules' and Van Ness and Abbott's correlations. Real behavior of HFC-32/143a system has very large deviation with Raoult's rule which is ideal behavior. But real behavior of HFC-143a/134a system is similar to ideal behavior. The calculated data from CSD equation are compared with the data in the open literatures and the calculated data from REFPROP. In the results for REFPROP, the relative deviations of bubble point pressure for HFC-32/143a system are within -2.16~0.84% for CSD equation and within -0.20~1.10% for RKS equation. And the relative deviations of bubble point pressure for HFC-143a/134a system are within -0.45~0.12% and -0.20~2.8% for CSD and RKS equations, respectively.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.123-138
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• 2009

This study examined the first- and second-best pricing by stable dynamics in congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. The first-best pricing in user equilibrium models introduces user-equilibrium in the system-equilibrium by tolling the difference between the marginal social cost and the marginal private cost on each link. Nevertheless, the second-best pricing, which levies the toll on some, but not all, links, is relevant from the practical point of view. In comparison with the user equilibrium model, the stable dynamic model provides a solution equivalent to system-equilibrium if it is focused on link flows. Therefore the toll interval on each link, which keeps up the system-equilibrium, is more meaningful than the first-best pricing. In addition, the second-best pricing in stable dynamic models is the same as the first-best pricing since the toll interval is separately given by each link. As an effect of congestion pricing in stable dynamic models, we can remove the inefficiency of the network with inefficient Braess links by levying a toll on the Braess link. We present a numerical example applied to the network with 6 nodes and 9 links, including 2 Braess links.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.4
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• pp.259-266
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• 2005

This paper presents a therapy that uses a constant drug dosage for leading HIV-infected patient to LTNP (Long-Term Non-Progressor). Based on analysis of CTLp (Cytotoxic T Lymphocyte precursor) concentration at equilibrium point and its bifurcation, we found the therapy with a drug whose efficacy is less than a certain level brings higher CTLp concentration at the equilibrium point. We observed a treatment with constant drug dosage whose efficacy is less than full treatment may lead HIV-infected patient to LTNP. It turns out that the treatment whose efficacy is less than full treatment is better in the point of performance on controllability.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.665-677
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• 2023

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.