• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• Resources Recycling
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• v.27 no.5
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• pp.9-13
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• 2018

The equilibrium constant of a chemical reaction is related to the standard Gibbs free energy change. Since equilibrium constant is defined as the ratio of the activities of the chemical species, it is necessary to consider the non-ideal behavior of the solutes as ionic strength of the solution increases. In this paper, the derivation of Debye-$H{\ddot{u}}ckel$ limiting law and its modification by which the activity coefficient of an ion can be calculated was explained. Moreover, the method to obtain the activity coefficient of an ion from the experimentally determined mean activity coefficients of an electrolyte was explained.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2006.11a
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• pp.150-153
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• 2006

Gas generator should be adopted either fuel rich or oxidizer rich combustion because of the temperature restriction to avoid any possible thermal damages to turbine blade. This study focuses to model the non-equilibrium chemical reaction of kerosene/LOx with detailed kinetics developed by Dagaut using Perfectly stirred reactor(PSR) assumption. To predict more reliable species fraction and other gas properties, Frenklach's soot model was added to Dagaut's detailed kinetics.

• Advances in environmental research
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• v.1 no.1
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• pp.69-82
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• 2012

Based on the measurement data of the particulate matter with an aerodynamic diameter of less than or equal to a nominal 10 ${\mu}m$ (PM10) by the ${\beta}$-ray absorption method (BAM) equipped with an inlet heater and the gravimetric method (GMM) at two coastal sites in Korea, the optimal inlet heater temperature was estimated. By using a gas/particle equilibrium model, Simulating Composition of Atmospheric Particles at Equilibrium 2 (SCAPE2), water content in aerosols was estimated with varying temperature to find the optimal temperature increase to make the PM10 concentration by BAM comparable to that by GMM. It was estimated that the heated air temperature inside the BAM should be increased up to $35{\sim}45^{\circ}C$ at both sites. At this temperature range, evaporation of volatile aerosol components was minor. Similar ($30{\sim}50^{\circ}C$) temperature range was also obtained from the calculation based on the absolute humidity which changed with ambient absolute humidity and chemical composition of hygroscopic species.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1411-1427
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• 2009

We propose a model based on Lotka-Volterra dynamics with two competing spices which are affected not only by harvesting but also by the presence of a predator, the third species. Hyperbolic and linear response functions are considered. We derive the conditions for global stability of the system using Lyapunov function. The optimal harvest policy is studied and the solution is derived in the interior equilibrium case using Pontryagin's maximal principle. Finally, some numerical examples are discussed. The nature of variations in the two prey species and one predator species is studied extensively through graphical illustrations.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.219-231
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• 2003

This paper aims to study the problem of combined harvesting of a system involving one predator and two prey species fishery in which the predator feeds more intensively on the more abundant species. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equiblibrium case by using Pontryagin's Maximum principle. Dynamic optimization of the harvest policy is also discussed by taking E(t), the combined harvest effort, as a dynamic variable. Biological and bioeconomic interpretations of the results associated with the optimal equilibirum solution are explained. The significance of the constraints required for the existence of an optimal singular control are also given.

• Journal of Species Research
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• v.1 no.1
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• pp.100-103
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• 2012

Nutria Myocastor coypus is one of a well known invasive riparian mammal found species around world from North America to Eurasia and Africa. In South Korea, feral nutrias inhabit areas from the Nakdonggang and Namgang (River) to their tributaries and Upo Wetland where they have had devastating effects on environment. Nevertheless, there has been little research about nutrias in Korea. This study is to analyze the genetic structure of the nutria population in the Upo Wetland and identify the origin of the source populations. Twenty individuals from the Upo Wetland were genotyped using 25 microsatellite loci. When compared with another introduced population, that of the Blackwater Nation Wildlife Refuge in U.S., the Upo population contains considerable genetic variations. Tests for Hardy-Weinberg equilibrium and Bayesian clustering analysis suggest the Upo population is genetically structured and has at least two source populations. This preliminary study presents the need for further in-depth studies about this species which should combine genetic and ecological studies.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2003.11a
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• pp.73-77
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• 2003

In order to predict the dynamic behaviors of uranium and cobalt in a fixed bed at various influent pH values of liquid waste, the adsorption system was regarded as multi-component adsorption between each ionic species in a solution. Langmuir isotherm parameters of each species were extracted by incorporating equilibrium data with the solution chemistry of uranium and cobalt using IAST. Prediction results were in good agreement with the experimental data, except for a high concentration and pH. Although there was some limitations in predicting the cobalt adsorption, this method may be useful in analyzing a complex adsorption system where various kinds of ionic species exist in a solution.

• Polymer(Korea)
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• v.26 no.4
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• pp.422-430
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• 2002

The kinetics of polycondensation of bishydroxyethyl naphthalate has been studied in the range of 241 -$260^{\circ}C$ using antimony trioxide catalyst. The reaction was performed in a batch reactor and the concentration of reaction mixture was measured with HPLC. The activation energy values of forward and reverse reaction determined from molecular species model were found to be 19.7 and 31.4 kcal/mole, respectively, and the equilibrium constants were in the range of 1.4-2.0, which were larger than that of polycondensation of PET and varied to some degree with temperature. It was confirmed by applying the Flory's distribution function that the reaction rate of the hyroxyethyl group does not depend on the molecular size. By applying functional group model, we observed that there was few difference between the activation energy of the forward reaction and that of reverse reaction, therefore the equilibrium constant has almost constant value of 1.4. The rate constants obtained from functional group model was about 3-4 times larger than that from molecular species model, which showed that both model explains the reaction system well. Although the molecular species model should predict the concentration of as many as ten molecules, it fits for the experimental results well.

• Journal of the Korean Electrochemical Society
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• v.5 no.4
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• pp.183-188
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• 2002

The structure of species formed in $NbCI_5-I-ethyl-3-methylimidazolium$ chloride (EMIC) room-temperature molten salt (RTMS) was examined with the Raman spectroscopic measurement and ab initio molecular orbital calculation. The equilibrium structures of $NbCl_5,\;NbCl_6^-,\;Nb_2CI_{10},\;Nb_2CI_{11}^-,\;Nb_3CI_6^-,\;NbCI_6^--EMI^+\;(in\;which\;NbCI_6^-$ anion approaches $EMI^+$ cation with strong interaction) and $Nb_2CI_{11}^--EMI^+$ were obtained with the HF/LANL2DZ level of calculation. The harmonic frequencies at each equilibrium structure were compared with Raman spectra. The harmonic frequencies of $NbCI_6^--EMI^+,\; Nb_2CI_{11}^--EMI^+,\;and\;Nb_2CI_{10}$ were in good agreement with the Raman spectra of RTMS melts. In the $NbCI_5-EMIC RTMS$, the main species were $NbCI_6^-\;and\;EMI^+$. In the $NbCl_5-EMIC$ RTMS added $NbCl_5\;over\;50mol\%$, small amount of $Nb_2CI_{11}^-\;and\; Nb_2CI_{10}$ were also formed. The structures of anions and cation in the RTMS distorted from free ions with Coulomb force.