• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.475-489
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• 2014

In this paper, a mathematical model for HIV infection with saturating infection rate and time delay is established. By some analytical skills, we study the global asymptotical stability of the viral free equilibrium of the model, and obtain the sufficient conditions for the local asymptotical stability of the other two infection equilibria. Finally, some related numerical simulations are also presented to verify our results.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.375-406
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• 2020

The anti-predator factor due to fear of predator in eco- epidemiological models has a great importance and cannot be evaded. The present paper consists of a modified Lesli-Gower predator-prey model with contagious disease in the predator population only and also consider the fear effect in the prey population. Boundedness and positivity have been studied to ensure the eco-epidemiological model is well-behaved. The existence and stability conditions of all possible equilibria of the model have been studied thoroughly. Considering the fear constant as bifurcating parameter, the conditions for the existence of limit cycle under which the system admits a Hopf bifurcation are investigated. The detailed study for direction of Hopf bifurcation have been derived with the use of both the normal form and the central manifold theory. We observe that the increasing fear constant, not only reduce the prey density, but also stabilize the system from unstable to stable focus by excluding the existence of periodic solutions.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.245-249
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• 2003

Vapor-liquid equilibrium data were obtained for system of propane + R227ea (Heptafluoropropane) over the temperature range from 253.15 K to 323.15 K at 10 K intervals. Experiments were performed in a circulation type apparatus by injecting vapor through liquid pool using a magnetic pump. This system forms azeotrope in the temperature range of this study. The experimental results were correlated with the Peng-Robinson (PR) equation of state and Redlich-Kwong-Soave (RKS) equation of state using the van der Walls one-fluid mixing rule and were compared with each other.

• Journal of the Korean Society of Industry Convergence
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• v.8 no.1
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• pp.37-45
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• 2005

Adsorption equilibrium data of pure solvent vapors (n-Hexane, Toluene, MEK) as well as their binary mixtures on activated carbon (sorbonorit $B_4$) were experimentally determined in the range of 293.2~323.2 K and beyond saturated vapor pressure corresponding to experimental temperature. Langmuir, Freundlich, LRC, W-VSM, FH-VSM were estimated for the predication of single component as well as binary mixtuer systems. The isosteric heat of adsorption at infinite dilution of pure n-hexane, toluene, MEK on activated carbon were 45.18, 25.85, 34.62 Kcal/mol, respectively, also, n-hexane-toluene binary adsorption of activated carbon formed an azeotrope at 293.2 K and total pressure 5.1~10.3 mmHg.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.317-335
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• 2014

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

• New & Renewable Energy
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• v.3 no.2 s.10
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• pp.47-52
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• 2007

Hydrate phase equilibrium for the binary $CO_{2}$+water and $CH_{4}$+water mixtures in silica gel pore of nominal 6, 30, and 100 nm were measured and compared with the cacluated results based on van der Waals and Platteeuw model. At a specific temperature three-phase hydrate-water-vapor (HLV) equilibrium curves for pore hydrates were shifted to the higher-pressure condition depending on pore sizes when compared with those of bulk hydrates. Notably, hydrate phase equilibria for the case of 100 nominal nm pore size were nearly identical with those of bulk hydrates. The activities of water in porous silica gels were modified to account for capillary effect, and the calculation results were generally in good agreement with the experimental data.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.61-69
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• 1997

In this paper, we study the dynamics of a two-parameter unfolding system $\chi$' = y, y' = $\beta$y＋$\alpha$f($\chi\alpha\pm\chiy$＋yg($\chi$), where f($\chi$,$\alpha$) is a second order polynomial in $\chi$ and g($\chi$) is strictly nonlinear in $\chi$. We show that the higher order term yg($\chi$) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small $\alpha$ and $\beta$ if the nontrivial fixed point approaches to the origin as $\alpha$ approaches zero.

• The Korean Journal of Ceramics
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• v.4 no.4
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• pp.387-393
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• 1998

The formation of titanium diboride ($TiB_2$ ) via the reduction of $TiO_2$ with boric oxide and carbon was studied in a partially reducing atmosphere of argon mixed with 4 vol.%H2. The effect of reaction time, temperature, partial pressure of nitrogen and $TiO_2/B_2_O3$ stoichiometric ratio on the reducibility of oxides has been studied. The phases formed were analysed by using X-ray rowder diffraction and scanning sosctron microscopic techniques. In this paper, we also investigated the presence of $CaC_2$ as a reducing agent on the reducibility of oxide mixtures and on the Ti-B-C-Ca-O phase equilibria. The morphology of $TiB_2$ formed in the presence of $CaC_2$ is compared with the microstructure of $TiB_2$ formed as a consequence of carbothermic reduction. The observed variation in $TiB_2$ crystals formed is also explained.

• Macromolecular Research
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• v.11 no.4
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• pp.241-249
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• 2003

A molecular-thermodynamic model to describe the salt-induced protein precipitation is developed based on the perturbation theory. We employed the modified perturbed hard-sphere-chain (PHSC) equation of state for copolymer mixtures to take into account the pre-aggregation effect among protein particles. Hypothetical pressure-composition diagrams are computed with various size differences and salt concentrations. The precipitation behaviors are also studied for various types of pre-aggregation effect for the given systems.

• Macromolecular Research
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• v.15 no.7
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• pp.682-687
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• 2007

The equation of state developed herein is predicated on a hard-sphere reference with perturbations introduced via a potential function to account for electrostatic forces and for attraction between protein particles. During this process, the generalized Lennard-Jones (GLJ) pair potential function is employed. The GLJ pair potential function is employed to represent the protein-protein interaction in two-protein systems. Via the use of the relation between the equation of state and the chemical potential, the phase behavior in the aqueous two-protein system can be estimated. The partition coefficients can be obtained via these processes. The calculated values of the coefficients agree fairly well with the experimental data in the given pH and ionic strength range, with no additional adjustable model parameters.