• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.107-121
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• 2023

An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

• Bulletin of the Korean Chemical Society
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• v.12 no.3
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• pp.309-315
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• 1991

The thermal transport coefficients-the self-diffusion coefficient, shear viscosity, and thermal conductivity-of liquid argon at 94.4 K and 1 atm are calculated by non-equilibrium molecular dynamics (NEMD) simulations of a Lennard-Jones potential and compared with those obtained from Green-Kubo relations using equilibrium molecular dynamics (EMD) simulations and with experimental data. The time-correlation functions-the velocity, pressure, and heat flux auto-correlation functions-of liquid argon obtained from the EMD simulations show well-behaved smooth curves which are not oscillating and decaying fast around 1.5 ps. The calculated self-diffusion coefficient from our NEMD simulation is found to be approximately 40% higher than the experimental result. The Lagrange extrapolated shear viscosity is in good agreement with the experimental result and the asymptotic formula of the calculated shear viscosities seems to be an exponential form rather than the square-root form predicted by other NEMD studies of shear viscosity. The agreement for thermal conductivity between the simulation results (NEMD and EMD) and the experimental result is within statistical error. In conclusion, through our NEMD and EMD simulations, the overall agreement is quite good, which means that the Green-Kubo relations and the NEMD algorithms of thermal transport coefficients for simple liquids are valid.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1248
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• 2011

The present paper is concerned with a two-competitor/oneprey population system with Holling type-II functional response and two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Particularly, by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs) explicit formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are derived. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.

• Nuclear Engineering and Technology
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• v.43 no.3
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• pp.287-300
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• 2011

Counting statistics modified by introducing two dead times in series under a Poisson input distribution are discussed. A previous study examined the two cases of series combinations of nonextended-extended (NE-E) and extended-extended (EE) dead times. The present study investigated the remaining two cases of extended-nonextended (E-NE) and nonextended-nonextended (NE-NE) dead times. For the three time origins of the counting processes - ordinary, equilibrium, and shifted processes - a set of formulae was newly developed from a general formulation and presented for the event time interval densities, total densities, and exact mean and variance of the counts in a given counting duration. The asymptotic expressions for the mean and variance of the counts, which are most convenient for applications, were fully listed. The equilibrium mean count rates distorted by the three dead times in series were newly derived from the information obtained in these studies. An application of the derived formulae is briefly discussed.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.275-282
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• 2008

Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}$ = $\frac{\alpha-{\beta}x_{n-1}}{\gamma+g(x_n)}$ under specified conditions. We show that the positive (or zero for $\alpha$ = 0) equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients and the function g(x).

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.349-358
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• 2018

In this article, we discuss the domain of attraction of HIV-1 system by using the moment theory. First, the asymptotic stabilities of the equilibrium point of the system are given, and then we introduce how to use the moment method to estimate domain of attraction. Finally, one simulation shows the effectiveness of moment method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.139-155
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• 2019

In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

• Journal of the Korean Solar Energy Society
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• v.36 no.3
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• pp.9-16
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• 2016

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.1-25
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• 2013

In this paper we have developed a mathematical model of alcohol abuse. It consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined. Sensitivity analysis of $R_0$ identifies ${\beta}_1$, the transmission coefficient from moderate and occasional drinker to heavy drinker, as the most useful parameter to target for the reduction of $R_0$. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0$ < 1. It is found that, when $R_0$ = 1, a backward bifurcation can occur and when $R_0$ > 1, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE. Our aim of this analysis is to identify the parameters of interest for further study with a view for informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.