• Proceedings of the KSME Conference
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• 2001.06e
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• pp.39-44
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• 2001

The thermocapillary flow in a differentially heated cylindrical liquid bridge under steady rotation of the hot disk is considered in the limit of zero capillary number. Steady flow states and their three-dimensional stability are calculated numerically. A linear stability analysis reveals that the most dangerous perturbations are oscillatory with azimuthal wavenumber m=1 or m=2 depending on the parameters.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1847-1854
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• 2013

The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.75-87
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• 2018

In this paper, we consider ratio-dependent predator-prey models with disease in the prey under Neumann boundary condition. We investigate sufficient conditions for the existence and non-existence of non-constant positive steady-state solutions by the effects of the induced diffusion rates.

• Journal of Korea Society of Industrial Information Systems
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• v.23 no.3
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• pp.131-142
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• 2018

Since income growth rate and poverty level are related, there is a possibility that the poverty rate may converge in the long run steady state as well. If the poverty rate converges, then for this study the state that begins with the high poverty rate would have a higher poverty reduction rate. To examine the convergence of poverty rate among the US states, this study uses two times series methodologies. First, in order to prevent the power loss from ignoring the structural break when testing for a unit root in a single time series, this study employs the newly developed panel LM unit root tests with level and trend shifts. The results of unit root tests of the log of poverty rate without allowing for structural breaks show that twenty six states reject the null hypothesis of unit root test for the ADF test, twenty five states for the LM test, and thirty five states for the RALS-LM test. The result of unit root tests that allow one structural break shows that the null hypothesis of a unit root test is rejected for twenty two states with the LM test, and thirty three states with the RALS-LM test. This supports poverty rates are converging among US states.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.175-187
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• 2002

The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.27 no.12
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• pp.633-638
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• 2015

This study evaluates the capacity of night purging in office buildings to reduce the cooling load. RTS-SAREK is used to estimate the performance of night purging on the steady state. To overcome steady state RTS program limitations, we added unsteady heat transfer equations. When the ACH (Air Change per Hour) increases, the wall temperature decreases in both the steady and unsteady states. The unsteady heat transfer rate is different from the steady transfer rate, which validates the unsteady calculation. When ACH is low, the heat transfer rate increases continuously with time. When ACH becomes higher, the heat transfer rate increases and decreases with time. When ACH is quite high, there exists a large difference in the heat transfer rate between the steady and unsteady calculations, which emphasizes the importance of the unsteady calculation.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.469-487
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• 2015

We consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indicate that hybrid on-off therapy protocols can move the model system to a "healthy" steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.309-312
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• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• Journal of Korean Institute of Industrial Engineers
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• v.8 no.2
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• pp.15-21
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• 1982

This paper offers an alternative to the common probability generating function approach to the solution of steady state equations when a Markovian queue has a multivariate state space. Identifying states and substates and grouping them into vectors appropriately, we formulate a two - dimensional Markovian queue as a Markov chain. Solving the resulting matrix equations the transition point steady state probabilities (SSPs) are obtained. These are then converted into arbitrary time SSPs. The procedure uses only probabilistic arguments and thus avoids a large and cumbersome state space which often poses difficulties in the solution of steady state equations. For the purpose of numerical illustration of the approach we solve a Markovian queue with one server and two classes of customers.

• Journal of Environmental Science International
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• v.4 no.1
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• pp.71-80
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• 1995

A discrete state space model for a multiple-reach river system is formulated using the dynamics of biochemical oxygen demand(BOD) and dissolved oxygen(DO). A hierarchical optimization technique, which is applicable to large-scale systems with time-delays in states, is also described to control stream quality in a river as an optimal manner based on the interaction prediction method. The steady state tracking error of the proposed method is determined analytically and a necessary and sufficient condition on which a constant target tracking problem has zero steady-state error is derived. Computer simulations for the river pollution model illustrate the algorithm.