• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.1
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• pp.55-65
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• 2013

The purpose of this paper is to prove existence of solutions of an SIRS epidemic model with time delay of continuous type and the variable incidence rate and to investigate some asymptotic behaviors of the SIRS epidemic model. An example illustrating the stability of the model is given. The results extend the corresponding results in the literature.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.1953-1960
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• 2002

The viscoplasticity theory based on overstress, one of the unified state variable theories, is generalized to model zero (no influence of loading rate) and negative (flow stress decreases with loading rate) as well as positive (flow stress increases with loading rate) rate sensitivity in a consistent way. On the basis of the long-time asymptotic solution the different types of rate sensitivity are classified with respect to an augmentation function that is introduced in the evolution law fur a state variable equilibrium stress. The theory predicts normal relaxation and creep behaviors even if unusual rate sensitivity is modeled. The constitutive model fir the behavior of a modified 9Cr-1 Mo steel at various temperatures is then compared with experimental data found in the literature.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.329-342
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• 2008

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.900-906
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• 2010

This note proposes vibration-free motor control through modified LQG/LTR methodology. A conventional LQG/LTR method is a design tool in the frequency domain. However, unlike the conventional one, the proposed one is a time response based design method. This feature is firstly designed by parameterized settling time control gain through the target loop design procedure and the feature is secondly realized by loop transfer recovery. In order to show convergence to the target loop transfer functions, asymptotic behaviors of the open and the closed loop transfer functions are shown. At the conclusion, it is verified that the proposed method is robustly stable to parametric uncertainties through ${\mu}$-plot.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.151-167
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• 2012

In this paper, we investigate the dynamic behaviors of a one-prey and two-predator system with Holling-type II functional response and defensive ability by introducing a proportion that is periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for predators at different fixed time. We establish conditions for the local stability and global asymptotic stability of prey-free periodic solutions by using Floquet theory for the impulsive equation, small amplitude perturbation skills. Also, we prove that the system is uniformly bounded and is permanent under some conditions via comparison techniques. By displaying bifurcation diagrams, we show that the system has complex dynamical aspects.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.819-833
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• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.205-215
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• 2021

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.753-762
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• 2009

A measure of agreement H in$2{\times}2$ contingency table was proposed by Park and Park (2007) to resolve the two paradoxes of k. In this study, we generalize H to where the number of categories is greater than two and derive its asymptotic large-sample variance. We also explain the relationships between k's paradoxes and marginal distributions. Using some examples of $3{\times}3$ contingency tables, the behaviors of H and other measures of agreement are compared.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.12
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• pp.1347-1355
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• 2009

This paper demonstrates the validity of spectral element analysis for modeling the high-frequency dynamic behaviors of a beam with a surface-bonded piezoelectric wafer through a laboratory test. In the spectral element analysis, the high-frequency electro-mechanical interaction can be considered properly with relatively low computational cost compared to the finite element analysis. In the verification test, a cantilever beam with a surface-bonded piezoelectric wafer is forced to be in steady-state motion by exerting the harmonic driving voltage signal on the piezoelectric wafer. A laser scanning vibrometer is used to obtain the overall dynamic responses of the structure such as resonance frequencies, the associated mode shapes, and frequency response functions up to 20 kHz. Then, these dynamic responses from the test are compared to those computed by the spectral element analysis. A two-dimensional finite analysis is conducted to obtain the asymptotic solutions for the comparison purpose as well.

• Journal of Communications and Networks
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• v.18 no.3
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• pp.429-438
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• 2016

In this paper, we investigate an interference mitigation scheme by antenna selection in device-to-device (D2D) communication underlaying downlink cellular networks. We first present the closed-form expression of the system achievable rate and its asymptotic behaviors at high signal-to-noise ratio (SNR) and the large antenna number scenarios. It is shown that the high SNR approximation increases with more antennas and higher ratio between the transmit SNR at the base station (BS) and the D2D transmitter. In addition, a tight approximation is derived for the rate and we reveal two thresholds for both the distance of the D2D link and the transmit SNR at the BS above which the underlaid D2D communication will degrade the system rate. We then particularize on the small cell setting where all users are closely located. In the small cell scenario, we show that the relationship between the distance of the D2D transmitting link and that of the D2D interfering link to the cellular user determines whether the D2D communication can enhance the system achievable rate. Numerical results are provided to verify these results.