• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1264-1275
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• 2002

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1722-1727
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• 1992

In this study, techniques of adaptive input-output linearizing control of a class of uncertain nonlinear system are investigated. It is shown through concepts of signal growth rates that bounded trackings yield by adaptive input-output linearizing control law using normalized estimator. The convergence characteristics are improved significantly by using the normalized estimator. Simple example is presented as illustration.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Journal of Forest and Environmental Science
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• v.38 no.1
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• pp.48-54
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• 2022

This study was conducted to examine litter inputs and litter decomposition rates following thinning, which is among the most important forest management activities that enhance the beneficial functions in Korean forests. Litter inputs and litter decomposition rates following a 2-year elapse from thinning in Pinus densiflora and following a 7-year elapse from thinning in Quercus variabilis stands were measured for 2 years from 16 sites in three regions (Sancheong-gun, Uiryeong-gun, and Jinju-si) in Gyeongsangnam-do, Korea. Annual needle litter inputs in P. densiflora stands were significantly decreased following thinning, whereas annual broadleaved leaf litter inputs in Q. variabilis stands were not significantly different between thinned and unthinned treatments. The annual mean total litter inputs in both tree species were significantly lower in the thinned (P. densiflora: 3,653 kg ha^-1 year^-1; Q. variabilis: 4,963 kg ha^-1 year^-1) compared to the unthinned stands (P. densiflora: 5,138 kg ha^-1 year^-1; Q. variabilis: 5,997 kg ha^-1 year^-1) during the study period. The mass loss rates from decomposing needle litter in P. densiflora stands were significantly lower (p<0.05) in the thinned stands than in the unthinned stands for two sampling dates of the eight included in the study, whereas the decomposition rates from decomposing leaf litter in Q. variabilis stands were not affected by thinning. The results indicate that thinning effects on total litter inputs remained clear following a 2-year elapse from thinning in P. densiflora stands and following a 7-year elapse from thinning in Q. variabilis stands.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1115-1126
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• 2020

The main purpose of this paper is to establish the rates of convergence in weak limit theorems for normalized geometric sums of independent identically distributed random variables via Zolotarev's probability metric.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.23-37
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• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.255-269
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• 2004

This paper develops log-density estimation for directional data. The methodology is to use expansions with respect to spherical harmonics followed by estimating the unknown parameters by maximum likelihood. Minimax rates of convergence in terms of the Kullback-Leibler information divergence are obtained.

• Journal of the Korea Convergence Society
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• v.8 no.8
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• pp.291-298
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• 2017

This study is to examine the status and trends of regional elderly group(pre-elderly and elderly segment)'s suicide rates and socio-economic factors, to analyze the relevance of suicide rates and socio-economic factors, and to understand differential factors of elderly group's suicide rates between metropolitan areas and small-medium sized areas. For this, analysis on relevance between socio-economic factors and elderly group's suicide rates has been done using regional statistical data for the past ten years(2006~2015) by National Statistical office. According to research findings, Socio-economic factors such as welfare budget ratio, divorce rates, economic activity rates, and financial independent rates have shown different effects on elderly group's suicide rates by age range and regional characteristics. Based on these analyses, this study suggested policy tasks for alleviating suicide rates of elderly group.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.917-924
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• 2003

Recurrent neural networks have been successfully applied to communications channel equalization. Major disadvantages of gradient-based learning algorithms commonly employed to train recurrent neural networks are slow convergence rates and long training sequences required for satisfactory performance. In a high-speed communications system, fast convergence speed and short training symbols are essential. We propose decision feedback equalizers using a recurrent neural network trained with Kalman filtering algorithms. The main features of the proposed recurrent neural equalizers, utilizing extended Kalman filter (EKF) and unscented Kalman filter (UKF), are fast convergence rates and good performance using relatively short training symbols. Experimental results for two time-varying channels are presented to evaluate the performance of the proposed approaches over a conventional recurrent neural equalizer.