• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Korean Journal of Applied Biomechanics
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• v.31 no.1
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• pp.24-29
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• 2021

Objective: The goal of this study is to calculate and compare the Maximum Lyapunov Exponent (MLE) for the anteroposterior, mediolateral and vertical displacement of the markers attached to bony land marks of the trunk and foot. Method: Ten young and healthy male subjects (age: 26.5±3.27 years, height: 167.44±5.12 cm, and weight 69.5±7.36) participated in the study. Three-dimensional positional coordinate of eight different trunk and foot marker during walking on tread mill were analysed. Results: MLE values for anteroposterior displacement of the marker were found to be significantly different with MLE values for mediolateral and vertical displacement whereas MLE values for mediolateral displacement of the marker shows no significant difference with the MLE values for vertical displacement of the markers at significance level 0.05. Conclusion: Finding of this study suggest that it is essential to consider the displacement in all three direction to examine the real characteristic of a gait signal.

• Journal of Bio-Environment Control
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• v.24 no.3
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• pp.135-146
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• 2015

To provide the data necessary to determine the design wind speed for calculating the wind load acting on a greenhouse, we measured the wind speed below 10m height and analyzed the power law exponents at Buan and Gunwi. A wind speed greater than $5m{\cdot}s^{-1}$ is appropriate for calculating the power law exponent necessary to determine the wind speed distribution function according to height. We observed that the wind speed increased according to a power law function with increased height at Buan, showing a similar trend to the RDC and JGHA standards. Therefore, this result should be applied when determining the power law function for calculating the design wind speed of the greenhouse structure. The ordinary trend is that if terrain roughness increases the value of power law exponent also increases, but in the case of Gunwi the value of power law exponent was 0.06, which shows contrary value than that of the ordinary trend. This contrary trend was due to the elevations difference of 2m between tower installed and surrounding area, which cause contraction in streamline. The power law exponent started to decrease at 7 am, stopped decreasing and started to increase at 3 pm, and stopped increasing and remained constant at 12 pm at Buan. These changes correspond to the general change trends of the power law exponent. The calculated value of the shape parameter for Buan was 1.51, confirming that the wind characteristics at Buan, a reclaimed area near the coast, were similar to those of coastal areas in Jeju.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1329-1338
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• 2007

In this paper, we study the location of zeros and Borel direction for the solutions of linear homogeneous differential equations $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+{\cdots}+A_1(z)f#+A_0(z)f=0$$ with entire coefficients. Results are obtained concerning the rays near which the exponent of convergence of zeros of the solutions attains its Borel direction. This paper extends previous results due to S. J. Wu and other authors.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

• Vacuum Magazine
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• v.1 no.1
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• pp.11-16
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• 2014

A variety of metal vacuum systems displays the celebrated 1/t pressure, namely, power-law dependence on time t, with the exponent close to unity, as to the origin of which there has been long-standing controversy. Here we propose a chemisorption model for water adsorbates, based on the argument for 2D fermion behavior of water adsorbed on a metal surface, and obtain analytically the power-law behavior of pressure with an exponent unity. Further, the model predicts that the pressure should depend on the temperature T according to $T^{1.5}$, which is indeed confirmed by our experiment.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.79-81
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• 2009

In this paper, we design a dynamic state feedback smooth stabilizer for a nonlinear system whose Jacobian linearization may have uncontrollable because its eigenvalues are on the right half-plane. After designing an augmented system, a dynamic exponent scaling and backstepping enable one to explicitly design a smooth stabilizer and a continuously differentiable Lyapunov function which is positive definite and proper.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.1
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• pp.65-82
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• 1996

This paper proposes a sequential procedure which can be used to determine a truncation point and run length to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state behavior. It is based on the idea of Lyapunov exponent in chaos theory. The performance measures considered are relative bias, coverage, estimated relative half-width of the confidence interval, and mean amount of deleted data.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2003.11a
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• pp.449-467
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• 2003

뇌전도(EEG), 심전도(ECG) 와 같은 생체 전기신호는 카오스적 특성을 가지고 있으므로, 신호특성 분석에 비선형 도구를 사용하므로 의미있는 정보를 얻을 수 있다. 분석하는 데에는 주파수 특성, 변이 특성과 같은 생체시스템의 상태를 검증하는 방법이 주로 이용되어 왔다. 이에 본 연구에서는 심장 맥파의 RR 간격의 값을 획득하여 비선형 분석하는 도구로 Hurst Exponent 값의 변화를 모델화 하여 두 개의 비교대상 집단을 대상으로 차별성을 검출하는데 그 목적이 있다.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.771-783
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• 2018

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type $$u_{tt}-{\Delta}u-{\Delta}u_t+m^2u+{\mid}u_t{\mid}^{p(x)-2}u_t={\mid}u{\mid}^{q(x)-2}u$$ associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.