• 한국측량학회지
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• 제25권1호
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• pp.63-68
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• 2007

The computations of an ultra-high degree associated Legendre functions and its first derivative up to degree and order of 10800 are reported. Not only the magnitude of orders for the ultra-high degree calculation is presented but the numerical stability and accuracy of the computed values are described in detail. The accuracy on the order of $10^{-25}\;and\;10^{-15}$ was obtained for the values of Legendre function and the first derivatives of Legendre functions, respectively. The computable highest degree and order of Legendre function in terms of latitudes and the linear relationship between the magnitude of the function with respect to degrees and orders is found. It is expected that the computed Legendre functions contribute in many geodetic and geophysical applications for simulations as well as theoretical verifications.

• Journal of the Korean Data and Information Science Society
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• 제23권3호
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.

• 대한수학회논문집
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• 제31권4호
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Bulletin of the Korean Chemical Society
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• 제22권7호
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• pp.732-738
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• 2001

The cross second-derivative of the activation energy,${\theta}$G${\neq}$ , with respect to the two component thermodynamic barriers, ${\theta}$G˚X and ${\theta}$G$^{\circ}C$Y, can be given in terms of a cross-interaction constant (CIC), $\betaXY(\rhoXY)$, and also in terms of the intrinsic barrier,${\theta}$G${\neq}$ , with a simple relationship between the two: $\betaXY$ = $-1}(6${\theta}$G${\neq}$).$ This equation shows that the distance between the two reactants in the adduct (TS, intermediate, or product) is inversely related to the intrinsic barrier. An important corollary is that the Ritchie N+ equation holds (for which $\betaXY$ = 0) for the reactions with high intrinsic barrier. Various experimental and theoretical examples are presented to show the validity of the relationship, and the mechanistic implications are discussed.

• 대한수학회지
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• 제59권6호
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• 대한수학회보
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• 제61권1호
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• pp.93-115
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• 2024

In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• 한국항해항만학회지
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• 제39권3호
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• pp.173-178
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• 2015

최근 국내외적으로 수중 유도무기체계 개발로 다양한 형태의 수중운동체 기술이 발전되고 있다. 특히 수중운동체 중 하나인 잠수함은 한국의 특수한 상황에서 최적의 선형설계를 위한 신뢰도 높은 조종성 평가 기술이 요구되며, 이를 위한 정확한 동유체력 계수의 추정 또한 중요한 연구 분야라 할 수 있다. 따라서 본 논문에서는 잠수함 모형을 대상으로 구속모형시험인 VPMM (Vertical Planar Motion Mechanism) 시험을 실시하여 정밀도 높은 동유체력 계수를 추정하였다. 그리고 추정된 연직면 운동에 대한 선형 (Linear) 동유체력 계수 (Hydrodynamic derivatives)들을 이용하여 동안정성 (Dynamic Stability)을 판별하였다. 그 결과, 이론추정치와의 비교를 통해 동유체력 계수의 타당성이 검증되었으며, 잠수함의 연직면 동안정성도 양호한 것으로 평가되었다. 즉, 무한수심으로 정의되는 심도 6.0의 깊은 수심으로 갈수록 주기에 따른 변화가 작아지며, 이론추정치에 근사함을 확인할 수 있었다. 한편 연직면 동안정성 판별에 있어서는, 0보다 큰 양(+)의 값을 가짐으로서 연직면 운동에 대한 동안정성을 만족하는 것으로 나타났다.

• Wind and Structures
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• 제14권5호
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• pp.413-434
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• 2011

Without output covariance estimation, one reference-based Stochastic Subspace Technique (SST) for extracting modal parameters and flutter derivatives of bridge deck is developed and programmed. Compared with the covariance-driven SST and the oscillation signals incurred by oncoming or signature turbulence that adopted by previous investigators, the newly-presented identification scheme is less time-consuming in computation and a more desired accuracy should be contributed to high-quality free oscillated signals excited by specific initial displacement. The reliability and identification precision of this technique are confirmed by a numerical example. For the 3-DOF sectional models of Sutong Bridge deck (streamlined) and Suramadu Bridge deck (bluff) in wind tunnel tests, with different wind velocities, the lateral bending, vertical bending, torsional frequencies and damping ratios as well as 18 flutter derivatives are extracted by using SST. The flutter derivatives of two kinds of typical decks are compared with the pseudo-steady theoretical values, and the performance of $H_1{^*}$, $H_3{^*}$, $A_1{^*}$, $A_3{^*}$ is very stable and well-matched with each other, respectively. The lateral direct flutter derivatives $P_5{^*}$, $P_6{^*}$ are comparatively more accurate than other relevant lateral components. Experimental procedure seems to be more critical than identification technique for refining the estimation precision.

• Bulletin of the Korean Chemical Society
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• 제31권7호
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• pp.1951-1955
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• 2010

A new blue light emitting anthracene derivative, 9,10-bis-(9',9'-diethyl-7'-t-butyl-fluoren-2'-yl)anthracene (BETF), has been designed and synthesized by a palladium catalyzed Suzuki cross-coupling. A theoretical calculation of the three-dimensional structure of BETF supports that it has a non coplanar structure and inhibited intermolecular interactions resulting in high luminescent efficiency and high color purity. BETF has good thermal stability with glass-transition temperature (Tg) of $131^{\circ}C$. The PL maximum of BETF in solution and film were 438 nm and 440 nm, respectively, showing pure blue emission. A multilayer device using BETF as emitting material exhibits maximum luminescence efficiency of 2.2 cd/A and a pure blue emission (Commission Internationale de L'Eclairage (CIE) coordinates of x = 0.15, y = 0.10).