• Journal of the Korean Applied Science and Technology
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• v.19 no.3
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• pp.222-244
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• 2002

A mixture of methyl ester derivatives of fatty acids from the oils of pine nuts was well resolved to five fractions differing by degree of unsaturation by silver ion solid-phase extraction column chromatography ($Ag^{+}$-SEC). Polyunsaturated fatty acid with non-methylene interrupted conjugated double bond (NMiDB) radical held more strongly to silver ions in the column than methylene interrupted conjugated double bond (MiDB) one when they had the same number of double bonds. Although both the picolinyl ester and DMOX derivative provided clear mass ion species powerful enough to elucidate the structure of the polyunsaturated fatty acid (PUFA) with NMiDB and/or methylene interrupted conjugated double bond (MiDB) radical in the oils, the picolinyl ester of PUFA with NMiDB radical did not provide a cluster of mass ions neighboring diagnostic mass ions induced by the double bond in the proximal to the carboxyl group. However, the DMOX derivative of PUFA with NMiDB group as well as MiDB showed abundant mass ion species differing by gaps of 12 amu, which made it possible with greater ease to locate the double bonds in the molecule. The oil contained $C_{18:2{\omega}6}$ (46.2 %) and $C_{18:1{\omega}9}$ (25.4 %) as main components, and considerable amounts of PUFAs with NMiDB radical such as ${\Delta}^{5.\;9.\;12}-C_{18:3}$ (16.0 %), ${\Delta}^{5.\;9}-C_{18:2}$ (2.3 %) and ${\Delta}^{5.\;11.\;14}-C_{20:3}$ (0.8 %).

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• East Asian mathematical journal
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• v.14 no.1
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• pp.107-116
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• 1998

This paper deals with functions of the form $f(z)=a_1z-{\sum}{\limits}_{n=2}^{\infty}a_nz^n(a_1>0,\;a_n{\geqslant}0)$ with $(1-{\mu})f(z_0)/z_0+{\mu}f'(z_0)=1(-1. We introduce the class $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$ with generalized fractional derivatives. Also we have obtained coefficient inequalities, distortion theorem and radious problem of functions belonging to the calss $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.35-35
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• 2022

최근에 딥 러닝(Deep learning) 기반의 많은 방법들이 수문학적 모형 및 예측에서 의미있는 결과를 보여주고 있지만 더 많은 연구가 요구되고 있다. 본 연구에서는 수자원의 가장 대표적인 모델링 구조인 강우유출의 관계의 규명에 대한 모형을 Long Short-Term Memory (LSTM) 기반의 변형 된 방법으로 제시하고자 한다. 구체적으로 본 연구에서는 반응변수인 유출량에 대한 직접적인 고려가 아니라 그의 1차 도함수 (First derivative)로 정의되는 Delta기반으로 모형을 구축하였다. 또한, Attention 메카니즘 기반의 모형을 사용함으로써 강우유출의 관계의 규명에 있어 정확성을 향상시키고자 하였다. 마지막으로 확률 기반의 예측를 생성하고 이에 대한 불확실성의 고려를 위하여 Denisty 기반의 모형을 포함시켰고 이를 통하여 Epistemic uncertainty와 Aleatory uncertainty에 대한 상대적 정량화를 수행하였다. 본 연구에서 제시되는 모형의 효용성 및 적용성을 평가하기 위하여 미국 전역에 위치하는 총 507개의 유역의 일별 데이터를 기반으로 모형을 평가하였다. 결과적으로 본 연구에서 제시한 모형이 기존의 대표적인 딥 러닝 기반의 모형인 LSTM 모형과 비교하였을 때 높은 정확성뿐만 아니라 불확실성의 표현과 정량화에 대한 유용한 것으로 확인되었다.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.665-684
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• 2008

Runge-Kutta-Nystr$\"{o}$m (RKN) methods provide a popular way to solve the initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance ${\delta}$, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing ${\delta}$, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in ${\delta}$ as ${\delta}{\rightarrow}0$, that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.47-61
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• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• The Journal of the Acoustical Society of Korea
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• v.36 no.6
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• pp.387-393
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• 2017

The dynamic interactions between benzoic acid derivative ($pH{\approx}7.0$)(guest) and ${\beta}$-cyclodextrin (${\beta}$-CD)(host) were investigated in an aqueous solutions in terms of ultrasonic absorption in the frequency range 0.2 MHz ~ 50 MHz with emphasis on the low-frequency range below 1 MHz at $25^{\circ}C$. We show that the interaction of ${\beta}$-CD and benzoic acid derivative complies with a typical spectrum of a single relaxation process around a few MHz. The ultrasonic relaxation observed in these solutions was due to a perturbation of a chemical equilibrium related to a reaction of an inclusion complex formed by the host and guest. The rate constant ($k_b=7.48{\times}10^6M^{-1}s^{-1}$) and equilibrium constant ($K=68.6M^{-1}$) were determined from the concentration dependences of benzoic acid on the relaxation frequency. The standard volume change (${\Delta}V=10.6{\times}10^{-6}m^3mol^{-1}$) of the reaction was also computed from the maximum absorption per wavelength. It was found that the hydrophobicity of guest molecules played an important role in the formation of the inclusion complex.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.10
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• pp.1012-1015
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• 2011

The decision-directed blind equalization algorithm is often used due to its simplicity and good convergence property when the eye pattern is open. However, in a channel where the eye pattern is closed, the decision-directed algorithm is not guaranteed to converge. Hence, a modified Bussgang-type algorithm using a hyperbolic tangent function for zero-memory nonlinear(ZNL) function has been proposed and applied to avoid this problem by Filho et al. But application of this algorithm includes the calculation of hyperbolic tangent function and its derivative or a look-up table which may need a large amount of memory due to channel variations. To reduce the computational and/or hardware complexity of Filho's algorithm, in this paper, an improved method for the decision-directed algorithm is proposed. In the proposed scheme, the ZNL function and its derivative are respectively set to be the original signum function and a narrow rectangular pulse which is an approximation of Dirac delta function. It is shown that the proposed scheme, when it is combined with decision-directed algorithm, reduces the computational complexity drastically while it retains the convergence and steady-state performance of the Filho's algorithm.