• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1365-1376
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• 2023

In this paper, we construct higher-order poly-tangent polynomials and study several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order poly-tangent polynomials.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.457-469
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• 2024

In this paper, we construct higher-order (p, q)-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order (p, q)-poly-tangent polynomials.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.1
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• pp.67-75
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• 2016

In this paper, a pressure-time history curve of blast load and Conwep model are presented, and a simplified blast load formula is suggested. Generally, a blast load are applied as a pressure-time history curve, and it is calculated by blast load formula such as Conwep model. The Conwep model which is used in most of the blast analysis is quiet difficult to calculate because of its complex process. Therefore, a simplified formula is proposed to calculate blast load by simple rational expressions and to make a simplified pressure-time history curve. In this process, a curve fitting method was used to find the simple rational expressions. The calculation results of the simplified formula have an error of less than 1% in comparison with the Conwep model. And, blast analyses using finite elements method are accomplished with the Conwep model and simplified formula for verification.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.207-220
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• 2016

Our goal is to construct a two-frequency-dependent formula $I_N$ which interpolates a product f of two functions with different frequencies at some N points. In the beginning, it is not clear to us that the formula $I_N$ satisfies $I_N=f$ at the points. However, it is later shown that $I_N$ satisfies the above equation. For this theoretical development, a one-frequency-dependent formula is introduced, and some of its characteristics are explained. Finally, our newly constructed formula $I_N$ is compared to the classical Lagrange interpolating polynomial and the one-frequency-dependent formula in order to show the advantage that is obtained by generating the formula depending on two frequencies.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Journal of electromagnetic engineering and science
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• v.13 no.4
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• pp.240-244
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• 2013

In this paper, we present an improvement of a closed-form formula for mutual impedance computation. Depending on the center-to-center spacing between two rectangular microstrip patch antennas, the mutual impedance formula is separated into two parts. The formula based on synthetic asymptote and variable separation is utilized for spacings of more than 0.5 ${\lambda}_0$. When the spacing is less than 0.5 ${\lambda}_0$, an approximate formula is proposed to improve the computation for closely spaced elements. Simulation results are compared to computational results of mutual impedances and mutual coupling coefficients as functions of normalized center-to-center spacing in both E- and H-plane coupling configurations. A good agreement between simulation and computation is achieved.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.21-41
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• 2020

In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.56 no.4
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• pp.374-383
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• 2020

At ship design stage, the maneuverability is generally estimated based on the empirical formula or the computational fluid dynamic (CFD), which is one of the numerical simulation methods. Using the hydrodynamic derivatives derived through these methods can quantitatively estimate the maneuverability of target vessels and evaluate indirect maneuverability. Nevertheless, research on estimating maneuverability is insufficient for ships not subject to IMO maneuverability standard, especially fishing vessels, and even at the design stage, the empirical formula developed for merchant ships is applied without modification. An estimation error may occur due to the empirical formula derived from the regression analysis results of a model test if the empirical formula developed for merchant ships with different hull shapes is applied to fishing vessels without any modification. In this study, the modified empirical formula that can more accurately estimate the fishing vessel's maneuverability was derived by including the hull shape parameter of target fishing trawlers in the regression analysis process that derives Kijima et al. (1990) formula. As a result, the modified empirical formula showed an average estimation error of 6%, and the result improved the average error of 49% of Kijima et al. (1990) formula developed for merchant ships.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.325-332
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• 2002

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.3
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• pp.277-290
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• 2008

In order to apply UTM coordinates conversion in zones larger than $14^{\circ}$ wide, a new conversion formula, based on the 12th expansion of Taylor series, is derived which is shown to be an extension of Thomas' formula(1952). Some examples of coordinate conversion between WGS84 and UTM are presented and convergences of computational results are also tested according to the order of formula. The present conversion formula can be used to make rectangular coordinate grid systems for numerical models to compute long wave propagation such as tide or tsunami around Korea.