• East Asian mathematical journal
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• v.37 no.3
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• pp.295-305
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• 2021

In this paper, we analyze the efficiency of a domain decomposition method for the two-dimensional telegraph equations. We formulate the theoretical spectral radius of the iteration matrix generated by the domain decomposition method, because the rate of convergence of an iterative algorithm depends on the spectral radius of the iteration matrix. The theoretical spectral radius is confirmed by the experimental one using MATLAB. Speedup and operation ratio of the domain decomposition method are also compared as the two measurements of the efficiency of the method. Numerical results support the high efficiency of the domain decomposition method.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.993-1010
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• 2022

In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.

• East Asian mathematical journal
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• v.39 no.1
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.47-55
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• 2008

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Journal of Navigation and Port Research
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• v.42 no.3
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• pp.201-206
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• 2018

The purpose of this study is to estimate a proper Domain Watch between anchored vessels in order to propose a method for the efficient management of VTS(Vessel Traffic Service) of the N-anchorage in Busan harbor, which is the largest port in Korea. For this purpose, we proposed the calculation method of Domain Watch and investigated the ship length(L), the distance between anchored vessels ($D_{ij}$), the domain radius(R), and the domain radius vs L(R/L) during the peak time of the vessels in the latest usage of anchorage. As a result of technical analysis for the surveyed data, the minimum R/L for securing the safety distance between anchored vessels was selected based on 2.85 corresponding to the 70th percentile of the total data. This result was applied to the N-anchorage of Busan and compared with the 'Guidelines of Port and Harbor Design(2014)', and we have confirmed that it is reasonable to set the Domain radius with the minimum 2.85L or more in VTS. This study considers the safety management of anchorage for VTS. This study could contribute to the safety of vessels using anchorage and the safety management plan of VTS when it is applied to other ports in operation such as it was in Busan.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.433-444
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• 2023

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w² - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

• 한국정보디스플레이학회:학술대회논문집
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• 2005.07a
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• pp.338-341
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• 2005

We have examined the aspects of the orientational ordering deformation of ferroelectric liquid crystal during bending performance of plastic substrate by analyzing the polarizing optical microscope texture and the birefringence of the cell. Striped texture becomes more prominent as the radius of curvature of substrate gets smaller. The optic axis of the adjacent stripes domain was not same and the relative angle between them becomes larger as the radius of curvature gets smaller. Especially, the optic axis rotation angle of one domain was lager than the other and the liquid crystal molecules in each domain became more coherent. In addition, the birefringence data with obliquely incident light shows the polar direction shift of liquid crystal molecule by bending performance.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.321-337
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• 2000