• East Asian mathematical journal
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• 제37권3호
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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.

• 대한수학회보
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• 제59권4호
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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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• 제39권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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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.

• 호남수학학술지
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• 제43권4호
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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.

• 한국항해항만학회지
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• 제42권3호
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• pp.201-206
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• 2018

본 연구는 우리나라 최대 항만인 부산항의 남외항 정박지를 VTS(Vessel Traffic Service)에서 효율적으로 관리하는 방안을 제시하기 위해 정박선간 적정한 영역감시(Domain Watch)를 산정하는 데 목적이 있다. 이를 위해 영역감시 산출 방법을 제시하고 최근 정박지 이용 현황 중 정박선이 가장 많았던 기간에 선박 길이(L), 정박선간 거리($D_{ij}$), 영역감시 반경(R), 선박 길이 대비 영역감시 반경(R/L)을 1시간 간격으로 조사하였다. 조사된 자료에 대해 기술 분석을 한 결과, 정박선 한 척이 다른 정박선과 안전거리를 확보할 수 있는 최소 R/L을 조사된 전체 자료의 70 %ile(백분위수)에 해당하는 2.85를 기준으로 산정할 수 있었다. 이 결과를 부산항 남외항 정박지에 적용하여 이를 '항만 및 어항 설계 기준(2014)과 비교한 결과 상당 부분 일치하였고, 이를 통해 VTS에서 정박선의 영역감시 반경을 최소 2.85L 이상으로 설정하는 것이 타당함을 확인하였다. 본 연구는 정박지 안전 관리를 VTS 차원에서 검토한 것으로, 부산항과 같은 집단 정박지를 운영 중인 타 항만에 적용할 경우 정박지를 이용하는 선박의 안전과 VTS의 안전 관리 방안 마련에도 기여할 수 있을 것으로 기대된다.

• Korean Journal of Mathematics
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• 제31권4호
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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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• 한국정보디스플레이학회 2005년도 International Meeting on Information Displayvol.I
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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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• 제13권1호
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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.

• 대한수학회지
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• 제37권2호
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• pp.321-337
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• 2000