• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.651-675
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• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.603-620
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• 2022

Several common fixed point theorems for a pair of weakly compatible mappings satisfying contractive inequalities of integral type in a metric space are proved. The results obtained in this paper improve or differ from a few results existing in the literature.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.885-897
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• 2024

The purpose of this paper is to introduce a class of distance altering functions that establish the existence and uniqueness of fixed points of 𝜈-admissible mappings that are subject to a generalized (𝜓, 𝜑)-almost weakly contraction on a generalized b₂-metric space.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.5
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• pp.450-454
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• 1997

본 논문에서는 볼테라 비선형 시스템의 선형화를 위한 새로운 적응 선행처리 기법을 제시한다. 특히, 제안된 적응 선행처리 기법은 (i) 순수 비선형 왜곡 보상을 위한 부분(pure nonlinear distortion compensator: PNDC)과, (ii) 선형 왜곡 보상을 위한 선형 역필터(linear inverse filter: LIF)의 두 부분으로 구성된다. 본 논문의 선형화 기법의 장점으로는 기존의 P차 역(Pth-order inverse) 기법에 비하여 계산량이 상당히 감소되며, 적응 알고리듬이 보다 빠르고 안정된 수렴 특성을 나타낸다. 끝으로, 모의실험을 통하여, 제안된 선행처리 기법의 성능및 실제 적용 가능성을 살펴본다.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.355-365
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• 2020

In this study, considering the hydroelastic response represented by the springing and whipping phenomena, we propose a method of estimating the fatigue damage in the longitudinal connections of ships. First, we screened the design sea states using a load transfer function based on the frequency domain. We then conducted a time domain fluid-structure interaction (FSI) analysis using WISH-FLEX, an in-house code based on the weakly nonlinear approach. To obtain an effective and robust analytical result of the hydroelastic response, we also conducted an experimental model test with a 1/50-scale backbone-based model of a ship, and compared the experimental results with those obtained from the FSI analysis. Then, by combining the results obtained from the hydroelastic response with those obtained from the numerical fatigue analysis, we developed a fatigue damage estimation method. Finally, to demonstrate the effectiveness of the developed method, we evaluated the fatigue strength for the longitudinal connections of the real ship and compared it with the results obtained from the model tests.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.587-603
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• 2001

The purpose of this paper is to study the nonlinear ergodic theorems and asymptotic behavior for an almost-orbit of asymptotically nonexpansive type mappings in a uniformly convex Banach space with Opial’s condition.

• International Journal of Naval Architecture and Ocean Engineering
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• v.12 no.1
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• pp.297-313
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• 2020

An Arctic Spar is characterized by its conical shape near the waterline. In this case, the nonlinear effects from its irregular hull shape would be significant if there is either a large amplitude floater motion or steep wave conditions. Therefore, in this paper, the nonlinear effects of an Arctic Spar are numerically investigated by introducing a weakly nonlinear time-domain model that considers the time dependent hydrostatic restoring stiffness and Froude-Krylov forces. Through numerical simulations under multiple regular and irregular wave conditions, the nonlinear behavior of the Arctic Spar is clearly observed, but it is not shown in the linear analysis. In particular, it is found that the nonlinear Froude-Krylov force plays an important role when the wave frequency is close to the heave natural frequency. In addition, the nonlinear hydrostatic restoring stiffness causes the structure's unstable motion at a half of heave natural period.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5B
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• pp.539-549
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• 2006

The performance of a pontoon-type floating breakwater (FB) is investigated numerically with the use of a second-order time domain model. The model has been developed based on potential theory, perturbation theory and boundary element method. This study is focused on the effects of weakly nonlinear wave on the hydrodynamic characteristics of the FB. Hydrodynamic forces, motion responses, surface elevation, and wave transmission coefficient around the floating breakwater are evaluated for various wave and geometric parameters. It is shown that the second-order wave component is of significant importance in calculating magnitudes of the hydrodynamic forces, mooring forces and the maximum response of a structure. The weak non-linearity of incident waves, however, can have little influence on the efficiency of the FB. From numerical simulations, the ratio of draft and depth, the relationship of wave number and width are presented for providing an effective means of reducing wave energy.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.1
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• pp.49-58
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• 2013

Recently, the design of commercial ships with less green-house gas is one of great interests in naval architecture fields. Ship designers are asked to find optimum hull forms with minimum resistance in ocean waves. The accurate computation of added resistance, therefore, is getting more important for the prediction of power increase in random ocean waves. This study focuses on the numerical computation of added resistance on ships with Ax-bow shapes which are designed to reduce added resistance. To this end, the time-domain Rankine panel methods based on weakly-nonlinear and weak-scatterer approaches are applied, which can reflect the influence of above-still-water bow shape. As computational models, KCS and KVLCC2 hull forms are considered. Each ship is combined with the three types of Ax-bow shape, and computational results are compared each other.