• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.183-194
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• 2003

We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given.

• Ocean Systems Engineering
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• 제1권4호
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

• 대한수학회지
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• 제58권6호
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• pp.1327-1345
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• 2021

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type $$u(x)=\vec{\;l\;}+C_{\ast}{{\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}^n}}}\;{\frac{(1-{\mid}u(y){\mid}^2){\mid}u(y){\mid}^2u(y)-\frac{1}{2}(1-{\mid}u(y){\mid}^2)^2u(y)}{{\mid}x-y{\mid}^{n-{\alpha}}}}dy.$$ Here u : ℝⁿ → ℝ^k is a bounded, uniformly continuous function with k ⩾ 1 and 0 < α < n, $\vec{\;l\;}{\in}\mathbb{R}^k$ is a constant vector, and C_* is a real constant. We prove that ${\mid}\vec{\;l\;}{\mid}{\in}\{0,\frac{\sqrt{3}}{3},1\}$ if u is the finite energy solution. Further, if u is also a differentiable solution, then we give a Liouville type theorem, that is either $u{\rightarrow}\vec{\;l\;}$ with ${\mid}\vec{\;l\;}{\mid}=\frac{\sqrt{3}}{3}$, when |x| → ∞, or $u{\equiv}\vec{\;l\;}$, where ${\mid}\vec{\;l\;}{\mid}{\in}\{0,1\}$.

• 호남수학학술지
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• 제45권1호
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• 한국전산구조공학회논문집
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• 제34권3호
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• pp.151-157
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• 2021

본 연구에서는 비국부 적분 연산기로 표현되는 페리다이나믹 방정식의 수렴성을 검토한다. 정적/준정적 손상 해석 문제를 효율적으로 해석하기 위해 페리다이나믹 방정식의 implicit 정식화가 필요하다. 이 과정에서 페리다이나믹 비국부 적분 방정식으로부터 대수방정식 형태가 나타나게 되어 시스템 행렬 계산을 위해 많은 시간이 소요되기 때문에, 효율적인 계산을 위해 수렴성이 중요한 요소가 된다. 특히 radial influence 함수를 적분 kernel로 사용하는 경우 fractional Laplacian 적분 방정식이 유도된다. 비국부 적분 연산기의 교윳값 성질에 의해 대수방정식의 condition number가 radial influence 함수의 차수 및 비국부 영역의 크기에 영향을 받는 것이 수학적으로 확인되었다. 본 연구에서는 이를 토대로 균열이 있는 페리다이나믹 정적 해석 문제를 Newton-Raphson 방법으로 해석할 때 적분 커널의 차수, 비국부 영역의 크기 등이 대수방정식의 condition number와 preconditioned conjugate gradient (PCG) 방법으로 계산 시 수렴성 및 계산 시간에 미치는 영향을 수치적으로 분석한다.

• 융합신호처리학회논문지
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• 제8권3호
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• pp.217-221
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• 2007

본 논문에서는 비선형시스템의 제어대상의 하나로 사용되고 있는 Chua회로를 대상으로 견실 출력귀환제어를 실현한다. 특히 비선형인 경우는 선형의 경우와 틀린 접근방법을 사용하여야 한다. 우선 기준신호발생기인 exosystem을 정의하고 출력추종오차식으로부터 오차방정식을 유도하고, 적분기 형태의 서보보상기를 사용하여 수정된 슬라이딩면을 설계한다. 수정된 슬라이딩면과 서보보상기에 사용되는 파라미터들은 슬라이딩면 및 서보보상기가 안정하도록 관련다항식이 Hurwitz조건을 만족하도록 정한다. 특히 모든 파라미터들이 미지여서, 오차신호들이 귀환으로부터 얻을 수 없기 때문에, 고이득 관측기를 설계하고, 이 추정값을 사용하여 안정화제어기를 얻는다. 시뮬레이션결과를 제시함으로서 알고리즘이 유용함을 증명한다.

• 한국해안해양공학회지
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• 제3권3호
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• pp.176-183
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• 1991

본 연구는 경계요소법을 이용하여 비선형 자유표면파을 해석한 것이며, 가상경계처리는 유체 연속성을 고려하여 mass-flux와 energy-flux를 사용하여 유한진폭파동의 해석수법을 제시했다. 유체의 비선형성 때문에 증분법을 적용했으며 경계요소법에 의해 얻어진 결과는 유한요소법의 결과와 실험치와 비교하여 보았으며 좋은 일치가 얻어 졌다. 따라서, 이 방법은 광범위한 파동문제 해석에 유효하게 이용될 수 있으리라 사료된다.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.83-108
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• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• 소음진동
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• 제8권3호
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• pp.408-419
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• 1998

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. Approach for both qulitative and quantitative analysis of the noise effect in a nonlinear system under harmonic excitation is presented. For the qualitative analysis, Lyapunov exponents are calculated and Poincar map is illustrated. For the quatitative analysis. Fokker-Planck equatin is solved numerical by means of a Path-integral solution procedure. Eigenvalue problem obtained from the numerical caculation is solved and the relation of eigenvalue, eigenvector and chaotic motion is investigated.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.171-182
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• 2005

An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures, the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the non-homogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only.