• 대한수학회보
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• 제58권5호
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Bulletin of the Korean Chemical Society
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• 제17권2호
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• pp.188-192
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• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• 대한수학회지
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• 제58권4호
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• pp.873-894
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• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• 호남수학학술지
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• 제45권3호
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• pp.457-470
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• 2023

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

• 대한수학회보
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• 제60권1호
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• pp.93-111
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• 2023

In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-α model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.

• 한국정밀공학회지
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• 제14권2호
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• pp.152-159
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• 1997

The asymptotic convergence of a coupled dynamic system, which is motivated from infinite dimensional adaptive systems, is investigated. The convergence analysis is formulated in abstract Banch spaces and is shown to applicable to a broad class of infinite dimensional systems including adaptive identification and adaptive control. Particularly it is shown that if a uniquely existing solution is p-th power integrable, then the solution converges to zero asymptotically. The persistence of excitation(PE) of a signal which arises in an infinite dimensional adaptive system is investigated. The PE property is not completely known yet for infinite dimensional adaptive systems, however it should be investigated in relation to spatial variable, boundary conditions as well as time variable.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• 대한조선학회논문집
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• 제45권5호
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• pp.477-486
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• 2008

Numerical analysis for slamming impact phenomena has been carried out when 2-dimensional wedge shaped structure with finite deadrise angles enter the free surface by using a commertial CFD code, FLUENT. Fluid is assumed incompressible and entry speed of the structure is kept constant. Geo-reconstruct scheme (or PLIC-VOF scheme) is used for the tracking of the deforming free surface. User defined function of 6 degrees of freedom motion and moving dynamic mesh option are used for the expression of the downward motion of the structure and deforming of unstructured meshes adjacent to the structure. The magnitude and the location of impact pressure and the total drag force which is the summation of pressures distributed at the bottom of the structure are analyzed. Results of the analysis show good agreement with the results of similarity solution, asymptotic solution and the solution of BEM.

• 대한화학회지
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• 제18권5호
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• pp.307-319
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• 1974

2-전향점 문제의 Uniform WKB 파동함수의 정밀도를 대응하는 수치해와 비교하고 검토한 결과 Uniform WKB 파동함수가 대단히 정밀하다는 것을 발견하였다. 그러한 파동함수의 응용의 예로서 model계에 대한 Franck-Condon 인자들을 계산하였으며 계산된 인자들의 정밀도도 역시 매우 높다는 것을 보였다. Uniform WKB파동함수를 이용하여 Franck-Condon 인자의 점근치를 검토하였으며 전환진동수에 대한 Mulliken 의 조건, $E'_{n'J'}-U'_{eff}(r_s)=E"_{n"J"}-U"_{eff}(r_s),$ 을 유도하였다.

• Nuclear Engineering and Technology
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• 제24권3호
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• pp.228-235
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• 1992

처분된 폐기물에서 용해도가 큰 핵종이 침출될 때, 그 핵종의 용해도에 의해 조절되거나 조화 용해하지 않는 경우가 있다. 예를 들면 원자로 운영시 핵분열 생성물의 일부는 그레인 경계나 핵연료와 피복재 사이의 틈새에 축적될 수가 있다. 사용후 핵연료 처분장에서 이와 같이 축적된 핵분열 생성물중 세슘이나 요오드와 같이 용해도가 큰 핵종은 용기가 부식되면 지하수내에 급격하게 녹게된다. 이와 같이 틈새에 녹아있는 용해도가 큰 핵종의 이동현상을 시간 및 공간의 함수로 모사하고 그 수치 결과를 제시하였다. 전구간에서 유효한 근사해를 제시하고 이를 초기 및 후기 접근해와 Laplace 변환을 수치 재변환으로 얻은 해들과 비교함으로 검증하였다.