• Nuclear Engineering and Technology
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• v.53 no.8
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• pp.2556-2563
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• 2021

Metaheuristic algorithms can work well in solving or optimizing problems, especially those that require approximation or do not have a good analytical solution. Particle swarm optimization (PSO) is one of these algorithms. The response quality of these algorithms depends on the objective function and its regulated parameters. The nonlinear nature of the pressurized light-water nuclear reactor (PWR) dynamics is a significant target for PSO. The two-point kinetics model of this type of reactor is used because of fission products properties. The proportional-integral-derivative (PID) controller is intended to control the power level of the PWR at a short-time transient. The absolute error (IAE), integral of square error (ISE), integral of time-absolute error (ITAE), and integral of time-square error (ITSE) objective functions have been used as performance indexes to tune the PID gains with PSO. The optimization results with each of them are evaluated with the number of function evaluations (NFE). All performance indexes achieve good results with differences in the rate of over/under-shoot or convergence rate of the cost function, in the desired time domain.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.33-45
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• 2002

An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.17-31
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• 2002

Using some techniques developed by Dragomir and Wang in the recent paper [2] in connection to Ostrowski integral inequality, we point out some approximation results for the Henkel's transform of absolutely continuous mapping.

• Journal of the Optical Society of Korea
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• v.2 no.2
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• pp.58-63
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• 1998

Cross-talk effects in high-density volume holographic interconnections are investigated using perturbative iteration method of the integral form of Maxwell's wave equation. In this method, the paraxial approximation and negligence of backward scattering introduced in conventional coupled mode theory is not assumed. Interaction geometries consisting of non-coplanar light waves and multiple index gratings are studied. Arbitrary light polarization is considered. Systematic analysis of cross-talk effects due to multiple index gratings is performed in increasing level of diffraction orders corresponding to successive iterations. Some numerical examples are given for first and third order diffraction.

• Journal of the Optical Society of Korea
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• v.1 no.2
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• pp.67-73
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• 1997

Light wave diffraction from multiple superposed volume gratings is inestigated using a perturbative iteration method of the integral equation of Maxwell's wave equation. The host material and index gratings are anisotropic and non-coplanar multiple volume gratings are considered. In this method, the paraxial approximation and lack of backward scattering in conventional coupled mode theory are not assumed. Systematic analysis of anisotropic wave diffraction due to multiple noncoplanar volume index gratings is performed in increasing level of diffraction orders corresponding to successive iterations.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.593-604
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• 2003

In this paper we introduce the integral type Lupas-$B{\acute{e}}zier$ operator $\tilde{B}_{n,{\alpha}}$, which is a new approximation operator of probabilistic type. We study the rate of pointwise convergence of the operators $\tilde{B}_{n,{\alpha}}$ for local bounded functions and get an asymptotically estimate by means of some methods and techniques of probability theory.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.337-348
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• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.801-812
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• 2000

Two-dimensional slow viscous flow on infinite half-plane past a perpendicular infinite cavity is considered on the basis of the Stokes approximation. Using complex representation of the two-dimensional Stokes flow, the problem is reduced to solving a set of Fredholm integral equations of the second kind. The streamlines and the pressure and vorticity distribution on the wall are numerically determined.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.795-802
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• 2002

For assessing significance of a defect in a component operating at high (creeping) temperatures, accurate estimation of fracture mechanics parameter, $C^{*}$-integral, is essential. Although the J estimation equation in the GE/EPRl handbook can be used to estimate the $C^{*}$-integral when the creep -deformation behavior can be characterized by the power law creep, such power law creep behavior is a very poor approximation for typical creep behaviors of most materials. Accordingly there can be a significant error in the $C^{*}$-integral. To overcome problems associated with GE/EPRl approach, the reference stress approach has been proposed, but the results can be sometimes unduly conservative. In this paper, a new method to estimate the $C^{*}$-integral for deflective components is proposed. This method improves the accuracy of the reference stress approach significantly. The proposed calculations are then validated against elastic -creep finite element (FE) analyses for four different cracked geometries following various creep -deformation constitutive laws. Comparison of the FE $C^{*}$-integral values with those calculated from the proposed method shows good agreements.greements.