• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.719-736
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• 2005

An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2000.11a
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• pp.29-33
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• 2000

The classical image reconstruction for stripmap SAR is based on the Fresnel approximation which utilizes deramping or chirp deconvolution in the synthetic aperture(slow-time) domain. Another approach in formulating stripmap SAR processing and imaging is based on the SAR wavefront reconsturction theory, and analysis of the SAR signal in the slow-time via the spherical wave Fourier decomposition of the radar radiation pattern. In this paper, we compare the Fresnel approximation and the wavefrong reconstruction methods using simulated stripmap SAR dada.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.4
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• pp.67-75
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• 1993

The Fourier series are employed to approximate the input/output(I/O) characteristics of a dynamic system and, based on the approximation, a new learing control algorithm is proposed in order to find iteratively the control input for tracking a desired trajectory. The use of the Fourier approximation of I/O renders at least a couple of useful consequences: the frequency characteristics of the system can be used in the controller design and the reconstruction of the system states is not required. The convergence condition of the proposed algorithm is provided and the existence and uniqueness of the desired control input is discussed. The effectiveness of the proposed algorithm is illustrated by computer simulation for a robot trajectory tracking. It is shown that, by adding feedback term in learning control algorithm, robustness and convergence speed can be improved.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.255-262
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• 1998

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the probability density function. In Section 3, we represent a numerical example which shows that the errors are small even for small sample size.

• Current Optics and Photonics
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• v.5 no.5
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• pp.491-499
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• 2021

A scalar Fourier modal method for the numerical analysis of the scalar wave equation in inhomogeneous space with an arbitrary permittivity profile, is proposed as a novel theoretical embodiment of Fourier optics. The modeling of devices and systems using conventional Fourier optics is based on the thin-element approximation, but this approach becomes less accurate with high numerical aperture or thick optical elements. The proposed scalar Fourier modal method describes the wave optical characteristics of optical structures in terms of the generalized transmittance function, which can readily overcome a current limitation of Fourier optics.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.415-428
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• 1999

In this paper, we study the saddlepoint approximations for the ratio of two independent sequences of random variables. In Section 2, we review the saddlepoint approximation to the probability density function. In section 3, we derive an saddlepoint approximation formular for the tail probability by following Daniels'(1987) method. In Section 4, we represent a numerical example which shows that the errors are small even for small sample size.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Tribology and Lubricants
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• v.17 no.5
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• pp.391-398
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• 2001

Two dimensional slow viscous flow around two counter-rotating equal cylinders is investigated based on Stokes'approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is also determined as the distance between two cylinders varies. Special attention is directed to the case of very small distance between two cylinders concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.06a
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• pp.142-149
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• 2000

Two dimensional slow viscous flow around two counter-rotating equal cylinders is Investigated based on Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution In the flow field is determined. By Integrating the stress distribution on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is determined as the distance between two cylinders vary. It Is also revealed that the velocity at the far field has finite non-zero value. Special attention is directed to the case of very small distances between two cylinders by way of the lubrication theory.