• Journal for History of Mathematics
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• v.21 no.3
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• pp.67-96
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• 2008

In the 19th century Fourier and Dirichlet studied the expansion of "arbitrary" functions into the trigonometric series and this led to the development of the Riemann's definition of the integral. Riemann's integral was considered to be of the highest generality and was discussed intensively. As a result, some weak points were found but, at least at the beginning, these were not considered as the criticism of the Riemann's integral. But after Jordan introduced the theory of content and measure-theoretic approach to the concept of the integral, and after Borel developed the Jordan's theory of content to a theory of measure, Lebesgue joined these two concepts together and obtained a new theory of integral, now known as the "Lebesgue integral".

• Aerospace Engineering and Technology
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• v.13 no.2
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• pp.60-65
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• 2014

In this paper, numerical integration method using operational matrix of integration is studied. Using the operational matrix of integration, modified fixed point iteration method is introduced in order to solve rapidly an initial value problem for non-linear equation of motion. As an example, an initial value problem for orbital motion is considered. Through the numerical example, it is shown that the algorithm is efficient from the computational time point of view.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.107-117
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• 2005

In this paper, we introduce linear approximate Henstock integral equations that is slightly different from linear Henstock integral equations, and we also offer an example which shows that some integral equation has a solution in the sense of the approximate Henstock integral but does not have any solutions in the sense of the Henstock integral. Furthermore, we investigate the existence and uniqueness of solution of the approximate Henstock integral equation.

• Journal of the Korea Society of Computer and Information
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• v.3 no.4
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• pp.55-62
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• 1998

This Paper proposed a systolic Arrays architecture for computing Romberg's integration method. It consists of systolic arrays of two stage, one for integration by Trapezoidal rule and the other for integration by using Richardson's extrapolation. the proposed its architecture is very high speed and regular. This paper illustrates how " mathematical hardware " package, as well as software library routines, may be part of the mathematical problem solver's tool kit in the future.he future.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.6
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• pp.8-14
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• 1998

The derivation of the dual integral equation in the spectral domain, which has total fields of the interfaces as unknowns, is investigated. It is analytically shown that the derivation of the dual integral equation is equivalent to deriving the Helmholtz-Kirchhoff integral equation from the Wiener-Hopf integral equation.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.28 no.6
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• pp.573-578
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• 2010

Precise determination of satellite positions is necessary to improve positioning accuracy in GNSS. In this study, GLONASS orbits were predicted from broadcast ephemeris using the 4th-order Runge-Kutta numerical integration method and their accuracy dependence on the integration step and the integration time was analyzed. The 3D RMS (Root Mean Square) differences between the results from I-second integration step and 300-second integration step was about 3 cm, but the processing time was one hundred times less for the I-second integration time case. For trials of different integration times, the 3D RMS errors were 8.3 m, 187.3 m, and 661.5 m for 30-, 150-, and 300-minutes of integration time, respectively. Though this integration-time analysis, we concluded that the accuracy gets higher with a shorter integration time. Thus we suggest forward and backward integration methods to improve GLONASS positioning accuracy, and with this method we can achieve a 5-meter level of 3-D orbit accuracy.

• Geophysics and Geophysical Exploration
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• v.3 no.1
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• pp.13-18
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• 2000

We describe the concept of the singularity in the integral equation of electromagnetic (EM) modeling in comparison with that in the integral representation of electric fields in EM theory, which would clarify the singular integral problems of the Green's tensor. We have also derived and classified the singular integrals of the Green's tensors in 3-D, 2.5-D and 2-D as well as in the thin sheet integral equations of the EM scattering problem, which have the most important effect on the accuracy of the numerical solution of the problems.

• Journal of Korean Society of Steel Construction
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• v.17 no.2 s.75
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• pp.243-251
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• 2005

The fracture mechanics analysis of a crack in a weld must consider residual stress generated during welding. The standard definition of the J-integral requires a path dependent value in the presence of a residual stress field. Therefore, it is necessary to develop a path independent J-integral definition for a crack in a residual stress field. This paper addresses the modification of the Rice-J-integral to produce a path- independent J-integral when residual stresses and external forces are present. The residual stress problem is treated as an initial strain problem and the J-integral proposed for this type of problems is used. A program which can evaluate the J-integral for a crack in a weld is developed using the proposed J-integral definition. The situation when only residual stress is present is examined as is the case when mechanical stresses are applied in conjunction with a residual stress.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.423-431
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• 2004

For the fracture mechanics analysis of cracks in welds of dissimilar steels, residual stress analysis and fracture analysis must be performed simultaneously. The standard definition of the J -integral leads to a path dependent value in the presence of a residual stress field. And unlike cracks in homogeneous materials, a bimaterial interface crack always induces both opening and shearing modes of stress in the vicinity of the crack tip. Therefore, it is necessary to develope a path independent J-integral definition for a crack in a residual stress field generated by welding of dissimilar steels. This paper addresses the modification of the Rice-J-integral to produce a path independent J -integral when residual stresses due to welding of dissimilar steels and external forces are present. The residual stress problem is treated as an initial strain problem and the J-integral proposed for this class of problems is used. And a program which can evaluate the J -integral for a crack in a weld of dissimialr steels is developed using proposed J integral definition.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.1
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• pp.96-102
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• 1983

복사 형상계수를 계산하는 새롭고도 간단한 수치적 방법이 개발되었다. 유한선분 적분법은 윤 곽적분을 이용하며, 윤곽은 유한한 수의 선분으로 구성된 것으로 가정한다. 미소면적으로부터 유한면적까지의 복사 형상계수는 적분로 상의 절점의 좌표값에만 관계되며, 전자 계산기에 쉽게 프로그램 될 수 있다. 가우스의 적분을 이용하여 두 유한 면적사이의 복사 형상계수를 구한다. 미소 면적에서 원판까지, 두 개의 평행원판 사이, 및 두 개의 직사각형 사이의 복사 형상계수를 구하여 엄밀해와 비교하여 유한선분 적분법의 정확성이 우수함을 보였다. 단위구와 단위 정사 각형에서 타원체까지의 보가 형상계수의 값도 구하였다.