• 비파괴검사학회지
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• 제31권6호
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• pp.665-670
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• 2011

In this paper, a new approach to detect surface cracks from a noisy thermal image in the infrared thermography is presented using an holomorphic characteristic of temperature field in a thin plate under steady-state thermal condition. The holomorphic function for 2-D heat flow field in the plate was derived from Cauchy Riemann conditions to define a contour integral that varies according to the existence and strength of a singularity in the domain of integration. The contour integral at each point of thermal image eliminated the temperature variation due to heat conduction and suppressed the noise, so that its image emphasized and highlighted the singularity such as crack. This feature of holomorphic function was also investigated numerically using a simple thermal field in the thin plate satisfying the Laplace equation. The simulation results showed that the integral image selected and detected the crack embedded artificially in the plate very well in a noisy environment.

• Journal of the Korean Statistical Society
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• 제17권1호
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• pp.24-29
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• 1988

The asymptotic distribution of the sample partial autocorrelation terms after lag p of an AR(p) model has been shown by Dixon(1944). The derivation is based on multivariate analysis and looks tedious. In this paper we present an interesting contour-integral derivation.

• 대한수학회논문집
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• 제36권2호
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• pp.277-298
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• 2021

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

• 한국해양공학회지
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• 제18권1호
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• pp.7-9
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• 2004

Using the solution to th contour integral of the complex logarithmic function ${\oint}_cIn(z-z_{0})dz$, the following definite integral, derived from the formula to calculate the forces exerted to n circular cylinder by the discrete vortices shed from it, has been evaluated (equation omitted)

• 대한수학회논문집
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• 제17권4호
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• pp.731-740
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• 2002

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

• Selected Papers of The Society of Naval Architects of Korea
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• 제2권1호
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• pp.1-17
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• 1994

For a planar curve-sided panel with constant or linear density distributions of source or doublet in the singularity methods, Cantaloube and Rehbach show that the surface integral can be transformed into contour integral by using Stokes'formulas. As an extension of their formulations, this paper deals with a planar polygonal panel for which we derive the closed-forms of the potentials and the velocities induced by the singularity distributions. Test calculations show that the analytical evaluation of the closed-forms is superior to numerical integration (suggested by Cantaloube and Rehbach) of the contour integral. The compact and explicit expressions may produce accurate values of matrix elements of simultaneous linear equations in the singularity methods with much reduced computer time.

• 대한수학회보
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• 제54권6호
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• pp.1951-1967
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• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

• 대한수학회논문집
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• 제17권1호
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• pp.15-20
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• 2002

We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

• 대한수학회논문집
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• 제37권1호
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• pp.207-212
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• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• 대한조선학회논문집
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• 제29권1호
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• pp.14-28
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• 1992

평면판 요소에 균일한 혹은 선형적인 세기를 갖는 쏘오스 또는 다이폴이 분포된 경우, Stokes 정리를 이용하여, 표면 특이점 분포방법에서 나타나는 표면 적분식을 선적분 형태로 변환할 수 있다. 더우기 판요소가 다각형인 경우, 유기 포텐시얼과 유기속도를 구하기 위한 이 선적분의 closed-forms을 유도하였다. 이들 적분식의 해석적 계산을 통해 계산시간을 단축하고 수치해의 정도를 향상시킬 수 있을 것이다. 몇개의 계산예를 통해 해석적 적분 계산이 수치적 적분보다 우수함을 알 수 있다.