• 대한수학회논문집
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• 제11권4호
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• pp.975-981
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• 1996

Let $D \subset C^2$ be a bounded convex domain with real analytic boundary. We get some Lipschitz regularity of the Cauchy transform on the convex domain D.

• 대한수학회보
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• 제56권4호
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• pp.929-937
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• 2019

The main purpose of this paper is to establish $H{\ddot{o}}lder$ estimates for the Cauchy transform in a class of finite/infinite type convex domains in $\mathbb{C}^2$.

• 대한수학회보
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• 제42권4호
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• pp.725-738
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• 2005

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.481-493
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• 2007

This paper deals with, by employing the relation between Cauchy representation and the Fourier transform and properties of the former in $L_1$-space, the investigation of the Cauchy representation of integrable Boehmians as a natural extension of tempered distributions, we have investigated Cauchy representation of tempered Boehmians. An inversion formula is also proved.

• 대한수학회보
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• 제39권4호
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• pp.543-559
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• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• 한국정밀공학회지
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• 제17권9호
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• pp.151-157
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• 2000

Stress intensity factors for the circumferential surface crack of a long composite cylinder under torsion is investigated. The problem is formulated as a singular integral equation of the first kind with a Cauchy type kernel using the integral transform technique. The mode III stress intensity factors at the crack tips are presented when (a) the inner crack tip is away from the interface and (b) the inner crack tip is at the interface.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Structural Engineering and Mechanics
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• 제91권5호
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• pp.459-468
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• 2024

This study presents a frictionless receding contact problem for an orthotropic elastic layer. It is assumed that the layer is supported by two rigid quarter planes and the material of the layer is orthotropic. The layer of thickness h is indented by a rigid cylindrical punch of radius R. The problem is modeled by using the singular integral equation method with the help of the Fourier transform technique. Applying the boundary conditions of the problem the system of singular integral equations is obtained. In this system, the unknowns are the contact stresses and contact widths under the punch and between the layer and rigid quarter planes. The Gauss-Chebyshev integration method is applied to the obtained system of singular integral equations of Cauchy type. Five different orthotropic materials are considered during the analysis. Numerical results are presented to interpret the effect of the material property and the other parameters on the contact stress and the contact width.

• 대한조선학회논문집
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• 제30권2호
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• pp.86-97
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• 1993

수치방법은 포텐셜 유동의 가정하에서 Semi-Lagrangian 기법을 사용하여 2차원 쇄기의 비선형운동과 축대칭 물체의 강제 상하동요 운동에 대해서 개발되었다. 2차원에서 Cauchy 이론은 경계를 따라서 복소포텐셜과 그것의 미분치를 계산하기 위해 적용되었고, 3차원에서 Rankinering 쏘오스가 사용되고 대수방정식을 풀기위해서 그린 제2정리를 이용하였다. 해는 완전한 사유표면 조건을 수치적분함으로서 시간전진시킨다. 수치계산 예는 정속도로 입수하는 쇄기형 주상체와 정지 상태로 부터 강제상하동요하는 문제를 택하였다. 쇄기입수 문제는 Chapman [4], Kim[11]의 계산결과와 비교된다. 위에서 적용된 기법을 이용하여 구한 시간영역에서 힘을 Fourier 변환함으로서 부가질량계수, 감쇄계수, 2차조화력등이 얻어지고 Yamashita[5]의 실험치와 비교된다.