• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.585-597
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• 2020

In this study, we classify surfaces of revolution of Type 1 in the three dimensional Galilean space 𝔾₃ in terms of the position vector field, Gauss map, and Laplacian operator of the first and the second fundamental forms on the surface. Furthermore, we give a classification of surfaces of revolution of Type 1 generated by a non-isotropic curve satisfying the pointwise 1-type Gauss map equation.

• Journal of the military operations research society of Korea
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• v.23 no.1
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• pp.76-87
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• 1997

This paper deals with reliability and MTTF analysis of a non-repairable man-machine system operating under different weather conditions. The system consists of a hardware(machine) and a two-operator standby subsystem such as the air combat maneuvering of fighters with dual seat. The failure times for the subsystems follow the exponential distribution with constant parameter. By considering not only the effect on hardware component but also the weather conditions and human performance factors such as the operator's errors, a Markov model is presented as a method for evaluating the system reliability of time continuous operation tasks. Laplace transforms of the various state probabilities have been derived and then reliability of the system, at any time t, has been computed by inversion process. MTTF has also been computed.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.10
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• pp.822-831
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• 2003

A computer-vision based pipe-inspection algorithm is developed. The algorithm uses the modified Hough transformation and a line-scanning approach to identify the edge line and the radius of the pipe image, from which the eccentricity and dimension of the pipe-end is calculated. Line and circle detection was performed using Laplace operator with input image, which are acquired from the front and side cameras. In order to minimize the memory usage and the processing time, a clustering method with the modified Hough transformation is introduced for line detection. The dimension of inner and outer radius of pipe is calculated by the proposed line-scanning method. The method scans several lines along the X and Y axes, calculating the eccentricity of inner and outer circle, by which pipes with wrong end-shape can be classified and removed.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1241-1254
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• 2017

In this paper, we classify translation surfaces in the three dimensional Galilean space ${\mathbb{G}}_3$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the second fundamental form of the surface. We also give explicit forms of these surfaces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.946-950
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• 2003

In this paper, a computer-vision based pipe shape inspection algorithm is developed. The algorithm uses the modified Hough transformation and a line-scanning approach to identify the edge line and radius of the pipe image, from which the eccentricity and dimension of the pipe-end is calculated. Line and circle detection was performed using Laplace operator with input image, which are acquired from the front and side cameras. In order to minimize the memory usage and the processing time, a clustering method with the modified Hough transformation for line detection. The dimension of inner and outer radius of pipe is calculated by proposed line-scanning method. The method scans several lines along the X and Y axes, calculating the eccentricity of inner and outer circle. by which pipes with wrong end-shape can be classified removed.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.953-965
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• 2017

In this paper, we classify translation surfaces of Type 2 in the three dimensional simply isotropic space ${\mathbb{I}}_3^1$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.521-525
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• 2002

In this paper, a computer-vision based pipe-inspection algorithm is developed. The algorithm uses the modified Hough transformation and a line-scanning approach to identify the edge line and radius of the pipe image, from which the eccentricity and dimension of the pipe-end is calculated. Line and circle detection was performed using Laplace operator with input image, which are acquired from the front and side cameras. In order to minimize the memory usage and the processing time, a clustering method with the modified Hough transformation for line detection. The dimension of inner and outer radius of pipe is calculated by proposed line-scanning method. The method scans several lines along the X and Y axes, calculating the eccentricity of inner and outer circle, by which pipes with wrong end-shape can be classified removed.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.149-158
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• 2013

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.