• Transactions of Materials Processing
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• v.12 no.2
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• pp.142-150
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• 2003

To construct the extrusion die surface, a B-Spline surface scheme based on the cubic B-Spline curve interpolation method is proposed in the present work. The inlet and outlet profiles are described with B-Spline curves by using the centripetal method for uniform parameterization. The interior control points of surface are generated using the derivative characteristics of B-Spline curve. A complete B-Spline surface is constructed by using appropriate coordinate transformation and knot deletion. In the present study, a quantitative measure for the control of surface is suggested by introducing the tangential vector and inclination angles at the inlet and outlet sections. To verify the validity of the proposed method, automatic surface generation is carried out for the various types of extrusion die surface.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.783-795
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• 2019

We prove that a Lorentzian concircular structure (LCS)-manifold does not admit any null hypersurface which is tangential or transversal to its characteristic vector field. Due to the above, we focus on its ascreen null hypersurfaces and show that such hypersurfaces admit a symmetric Ricci tensor. Furthermore, we prove that there are no totally geodesic ascreen null hypersurfaces of a conformally flat (LCS)-manifold.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.121-126
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• 2008

A plane strain problem of a crack on interface between an isotropic elastic conductor and a transversely isotropic piezoelectric ceramics is considered. The problem is reduced to system integrodifferential equations on the interface. These equations relate the normal and tangential components of the crack opening vector with distribution of normal and shear stresses on the crack surfaces. It therefore make it possible to obtain an exact solution as a function of the loading applied to the crack surfaces. As an example, some analytical solutions of the crack problem are given.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.185-195
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• 2012

We study the geometry of lightlike hypersurfaces M of an inde nite cosymplectic manifold $\bar{M}$ such that either (1) the characterist vector field $\zeta$ of $\bar{M}$ belongs to the screen distribution S(TM) of M or (2) $\zeta$ belongs to the orthogonal complement $S(TM)^{\perp}$ of S(TM) in $T\bar{M}$.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.7
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• pp.1061-1066
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• 1994

The eddy currents of 3-dimensional conductin medium are calculated using vectorial Boundary element Method with vector variables E and H. Boundary edge basis vectors are used to expand the tangential components of E and H fields. Especially for axisymmetric conductor the computer storage and the computation time are greatly saved with the help of block-circulant boundary meshes. to verify this method eddy currents of conducting sphere are computed and show good agreements with the analytic solutions.

• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.89-101
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• 2013

In this paper, we study half lightlike submanifolds M of an indefinite cosymplectic manifold $\bar{M}$, whose structure vector field is not tangent to M. First, we construct two types of such half lightlike submanifolds, named by transversal and normal half lightlike submanifolds. Next, we characterize the lightlike geometries of such two types half lightlike submanifolds.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.1
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• pp.8-15
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• 2003

The cylindrical object such as a water pipe or an oil pipeline are widely used in the infrastructure. Those pipes should be inspected periodically by human or a robot. However, since there is no edge or vertex in the pipe, it is very difficult for the robot to navigate along the pipe. In this paper in order to guide the robot along the axis of the pipe, an algorithm which find the axis using the measured range data from the robot to the pipe wall is developed The algorithm is verified using both the simulated range data and the measured one.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2003.04a
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• pp.234-239
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• 2003

A cylindrical shape object is widely used as a mechanical part and a water pipe or an oil pipeline which are of cylindrical shape are widely used in the infrastructure. In order to handling such objects automatically using a robot, the posture i.e. orientation in 3D space should be recognized. However, since there is no edge or vertex in the pipe, it is very difficult task for the robot. In this paper in order to guide the robot, two kind of algorithms which find the axis using the measured range data from the robot to the object surface are to be developed. The algorithms are verified using both the simulated range data and the measured one.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.9
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• pp.1005-1014
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• 2004

Experiments were done for the three dimensional unsteady flow in a counter-rotating axial flow fan under peak efficiency operating condition. Flow fields in a counter rotating axial flow fan were measured at cross-sectional planes of the upstream and downstream of each rotor. Cross sectional flow patterns were investigated through the acquired data by the 45$^{\circ}$ inclined hot-wire. Flow characteristics such as tip vortex, secondary flow and tip leakage flow were confirmed through axial, radial and tangential velocity vector plot. It has been found that the radial and tangential velocity components disappeared, while the axial velocity component highly increased as soon as the tip vortex was generated. It has been observed that secondary flow and turbulence intensity which were increased by the front rotor were dissipated passing through the rear rotor. As the result the energy loss of the counter rotating axial flow fan decreased at the downstream of rear rotor. Also, it has been verified that tip vortex pattern of the rear rotor was dampened because the tip vortex generated by front rotor was mixed with that of the rear rotor.