• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.267-277
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• 2019

In this study, we define the dual surfaces by z = f(u) + g(v) and also classify these surfaces in ${\mathbb{I}}{\frac{1}{3}}$ satisfying some algebraic equations in terms of the coordinate functions and the Laplace operators according to fundamental forms of the surface.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.185-195
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• 2019

In this work, we study the conditions between null geodesic curves and timelike ruled surfaces in dual Lorentzian space. For this study, we establish a system of differential equations characterizing timelike ruled surfaces in dual Lorentzian space by using the invariant quantities of null geodesic curves on the given ruled surfaces. We obtain the solutions of these systems for special cases. Regarding to these special solutions, we give some results of the relations between null geodesic curves and timelike ruled surfaces in dual Lorentzian space.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.421-424
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• 2007

Dry sliding wear behavior of ultra-fine grained (UFG) plain low carbon dual phase steel, of which microstructure consists of hard martensite in a ductile ferrite matrix, has been investigated. The wear characteristics of the UFG dual phase steel was compared with that of a coarse grained dual phase steel under various applied load conditions. Dry sliding wear test were carried out using a pin-on-disk type tester at various loads of 1N to 100N under a constant sliding speed condition of 0.20m/s against an AISI 52100 bearing steel ball at room temperature. The sliding distance was fixed as 1000m for all wear tests. The wear rate was calculated by dividing the weight loss, measured to the accuracy of 10-5g by the specific gravity and sliding distance. The worn surfaces and wear debris were analyzed by SEM, EDS and profilometer. Micro-vickers hardness of the cross section of worn surfaces were conducted to analyze strain hardening underneath the contact surfaces. The wear mechanism of the UFG dual phase steel was investigated with emphasis on the unstable nature of the grain boundaries of the UFG microstructure.

• Transactions of Materials Processing
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• v.16 no.4 s.94
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• pp.299-303
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• 2007

Dry sliding wear behavior of ultra-fine grained(UFG) plain low carbon dual phase steel, of which microstructure consists of hard martensite in a ductile ferrite matrix, has been investigated. The wear characteristics of the UFG dual phase steel was compared with that of a coarse grained dual phase steel under various applied load conditions. Dry sliding wear test were carried out using a pin-on-disk type tester at various loads of 1N to 100N under a constant sliding speed condition of 0.20m/s against an AISI 52100 bearing steel ball at room temperature. The sliding distance was fixed as 1000m for all wear tests. The wear rate was calculated by dividing the weight loss, measured to the accuracy of 10-5g by the specific gravity and sliding distance. The worn surfaces and wear debris were analyzed by SEM, EDS and profilometer. Micro-vickers hardness of the cross section of worn surfaces were conducted to analyze strain hardening underneath the contact surfaces. The wear mechanism of the UFG dual phase steel was investigated with emphasis on the unstable nature of the grain boundaries of the UFG microstructure.

• Korean Journal of Computational Design and Engineering
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• v.10 no.1
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• pp.27-39
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• 2005

Implicit surfaces are geometric shapes which are defined by implicit functions and exist in three-dimensional space. Recently, implicit surfaces have received much attention in solid modeling applications because they are easy to represent the location of points and to use boolean operations. However, it is difficult to chart points on implicit surfaces for rendering. As efficient rendering method of implicit surfaces, the original Adaptively Sampled Distance Fields (ADFs) $method^{[1]}$ is to use sampled distance fields which subdivide the three dimensional space of implicit surfaces into many cells with high sampling rates in regions where the distance field contains fine detail and low sampling rates where the field varies smoothly. In this paper, in order to maintain the sharp features efficiently with small number of cells, an extended ADFs method is proposed, applying the Dual/Primal mesh optimization $method^{[2]}$ to the original ADFs method. The Dual/Primal mesh optimization method maintains sharp features, moving the vertices to tangent plane of implicit surfaces and reconstructing the vertices by applying a curvature-weighted factor. The proposed extended ADFs method is applied to several examples of implicit surfaces to evaluate the efficiency of the rendering performance.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.482-487
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• 2002

This paper presents a robot trajectory generation method based on the dual curvature theory of ruled surfaces. Robot trajectory can be represented as a ruled surface generated by the TCP(Tool Center Point) and my unit vector among the tool frame. Dual curvature theory of ruled surfaces provides the robot control algorithm with the motion property parameters. With the differential properties of the ruled surface, the linear and angular motion properties of the robot end effector can be utilized in the robot trajectory planning.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.739-753
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• 2014

In this study, it is aimed to analyze how relationship among Blaschke vectors that the obtained formulae in [2, 3] change if parameter ruled surfaces of the spacelike line congruence are not choosed as principle ruled surfaces. Moreover, using the relation among Blaschke vectors, we obtain Manheim's and Liouville's formulae. This new method can be applied to congruences. Thus, we can obtain new formulae in lines space.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.05a
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• pp.149-152
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• 2006

Dry sliding wear behavior of low carbon dual phase steel, of which microstructure consists of hard martensite in a ductile ferrite matrix, has been investigated. The wear characteristics of the dual phase steel was compared with that of a plain carbon steel which was normalized at $950^{\circ}C$ for 30min and then air-cooled. Dry sliding wear tests were carried out using a pin-on-disk type tester at various loads of 1N to 10N under a constant sliding speed condition of 0.2m/sec against an AISI 52100 bearing steel ball at room temperature. The sliding distance was fixed as 1000m for all wear tests. The wear rate was calculated by dividing the weight loss measured to the accuracy of $10^{-5}g$ by the specific gravity and sliding distance. The worn surfaces and wear debris were analyzed by SEM, EDS and a profilomter. Micro vickers hardness values of the cross section of worn surface were measured to analyze strain hardening behavior underneath the wearing surfaces. The were rate of the dual phase steel was lower than the plain carbon steel. Oxidation on the sliding surface and strain hardening were attributed for the higher wear resistance of the dual phase steel.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1339-1355
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• 2006

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

• KSTLE International Journal
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• v.8 no.2
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• pp.26-28
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• 2007

Si(100) surfaces were topographically modified i.e. the surfaces were patterned at micro-scale using photolithography and DRIE (Deep Reactive Ion Etching) fabrication techniques. The patterned shapes included micro-pillars and microchannels. After the fabrication of the patterns, the patterned surfaces were chemically modified by coating a thin DLC film. The surfaces were then evaluated for their friction behavior at micro-scale in comparison with those of bare Si(100) flat, DLC coated Si(100) flat and uncoated patterned surfaces. Experimental results showed that the chemically treated (DLC coated) patterned surfaces exhibited the lowest values of coefficient of friction when compared to the rest of the surfaces. This indicates that a combination of both the topographical and chemical modification is very effective in reducing the friction property. Combined surface treatments such as these could be useful for tribological applications in miniaturized devices such as Micro-Electro-Mechanical-Systems (MEMS).