• Journal of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.415-427
• /
• 2020

By using the support functions on the xy-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.383-405
• /
• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Journal for History of Mathematics
• /
• v.12 no.2
• /
• pp.25-39
• /
• 1999

In Euclidean plane geometry, areas of polygons can be computed through a finite process of cutting and pasting. The Hilbert's third problem is that a theory of volume can not be based on the idea of cutting and pasting. This problem was solved by Dehn a few months after it was posed. The purpose of this article is not only to study Hilbert's third Problem and its proof but also to provide basis for the secondary school mathematics.

• The Mathematical Education
• /
• v.41 no.1
• /
• pp.79-90
• /
• 2002

In this article we study on connecting paper 131ding activities of triangle with mathematical proof Folding median, bisector of angle, and hight of paper triangle, we from and extract some ideas that help us to proof some important theorems of plane geometry. In this study using formed ideas in the process of paper folding activities, we suggest some interesting new mathematical proofs of the following theorems: 1. three medians of triangle are intersect in a point; 2. three bisectors of interior angles of triangle are intersect in a point; 3. three heights of triangle are intersect in a point.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2002.05a
• /
• pp.187-190
• /
• 2002

To study adiabatic shear band formation of tungsten heavy alloys, 5 prismatic specimens are loaded by high velocity impacts and treated as plane strain problems. Their volume percent of tungsten particles in WHA are 81%, 93% and 97% respectively and for the fixed 81% volume percent, small size particle model, large size particle model, undulated particle models are considered and then, the effects of particle's volume ratio, geometry and size to the formation of shear band are discussed.

• Journal of the Korean Society for Precision Engineering
• /
• v.5 no.1
• /
• pp.29-39
• /
• 1988

Plastically deformed layer beneath metal surface machined by orthogonal cutting was evaluated in terms of residual stress, microvickers hardness, side spread, and the side strain. An attempt was made to predict the depth of layer according to machining conditions particularly tool geometry and the shear plane angle. In this paper, we employed two models concerning the sliplines. The exact model was validated by comparision of computed and measured tool force and its angle, and the model offers an upper boundary of the deformed layer to be in good agreement with the experiment.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.849-866
• /
• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.45 no.3
• /
• pp.160-174
• /
• 2008

In this paper, we propose new coding techniques for photometry data of three-dimensional(3-D) mesh models. We make a good use of geometry and connectivity information to improve coding efficiency of color, normal vector, and texture data. First of all, we determine the coding order of photometry data exploiting connectivity information. Then, we exploit the obtained geometry information of neighboring vortices through the previous process to predict the photometry data. For color coding, the predicted color of the current vertex is computed by a weighted sum of colors for adjacent vortices considering geometrical characteristics between the current vortex and the adjacent vortices at the geometry predictor. For normal vector coding, the normal vector of the current vertex is equal to one of the optimal plane produced by the optimal plane generator with distance equalizer owing to the property of an isosceles triangle. For texture coding, our proposed method removes discontinuity in the texture coordinates and reallocates texture image segments according to the coding order. Simulation results show that the proposed compression schemes provide improved performance over previous works for various 3-D mesh models.

• Journal of Computational Design and Engineering
• /
• v.3 no.3
• /
• pp.198-214
• /
• 2016

Oval substrates are widely used in automobiles to reduce the exhaust emissions in Diesel oxidation Catalyst of CI engine. Because of constraints in space and packaging Oval substrate is preferred rather than round substrate. Obtaining the flow uniformity is very challenging in oval substrate comparing with round substrate. In this present work attempts are made to optimize the inlet cone design to achieve the optimal flow uniformity with the help of CATIA V5 which is 3D design tool and CFX which is 3D CFD tool. Initially length of inlet cone and mass flow rate of exhaust stream are analysed to understand the effects of flow uniformity and pressure drop. Then short straight cones and angled cones are designed. Angled cones have been designed by two methodologies. First methodology is rotating flow inlet plane along the substrate in shorter or longer axis. Second method is shifting the flow inlet plane along the longer axis. Large improvement in flow uniformity is observed when the flow inlet plane is shifted along the direction of longer axis by 10, 20 and 30 mm away from geometrical centre. When the inlet plane is rotated again based on 30 mm shifted geometry, significant improvement at rotation angle of $20^{\circ}$ is observed. The flow uniformity is optimum when second shift is performed based on second rotation. This present work shows that for an oval substrate flow, uniformity index can be optimized when inlet cone is angled by rotation of flow inlet plane along axis of substrate.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.5
• /
• pp.389-395
• /
• 2016

In this paper, vibration characteristics in terms of the airfoil cross-sectional shape was examined by using the EDISON co-rotational plane beam-transient analysis. Co-Rotational plane beam analysis is appropriate for large rotation and small strain. Assuming aircraft wing as a cantilevered beam, natural frequencies of each airfoil cross-sectional shape were estimated using VABS program and fast Fourier transformation(FFT). VABS conducts finite element analysis on the cross-section including the detailed geometry and material distribution to estimate the beam sectional properties. Under the same airfoil geometric configuration and material selection, variation of material induced difference in the deflection and natural frequencies. It was observed that variation of the natural frequency was dependent on variation of the airfoil shape and material.