• Transactions of Materials Processing
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• v.7 no.2
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• pp.177-185
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• 1998

The kinematically admissible veolcity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric lane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal one are determined by the minimization of the plastic work and that the curvature of the extruded products increase with the eccentricity.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1363-1372
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• 2007

We investigate the containment measure of one domain to contain in another domain in a plane $X^{\kappa}$ of constant curvature. We obtain some Bonnesen-type inequalities involving the area, length, radius of the inscribed and the circumscribed disc of a domain D in $X^{\kappa}$.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.83-90
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• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• Proceedings of the Korean Geotechical Society Conference
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• 1998.06a
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• pp.99-110
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• 1998

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1261-1269
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• 2023

For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1009-1038
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• 1996

R.L. Bishop and S.I. Goldberg [3] introduced the notion of totally real bisectional curvature B(X, Y) on a Kaehler manifold M. It is determined by a totally real plane [X, Y] and its image [JX, JY] by the complex structure J. where [X, Y] denotes the plane spanned by linealy independent vector fields X, and Y. Moreover the above two planes [X, Y] and [JX, JY] are orthogonal to each other. And it is known that two orthonormal vectors X and Y span a totally real plane if and only if X, Y and JY are orthonormal.

• Imaging Science in Dentistry
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• v.36 no.1
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• pp.55-62
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• 2006

Purpose : To find the cause of root curvature by use of panoramic and lateral cephalometric radiograph. Materials and Methods : Twenty six 1st graders whose mandibular 1st molars .just emerged into the mouth were selected. Panoramic and lateral cephalometric radiograph were taken at grade 1 and 6, longitudinally. In cephalometric radio graph, mandibular plane angle, ramus-occlusal plane angle, gonial angle, and gonion-gnathion distance (Go-Gn distance) were measured. In panoramic radio graph, elongated root length and root angle were measured by means of digital subtraction radiography. Occlusal plane-tooth axis angle was measured, too. Pearson correlations were used to evaluate the relationships between root curvature and elongated length and longitudinal variations of all variables. Multiple regression equation using related variables was computed. Results : The Pearson correlation coefficient between curved angle and longitudinal variations of occlusal plane-tooth axis angle and ramus-occlusal plane angle was 0.350 and 0.401, respectively (p<0.05). There was no significant correlation between elongated root length and longitudinal variations of all variables. The resulting regression equation was $Y=10.209+0.208X_1+0.745X_2$ (Y: root angle, $X_1$: variation of occlusal plane-tooth axis angle, $X_2$: variation of ramus-occlusal plane angle). Conclusion : It was suspected that the reasons of root curvature were change of tooth axis caused by contact with 2nd deciduous tooth and amount of mesial and superior movement related to change of occlusal plane.

• Journal of Mechanical Science and Technology
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• v.14 no.4
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• pp.441-447
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• 2000

Direct numerical simulation has been used to study turbulent boundary layers with convex curvature. A direct numerical simulation program has been developed to solve incompressible Navier-Stokes equations in generalized coordinates with the finite volume method. We considered two boundary layer thicknesses. When the curvature effect is small, mean velocity statistics show little difference with those of a plane channel flow. Turbulent intensity decreases as curvature increases. Contours suggest that streamwise vorticities are strong where large pressure fluctuations exist.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.250-253
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• 1998

The kinematically admissible velocity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric plane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal zone are determined by the minimization of the plastic work and that the curvature of the extruded products increases with the eccentricity.