• 대한수학회논문집
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• 제37권3호
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• pp.825-837
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• 2022

We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

• 소성∙가공
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• 제7권2호
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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.

• 대한기계학회논문집
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• 제18권9호
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• pp.2463-2476
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• 1994

Local mean fluctuating velocity components were measured in the separating and reattaching axisymmetrc region of turbulent boundary layer over the wall of convex cylinders placed in a water tunnel by using 2-color 4-beam fiber optics laser Doppler velocimetry. Measurements were made with three different diameters of cylinders with four different diameters of cylinders with four different diameter of the obstructions. The range of Reynolds number based on step height was between 5,000 to 25,200. The study demonstrates that the reattachment length decreases with decreasing cylinder radius and is always shorter than that for the two-dimensional backward-facing step flow at the condition of the same step height. It was also observed that the turbulent kinetic energy in the recirculating region increases with an increases in the radius of convex curvature. The measured velocity field suggests that the transverse curvature can effect definitely the formation of corner eddy.

• 소성∙가공
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• 제7권5호
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• pp.496-504
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• 1998

The eccentric extrusion and bending process for the forming of the curved rectangular hollow tube is newly developed. Generally the bending process of hollow tube is the secondary process followed by the extrusion process of the hollow tube from the round billet. So many defects such as wrinkling and the difference of wall thickness can be happened during the secondary bending process. In order to avoid the defects the new process named as "the eccentric extrusion and bending process" is suggested and applied to the U-bending of rectangular hollow tube. In this paper the kinematically admissible velocity field between the dies surface and the internal plug boundary surface s developed for the curving velocity. By the using of this curving velocity field the curvature of extruded products can be calculated with the parameters such as eccentricity dies length friction constant aspect ratio.

• 대한수학회지
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• 제57권4호
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• 한국연소학회:학술대회논문집
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• 한국연소학회 1998년도 제17회 KOSCI SYMPOSIUM 논문집
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• pp.91-101
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• 1998

The effect of secondary flow on both methane/air and propane/air premixed flame was investigated experimentally. By changing the radius of curvature, various flame behavior was observed. In the V-bend nozzles, flame surface is deformed from axisymmetry. As the exit velocity increased, flame lifted off partially. When the radius of curvature of the V-bend increased, the region where premixed flame is entirely on the rim increased. Since the axial velocity field is changed due to the secondary flow effect, comparison of V-bend and straight tube with the same diameter shows larger V-bend nozzle exit velocity for both flash back and flame blowout. The flame characteristics are mapped with a equivalence ratio, a velocity, and a nozzle radius of curvature. To identify physical reasoning on the flame surface deformation, numerical calculations are conducted. OH radical distributions in flames are visualized by PLIF technique.

• Journal of Advanced Marine Engineering and Technology
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• 제30권1호
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• pp.140-149
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• 2006

Characteristics of a laminar diffusion flame placed near wall in microgravity have been numerically analyzed in a two-dimension. The fuel for the flame is $C_2H_4$. The flame is initiated by imposing a high temperature ignition source. The flow field, temperature field, and flame shape in microgravity diffusion flame are detailed. Especially, effects of surrounding air velocity and fuel injection velocity on the microgravity diffusion flame have been discussed accounting for standoff distance. And, the effect of curvature rate has been also studied. The results showed that velocities in a diffusion flame were overshoot because of volumetric expansion and distribution of temperature showed regularity by free-buoyancy This means that the diffusion flame in microgravity is very stable, while the flame in normal gravity is not regular and unstable due to buoyancy. Standoff distance decreases with increase in surrounding air velocity and with decrease in fuel injection velocity. With increasing curvature rate, the position of reaction rate moves away the wall.

• 호남수학학술지
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• 제43권1호
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• pp.88-99
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• 2021

The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S2 in Euclidean 3-space R3 to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bézier curve that allows a curve to be characterized on the surface. Moreover, we give some important results and relations for the Darboux frame and geodesic curvature of a such curve. Then, in specific case, given characterizations for the quadratic rational Bézier curve are illustrated on a unit 2-sphere.

• Structural Engineering and Mechanics
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• 제35권4호
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• pp.493-510
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• 2010

This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).

• 대한수학회보
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• 제26권2호
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• pp.159-164
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• 1989

Let M be a hypersurface of dimension n(.geq.2) in an (n+1)-dimensional real space form over bar M(c) with constant curvature c and H the second fundamental tensor of M. M is said to be birecurrent if here exists a covariant tensor field .alpha. of order 2 such that .del.$^{2}$H=H .alpha., where .del. is the connection of M. Also, M is said to be recurrent if there exists a 1-form .betha. such that .del.H=H .betha.. Matsuyama [2] recently proved that a recurrent hypersurface M in a real space form is locally symmetric and a complete irreducible birecurrent hypersurface M in a real space form is recurrent. The main purpose of this paper is to characterize the birecurrent or recurrent hypersurface M of a Riemannian manifold with constant curvature c and to prove that M is classified as a cylinder, $M^{n}$ (c) or ( $c_{1}$)* $M^{n-r}$ ( $c_{2}$) where 1/ $c_{1}$+1/ $c_{2}$=1/c.