• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.51-54
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• 1983

Let M be a n-dimensional compact Riemannian manifold with sectional curvature bounded below by one. Then Li and Zhong[3], and Li and Treibergs [4] proved that if the first eigenvalue of the Laplacian .lambda.$_{1}$ is less than some universal constant and if n.leq.4, then M is diffeomorphic to the n-sphere S$^{n}$ . The purpose of this paper is to prove this pinching theorem for all n with some extra condition.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1097-1108
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• 2015

In this paper, we investigate p-biharmonic maps u : (M, g) $\rightarrow$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if ${\int}_M|{\tau}(u)|^{{\alpha}+p}dv_g$ < ${\infty}$ and ${\int}_M|d(u)|^2dv_g$ < ${\infty}$, then u is harmonic, where ${\alpha}{\geq}0$ is a nonnegative constant and $p{\geq}2$. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen's conjecture for p-biharmonic submanifolds).

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1259-1280
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• 2016

The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.613-623
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• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.335-342
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• 1999

It is well known that l-girders are weak in torsion and it might be more economical to use a box girder, which has great torsional rigidity. The use of box beams does, however, present a potential problem in that cross-sectional distortions can induce large warping normal stresses and transverse bending stress. Accordingly a sufficient number of diaphragms are provided to make the distortional effects minimal. In engineering practice, diaphragms are spaced in 5m intervals without reasonable basis. It is considered to be noneconomical design to the almost design engineers, and it may produce the unsafe structural systems in special cases such as curved bridges with large initial curvature. These problems have not been solved for the lack of adequate tools of structural analysis. In this study, on the basis of the parametric studies, the design formulas for the distortional warping stress and the reasonable diaphragm spacing of box girder were presented.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2006.05a
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• pp.281-284
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• 2006

Metallic sandwich plates with hi-directional inner structure are important new structures for forming applications. Bi-directional corrugated inner structures with less than 25% of relative density are fabricated by piecewise sectional forming process and then bonded with two face sheets by adhesive bonding. Drawing and U-bending experiments have performed and shown that the radius of curvature of sandwich plates is 75mm and sandwich plates are bended 90 degrees without collapse of inner structures. Bi-directional inner structures are suggested to improve formability of sandwich plates for bending and drawing.

• Journal of computational fluids engineering
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• v.19 no.1
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• pp.57-63
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• 2014

This study performed numerical analysis for the characteristics of flow-induced forces and the flow instability depending on the cross-sectional shape of the cylinder in laminar flow. To implement the cylinder cross-section, we adopted an Immersed Boundary Method with marker particles. We analyzed flow characteristics based on the radius of corner curvature. Main parameters are corner radius and Reynolds number (Re). With Re = 40, 50, 150 we calculated the flow field, drag coefficient, RMS of lift coefficient, pressure coefficient and Strouhal number in conjunction with the corner radius variation. Also, we calculated critical Reynolds number ($Re_c$) depending on the corner radius variation.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.96-101
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• 2000

In this paper, an experimental investigation of characteristics of developing transitional steady flows in a square-sectional 180 urved duct is presented. The experimental study is carried out to measure axial velocity profiles by using Laser Doppler Velocimeter (LDV) system. The flow development is found to depend upon Dean number and curvature ratio. For transitional steady flows, the maximum velocity position of axial velocity profiles begins to incline toward the outer wall from $\phi$=$30^{\circ}$bended angle, velocity profiles in center of the duct have lower value than those of the inner and outer walls because of the centrifugal forces.

• Journal of Advanced Marine Engineering and Technology
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• v.23 no.1
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• pp.33-39
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• 1999

In this paper an experimenatal investigation of characteristics of developing ransitional steady flows in a square-sectional $180^{\circ}$ curved duct is presented, The experimental study is carried out to measure axial velocity profiles secondary flow velocity profiles and entrance length by using Laser Dopper Velocimeter(LDV) system. The flow development is found to depend upon Dean number and curvature ratio. Of special interest is the secondary flow generated by centrifugal effects in the plane of the cross-section of the duct. The secondary flows becomes strong from $120^{\circ}$ of bended angle on the duct. The entrance length of transitional steady flow is obtained to $120^{\circ}$ of bended angle of the duct in this experimental conditions.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.740-745
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• 2001

The plastic deformation behavior of formed CICC fur the superconducting Tokamac fusion device was examined and appropriate manufacturing information was provided. A relation between travel of the bending roller and spring back displacement was obtained via virtual manufacturing. The radius of CICC after forming was expressed as a function of the bend-roll travel. The maximum von Mises stress after spring back was also monitored fur the SAGBO prediction. Next, the variation of the CICC cross-sectional area was examined during the first turn and during conduit bending with the largest curvature. Finally, the coil radius was measured and compared with the data generated from the virtual manufacturing. The measured data showed similar pattern as predicted one. Using the mapping function found to match with the real data, the data from the virtual manufacturing may facilitate accurate manufacturing.