• International Journal of Automotive Technology
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• v.8 no.3
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• pp.337-342
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• 2007

A multi-objective optimization technique was implemented to obtain optimal topologies of the inner reinforcement for a vehicle's hood simultaneously considering the static stiffness of bending and torsion and natural frequency. In addition, a smoothing scheme was used to suppress the checkerboard patterns in the ESO method. Two models with different curvature were chosen in order to investigate the effect of curvature on the static stiffness and natural frequency of the inner reinforcement. A scale factor was employed to properly reflect the effect of each objective function. From several combinations of weighting factors, a Pareto-optimal topology solution was obtained. As the weighting factor for the elastic strain efficiency went from 1 to 0, the optimal topologies transmitted from the optimal topology of a static stiffness problem to that of a natural frequency problem. It was also found that the higher curvature model had a larger static stiffness and natural frequency than the lower curvature model. From the results, it is concluded that the ESO method with a smoothing scheme was effectively applied to topology optimization of the inner reinforcement of a vehicle's hood.

• Journal of Korean Ophthalmic Optics Society
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• v.11 no.3
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• pp.181-185
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• 2006

The measurement of the radius of corneal curvature with keratometer was followed in 184 university students who wearing RGP contact lens and consisted of female(167), male(17) and keratoconus patients(3). Overall mean value in the radius of corneal curvature is 7.77mm, and right and left eyes is appeared the same mean value. Overall mean value in horizontal and vertical is 7.88mm and 7.65mm. Horizontal means is larger than vertical means by 0.22mm of the all female and male students. Male's mean value in the radius of corneal curvature(7.84mm) is larger than female's by 0.08mm, and right and left eyes is also the same mean value. Keratoconus patients' mean value in the radius of corneal curvature(6.86mm) is smaller than others students by 0.91mm.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.3
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• pp.444-453
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• 1987

In the present study, a new computational closure model is proposed in order to contain physical models in the k- and .epsilon.- equations. The time scale of the third-order diffusive transport of turbulent kinetic energy in a curved streamline flow field is assumed as a function of a velocity time scale and a curvature time scale, the latter being derived from the analogy between buoyancy and streamline curvature effects on turbulence. The curvature time scale is represented by a combination of Brunt-Vaisala frequency of the curvature instability and the velocity time scale. Besides the modification of diffusive transport time scale, the destruction term in the dissipation rate equation is modeled to incorporate the streamline curvature effect on the dissipation rate of turbulent kinetic energy as a function of the ratio between velocity time scale and curvature time scale. The new curvature dependent 2-equation model is found to yield very good prediction accuracy for the various turbulent recirculating flows. Particurarly, the recovery of the mean velocity profile in the redeveloping region after the reattachment is correctly simulated by the present model.

• The Journal of the Acoustical Society of Korea
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• v.43 no.2
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• pp.168-177
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• 2024

When designing an underwater Piezoelectric Energy Harvester (PEH), Vortex Induced Vibration (VIV) is generated throughout the cantilever through a change in curvature, and the generation of VIV increases the vibration displacement of the curved cantilever PEH, which is an important factor in increasing actual power. The material of the curved PEH selected a Polyvinyline Di-Floride (PVDF) piezoelectric film, and the flow velocity is set at 0.1 m/s to 0.50 m/s for 50 mm, 130 mm, and 210 mm with various curvatures. The strain energy change of PEH by VIV was observed. The smaller the radius of curvature, the larger the VIV, and as the flow rate increased, more VIV appeared. Rapid shape transformation due to the small curvature was effective in generating VIV, and strain energy, normalized voltage, average power, etc. To increase the amount of power of the PEH, it is considered that the average power will increase as the number of curved PEHs increases as well as the steep curvature is improved.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1245-1252
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• 2011

Consider the $L^2$-adjoint $s_g^{'*}$ of the linearization of the scalar curvature $s_g$. If ker $s_g^{'*}{\neq}0$ on an n-dimensional compact manifold, it is well known that the scalar curvature $s_g$ is a non-negative constant. In this paper, we study the structure of the level set ${\varphi}^{-1}$(0) and find the behavior of Ricci tensor when ker $s_g^{'*}{\neq}0$ with $s_g$ > 0. Also for a nontrivial solution (g, f) of $z=s_g^{'*}(f)$ on an n-dimensional compact manifold, we analyze the structure of the regular level set $f^{-1}$(-1). These results give a good understanding of the given manifolds.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.359-366
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• 2016

Let H be the 3-dimensional Heisenberg group, ($G=H{\times}S^1$, g) a product Riemannian manifold of Riemannian manifolds H and S with arbitrarily given left invariant Riemannian metrics respectively, and ${\Gamma}$ the discrete subgroup of G with integer entries. Then, on the Riemannian manifold ($M:=G/{\Gamma}$, ${\Pi}^*g=\bar{g}$), ${\Pi}:G{\rightarrow}G/{\Gamma}$, we evaluate the scalar curvature and the Ricci curvature.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.587-595
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• 2008

It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.713-724
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• 2005

We prove that a (k, $\mu$)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, $\mu$)­manifolds with C-Bochner curvature tensor B satisfying B $(\xi,\;X)\;\cdot$ S = 0, where S is the Ricci tensor, are classified. N(K)-contact metric manifolds $M^{2n+1}$, satisfying B $(\xi,\;X)\;\cdot$ R = 0 or B $(\xi,\;X)\;\cdot$ B = 0 are classified and studied.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.319-326
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• 2003

In this paper, we obtain the optimal condition of the curvature bounds guaranteeing that Euclidean cones over Aleksandrov spaces of curvature bounded above preserve the curvature bounds, by considering the Euclidean cone CS$_{r}$ $^{n}$ over n-dimensional sphere S$_{r}$ $^{n}$ of radius r. More precisely, we show that for r<1, the Euclidean cone CS$_{r}$ $^{n}$ of S$_{r}$ $^{n}$ is a CBB(0) space, but not a CBA($textsc{k}$)-space for any real $textsc{k}$$\in$R.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.