• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• 한국연소학회:학술대회논문집
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• 1998.10a
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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.

• Computers and Concrete
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• v.2 no.4
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• pp.309-324
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• 2005

The moment-curvature relationship of reinforced concrete beams made of normal- and high-strength concrete experiencing complex load history is studied using a numerical method that employs the actual stress-strain curves of the constitutive materials and takes into account the stress-path dependence of the concrete and steel reinforcement. The load history considered includes loading, unloading and reloading. From the results obtained, it is found that the complete moment-curvature relationship, which is also path-dependent, is similar to the material stress-strain relationship with stress-path dependence. However, the unloading part of the moment-curvature relationship of the beam section is elastic but not perfectly linear, although the unloading of both concrete and steel is assumed to be linearly elastic. It is also observed that when unloading happens, the variation of neutral axis depth has different trends for under- and over-reinforced sections. Moreover, even when the section is fully unloaded, there are still residual curvature and stress in the section in some circumstances. Various issues related to the post-peak behavior of reinforced concrete beams are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1235-1242
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• 2013

We give area and height estimates for cmc-graphs over a bounded planar $C^{2,{\alpha}}$ domain ${\Omega}{\subset}\mathbb{R}^3$. For a constant H satisfying $H^2{\mid}{\Omega}{\mid}{\leq}9{\pi}/16$, we show that the height $h$ of H-graphs over ${\Omega}$ with vanishing boundary satisfies ${\mid}h{\mid}$ < $(\tilde{r}/2{\pi})H{\mid}{\Omega}{\mid}$, where $\tilde{r}$ is the middle zero of $(x-1)(H^2{\mid}{\Omega}{\mid}(x+2)^2-9{\pi}(x-1))$. We use this height estimate to prove the following existence result for cmc H-graphs: for a constant H satisfying $H^2{\mid}{\Omega}{\mid}$ < $(\sqrt{297}-13){\pi}/8$, there exists an H-graph with vanishing boundary.

• Bulletin of the Korean Chemical Society
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• v.29 no.3
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• pp.585-589
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• 2008

Second-order rate constants (kN) have been measured for reactions of Y-substituted phenyl 2-thiophenecarboxylates (6a-h) with morpholine and piperidine in 80 mol % H2O/20 mol % DMSO at 25.0 0.1 oC. The Brnsted-type plot for the reactions of 6a-h with morpholine is linear with b lg = 1.29, indicating that the reactions proceed through a tetrahedral zwitterionic intermediate (T?). On the other hand, the Brnsted-type plot for the reactions of 6a-h with piperidine exhibits a downward curvature, implying that a change in the rate-determining step occurs on changing the substituent Y in the leaving group. Dissection of kN into microscopic rate constants (i.e., k1 and k2/k1 ratio) has revealed that k1 is smaller for the reactions of 6a-h than for those of Y-substituted phenyl 2-furoates (5a-h), while the k2/k1 ratio is almost the same for the reactions of 5a-h and 6a-h. It is also reported that modification of the nonleaving group from the furoyl (5a-h) to the thiophenecarbonyl (6a-h) does not influence pKao (defined as the pKa at the center of the Brnsted curvature) as well as the k2/k1 ratio.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.269-276
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• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.331-340
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• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.273-278
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• 2012

Using a comparison of the Jacobi differential equations instead of volume comparison by Itokawa in [3], the focal radius is estimated under the suitable Ricci and mean curvature conditions.

• Journal of Korea Multimedia Society
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• v.6 no.6
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• pp.985-990
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• 2003

This paper presents the representation and its shape analysis of face by features based on surface curvature estimation and proposed rotation vector of the human face. Curvature-based surface features are well suited to use for experimenting the 3D human face segmentation. Human surfaces are exactly extracted and computed with parameters and rotated by using active surface mesh model. The estimated features were tested and segmented by reconstructing surfaces from the face surface and analytically computing Gaussian (K) and mean (H) curvatures without threshold.

• Transactions of Materials Processing
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• v.22 no.6
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• pp.310-316
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• 2013

Recently, numerical predictions of surface deflection based on curvature analysis have been developed. In the current study, a measure of surface deflection is proposed as the maximum variation of curvature difference between the panel and the tool in order to account for surfaces that have high curvature. The current study focused on the assessment of accuracy for the surface deflection prediction with the consideration of planar anisotropy. As an example, a shallow rectangular drawn part with rectangular embossing was considered. In terms of the proposed surface deflection measure, the maximum variation of curvature difference, the prediction with a planar anisotropic model shows better correspondence with experiment than the one using a normal anisotropic model.