• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1101-1113
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• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.809-823
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• 2020

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.513-527
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• 2011

The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.3
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• pp.419-426
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• 1986

In an attempt to develop a method for the design of the aerial rope way, the traditional theories of rope way were examined and compared. The resulting formulas of the traditional and approximate parabolic curve theory were summarized and those of the catenary curve theory as an exact ones were summarized and newly developed when necessary. In particular, it was found that the resulting formulas from both of these theories can fully be expressed with only three dimensionless parameters $U^{*}$, $V^{*}$, and $W^{*}$, improving compactness and generality of these formulas. Comparision of the theories were done through error analysis, and it was shown that the error of the approximate parabolic curve is of order $U^{*2}$ and $V^{*}$. From this, it was concluded that the traditional parabolic curve theory has its limitation when the rope way becomes larger or steeper, leading to the necessity of the use of catenary curve theory.ve theory.

• Journal of KSNVE
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• v.7 no.2
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• pp.215-222
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• 1997

The flow and acoustic fields due to a vortex ring interaction with a rigid sphere are simulated numerically. The flow field is regarded as three-dimensional inviscid and incompressible. The vorticity is assumed to be concentrated inside the finite core of vortex filament. The vortex filament curve, described by parabolic blending curve function, is used to effectively solve the modified Biot-Savart equation. The interaction between a vortex ring and a rigid sphere using the parabolic blending curve is calculated. The trajectory of the vortex ring is obtained with several different initial positions between the ring and the sphere. The force variations acting on the sphere are calculated by using the boundary integral method. Finally, we can also obtain the acoustic signals at the far field observation positions from the force variations acting on the rigid surface. We can find that the dipole axis of the directivity patterns are rotated during the interacting phenomena.

• Journal of Industrial Technology
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• v.12
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• pp.69-76
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• 1992

An attempt has been made to determination the NC milling machine's tool-path through the adaptive parabolic interpolation method & the adaptive linear-parabolic interpolation method in consideration of the economical machining time. The algorithms for the above-mentioned interpolation methods have been designed and the numerical experiments for these methods have been conducted with the existing adaptive linear interpolation methods for comparision.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1613-1616
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• 2005

In this paper, we developed an algorithm of generating cam contour curve for hinge mechanism of folder-type mobile phone. The main feature of this hinge mechanism is that we can operate uniform torque to open or close the mobile phone. We divided the opening or closing intervals of the cam into finite sub-intervals, and then we determined the cam contour curve of each sub-interval as a parabolic curve. Finally, these finite parabolic curves form the total cam contour. We can design single cam, which composed moving cam with contour curve and fixed cam that plays only roller, and twin cam with contour curve that is made up the pair of two cams symmetrically.

• Journal of the Korean Institute of Landscape Architecture
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• v.20 no.4
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• pp.93-101
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• 1993

The purpose of this study is to analyze th especificity of landscape construction progress in order to develop the model of landscape construction schedule management. Nine case study area in housing complex was selected and the graphic curve of the accumulative payment by landscape construction schedule was analyzed. And the results are as follows: The graphic curve of common construction progress is S-curve but that of landscape construction progress is parabolic-curve, because landscape construction concentrally progress in last period of construction schedule. And particularly parabolic-curve seems to rise up suddenly in the last period when landscape construction amount is small.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.473-484
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• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.161-181
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• 2024

We describe the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one and its geometric structures in terms of the Hitchin map and a flat degeneration of the moduli space of Higgs bundles on an elliptic curve.