• Honam Mathematical Journal
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• v.45 no.3
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.5
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• pp.866-873
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• 2001

The governing partial differential equations of a helical spring with a circular section were derived from Frenet formulas and Timoshenko beam theory. These were solved to give the dispersion relationship between wave number and frequency along with wave form. Wave motions of helical springs are categorized by 4 regimes. In the first regime, the lower frequency area, the torsional and extensional waves of the spring are predominant and two waves are composite wave motions involving lateral motion of the coils and rotation of the coils about a horizontal axis. All waves are propagating in the second regime. The wave of the extensional motion of the spring and one wave of transverse motion of a wire change from travelling waves to near field waves in the third regime. Both waves excited by both axial and transverse motion are predominant in the fourth regime.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1339-1355
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• 2006

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

• The KIPS Transactions:PartB
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• v.13B no.4 s.107
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• pp.361-368
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• 2006

In this paper we present a snake-based scheme for efficiently detecting contours of objects with boundary concavities. The proposed method is composed of two steps. First, the object's boundary is detected using the proposed snake model. Second, snake points are optimized by inserting new points and deleting unnecessary points to better describe the object's boundary. The proposed algorithm can successfully extract objects with boundary concavities. Experimental results have shown that our algorithm produces more accurate segmentation results than the conventional algorithm.