• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.43-55
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• 1997

Suppose that D is a domain in the extended complex plane $\overline{C} = C \cup {\infty}$. For each $z_0 \in C$ and $C < r < \infty$, we let $B(z_0, r) = {z \in C : $\mid$z - z_0$\mid$ < r}$ and $S(z_0, r) = \partial B(z_0, r)$. For non-empty sets A, $B \subset \overling{C}$, diam (A) is the diameter of A and d(A, B) is the distance of A and B.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.901-909
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• 2014

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.147-155
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• 1999

Let {$C_t$} be a pencil of smooth quartics for $t{\neq}0$ degenerating to a plane quartic $C_0$ with an ordinary cusp of multiplicity 3. We compute the stable limit as $t{\rightarrow}0$ of {$C_t$} when the total surface of this family has a triple point at the singular point of $C_0$.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.939-949
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• 2016

In this paper, we give an algorithm to construct a space curve in Euclidean 3-space ${\mathbb{E}}^3$ from a plane curve which is called PDP-helix of order d. The notion of the PDP-helices is a generalization of a general helix and a slant helix in ${\mathbb{E}}^3$. It is naturally shown that the PDP-helix of order 1 and order 2 are the same as the general helix and the slant helix, respectively. We give a characterization of the PDP-helix of order d. Moreover, we study some geometric properties of that of order 3.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.171-182
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• 2009

In this paper, we consider the parameter space of the rational plane curves with uni-branched singularity. We show that such a parameter space is decomposable into irreducible components which are rational varieties. Rational parametrizations of the irreducible components are given in a constructive way, by a repeated use of Abhyankar-Moh Epimorphism Theorem. We compute an enumerative invariant of this parameter space, and include explicit computational examples to recover some classically-known invariants.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.313-317
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• 2011

In this article, we consider an unbounded minimal graph $M{\subset}R^3$ which is contained in a slab. Assume that ${\partial}M$ consists of two Jordan curves lying in parallel planes, which is symmetric with the reflection under a plane. If the asymptotic behavior of M is also symmetric in some sense, then we prove that the minimal graph is itself symmetric along the same plane.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.259-284
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• 2024

In present study, we introduce ruled surfaces whose base curve is the Salkowski curve in Euclidean 3-space and whose generating lines consist of the Frenet vectors of this curve (tangent, principal normal and binormal vectors). Then, we produce regular surfaces from a vector with real coefficients, which is a linear combination of these vectors, and we examine some special cases for these surfaces. Moreover, we present some geometric properties and graphics of all these surfaces.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.601-609
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• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

• Journal of Ocean Engineering and Technology
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• v.32 no.5
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• pp.297-309
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• 2018

After an accident involving mooring link failures in an offloading buoy, verification of the fatigue safety in terms of the out-of-plane bending (OPB) and in-plane bending (IPB) moments has become a key engineering item in the design of various floating offshore units. The mooring links for an 8 MW floating offshore wind turbine were selected for this study. To identify the OPB stiffness (OPB moment versus interlink angle), a numerical simulation model, called the 3-link model, is usually composed of three successive chain links closest to the fairlead or chain hawse. This paper introduces two numerical simulation techniques for the 3-link analyses. The conventional and advanced approaches are both based on the prescribed rotation approach (PRA) and direct tension approach (DTA). Comparisons of the nominal stress distributions, OPB stiffnesses, hotspot stress curves, and stress concentration curves are presented. The multiple link analyses used to identify the tension angle versus interlink angle require the OPB stiffness data from the 3-link analyses. A convergence study was conducted to determine the minimum number of links for a multi-link analysis. It was proven that 10 links were sufficient for the multi-link analysis. The tension angle versus interlink angle relations are presented based on multi-link analyses with 10 links. It was found that the subsequent results varied significantly according to the 3-link analysis techniques.