• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.741-752
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• 2015

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.399-411
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• 2021

We consider a Weierstrass semigroup at a generalized flex on a smooth plane curve. We find the candidates of a Weierstrass semigroup at a 2-flex of higher multiplicity on a smooth plane curve of degree d ≥ 5, and give some examples to show the existence of them.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2963-2971
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• 2000

In order to obtain more realistic fracture resistance curve, research is currently underway to introduce new parameter and to quantify the constraint effect. The objective of this study is to investigate the relationship between the constraint effect of a size(plane size and thickness) and the fracture resistance curve. In this paper fracture toughness tests were performed with various plane size and various thickness of specimens in two materials. The test results showed that the effects of plane size in th4 J-R curve were significant and the curve was risen with an increase in plane size. However, relatively weak influence was observed form the change of the specimen thickness and size. The stress fields near the crack tip of th specimen is close to the HRR field according to increasing the plane size and Q stress appears different value according to material properties and the plane size.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.251-267
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• 2020

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we find the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.113-129
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• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.2
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• pp.279-284
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• 2010

The plane curve approach which was proposed by Boukharouba et. al. is a multi-threshold selection method through searching peak-valley based on histogram cumulative distribution function. However the method is required to select parameters to compose plane curve, and the shape of plane curve is affected according to parameters. Therefore detection of peak-valley is effected by parameters. In this paper, we propose an entropy maximizing-based method to select optimal plane curve parameters, and propose a multi-thresholding method based on the selected parameters. The effectiveness of the proposed method is demonstrated by multi-thresholding experiments on various images and comparison with other conventional thresholding methods based on histogram.

• Structural Engineering and Mechanics
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• v.9 no.5
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• pp.469-482
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• 2000

A numerical study using nonlinear finite element analysis is performed to investigate the behavior of isolated reinforced concrete walls subjected to combined axial force and in-plane and out-of-plane bending moments. For a nonlinear finite element analysis, a computer program addressing material and geometric nonlinearities was developed. Through numerical studies, the internal force distribution in the cross-section is idealized, and then a new design method, different from the existing methods based on the plane section hypothesis was developed. According to the proposed method, variations in the interaction curve of the in-plane bending moment and axial force depends on the range of the permissible axial force per unit length, that is determined by a given amount of out-of-plane bending moment. As the out-of-plane bending moment increases, the interaction curve shrinks, indicating a decrease in the ultimate strength. The proposed method is then compared with an existing method, using the plane section hypothesis. Compared with the proposed method, the existing method overestimates the ultimate strength for the walls subjected to low out-of-plane bending moments, while it underestimates the ultimate strength for walls subject to high out-of-plane bending moments. The proposed method can address the out-of-plane local behavior of the individual wall segments that may govern the ultimate strength of the entire wall.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.611-624
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• 2018

In this paper, we study Weierstrass semigroups of ramification points on double covers of plane curves of degree 6. We determine all the Weierstrass semigroups when the genus of the covering curve is greater than 29 and the ramification point is on a total flex.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.567-580
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• 1999

We prove two variants of a base-point-free pencil trick, which are similar in the spirit of the proof, and apply them to the study of special divisors on a smooth plane curve involving a theorem of Max Noether.