• Research in Plant Disease
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• v.20 no.2
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• pp.119-125
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• 2014

Root-knot nematodes represent a significant problem in cucumber, causing reduction in yield and quality. To develop screening methods for resistance of cucumber to root-knot nematode Meloidogyne incognita, development of root-knot nematode of four cucumber cultivars ('Dragonsamchuk', 'Asiastrike', 'Nebakja' and 'Hanelbakdadaki') according to several conditions such as inoculum concentration, plant growth stage and transplanting period was investigated by the number of galls and egg masses produced in each seedling 45 days after inoculation. There was no difference in galls and egg masses according to the tested condition except for inoculum concentration. Reproduction of the nematode on all the tested cultivars according to inoculum concentration increased in a dose-dependent manner. On the basis of the result, the optimum conditions for root-knot development on the cultivars is to transplant period of 1 week, inoculum concentration of 5,000 eggs/plant and plant growth stage of 3-week-old in a greenhouse ($25{\pm}5^{\circ}C$). In addition, under optimum conditions, resistance of 45 commercial cucumber cultivars was evaluated. One rootstock cultivar, Union was moderately resistant to the root-knot nematode. However, no significant difference was in the resistance of the others cultivar. According to the result, we suggest an efficient screening method for new resistant cucumber to the root-knot nematode, M. incognita.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.235-244
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• 2015

It is known that there is an infinite family of general pretzel knots, each of which has Rasmussen s-invariant equal to the negative value of its signature invariant. For an instance, homologically ${\sigma}$-thin knots have this property. In contrast, we find an infinite family of 4-strand pretzel knots whose Rasmussen invariants are not equal to the negative values of signature invariants.

• East Asian mathematical journal
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• v.36 no.3
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• pp.359-364
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• 2020

It is known that a 2-generator knot K has a cyclic Alexander module ℤ[t, t^―1]/(Δ(t)) where Δ(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groups $$<\;x,\;y\;{\mid}\;(x^{{\alpha}_1})^{y^{{\gamma}_1}},\;{\cdots}\;,\;(x^{{\alpha}_k})^{y^{{\gamma}_k}}\;>$$ where a^b = bab^-1.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1247-1257
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• 2016

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.591-604
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• 2018

We consider a family of ribbon 2-knots with trivial Alexander polynomial. We give nonabelian SL(2, C)-representations from the groups of these knots, and then calculate the twisted Alexander polynomials associated to these representations, which allows us to classify this family of knots.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1989-2000
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• 2013

We show that for any given closed orientable 3-manifold M with a Heegaard surface of genus g, any positive integers b and n, there exists a knot K in M which admits a (g, b)-bridge splitting of distance greater than n with respect to the Heegaard surface except for (g, b) = (0, 1), (0, 2).

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.1-15
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• 2017

Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.165-170
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• 2008

We will examine the stick number of knots on the cubic lattice which is called the lattice stick number. The lattice stick numbers of knots $3_1$ and $4_1$ are known as 12 and 14, respectively. In this paper, we will show that only $3_1$ and $4_1$ have representations of irreducible non-trivial polygons, both numbers of whose sticks parallel to the y-axis and the z-axis are exactly four.

• Fibers and Polymers
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• v.5 no.2
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• pp.156-159
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• 2004

Novoloid fibers have high chemical, flame and thermal resistance; however they have low tensile properties. Effects of gamma irradiation on the tensile properties of novoloid fibers have been investigated. Loop and knot resistance have also been examined. Maximum tenacity of the single fiber increased with an increase of the radiation dose applied. According to the loop and knot tenacity results it is found that brittleness has been also affected by the amount of radiation dose.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.661-671
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• 2007

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.