• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.67-71
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• 2005

We call K a (1, 1)-knot in M if M is a union of two solid tori $V_1\;and\;V_2$ glued along their boundary tori ${\partial}V_1\;and\;{\partial}V_2$ and if K intersects each solid torus $V_i$ in a trivial arc $t_i$ for i = 1 and 2. Note that every (1, 1)-knot is a tunnel number one knot. In this article, we determine when a tunnel number one knot is a (1, 1)-knot. In other words, we show that any tunnel number one knot with bridge number 3 is a (1, 1)-knot.

• 호남수학학술지
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• 제32권1호
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• pp.157-165
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• 2010

Silver and Whitten proved that every knot in $S^3$ is invertibly concordant to a hyperbolic knot by a series of Nakanishi's construction. We prove that every knot in $S^3$ is invertibly concordant to a nonhyperbolic prime knot by a simple one step satellite construction.

• 한국컴퓨터정보학회논문지
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• 제6권1호
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• pp.1-6
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• 2001

본 논문에서는 B-spline의 근사방법 중의 한 방법으로써 knot 제거 알고리즘을 제안한다. 이 알고리즘은 제거되는 knot의 순서에 영향을 받지 않고 항상 같은 결과를 얻을 수 있을 뿐만 아니라 수학적으로도 단순하므로 이해와 구현이 용이하다. 내부 knot들이 multiplicity를 많이 갖는 경우에 더 큰 장점을 갖는다.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.205-212
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• 2021

We show that the forbidden detour move, essentially introduced by Kanenobu and Nelson, is an unknotting operation for virtual knots. Then we define the forbidden detour number of a virtual knot to be the minimal number of forbidden detour moves necessary to transform a diagram of the virtual knot into the trivial knot diagram. Some upper and lower bounds on the forbidden detour number are given in terms of the minimal number of real crossings or the coefficients of the affine index polynomial of the virtual knot.

• 대한수학회보
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• 제48권1호
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• pp.197-211
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• 2011

Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b $\geq$ 0, c $\geq$ 0, d = 2a+b+c, $r\;{\in}\;\mathbb{Z}_d$, and it is well known that all 2-bridge knots and torus knots are (1, 1)-knots. In this paper, we describe some conditions for 4-tuples which determine 2-bridge knots and determine all 4-tuples representing any given 2-bridge knot.

• Kyungpook Mathematical Journal
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• 제52권2호
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• pp.223-243
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• 2012

There is a special connection between the Alexander polynomial of (1, 1)-knot and the certain polynomial associated to the Dunwoody 3-manifold ([3], [10] and [13]). We study the polynomial(called the Dunwoody polynomial) for the (1, 1)-knot obtained by the certain cyclically presented group of the Dunwoody 3-manifold. We prove that the Dunwoody polynomial of (1, 1)-knot in $\mathbb{S}^3$ is to be the Alexander polynomial under the certain condition. Then we find an invariant for the certain class of torus knots and all 2-bridge knots by means of the Dunwoody polynomial.

• Kyungpook Mathematical Journal
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• 제57권1호
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• pp.145-161
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• 2017

If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be homotopic. There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic. For a sequence S of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams, we give a lower bound for the number of crossing changes in S by using the affine index polynomial introduced in [13]. In [10], the first author gave the q-polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams. We find how to apply Reidemeister moves by using the q-polynomial to show homotopy of two virtual knot diagrams.

• 대한수학회보
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• 제46권5호
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• pp.1019-1029
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• 2009

We show that every bridge surface of certain types of (1, 1) prime knot has the disjoint curve property. Also we determine when a bridge surface of a pretzel knot of type (.2, 3, n) has the disjoint curve property.

• 한국수산과학회지
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• 제9권1호
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• pp.1-7
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• 1976

그물실의 강도가 매듭에서 감소하는 기구를 명백히 하기위해, 매듭에서의 그물실의 파단현상울 관찰하고 강도 감소에 영향을 끼치는 요소들을 조사하여 매듭의 강도를 나타내는 식을 유도하고, mono-filament, multi-filament, 및 spun 그물실로 구분된 11종류의 그물실에 대해 매듭의 강도를 측정하여 상기 식에 의한 계산치와 비교했다. 실험의 결과, 매듭이 파만을 일으키는 부분은 매듭의 첨단, 즉 매듭과 다리와의 경계이었으며, 강도감소의 원인은 이 첨단에 마찰력이 작용함으로 인해, 첨단에 위치한 섬유들이 자신에 걸리는 장력에 의해서 재분포하는데 마찰력만큼 저항을 받게 되기 때문이라고 간주되었다. 매듭의 강도 T는 $$T=\frac{T_0}{1+{\mu}\frac{s}{\rho}\varrho^{\mu\theta}$$ 로 표시되었고, 이 식에 의한 계산치는 실험치와 거의 일치했다. 단, $T_0$는 그물실의 항장력, $\mu$는 그물실간의 마찰계수, S는 매듭의 첨단과 그 첨단을 압축하는 그물실과의 접촉길이, $\rho$는 그 첨단을 압축하는 그물실의 곡률반경, $\theta$는 그 첨단을 압축하는 그물실이 반대편 첨단에서 다른 그물실과 마찰되는 각도이다.

• International Journal of Industrial Entomology and Biomaterials
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• 제8권2호
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• pp.175-179
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• 2004

Trichoderma harzianum-THN1 parasitising the egg masses of root knot nematode Meloidogyne incognita was isolated from galled mulberry roots and evaluated for its potential to control root knot disease. In pot experiments root galling was reduced and leaf yield increased significantly following soil treatment with T. harzianum-THN1. The extracts obtained from the soils inoculated with T. harzianum-THN1 drastically inhibited the hatching of nematode eggs and the effect was irreversible even after the eggs were transferred to fresh water. The fungus was equally effective in controlling the disease in nematode infested mulberry garden under field conditions which was significant over the most commonly used egg parasitic fungus Paecilomyces lilacinus. The disease reduction recorded with T. harzianum was on par with the plants treated with the nematicide Carbofuran. The results suggest that T. harzianum- THN1 could be used as a potent ecofriendly biocontrol agent against M. incognita in mulberry without any residual toxicity to silkworms. T. harzianum- THN1 can form an important component of integrated disease management package in mulberry cultivation.