• Kyungpook Mathematical Journal
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• v.45 no.1
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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.

• Honam Mathematical Journal
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• v.32 no.1
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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.

• Journal of the Korea Society of Computer and Information
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• v.6 no.1
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• pp.1-6
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• 2001

In this paper, the problem of removing the interior knots from a B-spline is discussed. We present a new strategy for reducing the number of knots for splines. The method is the efficient for the visualization implementations and easy-to-use algorithms, and we need not to determine the knot sequence that will be removed.

• Kyungpook Mathematical Journal
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• v.61 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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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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• v.52 no.2
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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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• v.57 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.9 no.1
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• pp.1-7
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• 1976

1) The decrease in strength of netting twines at the knot may be regarded to be due mainly to the frictional force acting on the tip of the knot. The knot strength T may be given by $$T=\frac{T_0}{1+{\mu}\frac{s}{\rho}\varrho^{\mu\theta}$$ were $T_0$ is the tensile strength of unknotted netting twines, $\mu$ the coefficient of friction beween two netting twines forming a knot, s the contact length between the tip and the netting twine compressing it, $\rho$ the radius of curvature of the compressing, and $\theta$ the angle at which the compressing rubs with another one in the vicinity of the opposite tip. 2) Knots are arranged in order of strength as follows : the reef knot pulled lengthwise $\risingdotseq$ the trawler knot pulled breadtwise the reef knot pulled breadthwise.

• International Journal of Industrial Entomology and Biomaterials
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• v.8 no.2
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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.