• Clinics in Shoulder and Elbow
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• v.8 no.2
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• pp.127-130
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• 2005

We describe a secure and easy-to-tie knot with a lag bight, the SP knot. An optimal sliding knot is required to be a low-profile, easy to throw, slide well, and provide a good initial security. The SP knot easily slides and sets while avoiding premature locking during sliding. While maintaining tension on the post limb with a knot pusher, pulling the loop limb makes it to flip and distort post limb, resulting in creation of a snug knot on the exact location with desired tension. The SP knot has one knot configuration before pulling the loop limb, but it converts to two knots after pulling the loop limb, one half-hitch and one 'clove hitch', which could provide enough loop security before any additional half-hitches. The configuration of the completed SP knot is formed lying along the loop of the knot, rather than stacking up, which enables a very low profile. The SP knot has various characteristics of the optimal arthroscopic slip knot and may be a useful tool for successful arthroscopic surgery.

• 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.

• 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.

• Journal of the Korean Wood Science and Technology
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• v.36 no.5
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• pp.33-41
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• 2008

This study was aimed to develop the knot quantification method to predict bending strength, using x-ray scanner. The bending strength prediction model was proposed in this paper. The model was based on Knot Depth Ratio (KDR) and closely-spaced knot was taken into account. The previous paper reported that KDR is the ratio of the knot and transit zone to the lumber thickness. Even though KDR involves transit zone, it was verified that the ratio of the moment of inertia for knot to gross cross section ($I_k/I_g$) based on KDR was a good predictor for bending strength of lumber. To take closely-spaced knot into account, a projection method was also proposed. This projection method improved the predictive accuracy significantly. It showed coefficient of determinant of 0.65 and root mean square error (RMSE) of 9.17.

• Journal of Korean Society of Forest Science
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• v.97 no.5
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• pp.485-491
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• 2008

This study was performed in 14 unthinned Mongolian pine (Pinus sylvestris L. var. mongolica Litvin) plantations in northeast China. Data were collected on 70 sample trees of different canopy position with diameter at breast height (DBH) ranging from 6.9 cm to 34.5 cm. Diameter and length of knots per whorl below the living crown were studied by different vertical levels divided by relative knot height (RHK) in this paper. Models taking DBH and height to the crown base (HCB) as independent variables were developed to predict knot diameter (KD) in a sample whorl. According to the vertical distribution tendency and range of sound knot length (KLsound), KLsound was modeled as multiple linear function of DBH, KD and relative knot height (RHK). The loose knot length (KLloose) was described as a function of DBH, KD and height above the ground for knots (HK) in a mixed log-linear model. Results from this study can provide abundant knot information so as to describe the knot size and vertical distribution tendency of Mongolian pine plantation.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1139-1148
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• 2015

For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.

• 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.52 no.2
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• pp.201-208
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• 2012

By the works of Kondo and Sakai, it is known that Alexander polynomials of knots which are transformed into the trivial knot by a single crossing change are characterized. In this note, we will characterize Alexander polynomials of knots which are transformed into the trefoil knot (and into the figure-eight knot) by a single crossing change.

• 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.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.95-113
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• 2018

A mathematical knot is an embedded circle in ${\mathbb{R}}^3$. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n - move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.