• 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.

• 한국기계연구소 소보
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• s.13
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• pp.87-98
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• 1984

An experimental study carried out to predict the performance characteristics of a high speed planing boat at the two displacements whose hull form shows hard chines form transom to bow. In the resistance test the planing hull model was porpoising at and above 30 knots for both displacements of 30 tons and 24 tons. A small stern wedge was newly designed and attached across hull bottom. The planing hull model with the stern sedge did not show any porpoising up to the speed of 45 knots for both displacements and it analysed results shows the improvement of resistance performance and planing performance comparing with those of original hull form; i.e. for displacement of 30 tons the effective power and trim angle were reduced by 18.9% and 5.71 degrees at the speed of 28 knots, and for the displacement of 24 tons the effective power and trim angle were reduced by 23.63% and 4.37 degrees at the speed of 28 knots, respectively.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.609-617
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• 2004

To present graph of probability densities, many softwares and graphical tools use methods that link points or straight lines. However, the methods can't display exactly and smoothly the graph and are not efficient from the viewpoint of process time. One method to overcome these shortcomings is utilizing interpolation methods. In these methods, selecting the number and location of knots is an important factor. This article proposes an algorithm to select knots for graphically presenting densities and implements graph components based on the algorithm.

• Journal of the Korean Wood Science and Technology
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• v.31 no.6
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• pp.22-30
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• 2003

This study was performed to obtain the basic data for high quality timber production and efficient utilization by investigating the effect of pruning on timber quality of domestic plantation-grown Korean pine (Pinus koraiensis Sieb. et Zucc.). The results were summarized as follows:Dead knots (unsound knots) in the pruned logs occurred more at upper parts when compared with in non-pruned ones. The numbers of knots on surface in heavily pruned trees were less than those in non-pruned trees, but there was no significant difference in moderately pruned trees. The required period to reveal clear timber surface without defects after pruning increased proportionally with the increase of knot diameter. The yield of clear lumber production increased by about 10% after 14 years from moderate pruning. The quality grade of log improved with more pruning practices. Knots appeared the most important factor in lowering the log grades.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.223-245
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• 2024

We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.583-594
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• 2009

We give an estimation for the sharp-unknotting number of certain types of torus knots, and decide it for 39 torus knots.

• Archives of Plastic Surgery
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• v.37 no.2
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• pp.199-201
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• 2010

Purpose: Except for continuous suture in skin layer, stitching out in facial laceration, we have to hold each knots up and cut the knots by No. 11 blade or small scissors. However, we often have difficulty in stitching out the knots on children who do not cooperate well. Therefore we introduce an easy and fast stitch out method of pediatric lacerations. Methods: From January to May 2009, we studied 15 pediatric patients (mean age 5.6 years old) who had facial laceration on face or underwent any surgery on operation room. For easy stitch out, we left the one string of the first knot long enough to extend at the opposite end of laceration site. And then the extended string was fixed to skin using Steri-strip. Next we do simple interrupted suture including the extended traction nylon string inside the knot. Through this method, we can stitch out all knots simply by lifting up the traction nylon needless to hold the each knot one by one. Results: Until stitching out, the traction nylon was just right position and there was no normal tissue injury during stitch out all knots. Patients were satisfied with the short stitch out time. Conclusion: By using the traction nylon on pediatric laceration suture, we can stitch out all the knots with no normal tissue injury in less time.

• Journal of the Korean Arthroscopy Society
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• v.8 no.1
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• pp.37-44
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• 2004

Purpose: To evaluate the optimal number of additional half hitches for achieving an optimal knot-holding capacity (KHC) of Lockable sliding knots. Methods: Four configurations of arthroscopic knots (Duncan loop, Field knot, Giant knot, and SMC knot) were tested for their knot-holding capacity. For each knot configuration, 6 sequential knots were made including the initial sliding knot and additional 5 knots by incrementing one half hitches at a time. Each added half-hitch were in reversing half-hitches with alternate posts (RHAPs) fashion. For each sequential knot configuration, 12 knots were made by No. 2 braided sutures. On the servo-hydraulic material testing system (Instron 8511, MTS, Minneapolis, MN), cyclic loading, load to clinical failure (3-mm displacement), load to ultimate failure, and mode of failure were measured. Results: Most of the initial loop without additional half-hitch showed dynamic failure with cyclic loading. The mean displacement after the end of cyclic loading decreased with each additional half-hitches. SMC and Giant knot reached plateau to 0.1 mm or less displacement after one additional half-hitch, shereas Field and Duncan loop needed 3 additional half-hitches. The SMC and Duncan knots needed 1 additional half-hitch to reach greater than 80N at clinical failure, whefeas the other 2 knots needed2 additional half-hitches. For the load exceeding 100N for clinical failure, the SMC knot required 3 additional half-hitches and the other three knots needed 4 additional half-hitches. As the number of additional half-hitches incremented, the mode of failure switched from pure loop failure (slippage) to material failure (breakage). Duncan loop showed poor loop security in that even with 5 additional half-hitches, some failed by slippage (17%). On the other hand, after 3 additional half-hitches, the 3 other knots showed greater than 75% of failure by material breakage mode (SMC and Field 92%, Giant 75%). Conclusion: Even with its own locking mechanism, lockable sliding knot alone does not withstand the initial dynamic cyclic load. For all tested variables, SMC knot requires a minimum of 2 additional half-hitches. Duncan knot may need more than 3 additional half-hitches for optimal security. All knots showed a mear plateau in knot security with 3 or more additional half-hitches.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.67-70
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• 2001

Brittenham has shown how an incompressible Seifert surface F for a knot in $S^3$ can be used to find an infinite class of persistently laminar knots. We generalize this to create larger class of persistently laminar knots which therefore have property P.

• 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.