• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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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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• 통권13호
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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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• 제11권3호
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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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• 제31권6호
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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.

• 대한수학회논문집
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• 제39권1호
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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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• 제49권3호
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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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• 제37권2호
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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.

• 대한관절경학회지
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• 제8권1호
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• pp.37-44
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• 2004

목적: 잠김(Locking)이 가능한 이동 매듭의 (sliding knot) 최적 매듭 유지력 (knot-holdingcapacity KHC)을 가지기 위한 추가적인 반 매듭의 (additional half-hitches) 개수를 알아보고자 하였다. 대상 및 방법: 4가지의 관절경적 이동 매듭법 (Duncan매듭법, Field 매듭법, Giant매듭법, SMC매듭법)을 대상으로 매듭 유지력을 실험하였다. 각각의 매듭을 만들기 위해 처음의 이동 매듭과 추가적인 5개의 반 매듭으로 구성된 6개의 연속적인 매듭을 만들었다. 각각의 추가된 반 매듭은 서로 교차하며 매듭의 지대 (post)도 교차하여 매는 방식으로 (reversing half-hitches with alternate posts, RHAPS) 하였다. 각각의 연속적인 매듭을 구성하기위해 No.2 Ethibond봉합사를 이용하여 각각의 매듭 형태에 12개의 매듭을 만들었다. 매듭의 인장 및 유지력 실험은 servohydraulic material testing system(Instron 8511, MTS, Minneapolis, MN)으로 주기적 부하(cyclic loading)를 시켜, 임상적으로 실패라 규정한 3 mm의 전위가 생길 때까지의 부하 (load to clinical failure). 매듭이 완전히 실패했을 때의 부하 강도 (load to ultimate failure), 그리고 실패 형태 (mode of failure)를 측정하였다. 결과: 추가적인 반 매듭이 없는 최초의 이동 매듭 자체로는 대부분 주기적 부하에 의해 매듭의 실패를 보였다. 주기적 부하 검사에서 각각의 추가적인 반 매듭이 증가할수록 평균 전위 값은 감소하였다. SMC 매듭법과 Giant 매듭법은 하나의 추가적인 반 매듭 이후로 0.1 mm이하의 전위 값을 보였고 Field와 Duncan 매듭법은 3개의 추가 반매듭이 필요하였다. SMC 매듭법과 Duncan 매듭법은 80 N을 견디기 위해 단 하나의 추가 반 매듭이 필요하였고, Field와 Giant 매듭법은 2개의 추가 반 매듭이 필요하였다. 100 N이상의 부하를 견디기 위해서는 SMC 매듭법은 3개의 추가 반 매듭이 필요하였고, 다른 3가지의 매듭법은 4개의 추가 반 매듭이 필요하였다. 추가 반 매듭이 증가함에 따라 봉합사는 풀리는 것보다 끊어지는 양상을 보였다. Duncan매듭법은 5개의 추가 반 매듭 이후에도 풀림현상을 보였고, 다른 3개의 매듭법은 3개의 추가 반 매듭 이후엔 75%이상이 봉합사의 풀림 현상보다는 끊어지는 양상을 보였다. (SMC, Field 매듭법은 92%, Ciant 매듭법은 75%)결론: 어떤 매듭법이라도 이동 매듭법 만으로는 주기적 부하 검사를 견디지 못했다. 모든 종류의 실험에서 SMC 매듭법은 최소2개의 두개의 추가 반 매듭이 필요하였다. Duncan 매듭법은 최적 매듭 유지력을 위해 3개 이상의 추가 반 매듭이 필요하였다. 모든 매듭법에서 3개나 그 이상의 추가 반 매듭이 최적 유지력에서 정점에 가까운 양상을 보였다.

• 호남수학학술지
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• 제23권1호
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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.

• 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.