• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.801-809
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• 2009

By using a tangle decomposition of a knot, we give a method for the construction of a knot with the lowest trivial HOMFLY coefficient polynomial. Applying this, we show that there exist infinitely many 2-bridge knots with such a coefficient polynomial.

• East Asian mathematical journal
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• 제35권1호
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• pp.31-40
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• 2019

We introduce a family of polynomial invariants by using intersection index defined from a Gauss diagram of a long virtual knot, and we give some properties for long virtual knots. We extend these polynomials so that we give two-variable polynomial invariants and some example.

• 한국의상디자인학회지
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• 제17권1호
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• pp.83-92
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• 2015

The knots have been used practically and functionally in close relation to people's daily life, and it shows the beauty of its ornamental purpose. This study was to discover a new formativeness, such as the natural and symbolic beauty of knots, based on the interpretation of knots' basic image, recreating Korean beauty and characteristics within a modern sense. A bowknot is one of the beautiful Korean traditional knots and it is considered as a symbol of transformation. In this study, the formativeness of bowknots was shown and used, resulting in developing textile patterns that symbolize peace, love, joy, and hope. It was believed that the symbolism of bowknots could be suitable for a pattern of kindergarten uniforms which the children would experience for the first time. Considering the functional characteristics without discomfort while the children participate in various activities and movements, we made two pairs of boys' uniforms and two for girls.

• Journal of the Korean Wood Science and Technology
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• 제33권5호통권133호
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• pp.13-20
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• 2005

This paper deals with flexural vibration techniques as a means of predicting bending strength properties for quarter-sawn and flat-sawn planes of red pine containing knots. Dynamic modulus of elasticity $(MOE_d)$ was calculated from resonance frequency obtained from the flexural vibration induced by a magnetic driver in quarter-sawn and flat-sawn planes of red pine containing knots. The dynamic MOE were well correlated to bending strength properties. Their correlation coefficients ranged from 0.866 to 0.800 for the regression between dynamic MOE and static bending MOE or MOR. The difference of the values between quarter-sawn and flat-sawn was very small. These values were higher than correlation between percentage of total knot diameter to total width of red pine specimen $(K_T(%))$ as well as $K_O(%)$ base upon ASTM D 3737 and static bending strength properties (correlation coefficient r = 0.448~0.704), and were similar to those between static bending MOE and bending MOR (r = 0.850). These results indicate that dynamic MOE obtained from resonance frequency induced by flexural vibration of magnetic driver is able to effectively use for predicting of static bending strength of red pine containing knots as well as static MOE.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.1017-1045
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• 2016

Using a combination of calculational and theoretical approaches, we establish results that relate two knot invariants, the Alexander polynomial, and the number of quandle colourings using any finite linear Alexander quandle. Given such a quandle, specified by two coprime integers n and m, the number of colourings of a knot diagram is given by counting the solutions of a matrix equation of the form AX = 0 mod n, where A is the m-dependent colouring matrix. We devised an algorithm to reduce A to echelon form, and applied this to the colouring matrices for all prime knots with up to 10 crossings, finding just three distinct reduced types. For two of these types, both upper triangular, we found general formulae for the number of colourings. This enables us to prove that in some cases the number of such quandle colourings cannot distinguish knots with the same Alexander polynomial, whilst in other cases knots with the same Alexander polynomial can be distinguished by colourings with a specific quandle. When two knots have different Alexander polynomials, and their reduced colouring matrices are upper triangular, we find a specific quandle for which we prove that it distinguishes them by colourings.

• 해양환경안전학회지
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• 제20권2호
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• pp.228-233
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• 2014

본 연구에서는 실습선 가야호를 대상으로 하여 파랑 중 운동성능을 평가하였다. 그리고 쾌적한 승선감을 확보하기 위하여 실제 해상에서 운항중인 선박의 선내 위치별 수직가속도 성분을 선체운동 계산 기법을 통해서 구하고, 수직가속도 스펙트럼을 이용하여 가야호의 선속변화에 따른 가속도 계산 결과를 뱃멀미 지수(MSI; Motion Sickness Incidence)의 가이드라인과 비교 검토하여 멀미의 정도를 표시하였다. MSI 계산 결과는 선속이 5 knots, 10 knots, 12 knots로 커지는 순서대로 수직가속도의 가중치가 높게 나타나며, 입사각은 $180^{\circ}$와 $150^{\circ}$에 비해 선수사파인 $120^{\circ}$의 경우에 수직가속도의 가중치가 높게 나타났다.

• 한국의상디자인학회지
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• 제24권2호
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• pp.45-57
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• 2022

This study aims to analyze the macramé technique used in costume design based on the cases from 2011 to 2020, when the macramé technique became popular. The research data are the results of analyzing the materials, clothing items, and structural combination of macramé knots by season, year, and collection from 2011 S/S to 2020 F/W, focusing on the four major fashion collections New York, Paris, London, and Milan. Macramé appeared often in the S/S season, and in the 2019 and 2020 S/S seasons, macramé was identified as a keyword for fashion trends based on its frequent usage. Overhand knots were used the most for the types of macramé knots used in costumes, and overhand knots were also used the most in the S/S season and in the New York, Paris, and Milan collections. Rope was the most frequently used material for macramé knots, and it was confirmed that it appeared frequently in 2011 and 2019, and ropes were also used often in the London, Milan, and Paris collections. One-piece appeared the most in the S/S season and F/W season as costume items. In addition, the costumes used as layers in the S/S season appeared most often, and in 2019 and 2020, the layered combination appeared most frequently in London and New York collections. It is judged that macramé appears repeatedly in the S/S season depending on the type of knot and is used as a layered look, making it a decorative element rather than a practical element. This study is expected to help develop modern fashion design by drawing attention to the value of the macramé technique expressed as handcrafted work.

• 대한수학회지
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• 제47권3호
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• pp.585-598
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• 2010

We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs. Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.

• The Korean Journal of Ecology
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• 제13권3호
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• pp.203-214
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• 1990

The work reported here aims to assess how Knots, Calidris canutus, accumulate rapidly large energy and nutrient reserve at Red Car in England. Most of Knots in England belong to long billed, long winged population compare with subspecies in Korea. The rate of prey intake of Knot increases as a nearest neighbour distance decreases. Foraging rate and vigilance rate increases as flock size decreases. The calorific value of each sized of Common Mussel Mytilus edulis, main food species of Knot, are almost same each other but the calorific content of each size Mussels are quite different each other. The rate of daily energy intake of Knots have been estimated from 192 kcal to 270 kcal.

• 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.