• East Asian mathematical journal
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• v.35 no.1
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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.

• Journal of the Korea Fashion and Costume Design Association
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• v.17 no.1
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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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• v.33 no.5 s.133
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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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• v.56 no.3
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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.

• Journal of the Korean Society of Marine Environment & Safety
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• v.20 no.2
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• pp.228-233
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• 2014

In this paper, the motion performance in waves for the training ship Kaya of Pukyong National University is obtained by using a computer program based on Strip method. To guarantee the pleasant seafaring in ocean, the vertical acceleration of ship motion is calculated according to the location of the ship. The results of calculation by changes of ship speed are compared with the guideline of MSI(Motion Sickness Incidence). The degree of motion sickness is shown and discussed through the comparison between calculated vertical acceleration spectrum and MSI guideline. The computational results of MSI were as follow; when ship speed increased in the order of 5 knots, 10 knots, 12 knots and encounter angle became the bow quartering sea of $120^{\circ}$ compared to $180^{\circ}$ and $150^{\circ}$, the vertical acceleration values grew higher.

• Journal of the Korea Fashion and Costume Design Association
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• v.24 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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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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• v.13 no.3
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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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• 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.

• Journal of the Korea Furniture Society
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• v.12 no.1
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• pp.27-37
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• 2001

Automation of wood processing is strongly required to improve the productivity and quality of wood products in wood industry which is one of the most labor-intensive industries. Classification of surface defects on wood boards such as knots is one of the important steps towards a completely automated wood processing system. In this study the possibility of detection of knots by image processing technique was investigated. Algorithm for the automatic determination of threshold value was developed to enhance the flexibility of image processing system. Two different approaches, grid method and tile method, were developed to enhance the speed in extracting features from images. Grid method showed slightly higher processing speed and tile method proved much more stable in determining threshold values. Tile size of $5{\times}5$ pixels or $6{\times}6$ pixels was found to be proper to get stable results with resonable processing time.