• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• 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.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.115-128
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• 2015

Plumbing surfaces of links were introduced to study the geometry of the complement of the links. A basket surface is one of these plumbing surfaces and it can be presented by two sequential presentations, the first sequence is the flat plumbing basket code found by Furihata, Hirasawa and Kobayashi and the second sequence presents the number of the full twists for each of annuli. The minimum number of plumbings to obtain a basket surface of a knot is defined to be the basket number of the given knot. In present article, we first find a classification theorem about the basket number of knots. We use these sequential presentations and the classification theorem to find the basket number of all prime knots whose crossing number is 7 or less except two knots $7_1$ and $7_5$.

• 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.

• 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.

• 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.

• 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.

• 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.