• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.247-257
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• 2024

We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• Journal of the Korean Institute of Navigation
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• v.8 no.2
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• pp.51-70
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• 1984

In the North Pacific Ocean a lot of large waves set up in winter, affected by continued winds and swells owing to severe extratropical cyclones. Under this sea condition, if the ship is about 100,000L/T (in deadweight capacity tonnage), we can't find the danger involved in the ship at sea apparently. But when we compare the seaworthiness of ship's building strength with the stress given to the hull by waves, we can't insist that the former be more stronger than the latter. As a result, VLCC is in danger of destroying and cutting for lack of longitudinal strength in heavy weather. Up to this time, Naval Architects have actively studied the relation between ship's longitudinal strength and waves as a ship's projector; however, actually, they have never made more profound study on the problem of longitudinal strength in relation to navigation. The main puprpose of this thesis is to clarify these vivid actual states of ship's trouble unknown to ship's masters. In this thesis we picked up VLCC Pan Yard, a vessel of Pan Ocean Bulk Carrier company's, as a model ship. And in the North Pacific Ocean, we have chosen for this research the basins where the wind speed and the wave height are greater than average. The data used this thesis are quotes from the "winds and waves of the North Pacific Ocean('64-'73)", and wind speed more than 30 knots was made use of as an ocject of this study. By usinh the ITTC wave spectrum, we found out the significant waves for every 5 knots within the range of 20 knots to 45 knots of wind speed. According to this H1/1000 was calculated. The stress of ship's hull is determined by ship's speed and wave height. We compared the ship's longitudinal strength with a planned wave height by rules of several famous classification societies in the world. In the last analysis, we found out that ship's present planned strength in heavy weather is not enough. Finally we made a graph for avoiding heavy weather, with which we studied safe ship's handling in the North pacafic Ocean in winter.

• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.3
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• pp.274-282
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• 2015

This research is the result on calculating the logical speed limit through certain process which some elements must be considered on selecting the speed limit of harbour and waterway. The suggested speed limit select model on this research is processed from 1~6 steps by forming a professional group of experts. Each step has its information which 1st step(water division), 2nd step(selecting the model vessel and vessel applied with speed limit.), 3rd step(selecting the maximum and minimum speed range on each section), 4th step(evaluation on the safeness of traffic), 5th step(suggesting the appropriate speed limit), 6th step(execution and evaluation.). The appropriate speed limit was decided on consideration of the safety of maritime traffic on the range of the maximum speed and the minimum speed. This model was used to derive the appropriate speed limit on the harbour water and Busan harbour entrance waterway. As the result, the harbour water was calculated to be 6.9 knots, the appropriate speed limit of Busan entrance harbour was 9.3 knots. The present calculation of the speed limit on the approaching channel area is 10 knots, inner harbour area is 7 knots, which are similar to the result of the speed limit. This research is the first research on selecting the speed limit model and has its limits on finding the perfect speed limit result. More detailed standards on the safeness of traffic evaluation must be found and additional study is necessary on discriminating consideration of the elements. This research has its value which it provides instances of aboard cases on guidelines of selecting the speed limit.

• Journal of the Korea Institute of Military Science and Technology
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• v.23 no.4
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• pp.311-318
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• 2020

This study investigates the performance and blade airloads for a rigid coaxial rotor of high-speed compound unmanned rotorcrafts. The present compound unmanned rotorcraft uses not only a rigid coaxial rotor, but also wings and propellers for high-speed flights. For the rigid coaxial rotor in this work, CAMRAD II, a rotorcraft comprehensive analysis code, is used to study the performance at a flight speed of up to 250 knots and blade section lift forces at 230 knots. As the flight speed increases, the rotor power decreases; however, the power of propellers increases to overcome the drag force of a rotorcraft in high-speed flight. The effective lift-to-drag ratio of a rotor has the maximum value of about 11.6 which is much higher than the value of the conventional helicopter. The blade section lift forces of the upper and lower rotors at 230 knots show the similar variation trends for one rotor revolution, and the impulses because of the aerodynamic interaction between both rotors are observed.

• Bulletin of the Society of Naval Architects of Korea
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• v.11 no.1
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• pp.60-67
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• 1974

포항종합제철(浦項綜合製鐵)은 제품출하시(製品出荷時) 해송비(海送比)를 약(約) 80% 정도(程度)로 잡고 있으며, 현재(現在) 하루 평균(平均) 약(約) 3,000ton가량의 제품(製品)이 출하(出荷)되고 있다. 따라서 강재품(鋼材品) 수송(輸送)에 push-barge system을 적용(適用)했을 경우에 각(各) 주요예상소비지(主要豫想消費地)의 1일(日) 예상소비량(豫想消費量)을 장래의 시설확장(施設擴張)을 고려(考慮)하여 1,000ton/day에서 4,000ton/day까지 가정하였고 속도(速度)는 연안화물선(沿岸貨物船)의 예(例)를 따라 7knots에서 13knots까지에 걸쳐 조사(調査)하였다. 회항시(廻航時) 화물(貨物)은 일단 없는 것으로 가정하였으며 몇가지 생각될 수 있는 것은 schedule중(中)에서 "1 tugboats: 3 barges", "2 tugboats: 4 barges", "3 tugboats: 5 barges"의 3가지만을 대상(對象)으로 하였다. 조사(調査)한 결과(結果) 소비량(消費量) 1,000ton/day인 경우에 포항-울산(浦項-蔚山) : 1,000 DWT barge, 8 knots, 1 tugboat: 3 barges 포항-부산(浦項-釜山) : 1,550 DWT barge, 8 knots, 1 tugboat : 3 barges 포항-인천(浦項-仁川) : 2,690 DWT barge, 9 knots, 2 tugboats : 4 barges 등이 최적(最適)인 것으로 나타났다. 또 자항화물선(自航貨物船)과 비교(比較)하면 같은 크기의 자항화물선(自航貨物船) $2.5{\sim}3.0$척(隻)에 해당(該當)하는 효율(效率)을 가진다. 이 결과(結果)로 미루어 보건대 push-barge system은 앞으로 연구개발(硏究開發)의 충분(充分)한 가치(價値)가 있는 것으로 생각된다.

• Journal of the Society of Naval Architects of Korea
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• v.57 no.1
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• pp.52-59
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• 2020

This study aims to investigate the bow thruster performance of the research vessel "NARA" by full-scale maneuvering trials. The thruster test method refers to ITTC's recommended procedures and guidelines. Turning tests with the bow thruster are performed at speed conditions of 0, 2, and 4 knots. The test results indicate that the Rate of Turn (ROT) increased when the ship is in a higher speed condition. Due to the position of the propeller and the housing of the bow thruster, there is difference in the efficiency of the bow thruster according to the turning direction. Zigzag tests with the bow thruster were conducted at speed conditions of 2 and 4 knots. At speeds above 4 knots, it seems difficult to change the course only with the bow thruster.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.44.4-44.4
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• 2019

The supernova remnant Cassiopeia A (Cas A) provides a unique opportunity to observe the fine details of the explosion of core-collapse supernova (SN). Previous optical and near-infrared (NIR) observations of Cas A have shown that the spatial distribution of the metal-enriched SN ejecta is very complicated, indicating that the SN explosion should have been asymmetric and turbulent, especially near the core. Recently, we obtained a long-exposure (~10 hr) image of Cas A by using the UKIRT 3.6-m telescope with a narrow-band filter centered at [Fe II] 1.644 um emission. This 'deep [Fe II] image' provides an unprecedented panoramic view of Cas A, revealing the distribution of dense SN ejecta over the entire remnant. We have carried out NIR multi-object spectroscopic observations of the dense ejecta knots in the northeastern (NE) and eastern (E) outer regions of the remnant using the MMIRS attached on the MMT 6.5-m telescope. A total of 67 ejecta knots are detected. By analyzing their spectra, we have found that the knots in the NE area show strong [S II]/[S III] and [Fe II] lines but little or no [P II] line, while those in the E outer region show strong [Fe II] lines but weak [S II]/[S III] lines. In this talk, we present the preliminary results of our NIR spectroscopic observations and discuss the implications.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.3
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• pp.1-10
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• 2021

This study examines the dynamic pattern of the exchange rate volatilities of the ASEAN-5 currencies from January 2006 to August 2020. The exchange rates applied in this study comprise bilateral and effective exchange rates in order to investigate the influence of the US dollar on the stability of the ASEAN-5 currencies. Since a volatility model employed in this study is a natural cubic spline volatility model, the Monte Carlo simulation is consequently conducted to determine an appropriate criterion to select a number of quantile knots for this model. The simulation results reveal that, among four candidate criteria, Generalized Cross-Validation is a suitable criterion for modeling the ASEAN-5 exchange rate volatilities. The estimated volatilities showed the inconstant dynamic patterns reflecting the uncertain exchange rate risk arising in international transactions. The bilateral exchange rate volatilities of the ASEAN-5 currencies to the US dollar are more variable than their corresponding effective exchange rate volatilities, indicating the influence of the US dollar on the stability of the ASEAN-5 currencies. The findings of this study suggest that the natural cubic spline volatility model with the quantile knots selected by Generalized Cross-Validation is practical and can be used to examine the dynamic patterns of the financial volatility.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.287-299
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• 2022

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose-response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve.