• 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 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.

• Research in Plant Disease
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• v.14 no.1
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• pp.76-78
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• 2008

During the investigation of Allium decline in Pohang, Korea, root-knot nematode was found from root of Allium tuberosum Roth. It was identified as Meloidogyne incognita and was first reported from Allium tuberosum. Allium decline was associated with root-knot nematode, root mite and Fusarium sp. but root-knot nematode appeared to be the main cause of Allium decline.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.32 no.1
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• pp.98-104
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• 1999

To investigate the relationships between ocean environmental characteristics, the time-series data of temperature and salinity observed at a station near at Hanlim set net in 1995 and 1996 are analyzed, and the results are as follow ; 1. In hanlim set net, the diurnal range of temperature and salinity variation in summer is very large and the amplitude of short-period fluctuation of temperature and salinity is very large. That is, not only the water of the middle and bottom layers (low temperature and high salinity) but also the coalstal water (high temperature and low salinity) appears alternatively depending on the current direction 2. from the result of mooring for 22 days in Hanlim set net, the mean speed and direction of tidal current in neap tide were 9.1 cm/sec and south westward in ebb time, and 11.6 cm/sec and north or northeastward in flood time, respectively. The highest speed of the current was 15cm/sec in ebb time, and 22.6 cm/sec in flood time. The mean speed and direction of tidal current in spring tide were 10.4 cm/sec, and southwestward in ebb time, and 12.3 cm/sec, and north or northestward in flood time, respectively. The highest speed of the current was 19.4 cm/sec in ebb time, and 20 cm/sec in flood time respectively. The mean speed of the current in flood time was larger than that in ebb time. The velocity vector along the major axis of semidiurnal tide ($M_2$) component was 1.5 times larger than that of diurnal tide ($K_1$), The major directions of two compornants were northwestward and east-southeastward and residiual current were 3.25 cm/sec and northwestward-directed. Result of TGPS Buoy tracer for 3 days between Biyang-Do and Chgui-Do showed that the mean speed was 1.6 knot in ebb time and 1.3 knot in flood time. Direction of tidal was southwestward in ebb time and northeastward in flood time respectively. The maximum current speed was 4.8 knot in ebb time and 3.7 knot in flood time respectively. The mean speed and direction of tidal in of offshore were 1.7 knot and northwestward in flood time. The residual current appeared 0.3 knot northeastward.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.51 no.1
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• pp.146-153
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• 2015

A model net experiment of the gape net for anchovy in Jindo, Jeollanam-do was carried out to investigate the net shape and hydrodynamic resistance using circulating water channel. The model net was made 1/33 down scale by Tauti's similarity method and the range of experimental current speed was from 0.5 knot to 3.5 knot (increasing 0.5 knot interval). The net mouth height in 0.5 knot of the minimum experiment current speed was shown 26.0 cm (full-scale conversion value 8.58 m). The net mouth height and mouth area in 1.5 knot of the same current speed with a gape net fishing ground were shown 20.0 cm (full-scale conversion value : 6.60 m) and about $507.9cm^2$ (full-scale conversion value : $55.31m^2$). The net mouth height and area were decreased with increase the experimental current speed. The hydrodynamic resistance of the model net in 1.5 knot current speed was shown 1.11 kgf and the value of full-scale conversion by Tauti's method was shown 3.996 ton.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.39 no.3
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• pp.197-210
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• 2003

The non-float midwater pair trawl was effective in the mouth opening and control of the working depth in midwater and bottom. In contrast, we confirmed that it was difficult to keep the net at surface above 30 m of the depth by means of the full scale experiment in the field and the model test in the circulation water channel. To solve this problem, the kites were attached to the head rope of the non-float midwater pair trawl. In this study, four kinds of the model experiments were carried out with the purpose of applying the kite to the korean midwater pair trawl. The results obtained can be summarized as follows: 1. The working depth of the non-float midwater pair trawl with the kite was shallower than that of the proto type and non-float type. The working depth of the kite type was approximately 20m with 2 kites and about 5m with 4 kites under 4.0 knot. The working depth was almost constant but the depth of the head rope sank approximately 15m and 10m according to the increase in the front weight and the wing-end weight, respectively. The changing aspect of the working depth was constant, but the depth of the head rope sank approximately 22m according to the increase in the lower warp length (dL). 2. The hydrodynamic resistance of the kite type was almost increased in a linear form in accordance with the flow speed increase from 2.0 to 5.0 knot. The increasing grate of the hydrodynamic resistance tended to increase in accordance with the increase in flow speed. The hydrodynamic resistance of the kite type was larger approximately 5～10 ton larger than that of the non-float type and the proto type. The hydrodynamic resistance of the kite type increased approximately 3ton with the changing of the front weight from 1.40 to 3.50 ton and approximately 4 ton with the changing of the wing-end weight from 0 to 1.11 ton and approximately 5.5 ton with the changing lower warp length (dL) from 0 to 40 m, respectively. 3. The net height of the kite type was increased approximately 10 m with the change in the kite area from $2,270mm^2$ to 4,540 $\textrm{mm}^2$. The net height of the kite type was aproximately 50 m and 30 m larger than that of the proto type and the non-float type, respectively. The changed aspect of the net width was approximately 5m with the variation of the flow speed from 2.0 to 5.0 knot. 4. The filtering volume of the kite type was larger than that of the proto type and the non-float type by 28%, 34% at 2.0 knot of the flow speed and 42%, 41% at 3.0 knot, and 62%, 45% at 4.0 knot, and 74%, 54% at 5.0knot, respectively. The optimal towing speed was approximately 3.0 knot for the proto type and was over 4.0 knot for the non-float type, and the optimal towing speed reached 5.0 knot for the kite type. 5. The opening efficiency of the kite type was approximately 50% and 25% larger than that of the proto type and the non-float type, respectively.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.639-645
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• 2016

In [3] the main theorem was erroneously stated. We needed to assume that the irrationality measure of 1/r is finite to prove the theorem.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.639-653
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• 2014

In [9], Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials $V_K(t)$ of classical links to the f-polynomials $f_K(A)$ of virtual links by using bracket polynomials. In [4], M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots. In this paper, we give a necessary condition for a virtual knot invariant to be of finite type by using $t(a_1,{\cdots},a_m)$-sequences of virtual knots. Then we show that the higher derivatives $f_K^{(n)}(a)$ of the f-polynomial $f_K(A)$ of a virtual knot K at any point a are not of finite type unless $n{\leq}1$ and a = 1.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.869-877
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• 2022

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H₁(M; ℤ) ≅ ℤ_p and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H₁(L(p, q)).

• East Asian mathematical journal
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• v.38 no.1
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• pp.107-127
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• 2022

In this paper, we discuss the relationship between doubly-pointed Heegaard diagrams of (1, 1)-knots in lens spaces and Dunwoody 3-manifolds, and then give explicit representations of n-fold cyclic branched coverings of all (1, 1)-knots in S³ up to 10 crossings in Rolfsen's knot table as Dunwoody 3-manifolds.