• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.145-161
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• 2017

If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be homotopic. There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic. For a sequence S of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams, we give a lower bound for the number of crossing changes in S by using the affine index polynomial introduced in [13]. In [10], the first author gave the q-polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams. We find how to apply Reidemeister moves by using the q-polynomial to show homotopy of two virtual knot diagrams.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.103-112
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• 1998

In this paper insertion of numerous control points to be performed by using the Chebyshev polynomial root at the selection of knot vector. This method introduces a simple method of knot refinement and it is applied in a developed program. The Chebyshev roots exist densely in broth ends of the range and are proposed more effective knot refinement to modify a surface. Therefore, generated control points are relatively uniform in specified knot interval. In the surface generation, a local insertion of numerous control points are easily inserted by using the characteristic of Chebyshev polynomial roots at knot refinement. It is possible to create a complex surface with a single surface. The number of control point can be reduced by using the local insertion of control points in a required shape

• Clinics in Shoulder and Elbow
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• v.8 no.2
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• pp.117-121
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• 2005

A secure slip knot is very important in the arthroscopic surgery of the shoulder joint. The new 'Hallym Slider', developed by the first author(KCN), has the properties of being a simple sliding and one-way locking knot. This technique can be performed alone without an assistant and has no accidental premature locking during the knot tying. The initial slip knot determines the adequacy of tissue approximation and consequent healing. The 'Hallym Slider' has excellent initial holding capacity, maintaining tension on soft tissue while additional half-hitches are being tied. It locks readily, it takes less time to tie than numerous square knots, and it is not as bulky as other knots. Therefore, we introduce this new sliding and one-way locking knot during the arthroscpic surgery of shoulder.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.347-361
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• 2022

Two virtual knot diagrams are said to be equivalent, if there is a sequence S of Reidemeister moves and virtual moves relating them. The difference of writhes of the two virtual knot diagrams gives a lower bound for the number of the first Reidemeister moves in S. In previous work, we introduced a polynomial q_K(t) for a virtual knot diagram K which gave a lower bound for the number of the third Reidemeister moves in the sequence S. In this paper we define a new polynomial from a coloring of a virtual knot diagram. Using this polynomial, we give a lower bound for the number of the second Reidemeister moves in S. The polynomial also suggests the design of the sequence S.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.475-486
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• 2001

In this paper we give a relationship among the Minkowski units, for all odd prime number including $\infty$, of 2-periodic knot is $S^3$, its factor knot, and the 2-component link consisting of the factor knot and the set of fixed points of the periodic action.

• 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.

• Microbiology and Biotechnology Letters
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• v.22 no.3
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• pp.227-232
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• 1994

In order to microbially control root-knot nematode(Meloidogyne incognita) in tomato, a strain BtTH109 of Bacillus thuringiensis producing root-knot nematocidal toxin was isolated. The strain BtTH109 was identified B. thuringiensis subsp. indiana(serotype 16) based on flagella antigenicity, biochemical properties, and morphological charcateristics. The strain BtTH109 have extracellularly produced a root-knot nematocidal toxin, which was very toxic against not only egghatch but also the 2nd-nematode larva of root-knot nematode in vitro.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.205-215
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• 2011

Given a knot diagram D, we construct a semi-threading circle of it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles of minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we try to give another proof of the fact that, for every nontrivial knot K, the braid index b(K) of K is not less than the minimum number l(K) of overpasses of diagrams. Also, they are the same for a torus knot.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.866-871
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• 1994

B-spline curves and surfaces are effective solutions for design and modelling of the freeform models. The control methods of these are using with control points, knot vectors and weight of NURBS. Using control point is easy and resonable for representation of general models. But the movement of control points bring out the reformation of original convex hull. The B-splines with nonuniform knot vector provide good result of the shape modification without convex hull reforming. B-splines are constructed with control points and basis functions. Nonuniform knot vectors effect on the basis functions. And the blending curves describe the prorities of knot vectors. Applying of these, users will forecast of the reformed curves after modifying controllabler primitives.

• Korean Journal of Organic Agriculture
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• v.19 no.spc
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• pp.267-270
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• 2011

Root-knot nematodes cause a significant damage on fruit yield and quality of green house growing crops. To asses the effect of eggplant rootstock, Torvum vigor', TaibyouVF' and 'Daitaro' were grafted on eggplants(Solanum melongena cv. Chookyang) and planted in root-knot nematode infested microplot in green house and compared their fruit yield, quality and plant growth with non-grafted control. Eggplant grafted with Torvum vigor had the highest fruit yield and top growth and followed by Daitaro. Non-grafted eggplant had lower yield but had higher root weight because of heavy root-knot nematode infection. Rootstock grafting in eggplant farming is a good alternative technique in root-knot nematode infested green houses without compromising fruit yield and can be applied instantly as organic farming practice.