• Kyungpook Mathematical Journal
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• 제57권1호
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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.

• 한국CDE학회논문집
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• 제3권2호
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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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• 제8권2호
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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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• 제62권2호
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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.

• 대한수학회보
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• 제38권3호
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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.

• 대한관절경학회지
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• 제8권1호
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• pp.37-44
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• 2004

목적: 잠김(Locking)이 가능한 이동 매듭의 (sliding knot) 최적 매듭 유지력 (knot-holdingcapacity KHC)을 가지기 위한 추가적인 반 매듭의 (additional half-hitches) 개수를 알아보고자 하였다. 대상 및 방법: 4가지의 관절경적 이동 매듭법 (Duncan매듭법, Field 매듭법, Giant매듭법, SMC매듭법)을 대상으로 매듭 유지력을 실험하였다. 각각의 매듭을 만들기 위해 처음의 이동 매듭과 추가적인 5개의 반 매듭으로 구성된 6개의 연속적인 매듭을 만들었다. 각각의 추가된 반 매듭은 서로 교차하며 매듭의 지대 (post)도 교차하여 매는 방식으로 (reversing half-hitches with alternate posts, RHAPS) 하였다. 각각의 연속적인 매듭을 구성하기위해 No.2 Ethibond봉합사를 이용하여 각각의 매듭 형태에 12개의 매듭을 만들었다. 매듭의 인장 및 유지력 실험은 servohydraulic material testing system(Instron 8511, MTS, Minneapolis, MN)으로 주기적 부하(cyclic loading)를 시켜, 임상적으로 실패라 규정한 3 mm의 전위가 생길 때까지의 부하 (load to clinical failure). 매듭이 완전히 실패했을 때의 부하 강도 (load to ultimate failure), 그리고 실패 형태 (mode of failure)를 측정하였다. 결과: 추가적인 반 매듭이 없는 최초의 이동 매듭 자체로는 대부분 주기적 부하에 의해 매듭의 실패를 보였다. 주기적 부하 검사에서 각각의 추가적인 반 매듭이 증가할수록 평균 전위 값은 감소하였다. SMC 매듭법과 Giant 매듭법은 하나의 추가적인 반 매듭 이후로 0.1 mm이하의 전위 값을 보였고 Field와 Duncan 매듭법은 3개의 추가 반매듭이 필요하였다. SMC 매듭법과 Duncan 매듭법은 80 N을 견디기 위해 단 하나의 추가 반 매듭이 필요하였고, Field와 Giant 매듭법은 2개의 추가 반 매듭이 필요하였다. 100 N이상의 부하를 견디기 위해서는 SMC 매듭법은 3개의 추가 반 매듭이 필요하였고, 다른 3가지의 매듭법은 4개의 추가 반 매듭이 필요하였다. 추가 반 매듭이 증가함에 따라 봉합사는 풀리는 것보다 끊어지는 양상을 보였다. Duncan매듭법은 5개의 추가 반 매듭 이후에도 풀림현상을 보였고, 다른 3개의 매듭법은 3개의 추가 반 매듭 이후엔 75%이상이 봉합사의 풀림 현상보다는 끊어지는 양상을 보였다. (SMC, Field 매듭법은 92%, Ciant 매듭법은 75%)결론: 어떤 매듭법이라도 이동 매듭법 만으로는 주기적 부하 검사를 견디지 못했다. 모든 종류의 실험에서 SMC 매듭법은 최소2개의 두개의 추가 반 매듭이 필요하였다. Duncan 매듭법은 최적 매듭 유지력을 위해 3개 이상의 추가 반 매듭이 필요하였다. 모든 매듭법에서 3개나 그 이상의 추가 반 매듭이 최적 유지력에서 정점에 가까운 양상을 보였다.

• 한국미생물·생명공학회지
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• 제22권3호
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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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• 제51권2호
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1994년도 추계학술대회 논문집
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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.

• 한국유기농업학회지
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• 제19권spc호
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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.