• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1927-1933
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• 2017

We prove that there are rational homology balls $B_p$ smoothly embedded in the 2-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the 2-handlebody along the embedded rational homology ball $B_p$, then the resulting 4-manifold cannot be obtained just by a sequence of ordinary blow ups from the 2-handlebody under a certain mild condition.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1989-2000
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• 2013

We show that for any given closed orientable 3-manifold M with a Heegaard surface of genus g, any positive integers b and n, there exists a knot K in M which admits a (g, b)-bridge splitting of distance greater than n with respect to the Heegaard surface except for (g, b) = (0, 1), (0, 2).

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-71
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• 1999

We classify all conjugacy classes of 3-braids that are related by flypes on representatives. Among them we determine which classes have representatives that admit both (+) and (-) flypes as an effort to search for a potential example of a pair of transversal knots that are topologically isotopic and have the same Bennequin number but are not transversally isotopic.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.271-292
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• 2014

We introduce a new method to transform a knot diagram into a diagram of an unknot using a polynomial representation of the knot. Here the unknotting sequence of a knot diagram with least number of crossing changes can be realized by a family of polynomial maps. The number of singular knots in this family is defined to be the singularity index of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.522-526
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• 1993

The first objective of this study is to derive an automated method that minimizes the number of spline regions and optimizes the locations of the knots to provide and adequate fit of a given nonlinear function. This has been accomplished by the development of the Optimal Spline Method discussed herein. The second objective is to apply the derived automated method to an important application. This objective has been accomplished by the successful application of the Optimal Spline Method to ship classification.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.485-506
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• 2015

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

• Journal of Korea Ship Safrty Technology Authority
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• s.31
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• pp.60-70
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• 2011

The slamming impact pressures at the bottom area of the Open60' are evaluated by the rules and regulations of various organizations - ISO and classification societies. The enhanced performance of the modern racing yacht in terms of speed which achieves well over 20 knots needs special consideration. The calculated design impact pressures are compared a experimental results. Severe difference can be found in these calculation results but the final conclusion shall be obtained after the scantling calculation under the evaluated design impact pressure so far.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.927-938
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• 2016

In this note, we study a monodromy map of a fibered 2-bridge knot. We show the monodromy map of a fibered 2-bridge knot as an element in the automorphism group of a free group.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.355-360
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• 2000

This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"＋ λ²u＝0, u(0.0)＝u(0.0)＝0, 0≤x≤1.0.