• Journal of the Korea Society of Computer and Information
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• v.6 no.1
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• pp.1-6
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• 2001

In this paper, the problem of removing the interior knots from a B-spline is discussed. We present a new strategy for reducing the number of knots for splines. The method is the efficient for the visualization implementations and easy-to-use algorithms, and we need not to determine the knot sequence that will be removed.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.367-382
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• 2011

We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.165-170
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• 2008

We will examine the stick number of knots on the cubic lattice which is called the lattice stick number. The lattice stick numbers of knots $3_1$ and $4_1$ are known as 12 and 14, respectively. In this paper, we will show that only $3_1$ and $4_1$ have representations of irreducible non-trivial polygons, both numbers of whose sticks parallel to the y-axis and the z-axis are exactly four.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.92-97
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• 1988

The path planning is done at the joint level. Cubic spline functions are used for constructing joint trajectories for industrial robots. For N-joint robot, Cartesian knots are transformed into N sets of joint displacements, with one set for each joint. For industrial application the speed of operation affects the productivity. An algorithm is developed to schedule the time intervals between each pair of adjacent knots such that the total traveling time is minimized subject to the physical constraints on joint velocties acceleration and jerks.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.859-868
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• 2011

In this article, by considering error inequalities, we propose a new way to treat the Fej$\'{e}$r and Hermite-Hadamard inequalities involving n knots and m-th derivative on H$\"{o}$lder spaces. Moreover, some new related estimations are also given.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.661-671
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• 2007

We investigate the number of knots and links in linear embeddings of $K_6$, the complete graph with 6 vertices. Concretely, we show that any linear embedding of $K_6$ contains either only one Hopf link, or three Hopf links and one trefoil knot.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.447-458
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• 1999

In this paper we introduce a method of presenting 3-manifolds by polyhedral schemata with 2 vertices so that they may be naturally associated with given crystallizations of 3-manifolds. As applications, we explicitly present crystallizations of n-fold cyclic branched coverings of S over 2-bridge knots.

• 한국해양학회지
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• v.8 no.1
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• pp.46-52
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• 1973

From available data, the movement of the cold water in the Korea Strait was investigated. The cold water forms an undercurrent with a speed of 0.10knots near Ulgi in June. Sometimes it reaches a speed of 0.35knots. The cold water forms a sharp wdege in the western channel like a salt wedge in an estuary. The calculated volume transport of the cold water is 17,135 cubic meters per second in June. The external influences are also discussed.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.321-348
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• 2009

In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.

• 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)).