• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.585-598
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• 2010

We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs. Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1433-1441
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• 2016

Small area model provides reliable and accurate estimations when the sample size is not sufficient. Our dataset has an inherent nonlinear pattern which signicantly affects our inference. In this case, we could consider semiparametric models such as truncated polynomial basis function and radial basis function. In this paper, we study four Bayesian semiparametric models for small areas to handle this point. Four small area models are based on two kinds of basis function and different knots positions. To evaluate the different estimates, four comparison measurements have been employed as criteria. In these comparison measurements, the truncated polynomial basis function with equal quantile knots has shown the best result. In Bayesian calculation, we use Gibbs sampler to solve the numerical problems.

• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.181-192
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• 1992

We consider the estimation of the regression surface in generalized linear models based on tensor-product B-splines in a data-dependent way. Our approach is to use maximum likelihood method to estimate the regression function by a function from a space of tensor-product B-splines that have a finite number of knots and are linear in the tails. The knots are placed at selected order statistics of each coordinate of the sample data. The number of knots is determined by minimizing a variant of AIC. A numerical example is used to illustrate the performance of the tensor spline estimates.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.303-318
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• 2022

n-writhes denoted by J_n(K) are virtual knot invariants for n ≠ 0 and are closely associated with coefficients of some polynomial invariants of virtual knots. In this work, we investigate the variations of J_n(K) under arc shift move and conclude that n-writhes J_n(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n ≠ 0 we provide an infinite family of virtual knots which can be distinguished by n-writhes J_n(K), whereas odd writhe J(K) fails to do so.

• The Korean Journal of Ecology
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• v.13 no.3
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• pp.203-214
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• 1990

The work reported here aims to assess how Knots, Calidris canutus, accumulate rapidly large energy and nutrient reserve at Red Car in England. Most of Knots in England belong to long billed, long winged population compare with subspecies in Korea. The rate of prey intake of Knot increases as a nearest neighbour distance decreases. Foraging rate and vigilance rate increases as flock size decreases. The calorific value of each sized of Common Mussel Mytilus edulis, main food species of Knot, are almost same each other but the calorific content of each size Mussels are quite different each other. The rate of daily energy intake of Knots have been estimated from 192 kcal to 270 kcal.

• 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 $\mathbb{R}^3$.

• 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.

• 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)).

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.247-257
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• 2024

We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.