• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.4
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• pp.772-780
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• 2008

K-means is one of the simplest unsupervised learning algorithms that solve the clustering problem. However K-means suffers the basic shortcoming: the number of clusters k has to be known in advance. In this paper, we propose extensions of X-means, which can estimate the number of clusters using Bayesian information criterion(BIC). We introduce two different versions of algorithm: modified X-means(MX-means) and generalized X-means(GX-means), which employ one full covariance matrix for one cluster and so can estimate the number of clusters efficiently without severe over-fitting which X-means suffers due to its spherical cluster assumption. The algorithms start with one cluster and try to split a cluster iteratively to maximize the BIC score. The former uses K-means algorithm to find a set of optimal clusters with current k, which makes it simple and fast. However it generates wrongly estimated centers when the clusters are overlapped. The latter uses EM algorithm to estimate the parameters and generates more stable clusters even when the clusters are overlapped. Experiments with synthetic data show that the purposed methods can provide a robust estimate of the number of clusters and cluster parameters compared to other existing top-down algorithms.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.485-498
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• 2013

In this paper, the Schur convexity is generalized to Schur $f$-convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When $f$ : ${\mathbb{R}}_+{\rightarrow}{\mathbb{R}}$ is defined as $f(x)=(x^m-1)/m$ if $m{\neq}0$ and $f(x)$ = ln $x$ if $m=0$, the necessary and sufficient conditions for $f$-convexity (is called Schur $m$-power convexity) of Gini means are given, which generalize and unify certain known results.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.61-67
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• 2017

Low-dose X-ray fluoroscopic image sequences to avoid radiation exposure risk are contaminated by quantum noise. To restore these noisy sequences, we propose a 3D nonlocal means (NLM) filter based on stochastic distancesed can be applied to the denoising of X-ray fluoroscopic image sequences. The stochastic distance is obtained within motion-compensated noise filtering support to remove the Poisson noise. In this paper, motion-adaptive weight which reflected the frame similarity is proposed to restore the noisy sequences without motion artifact. Experimental results including comparisons with conventional algorithms for real X-ray fluoroscopic image sequences show the proposed algorithm has a good performance in both visual and quantitative criteria.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1495-1500
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• 2015

We obtain means and variances of max {X, Y} and min {X, Y} in the underlying Morgenstern type bivariate uniform variables X and Y with same scale parameters and different scale parameters respectively. And we obtain the conditional expectations in the underlying Morgenstern type bivariate uniform variables. Here, we shall consider the conditional expectations to know the dependence of one variable on the other variable and we consider the behaviors of means and variances of max {X, Y} and min {X, Y} with respect to changes in means, variances, and the correlation coeffcient of the underlying Morgenstern type bivariate uniform variables.

• Korean Journal of Applied Biomechanics
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• v.15 no.3
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• pp.153-159
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• 2005

The purpose of this study was to investigate the Effective X-Factor in golf swing. The term X-Factor means the relative rotation of shoulders with respect to hips during the golf swing. To ascertain the Effective X-Factor that resulted in a high club head speed at impact six golfers' swing motions were videotaped and analyzed using three-dimensional techniques. The results can be summarized as follows. The standard deviations of the professionals' average club head speeds were higher than the amateurs'. This means that the professionals' swing skills were better than amateurs' in driving accuracy and consistency. As the club head speeds were increased gradually the X-Factors and the club head speeds had reached to the subjects' average club head speeds, but the X-Factors and the club head speeds were not increased above the subjects' average club head speeds. The X-Factor Stretch early in the down swing was existed and Professional stretched values were higher than the amateurs. In conclusion my research results suggested that the increase in Effective X-Factors had no relationship to the increase in club head speeds.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.241-263
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• 2022

We consider a nonlinear Schrödinger equation with critical frequency, (P_𝜀) : 𝜀²∆v(x) - V(x)v(x) + |v(x)|^p-1v(x) = 0, x ∈ ℝ^N, and v(x) → 0 as |x| → +∞, for the infinite case as described by Byeon and Wang. Critical means that 0 ≤ V ∈ C(ℝ^N) verifies Ƶ = {V = 0} ≠ ∅. Infinite means that Ƶ = {x₀} and that, grossly speaking, the potential V decays at an exponential rate as x → x₀. For the semiclassical limit, 𝜀 → 0, the infinite case has a characteristic limit problem, (P_inf) : ∆u(x)-P(x)u(x) + |u(x)|^p-1u(x) = 0, x ∈ Ω, with u(x) = 0 as x ∈ Ω, where Ω ⊆ ℝ^N is a smooth bounded strictly star-shaped region related to the potential V. We prove the existence of an infinite number of solutions for both the original and the limit problem via a Ljusternik-Schnirelman scheme for even functionals. Fixed a topological level k we show that v_k,𝜀, a solution of (P_𝜀), subconverges, up to a scaling, to a corresponding solution of (P_inf ), and that v_k,𝜀 exponentially decays out of Ω. Finally, uniform estimates on ∂Ω for scaled solutions of (P_𝜀) are obtained.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.

• Korean Journal of Materials Research
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• v.13 no.1
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• pp.48-52
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• 2003

The substituted yttrium iron garnet systems $Y_{ 3-x}$/Gd$_{x}$X$0.2_{0.2}$ $Fe_{4.8}$ $O _{12}$ (x = 0.2, 0.4, 0.6) have been investigated by means of X-ray diffraction, Mossbauer spectroscopy and SQUID. The X-ray diffraction patterns at room temperature confirm the samples to have a single phase of the garnet structure over the whole composition range. The lattice constants of all the samples linearly change with increasing x due to the size of substituted ions in the dodecahedral sites. $Y_{3-x}$ $Gd_{x}$ X$Fe_{4.8}$ $In_{0.2}$ $O_{12}$ system which $Y_{3-x}$ ions are substituted with Gd$^{ 3＋}$ ions, the Mossbauer spectrum consists of three Zeeman sextets at room temperature, one due to the $Fe^{3＋}$ ions on the octahedral(a-) sites and the others due to the $Fe^{3＋}$ ions on the tetrahedral(d-, d'-) sites, respectively. From the hysteresis loop measured by means of SQUID over the whole composition range, the saturation magnetization $M_{s}$ and magnetic moments $\mu_{ B}$ per unit cell have been obtained. The increment of Gd-ion content causes $M_{s}$ and $\mu_{B}$ decrease while the increment of In-ion content does not.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.167-181
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• 2009

Based on Ricatti equation $XA^{-1}X=B$ for two (positive invertible) operators A and B which has the geometric mean $A{\sharp}B$ as its solution, we consider a cubic equation $X(A{\sharp}B)^{-1}X(A{\sharp}B)^{-1}X=C$ for A, B and C. The solution X = $(A{\sharp}B){\sharp}_{\frac{1}{3}}C$ is a candidate of the geometric mean of the three operators. However, this solution is not invariant under permutation unlike the geometric mean of two operators. To supply the lack of the property, we adopt a limiting process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for all integers $k{\geq}2$ by induction. For three positive operators, in particular, we define the weighted geometric mean as an extension of that of two operators.

• YAKHAK HOEJI
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• v.32 no.1
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• pp.80-85
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• 1988

QSAR of Salicylic acid derivatives, as anti-inflammatory agent, classified into Group I (not-having-5-phenyl ones) and Group II (having-5-phenyl ones) were investigated by quantum chemical calculations. The results are below: not significant statistically for both of Group I and Group II, but significant for each Group. $potency=-8.46X_{5}+1.639\;n=5\;r=0.77\;se=0.31\;for\;Group\;I.$ $({\pm}4.05)\;({\pm}0.5)$ where $X_5$ means charge of carbon atom bonded to hydroxyl radical. $potency=0.16X_{19}+7427.38HO-6629.85X_{15}+4977.40X_{10}+351.51X_5+3378.84$ $({\pm}0.17)\;({\pm}10.18)\;({\pm}11.70)\;({\pm}33.78)\;({\pm}4.41)\;({\pm}13.13)$ n=7 r=0.99 se=0.019 for Group II. where $X_{19}$ and $X_{15}$ stand for charges of the para carbon and the first carbon atoms in phenyl radical, respectively and $X_{10}$, charge of carboxylic carbon atom, HO, HOMO energy. It seems to be possible to qualitatively predict potency of drug by Pearson's HSAB theory. It means that drug should possess low LUMO energy and high HOMO energy.