• East Asian mathematical journal
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• v.23 no.1
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• pp.37-43
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• 2007

We study a maximal operator defined on spaces of homogeneous type, and we prove that this operator is of weak type (1,1). As a consequence we show that the maximal operator belongs to the Muckenhoupt's class $A_1$.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.307-314
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• 2010

By introducing a homogeneous kernel of 0-degree with an independent parameter and estimating the weight coefficient, a bilateral form of the Hilbert-type series inequality with a best constant factor is established.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.495-498
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• 2008

Every totally disconnected space is hereditarily disconnected. In this note, we provide an example of a hereditarily disconnected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.05a
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• pp.369-369
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• 2009

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.7-13
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• 1987

This paper is a study of the oscillatory and asymptotic behaviour of solutions of the second order nonhomogeneous linear differential equation y"+P(x)y=f(x), and the associated homogeneous equation. Conditions are determined, under which the nonhomogeneous equation is oscillatory if and only if the homogeneous equation is oscillatory.

• Bulletin of the Korean Chemical Society
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• v.24 no.12
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• pp.1859-1861
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• 2003

• Honam Mathematical Journal
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• v.22 no.1
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• pp.99-106
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• 2000

We prove that a certain class of real hypersurfaces in $P_3({\mathbb{C}})$ has the rigidity. Making use of this we classify all homogeneous real hypersurfaces in $P_3({\mathbb{C}})$.

• Journal of the Korean Ceramic Society
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• v.35 no.11
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• pp.1212-1221
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• 1998

• Journal of the Korean Geotechnical Society
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• v.15 no.6
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• pp.29-44
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• 1999

This paper shows the results of model tests on the lateral behavior of single rigid pile, which was constructed by driving, in homogeneous and non-homogeneous (two layered) NakDong River sands. The purpose of the present paper is to investigate the effect of ratio of lower layer thickness to embedded pile length, relative density of sand and pile construction conditions (Driven & Embedded piles) on the characteristics of lateral behavior of single pile. These effects can be quantified only by the results of model tests. As a model result, the lateral behavior depends upon the pile construction condition in loose-density soil more than in high-density soil. If the pile construction depends upon driving construction, the decrease of deflection remarkably increases for both loose homogeneous sand and non-homogeneous soil$(E_{h1}/E_{h2}/=0.18)$ with high thickness of upper layer but the decrease of maximum bending moment shows the opposite result to the decrease of deflection. And, with respect to deflection, it was found that the deflection ratio $(y_{Driven}y_{Embedded})$ of embedded to driven piles has the ranges of 0.65 - 0.88 $(D_r=90%)$0.38 - 0.65 $(D_r=61.8%)$ for each relative density of homogeneous soil and the range of 0.6 - 0.88 for non-homogeneous soil. Also, in this study, the experimental equation for the effects of drop height (DH) and H/L on the ratios of $y_D/y_E\; and MBM_D/MBM_ E$ is suggested from model tests.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.853-858
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• 2006

TMHMM(Tied Mixture Hidden Markov Model) is an important approach to reduce the number of free parameters in speech recognition. However, this model suffers from a degradation in recognition accuracy due to its GPDF (Gaussian Probability Density Function) clustering error. This paper proposes a clustering algorithm, called HCNN(Homogeneous Centroid Neural network), to cluster acoustic feature vectors in TMHMM. Moreover, the HCNN uses the heterogeneous distance measure to allocate more code vectors in the heterogeneous areas where probability densities of different states overlap each other. When applied to Korean digit isolated word recognition, the HCNN reduces the error rate by 9.39% over CNN clustering, and 14.63% over the traditional K-means clustering.