• Korean Journal of Mathematics
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• v.4 no.2
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• pp.163-171
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• 1996

We investigate change of the torsion tensor induced by the conformal change in 6-dimensional $g$-unified field theory. These topics will be studied for the second class with the second category in 6-dimensional case.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.185-191
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• 2004

We investigate change of the vector $U_{\mu}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.209-215
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• 2005

We investigate change of the vector $S_{\omega}$ induced by the conformal change in 7-dimensional $g$-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.141-149
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• 1997

We investigate chnage of the tensor $U^{\nu}{_{\lambda}{\mu}}$ induced by the conformal change in 6-dimensional $g$-unified field theory. These topics will be studied for the second class with the second category in 6-dimensional case.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.199-205
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• 1999

We investigate change of the tensor $U^{\nu}_{{\lambda}{\mu}}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• 한국기계연구소 소보
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• s.20
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• pp.13-20
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• 1990

An algorithm is presented for 3-dimensional contour lines with a hidden line removal ~technique developed by T.L. Janssen(l). Contour line algorithm on any 3-dimensional plane cutting solid body is also shown. NUFIG(2) algorithm is adopted for searching contour lines. Test problems show well-established contour lines on the surface and also on the cutting plane of the structure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.9
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• pp.2991-3007
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• 2022

Two dimensional locality preserving projections (2D-LPP) is an improved algorithm of 2D image to solve the small sample size (SSS) problems which locality preserving projections (LPP) meets. It's able to find the low dimension manifold mapping that not only preserves local information but also detects manifold embedded in original data spaces. However, 2D-LPP is simple and elegant. So, inspired by the comparison experiments between two dimensional linear discriminant analysis (2D-LDA) and linear discriminant analysis (LDA) which indicated that matrix based methods don't always perform better even when training samples are limited, we surmise 2D-LPP may meet the same limitation as 2D-LDA and propose a novel matrix exponential method to enhance the performance of 2D-LPP. 2D-MELPP is equivalent to employing distance diffusion mapping to transform original images into a new space, and margins between labels are broadened, which is beneficial for solving classification problems. Nonetheless, the computational time complexity of 2D-MELPP is extremely high. In this paper, we replace some of matrix multiplications with multiple multiplications to save the memory cost and provide an efficient way for solving 2D-MELPP. We test it on public databases: random 3D data set, ORL, AR face database and Polyu Palmprint database and compare it with other 2D methods like 2D-LDA, 2D-LPP and 1D methods like LPP and exponential locality preserving projections (ELPP), finding it outperforms than others in recognition accuracy. We also compare different dimensions of projection vector and record the cost time on the ORL, AR face database and Polyu Palmprint database. The experiment results above proves that our advanced algorithm has a better performance on 3 independent public databases.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.173-179
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• 1996

M be an ($n\geq3$)-dimensional compact connected and oriented Riemannian manifold isometrically immersed on an (n ＋ 2)-dimensional sphere $S^{n＋2}$(c). If all sectional curvatures of M are not less than a positive constant c, show that M is a real homology sphere.

• Bulletin of the Korean Chemical Society
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• v.22 no.9
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• pp.1041-1044
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• 2001

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6B
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• pp.515-522
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• 2011

The hydrodynamic models are widely used in the research for analysis of flow characteristics and design of hydraulic structure and river channel. These models need to be calibrated with observed data. But, there are few field data of two-dimensional flow velocity in flood because the direct measurement of the flood flow velocity are very dangerous. For this reason the results of two-dimensional numerical models are usually calibrated and verified with only a few observed data. Moreover, the verification of numerical models for the design flood is usually carried out using the result of one-dimensional model, HEC-RAS. In this study, using the flow velocity profile extracted from the aerial photos of a flood of the Tone River in Japan, two-dimensional numerical models, RAM2 in RAMS, RMA2 in SMS, and one-dimensional numerical model, HEC-RAS which are most widely used in research and design work are verified and the validity for verification of two-dimensional models with HEC-RAS is reviewed. The results showed that the water surface elevation of HEC-RAS, RAM2 and RMA2 models have similar results with observed data. But, the velocity results of RAM2 and RMA2 models in the floodplain have some difference with the velocity from aerial photo analysis. And the velocity result of HEC-RAS has big difference with the sectional averaged value of velocity from aerial photo analysis.