• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.189-201
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• 2005

In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.683-699
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• 2017

We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric $Q^{m*}=SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field N becomes A-principal or A-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^{m*}=SO_{m,2}/SO_mSO_2$ with Killing shape operator.

• Proceeding of Spring/Autumn Annual Conference of KHA
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• 2009.11a
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• pp.104-108
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• 2009

Rapid urbanization resulted in expansion of urban area and increase of population bringing deepened housing shortage. Supply-oriented housing policy made apartment a representative residential space in Korea in spite of the short history of apartment. This study analyzed the shape and arrangement of main building by year and the microclimate in the complex depending on the number of floors. The purpose of this study was to present the basic data in developing apartment complex to solve problems like the stagnation of pollution source and the rise of temperature due to the declined ventilation in apartment complex, and the worsened urban heat island phenomenon due to the impeded flow of wind. This study rearranged the shape and arrangement of main building by year and the tendency of the number of floors by year in the process of change, by generalizing the process of change of apartment complex, a representative modern residential space through preliminary research. Based on it, 8 object lot by age was selected and simulated by using Envi-met. Simulation identified that the change of apartment complex takes place having a positive effect on microclimate in the apartment complex and the microclimate in the apartment complex is influenced a lot by the shape of complex. If in future apartment complex plan, a systematic legal criteria of design is made about the shape and arrangement of main building, it might have a positive effect on the improvement of microclimate in the apartment complex, a representative residential space in Korea.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.57-68
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• 2015

In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, $m{\geq}3$, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection $\hat{\nabla}^{(k)}$.

• Journal of Plant Biology
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• v.34 no.3
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• pp.229-238
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• 1991

The main objective of this study was to clarify the taxonomic status and the speciation mechanism of Viola albida complex in Korea. The complex includes three very closely related taxa, taxonomic ranks of which are much in dispute. These taxa in the complex are sympatric in distribution, and they are very similar in most morphological characteristics. Comparative morphological analyses revealed that they can be distinguished on the basis of leaf shape, although they show complicated patterns of variation in leaf shape. The variation of leaf shape in each taxon appeared to be maintained through developmental process, and extensive cleistogamy and vegetative reproduction in these taxa are suggested as the mechanisms maintaining the variation. Genetic variation in this complex was monomorphic in all 14 loci examined. Palynological study also showed that these taxa have the same pollen morphology. These results strongly suggested that they should be recognized as varieties of V. albida; var, albida, var. chaerophylloides, and var. takahashii. The results also suggested that some individuals that can be assigned to var. takahashii might be hybrids between var. albida and var. chaerophylloides.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.525-535
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• 2017

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

• Journal of Digital Convergence
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• v.15 no.4
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• pp.267-273
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• 2017

With the development of various devices and communication technologies, the production and distribution of various multimedia contents are increasing exponentially. In order to retrieve multimedia data such as images and videos, an approach different from conventional text-based retrieval is needed. Color and shape are key features used in content-based image retrieval, which quantifies and analyzes various physical features of images and compares them to search for similar images. Color and shape have been used as independent features, but the two features are closely related in terms of cognition. In this paper, a method of describing the spatial distribution of color using a complex color model that projects three-dimensional color information onto two-dimensional complex form is proposed. Experimental results show that the proposed method can efficiently represent the shape of spatial distribution of colors by frequency transforming the complex image and reconstructing it with only a few coefficients in the low frequency.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.575-578
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• 2005

Topographical images, in case of aerial or satellite images, are usually similar in colors and textures, and complex in shapes. Thus we have to use shape features of images for efficiently retrieving a query image from topographical image databases. In this paper, we propose a shape feature extraction method which is suitable for topographical images. This method, which improves the existing projection in the Cartesian coordinates, performs the projection operation in the polar coordinates. This method extracts three attributes, namely the number of region pixels, the boundary pixel length of the region from the centroid, the number of alternations between region and background, along each angular direction of the polar coordinates. It extracts the features of complex shape objects which may have holes and disconnected regions. An advantage of our method is that it is invariant to rotation/scale/translation of images. Finally we show the advantages of our method through experiments by comparing it with CSS which is one of the most successful methods in the area of shape feature extraction

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.535-565
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• 2004

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$_1$, ξ$_2$, ξ$_3$｝.X>｝.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.897-904
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• 2022

In this paper, we obtain an inequality involving the squared norm of the covariant differentiation of the shape operator for a real hypersurface in nonflat complex space forms. It is proved that the equality holds for non-Hopf case if and only if the hypersurface is ruled and the equality holds for Hopf case if and only if the hypersurface is of type (A).