• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.133-166
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• Journal of Information Technology and Architecture
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• v.10 no.1
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• pp.79-91
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• 2013

This paper proposes a systematic methodology that could be used to decide which one shows the best performance among space filling curves (SFCs) in applying lower-dimensional transformations to histogram sequences. A histogram sequence represents a time-series converted from an image by the given SFC. Due to the high-dimensionality nature, histogram sequences are very difficult to be stored and searched in their original form. To solve this problem, we generally use lower-dimensional transformations, which produce lower bounds among high dimensional sequences, but the tightness of those lower-bounds is highly affected by the types of SFC. In this paper, we attack a challenging problem of evaluating which SFC shows the better performance when we apply the lower-dimensional transformation to histogram sequences. For this, we first present a concept of spatial locality, which comes from an intuition of "if the entries are adjacent in a histogram sequence, their corresponding cells should also be adjacent in its original image." We also propose spatial locality preservation metric (slpm in short) that quantitatively evaluates spatial locality and present its formal computation method. We then evaluate five SFCs from the perspective of slpm and verify that this evaluation result concurs with the performance evaluation of lower-dimensional transformations in real image matching. Finally, we perform k-NN (k-nearest neighbors) search based on lower-dimensional transformations and validate accuracy of the proposed slpm by providing that the Hilbert-order with the highest slpm also shows the best performance in k-NN search.

• Journal of the Korean Institute of Landscape Architecture
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• v.31 no.2
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• pp.1-11
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• 2003

The purpose of this study is to investigate how five winning design proposals for the Seoul City Hall Plaza Design Competition have shown the spatial characteristics by comparing and reviewing them. Each design proposal shown different approaches that reveal the spatial characteristics. Through scrutinizing these design proposals, some similar and different aspects among them were identified. In order to examine these aspects, the winning design proposals were analysed and compared based on five categories such as design concepts, main facilities, representation of historical images, spatial connection, and event programs. Gilles Deleuze explained the spatial characteristics as striated space and smooth space. Striated space could be defined as sedentary space. It is distant vision-optical space that has dimensional, metric, and centered characteristics, whereas smooth space is defined as nomadic, close vision-haptic space that has directional and acentered characteristics. This study focused on the analysis of spatial characteristics according to smooth space and striated space. Based on the analysis of the spatial characteristics according to the smooth and striated space, some design proposals shown more characteristics of striated space while other proposals shown more characteristics of smooth space. Those design proposals that shown more characteristics of smooth space reveal flexible or changeable shape and void space, whereas the others that shown more characteristics of striated space try to suggest apparent guidelines for the future use by retaining the idea of a plaza through the concrete shape. This study, which analyzed the winning design proposals based on the spatial characteristics according to the smooth and striated space, can be used to analyze the designs and could help to develop a new methodology with a different perspective. furthermore, it could provide practical and creative design strategies for landscape design.

• Korean Institute of Interior Design Journal
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• v.21 no.1
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• pp.148-158
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• 2012

The objective of this study is to find a possible application of small space utilization of GangSo Housing, so called compact-but-effective housing, through analyzing that of Japanese small housing. We analyze openness of view and flexibility of spaces divided by the physical and architectural aspects as first component and the psychological and interior space aspects as second component. The results showed that Japanese small houses have various unit plan compared to uniformity of Korean houses. Openness of view in Japanese small housing is accomplished by letting in light from the outside using position and shape of the window, looking more spacious using courtyard, void spaces, or sliding door hanging from the ceiling, and creating deception of view using floor-wall plan and appropriate materials. Flexibility of spaces is achieved by combination of first and second components, multipurpose of space and furniture, and variety of storage methods. It is necessary to improve spatial efficiency with consideration of volume-metric planing rather than flat-plane and develop various unit plans to meet residents' needs and demands on compact-but-effective houses.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.917-931
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• 2013

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.513-520
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• 2006

The purpose of this note is to prove some properties related to the higher order Kobayashi metrics(resp. pseudodistances) as the counterpart for the usual Kobayashi metrics(resp. pseudo distances).

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.377-384
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• 2015

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.657-661
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• 2016

Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.427-446
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• 1995

Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.