• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.23-76
• /
• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Journal of the Korean housing association
• /
• v.17 no.2
• /
• pp.97-106
• /
• 2006

The purpose of this study is to provide basic data for the planning of adolescents preferred space, and fur the purpose of the study analyzed the spaces made by them in the web site where 3-dimension space manipulating is possible and captured their consciousness of space. The study was to interview 60 adolescents in the web-site by video chatting and observation by video ethnography. The results are as follows. 1) Three-dimension space is where adolescents express their present preference for spaces of residence, leisure and outer activities, and where they reveal their desire to be realized in the future. 2) Adolescents foster friendship in the cyberspace, where they meet friends and enjoy talking and share their desire for space creation which is hardly come true in reality. 3) It is possible to grasp their latent preference of space, and actualization of the cyber preference would give them more satisfaction.

• Korean Institute of Interior Design Journal
• /
• v.19 no.5
• /
• pp.56-66
• /
• 2010

This study proposes a thesis of architectural concepts and visual dimension systems, and the comparison between steps of spatial formation and dimensional alteration. The second chapter, to form the basis of this study, explains the dimensional alterations and changes of fundamental notion of space. In the third chapter, history of space, architectural formations, and changes of the viewpoint are analyzed as objects of study. The forth chapter presents the interrelation between dimensional alteration and the transition in fundamental notion of space, demonstrating that modern architecture has been born from these cultural movements. Lastly, the fifth chapter suggests possibilities on further studies and the following conclusions: First, architectural spaces have been changed, in accordance with the changes of culture, art and the tools that regulate architectural design. Proportional regulations by two-dimensional tools and depth through three-dimensional drawings are created. Second, architectural spaces gained depth by recognizing movement and time that have induced formations to change, creating various aesthetic backgrounds and attempts. Third, the aesthetic background and cosmologic spatial concept have led the visualization and changes of architectural experience. It created the design tools and shapes originated in dynamism and vitality. Forth, diversification of fundamental spatial concepts has become palimpsest and complex, and been divided into four dimensions; expressional two-dimensional space, perspective three-dimensional space, forth-dimensional space of time and experience, and imagery space formed by body movement. Fifth, architecture has been influenced by the elevated viewpoint that understands the whole world as a space. It has evolved from the two-dimensional proportion principle, change of depth and vanishing point to multidimensional space of movement and time. Sixth, changes of fundamental notion of space have arisen from changes of visual dimensions in times. In other words, space has been developed from two-dimensional space to multidimensional space by accepting visual dimension, grasping distance, direction, depth, height, velocity, movement, gravity, power and structure.

• Speech Sciences
• /
• v.3
• /
• pp.148-155
• /
• 1998

As an application of dimensional analysis in the theory of chaos and fractals, we studied and estimated the information dimension for various phonemes. By constructing phase-space vectors from the time-series speech signals, we calculated the natural measure and the Shannon's information from the trajectories. The information dimension was finally obtained as the slope of the plot of the information versus space division order. The information dimension showed that it is so sensitive to the waveform and time delay. By averaging over frames for various phonemes, we found the information dimension ranges from 1.2 to 1.4.

• Journal of The Korean Astronomical Society
• /
• v.41 no.6
• /
• pp.157-161
• /
• 2008

We have estimated the fractal dimension of the molecular clouds associated with the Hii region Sh 156 in the Outer Galaxy. We selected the $^{12}CO$ cube data from the FCRAO CO Survey of the Outer Galaxy. Using a developed code within IRAF, we identified slice-clouds (2-dimensional clouds in velocity-channel maps) with two threshold temperatures to estimate the fractal dimension. With the threshold temperatures of 1.8 K, and 3 K, we identified 317 slice-clouds and 217 slice-clouds, respectively. There seems to be a turn-over location in fractional dimension slope around NP (area; number of pixel) = 40. The fractal dimensions was estimated to be D = $1.5\;{\sim}\;1.53$ for $NP\;{\geq}\;40$, where $P\;{\propto}\;A^{D/2}$ (P is perimeter and A is area), which is slightly larger than other results. The sampling rate (spatial resolution) of observed data must be an important parameter when estimating fractal dimension. Fractal dimension is apparently invariant when varying the threshold temperatures applied to slice-clouds identification.

• Journal of Information Technology Applications and Management
• /
• v.14 no.3
• /
• pp.179-197
• /
• 2007

This paper analyzed the effects of interactions among participants on the satisfaction and commitment of cyber education. Even if the quality of interactions in cyber education may not be so good as that of interactions in face to face education. various kinds of interactions could be introduced in cyber education. An email or Q/A between lecturer and students could be a good way to compensate the deficiency of cyber education. Common News Boards or Discussion Rooms among students themselves are also a powerful means to learn each other in cyber space. The result of this study shows that as interactions among participants increase. satisfaction and commitment of the lecture also increase. This study also analyzed how cyber educational effects differs as interaction type changes in space dimension and time dimension. The result shows interactions in the same cyber space such as News Board brings more desirable outcome than those in the different cyber space. But the effects of interactions classified by time dimension does not show statistically significant differences.

• Korean Journal of Mathematics
• /
• v.6 no.2
• /
• pp.243-257
• /
• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.

• Communications of the Korean Mathematical Society
• /
• v.16 no.2
• /
• pp.265-275
• /
• 2001

In the previous paper we studied n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space CP(sup)(n+p)/2, and especially determined such submanifolds under curvature conditions related to vertical direction; In the present article we determine such submanifolds under curvature conditions related to horizontal directions.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.613-631
• /
• 2003

The purpose of this paper is to study n-dimensional QR-submanifolds of (p - 1) QR-dimension in a quaternionic projective space $QP^{(n+p)/4}$ and especially to determine such submanifolds under the curvature conditions appeared in (5.1) and (5.2).

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.575-586
• /
• 2001

The purpose of this paper is to study n-dimensional CR-submanifolds of (n-1) CR-dimension immersed in a complex projective space $CP^{(n+p)/2}$, and especially to determine such submanifolds under some curvature conditions.