• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.895-905
• /
• 2009

Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.643-649
• /
• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.

• The KIPS Transactions:PartD
• /
• v.12D no.2 s.98
• /
• pp.233-246
• /
• 2005

To enhance the user response time of content-based retrieval service for multimedia information, several multi-dimensional index schemes have been proposed. M-tree, a well-known multidimensional index scheme is of metric space access method, and is based on the distance between objects in the metric space. However, since the overlap between index spaces of nodes might enlarge the number of nodes of M-tree accessed for query processing, the user response time for content-based multimedia information retrieval grows longer. In this paper, we propose a node split algorithm which is able to reduce the sire of overlap between index spaces of nodes in M-tree. In the proposed scheme, we choose a virtual center point as the routing object and entry redistribution as the postprocessing after node split in order to reduce the radius of index space of a node, and finally in order to reduce the overlap between the index spaces of routing nodes. From the experimental results, we can see the proposed split algorithm reduce the overlap between index space of nodes and finally enhance the user response time for similarity-based query processing.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.355-359
• /
• 1994

It would be interesting to know if energy minimizing harmonic maps between manifolds have symmetric properties when the manifolds under consideration have some. In this paper, we consider among others radial symmetry. A radially symmetric manifold M of dimension m is the one with a point, called a pole, and an O(m) action as an isometric rotation with respect to the pole, or more precisely a radially symmetric manifold M has a coordinate on which the metric is of the form $ds_{M}$$^2$ = d$r^2$ + m(r)$^2$d$\theta^2$ for some function m(r) depending only on r. Of course m(0) = 0, m'(0) = 1, and when m(r) = r, (M, $ds_{ M}$/$^2$) is the Euclidean space $R^2$.(omitted)

• 한국HCI학회:학술대회논문집
• /
• 2006.02a
• /
• pp.355-361
• /
• 2006

In large scale environments like airport, museum, large warehouse and department store, autonomous mobile robots will play an important role in security and surveillance tasks. Robotic security guards will give the surveyed information of large scale environments and communicate with human operator with that kind of data such as if there is an object or not and a window is open. Both for visualization of information and as human machine interface for remote control, a 3D model can give much more useful information than the typical 2D maps used in many robotic applications today. It is easier to understandable and makes user feel like being in a location of robot so that user could interact with robot more naturally in a remote circumstance and see structures such as windows and doors that cannot be seen in a 2D model. In this paper we present our simple and easy to use method to obtain a 3D textured model. For expression of reality, we need to integrate the 3D models and real scenes. Most of other cases of 3D modeling method consist of two data acquisition devices. One for getting a 3D model and another for obtaining realistic textures. In this case, the former device would be 2D laser range-finder and the latter device would be common camera. Our algorithm consists of building a measurement-based 2D metric map which is acquired by laser range-finder, texture acquisition/stitching and texture-mapping to corresponding 3D model. The algorithm is implemented with laser sensor for obtaining 2D/3D metric map and two cameras for gathering texture. Our geometric 3D model consists of planes that model the floor and walls. The geometry of the planes is extracted from the 2D metric map data. Textures for the floor and walls are generated from the images captured by two 1394 cameras which have wide Field of View angle. Image stitching and image cutting process is used to generate textured images for corresponding with a 3D model. The algorithm is applied to 2 cases which are corridor and space that has the four wall like room of building. The generated 3D map model of indoor environment is shown with VRML format and can be viewed in a web browser with a VRML plug-in. The proposed algorithm can be applied to 3D model-based remote surveillance system through WWW.

• Honam Mathematical Journal
• /
• v.1 no.1
• /
• pp.27-34
• /
• 1979

근래(近來) Skorokhod는 확률론(確率論)의 극한문제(極限問題)와 관련(關聯)하여 모든 불연속함수공간(不連續函數空間)에 관(關)한 위상(位相)을 정의(定義)하였다. 본(本) 논문(論文)에서는 Skorokhod 수렴위상(收斂位相)을 쌍위상(雙位相)(bitopology)형(型)으로 일반화(一般化)하고 잘 알려져 있는 여러위상(位相)과 비교(比較)하여 다음과 같은 결과(結果)를 새로 얻었다. (정리(定理) 2-11); 공간(空間) X와 Y가 완비준거이가분공간(完備準距離可分空間) (Completdy quasi-metric separable space)이라면 쌍개수렴위상(雙槪收斂位相)(pairwise almost convergent topology)는 Skorokhod 쌍수렴위상(雙收斂位相) 보다 약(弱)하다. 그리고 (정리(定理) 2-12); 쌍(雙) graph 위상(位相)은 Skorokhod $J_1$-수렴위상(收斂位相)과 일치(一致)한다. 끝으로 주정리(主定理)인 (정리(定理( 3-1)과 (정리(定理) 3-2)에서 Skorokhod 쌍수렴위상(雙收斂位相)의 Compact성(性)에 관(關)한 필요충분조건(必要充分條件)을 밝혔다.

• Journal of Broadcast Engineering
• /
• v.24 no.2
• /
• pp.353-356
• /
• 2019

The main functionality of occupancy sensors is to determine the existence of humans in the space. If the space is occupied, a light is on and for vacancy, the light automatically turns off. In this letter, the functionality is realized by the utilization of color information. The color information of incoming people is saved. For outgoing people, their color distribution is compared with the saved information, thus providing the recognition of the outgoing people. For the comparison, four similarity metrics are examined to validate the proposed method.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.225-236
• /
• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

• The Pure and Applied Mathematics
• /
• v.26 no.3
• /
• pp.111-131
• /
• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.24 no.6
• /
• pp.18-26
• /
• 2010

Outdoor lighting has become a necessary essential part of society for safety and comfortable space. However, inappropriate outdoor lighting leads to energy waste and poor landscape. Outdoor lighting is a very important social element, which enables us to conduct various activities at night in a safe, efficient and comfort way. River Thames in UK, Venice in Italy and Sydney in Australia is a good example of the coastal area. This paper aims to evaluate the light pollution of outdoor lighting in coastal area in Busan city. The Radiant Imaging ProMetric-1400 was used to measure the luminance of Gwangalli Beach, Marine City and Haeundae Beach. Compare to the CIE recommendation level the luminance of the all outdoor lighting were about 2~20 times higher. Outdoor lighting of the building facade luminance level and color should be particularly limited.