• 대한수학회지
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• 제55권3호
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• pp.735-747
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• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• 호남수학학술지
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• 제39권3호
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• pp.363-377
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

• 대한수학회지
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• 제54권3호
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• pp.999-1013
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean (n + 1)-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^4$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.842-847
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• 2005

Although there are many applications of Euclidean Voronoi diagram for spheres in a 3D space in various disciplines from sciences and engineering, it has not been studied as much as it deserves. In this paper, we present an edge-tracing algorithm to compute the Euclidean Voronoi diagram of 3-dimensional spheres in O(mn) in the worst-case, where m is the number of edges of Voronoi diagram and n is the number of spheres. After building blocks for the algorithm, we show an example of Voronoi diagram for atoms using actual protein data and discuss its applications for protein analysis.

• 한국지역지리학회지
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• 제6권3호
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• pp.83-99
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• 2000

이 논문의 연구목적은 초등학교 아동의 사회 교과서 내용 중 지리영역 학습내용구성의 개선에 기여할 수 있는 기초자료를 제공하는 데 있다. 이러한 목적을 위하여 공간인지발달이론을 초등학교 학생의 그림분석을 통해 검증하였다. 분석의 결과, 공간의 조작능력은 연령의 종가와 더불어 형상적 공간에서 투영적 공간을 거쳐 기하학적 공간을 조작하는 과정으로 진행됨을 알 수 있었다. 이는 피아제와 인헬데르의 인지발달이론에서 주장하는 바와 일치하였다. 그러나 그들이 제시한 각 조작기별 해당 연령은 실제와 비교하면 조작기 구분의 엄밀한 기준이 되지 않음을 보여 주었다. 그 이유는 같은 연령의 아동간에도 현격한 개인차를 지니기 때문이다. 이와 같은 연구의 결과는 지리 교육적으로 다음과 같은 시사점을 제공한다: 첫째, 초등학교 3학년 교과서의 내용 중 사진과 그림지도와 삽화 등이 아동의 지적 수준에 맞는지 의문스럽다. 둘째, 3학년 아동에게 그림지도를, 4학년 아동에게 실측도와 유사한 지도를 직접 그리게 하는 것은 기하학적 공간의 조작에 속하므로 큰 무리가 따른다.

• 한국컴퓨터그래픽스학회논문지
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• 제9권3호
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• pp.15-21
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• 2003

An algorithm is developed for augmenting a real video with virtual graphics objects without computing Euclidean information. Real motion of the camera is obtained in affine space by a direct linear method using image matches. Then, virtual camera is provided by determining the locations of four basis points in two input images as initialization process. The four pairs of 2D location and its 3D affine coordinates provide Euclidean orthographic projection camera through the whole video sequence. Our method has the capability of generating views of objects shaded by virtual light sources, because we can make use of all the functions of the graphics library written on the basis of Euclidean geometry. Our novel formulation and experimental results with real video sequences are presented.

• 디지털융복합연구
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• 제17권10호
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• pp.233-242
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• 2019

수많은 공간지각 연구 결과, Euclidean 3-D 구조는 양안 입체시, 움직임, 입체시와 움직임의 결합, 또는 여러 광학 정보의 결합으로도 복구될 수 없다는 사실이 밝혀졌다. 그러나 인간은 이러한 부정확한 공간지각에도 불구하고 특정 과제를 수행하는 데는 어려움이 전혀 없다. 우리는 인공지능과 컴퓨터 비전에 인간의 기술과 능력을 적용해 왔지만 이러한 기계들은 여전히 인간의 능력보다 훨씬 뒤떨어져 있다. 따라서 우리는 인간이 공간의 깊이를 어떻게 지각하는지, 과제를 수행하기 위해 어떠한 정보들을 사용하여 3차원 공간을 정확하게 지각하는지 이해해야 한다. 이 논문의 목적은 미래에 더욱 발전된 인공지능 로봇에 인간의 능력을 적용하기 위해 공간지각 문헌을 검토하는 것이다.

• Korean Journal of Acupuncture
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• 제33권1호
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• pp.18-32
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• 2016

Objectives : This study aims to analyze the co-occurrence of pathological symptoms and corresponding acupoints as documented by the comprehensive acupuncture and moxibustion records in the classical texts of Far East traditional medicine as an aid to a more efficient understanding of the tacit treatment principles of ancient physicians. Methods : The Classic of Nourishing Life with Acupuncture and Moxibustion(Zhenjiu Zisheng Jing; hereinafter ZZJ) was selected as the primary reference book for the analysis. The pathology-acupoint co-occurrence analysis was performed by applying 4 values of vector space measures(weighted Euclidean distance, Euclidean distance, $Cram\acute{e}r^{\prime}s$ V and Canberra distance), which measure the distance between the observed and expected co-occurrence counts, and 3 values of probabilistic measures(association strength, Fisher's exact test and Jaccard similarity), which measure the probability of observed co-occurrences. Results : The treatment records contained in ZZJ were preprocessed, which yielded 4162 pathology-acupoint sets. Co-occurrence was performed applying 7 different analysis variables, followed by a prediction simulation. The prediction simulation results revealed the Weighted Euclidean distance had the highest prediction rate with 24.32%, followed by Canberra distance(23.14%) and association strength(21.29%). Conclusions : The weighted Euclidean distance among the vector space measures and the association strength among the probabilistic measures were verified to be the most efficient analysis methods in analyzing the correlation between acupoints and pathologies found in the classical medical texts.

• 복식
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• 제60권5호
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• pp.117-127
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• 2010

In this study, hyperspace is a result of imagination created by means of facts and fiction, represents a transfer to determination and indetermination, and means an extension to an open form. In other words, hyperspace is a high dimensional space expanded to imagination through the combination of the viewpoint on facts in this dimension and fiction. When the 2D plane surface or 3D symmetry is destroyed, or when the frame is twisted or entangled, the non-Euclidean geometry is created eventually. And when the twisting leads to transmutation and the destruction of the form reaches the extreme; this in turn became the twisting like Mbius band. Likewise, the non-Euclidean geometry is co-related to the asymmetry of the Higgs mechanism. When the 'destruction of symmetry' is considered, symmetric theory and asymmetric world can be connected. The asymmetry in turn can maintain balance by arranging the uneven weights at different distances from the shaft. Moreover, at this the concept of the upper, lower, left and right, which was included in the original form, may be crumbled down. The destruction of the symmetry is essential in order to present forecast that coincides with the phenomenon of the real world. Non-Euclidean geometry characteristic is expressed by asymmetry, twists, and deconstruction and its representative characteristic is ambiguity. The boundary between the front, back, upper, lower, inner and outer is unclear, and it is difficult and vague to pinpoint specific location. The design that does not clearly define or determine the direction of wearing costume is indeed the non-oriented design that can be worn without getting restricted by specific direction such as front and back. Non-Euclidean geometry characteristic of hyperspace have been applied to create new shapes through the modification of the substance from traditional clothing of the eastern world to modern fashion. The way of thinking in the 'hyperspace' that used to be expressed in the costumes of the east and the west in the past became the forum for unlimited creation.

• Kyungpook Mathematical Journal
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• 제3권2호
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• pp.49-54
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• 1960