• 대한전자공학회논문지TC
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• 제47권11호
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• pp.1-6
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• 2010

센서네트워크 등에서 단말 또는 노드들을 한 번씩 모두 방문하는 최적의 라우팅 경로를 동적으로 찾는 문제가 대두된다. 이러한 문제를 근사하게 해결 할 수 있는 일반화된 scheme을 제시하고, 이를 기반으로 구성되는 알고리즘의 실행시간 및 그 결과의 바운드를 수리적으로 정립하면, 주어진 네트워크에서 구축되는 라우팅 경로를 수리적으로 분석 할 수 있게 된다. 본 논문은 이러한 문제를 대표하는 Euclidean TSP(Euclidean Travelling Sales Person) 문제를 대상으로 하여, 근사 Euclidean TSP를 병렬처리 형태로 구성할 수 있는 scheme을 제공하고, 이 scheme에 의해 구해 질 수 있는 근사 Euclidean TSP가 최적의 Euclidean TSP와 어느 정도의 차이를 가지게 되는지 판단할 수 있는 기준을 제시한다.

• 대한수학회지
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• 제46권5호
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• pp.967-977
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• 2009

There are three standard weight functions on a linear code viz. Hamming weight, Lee weight, and Euclidean weight. Euclidean weight function is useful in connection with the lattice constructions [2] where the minimum norm of vectors in the lattice is related to the minimum Euclidean weight of the code. In this paper, we obtain an upper bound over the number of parity check digits for Euclidean weight codes detecting and correcting burst errors.

• 대한수학회보
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• 제55권6호
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• pp.1823-1834
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• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권2호
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• pp.297-306
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• 2005

In this paper, we propose a computer environment class for student's mental representations about non-Euclidean geometry. Through the software Cinderella, students construct knowledge about non-Euclidean geometry and recognize differentness between Euclidean and non-Euclidean geometry. Also they recognize an existence of non-Euclidean geometry newly and its mental representations with images represented in Cinderella. In geometry class, we make students can use many representations systematically and can figure a visual internal image by emphasizing a transform process. And then students can reason about non-Euclidean geometry.

• 대한수학회지
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• 제31권3호
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• pp.393-400
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• 1994

Subminifolds of Euclidean spaces have been studied by examining geodesics of the submanifolds viewed as curves of the ambient Euclidean spaces ([3], [7], [8], [9]). K.Sakamoto ([7]) studied submanifolds of Euclidean space whose geodesics are plane curves, which were called submanifolds with planar geodesics. And he completely calssified such submanifolds as either Blaschke manifolds or totally geodesic submanifolds. We now ask the following: If there is a point p of the given submanifold in Euclidean space such that every geodesic of the submanifold passing through p is a plane curve, how much can we say about the submanifold\ulcorner In the present paper, we study submanifolds of euclicean space with such property.

• East Asian mathematical journal
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• 제31권3호
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• pp.357-362
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• 2015

For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.

• 대한임베디드공학회논문지
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• 제16권5호
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• pp.215-223
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• 2021

3D data can be categorized into two parts : Euclidean data and non-Euclidean data. In general, 3D data exists in the form of non-Euclidean data. Due to irregularities in non-Euclidean data such as mesh and point cloud, early 3D deep learning studies transformed these data into regular forms of Euclidean data to utilize them. This approach, however, cannot use memory efficiently and causes loses of essential information on objects. Thus, various approaches that can directly apply deep learning architecture to non-Euclidean 3D data have emerged. In this survey, we introduce various deep learning methods for mesh and point cloud data. After analyzing the operating principles of these methods designed for irregular data, we compare the performance of existing methods for shape classification and segmentation tasks.

• 호남수학학술지
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• 제35권1호
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• pp.17-27
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• 2013

We survey and study several volume formulas of a Euclidean tetrahedron.

• 음성과학
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• 제11권2호
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• pp.211-216
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• 2004

In this paper, we present a fast encoding algorithm for vector quantization with an approximate Euclidean distance calculation. An approximation is performed by converting floating point to the near integer. An inequality between the approximate Euclidean distance and the nearest distance is developed to avoid unnecessary distance calculations. Since the proposed algorithm rejects those codewords that are impossible to be the nearest codeword, it produces the same output as conventional full search algorithm.

• 한국정보통신학회논문지
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• 제14권4호
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• pp.875-885
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• 2010

사례기반추론(CBR:Case-Based Reasoning)은 기존 데이터와 사례 데이터들의 관계성을 추론하는 기법으로 유사도(Similarity)와 유클리디안(Euclidean) 거리 계산 방법이 가장 많이 사용되고 있다. 그러나 이 방법들은 기존 데이터와 사례 데이터를 모두 비교하기 때문에 데이터 검색과 필터링에 많은 시간이 소요되는 단점이 있다. 따라서 이를 해결하기 위한 다양한 연구들이 진행되고 있다. 본 논문에서는 기존의 유사도와 유클리디안 계산과정에서 발견된 패턴을 활용한 SE(Speed Euclidean-distance) 계산방법을 제안한다. SE 계산방법은 새로운 사례입력에 발견된 패턴과 가중치를 적용하여 빠른 데이터 추출과 수행시간 단축으로 시간적 공간적 제약사항에 대한 연산 속도를 향상시키고 불필요한 연산 수행을 배제하는 것이다. 실험을 통해 유사도나 유클리디안 방법으로 데이터를 추출하는 기존의 방법보다 제안하는 방법이 다양한 컴퓨터 환경과 처리 속도에서 성능이 향상됨을 확인할 수 있었다.