• 대한수학회지
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• 제46권1호
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• 말소리와 음성과학
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• 제5권2호
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• pp.25-31
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• 2013

This study examined cross-generational changes in the vowel system of Seoul Korean. Acoustic analyses of the vowel formants of /o/ and /u/, and their Euclidean distances in the vowel space were undertaken to explore an on-going merger of these two vowels as proposed in previous acoustic studies and a phonological analysis by Chae (1999). A robust cross-generational change of /o/ and /u/ was found, more evident for female speakers than for male speakers. For female speakers, with each successive generation, /o/ became increasingly approximated with /u/, regardless of the syllable positions that the target vowels were posited, whereas the cross-generational differences in the Euclidean distances were only shown in the second syllable position for the male speakers. These results demonstrate that 1) women are more advanced than men in the on-going approximation of /o/ and /u/; 2) the approximation of /o/ and /u/ is common in the non-initial position. Taken together, the merger of /o/ and /u/ appears to be in progress in Seoul Korean.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.79-86
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• 2013

Taxicab plane geometry and Cinese-Checker plane geometry are non-Euclidean and more practical notion than Euclidean geometry in the real world. The ${\alpha}$-distance is a generalization of the Taxicab distance and Chinese-Checker distance. It was first introduced by Songlin Tian in 2005, and generalized to n-dimensional space by Ozcan Gelisgen in 2006. In this paper, we studied the isoperimetric inequality in ${\alpha}$-plane.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.103-112
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• 2022

A definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. The formulas for Euclidean norm of the fractional vector cross product of two vectors, and for fractional triple vector cross product are obtained.

• 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.

• 대한수학회지
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• 제32권3호
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• pp.471-482
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• 1995

A complex n-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a comples space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form consists of a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. The induced almost contact metric structure of a real hypersurface M of $M_n(c)$ is denoted by $(\phi, \zeta, \eta, g)$.

• 대한수학회보
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• 제34권2호
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• pp.173-184
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• 1997

An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

• 대한수학회지
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• 제32권4호
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• 대한수학회논문집
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• 제9권2호
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• pp.369-383
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• 1994

A complex n-dimensional Kahler manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_{n}$ (c). A complete and simply connected complex space form consists of a complex projective space $P_{n}$ C, a complex Euclidean space $C^{n}$ or a complex hyperbolic space $H_{n}$ C, according as c > 0, c = 0 or c < 0.(omitted)

• 대한수학회지
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• 제32권2호
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.