• 대한수학회보
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• 제23권2호
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• pp.149-154
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• 1986

• 대한수학회지
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• 제26권1호
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• pp.117-142
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• 1989

• 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 $H_nC$.

• 대한수학회보
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• 제39권2호
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권3호
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• pp.1650-1669
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• 2017

In this study, each pixel in an ear is used as a centroid to generate a cake. Subsequently the major axis length of this cake is computed and obtained. This obtained major axis length serves as a feature to recognize an ear. Later, the ear hole is used as a centroid and a 16-circle template is generated to extract the major axis lengths of the ear. The 16-circle template extracted signals are used to recognize an ear. In the next step, a ring-to-line mapping technique is used to map these major axis lengths to several straight-line signals. Next, the complex plane vector computing technique is used to determine the similarity of these major axis lengths, whereby a solution to the image-rotating problem is achieved. The aforementioned extracted signals are also compared to the ones that are extracted from its neighboring pixels, whereby solving the image-shifting problem. The algorithm developed in this study can precisely identify an ear image by solving the image rotation and image shifting problems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.257-270
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• 2014

In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.

• 대한수학회보
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• 제26권1호
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• pp.43-46
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• 1989

In this paper, we are concerned with the pointwise-hypoellipticity (see Definition 2.1) of an m-dimensional Frobenious Lie algebra L of analytic complex vector fields in somel open subset .ohm. of $R^{m+1}$. That is, L is a set of complex vector fields in .ohm. with (real-) analytic coefficients satisfying: (A) each point of .ohm. has an open neighborhood in which L is generated by m linearly independent elements of L; (B) L is closed under the commutation bracket [A, B]. The pointwise-analytic hypoellipticity of L is completely characterized by M.S. Baouendi and F. Treves in [1]. Here, we shall prove that if L is hypoelliptic at a point then it must be analytic hypoelliptic in a full neighborhood of the same point. When the coefficients are $C^{\infty}$, hypoellipticity of L was discussed in [2].2].

• 지능정보연구
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• 제25권3호
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• pp.19-41
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• 2019

텍스트 데이터에 대한 다양한 분석을 위해 최근 비정형 텍스트 데이터를 구조화하는 방안에 대한 연구가 활발하게 이루어지고 있다. doc2Vec으로 대표되는 기존 문서 임베딩 방법은 문서가 포함한 모든 단어를 사용하여 벡터를 만들기 때문에, 문서 벡터가 핵심 단어뿐 아니라 주변 단어의 영향도 함께 받는다는 한계가 있다. 또한 기존 문서 임베딩 방법은 하나의 문서가 하나의 벡터로 표현되기 때문에, 다양한 주제를 복합적으로 갖는 복합 문서를 정확하게 사상하기 어렵다는 한계를 갖는다. 본 논문에서는 기존의 문서 임베딩이 갖는 이러한 두 가지 한계를 극복하기 위해 다중 벡터 문서 임베딩 방법론을 새롭게 제안한다. 구체적으로 제안 방법론은 전체 단어가 아닌 핵심 단어만 이용하여 문서를 벡터화하고, 문서가 포함하는 다양한 주제를 분해하여 하나의 문서를 여러 벡터의 집합으로 표현한다. KISS에서 수집한 총 3,147개의 논문에 대한 실험을 통해 복합 문서를 단일 벡터로 표현하는 경우의 벡터 왜곡 현상을 확인하였으며, 복합 문서를 의미적으로 분해하여 다중 벡터로 나타내는 제안 방법론에 의해 이러한 왜곡 현상을 보정하고 각 문서를 더욱 정확하게 임베딩할 수 있음을 확인하였다.

• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.