• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.601-603
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• 2013

We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone $C{\subset}\mathbb{R}^{n+1}$ is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ${\partial}C$.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.725-736
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• 1999

In the present paper we will give a characterization of homogeneous real hypersurfaces of type A1, A2 and B of a complex projective space.

• The Korean Journal of Applied Statistics
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• v.33 no.3
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• pp.281-296
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• 2020

Repeated outcomes from the same subjects are referred to as longitudinal data. Analysis of the data requires different methods unlike cross-sectional data analysis. It is important to model the covariance matrix because the correlation between the repeated outcomes must be considered when estimating the effects of covariates on the mean response. However, the modeling of the covariance matrix is tricky because there are many parameters to be estimated, and the estimated covariance matrix should be positive definite. In this paper, we consider analysis of multivariate longitudinal data via two modeling methodologies for the covariance matrix for multivariate longitudinal data. Both methods describe serial correlations of multivariate longitudinal outcomes using a modified Cholesky decomposition. However, the two methods consider different decompositions to explain the correlation between simultaneous responses. The first method uses enhanced linear covariance models so that the covariance matrix satisfies a positive definiteness condition; in addition, and principal component analysis and maximization-minimization algorithm (MM algorithm) were used to estimate model parameters. The second method considers variance-correlation decomposition and hypersphere decomposition to model covariance matrix. Simulations are used to compare the performance of the two methodologies.

• Journal of KIISE:Software and Applications
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• v.26 no.11
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• pp.1270-1281
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• 1999

피라미드 기법 1 은 d-차원의 공간을 2d개의 피라미드들로 분할하는 특별한 공간 분할 방식을 이용하여 고차원 데이타를 효율적으로 색인할 수 있는 새로운 색인 방법으로 제안되었다. 피라미드 기법은 고차원 사각형 형태의 영역 질의에는 효율적이나, 유사성 검색에 많이 사용되는 고차원 구형태의 영역 질의에는 비효율적인 면이 존재한다. 본 논문에서는 고차원 데이타를 많이 사용하는 유사성 검색에 효율적인 새로운 색인 기법으로 구형 피라미드 기법을 제안한다. 구형 피라미드 기법은 먼저 d-차원의 공간을 2d개의 구형 피라미드로 분할하고, 각 단일 구형 피라미드를 다시 구형태의 조각으로 분할하는 특별한 공간 분할 방법에 기반하고 있다. 이러한 공간 분할 방식은 피라미드 기법과 마찬가지로 d-차원 공간을 1-차원 공간으로 변환할 수 있다. 따라서, 변환된 1-차원 데이타를 다루기 위하여 B+-트리를 사용할 수 있다. 본 논문에서는 이렇게 분할된 공간에서 고차원 구형태의 영역 질의를 효율적으로 처리할 수 있는 알고리즘을 제안한다. 마지막으로, 인위적 데이타와 실제 데이타를 사용한 다양한 실험을 통하여 구형 피라미드 기법이 구형태의 영역 질의를 처리하는데 있어서 기존의 피라미드 기법보다 효율적임을 보인다.Abstract The Pyramid-Technique 1 was proposed as a new indexing method for high- dimensional data spaces using a special partitioning strategy that divides d-dimensional space into 2d pyramids. It is efficient for hypercube range query, but is not efficient for hypersphere range query which is frequently used in similarity search. In this paper, we propose the Spherical Pyramid-Technique, an efficient indexing method for similarity search in high-dimensional space. The Spherical Pyramid-Technique is based on a special partitioning strategy, which is to divide the d-dimensional data space first into 2d spherical pyramids, and then cut the single spherical pyramid into several spherical slices. This partition provides a transformation of d-dimensional space into 1-dimensional space as the Pyramid-Technique does. Thus, we are able to use a B+-tree to manage the transformed 1-dimensional data. We also propose the algorithm of processing hypersphere range query on the space partitioned by this partitioning strategy. Finally, we show that the Spherical Pyramid-Technique clearly outperforms the Pyramid-Technique in processing hypersphere range queries through various experiments using synthetic and real data.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.503-514
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• 1998

We want to treat this problem for real hypersurfaces in a complex hyperbolic space $J_n(C)$. Thus it seems to be natural to consider some problems concerned with the estimation of the Ricci tensor for real hypersurfaces in $H_n(C)$. In this paper we will find a new tensorial formula concerned with the Ricci tensor and give it a characterization of horospheres and geodesic hyperspheres in a complex hyperbolic space $H_n(C)$.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.507-512
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• 1996

A totally umbilic submanifold of a pseudo-Riemanian manifold is a submanifold whose first fundamental form and second fundamental form are proportiona. An ordinary hypersphere $S^n(r)$ of an affine (n + 1)-space of the Euclidean space $E^m$ is the best known example of totally umbilic submanifolds of $E^m$.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.7-18
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• 2000

Let M be an n-dimensional CR submanifold CR dimension n - l of a complex projective space M. We characterize M of $\bar{M}$ in terms of an estimations of the length of the derivative of Ricci tensor of the length of Ricci tensor.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.197-206
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• 2004

We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.327-335
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• 2005

For a compact and orientable minimal real hypersurface $M\;in\;QP^n$, we prove that if the minimum of the sectional curvatures of Mis 3/(4n - 1), then M is isometric to the geodesic minimal hypersphere $M_{0,n-1}^Q$.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.25-33
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• 1994

In [2] we proved that if the minimum of the sectional curvature of a compact real minimal hypersurface of CP$^{m}$ is 1/(2m-1), then M is the geodesic hypersphere. This result was generalized in [8] to the case of M is a generic submanifold with flat normal connection. The purpose of the present paper is to prove a following generalization of theorems in [2] and [8].