• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.183-195
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• 1995

For a distribution on the unit sphere, the set of eigenvectors of the second moment matrix is a conventional measure of orientation. Asymptotic confidence cones for eigenvector under the parametric assumptions for the underlying distributions and nonparametric confidence cones for eigenvector based on bootstrapping were proposed. In this paper, to reduce the level error of confidence cones for eigenvector, double bootstrap confidence cones based on prepivoting are considered, and the consistency of this method is discussed. We compare the perfomances of double bootstrap method with the others by Monte Carlo simulations.

• 대한수학회보
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• 제52권3호
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• pp.771-788
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• 2015

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

• 대한수학회논문집
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• 제35권1호
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• pp.251-260
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• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• 대한수학회논문집
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• 제11권3호
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• pp.807-814
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• 1996

Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x \times Y \to S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X \times RP^{2n-k} \to S^{2n}$ is homotopically trivial.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.853-861
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• 2003

An improved K-means document clustering method has been presented, where a concept vector is manipulated for each cluster on the basis of cosine similarity of text documents. The concept vectors are unit vectors that have been normalized on the n-dimensional sphere. Because the standard K-means method is sensitive to initial starting condition, our improvement focused on starting condition for estimating the modes of a distribution. The improved K-means clustering algorithm has been applied to a set of text documents, called Classic3, to test and prove efficiency and correctness of clustering result, and showed 7% improvements in its worst case.

• Journal of the Korean Data and Information Science Society
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• 제3권1호
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• pp.33-46
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• 1992

The set of eigenvectors of the second moment matrix and the mean vector are the measures of orientation for a distribution supported on the unit sphere. Bootstrap confidence cone for the eigenvector is constructed and the consistency of this method is discussed. The performance of our bootstrap cone for the eigenvector is compared with that of the asymptotic confidence cones for two measures under the parametric assumptions for the underlying distributions and that of the bootstrap cone for the mean vector by Monte Carlo simulation.

• 대한수학회보
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• 제33권4호
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• pp.537-544
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• 1996

Crofton's formula on Euclidean plane $E^2$ states: Let $\Gamma$ be a rectifiable curve of length L and let G be a straight line. Then $$ \int_{G \cap \Gamma \neq \phi} n dG = 2L $$ where n is the number of the intersection points of G with the curve $\Gamma$.

• Communications for Statistical Applications and Methods
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• 제20권1호
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• pp.77-84
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• 2013

This paper deals with the relative efficiency of two kernel estimators $\hat{f}_n$ and $\hat{g}_n$ by using spherical data, as proposed by Park (2012), and Bai et al. (1988), respectively. For this, we suggest the computing flows for the relative efficiency on the 2-dimensional unit sphere. An evaluation procedure between two estimators (given the same kernels) is also illustrated through the observed data on normals to the orbital planes of long-period comets.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.67-77
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• 1999

For a orientation-shift model supported on the unit sphere, Euler angles are the conventional measure to parametrize orientation-shifts. The essential role which is played by rotationally symmetry of an underlying distribution is reviewed. In this paper we propose the inference procedure based on Euler angles for the rotationally symmetric spherical distribution. The likelihood ratio test(LRT) based on the Euler angles is worked out. The asymptotic distribution of the test under the null hypotheses and certain contiguous alternatives is obtained.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.