• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.49-59
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• 2012

In this article, using the example of C. Camci([7]) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.35-46
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• 2019

Multivariate Confidence Region (MCR) cannot be used to obtain the confidence region of the mean vector of multivariate data when the normality assumption is not satisfied; however, the Quantile Confidence Region (QCR) could be used with a Multivariate Quantile Vector in these cases. The coverage rate of the QCR is better than MCR; however, it has a disadvantage because the QCR has a wide shape when the probability density function follows a bimodal form. In this study, we propose a Quantile Confidence Region using the Highest density (QCRHD) method with the Highest Density Region (HDR). The coverage rate of QCRHD was superior to MCR, but is found to be similar to QCR. The QCRHD is constructed as one region similar to QCR when the distance of the mean vector is close. When the distance of the mean vector is far, the QCR has one wide region, but the QCRHD has two smaller regions. Based on these features, it is found that the QCRHD can overcome the disadvantages of the QCR, which may have a wide shape.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.547-557
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• 1998

In this paper, we study submanifolds in the Euclidean space with parallel normal mean curvature vectorand special quadric representation. Especially we give a complete classification result relative to surfaces satisfying these conditions.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.894-900
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• 2005

A new approach to the straightforward implementation of the unscented filter in a unit quaternion space is proposed for spacecraft attitude estimation. Since the unscented filter is formulated in a vector space and the unit quaternions do not belong to a vector space but lie on a nonlinear manifold, the weighted sum of quaternion samples does not produce a unit quaternion estimate. To overcome this difficulty, a method of weighted mean computation for quaternions is derived in rotational space, leading to a quaternion with unit norm. A quaternion multiplication is used for predicted covariance computation and quaternion update, which makes a quaternion in a filter lie in the unit quaternion space. Since the quaternion process noise increases the uncertainty in attitude orientation, modeling it either as the vector part of a quaternion or as a rotation vector is considered. Simulation results illustrate that the proposed approach successfully estimates spacecraft attitude for large initial errors and high tip-off rates, and modeling the quaternion process noise as a rotation vector is more optimal than handling it as the vector part of a quaternion.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.33-39
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

• Proceedings of the Korean Society of Computer Information Conference
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• 2009.01a
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• pp.49-54
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• 2009

A fuzzy weighted mean method on a 2D shape recognition system is introduced in this paper. The bispectrum based on third order cumulant is applied to the contour sequence of each image for the extraction of a feature vector. This bispectral feature vector, which is invariant to shape translation, rotation and scale, represents a 2D planar image. However, to obtain the best performance, it should be considered certain criterion on the calculation of weights for the fuzzy weighted mean method. Therefore, a new method to calculate weights using means by differences of feature values and their variances with the maximum distance from differences of feature values. is developed. In the experiments, the recognition results with fifteen dimensional bispectral feature vectors, which are extracted from 11.808 aircraft images based on eight different styles of reference images, are compared and analyzed.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.95-115
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• 2003

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Journal of Integrative Natural Science
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• v.11 no.3
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• pp.154-160
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• 2018

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-r{\geq}3)$, r = rank(K) with a projection matrix K under the quadratic loss, based on a sample $Y_1$, $Y_2$, ${\cdots}$, $Y_n$. In this paper a James-Stein type estimator with shrinkage form is given when it's variance distribution is specified and when the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is constrain, where K is an idempotent and symmetric matrix and rank(K) = r. It is characterized a minimal complete class of James-Stein type estimators in this case. And the subclass of James-Stein type estimators that dominate the sample mean is derived.