• Bulletin of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.215-236
• /
• 1994

The purpose of the present paper is to study generic submanifolds of a Sasakian space form with nonvanishing parallel mean curvature vector field such that the shape operator in the direction of the mean curvature vector field commutes with the structure tensor field induced on the submanifold. In .cint. 1 we state general formulas on generic submanifolds of a Sasakian manifold, especially those of a Sasakian space form. .cint.2 is devoted to the study a generic submanifold of a Sasakian manifold, which is not tangent to the structure vector. In .cint.3 we investigate generic submanifolds, not tangent to the structure vector, of a Sasakian space form with nonvanishing parallel mean curvature vactor field. In .cint.4 we discuss generic submanifolds tangent to the structure vector of a Sasakian space form and compute the restricted Laplacian for the shape operator in the direction of the mean curvature vector field. As a applications of these, in the last .cint.5 we prove our main results.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.647-659
• /
• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.9B
• /
• pp.1731-1741
• /
• 1999

Color images are often corrupted by the noise due to noisy sensors or channel transmission errors. Some filters such as vector media and vector $\alpha$-trimmed mean filter have bee used for color noise removal. In this paper, We propose the fuzzy cluster filters based on the possibilistic c-means clustering, because the possibilistic c-means clustering can get robust memberships in noisy environments. Also, we propose weighted vector $\alpha$-trimmed mean filter to improve the conventional vector $\alpha$-trimmed mean filter. In this filter, the central data are more weighted than the outlying data. In this paper, we implemented the color noise generator to evaluate the performance of the proposed filters in the color noise environments. The NCD measure and visual measure by human observer are used for evaluation the performance of the proposed filters. In the experiment, proposed fuzzy cluster filters in the sense of NCD measure gave the best performance over conventional filters in the mixed noise. Simulation results showed that proposed weighted vector $\alpha$-trimmed mean filters better than the conventional vector $\alpha$-trimmed mean filter in any kinds of noise.

• Journal of Korean Society for Quality Management
• /
• v.29 no.1
• /
• pp.1-10
• /
• 2001

We consider the problem of detecting special variations in multivariate $T^2$-control chart when two or more multivariate outliers are present. Since a multivariate outlier may reflect slippage in mean, variance, or correlation, it can distort the sample mean vector and sample covariance matrix. Damaged sample mean vector and sample covariance matrix have difficulty in examining special variations clearly, An alternative to detection outliers or special variations is to use robust estimators of mean vector and covariance matrix that are less sensitive to extreme observations than are the standard estimators $\bar{x}$ and $\textbf{S}$. We applied popular minimum volume ellipsoid(MVE) and minimum covariance determinant(MCD) method to estimate mean vector and covariance matrix and compared its results with standard $T^2$-control chart using simulated multivariate data with outliers. We found that the modified $T^2$-control chart based on the above robust methods were more effective in detecting special variations clearly than the standard $T^2$-control chart.

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.1-16
• /
• 2018

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in [10]. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of [1, 14].

• Communications for Statistical Applications and Methods
• /
• v.30 no.3
• /
• pp.245-258
• /
• 2023

This study proposes a modification to the objective function of the support vector machine for the linearly non-separable case of a binary classifier y_i ∈ {-1, 1}. The modification takes into account the position of each data item x_i from its corresponding class centroid. The resulting optimization function involves the centroid mean vector, and the spread of data besides the support vectors, which should be minimized by the choice of hyper-plane β. Theoretical assumptions have been tested to derive an optimal separable hyperplane that yields the minimal misclassification rate. The proposed method has been evaluated using simulation studies and real-life COVID-19 patient outcome hospitalization data. Results show that the proposed method performs better than the classical linear SVM classifier as the sample size increases and is preferred in the presence of correlations among predictors as well as among extreme values.

• Journal of Power System Engineering
• /
• v.4 no.4
• /
• pp.25-31
• /
• 2000

This paper represents the vector fields and three dimensional mean velocities in the X-Y plane of cone type swirl gas burner measured by using X-probe from the hot-wire anemometer system. This experiment is carried out at flowrate 350 and $450{\ell}/min$ respectively in the test section of subsonic wind tunnel. The vector plot shows that the maximum axial mean velocity component is focused in the narrow slits distributed radially on the edge of a cone type swirl burner, for that reason, there is some entrainment of ambient air in the outer region of the burner and the rotational flow can be shown in the inner region of the burner because mean velocity W is distributed about twice as large as mean velocity V due to inclined flow velocity ejecting from the swirl vanes of a cone type baffle plate of burner. Moreover, the mean velocities are largely distributed near the outer region of burner within $X/R{\fallingdotseq}1.5$, hence, the turbulent characteristics are anticipated to be distributed largely in the center of this region due to the large inclination of mean velocity and swirl effect.

• Journal of the Korean Statistical Society
• /
• v.15 no.2
• /
• pp.97-106
• /
• 1986

Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2007.11a
• /
• pp.267-271
• /
• 2007

본 논문은 원본이미지와 은닉이미지의 좋은 압축률과 만족할만한 이미지의 질, 그리고 외부공격에 강인한 이미지은닉의 한 방법으로 특이치 분해와 퍼지 군집화를 이용한 벡터양자화를 이용한 워터마킹 방법을 소개하였다. 실험에서는 은닉된 이미지의 비가시성과 외부공격에 대한 강인성을 증명하였다.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.25 no.6
• /
• pp.672-679
• /
• 1988

In this paper, attempts have been made to code images employing a separating mean vector quantizer(SMVQ). Then we analyzed the performance of the SMVQ experimentally as well as analytically. The results of simulation with natural images are presented. But, conclusively the performance of the SMVQ technique is not better than that of the conventional vector quantizer. In this paper, a brief analysis in which we revealed that the performance, based on the mean square error measure, of the SMVQ is not favorable is favorable is discussed.