• 대한수학회논문집
• /
• 제29권1호
• /
• pp.141-153
• /
• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• Journal of the Korean Statistical Society
• /
• 제8권1호
• /
• pp.37-64
• /
• 1979

Criteria and designs are developed for estimating derivatives of P-variable second order polynomial response surfaces. The basic criterion used is mean square error of the estimated derivative, averaged over all directions and then averaged over a region of interest. A new design concept called slope-rotatability is introduced. A simplex optimization program is used to find minimum mena square error designs for the two variable case for $6 \leq N \leq 12$.

• 응용통계연구
• /
• 제15권1호
• /
• pp.179-186
• /
• 2002

반응표면분석시 모든 실험이 동일한 조건 하에서 이루어지어야 하는 데 그렇지 못할 경우 우리는 블럭화를 행하게 된다. 반응 표면분석모형으로서 우리는 주로 2차 모형을 사용한다. 본 논문은 우리가 반응표면분석모형으로서 2차 모형을 사용할 때 근사직교블럭화를 평가하기 위한 간단한 측도들을 제시한다.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2001년도 가을 학술발표논문집 Vol.28 No.2 (2)
• /
• pp.304-306
• /
• 2001

Various methods for blind source separation (BSS) are based on independent component analysis (ICA) which can be viewed as a nonlinear extension of principal component analysis (PCA). Most existing ICA methods require certain nonlinear functions, the shapes of which depend on the probability distributions of sources (which is not known in advance), whereas FCA is a linear learning method based on only second-order statistics. In this paper we show how BSS can be achieved by FCA, provided that sources are spatially uncorrelated but temporally correlated.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1999년도 하계학술대회 논문집 G
• /
• pp.2956-2958
• /
• 1999

The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in non-parametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion common to most application. For the prior specified, the posterior median yields a thresholding procedure

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
• /
• pp.305-309
• /
• 2000

In this paper, we presents a new methodology for face recognition after analysing conventional ICA(Independent Component Analysis) based approach. In the literature we found that ICA based methods have followed the same procedure without any exception, first PCA(Principal Component Analysis) has been used for feature extraction, next ICA learning method has been applied for feature enhancement in the reduced dimension. However, it is contradiction that features are extracted using higher order moments depend on variance, the second order statistics. It is not considered that a necessary component can be located in the discarded feature space. In the new methodology, features are extracted using the magnitude of kurtosis(4-th order central moment or cumulant). This corresponds to the PCA based feature extraction using eigenvalue(2nd order central moment or variance). The synergy effect of PCA and ICA can be achieved if PCA is used for noise reduction filter. ICA methodology is analysed using SVD(Singular Value Decomposition). PCA does whitening and noise reduction. ICA performs the feature extraction. Simulation results show the effectiveness of the methodology compared to the conventional ICA approach.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2000년도 춘계학술대회논문집
• /
• pp.1127-1132
• /
• 2000

Impulsive acoustic and vibration signals within rotating machinery are often induced by irregular impacting. The detection of these impulses can be useful for fault diagnosis purposes. Recently there has been an increasing trend towards the use of higher order statistics for fault detection within mechanical systems based on the observation that impulsive signals tend to increase the kurtosis values. This paper considers the use of the third and fourth order Wigner moment spectra, called the Wigner bi- and tri- spectra receptively, for analysing such signals. Expressions for the auto-and cross-terms in these distributions are presented and discussed. It is shown that the Wigner trispectrum is a more suitable analysis tool and it performance is compared to its second order counterpart for detecting impulsive signals. These methods are also applied to measured data sets from an industrial gearbox.

• Korean Journal of Mathematics
• /
• 제23권4호
• /
• pp.537-555
• /
• 2015

This paper is concerned with the existence of solutions to the following fractional differential inclusion $$\{-{\frac{d}{dx}}\(p_0D^{-{\beta}}_x(u^{\prime}(x)))+q_xD^{-{\beta}}_1(u^{\prime}(x))\){\in}{\partial}F_u(x,u),\;x{\in}(0,1),\\u(0)=u(1)=0,$$ where $_0D^{-{\beta}}_x$ and $_xD^{-{\beta}}_1$ are left and right Riemann-Liouville fractional integrals of order ${\beta}{\in}(0,1)$ respectively, 0 < p = 1 - q < 1 and $F:[0,1]{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants p and q, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

• 한국데이터정보과학회:학술대회논문집
• /
• 한국데이터정보과학회 2005년도 추계학술대회
• /
• pp.71-84
• /
• 2005

The Fieller-Creasy problem involves statistical inference about the ratio of two independent normal means. It is difficult problem from either a frequentist or a likelihood perspective. As an alternatives, a Bayesian analysis with noninformative priors may provide a solution to this problem. In this paper, we extend the results of Yin and Ghosh (2001) to unbalanced sample case. We find various noninformative priors such as first and second order matching priors, reference and Jeffreys' priors. The posterior propriety under the proposed noninformative priors will be given. Using real data, we provide illustrative examples. Through simulation study, we compute the frequentist coverage probabilities for probability matching and reference priors. Some simulation results will be given.

• Journal of the Korean Statistical Society
• /
• 제36권4호
• /
• pp.489-500
• /
• 2007

In this paper, we consider Bayesian approach to the Fieller-Creasy problem using noninformative priors. Specifically we extend the results of Yin and Ghosh (2000) to the unbalanced case. We develop some noninformative priors such as the first and second order matching priors and reference priors. Also we prove the posterior propriety under the derived noninformative priors. We compare these priors in light of how accurately the coverage probabilities of Bayesian credible intervals match the corresponding frequentist coverage probabilities.