• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.239-244
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved by successively in the moving least square sense. Some weighing functions were tested in order to investigate the up-winding effect for the convection term. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as FVM.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.121-142
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• 2002

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In [1] the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm if mainly based on the steepest descent procedure with the view of ensuring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Analytical Science and Technology
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• v.33 no.2
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• pp.98-107
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• 2020

Methamphetamine (MA) is currently the most abused illicit drug in Korea. MA is produced by chemical synthesis, and the final target drug that is produced contains small amounts of the precursor chemicals, intermediates, and by-products. To identify and quantify these trace compounds in MA seizures, a practical and feasible approach for conducting chromatographic fingerprinting with a suite of traditional chemometric methods and recently introduced machine learning approaches was examined. This was achieved using gas chromatography (GC) coupled with a flame ionization detector (FID) and mass spectrometry (MS). Following appropriate examination of all the peaks in 71 samples, 166 impurities were selected as the characteristic components. Unsupervised (principal component analysis (PCA), hierarchical cluster analysis (HCA), and K-means clustering) and supervised (partial least squares-discriminant analysis (PLS-DA), orthogonal partial least squares-discriminant analysis (OPLS-DA), support vector machines (SVM), and deep neural network (DNN) with Keras) chemometric techniques were employed for classifying the 71 MA seizures. The results of the PCA, HCA, K-means clustering, PLS-DA, OPLS-DA, SVM, and DNN methods for quality evaluation were in good agreement. However, the tested MA seizures possessed distinct features, such as chirality, cutting agents, and boiling points. The study indicated that the established qualitative and semi-quantitative methods will be practical and useful analytical tools for characterizing trace compounds in illicit MA seizures. Moreover, they will provide a statistical basis for identifying the synthesis route, sources of supply, trafficking routes, and connections between seizures, which will support drug law enforcement agencies in their effort to eliminate organized MA crime.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.229-239
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• 2007

We present a diagnostic method for the quasi-likelihood estimators in generalized linear models. Since these estimators can be usually obtained by iteratively reweighted least squares which are well known to be very sensitive to unusual data, a diagnostic step is indispensable to analysis of data. We extend the local influence approach based on the maximum likelihood function to that on the quasi-likelihood function. Under several perturbation schemes local influence diagnostics are derived. An illustrative example is given and we compare the results provided by local influence and deletion.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.445-456
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• 2003

Spatial data are usually obtained at selected locations even though they are potentially available at all locations in a continuous region. Moreover the monitoring locations are clustered in some regions, sparse in other regions. One important goal of spatial data analysis is to predict unknown response values at any location throughout a region of interest. Thus, an appropriate space model should be set up and their estimates and predictions must be accompanied by measures of uncertainty. In this study we see that a space model proposed allows a best interpolation to annual rainfall data in South Korea.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.639-647
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• 2002

Efforts to obtain more power for unit root tests have continued. Pantula at el.(1994) compared empirical powers of several unit root test statistics and addressed that the weighted symmetric estimator(WSE) and the unconditional maximum likelihood estimator(UMLE) are the best among them. One can easily see that the powers of these two statistics are almost the same. In this paper we explain a connection between WSE and UMLE and suggest a unit root test statistic which may explain the connection between them.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.629-637
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• 2002

Shapiro and Wilk(1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test based on the statistic is inconsistent Kim(2001a) proposed a modified Shapiro-Wilk's test statistic using the ratio of two asymptotically efficient estimators of scale. In this paper, we study the consistency of the proposed test.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1147-1157
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• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.75-81
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• 1996

Polynomial measurement error model(MEM) with one predictor is considered. It is briefly mentioned that Chan and Mak's generalized least squares estimator(GLSE) can be derived more easily if Hermite polynomial concept is applied. It is proved that GLSE derived using new procedure is equivalent to the estimator obtained from corrected score function. Finally, much simpler proof of the asymptotic behavior of GLSE than that of Chan and Mak is provided. Much simpler formula of asymptotic covariance matrix of GLSE is a part of that proof.