• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.357-365
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• 2007

In this paper we present characterizations of the Pareto, Lomax, exponential and beta models by some properties of their $r^{th}$ partial moment defined as ${\alpha}_r(t)=E[(X-t)^+]^r$, where $(X-t)^+ = max(X-t,0)$. Given the partial moments at a few truncation points, these results enable us to calculate the moments at many other points.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.65-81
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• 2024

In this paper, we announce that the strategy of comparing the complex moments of L(1, χ_u) to that of a random Euler product L(1, 𝕏) is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of L(1, χ_u) in a large uniform range. We also give Ω-results for the extreme values of L(1, χ_u).

• Magazine of the Korean Society of Agricultural Engineers
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• v.44 no.5
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• pp.41-53
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• 2002

This study was conducted to derive the regional design rainfall by the regional frequency analysis based on the regionalization of the precipitation suggested by the first report of this project. According to the regions and consecutive durations, optimal design rainfalls were derived by the regional frequency analysis for L-moment in the second report of this project. Using the LH-moment ratios and Kolmogorov-Smirnov test, the optimal regional probability distribution was identified to be the Generalized extreme value (GEV) distribution among applied distributions. regional and at-site parameters of the GEV distribution were estimated by the linear combination of the higher probability weighted moments, LH-moment. Design rainfall using LH-moments following the consecutive duration were derived by the regional and at-site analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE), relative bias (RBIAS) and relative reduction (RR) in RRMSE for the design rainfall were computed and compared in the regional and at-site frequency analysis. Consequently, it was shown that the regional analysis can substantially more reduce the RRMSE, RBIAS and RR in RRMSE than at-site analysis in the prediction of design rainfall. Relative efficiency (RE) for an optimal order of L-moments was also computed by the methods of L, L1, L2, L3 and L4-moments for GEV distribution. It was found that the method of L-moments is more effective than the others for getting optimal design rainfall according to the regions and consecutive durations in the regional frequency analysis. Diagrams for the design rainfall derived by the regional frequency analysis using L-moments were drawn according to the regions and consecutive durations by GIS techniques.

• Journal of the Korean Chemical Society
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• v.24 no.2
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• pp.91-100
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• 1980

A formula for calculation of the magnetic moments for octahedral $[Ti(III)A_3B_3]$ type complexes with axial symmetry has been developed and the magnetic moments for these complexes are calculated, using the experimental values of the distortion parameters$({\delta})$, spin-orbit coupling constants and orbital reduction factors. The calculated magnetic moments for axially distorted octahedral $[Ti(III)A_3B_3]$ type complexes are in resonable agreement with the experimental valuest It is found that the calculated magnetic moments decrease as the extent of axial distortion increases and the orbital reduction factor decreases. A calculation method of the magnetic moments for octahedral $[Ti(III)A_3B_3]$ type complexes which are in a ligand field of lower than axial symmetry has also been developed and the structure of distorted octahedral $[Ti(III)A_3B_3]$ type complexes are discussed on the basis of the of the calculated magnetic moments.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• East Asian mathematical journal
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• v.14 no.1
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• pp.1-14
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• 1998

Using some inequalities for real numbers and integrals we print out here some new inequalities for the moments of guessing mapping which complement the recent results of Arikan [1] and Boztas [2].

• Bulletin of the Korean Chemical Society
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• v.2 no.2
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• pp.48-55
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• 1981

A new approach in calculating the dipole moments for transition metal complexes has been proposed and the calculated results are tabulated with the experimental values. The calculated dipole moments are applied to the theoretical prediction or confirmation of the geometric structure for the transition metal complexes.

• East Asian mathematical journal
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• v.39 no.3
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• pp.331-347
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• 2023

We present an identity on moments of a compound random variable by using an auxiliary counting random variable. Based on this identity, we develop a new recurrence formula for obtaining the raw and central moments of any order for a given compound random variable.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.183-186
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• 2001

In this paper, we first propose new texture features, BVLC (block variation of local correlation coefficients) moments, for content-based image retrieval (CBIR) and then present an image retrieval method based on the fusion of BDIP and BVLC moments. BDIP uses the local probabilities in image blocks to extract valley and edges well. BVLC uses the variations of local correlation coefficients in images blocks to measure texture smoothness well. In order not to be affected with the movement, rotation, and size of an object, the first and second moments of BDIP and BVLC are used for CBIR. Corel DB and Vistex DB are used to evaluate the performance of the proposed retrieval method. Experimental results show that the presented retrieval method yields average 12% better performance than the method using only BDIP or BVLC moments and average 13% better performance than the method using wavelet moments.

• ETRI Journal
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• v.30 no.2
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• pp.335-337
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• 2008

An eye detection method for facial images using Zernike moments with a support vector machine (SVM) is proposed. Eye/non-eye patterns are represented in terms of the magnitude of Zernike moments and then classified by the SVM. Due to the rotation-invariant characteristics of the magnitude of Zernike moments, the method is robust against rotation, which is demonstrated using rotated images from the ORL database. Experiments with TV drama videos showed that the proposed method achieved a 94.6% detection rate, which is a higher performance level than that achievable by the method that uses gray values with an SVM.