• Title/Summary/Keyword: Moments Method

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Estimation of Ground and Excited State Dipole Moments of Coumarin 450 by Solvatochromic Shift Method

  • Naik, L.R.;Math, N.N.
    • Journal of Photoscience
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    • v.12 no.2
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    • pp.57-61
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    • 2005
  • The ground and excited state dipole moments of Coumarin 450 (C 450) laser dye were measured at room temperature in several solvents of varying dipole moments. The ground state dipole moment (${\mu}_g$) is estimated by using the modified Onsagar model and the excited state dipole moments (${\mu}_e$) were estimated by the method of solvatochromism as well as by utilizing the microscopic solvent polarity parameter ($E^N_T$). Further, the deviation of some of the points from the linearity of the $E^N_T$ versus Stokes shift indicates the existence of specific type of solute-solvent interaction. The excited state dipole moment of C 450 were found to be higher than those of the ground state and is interpreted in terms of the resonance structure of the molecule. A reasonable agreement has been observed between the values obtained by the method of solvatochromism and modified Onsagar model. It is observed that, corresponding to cyclohexane solution, the fluorescence maxima shift towards the red region with increasing the polarity of the solvents, hence the transition involved are of ${\pi}-{\pi}^*$ type.

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Calculation of the Dipole Moments for Trigonal Bipyramidal Complexes (Trigonal Bipyramid 구조를 갖는 착물의 쌍극자모멘트의 계산)

  • Sangwoon Ahn;Ja Hong Kim;Kee Hag Lee;Gap Choul Shin
    • Journal of the Korean Chemical Society
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    • v.26 no.1
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    • pp.18-23
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    • 1982
  • A new method for calculation of the the dipole moments for trigonal bipyramidal complexes has been developed in this work. Illustrative calculations are performed on a few trigonal bipyramidal complexes with the approximate molecular orbital and the valence bond method. The calculated values of the dipole moments by the approximate molecular orbital method are very close to the experimental values. The calculated dipole moments may be used to predict the geometric structure of trigonal bipyramidal complexes.

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Review of the reinforcement sizing in the strength design of reinforced concrete slabs

  • Gil-Martina, Luisa Maria;Hernandez-Montes, Enrique
    • Computers and Concrete
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    • v.27 no.3
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    • pp.211-223
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    • 2021
  • This paper presents a review of the two widespread approaches which deal with the ultimate strength design of RC slabs subjected to bending moments and torsion: The Field of Moments Method (FoMM) and the Sandwich method (SM). Special attention is paid to the ultimate strain distribution implicitly assumed when using each one of the methodologies, in particular, the yielding of the steel reinforcement. This work analyzes the initial assumption regarding ultimate strain distribution in the SM. Furthermore, this work studies the resisting moments field on which the Wood-Armer method is based, and it finds some inconsistencies. Several examples have been developed.

Comparative Analysis of Regional and At-site Analysis for the Design Rainfall by Gamma and Non-Gamma Family (I) (Gamma 및 비Gamma군 분포모형에 의한 강우의 지점 및 지역빈도 비교분석 (I))

  • Ryoo, Kyong-Sik;Lee, Soon-Hyuk
    • Journal of The Korean Society of Agricultural Engineers
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    • v.46 no.4
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    • pp.25-36
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    • 2004
  • This study was conducted to derive the design rainfall by the consecutive duration using the at-site frequency analysis. Using the errors, K-S tests and LH-moment ratios, Log Pearson type 3 (LP3) and Generalized Extreme Value (GEV) distributions of Gamma and Non-Gamma Family, respectively were identified as the optimal probability distributions among applied distributions. Parameters of GEV and LP3 distributions were estimated by the method of L and LH-moments and the Indirect method of moments respectively. Design rainfalls following the consecutive duration were derived by at-site frequency analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE) and relative efficiency (RE) in RRMSE for the design rainfall derived by at-site analysis in the observed and simulated data were computed and compared. It has shown that at-site frequency analysis by GEV distribution using L-moments is confirmed as more reliable than that of GEV and LP3 distributions using LH-moments and Indirect method of moments in view of relative efficiency.

Out-of-Plane Buckling Analysis of Curved Beams Using DQM (미분구적법(DQM)을 이용한 곡선보의 외평면 좌굴해석)

  • Kang, Ki-Jun
    • Journal of the Korean Society of Safety
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    • v.17 no.4
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    • pp.189-195
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    • 2002
  • The differential quadrature method (DQM) is applied to computation of the eigenvalues of out-of-plane bucking of curved beams. Critical moments including the effect of radial stresses are calculated for a single-span wide-flange beam subjected to equal and opposite in-plane bending moments with various end conditions, and opening angles. Results are compared with existing exact solutions where available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used. New results are given for two sets of boundary conditions not previously considered for this problem: clamped-clamped and clamped-simply supported ends.

Review of Parameter Estimation Procedure of Freund Bivariate Exponential Distribution (Freund 이변량 지수분포의 매개변수 추정과정 검토)

  • Park, Cheol-Soon;Yoo, Chul-Sang
    • Journal of Korea Water Resources Association
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    • v.45 no.2
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    • pp.191-201
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    • 2012
  • This study reviewed the parameter estimation procedure of the Freund bivariate exponential distribution for the decision of the annual maximum rainfall event. The method of moments was reviewed first, whose results were compared with those from the method of maximum likelihood. Both methods were applied to the hourly rainfall data of the Seoul rain gauge station measured from 1961 to 2010 to select the annual maximum rainfall events, which were also compared each other. The results derived are as follows. First, when applying the method of moments for the parameter estimation, it was found necessary to consider the correlation coefficient between the two variables as well as the mean and variance. Second, the method of maximum likelihood was better to reproduce the mean, but the method of moments was better to reproduce the annual variation of the variance. Third, The annual maximum rainfall events derived were very similar in both cases. Among differently selected annual maximum rainfall events, those with the higher rainfall amount were selected by the method of maximum likelihood, but those with the higher rainfall intensity by the method of moments.

Stochastic Estimation of Phasor Voltage of Harmonics Using Multivariate Gram-Charlier Type A Series (다변수 그램-샬리어 급수 A형을 이용한 고조파 페이서 전압의 확률적 예측 계산)

  • Kim, Tae-Hyun;Park, In-Gyu;Park, Jong-Keun;Kang, Young-Shuk
    • Proceedings of the KIEE Conference
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    • 1987.11a
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    • pp.469-473
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    • 1987
  • This paper presents a method to estimate p.d.f.(probability density function) of harmonic phasor voltage. Because the quantity of harmonics is not fixed, stochastic analysis of harmonics is needed. Because it is impossible to obtain p.d.f. of voltage from p.d.f. of current directly, the moments of voltage and current are used. Firstly, the moments of current is calculated from p.d.f. of current. Secondly, the moments of voltage are calculated from the moments of current using the linearity of the moments. Finally, p.d.f. of voltage is estimated from the moments of voltage using Gram-Charlier Type A Series. [1] The moments of the p.d.f. obtained by the series and of the true p.d.f. is same up to given finite moments. Because current and voltage of harmonics are represented as not instantaneous values but phasors, the estimated value can be compared with the measured value and harmonic phasor voltage can be analyzed when the p.d.f. of phase is nonuniform as well as uniform.

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Estimation of Design Rainfall by the Regional Frequency Analysis using Higher Probability Weighted Moments and GIS Techniques (III) - On the Method of LH-moments and GIS Techniques - (고차확률가중모멘트법에 의한 지역화빈도분석과 GIS기법에 의한 설계강우량 추정 (III) - LH-모멘트법과 GIS 기법을 중심으로 -)

  • 이순혁;박종화;류경식;지호근;신용희
    • 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.

Comparative Analysis of Design Drought Flow by L-Moment in the Weibull-3 and Wakeby distributions (Weibull -3 및 Wakeby 분포의 L-모멘크법에 의한 설계갈수량 비교분석)

  • 이순혁;박종화;맹승진;류경식;지호근
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 1999.10c
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    • pp.531-536
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    • 1999
  • This study was carried out to derive optimal design drought flows by the Weibull-3 and Wakeby distributions for the annual drought flows series at seven watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. L-coefficient of variation , L-skewness and L-kurtosis were calculated by the L-moment ratio respectivley. Parameters were estimated by the Methods o fL-Moments with continuous duration. Design drought flows obtained by Methods of L-Moments using Weibull plotting positions formula in the Weibull-3 and Wakeby distributions were compared by the Relative Mean Errors(RME), Relative Absolute Errors (RAE) and Root Mean Square Errors(RMSE). It has shown that design drought flows by the Wakeby distribution using method of L-moments are much closer to those of the observed data in comparison with those obtained by the Weibull-3 distribution using method of L-moments.

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Eye Detection Using Zernike Moments and SVM (Zernike 모멘트와 SVM을 이용한 눈 검출)

  • Kim, Hyoung-Joon;Baek, Yeul-Min;Kim, Whoi-Yul
    • Proceedings of the IEEK Conference
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    • 2007.07a
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    • pp.285-286
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    • 2007
  • This paper presents a method to detect eyes in the facial image using Zernike moments and SVM After detecting eye candidate regions from the facial image, Zernike moments are computed on those regions with moving a $15{\times}15$ window. Then, SVM that uses Zernike moments as an input vector detects eyes. In the experimental results, the proposed method shows the eye detection rate of about 90%.

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