• Honam Mathematical Journal
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• v.42 no.1
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• pp.187-195
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• 2020

In this paper, we investigate the vectorial moments of Bäcklund transformations of a space curve in 𝔼³. Firstly, it is obtained the vectorial moments which named α𝓖 dual curve, β𝓖 dual curve, and γ𝓖 dual curve of Bäcklund transformations. Then we give the Euler elastic bending energies of these curves. Finally, we provide some examples of α𝓖 dual, β𝓖 dual, and γ𝓖 dual, and their Euler elastic bending energies.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.7
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• pp.39-47
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• 1992

This paper showed that theoretical site attenuation curves were obtained simply by the method of moments analysis for current integral equations on antennas. Since the expansion coefficients of driving and receiving points were calculated from the method of moments procedure, site attenuations were evaluated simply using these basic antenna parameters. Theoretical site attenuations were calculated with half-wave resonant dipoles connected directly to a 50 ohm receiving system and connected to a 72/50 ohm matching network, respectively. Results were compared with other theoretical studies reported so far. Also included were experimental results for site attenuations to prove the validity of theoretical analysis.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.347-361
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• 2014

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.391-403
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• 2002

In this paper, some general results for obtaining recurrence relations between product moments of order statistics for doubly truncated distributions are established. These results are then applied to some specific doubly truncated distributions, viz. doubly truncated Weibull, Exponential, Pareto, power function, Cauchy, Lomax and Rayleigh.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.283-290
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• 1996

For finite discrete distributions with prescribed moments, there is a well-known upper bound on the index of the support. In this paper, we are interested in the smoothest density with prescribed moments among the class of smooth functions. We define an index of continuous distribution through the support and derive an upper bound on the index of the smoothest density. Some examples are given, some of which achieve the upper bound.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.1-12
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• 2022

In this paper we prove an even characteristic analogue of the result of Andrade on lower bounds for moment of quadratic Dirichlet L-functions in odd characteristic. We establish lower bounds for the moments of Dirichlet L-functions of characters defined by Hasse symbols in even characteristic.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.852-857
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• 2004

A new and efficient method for estimating the statistical moments of a system performance function has been developed. The method consists of two steps: (1) An approximate response surface is generated by a quadratic regression model, and (2) the statistical moments of the regression model are then calculated by experimental design techniques proposed by Seo and $Kwak^{(4)}$. In this approach, the size of experimental region affects the accuracy of the statistical moments. Therefore, the region size should be selected suitably. The D-optimal design and the central composite design are adopted over the selected experimental region for the regression model. Finally, the Pearson system is adopted to decide the distribution type of the system performance function and to analyze structural reliability.

• 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.