• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.231-243
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• 2015

We suggest and analyze a family of multi-step iterative methods for solving nonlinear equations using the decomposition technique mainly due to Rafiq et al. [13].

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.663-676
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• 2016

In this paper we propose a new family of eighth order optimal methods for solving nonlinear equations by using weight function methods. The methods of the family require three function and one derivative evaluations per step and has order of convergence eight, and so they are optimal in the sense of Kung-Traub hypothesis. Precise analysis of convergence is given. Some members of the family are compared with several existing methods to show their performance and as a result to confirm that our methods are as competitive as compared to them.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.687-696
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• 2003

This article presents a new family of the estimating functions related with minimum distance estimations, and discusses its relationship to the family of the minimum density power divergence estimating equations. Two representative minimum distance estimations; the minimum $L_2$ distance estimation and the minimum Hellinger distance estimation are studied in the light of the theory of estimating equations. Despite of the desirable properties of minimum distance estimations, they are not widely used by general researchers, because theories related with them are complex and are hard to be computationally implemented in real problems. Hopefully, this article would be a help for understanding the minimum distance estimations better.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.759-770
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• 2021

The purpose of this paper is to prove unique existence of bounded solution and periodic solution to inhomogeneous linear evolution equations which trajectories of these solutions belong to given admissible Banach function space.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.417-423
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• 2019

In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.293-305
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• 2004

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.579-587
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• 2012

A fourth-order family of triparametric extensions of Jarratt's method are proposed in this paper to find a simple root of nonlinear algebraic equations. Convergence analysis including numerical experiments for various test functions apparently verifies the fourth-order convergence and asymptotic error constants.

• Nutrition Research and Practice
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• v.15 no.1
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• pp.95-105
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• 2021

BACKGROUND/OBJECTIVES: The measurement of body composition, including muscle and fat mass, remains challenging in large epidemiological studies due to time constraint and cost when using accurate modalities. Therefore, this study aimed to develop and validate prediction equations according to sex to measure lean body mass (LBM), appendicular skeletal muscle mass (ASM), and body fat mass (BFM) using anthropometric measurement, serum creatinine level, and lifestyle factors as independent variables and dual-energy X-ray absorptiometry as the reference method. SUBJECTS/METHODS: A sample of the Korean general adult population (men: 7,599; women: 10,009) from the Korean National Health and Nutrition Examination Survey 2008-2011 was included in this study. The participants were divided into the derivation and validation groups via a random number generator (with a ratio of 70:30). The prediction equations were developed using a series of multivariable linear regressions and validated using the Bland-Altman plot and intraclass correlation coefficient (ICC). RESULTS: The initial and practical equations that included age, height, weight, and waist circumference had a different predictive ability for LBM (men: R2 = 0.85, standard error of estimate [SEE] = 2.7 kg; women: R2 = 0.78, SEE = 2.2 kg), ASM (men: R2 = 0.81, SEE = 1.6 kg; women: R2 = 0.71, SEE = 1.2 kg), and BFM (men: R2 = 0.74, SEE = 2.7 kg; women: R2 = 0.83, SEE = 2.2 kg) according to sex. Compared with the first prediction equation, the addition of other factors, including serum creatinine level, physical activity, smoking status, and alcohol use, resulted in an R2 that is higher by 0.01 and SEE that is lower by 0.1. CONCLUSIONS: All equations had low bias, moderate agreement based on the Bland-Altman plot, and high ICC, and this result showed that these equations can be further applied to other epidemiologic studies.

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.108-114
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• 2022

Most studies on the shape of the steady vortex ring have been based on the Stokes stream function approach. In this study, the velocity approach is introduced as a trial approach. A contour dynamics method for fluid velocity is used to analyze the Norbury-Fraenkel family of vortex rings. Analytic integration is performed over the logarithmic-singular segment. A system of nonlinear equations for the discretized shape of the vortex core is formulated using the material boundary condition of the core. An additional condition for the velocities of the vortical and impulse centers is introduced to complete the system of equations. Numerical solutions are successfully obtained for the system of nonlinear equations using the iterative scheme. Specifically, the evaluation of the kinetic energy in terms of line integrals is examined closely. The results of the proposed method are compared with those of the stream function approaches. The results show good agreement, and thereby, confirm the validity of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1127
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• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.