• Korean Journal of Mathematics
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• v.29 no.3
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• pp.527-545
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• 2021

The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1079-1092
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• 2011

We consider the Newton's method for an direct solver of the optimal control problems of the Navier-Stokes equations. We show that the finite element solutions of the optimal control problem for Stoke equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to the optimal control problem for the Navier-Stokes equations provided there are sufficiently small mesh size h and the moderate Reynold's number.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.109-121
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• 2009

In this paper, we use He's polynomials for solving higher order integro differential equations (IDES) by converting them to an equivalent system of integral equations. The He's polynomials which are easier to calculate and are compatible to Adomian's polynomials are found by using homotopy perturbation method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to verify the reliability and efficiency of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.653-660
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05b
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.151-156
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• 1999

Under the heavy irradiation of crystalline materials when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriate transformation of these nonlinear differential equations to more solvable Poisson's equations, finally analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Publications of The Korean Astronomical Society
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• v.5 no.1
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• pp.17-25
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• 1990

Rapid progress in modern computer industries now enables us to solve the Einstein equations numerically. In the first part of this paper we briefly review how to deal with those equations in relativistic astrophysics and cosmology. In the second part we introduce two examples-the Centrella and Wilson's cosmology and the Shapiro and Teukolsky's relativistic stellar cluster.

• Journal of Biosystems Engineering
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• v.22 no.1
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• pp.11-20
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• 1997

Thin layer drying tests of short gain rough rice were conducted in an experimental dryer equiped with air conditioning unit. The drying tests were performed in triplicate at three air temperatures of $35^circ$, $45^circ$, $55^circ$, and three relative humidities of 40%, 55%, 70%, respectively. Previously published thin layer equations were reviewed and four different models widely used as thin layer drying equations for cereal grains were selected. The selected four models were Pages, simplified diffusion, Lewis's and Thompson's models. Experimental data were fitted to these equations using stepwise multiple regression analysis. The experimental constants involved in tow equations were represented as a function of temperature and relative humidity of drying air. The results of comparing coefficients of determination and root mean square errors of miosture ratio for low equations showed that Page's and Thompsons models were found to fit adequately to all drying test data with coefficient of determination of 0.99 or better and root mean square error of moisture ratio of 0.025.