• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.267-289
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• 2009

Students have difficulties in solving linear equation problems with a variable on the right side rather than linear equation problems a variable on the left side of the sign of equality. In order for students to overcome such difficulties, opportunities to experience many types of basic linear equation problems would have to be provided. Also, it is necessary to examine the process of students' problem solving process by constructing various types of evaluation item and test them in instruction and learning of linear equations, or grasp students' studying statues through individual interview and based on theses, error correction through feedbacks have to be achieved.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.760-767
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• 2014

This paper proposes a method to calculate pressure and flow of the fluid dynamic bearings (FDBs) with a recirculation channel (RC) by solving the Reynolds and the Hagen-Poiseuille equations at the same time. The Hagen-Poiseuille equation is one-dimensional equation which describes the flow in a circular pipe such as the RC. This research developed a finite element program to solve the Reynolds and the Hagen-Poiseuille equation together. The proposed method was applied to calculate the pressure and flow of the FDBs which are composed of grooved or plain journal and thrust bearings, and RC. To verify the proposed method, it also developed a finite volume model of the FDBs, and pressure and flow were calculated by the commercial CFD solver. They agree well with the pressure and flow calculated by the proposed method. Finally, this research investigated the characteristics of the FDBs due to the radius change of the RC.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.6
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• pp.55-68
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• 1995

Approximately 30 to 70 % of the mechanical losses in a reciprocating engine are contributed by the friction at the piston ring-cylinder interface. The friction characteristics of the piston ring during engine operation is known to as mixed lubrication experimentally. The mixed lubrication models based on the Average Reynolds Equation have been used by this time in order to study the tribological performance of the ring. However, the Average Reynolds Equation contains the expected value term(${\bar{h}}_r$) of local film thickness as well as nominal film thickness(h), so that the work of numerically solving ${\bar{h}}_r$ must be included to obtain the pressure in the oil film. The process of solving ${\bar{h}}_T$ causes a greater multiplying in the numerical solution. In this paper the mixed lubrication analysis using the Simplified Average Reynolds Equation in the piston ring is presented. This equation has only h as oil film thickness term. Therefore the tedious numerical procedure required to obtain ${\bar{h}}_T$ is not needed, and also, computation time can be reduced.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.327-342
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• 2018

In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-{\sum_{i=1}^{m}}A^{\ast}_iX^{-p_i}A_i=I$ with $p_i$ > 1 is proposed, which does not depend on a good initial approximation to the solution of matrix equation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.17-30
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• 2007

A new scheme for solving the Vlasov equation using a compactly supported wavelets basis is proposed. We use a numerical method which minimizes the numerical diffusion and conserves a reasonable time computing cost. So we introduce a representation in a compactly supported wavelet of the derivative operator. This method makes easy and simple the computation of the coefficients of the matrix representing the operator. This allows us to solve the two equations which result from the splitting technique of the main Vlasov equation. Some numerical results are exposed using different numbers of wavelets.

• 전기의세계
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• v.22 no.2
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• pp.40-44
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• 1973

A method for obtaining state equation for nonlinear time-varying RLC networks is presented. The nonlinear time-varying RLC elements are decomposed by using Murata method to formulate nonlinear state equation. A nonlinear time-varying RLC network containing twin tunnel diode is solved as an example. In consequence of solving the examjple, simple methods are presented for revising the original network model so that the formulation of state equation is simplified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.381-394
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• 2019

In this paper, we are extending fractional partial differential equations to fuzzy fractional partial differential equation under Riemann-Liouville and Caputo fractional derivatives, namely Variational iteration methods, and this method have applied to the fuzzy fractional wave equation with initial conditions as in fuzzy. It is explained by one and two-dimensional wave equations with suitable fuzzy initial conditions.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1227-1237
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• 2010

In this paper, a Klein-Gordon equation is solved by using the homotopy analysis method (HAM), homotopy perturbation method (HPM) and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. The uniqueness of the solution and the convergence of the proposed methods are proved. The accuracy of these methods are compared by solving an example.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.471-480
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• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.