• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.933-942
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• 2014

We give a representation of the component of solutions with characteristic multiplier 1 in a periodic linear inhomogeneous continuous system. It follows from this representation that asymptotic behaviors of the component of solutions to the system and to its associated homogeneous system are quite different, though they are similar in the case where the characteristic multiplier is not 1. Moreover, the representation is applicable to linear discrete systems with constant coefficients.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.287-296
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• 2007

Using the representation of the solution by means of the resolvent, we study the boundedness of the solutions of some Volterra difference equations.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.253-263
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• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

• Journal of the Korean Society of Safety
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• v.14 no.1
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• pp.10-18
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• 1999

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, the integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in finite plane bodies. The method was developed for in-plane(mode I and II) loadings only. In this paper, the method is formulated and applied to various crack problems involving multiple and branch cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.implicity.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.409-431
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• 2022

In this paper, we deal with the existence of solutions of the following system of nonlinear rational difference equations with order five $x_{n+1}=\frac{y_{n-3}x_{n-4}}{y_n(a+by_{n-3}x_{n-4})}$, $y_{n+1}=\frac{x_{n-3}y_{n-4}}{x_n(c+dx_{n-3}y_{n-4})}$, n = 0, 1, ⋯, where parameters a, b, c and d are not executed at the same time and initial conditions x_-4, x_-3, x_-2, x_-1, x₀, y_-4, y_-3, y_-2, y_-1 and y₀ are non zero real numbers.

• The Mathematical Education
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• v.23 no.1
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• pp.35-38
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• 1984

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.45-51
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• 2017

In this paper, we propose an accelerating scheme of convergence of numerical solutions of fuzzy non-linear equations. Numerical experiments show that the new method has significant acceleration of convergence of solutions of fuzzy non-linear equation. Three-dimensional graphical representation of fuzzy solutions is also provided as a reference of visual convergence of the solution sequence.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.111-129
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• 1998

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, an integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in plane finite bodies. The method was developed for in-plane(modes I and II) loadings only. In this paper, the method is formulated and applied to mode III problems involving smooth or kinked cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.

• Journal of Welding and Joining
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• v.18 no.4
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• pp.104-110
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• 2000

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, an integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in plane finite bodies. The method was developed for in-plane (modes I and II) loadings only. In this paper, the method is formulated and applied to mode III problems involving smooth or kinked cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.implicity.

• Industrial Engineering and Management Systems
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• v.7 no.2
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• pp.84-92
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• 2008

Scheduling is one of the most important issues in the planning and operation of production systems. This paper investigates a general job shop scheduling problem with reentrant work flows and sequence dependent setup times. The disjunctive graph representation is used to capture the interactions between machines in job shop. Based on this representation, four two-phase heuristic procedures are proposed to obtain near optimal solutions for this problem. The obtained solutions in the first phase are substantially improved by reversing the direction of some critical disjunctive arcs of the graph in the second phase. A comparative study is conducted to examine the performance of these proposed algorithms.