• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.495-502
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• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.27-40
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• 2012

The two-dimensional incompressible flow of a linear viscoelastic fluid we considered in this research has rapidly oscillating initial conditions which contain both the large scale and small scale information. In order to grasp this double-scale phenomenon of the complex flow, a multiscale analysis method is developed based on the mathematical homogenization theory. For the incompressible flow of a linear viscoelastic Maxwell fluid, a well-posed multiscale system, including averaged equations and cell problems, is derived by employing the appropriate multiple scale asymptotic expansions to approximate the velocity, pressure and stress fields. And then, this multiscale system is solved numerically using the pseudospectral algorithm based on a time-splitting semi-implicit influence matrix method. The comparisons between the multiscale solutions and the direct numerical simulations demonstrate that the multiscale model not only captures large scale features accurately, but also reflects kinetic interactions between the large and small scale of the incompressible flow of a linear viscoelastic fluid.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.440-445
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• 1992

The major purpose here is to estimate the drying time required in the fish-drying process employed. The basic element of the prediction of the drying time is the model or the equation, which governs the change in weight. By an intuitive consideration on the mechanism of dehydration, a mathematical model of the fish-drying process is built, which is described by a system of linear differential equations. Further, a modified system of linear differential equations for a model of drying is also proposed for more accurate estimation. The parameter estimation of this system of equations provides the prediction of necessary drying time.

• Industrial Engineering and Management Systems
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• v.7 no.1
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• pp.23-33
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• 2008

This paper proposes an approach to monitoring and scheduling methods for repetitive MIMO-FIFO DESs. We use max-plus algebra for modeling and formulation, known as an effective approach for controller design for this type of system. Because a certain type of linear equations in max-plus algebra can represent the system's behavior, the principal concerns in past researches were how to solve the equations. However, the researches focused mainly on analyses of the relation between inputs and outputs of the system, which implies that the changes or the slacks of internal states were not clarified well. We first examine several properties of the corresponding state variables, which contribute to finding and tracing the float times in each process. Moreover, we provide a rescheduling method that can take into account delays or changes of the internal states. These methods would be useful in schedule control or progress management.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.7
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• pp.553-564
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• 1990

The co-efficient matrix of linear second-order partial differential equations in the general form is partitioned with (n-1)x(n-1) submartices and is transformed into the block tridiagonal system. Then the cyclic odd-even reduction technique is applied to this system with the large-grain data granularity and the block cyclic reduction algorithm to solve unknown vectors of this system is created. But this block cyclic reduction technique is not suitable for the parallel processing system because of its parallelism chanigng at every computing stages. So a new algorithm for solving linear second-order partical differential equations is presentes by the block cyclic reduction technique which is modified in order to keep its parallelism constant, and to reduce gteatly its execution time. Both of these algoriths are compared and studied.

• Journal of Advanced Navigation Technology
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• v.13 no.1
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• pp.62-67
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• 2009

The demand for high performance computer grows to solve large linear systems of equations in such engineering fields - circuit simulation for VLSI design, image processing, structural engineering, aerodynamics, etc. Many various parallel processing systems have been proposed and manufactured to satisfy the demand. The properties of linear system determine what algorithm is proper to solve the problem. Direct methods or iterative methods can be used for solving the problem. In this paper, an intelligent parallel iterative method for solving linear systems of equations with large sparse matrices is proposed and its efficiency is proved through simulation.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.215-224
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• 2017

In this paper, we propose a method of order two for the computation of positive solutions to a boundary value problem of the linear beam equation. The method is based on the Power method for the eigenvector associated with the dominant eigenvalue and the Crout-like factorization algorithm for the banded system of linear equations. It is extremely fast due to the linear complexity of the linear system solver. Numerical result of a test problem is included.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• Journal of the Korean Society for Railway
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• v.17 no.5
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• pp.321-327
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• 2014

In this paper, linear dynamic equations are derived from nonlinear dynamic equations of constrained multibody systems using the QR decomposition method. The derived linear equations are applied to a railway vehicle bogie. The vibration characteristics of the railway vehicle are investigated by calculating the natural mode and transfer function of the bogie frame in relation to rail-roughness input. The main modes of the bogie were found below 35Hz, and the local modes above 198Hz. The magnitude of the vertical transfer function varied with the forward velocity due to vertical and pitch modes, which were influenced by the forward velocity. The magnitude of the lateral transfer function was negligibly small, and the mode in the longitudinal direction was excited for longitudinal transfer function regardless of the forward velocity.