• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.823-832
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• 2013

We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

• Journal of Power System Engineering
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• v.12 no.1
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• pp.72-79
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• 2008

This paper designs a looper-tension controller for mass-flow stabilization in hot strip finishing mills. By Newton's 2nd law and Hooke's law, nonlinear dynamic equations on the looper-tension system are firstly derived, and linearized by a linearization algorithm using a Taylor's series expansion. Moreover, a tension calculation model is obtained from the nonlinear dynamic equations which is called as a soft sensor of strip tension between two neighboring stands. Next, a looper-tension servo controller is designed by an ILQ(Inverse Linear Quadratic optimal control) algorithm, and it is combined with a minimal disturbance observer which to attenuate speed disturbances by AGC and operator interventions, etc.. Finally, it is shown from by a computer simulation that the proposed ILQ controller with a disturbance observer is very effective in stabilizing the strip mass-flow under some disturbances, moreover it has a good command following performance.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.349-353
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• 2008

Using the recently developed ABS algorithm for solving linear Diophantine equations we introduce an algorithm for solving a system of m linear integer inequalities in n variables, m $\leq$ n, with full rank coefficient matrix. We apply this result to solve linear integer programming problems with m $\leq$ n inequalities.

• Korean Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.158-162
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• 1996

Algorithms to find the Bezier control points of the image of a Bezier domain curve on a Bezier surface are described. The diagonal image curve is analysed and the general linear case is transformed to the diagonal case. This proposed algorithm gives the closed form solution to find the control points of the image curve of a linear domain curve. If the domain curve is not linear, the image curve can be obtained by solving the system of linear equations.

• Water Engineering Research
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• v.5 no.4
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• pp.177-183
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• 2004

This paper introduces an eigenvalue method of transforming the hyperbolic partial differential equations of a particular unsteady friction water hammer model into characteristic form. This method is based on the solution of the corresponding one-dimensional Riemann problem that transforms hyperbolic quasi-linear equations into ordinary differential equations along the characteristic directions, which in this case arises as the eigenvalues of the system. A mathematical justification and generalization of the eigenvalues method is provided and this approach is compared to the traditional characteristic method.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.267-284
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• 2014

The multiresolution analysis for Legendre multiwavelets are given, anti-derivatives of Legendre multiwavelets are used for the numerical solution of differential equations, a special form of multilevel augmentation method algorithm is proposed to solve the disrete linear system efficiently, convergence rate of the Galerkin methods is given and numerical examples are presented.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Structural Engineering and Mechanics
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• v.26 no.6
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• pp.635-650
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• 2007

In this paper, the equivalent exciting force caused by electric excitation is derived. By dividing load and displacement vectors into mean values and time-varying ones, the dynamic equations of the system are transformed into linear ones for time-varying portion of the displacements. The analytical equations of the forced time responses of the drive system to electric excitations are obtained. Using the Laplace transformation, the transfer function of the drive system is obtained. These equations are used to analyze the time and frequency responses of the drive system to the electric excitation. It is known that electric excitation can cause forced responses of the drive system, the total dynamic responses are decided by three phase exciting voltages, exciting frequency and natural frequencies of the drive system, and the drive parameters have obvious influence on the time and frequency responses.