• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

• Bulletin of the Korean Chemical Society
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• v.20 no.7
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• pp.815-818
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• 1999

The method of calculating the excess Helmholtz free energy from the averaged effective acceptance ratio for the Lennard-Jones fluid and the inverse twelve fluid has been slightly modified and applied to the two-center-Lennard-Jones liquid. The excess Helmholtz free energy is calculated directly from the average of the modified effective acceptance ratio through a single Metropolis Monte Carlo simulation. Therefore this method does not need any reference system. The results of the present method were satisfactory compared with those of the perturbation theories and the overlap ratio method.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.175-184
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• 1999

Along with the computation and analysis for nonlinear system being more and more involved in the fields such as automation control electronic technique and electrical power system the nonlin-ear theory has become quite a attractive field for academic research. In this paper we derives the solutions for state equation of nonlinear system by using the inverse operator expression of the so-lutions is obtained. An actual computation example is given giving a comparison between IOM and Runge-kutta method. It has been proved by our investigation that IOM has some distinct advantages over usual approximation methods in that it is computationally con-venient rapidly convergent provides accurate solutions not requiring perturbation linearization or the massive computation inherent in discrietization methods such as finite differences. So the IOM pro-vides an effective method for the solution of nonlinear system is of potential application valuable in nonlinear computation.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.23 no.2
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• pp.69-74
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• 2015

We propose a rigorous and practical methodology to evaluate the performance of symbolic manipulation program such as Mathematica, Maple, and Maxima. First, we demonstrate an inverse method to construct the benchmark problems of an initial value problems. The benchmark problems associated with the discrete version of the Chebyshev polynomials provide a rigorous and objective measure to evaluate the performance of symbolic manipulation programs. We compare three symbolic manipulation programs, which are Mathematica, Maple and Maxima, using this methodology. The computation time, the used memory and the perturbation terms are chosen for comparison parameters.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.301-309
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• 2023

In this paper, a new modified conjugate gradient (MCG) method is presented which is based on a new gradient regularizer, and this method is used to identify the dynamic load on airfoil structure without and with considering random structure parameters. First of all, the newly proposed algorithm is proved to be efficient and convergent through the rigorous mathematics theory and the numerical results of determinate dynamic load identification. Secondly, using the perturbation method, we transform uncertain inverse problem about force reconstruction into determinate load identification problem. Lastly, the statistical characteristics of identified load are evaluated by statistical methods. Especially, this newly proposed approach has successfully solved determinate and uncertain inverse problems about dynamic load identification. Numerical simulations validate that the newly developed method in this paper is feasible and stable in solving load identification problems without and with considering random structure parameters. Additionally, it also shows that most of the observation error of the proposed algorithm in solving dynamic load identification of deterministic and random structure is respectively within 11.13%, 20%.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.30-40
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• 1995

In this paper, it is proposed a robust control scheme for real time control of a robot manipulator with parameter uncertainties. The focus of this paper is a new approach of multivariable control schemes for an assembly robot manipulator to achieve the accurate trajectory tracking by joint angles. The proposed control scheme consists of a multivariable feedforward controller and feedback controller. In this control scheme, the feedback controller consists of proportional-derivative type and is designed by the pole placement method. The feedforward controller uses the inverse of the linealized model of robot manipulator dynamics. This feedback controller ensures that each joint enables to track any reference trajectory. The proposed robot controller scheme has a computational efficiency.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.4
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• pp.115-120
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• 2012

In multi-user multi-input multi-output (MU-MIMO) system, zero forcing beamforming (ZFB) is regarded as a realistic solution for transmitting scheme due to its low complexity and simple structure. However, ZFB shows a significant performance degradation when channel matrix has large condition number. In this case, the largest singular value of the channel inversion matrix has a dominant effect on transmit power. In this paper, we propose a perturbation method for reducing an effect of the dominant singular value. In the proposed algorithm, channel inverse matrix is first decomposed by SVD for the transmit signal to be expressed as a combination of singular vectors. Then, the transmit signal is perturbed to reduce the coefficient of the singular vector corresponding to the largest singular value. When a number of transmit antennas is 4, the simulation results of this paper shows that the proposed method shows 8dB performance enhancement at 10-3 uncoded bit error rate (BER) compared with conventional ZFB. Also, the simulation results show that the proposed method provides a comparable performance to Tomlinson-Harashima Precoding (THP) with much lower complexity.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.18 no.2
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• pp.23-28
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• 2004

In EIT, various image reconstruction algorithms have been used in order to compute the internal resistivity distribution of the unknown object with its electric potential data at the boundary. Mathematically the EIT image reconstruction algorithm is a nonlinear ill-posed inverse problem. In this paper, a SPSA approach is proposed for the solution of the EIT image reconstruction. Results of numerical experiments of EIT solved by the SPSA approach are presented and compared to that obtained by the modified Newton-Raphson(mNR) method.

• Journal of Korean Society of Water and Wastewater
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• v.36 no.4
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• pp.219-228
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• 2022

In this study, we propose a flow velocity evaluation scheme based on pressure measurement in pressurized pipeline systems. Conservation of mass and momentum equations can be decomposed into mean and perturbation of pressure head and flowrate, which provide the pressure head and flowrate relationship between upstream and donwstream point in pressurized pipeline system. The inverse impedance formulations were derived to address measured pressure at downstream to evaluation of flow velocity or pressure at any point of system. The convolution of response function to pressure head in downstream valve provides the flow velocity response in any point of the simple pipeline system. Simulation comparison between traditional method of characteristics and the proposed method provide good agreements between two distinct approaches.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.