• Journal of Korea Society of Digital Industry and Information Management
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• v.9 no.1
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• pp.95-102
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• 2013

This paper covers nulling algorithm. In this algorithm, we assume that nulling points are already known. In general, nulling algorithm using matrix equation was utilized. But, this algorithm is pointed out that computational complexity is disadvantage. So, we choose gradient method to reduce the computational complexity. In order to further reduce the computational complexity, we propose approximate gradient method using characteristic of trigonometric functions. The proposed method has same performance compared with conventional method while having half the amount of computation when the number of antenna and nulling point are 20 and 1, respectively. In addition, we could virtually eliminate the trigonometric functions arithmetic. Trigonometric functions arithmetic cause a big problem in actual implementation like FPGA processor(Field Programmable gate array). By utilizing the above algorithm in a multi-cell environment, beamforming gain can be obtained and interference can be reduced at same time. By the above results, the algorithm can show excellent performance in the cell boundary.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.647-671
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• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.4
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• pp.105-117
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• 1998

In this paper, the general formula of disparity estimation based on Bayesian Maximum A Posteriori (MAP) algorithm is derived and implemented with simplified probabilistic models. The probabilistic models are independence and similarity among the neighboring disparities in the configuration.The formula is the generalized probabilistic diffusion equation based on Bayesian model, and can be implemented into the some different forms corresponding to the probabilistic models in the disparity neighborhood system or configuration. And, we proposed new probabilistic models in order to simplify the joint probability distribution of disparities in the configuration. According to the experimental results, the proposed algorithm outperformed the other ones, such as sum of swuared difference(SSD) based algorithm and Scharstein's method. We canconclude that the derived formular generalizes the probabilistic diffusion based on Bayesian MAP algorithm for disparity estimation, and the propsoed probabilistic models are reasonable and approximate the pure joint probability distribution very well with decreasing the computations to 0.01% of the generalized formula.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.57 no.2
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• pp.115-120
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• 2008

The EKF(Extended Kalman filter) method which is the state estimation algorithm of nonlinear stochastic system depends on the initial error and the estimated states. Therefore, the divergence of the estimated state can be caused if the initial values of the estimated states are not chosen as approximate real state values. In this paper, the demerit of the existing EKF method is improved using the EKF algorithm transformated by STWS(Single Term Walsh Series). This method linearizes each sampling interval of continous-time system through the derivation of an algebraic iterative equation without discretizing continuous system by the characteristic of STWS, the convergence of the estimated states can be improved. The validity of the proposed method is checked through comparison with the existing EKF method in simulation.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.241-243
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• 1998

This paper describes a new method for the faster shape optimization of the electromagnetic devices. In a conventional iterative method of shape design optimization using design sensitivity based on a finite element method, meshes for a new shape of the model are generated and a discretized system equation is solved using the meshes in each iteration. They cause much design time. To save this time, a polynomial approximation of the finite element solution with respect to the geometric design parameters using Taylor expansion is constructed. This approximate state variable expressed explicitly in terms of design parameters is employed in a gradient-based optimization method. The proposed method is applied to the shape design of quadrupole magnet.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.59-80
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• 2003

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.411-425
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• 1998

The effective length factor of a framed column may be determined by means of the alignment chart procedure. This method is based on many unrealistic assumptions, among which is that all columns have the same stiffness parameter, which is dependent on the length, axial load, and moment of inertia of the column. A new approximate method is developed for the determination of effective length factors for columns in unbraced frames. This method takes into account the effects of inelastic column behaviour, far end conditions of the restraining beams and columns, semi-rigid beam-to-column connections, and differentiated stiffness parameters of columns. This method may be implemented on a microcomputer. A numerical study was carried out to demonstrate the extent to which the involved parameters affect the K factor. The beam-to-column connection stiffness, the stiffness parameter of columns, and the far end conditions of restraining members have a significant effect on the K factor of the column under investigation. The developed method is recommended for design purposes.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.1
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• pp.34-42
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• 1992

This paper presents two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good numerical properties. Furthermore, the computational complexity of the algorithms is an order of magnitude snaller than previously algorithm is an order of magnitude smaller than previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to comprte the adaptive filter outputs. This method is conceptually very simple`however, it will result in biased system models in the presence of measurement noise. The second approach is an approximate least-squares output error solution. In this case, the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results of several experiments that demonstrate and compare the properties of the adaptive bilinear filters are also presented in this paper. These results indicate that the output error algorithm is less sensitive to output measurement noise than the squation error method.