• Journal of Power Electronics
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• v.16 no.2
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• pp.598-609
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• 2016

The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.115-117
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• 1972

The purpose of the present paper is to evaluate certain integrals involving Laguerre, Jacobi and Hermite polynomials. These integrals are very useful in case of expansion of any polynomial in a series of Orthogonal polynomials [1, Theo. 56].

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1013-1024
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• 2018

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.91-102
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• 1991

Traditionally, a dynamic programming(DP) technique has been used to the multireservoir control system. The algorithm has inherent problem to increase computational requirements exponentially due to discretization of variables and expanding the dimension of the system. To solve this problem, this paper describes transforming the optimal control system into a quadratic programming(QP), using Laguerre polynomials(LP) and its properties. The objective function of the proposed QP is independent of time variable. The solution of the QP is obtained by nonlinear programming(NLP) using augmented Lagrangian multiplier method. The numerical experiment shows that the water level of reservoirs is higher than Lee's and the evaluated benefit value is about the same as other researcher's.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.67-75
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• 2004

Paul Turan observed that the Legendre polynomials satisfy the inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)$ > 0, $-1{\leq}x{\leq}1$. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved $P^{\alpha}_n(x)P^{\beta}_{n+1}(x)-P^{\alpha}_{n+1}(x)P{\beta}_n(x)$ > 0, $\frac{1}{2}{\leq}{\alpha}$ < ${\beta}{\leq}{\alpha}+2.0$ < $x$ < 1, for the ultraspherical polynomials (respectively, Laguerre ploynomials). The Bustoz-Savage inequalities hold for Laguerre and ultraspherical polynomials which are symmetric. In this paper, we prove some similar inequalities for non-symmetric Jacobi polynomials.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.18 no.9
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• pp.1023-1029
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• 2007

In this paper, we propose the method to solve the BLT equations using Laguerre polynomials in time domain. The solution of BLT equations is obtained by recursive, differential and integral properties of Laguerre polynomials. The verification of the proposed method is tested by applying it to the two-wired transmission line with resistors and capacitors, which is illuminated by the electromagnetic plane wave pulse. And the result is compared with the corresponding transient responses obtained from inverse fast Fourier transform(IFFT) of the frequency domain solutions of BLT equations.

• Proceedings of the Korea Water Resources Association Conference
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• 1991.07a
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• pp.61-68
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• 1991

• Wind and Structures
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• v.7 no.2
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• pp.89-106
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• 2004

The response of tall buildings to gust buffeting is usually evaluated assuming that the structural damping is of a viscous nature. In addition, when dampers are incorporated in the design to mitigate the response, their effect is allowed for increasing the building modal damping ratios by a quantity corresponding to the additional energy dissipation arising from the presence of the devices. Even though straightforward, this procedure has some degree of inaccuracy due to the existence of a memory effect, associated with the damping mechanism, which is neglected by a viscous model. In this paper a more realistic viscoelastic model is used to evaluate the response to gust buffeting of tall buildings provided with energy dissipation devices. Both cases of viscous and hysteretic inherent damping are considered, while for the dampers a generic viscoelastic behaviour is assumed. The Laguerre Polynomial Approximation is used to write the equations of motion and find the frequency response functions. The procedure is applied to a 25-story building to quantify the memory effects, and the inaccuracy arising when the latter is neglected.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.3
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• pp.140-148
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• 2014

In this paper, We proposed Gaussian function as a basis of hybrid method. Hybrid method is to extrapolate late time and high frequency data using early time and low frequency data. This method takes advantages of both MOT and MOM as well as having shorter running time and smaller error. For this method a better basis function is required. We compared the performance of the result with proposed function and conventional basis including Hermite and Laguerre polynomial.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.447-460
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• 2022

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space A^α,m_q (ℂ) of q-analytic functions with the weight ϕ(z) = -α log |z|²+|z|^2m for any positive integer m. We obtain the corresponding reproducing kernel K^ℂ_α,q,m(z, w) using the weighted Laguerre polynomials and the Mittag-Leffler functions. Finally, we investigate the necessary and sufficient condition on (α, q, m) such that K^ℂ_α,q,m(z, w) is zero-free.