• Korean Journal of Mathematics
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• v.16 no.1
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• pp.51-55
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• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.28 no.11
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• pp.106-111
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• 2014

Currently, the commonly used method for PWM(Pulse Width Modulation) Inverter of the Solar Power Plant. However, the limit of the developing performance to the non-linear and switch devices of the Inverter. Therefore, we propose a model predictive control techniques applied to Laguerre functions. LMPC(Laguerre functions model predictive control) reduces the number of computations made and so online implementation becomes possible where traditional MPC would have fail. In this paper, we comment on the appropriate scope and functions degree of the LMPC inverter control. The simulation results from MATLAB are also provided.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.2
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• pp.40-46
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• 2015

This paper presents a method of controlling a three-phase VSI (Voltage Source Inverter) using MPC (Model Predictive Control) designed using Laguerre functions. It also provides a model of the three-phase VSI and its resistive-inductive load and then an overview of MPC design using Laguerre functions. The biggest challenge in using MPC is the high number of computations involved, which makes online implementation difficult. On the other hand, the LMPC (Laguerre Model Predictive Control) reduces the number of computations made and so online implementation becomes possible where traditional MPC would be unteneble. The simulation results from MATLAB are also provided.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.299-312
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• 2021

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.141-151
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• 2021

The main object of the present paper is to introduce the generalized Laguerre matrix polynomials for two variables. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, generating functions and some recurrence relations are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.4
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• pp.185-191
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• 2003

In this Paper, we propose an accurate and stable solution of the transient electromagnetic response from three-dimensional arbitrarily shaped conducting objects by using a time domain magnetic field integral equation. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of temporal expansion functions with decaying exponential functions and Laguerre·polynomials. Since these temporal expansion functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation and converges to zero unconditionally. To show the validity of the proposed method, we solve a time domain magnetic field integral equation for three closed conducting objects and compare the results of Mie solution and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• 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.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.201-209
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• 2008

In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[{\delta}]x^{\lambda}_+={\delta}[x^{\lambda}_+]=0\;and\;[x^{\lambda}_+]x^{\mu}_+=x^{{\lambda}+{\mu}}_+$ for appropriate ${\lambda}$ and ${\mu}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.355-369
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• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.5
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• pp.458-465
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• 2003

In this paper, we analyze the transient electromagnetic response from three-dimensional(3-D) dielectric bodies using a time-domain electric field integral equation formulation. The solution method in this paper is based on the Galerkin＇s method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed method are presented.