• Journal of the Society of Naval Architects of Korea
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• 제57권5호
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• pp.305-311
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• 2020

This study presents a probabilistic time series forecast of ship structural response using Bayesian inference combined with Volterra linear model. The structural response of a ship exposed to irregular wave excitation was represented by a linear Volterra model and unknown uncertainties were taken care by probability distribution of time series. To achieve the goal, Volterra series of first order was expanded to a linear combination of Laguerre functions and the probability distribution of Laguerre coefficients is estimated using the prepared data by treating Laguerre coefficients as random variables. In order to check the validity of the proposed methodology, it was applied to a linear oscillator model containing damping uncertainties, and also applied to model test data obtained by segmented hull model of 400,000 DWT VLOC as a practical problem.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.205-228
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• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.239-244
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• 1978

The object of the present paper is to obtain certain results involving the H function of several complex variables. An integral involving the generalized Whittaker functions and the multiple H function has been evaluated and this result has been further utilized in finding out an expansion formula for the multiple H function in terms of the Laguerre polynomials. Some particular cases of interest have also been indicated.

• Bulletin of the Korean Mathematical Society
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• 제60권3호
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제14권5호
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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.

• Kyungpook Mathematical Journal
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• 제19권1호
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• pp.135-139
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• 1979

We consider the problem that how must the production of certain item vary as a function of time, if for known losses due to depreciation the total amount of the product is to have a constant value. The integral equation associated with the problem is solved by an appeal to the convolution quotients. The production function comes out to be an expression containing the generalized Laguerre polynomials. The loss function and the production function are tabulated for different values of the parameter by using an IBM 370/145 computer.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제22권10호
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• pp.1005-1011
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• 2011

In this paper, we present a marching-on-in-degree(MOD) finite difference method(FDM) based on the Helmholtz wave equation for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time consuming convolution operations are handled analytically using the properties of the Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity with a finite sum of orthogonal Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from finite difference time-domain(FDTD) to a finite difference formulation through a Galerkin testing. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, and Lorentz dispersive medium.

• Honam Mathematical Journal
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• 제44권3호
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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.

• Communications of the Korean Mathematical Society
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• 제26권4호
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• pp.611-622
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• 2011

The present paper deals with generalization of several families of bilinear and bilateral generating functions for the heat type polynomials suggested by Jacobi polynomials with different argument.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.26.1-26
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• 2001

In this paper, we will expand and generalize the orthogonal functions as basis functions for dynamical system representations. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown row we can exploit these generalized basis functions to increase the speed of convergence in a series expansion. The set of Kautz functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained. And so we will present the influence of noises to use Kautz function on the identification accuracy.