• Journal of applied mathematics & informatics
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• v.18 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.63-78
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• 1999

Let $\mu$(x) be an increasing function on the real line with finite moments of all oeders. We show that for any linear operator T on the space of polynomials and any interger n $\geq$ 0, there is a constant $\gamma n(T)\geq0$, independent of p(x), such that $\parallel T_p\parallel\leq\gamma n(T)\parallel P\parallel$, for any polynomial p(x) of degree $\leq$ n, where We find a formular for the best possible value $\Gamma_n(T)\;of\;\gamma n(T)$ and estimations for $\Gamma_n(T)$. We also give several illustrating examples when T is a differentiation or a difference operator and $d\mu$(x) is an orthogonalizing measure for classical or discrete orthogonal polynomials.

• Journal of Power Electronics
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• v.19 no.3
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• pp.771-783
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• 2019

Due to nonlinear-synthetic uncertainty including the total unknown nonlinear load torque, the total parameter variation and the fixed load torque, a synchronous reluctance motor (SynRM) driving a continuously variable transmission (CVT) system causes a lot of nonlinear effects. Linear control methods make it hard to achieve good control performance. To increase the control performance and reduce the influence of nonlinear time-synthetic uncertainty, an admixed recurrent Gegenbauer orthogonal polynomials neural network (ARGOPNN) with a modified particle swarm optimization (MPSO) control system is proposed to achieve better control performance. The ARGOPNN with a MPSO control system is composed of an observer controller, a recurrent Gegenbauer orthogonal polynomial neural network (RGOPNN) controller and a remunerated controller. To insure the stability of the control system, the RGOPNN controller with an adaptive law and the remunerated controller with a reckoned law are derived according to the Lyapunov stability theorem. In addition, the two learning rates of the weights in the RGOPNN are regulating by using the MPSO algorithm to enhance convergence. Finally, three types of experimental results with comparative studies are presented to confirm the usefulness of the proposed ARGOPNN with a MPSO control system.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.21-30
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• 1994

We give a simple unified proof of various characterizations of discrete classical orthogonal polynomials.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.505-513
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• 2019

In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

• Journal of Convergence for Information Technology
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• v.11 no.1
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• pp.109-117
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• 2021

In this paper, the meta-model based approximate optimization was carried out for the structure design of an ocean automatic salt collector in order to minimize the structure weight. The structural analysis was performed by using the finite element method to evaluate the strength performance of the ocean automatic salt collector in its initial design. In the structural analysis, it was evaluated the strength performance of the design load conditions. The optimum design problem was formulated so that design variables of main structure thickness would be determined by minimizing the structure weight subject to strength performance constraints. The meta-models used in the approximate optimization were the response surface method, Kriging model, and Chebyshev orthogonal polynomials. Regarding to the numerical characteristics, the solution results from approximate optimization techniques were compared to the results of non-approximate optimization. The Chebyshev orthogonal polynomials among the meta-models used in the approximate optimization showed the most appropriate optimum design results for the structure design of the ocean automatic salt collector.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1273-1279
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• 2011

The variable-swash-plate compressor has recently been adopted as a vehicle compressor to improve fuel efficiency. The rotation torque in the variable-swash-plate compressor and the pressure-affected piston have a great influence on the swash-plate design and deformation. This paper suggests the optimal configuration design by using Chebyshev orthogonal polynomial and optimization techniques. The orthogonal array (OA) and analysis of variance (ANOVA) techniques and response surface optimization, are employed to determine the main effects and their optimal design variables. According to the optimal design, we confirm an effective design variable in swash plate and explain the optimal solution, the usefulness for satisfying the constraints of maximum stress and deformation.

• Journal of the Institute of Convergence Signal Processing
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• v.5 no.1
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• pp.53-59
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• 2004

In case of load forcasting the most important problem is to deal with the load of special days. According this paper presents forecasting method for speaial days peak load by neural networks model. by means of neural networks mothod using the historical past special- days load data, special-days load was directly forecasted, and forecasting % error showed good result as 1∼2% except vacation season in summer Consequently, it is capable of directly special days load, With the models, precision of forecasting was brought satisfactory result. When neural networks was compared with the orthogonal polynomials models at a view of the results of special-days load forecasting, neural networks model which used pattern conversion ratio was more effective on forecasting for special-days load. On the other hand, in case of short special-days load forecasting, both were valid.