• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.43-55
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• 1996

Explicit formulas for bi-Hermite polynomials are found and their combinatorial model is considered. This combinatorial model is a generalization of the combinatorial model of Hermite polynomials as matching polynomials.

• Journal of Power Electronics
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• v.18 no.5
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• pp.1380-1397
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• 2018

The synchronous reluctance motor (SynRM) servo-drive system has highly nonlinear uncertainties owing to a convex construction effect. It is difficult for the linear control method to achieve good performance for the SynRM drive system. The nonlinear backstepping control system using upper bound with switching function is proposed to inhibit uncertainty action for controlling the SynRM drive system. However, this method uses a large upper bound with a switching function, which results in a large chattering. In order to reduce this chattering, a nonlinear backstepping control system using an adaptive law is proposed to estimate the lumped uncertainty. Since this method uses an adaptive law, it cannot achiever satisfactory performance. Therefore, a nonlinear backstepping control system using a reformed recurrent Hermite polynomial neural network with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SynRM drive system. Further, the reformed recurrent Hermite polynomial neural network with two learning rates is derived according to an increment type Lyapunov function to speed-up the parameter convergence. Finally, some experimental results and a comparative analysis are presented to verify that the proposed control system has better control performance for controlling SynRM drive systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9A
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• pp.909-916
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• 2008

In this paper, we propose and analyze M-ary pulse order time hopping multiple access ultra wideband (PO-THMA UWB) system using modified Hermite polynomial (MHP). The MHP pulses have a mutually orthogonal property between different ordered pulses and that property makes simultaneous transmission at the same time slot regardless of collision in the THMA-UWB system. Therefore, we derive the cross-correlation furlction of MHP pulses and analyze the BER of the proposed system and show that the BER performance and the transmission capacity are improved dramatically when compared with those of conventional THMA-UWB system.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• 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 for Statistical Applications and Methods
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• v.2 no.1
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• pp.1-12
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• 1995

An estimator of coefficients of polynomial measurement error model with vector predictor and first-order interaction terms is derived using Hermite polynomial. Asymptotic normality of estimator is provided and some simulation study is performed to compare the small sample properties of derived estimator with those of OLS estimator.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.585-596
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• 2000

We developed a macro for prediction and classification using profection pursuit regression based on Friedman (1984b) and Hwang, et al. (1994). In the macro, the order of the Hermite functions can be selected automatically. In projection pursuit regression, we compare several smoothing methods such as super smoothing, smoothing with the Hermite functions. Also, classification methods applied to German credit data are compared.

• East Asian mathematical journal
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• v.38 no.3
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• pp.365-377
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• 2022

In this paper, we present a new class of interpolatory Hermite subdivision schemes of order 2 reproducing polynomials. Each member in this class, denoted by H_n for n ≥ 1, preserves polynomials of degree up to 4n + 1 admitting the approximation order of 4n + 2. Furthermore, it has free parameters which provide flexibility in designing curves/surfaces. H₁, the simplest and the most attractive scheme in this class, achieves C⁴ smoothness with the parameters in certain ranges, and its performance is demonstrated with numerical examples.

• Journal of Power Electronics
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• v.18 no.5
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• pp.1409-1423
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• 2018

Compared with classical linear controllers, a nonlinear controller can result in better control performance for the nonlinear uncertainties of continuously variable transmission (CVT) systems that are driven by a synchronous reluctance motor (SynRM). Improved control performance can be seen in the nonlinear uncertainties behavior of CVT systems by using the proposed mingled revised recurrent Hermite polynomial neural network (MRRHPNN) control with mend ant colony optimization (ACO). The MRRHPNN control with mend ACO can carry out the overlooker control system, reformed recurrent Hermite polynomial neural network (RRHPNN) control with an adaptive law, and reimbursed control with an appraised law. Additionally, in accordance with the Lyapunov stability theorem, the adaptive law in the RRHPNN and the appraised law of the reimbursed control are established. Furthermore, to help improve convergence and to obtain better learning performance, the mend ACO is utilized for adjusting the two varied learning rates of the two parameters in the RRHPNN. Finally, comparative examples are illustrated by experimental results to confirm that the proposed control system can achieve better control performance.