• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1557-1566
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• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.271-283
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• 2021

The asymptotics behavior orthogonal polynomials have been in the spotlight since the result of G. Szegő in 1921. In this paper we study the pointwise asymptotics inside the unit disk for orthogonal polynomials with respect to a polynomial Szegő measure with an infinite masses points.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1436-1439
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• 1997

The objective of this paper is to present an efficient and practical approach to the automatic classification of power quality(PQ) disturbances, where and orthogonal polynomial approximation method is emloyed for the detection and localization of PQ disturbances, and a feature vector, newly extracted form the bispectra of the detected signal, is utilized for the automatic rectgnition of the various types of PQ disturbances. To demonstrae the performance and applicabiliyt of the proposed approach, some simulation results are provided.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.779-797
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• 1999

We find necessary and sufficient conditions for an orthogonal polynomial system to be compatible with another orthogonal polynomial system. As applications, we find new characterizations of semi-classical and clasical orthorgonal polynomials.

• East Asian mathematical journal
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• v.40 no.1
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• pp.25-36
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• 2024

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.359-376
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• 2002

We give a new interpretation of Darboux transforms in the context of orthogonal polynomials and find conditions in or-der for any Darboux transform to yield a new set of orthogonal polynomials. We also discuss connections between Darboux trans-forms and factorization of linear differential operators which have orthogonal polynomial eigenfunctions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2546-2554
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• 1996

In order to investigate the characteristics of sound-structure interaction problems, we modeled a rectangular cavity and the flexible wall of the cavity. Because the governing equations of motion are coupled through velocity terms, we could redefine them using the velocity potential. We calculated the natural frequencies of plate using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz Method. As the result, comparisons of theory and experiment show good agreement. and using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz method show useful method for sound-structure interaction problems too.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.463-474
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• 2001

We find Rodrigues type formula for multi-variate orthogonal polynomial solutions of second order partial differential equations.