• 제목/요약/키워드: orthogonal polynomial

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ORTHOGONAL POLYNOMIALS SATISFYING PARTIAL DIFFERENTIAL EQUATIONS BELONGING TO THE BASIC CLASS

  • Lee, J.K.;L.L. Littlejohn;Yoo, B.H.
    • 대한수학회지
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    • 제41권6호
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    • pp.1049-1070
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    • 2004
  • We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ + 2B($\chi$, y) $u_{{\chi}y}$ + C(y) $u_{yy}$ + D($\chi$) $u_{{\chi}}$ + E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

부분적으로 열린 구조-음향 연성평판의 자유진동해석 (A free vibration analysis of sound-structure interaction plate having a small cut-out)

  • 오재응;이동익
    • 대한기계학회논문집A
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    • 제21권10호
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    • pp.1666-1673
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    • 1997
  • In order to investigate the characteristics of sound-structure interaction plate having a cut-out, we modeled a rectangular cavity and the flexible plate of the cavity. Because the particle velocity of air is the same as that of plate on the plate, we could easily redefine vibration equation 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. For the change of vibration characteristics, the effect of sound-structure interaction is more dominant than that of cut-out size.

INTEGRALS INVOLVING LAGUERRE, JACOBI AND HERMITE POLYNOMIALS

  • Nath, B.
    • Kyungpook Mathematical Journal
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    • 제12권1호
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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].

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ON ASYMPTOTIC METHOD IN CONTACT PROBLEMS OF FREDHOLM INTEGRAL EQUATION OF THE SECOND KIND

  • Abdou, M.A.
    • Journal of applied mathematics & informatics
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    • 제9권1호
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    • pp.261-275
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    • 2002
  • Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

A non-standard class of sobolev orthogonal polynomials

  • Han, S.S.;Jung, I.H.;Kwon, K.H.;Lee, J.K..
    • 대한수학회논문집
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    • 제12권4호
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    • pp.935-950
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    • 1997
  • When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

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A Six-Phase CRIM Driving CVT using Blend Modified Recurrent Gegenbauer OPNN Control

  • Lin, Chih-Hong
    • Journal of Power Electronics
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    • 제16권4호
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    • pp.1438-1454
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    • 2016
  • Because the nonlinear and time-varying characteristics of continuously variable transmission (CVT) systems driven by means of a six-phase copper rotor induction motor (CRIM) are unconscious, the control performance obtained for classical linear controllers is disappointing, when compared to more complex, nonlinear control methods. A blend modified recurrent Gegenbauer orthogonal polynomial neural network (OPNN) control system which has the online learning capability to come back to a nonlinear time-varying system, was complied to overcome difficulty in the design of a linear controller for six-phase CRIM driving CVT systems with lumped nonlinear load disturbances. The blend modified recurrent Gegenbauer OPNN control system can carry out examiner control, modified recurrent Gegenbauer OPNN control, and reimbursed control. Additionally, the adaptation law of the online parameters in the modified recurrent Gegenbauer OPNN is established on the Lyapunov stability theorem. The use of an amended artificial bee colony (ABC) optimization technique brought about two optimal learning rates for the parameters, which helped reform convergence. Finally, a comparison of the experimental results of the present study with those of previous studies demonstrates the high control performance of the proposed control scheme.

서보모터의 가감속형태에 따른 운도오차에 관한 연구 (A study on motion errors due to acceleration and deceleration types of servo motors)

  • 신동수;정성종
    • 대한기계학회논문집A
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    • 제21권10호
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    • pp.1718-1729
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    • 1997
  • This paper describes motion errors due to acceleration and deceleration types of servo motors in NC machine tools. Motion errors are composed of two components : one is due to transient response of a servomechanism and the other comes from gain mismatching of positioning servo motors. It deals with circular interpolation to identify motion errors by using Interface card. Also in order to minimize motion errors, this study presents an effective method to optimize parameters which are connected with motion errors. The proposed method is based upon a second order polynomial regression model and it includes an orthogonal array method to make the effective results of experiments. The validity and reliability of the study were verified on a vertical machining center equipped with FANUC 0MC through a series of experiments and analysis.

A Backstepping Control of LSM Drive Systems Using Adaptive Modified Recurrent Laguerre OPNNUO

  • Lin, Chih-Hong
    • Journal of Power Electronics
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    • 제16권2호
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    • pp.598-609
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    • 2016
  • The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.

탄성지반 위에 놓여있는 다지지 보의 동적해석 제1보 : 고유진동수 (Dynamic Analysis of the Multi-Span Beam on Elastic Foundation Part one : Natural Frequencies)

  • 김용철;최교준
    • 대한조선학회논문집
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    • 제28권1호
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    • pp.83-91
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    • 1991
  • 본 연구에서는 병진 및 회전 스프링을 포함하는 탄성지반 위에 놓여 있는 다지지보의 동적 해석이 수행되었다. 특히 중간 지지점이 있는 경우에 대한 영향도 조사하였다. 문제의 해석방법으로서 우선 기하학적 및 동적 경계조건을 동시에 만족하는 직교 다항식 함수를 구하였으며, Galerkin 방법을 이용하여 시스템의 고유진동수틀 구하였다. 본 연구에서 제시한 방법으로 구한 고차 직교 다항식 함수를 사용하면 정확한 해를 얻을 수 있다는 것을 여러가지 경우에 대한 수치 계산 결과로부터 알 수 있었다.

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