New $$(3+1)$$-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion

Abstract Points of intersection of a circle and a torus are used to find a solution to the inverse kinematics problem for a three revolute manipulator. Both geometrical and algebraic solution procedures are discussed. The algebraic procedure begins with a third order equation instead of the usual fourth order equation. Since the procedure is basically geometrical it lends itself to a computer implementation which graphically displays each steps in the solution procedure. The potential of this approach for both design and pedagogy is discussed.

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On the Construction of the Optimal Control for a Linear Third Order Equation with a Quadratic Quality Criterion Using the Method of Moments

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v48.i8.80 ◽

2016 ◽

Vol 48 (8) ◽

pp. 80-88

Author(s):

Mekhriban Mamed kyzy Yagubova

Keyword(s):

Optimal Control ◽

Method Of Moments ◽

Quality Criterion ◽

Order Equation ◽

Third Order

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Design and Analysis of a Repetitive Current Controller for a Single-Phase Bridgeless SEPIC PFC Converter

Energies ◽

10.3390/en12010131 ◽

2018 ◽

Vol 12 (1) ◽

pp. 131 ◽

Cited By ~ 3

Author(s):

Jinwoo Kim ◽

Sanghun Han ◽

Wontae Cho ◽

Younghoon Cho ◽

Hyunsoo Koh

Keyword(s):

Controller Design ◽

Harmonic Distortion ◽

Input Current ◽

Order Model ◽

Third Order ◽

Current Controller ◽

The Stability ◽

Small Signal Modeling ◽

Fifth Order ◽

Repetitive Controller

This paper studies a repetitive controller design scheme for a bridgeless single-ended primary inductor converter (SEPIC) power factor correction (PFC) converter to mitigate input current distortions. A small signal modeling of the converter is performed by a fifth-order model. Since the fifth-order model is complex to be applied in designing a current controller, the model is approximated to a third-order model. Using the third-order model, the repetitive controller is designed to reduce the input current distortion. Then, the stability of the repetitive controller is verified with an error transfer function. The proposed controller performance is validated by simulation, and the experiment results show that the input current total harmonic distortion (THD) is improved by applying the proposed controller for an 800 W bridgeless SEPIC PFC converter prototype.

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Asymptotic formulae for linear equations

Glasgow Mathematical Journal ◽

10.1017/s0017089500001579 ◽

1972 ◽

Vol 13 (2) ◽

pp. 147-152 ◽

Cited By ~ 3

Author(s):

Don B. Hinton

Keyword(s):

Asymptotic Behaviour ◽

Fourth Order ◽

Linear Equations ◽

Order Equation ◽

Third Order ◽

Fourth Order Equation ◽

The Third ◽

Asymptotic Formulae ◽

Image Position

Numerous formulae have been given which exhibit the asymptotic behaviour as t → ∞solutions ofwhere F(t) is essentially positive and Several of these results have been unified by a theorem of F. V. Atkinson [1]. It is the purpose of this paper to establish results, analogous to the theorem of Atkinson, for the third order equationand for the fourth order equation

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Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations

Canadian Journal of Mathematics ◽

10.4153/cjm-1975-012-8 ◽

1975 ◽

Vol 27 (1) ◽

pp. 106-110 ◽

Cited By ~ 1

Author(s):

J. Michael Dolan ◽

Gene A. Klaasen

Keyword(s):

Linear Equation ◽

Linear Space ◽

Nontrivial Solution ◽

Linear Equations ◽

Order Equation ◽

Third Order ◽

Nonoscillatory Solutions ◽

Oscillatory Solutions ◽

The Third ◽

All Solutions

Consider the nth order linear equationand particularly the third order equationA nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.

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