scholarly journals The optimal upper bound for the first eigenvalue of the fourth order equation

2017 ◽  
Vol 37 (12) ◽  
pp. 6369-6382 ◽  
Author(s):  
Gang Meng ◽  
Keyword(s):  
Fourth Order ◽  
Upper Bound ◽  
Order Equation ◽  
First Eigenvalue ◽  
Fourth Order Equation ◽  
The First Eigenvalue

scholarly journals Optimal lower bound for the first eigenvalue of the fourth order equation

2016 ◽  
Vol 261 (6) ◽  
pp. 3149-3168 ◽  
Author(s):  
Gang Meng ◽  
Ping Yan
Keyword(s):  
Lower Bound ◽  
Fourth Order ◽  
Order Equation ◽  
First Eigenvalue ◽  
Fourth Order Equation ◽  
The First Eigenvalue ◽  
Optimal Lower Bound

scholarly journals THE QUANTIZATION OF A FOURTH-ORDER EQUATION WITHOUT A SECOND-ORDER LAGRANGIAN

2010 ◽  
Vol 17 (4) ◽  
pp. 485-490 ◽  
Author(s):  
M. C. NUCCI ◽  
P. G. L. LEACH
Keyword(s):  
Fourth Order ◽  
Order Equation ◽  
Second Order ◽  
Fourth Order Equation

A Geometrical Solution for the Inverse Kinematics of Three Revolute Manipulators

1993 ◽  
Author(s):  
Eugene F. Fichter
Keyword(s):  
Fourth Order ◽  
Inverse Kinematics ◽  
Solution Procedure ◽  
Order Equation ◽  
Algebraic Solution ◽  
Computer Implementation ◽  
Third Order ◽  
Fourth Order Equation ◽  
Inverse Kinematics Problem

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.

26.—The Strong Limit-2 Case of Fourth-order Differential Equations

1974 ◽  
Vol 71 (4) ◽  
pp. 297-304
Author(s):  
V. Krishna Kumar
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Order Equation ◽  
Complex Numbers ◽  
Strong Limit ◽  
Fourth Order Equation ◽  
Linearly Independent ◽  
Image Position ◽  
Adjoint Operators ◽  
Bounded Below

SynopsisThe fourth-order equation considered isConditions are given on the coefficients r, p and q which ensure that this differential equation (*) is in the strong limit-2 case at ∞, i.e. is limit-2 at ∞. This implies that (*) has exactly two linearly independent solutions which are in the integrable-square space ℒ2(0, ∞) for all complex numbers λ with im [λ] ≠ 0. Additionally the conditions imply that self-adjoint operators generated by M[·] in ℒ2(0, ∞) are semi-bounded below. The results obtained are applied to the case when the coefficients r, p and q are powers of x ∈ [0, ∞).

scholarly journals Asymptotic formulae for linear equations

1972 ◽  
Vol 13 (2) ◽  
pp. 147-152 ◽  
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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