scholarly journals Local asymptotics for orthonormal polynomials in the interior of the support via universality

2019 ◽  
Vol 147 (9) ◽  
pp. 3877-3886 ◽  
Author(s):  
D. S. Lubinsky
Keyword(s):  
Orthonormal Polynomials ◽  
Local Asymptotics

Local Asymptotics of Unfoldings of Edge and Corner Catastrophes

2020 ◽  
Vol 27 (4) ◽  
pp. 446-455
Author(s):  
J. I. Bova ◽  
A. S. Kryukovskii ◽  
D. S. Lukin
Keyword(s):  
Local Asymptotics

The Sector Problem

1957 ◽  
Vol 24 (4) ◽  
pp. 574-581
Author(s):  
G. Horvay ◽  
K. L. Hanson
Keyword(s):  
Variational Method ◽  
Orthogonal Polynomials ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Circular Sector ◽  
Orthonormal Polynomials ◽  
Circular Boundary ◽  
Stress Functions ◽  
Complete Set ◽  
Derivatives Of

Abstract On the basis of the variational method, approximate solutions f k ( r ) h k ( θ ) , f k ( r ) g k ( θ ) , F k ( θ ) H k ( r ) , F k ( θ ) G k ( r ) of the biharmonic equation are established for the circular sector with the following properties: The stress functions fkhk create shear tractions on the radial boundaries; the stress functions fkgk create normal tractions on the radial boundaries; the stress functions FkHk create both shear and normal tractions on the circular boundary, and the stress functions FkGk create normal tractions on the circular boundary. The enumerated tractions are the only tractions which these function sets create on the various boundaries of the sector. The factors fk(r) constitute a complete set of orthonormal polynomials in r into which (more exactly, into the derivatives of which) self-equilibrating normal or shear tractions applied to the radial boundaries of the sector may be expanded; the factors Fk(θ) constitute a complete set of orthonormal polynomials in θ into which shear tractions applied to the circular boundary of the sector may be expanded; and the functions Fk″ + Fk constitute a complete set of non-orthogonal polynomials into which normal tractions applied to the circular boundary of the sector may be expanded. Function tables, to facilitate the use of the stress functions, are also presented.

New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials

2016 ◽  
Vol 174 (1) ◽  
pp. 295-320 ◽  
Author(s):  
Samer S. Ezz-Eldien ◽  
Ramy M. Hafez ◽  
Ali H. Bhrawy ◽  
Dumitru Baleanu ◽  
Ahmed A. El-Kalaawy
Keyword(s):  
Variational Problems ◽  
Numerical Approach ◽  
Orthonormal Polynomials ◽  
Fractional Variational Problems
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