scholarly journals New Pieri Type Formulas for Jack Polynomials and their Applications to Interpolation Jack Polynomials

2020 ◽  
Author(s):  
Genki Shibukawa ◽  
Keyword(s):  
Kernel Function ◽  
Difference Equations ◽  
Higher Order ◽  
Jack Polynomials ◽  
Order Difference ◽  
Pieri Formulas

We present new Pieri type formulas for Jack polynomials. As an application, we give a new derivation of higher order difference equations for interpolation Jack polynomials originally found by Knop and Sahi. We also propose Pieri formulas for interpolation Jack polynomials and intertwining relations for a kernel function for Jack polynomials.

scholarly journals Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 108
Author(s):  
Kgatliso Mkhwanazi ◽  
Mensah Folly-Gbetoula
Keyword(s):  
Difference Equations ◽  
Variable Coefficients ◽  
Higher Order ◽  
Order Difference

We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.

TRANSFER EQUIVALENCE AND REALIZATION OF NONLINEAR HIGHER ORDER INPUT/OUTPUT DIFFERENCE EQUATIONS USING MATHEMATICA

1999 ◽  
Vol 09 (01n02) ◽  
pp. 23-35 ◽  
Author(s):  
ÜLLE KOTTA ◽  
MARIS TÕNSO
Keyword(s):  
Control Systems ◽  
Difference Equations ◽  
Space Form ◽  
Higher Order ◽  
Nonlinear Control Systems ◽  
Input Output ◽  
Nonlinear Case ◽  
State Equations ◽  
Order Difference ◽  
Classical State

This paper presents a contribution to the development of symbolic computation tools for discrete-time nonlinear control systems. A set of functions is developed in Mathematica 3.0 that test if the higher order input/output difference equation is realizable in the classical state-space form, and for simple examples, also find such state equations. The approach relies on a new notion of equivalence of higher order difference equations which yields a minimal (i.e. accessible and observable) realization and generalizes the notion of transfer equivalence to the nonlinear case. The application of the developed functions is demonstrated on three examples obtained via identification.

scholarly journals Stabilization with target oriented control for higher order difference equations

2015 ◽  
Vol 379 (16-17) ◽  
pp. 1102-1109 ◽  
Author(s):  
Elena Braverman ◽  
Daniel Franco
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Order Difference
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