Holonomic $q$ -difference system of the first order associated with a Jackson integral of Selberg type

1994 ◽  
Vol 73 (2) ◽  
pp. 453-468 ◽  
Author(s):  
Katsuhisa Mimachi
Keyword(s):  
Difference System ◽  
First Order ◽  
Jackson Integral

scholarly journals A Peek into Theory of Automation with Applications to Various Branches of Science

2020 ◽  
Vol 9 (09) ◽  
pp. 25156-25160
Author(s):  
Divyalaxmi N.
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Least Square ◽  
Uniqueness Of Solution ◽  
Characteristic Matrix ◽  
Point Boundary ◽  
Difference System ◽  
Lattice Vector ◽  
First Order

In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. 

scholarly journals Oscillation Criteria for Forced first Order Nonlinear Neutral Impulsive Difference System

2018 ◽  
Vol 71 (1) ◽  
pp. 175-193
Author(s):  
Arun Kumar Tripathy ◽  
Gokula Nanda Chhatria
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Impulsive Effect ◽  
Difference System ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillation And Nonoscillation

Abstract In this work, we have established sufficient conditions for oscillation and nonoscillation of a class of forced first order neutral impulsive difference equations with deviating arguments and fixed moments of impulsive effect.

scholarly journals First order difference system- existence and uniqueness

1997 ◽  
Vol 125 (12) ◽  
pp. 3533-3539 ◽  
Author(s):  
K. N. Murty ◽  
P. V. S. Anand ◽  
V. Lakshmi Prasannam
Keyword(s):  
Existence And Uniqueness ◽  
Difference System ◽  
Order Difference ◽  
First Order

scholarly journals q-Difference Systems for the Jackson Integral of Symmetric Selberg Type

2020 ◽  
Author(s):  
Masahiko Ito ◽  
Keyword(s):  
Explicit Expression ◽  
Matrix Decomposition ◽  
Coefficient Matrix ◽  
Gauss Hypergeometric Function ◽  
Symmetric Polynomials ◽  
Difference System ◽  
Difference Systems ◽  
Repeated Use ◽  
Jackson Integral ◽  
Interpolation Polynomials

We provide an explicit expression for the first order q-difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of q-analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system we use a set of the symmetric polynomials introduced by Matsuo in his study of the q-KZ equation. Our main result is an explicit expression for the coefficient matrix of the q-difference system in terms of its Gauss matrix decomposition. We introduce a class of symmetric polynomials called interpolation polynomials, which includes Matsuo's polynomials. By repeated use of three-term relations among the interpolation polynomials we compute the coefficient matrix.

scholarly journals Connection problem in holonomic q-difference system associated with a Jackson integral of Jordan-Pochhammer type

1989 ◽  
Vol 116 ◽  
pp. 149-161 ◽  
Author(s):  
Katsuhisa Mimachi
Keyword(s):  
Difference Equations ◽  
Complex Number ◽  
Difference Operators ◽  
Difference System ◽  
Several Variables ◽  
Connection Problem ◽  
Jackson Integral

Fix a complex number q with |q| < 1. Let T1…, Tn be n-commuting q-difference operators defined byfor a function f(x), x = (x1,…,xn) ε (C*)n. Consider a system of linear q-difference equations in several variables for a matrix valued function on (C*)n as follows:

scholarly journals Permanence for a class of nonlinear difference systems

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Binxiang Dai ◽  
Xingfu Zou
Keyword(s):  
Difference System ◽  
Order Difference ◽  
First Order ◽  
Difference Systems ◽  
The Relationship

A class of nonlinear difference systems is considered in this paper. By exploring the relationship between this system and a correspondent first-order difference system, some permanence results are obtained.

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