The discrete Painleveequations are nonlinear difference equations
that arise as compatibility conditions of linear systems, says Joshi, then warns that the deceptive simplicity of this statement hides deep layers of mathematical properties, which she outlines here.
Implementing the Dynamic Back-Propagation algorithm requires the difference equations
of each parameter to be used in equations (14), (15), and (16).
The remaining part of the proof is similar to that of Theorem 0.1, by observing that Appell's O-functions satisfy the following difference equations
The general theory of linear quantum difference equations
was published in 1912 by Carmichael .
The following neutral difference equations/delay difference equations
are obtained as particular case of (2).
In the past few years, there is a great interest in studying the oscillatory and asymptotic behavior of solutions of higher order neutral type difference equations
, since such type of equations naturally arises in the applications including problems in population dynamics or in cobweb models in economics and so on.
are powerful tool that describe the law of nature.
The initial system of difference equations
on one layer (2.2), (2.3) is equivalent to the newly obtained system (2.10)-(2.11) with formulas (2.3).
Drazin inverse is applied to (3) corresponding to the difference equations
; we will establish sufficient and necessary conditions for the solution of (3).
Differential and difference equations
are used for modeling, solving, and discussing many problems arising in engineering and natural sciences.
On the spectrum of eigenparameter-dependent quantum difference equations
For difference equations
there will be studied such issues as solvability, equilibrium existence and stability.