This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness initial value problems for these are derived, then the classification them obtained a similar classical Weyl's method by selecting suitable quasi-difference. An equivalent characterization this given in terms number linearly independent square summable solutions equation. influence off...

Researchers are currently considering membranes separation processes due to their eco-friendly, process simplicity and high efficiency. Selecting a suitable efficient operation is the primary concern of researchers in field industries. In recent decades, polymeric inorganic industry have made significant progress. The been challenged competitiveness permeability selectivity factors. A combinati...