Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY | REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY J. DIBLÍK AND D. YA. KHUSAINOV Received 16 January 2006 Accepted 22 January 2006 The purpose of this contribution is to develop a method for construction of solutions of linear discrete systems with constant coefficients and with pure delay. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential having between every two adjoining knots the form of a polynomial. These polynomials have increasing degrees in the right direction. Such approach results in a possibility to express initial Cauchy problem in the closed form. Copyright 2006 J. Diblik and D. Y. Khusainov. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction We use following notation for integers s q s q we define s s 1 . q where possibility s -TO or q TO is admitted too. Throughout this paper using notation Zq or another one with a couple of integers s q we suppose s q. In this paper we deal with the discrete system Ax k Bx k - m f k where m 1 is a fixed integer k e ZTO B bij is a constant n X n matrix f ZTO Rn Ax k x k 1 - x k x ZTOm Rn. Following the terminology used . in 1 3 we refer to as a delayed discrete system if m 1 and as a nondelayed discrete system if m 0. Together with we consider the initial conditions x k p k with given ỹ Z m Rn. The existence and uniqueness of solution of the problem on ZTOm is obvious. We recall that solution x ZTOm Rn of the problem is defined as an Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 80825 Pages 1-13 DOI ADE 2006 80825 2 Representation of solutions of linear discrete systems infinite sequence ty -m q -m 1 . p 0 x 1 x 2 . x k . such that for any k e Z equality .
