In this work we provide low rank estimations for coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP) over Galois ring R = GR(pn, r), p ≥ 5, r ≥ 2, with numbers s such that s = kr + 2, k ∈ N0.

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R → ∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.

In this paper, we investigate the global behavior of the difference equation of order three xn+1 = α+ xn−2 xn , n = 0, 1, . . . where the parameters α, k ∈ (0,∞) and the initial values x−2, x−1 and x0 are arbitrary positive real numbers.

In this paper, existence criteria for single and multiple positive solutions of periodic boundary value problems for first order difference equations of the form

and Applied Analysis 3 After k steps we obtain the following formula xn A ⎛ ⎝ A x r/p n−k ⎛ ⎝ A x r/p2 n−k x r/p n−k−1 ⎛ ⎝ A x r/p3 n−k x r/p2 n−k−1x r/p n−k−2

Recently, Bouvel and Pergola initiated the study of a special class of permutations, minimal permutations with a given number of descents, which arise from the whole genome duplication-random loss model of genome rearrangement. In this paper, we show that the number of minimal permutations of length 2d− 1 with d descents is given by 2d−3(d− 1)cd, where cd is the d-th Catalan number. We also der...