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.

Proof. (1) These are the well known classical Plücker relations. For completeness’ sake we include a proof. Let P ∈ ΛV and consider the induced linear mapping ♯P : Λ V ∗ → V . Its image, W , is contained in each linear subspace U of V with P ∈ ΛU . Thus W is the minimal subspace with this property. P is decomposable if and only if dimW = s, and this is the case if and only if w ∧ P = 0 for each...

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

UK Abstract We describe a computational system which parses discourses consisting of sequences of simple sentences. These contain a range of temporal constructions, including time adverbials, progressive aspect and various aspectual classes. In particular, the grammar generates the required readings, according to the theoretical analysis of (Glasbey, forthcoming), for sentence-final 'then'. 1 S...

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...