Template dependencies (TD’s) are a class of data dependencies that include multivalued and join dependencies and embedded versions of these. A collection of techniques, examples and results about TD’s are presented. The principal results are: 1) Finite implication (implication over relations with a finite number of tuples) is distinct from unrestricted implication for TD’s. 2) There are, for TD...

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...