The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature.

The Legendre-Stirling numbers are the coeffi cients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejoh...

Differential-difference equations (DDEs) of the form u n (t) = Fn(t, un+a, . . . , un+b) with k ≥ 2 are studied for Lie symmetries and preliminary classification. Explicit forms of equations are given for those admitting at least one intrinsic Lie symmetry. An algorithmic mechanism is also proposed to automate the symmetry calculation for fairly general DDEs via computer algebras.

Discourse relation may entail sentiment information. In this work, we annotate both discourse relation and sentiment information on a moderate-sized Chinese corpus extracted from the ClueWeb09. Based on the annotation, we investigate the association between the relation type and the sentiment polarity in Chinese and interpret the data from various aspects. Finally, we highlight some language ph...

In this paper, we describe an annotation environment developed for the marking of discourse structures in Turkish, and the kinds of discourse relation configurations that led to its design.

and Applied Analysis 3 Then (a) for any L ∈ (N,M), there exist θ ∈ (0, 1) and T ≥ n 0 + τ + β such that for each x 0 = {x 0n } n∈N β ∈ A(N,M), the Mann iterative sequence with errors {x m } m∈N 0 = {x mn } (m,n)∈N 0 ×N β generated by the scheme