The lower bound on the number of n-variable balanced symmetric functions over finite fields GF(p) presented in [1] is improved in this paper.

We prove that the range of a symmetric matrix over GF (2) always contains its diagonal. This is best possible in several ways, for example GF (2) cannot be replaced by any other field.

We determine lower bounds for the number of random vectors in GF (q), chosen uniformly from vectors having k non-zero co-ordinates, needed to obtain a dependent set over GF (q).

Let F be a totally real field, and v a place of F dividing an odd prime p. We study the weight part of Serre’s conjecture for continuous totally odd representations ρ : GF → GL2(Fp) that are reducible locally at v. Let W be the set of predicted Serre weights for the semisimplification of ρ|GFv . We prove that when ρ|GFv is generic, the Serre weights inW for which ρ is modular are exactly the on...

This chapter considers some of the basic ideas about language and linguistic analysis that define the family of feature-based grammars. Underlying the complex constraint languages and representations that give this family its characteristic ‘look and feel’ are a number of relatively straightforward claims and hypotheses. Foremost among these is the idea that many of the distinctive properties w...

A novel Grammatical Genetic Algorithm, the meta-Grammar Genetic Algorithm (mGGA) is presented. The mGGA borrows a grammatical representation and the ideas of modularity and reuse from Genetic Programming, and in particular an evolvable grammar representation from Grammatical Evolution by Grammatical Evolution. We demonstrate its application to a number of benchmark problems where significant pe...

The purpose of the present study is to analyse abstracts related to Applied Linguistics, and more precisely the discourse functions of grammatical subjects and verbs. The corpus consisted of 50 PhD thesis abstracts written on the subject of Applied Linguistics. All of the abstracts were written from 2010 to 2014. The theses from which the abstracts were extracted are available in the ProQuest d...