A new approach to character recognition problem, based on meta sets, is introduced and developed. For the given compound character pattern consisting of a number of character samples accompanied by their corresponding quality degrees, and for the given testing character sample, the main theorem of the paper gives means to evaluate the correlation between the testing sample and the compound patt...

We prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley’s theorem: if a countable Hausdorff cat T has a unique complete model of density character λ ≥ ω1, then it has a unique complete model of density character λ for every λ ≥ ω1.

In this paper we provide a geometric framework for the study of characters of depth-zero representations of unramified groups over local fields with finite residue fields which is built directly on Lusztig's theory of character sheaves for groups over finite fields. We introduce depth-zero character sheaves, which are coefficient systems of ℓ-adic sheaves on Bruhat-Tits buildings for p-adic gro...