In answering questions from [7] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V , and let st : V → k be the corresponding standard part map. Under a mild assumption on (R, V) we show that definable sets X ⊆ V n admit a triangulation that induces a triangulation of its standard part st(X) ⊆ k n .

Although language-impaired children have been observed to follow many nor­ mal language acquisition patterns, research to date has not fully explored the re­ lationships between various linguistic domains. The hypotheses investigated in this study are that language-impaired children produce fewer logical proposi­ tions per utterance and evidence less control of formal syntactic markers. lan­ gu...

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings – Noetherian semirings, natural numbers – are proper. Properness matters as the equivalence problem for weighted automata over a semiring which is proper and finitely and effectively presented is decidable. Milius generalised the notion of properness from a semiring to a functor. As...

An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices (u,v), the contains a directed path (a walk) from u to v such that arcs adjacent on (on have distinct colors. The proper connection number pc→(D) (the proper-walk wc→(D)) minimum colours make (properly-walk connected). We prove pc→(Cn(S))≤2 every circulant Cn(S) with S⊆{1,…,n−1},|S|≥2 and 1∈S. Fu...

We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

Distributed Arithmetic Coding (DAC) is an effective implementation of Slepian-Wolf coding, especially for short data blocks. To research its properties, the concept of DAC codeword distribution along proper and wrong decoding paths has been introduced. For DAC codeword distribution of equiprobable binary sources along proper decoding paths, the problem was formatted as solving a system of funct...