We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all 2× 2 and...

We present a novel implementation of the eventually perfect failure detector (3P) from the original hierarchy of Chandra-Toueg oracles. Previous implementations of 3P have assumed models of partial synchrony where point-to-point message delay is bounded and/or communication is reliable. We show how to implement this important oracle under even weaker assumptions using Average Delayed/Dropped (A...

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Some elements of the theory and algorithmics corresponding to computation semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic signals, that is, can exhibit an aperiodic behavior initial amount time, then become afterwards. The considered in study obtained by combining representation methods, linear autoregressive GR...

In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s in S$, there exists a natural number $n = n_ {(s, A_{S})} in mathbb{N}$ such that the functor $A_{S} otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We...