In this expository lecture, we explain how problems of classical polynomial algebra may be understood and numerically solved when they appear in the context of Scientific Computing, i.e. with data of limited accuracy. A suitable conceptual framework is introduced and its use explained in a number of situations.

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively , in the context of (locally) essential domains.

In the past, most threshold models considered a single variable. However, for some practical applications, with two variables may be needed. this paper, we propose two-threshold-variable integer-valued autoregressive model based on binomial thinning operator and discuss of its basic properties, including mean, variance, strict stationarity, ergodicity. We consider conditional least squares (CLS...