The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

Questioning practice constitutes one of the typical and fundamental interactional tools in L2 teaching. Much L2 research on teacher questions has been quantitative studies focusing on identifying question types and their roles in language acquisition and meaning negotiation. However, by drawing on conversation analysis within a sociocultural perspective, this study examines qualitatively how EF...

We consider real univariate polynomials with all roots real. Such a polynomial c sign changes and p preservations in the sequence of its coefficients has positive negative counted multiplicity. Suppose that moduli are distinct; we them as ordered on half-axis. ask question: If positions known, what can be? prove several new results which show how far from trivial answer to this question is.

Consider a linear functional L defined on the space $${\mathcal {D}}[s]$$ of Dirichlet polynomials with real coefficients and set {D}}_+[s]$$ non-negative elements in {D}}[s].$$ An analogue Riesz–Haviland theorem this context asks: What are all -positive functionals L, which moment functionals? Since {D}}[s],$$ when considered as subspace $$C([0, \infty ), {\mathbb {R}}),$$ fails to be an adapt...

Using the Stanford Question and Answering Dataset (SQuAD) released by Rajpurkar et al. [1], we leverage a modified Recurrent Span Representation (RaSoR) model by Lee et al. [2] but with linear space complexity. This contrasts the original model by Lee et. al which requires a demanding quadratic space requirement to enumerate all answer spans. In addition, we introduce a novel architecture, Sequ...