The purpose of this paper is to show that a duality exists between the fractional ideal approach [23, 26] and the operator-theoretic approach [4, 6, 8, 9, 33, 34] to stabilization problems. In particular, this duality helps us to understand how the algebraic properties of systems are reflected by the operator-theoretic approach and conversely. In terms of modules, we characterize the domain and...

Habiro–Le invariants dominate sl2 Witten–Reshetikhin–Turaev invariants of rational homology 3–spheres at roots of unity of order coprime with the torsion. In this paper we give a formula for the Habiro–Le invariant of a rational homology 3–sphere obtained by rational surgery on a link in S. As an application, we compute this invariant for Seifert fibered spaces and for Dehn surgeries on twist k...

The asymptotic behaviour of the sequence with general term $P_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/pi^2$ is found.