The Mackey–Zimmer theorem classifies ergodic group extensions $X$ of a measure-preserving system $Y$ by compact $K$, showing that such are isomorphic to skew-product $X \equiv Y \rtimes _\rho H$ for some closed subgroup $

Our paper deals with the investigation of extensions commutative groups by loops so that quasigroups result in multiplication between cosets kernel subgroup are T-quasigroups. We limit our study to which determining linear functions without constant term, called abelian extensions. characterize constructively such left-, right-, or inverse properties using a general construction according an eq...

Introduction The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field Q of rational numbers. We then say that G is realizable over Q. This problem goes back to Hilbert [Hil] who realized Sn and An over Q. Many more groups have been realized over Q since 1892. For example, Shafarevich [Sha] finished in 1958 the work started by Scholz 1936 [Slz] and Rei...

We study the problem of lifting ergodicity to certain skew-product extensions over shifts of nite type. This can be done by computing the asymptotic range of the deening cocycle. For a class of ergodic shift-invariant measures and a class of functions (deening conservative extensions) we give a characterisation of ergodicity in terms of weights of periodic orbits in the shift space.

In this paper, we discuss some open problems of non-commutative algebra and algebraic geometry from the approach skew PBW extensions semi-graded rings. More exactly, will analyze isomorphism arising in investigation Gelfand–Kirillov conjecture about commutation between center total ring fractions an Ore domain. The Serre’s be discussed for a particular class extensions. questions Noetherianity ...

To conserve energy, a design which utilizes different power modes has been widely adopted. However, when a design has many different power modes, clock tree optimization (CTO) becomes very difficult. In this paper, we propose a two-level power-mode-aware CTO methodology. Among all different power modes, the chip-level CTO globally reduces clock skew among modules, whereas the module-level CTO r...