Transposition Regular TA-Groupoids and Their Structures

Polynomial evaluation groupoids and their groups

In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can beobtained as a polynomial evaluation groupoid.

Linearization of Regular Proper Groupoids

Let G be a Lie groupoid over M such that the target-source map from G to M ×M is proper. We show that, if O is an orbit of finite type (i.e. which admits a proper function with finitely many critical points), then the restriction G|U of G to some neighborhood U of O in M is isomorphic to a similar restriction of the action groupoid for the linear action of the transitive groupoid G|O on the nor...

PLA-based regular structures and their synthesis

Two regular circuit structures based on the programmable logic array (PLA) are proposed. They provide alternatives to the widely used standard-cell structure and have better predictability and simpler design methodologies. A whirlpool PLA is a cyclic four-level structure, which has a compact layout. Doppio-ESPRESSO, a four-level logic minimization algorithm, is developed for the synthesis of Wh...

Holomorphic Poisson Structures and Groupoids

We study holomorphic Poisson manifolds, holomorphic Lie algebroids and holomorphic Lie groupoids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bu...

Finite idempotent groupoids and regular languages