Combinatorics of Hall trees and Hall words

اثر هال (hall effect)

Feynman Graphs, Rooted Trees, and Ringel-hall Algebras

We construct symmetric monoidal categoriesLRF ,LFG of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf algebras of LRF ,LFG, HLRF ,HLFG are dual to the corresponding Connes-Kreimer Hopf algebras on rooted trees and Feynman diagrams. We thus obtain an interpretation...

linear analogues of theorems of schur, baer and hall

a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...

Canonical Bases of Singularity Ringel-hall Algebras and Hall Polynomials

In this paper, the singularity Ringel-Hall algebras are defined. A new class of perverse sheaves are shown to have purity property. The canonical bases of singularity RingelHall algebras are constructed. As an application, the existence of Hall polynomials in the tame quiver algebras is proved.

Scanning hall probe microscopy technique for investigation of magnetic properties

Scanning Hall Probe Microscopy (SHPM) is a scanning probe microscopy technique developed to observe and image magnetic fields locally. This method is based on application of the Hall Effect, supplied by a micro hall probe attached to the end of cantilever as a sensor.  SHPM provides direct quantitative information on the magnetic state of a material and can also image magnetic induction under a...