R. D. Brauer

R–cross-sections in the Brauer semigroup

We classify all cross-sections of Green’s relations L and R in the Brauer semigroup. The regular behavior of such cross-sections starts from n = 7. We show that in the regular case there are essentially two different cross-sections and all others are Sn-conjugated to one of these two. We also classify all cross-sections up to isomorphism.

Collimator R&d Collimator R&d

The importance of collimator R&D with test beam facilities is demonstrated with the example of ILC collimator studies at SLAC End Station A. Related LHC collimator aspects and longer term plans are addressed. Presented at IDTB07, ILC Detector Test Beam workshop, Fermilab, USA, 2007.

بررسی تئوریک D&R با استفاده از مدلهای رشد وتحلیل مقایسه ای هزینه های D&R در کشورهای مختلف

Brauer Groups

I define the Brauer group of a field k as similarity classes of central simple algebras over k. Then I introduce non-abelean cohomology and use it to prove that the Brauer group is isomorphic to a certain cohomology group. Brauer groups show up in global class field theory.

(r, R+1)-factorizations of (d, D+1)-graphs

A (d, d + 1)-graph is a graph whose vertices all have degrees in the set {d, d + 1}. Such a graph is semiregular. An (r, r + 1)-factorization of a graph G is a decomposition of G into (r, r + 1)-factors. For d-regular simple graphs G we say for which x and r G must have an (r, r + 1)-factorization with exactly x (r, r + 1)-factors. We give similar results for (d, d + 1)-simple graphs and for (d...