Moroccan Multiplicities

Hadron Multiplicities

We review results on hadron multiplicities in high energy particle collisions. Both theory and experiment are discussed. The general procedures used to describe particle multiplicity in Quantum Chromo-dynamics (QCD) are summarized. The QCD equations for the generating functions of the multiplicity distributions are presented both for fixed and running coupling strengths. The mean multiplicities...

Multiplicities and Reduction Numbers

Let (R,m) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.

Multidiameters and Multiplicities

The k-diameter of a graph 0 is the largest pairwise minimum distance of a set of k vertices in 0, i.e., the best possible distance of a code of size k in 0. A k-diameter for some k is called a multidiameter of the graph. We study the function N (k,1, D), the largest size of a graph of degree at most1 and kdiameter D. The graphical analogues of the Gilbert bound and the Hamming bound in coding t...

Eigenfamilies, Characters and Multiplicities

Cyclic dimensions , kernel multiplicities

||||||||||||||||||||||||||||||||||||||| ABSTRACT Two geometric characteristics, namely cyclic dimensions and kernel multiplicities, are introduced for a square matrix. The connection between these characteristics and Gohberg{ Kaashoek numbers is studied. On this basis two simple geometric proofs are given for the theorem about the change of the Jordan structure of a given matrix under small per...