Though algebraic geometry over C is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the n × n × n tensors of rank n over C, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose non-v...

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

peripheral blood t lymphocytes and their subsets were studied in 31 patients with beta thalassemia major (age 2-12years) and compared with 14 age-arid sex-matched healthy controls. three monoclonal antibodies (anti-cd3, anti cd-f, unti-cds) were simultaneously applied for detection of th (cd3-, cd4^), tsk (cd3+, cd8+) and th/ts ratio by flow-cytometry respectively. the results of this study sho...

We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality”

A group of finite Morley rank is a group whose definable subsets have a notion of dimension satisfying several basic axioms [BN94, p. 57]. Such groups arise naturally in model theory; initially as א1-categorical groups, i.e. as groups determined up to isomorphism by their first order theory, and here the simple groups correspond exactly. More recently groups of finite Morley rank have appeared ...

Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that inclu...

We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality” of the free group.

In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoids. These automata allow us to compute explicitly generating functions, λ−measures and Cesaro meas...

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got use...

We establish monotone bijections between the Farey sequences of order m and the halfsequences of Farey subsequences associated with the rank m elements of the Boolean lattice of subsets of a 2m-set. We also present a few related combinatorial identities. Subject class: 05A19, 11B65.