A word is abelian square-free if it does not contain two adjacent subwords which are permutations of each other. Over an alphabet Σk on k letters, an abelian squarefree word is maximal if it cannot be extended to the left or right by letters from Σk and remain abelian square-free. Michael Korn proved that the length `(k) of a shortest maximal abelian square-free word satisfies 4k − 7 ≤ `(k) ≤ 6...

Let ` be a prime number and let k be an algebraically closed field with char(k) 6= `. Let K/k be a function field of transcendence degree td(K/k) > 1 with absolute Galois group GK . Take G K = GK and for all i ≥ 1, let G (i+1) K = [G , G](G) ∞ . In other words, the groups {G K }i≥1 form the descending central `∞-series of GK . Then ΠK = G /G = Gal(K ′/K) is the Galois group of the maximal pro-`...

Gossiping is an information dissemination problem in which each node of a communication network has a unique piece of information that must be transmitted to all other nodes using two-way communications between pairs of nodes along the communication links of the network. In this paper, we study gossiping using a linear cost model of communication which includes a start-up time and a propagation...

In 1965 Motzkin and Straus established a remarkable connection between the local/global maximizers of the Lagrangian of a graph G over the standard simplex ∆ and the maximal/maximum cliques of G. In this work we generalize the Motzkin-Straus theorem to k-uniform hypergraphs, establishing an isomorphism between local/global minimizers of a particular function over ∆ and the maximal/maximum cliqu...

For positive integers k, n let f(n, k) be the maximal cardinality of subsets of integers in the interval < 1, n > , which don’t have k + 1 pairwise coprimes. The set E(n, k) of integers in < 1, n > , which are divisible by one of the first k primes, certainly does not have k + 1 pairwise coprimes. Whereas we disproved in [1] an old conjecture of Erdös ([4], [5], [6], [7]) by showing that the eq...

We study hidden geometry of Bier spheres Bier(K) = K * ? K? by describing their natural geometric realizations, compute volume, describe an effective criterion for polytopality, and associate to a coarsening Fan(K) the Braid fan. also establish connection maximal volume with recent generalizations classical Van Kampen-Flores theorem clarify role in theory generalized permutohedra.

Let G be a semisimple real Lie group of non-compact type, K a maximal compact subgroup and S ⊆ G a semigroup with nonempty interior. We consider the ideal boundary ∂∞(G/K) of the associated symmetric space and the flag manifolds G/PΘ . We prove that the asymptotic image ∂∞(Sx0) ⊆ ∂∞(G/K), where x0 ∈ G/K is any given point, is the maximal invariant control set of S in ∂∞(G/K). Moreover there is ...

homocysteine thiolactone was demonstrated to inhibit the growth of 10–12-day-old chicken embryo cardiac tissue explants at 7 × 10−9 −1 × 10−3 m concentrations in a dose-dependent manner. the maximal cardiotoxic effect of homocysteine thiolactone was detected at 1 × 10−3 m, which corresponds to severe hyperhomocysteinemia. the results of experiments on culturing of cardiac tissue explants in the...

Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees: starting with Kk+1 one repeatedly chooses a k-clique C and adds a new vertex adjacent to vertices in C. In this paper we give an analogous algorithm for generating the graphs of branchwidth at most k. To this end we first inv...