Let ` be a fixed rational prime number. Consider function fields K|k over algebraically closed fields k of characteristic 6= `. For each such a function field K|k, let Π K := Gal(K ′′|K) be the Galois group of a maximal pro-` abelian-by-central Galois extension K ′′|K, and ΠK = Gal(K ′|K) be the Galois group of the maximal pro-` abelian sub-extension K ′|K of K ′′|K. At the beginning of the 199...

In this paper, we study the minimality of the boundary of a Coxeter system. We show that for a Coxeter system (W,S) if there exist a maximal spherical subset T of S and an element s0 ∈ S such that m(s0, t) ≥ 3 for each t ∈ T and m(s0, t0) = ∞ for some t0 ∈ T , then every orbit Wα is dense in the boundary ∂Σ(W,S) of the Coxeter system (W,S), hence ∂Σ(W,S) is minimal, where m(s0, t) is the order ...

Recently, the authors studied the connection between each maximal monotone operator T and a family H(T ) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a uniq...

We are concerned with the poset P(n)=P([1, 2, ..., n]). This is the power set of [n]=[1, 2, ..., n], ordered by inclusion. A set system is simply a subset of P(n). A set system is an antichain if no two of its members are comparable. Conversely a chain is a totally ordered set system. We shall often consider maximal chains; those chains which cannot be extended. In particular such chains contai...

We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by ...

We show that, for any n-vertex graph G and integer parameter k, there are at most 34k−n4n−3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(34k−n4n−3k). These bounds are tight when n/4 ≤ k ≤ n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 3/4)) ≈ 2.4150, improving a previous O((1 + 3)) ≈ 2.4422 alg...

In this article, we proved the following results. Let L(F (ni)) be the free group factor on ni generators and λ(gi) be one of standard generators of L(F (ni)) for 1 ≤ i ≤ N . Let Ai be the abelian von Neumann subalgebra of L(F (ni)) generated by λ(gi). Then the abelian von Neumann subalgebra ⊗i=1Ai is a maximal injective von Neumann subalgebra of ⊗i=1L(F (ni)). When N is equal to infinity, we o...

For any finite dimensional C∗-algebra A , we give an endomorphism Φ of the hyperfinite II1 factor R of finite Jones index such that: ∀ k ∈ N, Φk(R)′ ∩R = ⊗kA. The Jones index [R : Φ(R)] = (rank (A)), here rank (A) is the dimension of the maximal abelian subalgebra of A.

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

Teichmüller’s classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given point of the domain to another given point of the domain. For a domain D ⊂ Rn , n ≥ 2 , we consider the class of all Kquasiconformal maps of D onto itself with...