Given compact Lie groups H ⊂ G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H . Such an enlarging is possible if (K, H) is a symmetric pair, which yields many new examples of nonnegatively curved homogeneo...

We define two categories, the category $\mathfrak{F}\mathfrak{G}$ of fuzzy subgroups, and $\mathfrak{F}\mathfrak{C}$ $F$-inverse covers inverse monoids, prove that fully embeds into $\mathfrak{F}\mathfrak{C}$. This shows that, at least from a categorical viewpoint, subgroups belong to standard mathematics as much they do one.

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

In any graph $G$, the domination number $\gamma(G)$ is at most independence $\alpha(G)$. The \emph{Inverse Domination Conjecture} says that, in isolate-free there exists pair of vertex-disjoint dominating sets $D, D'$ with $|D|=\gamma(G)$ and $|D'| \leq \alpha(G)$. Here we prove that this statement true if upper bound $\alpha(G)$ replaced by $\frac{3}{2}\alpha(G) - 1$ (and $G$ not a clique). We...

is called the Drazin inverse of A and is denoted by X = A, where k is the index of A, i.e., the smallest non-negative integer such that rank(A) = rank(A). We denote such a k by Ind(A). It is well-known that A exists and is unique (see [2]). If Ind(A) = 1, A is also called the group inverse of A and is denoted by A. Then A exists if and only if rank(A) = rank(A) (see [1, 3, 11-14, 24, 25, 29]). ...

In this paper, we study the approximate biprojectivity and biflatness of a Banach algebra A find some relations between theses concepts with ?-amenability ? -contractibility, where is character on A. Among other things, show that ?-Lau product L1(G) ?? A(G) approximately biprojective if only G finite, are group Fourier locally compact G, respectively. We also characterize biflat semigroup algeb...

We study the following inverse graph-theoretic problem: how many vertices should a graph have given that it has a specified value of some parameter. We obtain asymptotic for the minimal number of vertices of the graph with the given number n of maximal independent sets for a class of natural numbers that can be represented as concatenation of periodic binary words. Problems of estimating variou...

Over the last decade, the ability to detect agonist-independent signal transduction by G protein-coupled receptors has in turn resulted in the detection and study of ligands able to block this activity. Such ligands are generically described as inverse agonists. Considerable attention has recently been devoted to the presence and roles of endogenous antagonist/inverse agonists and the concept t...

To prove that a pattern p is avoidable on a given alphabet, one has to construct an innnite language L that avoids p. Usually, L is a DOL-language (obtained by iterating a morphism h) or a HDOL-language (obtained by coding a DOL-language with another morphism g). Our purpose is to nd an algorithm to test, given a HDOL-system G, whether the language L(G) generated by this system avoids p. We rst...

Since Wiener's original proof of his theorem about periodic functions whose Fourier series are absolutely summable, a variety of quite different proofs have been devised. Some of these are described in [2, Sect. B.9.4]. In this paper we rewrite the beautiful proof of Newman [1] in a slightly more general form, so that it may be readily applied to a variety of related problems. Although we use t...