In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Let V be a compact, oriented 2n-dimensional (C--)differentiable manifold. If V admits a complex structure, compatible with its differentiable structure, the structural group of the tangent bundle of V can be restricted in a natural way from GL(2n,R) to GL(n,C). This gives for V a necessary condition of topological nature, which led Ch. Ehresmann and H. Hopf some 20 years ago to the concept of a...

We provide a general framework on the coefficients of graph polynomials graphs which are Cartesian products. As corollary, we prove that if $G=(V,E)$ is with degrees vertices $2d(v), v\in V$, and polynomial $\prod_{(i,j)\in E} (x_j-x_i)$ contains an "almost central" monomial (that means $\prod_v x_v^{c_v}$, where $|c_v-d(v)|\leqslant 1$ for all $v\in V$), then product $G\square C_{2n}$ $(d(\cdo...

The vertex isoperimetric number of a graph G = (V ,E) is the minimum of the ratio |∂V U |/|U | where U ranges over all nonempty subsets of V with |U |/|V | ≤ u and ∂V U is the set of all vertices adjacent to U but not in U . The analogously defined edge isoperimetric number—with ∂V U replaced by ∂EU , the set of all edges with exactly one endpoint in U —has been studied extensively. Here we stu...

The aim of our work is to study vertex-reinforced jump processes with super-linear weight function $w(t) = t^\alpha$ , for some $\alpha>1$. On any complete graph $G (V, E)$, we prove that there one vertex $v \in V$ such the total time spent at $v$ almost surely tends infinity while remaining vertices bounded.