A transformation F between protocols associates the messages sent and received by participants in a protocol Π1 with messages sent and received in some Π2. Transformations are useful for modeling protocol design, protocol composition, and the services that protocols provide. A protocol transformation determines a map from partial behaviors A1 of Π1—which we call “skeletons”—to skeletons F (A1) ...

We investigate interpretations ‖ψ‖D of formulas ψ in a first order fuzzy logic in models D which are based on Ω-sets, i.e. sets with similarity relations with values in a complete MV-algebra Ω. These interpretations are fuzzy sets in some Ωsets. We show that if φ : D1 → D2 is a strong homomorphism between two models then there are also strong relationships between interpretations ‖ψ‖D1 and ‖ψ‖D...

For almost finite groupoids, we study how their homology groups reflect dynamical properties of their topological full groups. It is shown that two clopen subsets of the unit space has the same class in H0 if and only if there exists an element in the topological full group which maps one to the other. It is also shown that a natural homomorphism, called the index map, from the topological full...

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf spaces of rank 2. We also study the nilpotency of semigroups for Lie groups of higher rank. Especially, we give Lie groups with the nilpotency of the semigr...

Let A and B be unital separable simple amenable C*-algebras which satisfy the Universal Coefficient Theorem. Suppose that A and B are Z-stable and are of rationally tracial rank no more than one. We prove the following: Suppose that φ, ψ : A → B are unital *monomorphisms. There exists a sequence of unitaries {un} ⊂ B such that lim n→∞ unφ(a)un = ψ(a) for all a ∈ A, if and only if [φ] = [ψ] in K...

We show that the Green correspondence induces an injective group homomorphism from linear source Picard L(B) of a block B finite algebra to L(C), where C is Brauer correspondent B. This maps trivial T(B) T(C). further endopermutation E(B) bounded in terms defect groups and when has normal E(B)=L(B). Finally we prove rank any invertible B-bimodule by

A geometric graph G is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph are geo-isomorphic if there is a vertex bijection between them that preserves vertex adjacencies and non-adjacencies, as well as edge crossings and non-crossings. A natural extension of graph homomorphisms, geo-homomo...

A subgroup G ≤ Z exhibits the Specker phenomenon if every homomorphism G → Z maps almost all unit vectors to 0. We give several combinatorial characterizations of the cardinal se, the size of the smallest G ≤ Z exhibiting the Specker phenomenon. We also prove the consistency of b < e, where b is the unbounding number and e the evasion number. Our results answer several questions addressed by Bl...

If H is a finitely generated subgroup of the finitely generated group G, then H is undistorted in G for their word metrics iff the induced homomorphism on the zero-dimensional l1-homology group is injective. The Mayer-Vietoris exact sequence for l1-homology is established and applications are given to hyperbolic groups and relative hyperbolicity. The notion of relative distortion of two maps is...

In this article we generalize both ordinary and permutation voltage constructions to obtain all branched coverings of maps. We approach a map as a set of flags together with three fixed-point-free involutions and relate this approach with other standard representations. We define a lift as a function from these flags into a group. Ordinary voltage and ordinary current assignments are special ca...