Let CRF S denote the category of S-colored rooted forests, and HCRFS denote its Ringel-Hall algebra as introduced in [6]. We construct a homomorphism from a K+ 0 (CRF S)–graded version of the Hopf algebra of noncommutative symmetric functions to HCRFS . Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a K+ 0 (CRF S)–graded version of the algebra of quasisymmetric func...

conclusions the patient underwent surgery applying a midline incision. the left kidney showed a lump pattern embedded in lower pole of the right kidney. left sided nephrectomy was performed while temporary right renal artery was clamped temporarily. histopathological evaluation revealed clear cell carcinoma with severe nuclear atypia (fuhrman grade 4/4). however, local recurrence was not detect...

Many fundamental theorems in extremal graph theory can be expressed as algebraic inequalities between subgraph densities. As is explained below, for dense graphs, it is possible to replace subgraph densities with homomorphism densities. An easy observation shows that one can convert any algebraic inequality between homomorphism densities to a linear inequality. Inspired by the work of Freedman,...

Given a closed ideal I in a C-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism α : A → M(I) and a map L : J → A with some properties, based on [3] and [9] we define a C-algebra O(A,α, L) which we call the Crossed Product by a Partial Endomorphism. In the second section we introduce the Crossed Product by a Partial Endomorphism O(X,α, L) induced by a local homeomorphism σ : ...

In this paper we construct new obstructions for the surjectivity of the Johnson homomorphism of the automorphism group of a free group. We also determine the structure of the cokernel of the Johnson homomorphism for degree 2 or 3.

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.