We construct the homomorphism of presheaves ${\mathrm{K}}^\mathrm{MW}_* \to {\pi}^{*,*}$ over an arbitrary base scheme $S$, where $\mathrm{K}^\mathrm{MW}$ is (naive) Milnor-Witt K-theory presheave. Also we discuss some partly alternative proof (or proofs) isomorphism sheaves $\unKMW_n\simeq \underline{\pi}^{n,n}_s$, $n\in \mathbb Z$, a filed $k$ originally proved in \cite{M02} and \cite{M-A1Top}.

Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...

The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...

In this talk we will discuss some examples of graph homomorphisms. More precisely, the graph parameters which can be represented by counting the graph homomorphisms. The main reference is Section 2 in [2].

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

A graph homomorphism is a vertex map which carries edges from a source graph to edgesin a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem(MAX H -COL) are edge-weighted graphs G and the objective is to find a subgraph of G that hasmaximal total edge weight, under the condition that the subgraph has a homomorphism to H ;note that for H = Kk th...

In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.