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.

In this paper we introduced homomorphism, strong homomorphism in bipolar fuzzy finite state machines and discuss their properties using bipolar-valued fuzzy set. Mathematics Subject Classification: 18B20, 68Q45, 68Q70, 03E72

This paper is an introduction to the series of papers [26, 28, 29, 30], in which we develop a combinatorial theory of certain important operads and their actions. The operads we consider are A∞ operads, E∞ operads, the little n-cubes operad and the framed little disks operad. Sections 2, 6 and 9, which can be read independently, are an introduction to the theory of operads. The reader is also r...

We prove a recognition principle for motivic infinite P1-loop spaces over perfect field. This is achieved by developing theory of framed spaces, which analogue the E-infinity-spaces. A space equipped with transfers along finite syntomic morphisms trivialized cotangent complex in K-theory. Our main result that grouplike are equivalent to full subcategory spectra generated under colimits suspensi...

It is not difficult to see that every group homomorphism from Z to R extends to a homomorphism from R to R. We discuss other examples of discrete subgroups Γ of connected Lie groups G, such that the homomorphisms defined on Γ can (“virtually”) be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that Γ has this property if it is Zariski dens...

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.

For digraphs D and H, a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V (D) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (D) cf(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem for H. The problem is to decide, for an input graph D with costs ci(u), u...

For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by ...