The aim of this work is to introduce an approach for interval-valued R-implications, which satisfy some analogous properties of R-implications. We show that the best interval representation of an R-implication that is obtained from a left continuous tnorm coincides with the interval-valued R-implication obtained from the best interval representation of such t-norm, whenever this is an inclusion...

This paper establishes decomposability for composition operators induced on the Hardy spaces H (1 ≤ p < ∞) by parabolic linear fractional self-maps of the unit disc that are not automorphisms. This result, along with a recent theorem of Miller and Miller [15], shows that no such composition operator is supercyclic. The work here completes part of a previous investigation [1] where the author an...

The transition graph of a cellular automaton (CA) represents the CA’s global dynamics. The automorphisms of the transition graph are its self-isomorphisms or “symmetries”, and in a sense these are precisely the symmetries of the CA’s dynamics. Previously we have argued that studying how the total number of automorphisms varies with the number of cells on which the CA operates yields a partial c...

A class of structures C is said to have the extension property for partial automorphisms (EPPA) if, whenever C1 and C2 are structures in C, C1 finite, C1 ⊆ C2, and p1, p2, . . . , pn are partial automorphisms of C1 extending to automorphisms of C2, then there exist a finite structure C3 in C and automorphisms α1, α2, . . . , αn of C3 extending the pi. We will prove that some classes of structur...

The automorphisms of free groups with boundaries form a family of groups An,k closely related to mapping class groups, with the standard automorphisms of free groups as An,0 and (essentially) the symmetric automorphisms of free groups as A0,k . We construct a contractible space Ln,k on which An,k acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomolog...

Let $\mathcal{C}$ be a smooth, projective, genus $g\geq 2$ curve, defined over $\mathbb{C}$. Then has \emph{many automorphisms} if its corresponding moduli point $p \in \mathcal{M}_g$ neighborhood $U$ in the complex topology, such that all curves to points $U \setminus \{p \}$ have strictly fewer automorphisms than $\mathcal{C}$. We compute completely list of superelliptic having many automorph...

Recently, Shestakov-Umirbaev solved Nagata’s conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I–IV for automorphisms of a polynomial ring. An automorphism admitting a reduction of type I was first found by Shestakov-Umirbaev. Using a computer, van den Essen–Makar-Limanov–Willems gave a family of such automorphisms. In t...

We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Autc(G) = Inn(G), where Autc(G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Autc(G) ∼= Autc(H). Finally we study class preserving automorphisms of groups o...

In this paper we define a quantity called the rank of an outer automorphism of a free group which is the same as the index introduced in [3] without the count of fixed points on the boundary. We proceed to analyze outer automorphisms of maximal rank and obtain results analogous to those in [5]. We also deduce that all such outer automorphisms can be represented by Dehn twists, thus proving the ...

Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrary different. Particularly, there exist codes with the fu...