Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces...

A cellular automaton (CA) is a discrete dynamical system, and the transition graph is a representation of the CA’s phase space. Automorphisms of the transition graph correspond to symmetries of the phase space; studying how the total number of automorphisms varies with the number of cells on which the CA operates yields a (partial) classification of the space of CA rules according to their dyna...

We analyze the mapping class group Hx(W ) of automorphisms of the exterior boundary W of a compression body (Q,V ) of dimension 3 or 4 which extend over the compression body. Here V is the interior boundary of the compression body (Q,V ). Those automorphisms which extend as automorphisms of (Q,V ) rel V are called discrepant automorphisms, forming the mapping class group Hd(W ) of discrepant au...

In this paper is proved that the group of automorphisms of semi-group End(P [X]), if P is algebraically closed field, is generated by semi-inner automorphisms.

This paper studies several concepts about subgroups of automorphisms of linearly ordered relational structures. In particular, it focuses on conditions that are equivalent to the translations (automorphisms with no fixed points plus the identity) forming a homogeneous, Archimedean ordered group under the asymptotic order. For the automorphisms of an ordered relational structure, these propertie...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact Kähler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation between the dynamics of automorphisms/endomorphisms and the geometry of the underlying manifolds.

For a substitution satisfying the Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in the construction of Rauzy fractals (see [15, 3]). To try extending techniques developed for substitutions to automorphisms, [6] gives the way to construct Rauzy fractals by using tiling substitutions for automorphisms related to hyperbolic companion matrices of quadratic polynom...

For any field k we fix an algebraic closure of k, denoted by k. For a variety X ⊂ P k we set X = X×k k, we say thatX is smooth ifX is regular, and we let AutX denote the group of k-automorphisms ofX, while LinX denotes the group of linear automorphisms of X , i.e., automorphisms induced by a linear transformation of the coordinates of P. The following theorem was proved by Poonen, see [Po2], Th...

We study the nilpotent part N′ of a pseudo-periodic automorphism h real oriented surface with boundary Σ. associate quadratic form Q defined on first homology group (relative to boundary) Using twist formula and techniques from mapping class theory, we prove that Q̃ obtained after killing kerN is positive definite if all screw numbers associated certain orbits annuli are positive. also restricti...