An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expressed as an integral average of the logarithmic distance to the closure of the periodic points of the underlying morphism. The results may be though...

Relatively morphic submodules are defined and a new class of modules between morphic and Hopfian modules is singled out. Special care is given to the Abelian groups case.

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order σ on A, we call the smallest word with respect to σ starting with b in the shift orbit closure of x an extremal word of x. In this paper we consider the extremal words of morphic words. If x = g(fω(a)) for some morphisms f and g, we give two simple conditions on f and g that guarantees that all extremal wo...

Given a quasi-projective complex variety X and a projective variety Y , one may endow the set of morphisms, Mor(X, Y ), from X to Y with the natural structure of a topological space. We introduce a convenient technique (namely, the notion of a functor on the category of “smooth curves”) for studying these function complexes and for forming continuous pairings of such. Building on this technique...

From the homotopy groups of two cubic spherical 3-manifolds we construct the iso-morphic groups of deck transformations acting on the 3-sphere. These groups become the cyclic group of order eight and the quaternion group respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmoni...

Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible binary patterns can be morphically compressed, with respect to the local connec-tivities, in a binary morphic program. From the local connectivites, there emerges...