following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

We explore several concepts for analyzing the intuitive notion of computational irreducibility and we propose a robust formal definition, first in the field of cellular automata and then in the general field of any computable function f from N to N. We prove that, through a robust definition of what means "to be unable to compute the n th step without having to follow the same path than simulat...

Basic properties in Perron-Frobenius theory are strict positivity, primitivity, and irreducibility. Whereas for nonnegative matrices, these properties are equivalent to elementary graph properties which can be checked in polynomial time, we show that for Kraus maps the noncommutative generalization of stochastic matrices checking strict positivity (whether the map sends the cone to its interior...

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.  

In this note, we give an arithmetic criterion for the Lie-irreducibility of linear differential equations based on p-curvatures.

Let f be a function on a finite field F . The decomposition of the generalized Fermat variety X defined by the multivariate polynomial of degree n, φ(x, y, z) = f(x) + f(y) + f(z) in P(F2), plays a crucial role in the study of almost perfect non-linear (APN) functions and exceptional APN functions. Their structure depends fundamentally on the Fermat varieties corresponding to the monomial funct...