We present some new results on the existence and the approximationof common fixed point of expansive mappings and semigroups in probabilisticmetric spaces.

The recent frantic surge of machine learning and, more broadly, artificial intelligence (AI) brings to light old and new open issues, among them, the so-called eXplainable (XAI) – AI that humans can understand as opposed black-box systems where even their designers cannot explain decisions. One major XAI questions is how design transparent incorporate prior knowledge. These topics are becoming ...

Recent observations of the Universe have led to a conclusion suppressing an up-to-now supposed deceleration of the Universe caused by attractive gravitational forces. Contrary, there is a renaissance of the cosmological member Λ and introduction of enigmatic repulsive dark energy in attempts to rationalize a would-be acceleration of the Universe expansion. It is documented that the model of Exp...

This paper investigates the structure of general affine subspaces of ( )  L . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a ...

In this paper we consider Z-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z-actions of expansive rank one). If α is such a Z-action on an infinite compact connected abelian group X, then every expansive element α of this action has a dense group ∆αn(X) of homoclinic points. For different ...