Abstract In this work we study the space of derivations non-degenerate evolution algebras. We improve some results obtained recently in literature and, as a consequence, advance description for n -dimensional Volterra addition, introduce notion loop an algebra and analyze under which conditions set loops is invariant change basis.

ABSTRACT In this paper, we analyze the existence of Weyl distance in general metric and various classes multi-dimensional p -almost periodic functions metric. The main structural properties for introduced almost type are established. We also provide some applications our theoretical results to abstract Volterra integro-differential equations.

We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identif...

We consider a quasistatic system involving a Volterra kernel modelling an hereditarilyelastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near t...