In this article, first we introduce and study the concept of Sγ pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in Sγ -pseudo almost automorphic spaces. T...

For an o-minimal expansion R of a real closed eld and a set V of Th(R)-convex valuation rings, we construct a \pseudo completion" with respect to V. This is an elementary extension S of R generated by all completions of all the residue elds of the V 2 V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to ...

Orthogonal time frequency space (OTFS) modulation is a 2-dimensional (2D) modulation scheme designed in the delay-Doppler domain, unlike traditional modulation schemes which are designed in the time-frequency domain. Through a series of 2D transformations, OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain. In this domain, each symbol in a fr...

It is proven that each indecomposable injective module over a valuation domain R is polyserial if and only if each maximal immediate extension R̂ of R is of finite rank over the completion R̃ of R in the R-topology. In this case, for each indecomposable injective module E, the following invariants are finite and equal: its Malcev rank, its Fleischer rank and its dual Goldie dimension. Similar res...

In this paper, on a non-standard extension (∗X ,∗d) of a metric space (X ,d), we construct a chain of new non-standard topologies in terms of convex subrings of ∗R, its minimal element is the Stopology and its maximal is the Q-topology. Next, we construct X̂ , the F -asymptotic hull of X , and we prove that such space is metrizable and complete when F is generated by an asymptotic scale. Finally...

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...