In this paper we prove existence results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces and nonlocal conditions, via a Nonlinear Alternative for condensing maps. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families. Mathematics subject clas...

We characterize the monoid of endomorphisms semigroup all oriented full transformations a finite chain, as well partial and permutations chain. Characterizations monoids subsemigroups orientation-preserving three semigroups aforementioned are also given. In addition, we compute number each these six semigroups.

Given a regular language L, we effectively construct unary semigroup that recognizes the topological closure of L in free relative to variety semigroups generated by pseudovariety R all finite R-trivial semigroups. In particular, obtain new effective solution separation problem languages R-languages.

We obtain hypercontrativity estimates for a large class of semigroups defined on finite-dimensional matrix algebras Mn. These semigroups arise from Poisson-like length functions ψ on Zn × Zn and provide new hypercontractive families of quantum channels when ψ is conditionally negative. We also study the optimality of our estimates.

we prove that if $m$ is a monoid and $a$ a finite set with more than one element‎, ‎then the residual finiteness of $m$ is equivalent to that of the monoid consisting of all cellular automata over $m$ with alphabet $a$‎.