In this paper we consider the semilinear differential equation with deviated argument in a Fréchet space x(t) = Ax(t) + f(t, x(t), x[α(x(t), t)]), t ∈ R, where A is the infinitesimal (bounded) generator of a C0-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions f and α we prove the existence and uniqueness of an almost automorphic mild solu...

Let f be a univalent self-map of the unit disc. We introduce technique, that we call semigroup-fication, which allows to construct continuous semigroup (ϕ t ) holomorphic self-maps disc whose time one map ϕ 1 is, in sense, very close f. The semigroup-fication is same type as (elliptic, hyperbolic, parabolic positive step or zero step) and there one-to-one correspondence between set boundary reg...

If T is a numerical semigroup with maximal ideal N , define associated semigroups B(T ) := (N −N) and L(T ) = ∪{(hN −hN) : h ≥ 1}. If S is a numerical semigroup, define strictly increasing finite sequences {Bi(S) : 0 ≤ i ≤ β(S)} and {Li(S) : 0 ≤ i ≤ λ(S)} of semigroups by B0(S) := S =: L0(S), Bβ(S)(S) := N =: Lλ(S)(S), Bi+1(S) := B(Bi(S)) for 0 < i < β(S), Li+1(S) := L(Li(S)) for 0 < i < λ(S). ...

For linear evolution control system described by ẋ = Ax(t) + Bu(t), x(0) = x0 (A generates a strongly continuous semigroup {S(t)}t≥0 on a Banach space X; B is a linear unbounded operator), the attainable set K (t) set is studied. Conditions of the independence of t for its closure K(t) are established. Controllability conditions for some classes of evolution systems are obtained.

We study numerical semigroups generated by intervals and solve the following problems related to such semigroups: the membership problem, give an explicit formula for the Frobe-nius number, decide whether the semigroup is a complete intersection and/or symmetric, and computation of the cardi-nality of a (any) minimal presentation of this kind of numerical semigroups. A numerical semigroup is a ...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

Let A be the generator of an analytic semigroup T on L 2 ((), where is a homogeneous space with doubling property. We prove maximal L p ? L q a-priori estimates for the solution of the parabolic evolution equation u 0 (t) = Au(t) + f(t); u(0) = 0 provided T may be represented by a heat-kernel satisfying certain bounds (and in particular a Gaussian bound).

the known theory for an oid t shows how to find a subset t of ?t, which is a compact right topological semigroup [i]. the success of the methods in [2] for obtaining properties of-t has prompted us to see how successful they would be in another context. thus we find (theorem 4.8) that t cont ains copies of free semigroups on 2? generators, is an immediate consequence of the stronger result and ...

In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer seq...