We propose an authentication scheme where forgery (a.k.a. impersonation) seems infeasible without finding the prover’s long-term private key. The latter is equivalent to solving the conjugacy search problem in the platform (noncommutative) semigroup, i.e., to recovering X from X−1AX and A. The platform semigroup that we suggest here is the semigroup of n×n matrices over truncated multivariable ...

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration

Let G be a semigroup of rational functions of degree at least two where the semigroup operation is composition of functions. We prove that the largest open subset of the Riemann sphere on which the semigroup G is normal and is completely invariant under each element of G, can have only 0, 1, 2, or infinitely many components.

In this paper we prove that if S is an irreducible numerical semigroup and S is generated by an interval or S has multiplicity 3 or 4, then it enjoys Toms decomposition. We also prove that if a numerical semigroup can be expressed as an expansion of a numerical semigroup generated by an interval, then it is irreducible and has Toms decomposition.

We study the conditions under which a semigroup is obtained upon convex combinations of channels. In particular, we set Pauli and generalized find that mixing only semigroups can never produce semigroup. Counter-intuitively, for combination to yield semigroup, most input channels have be noninvertible.

‎we present a characterization of arens regular semigroup algebras‎ ‎$ell^1(s)$‎, ‎for a large class of semigroups‎. ‎mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $s$ is finite‎, ‎then $ell^1(s)$ is arens regular if and only if $s$ is finite‎.

We give a characterization for irreducible numerical semi-groups. From this characterization we obtain that every irre-ducible numerical semigroup is either a symmetric or pseudo-symmetric numerical semigroup. We study the minimal presentations of an irreducible numerical semigroup. Separately, we deal with the cases of maximal embedding dimension and multiplicity 3 and 4.

A subsemigroup S of an inverse semigroup Q is a left I-order in Q, if every element in Q can be written as a−1b where a, b ∈ S and a−1 is the inverse of a in the sense of inverse semigroup theory. We study a characterisation of semigroups which have a primitive inverse semigroup of left I-quotients.