We study syndetic sensitivity and mean for linear dynamical systems. For the aspect, we obtain some properties of adjoint operators left multiplication operators. also show that there exists a system (X×Y,T×S) such is cofinitely sensitive but (X,T) (Y,S) are not syndetically sensitive. if sensitive, where Y complex Banach space, spectrum T meets unit circle. results regarding perturbations.

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing...