On synchronization of partial automata

A goal of this paper is to introduce the new construction of an automaton with shortest synchronizing word of length $O(d^{\frac{n}{d}})$, where $d \in $\mathbb{N}$$and$n$ is the number of states for that automaton. Additionally we introduce new transformation from any synchronizable DFA or carefully synchronizable PFA of $n$ states to carefully synchronizable PFA of $d\cdot n$ states with shortest synchronizing word of length $\mathrm{\Omega }(d^{\frac{n}{d}})$.