  In this paper, we show that there exists a monoid, on which neither the
syndetic property nor the dual syndetic property holds, and there exists a
strongly mixing semi-flow with this monoid action which does not have thick
sensitivity, syndetic sensitivity, thickly syndetic sensitivity, or thickly
periodical sensitivity. Meanwhile, we show that there exists a thickly
sensitive cascade which is not multi-sensitive. The first result answers
positively Question 2, and the first and the second results answer negatively
Question 3 in [A. Miller, A note about various types of sensitivity in general
semiflows, Appl. Gen. Topol., 2018].
