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 (Miller in Appl Gen Topol 19:281–289, 2018).

中文翻译：

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一般半流中几种灵敏度之间的关系

在本文中，我们证明存在一个既不具有合合性质也不具有对偶合合性质的幺半群，并且存在具有这种幺半群作用的强混合半流，它不具有厚敏性、合敏性、厚合性敏感性，或厚周期性敏感性。同时，我们表明存在一个不是多重敏感的厚敏感级联。第一个结果对问题 2 的回答是肯定的，第一个和第二个结果对问题 3 的回答是否定的 (Miller in Appl Gen Topol 19:281–289, 2018)。