周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保...周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保持单位圆周不动的存在性证明。同时讨论了一般显示构造的方法。In A Note on Herman, Hongyi Zhou gave an example of a cubic rational function whose critical points strictly lie on the boundary of the Herman ring. The construction mainly relies on the existence of rational functions whose critical points are located on the unit circle and keep the unit circle invariant. In this paper, we provide a general proof for the existence of rational functions whose critical points are all on the unit circle and keep the unit circle invariant. Additionally, we discuss the general methods for explicit constructions.展开更多
In this paper,we mainly study fuzzy(quasi-)pseudo-b-metrics on algebraic structures.We mainly establish the following results:(1)If a group G with a topology τ,which is induced by a left invariant fuzzy quasi-pseudo-...In this paper,we mainly study fuzzy(quasi-)pseudo-b-metrics on algebraic structures.We mainly establish the following results:(1)If a group G with a topology τ,which is induced by a left invariant fuzzy quasi-pseudo-b-metric(resp.,pseudo-b-metric)on the G,is a right topological group,then G with the topology τ is a paratopological group(resp.,a topological group)and(2)If a semigroup S with a topology τ is induced by an invariant fuzzy quasi-pseudob-metric,then S with the topology τ is a topological semigroup.展开更多
文摘周宏毅在论文关于Herman环与临界点中给出了三次有理函数且其临界点严格位于Herman环的边界分支的例子。该构造中主要用到临界点都位于单位圆周且保持单位圆周不动的有理函数的存在性。本文给出了一般的有理函数临界点均在单位圆周且保持单位圆周不动的存在性证明。同时讨论了一般显示构造的方法。In A Note on Herman, Hongyi Zhou gave an example of a cubic rational function whose critical points strictly lie on the boundary of the Herman ring. The construction mainly relies on the existence of rational functions whose critical points are located on the unit circle and keep the unit circle invariant. In this paper, we provide a general proof for the existence of rational functions whose critical points are all on the unit circle and keep the unit circle invariant. Additionally, we discuss the general methods for explicit constructions.
基金Supported by the Natural Science Foundation of Guangdong Province(Grant No.2021A1515010381)the Innovation Project of Department of Education of Guangdong Province(Grant No.2022KTSCX145)。
文摘In this paper,we mainly study fuzzy(quasi-)pseudo-b-metrics on algebraic structures.We mainly establish the following results:(1)If a group G with a topology τ,which is induced by a left invariant fuzzy quasi-pseudo-b-metric(resp.,pseudo-b-metric)on the G,is a right topological group,then G with the topology τ is a paratopological group(resp.,a topological group)and(2)If a semigroup S with a topology τ is induced by an invariant fuzzy quasi-pseudob-metric,then S with the topology τ is a topological semigroup.
