论文标题
对数洞穴的新特征
New characterizations of log-concavity
论文作者
论文摘要
我们介绍了$ f $ conccavity的概念，该概念在很大程度上概括了通常的凹陷。通过在正量表下的正量表乘法和闭合度下的闭合概念，我们分别表征了非平凡$ f $ conccavities之间的功率凹陷和功率对数coven。特别是，我们将log-concavity的特征描述为唯一在正标乘积和正向指数下关闭的$ f $ concancavity。此外，我们讨论了Dirichlet热流保留的最强$ f $ conccavity，在这方面也表征了对数c-Concavity的表征。
We introduce a notion of $F$-concavity which largely generalizes the usual concavity. By the use of the notions of closedness under positive scalar multiplication and closedness under positive exponentiation we characterize power concavity and power log-concavity among nontrivial $F$-concavities, respectively. In particular, we have a characterization of log-concavity as the only $F$-concavity which is closed both under positive scalar multiplication and positive exponentiation. Furthermore, we discuss the strongest $F$-concavity preserved by the Dirichlet heat flow, characterizing log-concavity also in this connection.
