English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $m$ and $k \geq 2$ be positive integers. We show that polynomial $P =(1+x)^m(1+x^k)$ is strongly unimodal (frequently known as {\it log concave\/})if and only if $m \geq k^2 -3$; this is also the criterion for $P$ to be merelyunimodal (that is, for $P$ of this form, unimodality implies strongunimodality).{ }In section 2, we investigate an analogous question, concerningthe property $\EE$ of functions $f$ analytic on a neighbourhood of the unitcircle [H2], and show that the corresponding minimal $m$ is rather surprisinglyof order $k^4$.

Log concavity of $(1+x)^m (1+ x^k)$