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

For any $n$-by-$n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & &\\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we considertwo $k$-by-$k$ matrices \[A'=[\begin{array}{cccc} 0 & \|A_1\| & & \\ & 0 &\ddots & \\ & & \ddots & \|A_{k-1}\| \\ & & & 0\end{array}] \ {and} \A''=[\begin{array}{cccc} 0 & m(A_1) & & \\ & 0 & \ddots & \\ & & \ddots &m(A_{k-1}) \\ & & & 0\end{array}],\] where $\|\cdot\|$ and $m(\cdot)$ denotethe operator norm and minimum modulus of a matrix, respectively. It is shownthat the numerical radii $w(\cdot)$ of $A$, $A'$ and $A''$ are related by theinequalities $w(A'')\le w(A)\le w(A')$. We also determine exactly when eitherof the inequalities becomes an equality.

Upper and Lower Bounds for Numerical Radii of Block Shifts