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 an $m$-order $n-$dimensional Hilbert tensor (hypermatrix)$\mathcal{H}_n=(\mathcal{H}_{i_1i_2\cdots i_m})$, $$\mathcal{H}_{i_1i_2\cdotsi_m}=\frac1{i_1+i_2+\cdots+i_m-m+1},\ i_1,\cdots, i_m=1,2,\cdots,n$$ itsspectral radius is not larger than $n^{m-1}\sin\frac{\pi}{n}$, and an upperbound of its $E$-spectral radius is $n^{\frac{m}2}\sin\frac{\pi}{n}$. Moreover,its spectral radius is strictly increasing and its $E$-spectral radius isnondecreasing with respect to the dimension $n$. When the order is even, bothinfinite and finite dimensional Hilbert tensors are positive definite. We alsoshow that the $m$-order infinite dimensional Hilbert tensor (hypermatrix)$\mathcal{H}_\infty=(\mathcal{H}_{i_1i_2\cdots i_m})$ defines a bounded andpositively $(m-1)$-homogeneous operator from $l^1$ into $l^p$ ($1<p<\infty$),and the norm of corresponding positively homogeneous operator is smaller thanor equal to $\frac{\pi}{\sqrt6}$.

Infinite and finite dimensional Hilbert tensors