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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

For any stochastic matrix A of order n, denote its eigenvalues as λ1(A) ,...,λ n(A), ordered so that 1 = |λ1(A) |≥| λ2(A) |≥ ... ≥| λn(A)|. Let c T be a row vector of order n whose entries are nonnegative numbers that sum to n. Define S(c), to be the set of n × n row-stochastic matrices with column sum vector c T. In this paper the quantity λ(c )=m ax{|λ2(A)||A ∈S (c)} is considered. The vectors c T such that λ(c) < 1 are identified and in those cases, nontrivial upper bounds on λ(c) and weak ergodicity results for forward products are provided. The results are obtained via a mix of analytic and combinatorial techniques.

Subdominant eigenvalues for stochastic matrices with given column sums