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 $\Lambda^{\ast}$ be the free monoid of (finite) words over a notnecessarily finite alphabet $\Lambda$, which is equipped with some (partial)order. This ordering lifts to $\Lambda^{\ast}$, where it extends thedivisibility ordering of words. The MacNeille completion of $\Lambda^{\ast}$constitutes a complete lattice ordered monoid and is realized by the system of"closed" lower sets in $\Lambda^*$ (ordered by inclusion) or its isomorphiccopy formed of the "closed" upper sets (ordered by reverse inclusion). Undersome additional hypothesis on $\Lambda$, one can easily identify the closedlower sets as the finitely generated ones, whereas it is more complicated todetermine the closed upper sets. For a fairly large class of ordered sets$\Lambda$ (including complete lattices as well as antichains) one can generatethe closure of any upper set of words by means of binary operations ("syntactic rules") thus obtaining an efficient procedure to test closedness.Closed upper set of words are involved in an embedding theorem for valuatedoriented graphs. In fact, generalized paths (so-called "zigzags") are encodedby words over an alphabet $\Lambda$. Then the valuated oriented graphs whichare "isometrically" embeddable in a product of zigzags have the characteristicproperty that the words corresponding to the zigzags between any pair ofvertices form a closed upper set in $\Lambda$.

A syntactic approach to the MacNeille completion of $\bold\Lambda^{\ast}$, the free monoid over an ordered alphabet $\bold \Lambda$