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

The Lattice String Approximation algorithm (or LSA algorithm) of M. L.Lapidus and M. van Frankenhuijsen is a procedure that approximates the complexdimensions of a nonlattice self-similar fractal string by the complexdimensions of a lattice self-similar fractal string. The implication of thisprocedure is that the set of complex dimensions of a nonlattice string has aquasiperiodic pattern. Using the LSA algorithm, together with themultiprecision polynomial solver MPSolve which is due to D. A. Bini, G.Fiorentino and L. Robol, we give a new and significantly more powerfulpresentation of the quasiperiodic patterns of the sets of complex dimensions ofnonlattice self-similar fractal strings. The implementation of this algorithmrequires a practical method for generating simultaneous Diophantineapproximations, which in some cases we can accomplish by the continued fractionprocess. Otherwise, as was suggested by Lapidus and van Frankenhuijsen, we usethe LLL algorithm of A. K. Lenstra, H. W. Lenstra, and L. Lov\'asz.

Quasiperiodic patterns of the complex dimensions of nonlattice self-similar strings, via the LLL algorithm