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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

More importantly, our argument for Case B on the basis of uniform distribution modulo 1 of the sequence ( 2x ) n∈N for almost all x ∈ R is incomplete, because the function f defined by f(x) = log ( 1 − cos(2πx) ) is only Riemann integrable on [0, 1] in the generalised sense (meaning that it is an improper integral), which is insufficient here. However, f is properly integrable on [0, 1] in the Lebesgue sense and has an obvious 1-periodic extension to R. Consequently, rather than employing uniform distribution, one can argue with the dynamical system defined by the map T of the unit interval [0, 1] into itself, given by x 7→ 2x mod 1. It is well-known that T leaves Lebesgue measure invariant and is ergodic relative to it, so that the Birkhoff sums satisfy

Scaling of the Thue-Morse Diffraction Measure (Acta Physica Polonica A 125, 431 (2014)), ERRATUM