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 study of the luminosity measurements of the pre-white dwarf PG 1159-035has established the properties of the rich power spectrum of the detectedradiation and, derived thereof, the physical properties of this celestial body.Those of the measurements which are available online are analysed in this workfrom a different perspective. After the measurements were band-passed, theywere split into two parts (of comparable sizes), one yielding the training(learning) set (i.e., the database of embedding vectors and associatedpredictions), the other the test set. The optimal embedding dimension $m_0=10$was obtained using Cao's method; this result was confirmed by an analysis ofthe correlation dimension. Subsequently, the extraction of the maximal Lyapunovexponent $\lambda$ was pursued for embedding dimensions $m$ between $3$ and$12$; results were obtained after removing the prominent undulations of theout-of-sample prediction-error arrays $S (k)$ by fitting a monotonic functionto the data. The grand mean of the values, obtained for sufficient embeddingdimensions ($10 \leq m \leq 12$), was: $\lambda = (9.2 \pm 1.0 ({\rm stat.})\pm 2.7 ({\rm syst.})) \cdot 10^{-2}~\Delta \tau^{-1}$, where $\Delta \tau=10$s is the sampling interval in the measurements. On the basis of thissignificantly non-zero result, it may be concluded that the physical processes,underlying the variation of the luminosity of PG 1159-035, are non-linear. Theaforementioned result for $\lambda$ was obtained using the $L^\infty$-normdistance; a larger, yet not incompatible, result was extracted with theEuclidean ($L^2$-norm) distance.

Analysis of luminosity measurements of the pre-white dwarf PG 1159-035