Asymptotic approximation of central binomial coefficients with rigorous error bounds

We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of Pólya and Szegö, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We consider closely related asymptotic series for Binet's function, for \(\ln\Gamma(z+\frac12)\), and for the Riemann-Siegel theta function, and make some historical remarks.

The Bicentenary of Bell’s Description of the Neuroanatomical Basis of Facial Paralysis: Historical Remarks

Charles Bell was a talented and versatile Scottish anatomist, neurophysiologist, artist, and surgeon. On July 12, 1821, he reported his studies regarding facial innervation in the essay “On the Nerves,” read before the Royal Society in London. Since then, idiopathic peripheral facial paralysis has been named “Bell’s palsy.” He was the first author to describe the neuroanatomical basis of facial paralysis, in an essay enriched by beautifully self-made illustrations. The aim of this article is to trace the history of Bell’s description of the neuroanatomy of the facial nerve, reexamining his 1821 article, in which he stated that the lower facial expression muscles were dually innervated by both the fifth and seventh cranial nerves. In 1829, he rectified this conclusion, recognizing the exclusive role of the facial nerve, which he defined as the “respiratory nerve.” We offer a tribute to this polymath scientist on the bicentenary of his 1821 publication.

Problem of the 8-th Experimental Physics Olympiad, Skopje, 8 May 2021 Determination of Planck Constant by LED

This is the problem of the 8th International Experimental Physics Olympiad (EPO8). The task of the EPO8 is to determine Planck constant ħh/2 using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items – they are instructive for physics education in general. Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.

Pentacalia gonocaulos (Asteraceae, Senecioneae), new combination for a species from Peru

On the basis of the revision of the original material and protologues, as well as the study of all the specimens at our disposal, Senecio gonocaulos DC. is transferred to the genus Pentacalia and the name P. poeppigiana A.Granda is included in the synonymy of the former name. Additionally, a lectotype is designated for S. gonocaulos and some observations and historical remarks on the type material of this species are provided.