In this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion solution following non-local problem: [Formula: see text] where is bounded domain in with smooth boundary such problem derived as shadow limit singular Gierer–Meinhardt system, Kavallaris and Suzuki [On dynamics parabolic equation arising from Nonlinearity (2017) 1734–1761; Non-Local Partial Diff...

We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a 1751-paper and 1734-letter to Daniel Bernoulli. The corresponding q-analogue of the dilogarithm is introduced. The relation to the values at 1 and 2 of a q-analogue o...

∗ This work was supported by the National Institutes of Health Grants 34509 (KN) and EY12951 (JRS), the Charina Foundation (JRS), the Macula Vision Research Foundation (JRS) and unrestricted funds from Research to Prevent Blindness. JRS is a recipient of a Research to Prevent Blindness Lew R. Wasserman Merit Award. The costs of publication of this article were defrayed in part by the payment of...

While IMAP4 supports a number of strong authentication mechanisms as described in RFC 1731, it lacks any mechanism that neither passes cleartext, reusable passwords across the network nor requires either a significant security infrastructure or that the mail server update a mail-system-wide user authentication file on each mail access. This specification provides a simple challenge-response aut...

This study aims to analyze Johann Gottlieb Walter's biography (1734-1818), a German physician that specialized in human anatomy, who received an award of the Göttingen Royal Academy of Sciences. Here, we describe his technique of preparing bones for educational purposes through the comparison of other widely used techniques. The article also focuses on the great historical, scientific and didac...