A new look at E.G. Björling and the Cauchy sum theorem

We give a new account of Björling’s contribution to uniform convergence in connection with Cauchy’s theorem on the continuity of an infinite series. Moreover, we give a complete translation from Swedish into English of Björling’s 1846 proof of the theorem. Our intention is also to discuss Björling’s convergence conditions in view of Grattan-Guinness’ distinction between history and heritage. In connection to Björling’s convergence theory we discuss the interpretation of Cauchy’s infinitesimals.     

Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-nineteenth Century

In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Bj?rling’s general view of real- and complexvalued functions. We argue that Bj?rling had a tendency to sometimes consider mathematical objects in a naturalistic way. One example is how Bj?rling interprets Cauchy’s definition of the logarithm function with respect to complex variables, which is investigated in the paper. Furthermore, in view of an article written by Bj?rling (Kongl Vetens Akad F?rh Stockholm 166–228, 1852) we consider Cauchy’s theorem on power series expansions of complex valued functions. We investigate Bj?rling’s, Cauchy’s and the Belgian mathematician Lamarle’s different conditions for expanding a complex function of a complex variable in a power series. We argue that one reason why Cauchy’s theorem was controversial could be the ambiguities of fundamental concepts in analysis that existed during the mid-nineteenth century. This problem is demonstrated with examples from Bj?rling, Cauchy and Lamarle.     

Nanocontacts give efficient hole injection in organic electronics

A key requirement for well performing devices based on organic semiconductors is to ensure ohmic contacts, where an efficient hole and electron injection and ex...