RECENT ADVANCES IN SCIENCE 



MATHEMATICS. By Philip E. B. Jourdain, M.A. Cambridge. 



The two chief alterations that strike one in the new (third) 

 edition of the Index du Repertoire Bibliographique des Sciences 

 Mathematiques (Amsterdam and Paris, 1916), which has just 

 been published by the Mathematical Society of Amsterdam, 

 are in the classes devoted to the general theory of functions 

 (D) and the theory of differential and functional equations (H). 

 Instead of the old subdivision of the class D into " theory of 

 functions from the points of view of Cauchy, Weiers trass, and 

 Riemann " (D3 — D5), the new edition substitutes sections : 

 " General properties of analytic functions of one variable " ; 

 " Conformal representation and analogous subjects " ; and 

 " Functions of many complex variables." In the class H, 

 the section con" Particular functional equations " is amplified 

 with subdivisions on : " Linear integral equations (resolving 

 kernel ; fundamental functions) " ; " Non-linear integral 

 equations " ; and " Integro-differential equations." It may 

 be remarked that Di e (in the class devoted to functions of 

 real variables) is a new section on " Functions of lines and 

 their applications in the theory of integral and integro-differ- 

 ential equations," with a reference to the section (Hn c) 

 just spoken of ; but there is no cross-reference in the section 

 H 1 1 c to D 1 e, which would probably be convenient to readers . 

 The Index is adopted in that exceedingly useful publication 

 the Revue semestrielle des publications mathematiques, as well as 

 in some other publications in Great Britain and France, and 

 this new edition is still more useful than the preceding one in 

 the classification of modern mathematical work. 



The first of the three parts of the Jahrbuch iiber die Fort- 

 schritte der Mathematik for 191 3 was published at the end of 

 1916. It may be remarked that efforts are now being made 

 to wake up the nations of the Entente to the advisability of 

 their not being dependent, owing to their inertia, on Germany 

 for the good work of organising the results of scientific research 

 (see E. Rignano, Nature, 191 7, 98, 408-9, 413-14). 



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