MATHEMATICS 177 



A. R. Forsyth {Proc. Roy. Soc. Edin., 42, 1922, 147-212) 

 discusses in great detail the concomitants of quadratic differ- 

 ential forms in four variables. 



G. Ricci {Rend. Lincei, 31, 1922, 65-71) gives conditions 

 for a quadratic differential form in n variables to be reducible so 

 as to contain only the differentials of n—p independent variables. 



R. Lagrange {C.R., 173, 1921, 1325; 174, 1922, 521, 658) 

 makes some applications of the absolute differential calculus ; 

 and J, Lipka {Rend. Lincei, 31, 1922, 242-5) discusses the 

 systems E. H. Villat {C.R., 174, 1922, 656) discusses the con- 

 formal representation of the half plane on a region for which 

 two portions of the frontier can be brought into coincidence 

 by a simple translation. 



G. Julia {C.R., 174, 1922, 517, 653, 800) applies conformal 

 representation to the study of functional equations. 



S. Minetti {Rend. Lincei, 31, 1922, 12, 202) studies the 

 functional equation f{x-{-y) = f{x)f{y) ; and H. Mineur {C.R., 

 174, 1922, 1678) certain other algebraic functional equations. 



Papers on integral equations are by A. Vergerio {Rend. 

 Lincei, 31, 1922, 15, 49), G. Usai {Rend. Lombardo, 54, 1921, 

 477-89), G. AndreoU {Rend. Napoli, 27, 1921, 71-5), and 

 I. Fredholm {C.R., 174, 1922, 980). 



H. Geiringer {Math. Zs., 12, 1922, 1-17) and O. D. Kellogg 

 {Math. Ann., 86, 1922, 14-17) discuss the characteristic 

 functions of self-adjoint linear differential equations ; G. 

 Andreoli {Rend. Napoli, 27, 1921, 135, 149) generahsations of 

 Riccati's equation ; J. Sommer {Math. Ann., 85, 1922, 65-73) 

 what is the significance of the ' degree ' of a differential 

 equation ; and A. Cahen {C.R., 174, 1922, 276) first order 

 equations with fixed critical points. 



J. Drach {C.R., 174, 1922, 797) determines second order 

 equations which are integrable by quadratures. W. L. Hart 

 {Amer. Journ. Math., 43, 1921, 226-31) writes on the Cauchy- 

 Lipschitz method for infinite systems of differential equations. 



E. Hilb {Math. Ann., 85, 1922, 89-98) solves Hnear difference 

 equations by means of differential equations of infinitely high 

 order. 



R. D. Carmichael {Amer. Journ. Math., 43, 1921, 232-70) 

 continues his systematic treatment of transcendental problems 

 as limiting cases of algebraic problems (see Science Progress, 

 63, 1922, 351). . , ,. 



K. Popoff {C.R., 174, 1922, 731) considers hnear partial 

 differential equations of the second order of elliptic type ; 

 G. Giraud {ibid., 853) non-hnear equations ; M. Gosse {ibid., 

 1612) equations integrable by Darboux's method; and M. 

 Riquier {ibid., 1392, 151 7, 1604) systems of the first order to 

 which Jacobi's method applies. 



