5210 



Linear Differential Forms; Pfaffians 



5210 



Linear congruences. Giddberg, A. Christi- 

 ania Skr. (Mth. Nt. Kl.) (1897) No. 10, 

 23 pp. 



differential expressions, adjoint. Frobenius, 

 G. [1877] Crelle J. Mth. 8-5 (1878) 185-. 



Primary forms. Cockle, (Sir) Jas. Ph. Mg. 

 49 (1875) 134- ; 9 (1880) 348-. 



Surfaces with infinitesimal and linear trans- 

 formations. Lie, M. 

 7 (1882) 179-. 



Transformation of variables. Gasparis, A. de. 

 Nap. Ac. At. 7 (1878) No. 15, 8 pp. ; 8 (1879) 

 No. 2, 16 pp. ; Km. R. Ac. Line. T. 2 (1878) 

 192-. 



5210 



Linear differential 

 Pfaffians. 



Integrating factors. Saurel, P. J. Ps. C. 2 



(1898) 116-. 

 Integration of equation, 1st order. Petersen, J. 



Mth. Ts. 1 (1859) 90-. 

 total differential equations. Bertrand, J. 



C. R. 83 (1876) 1191-. 

 . Du Bois-Eeymond, P. Mth. 



A. 12 (1877) 123-. 

 Arch. Mth. Ntvd. , 1st order and degree. Fais, A. 



G. Mt. 13 (1875) 344-. 



in 3 variables. Fais, A. 

 Bologna Rd. (1893-94) 66-. 



dz = Hdx + Kdy + Ldp + Mdq + Ndr + etc. 



Eaabe, J. L. Crelle J. 14 (1835) 123-. 



X 1 dx + x 2 dx 1 + x 3 dx 2 + xdx 3 = (). Spitzer, 

 S. Grunert Arch. 23 (1854) 453- ; 30 (1858) 



forms; 



Algebraic integral of two differential equations. 

 Roberts, R. A. [1890] L. Mth. S. P. 22 

 (1891) 28-. 



integrals of differential equations, 1st order 

 and degree. Poincare, H. Palermo Cir. Mt. 

 Rd. 5 (1891) 161-. 



Binomial differentials. Combescure, E. Bll. 



So. Mth. 11 (1887) 245-. 

 . Kapteyn, W. Bll. Sc. Mth. 12 (1888) 



44-. 



Common multiples of linear differential ex- 

 pressions. Heffter, L. Crelle J. Mth. 116 



(1896) 157-. 



Condition that total differential equation 

 Pdx + Qdy + Rdz + etc. = 



admit of single primitive. Van Velzer, C. A. 



[1879] (xn) J. H. Un. Cir. [1] (1882) 



35. 

 be integrable. Lovett, E. 0. 



A. Mth. 1 (1900) 175-. 

 Differential expressions and Pfaff's problem. 



Cartan, E. Par. EC. Norm. A. 16 (1899) 



239-. 

 , problem. Torelli, G. A. Mt. 13 (1885) 



23-. 



forms. Combescure, E. C. R. 70 (1870) 

 1164-. 



parameters, 1st order. Banal, E. G. Mt. 

 30 (1892) 235-. 



problem, theory. Lie, S. Christiania F. 

 14 (1872) 132-. 



systems - with uniform general integral. 

 Painleve, P. C. R. 131 (1900) 497-, 534. 



Equation xdx + x^d.^ + x 2 dx 2 + ... + x n dx n = 

 integrable by a primitive equation. Zajacz- 

 kowski, W. Par. T. Nauk Sc. Pam. 6 (*1875) 

 Art. 4, 14 pp. 



Equations of form dz = Z (Udx + Vdy) , where 

 U, V, z, are functions of x and y, and Z a 

 function of z. Hansen, C. (xn) Ts. Mth. 

 4 (1868) 188-. 



Exact homogeneous differentials. Combescure, 

 E. Bll. Sc. Mth. 11 (1887) 243-. 



Integrability conditions. Laurent, H. N. A. 

 Mth. 6 (1887) 274-, 305-. 



of certain differential expressions. Sincov, 

 D. Kazan S. Ps.-Mth. Bll. 9 (1900) 38-. 



(A + Cz) dx+(B + Dz) dy + Kdz = 0. Sonln, 



N. Y. [1870] (xn) Rec. Mth. (Moscou) 6 

 (1872-73) (Pt. 1) 278-. 



dv=Mdx + Ndy +Pdz. PerevoScikov , 

 D. M. St Pet. Ac. Sc. Mm. (Es.) 22 

 (*1873) 201-. 



X^ + X.-,dx. 2 +... + X n dx n = 0. Stodotkie- 



wicz, A. J.' Prace Mt.-Fiz. 7 (1896) 6-; 

 Fschr. Mth. (1896) 271. 



Linear differential forms. Pincherle, S. Rm. 

 R. Ac. Line. Rd. 1 (1892) (Sem. 1) 273-. 



, theory. Bortolotti, E. A. Mt. 23 



(1895) 309-. 



equations with total differentials. Bianchi, 

 L. Rm. R. Ac. Line. Rd. 5 (1889) (Sem. 1) 

 312-. 



MacMahon's differential equation. Cayley, A. 



QJ. Mth. 19 (1883) 182-. 

 Normals to surface. Bertrand, J. C. R. 17 



(1843) 1277-. 



Operation O having reference to Cayley 's func- 

 tions A (x). Cayley, A. QJ. Mth. 13 (1875) 



369-. 

 (Cayley's), reduction to polar operations. 



Capelli, A. Mth. A. 29 (1887) 331-. 

 Pfaffian equation, infinitesimal automorphic 



transformations. Vivanti, G. Palermo Cir. 



Mt. Rd. 12 (1898) 1-. 

 , . Weber, E. von. Palermo 



Cir. Mt. Rd. 12 (1898) 133-. 



, transformations. Enqel, F. Leip. 

 Mth. Ps. B. 51 (1899) (Mth.) 296-. 



, integration, Clebsch's 2nd method. 

 Brill, J. L. Mth. S. P. 31 (1900) 315-. 



, , general. Sauer, C. G. Oken Isis 



(1825) 1294-. 

 , shortest integral curves. Lilientlml, E. 



von. Mth. A. 52 (1899) 417-. 

 2Xdx = Q. Eussjan, C. Fschr. Mth. 



(1896) 269-. 



equations. Lovett, E. 0. C. R. 129 (1899) 

 274-. 



and line complexes. Weber, E. von. 

 [1900] Munch. Ak. Sb. 30 (1901) 393-. 



of special type, systems. Brill, J. Mess. 



Mth. 26 (1897) 183-. 

 , system. Eusjan, C. K. Fschr. Mth. 



(1899) 315-. 



, , normal number of complete in- 

 tegrals. Eusjan, C. K. Fschr. Mth. (1900) 

 367. 



394 



