Schouten J.A., van der Kulk W. — Pfaffs Problem and Its Generalizations :: Электронная библиотека попечительского совета мехмата МГУ

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Schouten J.A., van der Kulk W. — Pfaffs Problem and Its Generalizations

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Название: Pfaffs Problem and Its Generalizations

Авторы: Schouten J.A., van der Kulk W.

Аннотация:

In its simplest form, the Pfaff problem (formulated by Pfaff in 1819) consists of determining the maximal integrable manifold of a Pfaffian system, i.e. of a system of vector fields in R^n. This book gives a solution of this problem and discusses various generalizations, giving an essentially complete treatment of the theory as it was known in 1949.

Язык:

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 542

Добавлена в каталог: 15.04.2005

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Предметный указатель

Prolongation, Cartan's theorem of      602 ff
Prolongation, of PC-system      467 ff
Prolongation, of PNRSC-Byatem      493 ff
Prolongation, partial      469
Prolongation, partial prolongation of PC-system      505
PRSC-system      472
Pseudo, affinor      7
Pseudo, group $\mathfrak{B}$       32
Pseudo, p-vector      13
Pseudo, tensor      12
Pseudo, vector      4 6
q-vector field, covariant, class of      321 ff
q-vector field, covariant, normal form of      327
Quadrivector      13
Quantity, in       4
Quantity, in       48 ff
Quasi-linear, $\mathfrak{S}_d^m$ -field      418 445
Randpunkt, unwesentlicher      516
Rank      10 f
Rank $w_\lambda$ -rank of $\mathfrak{N}_m$       274
Rank of -transformation      216
Rank of function group      266
Rank of systems of functions      33
Reduced genus      378 384
Reduced system      111
Reduction      3 23
Reduction number      26 26
Reduction with respect to       63
Reduction with respect to in       52
Reduction with respect to normal system      45
Region      29
Region fundamental      33
Region of constant class      149 185
Region of constant rank      47
Regular chain      351 358
Regular decomposition of regular systems      63
Regular integral element      351
Regular integral-      351 358
Regular null form      35
Regular parametric form      46
Regular systems of equations      35
Regular tests for, chains      397 ff
Relative integral invariant of       76
Relative integral invariant of       77
Relative invariant field with respect to       76 98
Relative invariant field with respect to       77 98
Relative invariant field with respect to $[v^{k_1...k_p}]$       135
Representation canonical      147
Representation characteristic number of      147
Representation general      147
Representation normal      147
Rice, L.H.      10
Rigging      23 ff
Ring of closed Goursat system      412
Riquier arrangement      507
Riquier's existence theorem      608
Riquier, C.      606
Rot, rotation      64 135
Rotation class of $w_\lambda$       149
Rotation class of $w_{\lambda_1...\lambda_q}$       175
Rotation class of $\mathfrak{N}_m$       279
Rotation class under C-transformations      280
RSC-system      412 422 472
RSC-system preferred      472
RSC-system, cutting off of      473
Running indices      1
S, , , , of $w_\lambda$       148
S, , , , of $w_{\lambda_1...\lambda_q}$       175
S, , , , , completeness of S, , , ,       151 177
Saturated indices      9
SC-system      410
SC-system, prolongation of      467 ff
scalar      4
Scalar, density      19
Scalar, free Goursat system      355
Schouten, J.A.      19 20 51 54 61 67 70 80 81 232 273 275 278 286 296 320 321 327 332
Screw-sense      3
Section      23
Section of and       3
Section of covariant bivector      25
Section of with respect to a set of functions      153
Section with       3
Section with       62
Section with       63
Semi-conjugate set of functions      158 ff 173
Semi-regular systems of equations      35

Signs $\overset{=}{*}$       5
Signs () for infinitesimal transformations      136
Signs () Poisson brackets      246 ff 253
Signs ::      5
Signs [] generalized Poisson brackets      172 ff 272
Signs {} Lagrange brackets      246 ff
Similarity class of $w_\lambda$       149 168
Similarity class of $w_{\lambda_1...\lambda_q}$       175 f 184
Similarity class of $\mathfrak{N}_m$       279
Similarity class of Goursat system      378 417
Similarity class under C-transformations      280
Similarity transformation of $w_\lambda$       167 ff
Similarity transformation of $w_{\lambda_1...\lambda_q}$       181
Simple p-vector      14
Simple Pfaff's problem      vi vii
Singular functions of function group      256
Slebodzinski, W.      70
Solution complete      307
Solution of complete system of homogeneous linear partial equations      107
Solution of complete system of non-homogeneous, linear partial equations      109
Solution of one homogeneous linear partial equation      89
Solution of one non-homogeneous linear partial equation      94
Solution of systems in involution      306 ff
Solution principal      91 108 114
Spanning of       3
Spanning of domain      6
Special Jacobian system      105 115 122
Stationarity of $\mathfrak{S}_{dp}^p(\xi^k)$       436 f
Stationarity of cone $\mathfrak{C}(\xi^k)$       429
Stokes, theorem of      69
Strangling      7 9
Streamlines      89 233
Struik, D.J.      1 19 20 51 61 70 80
Supernumerary coordinates      64 ff
Supernumerary functions      166
Supernumerary regular parametric form      46
Supernumerary regular system of equations      35
Support      4 152 161
Support of domain      4
Support of rotation      152 161
Surface, m-dimensional      39
symmetric      9
Symmetric multiplication      12
Tangent m-direction      52
Tangent space      52
Tensor      12
Tensor density      19
Tensor irreducible      12
Tensor pseudo      12
Theorem of adaption      34
Thomas, J.M.      349 355 388 391 506 510
Thullon, P.      29 516
Totally intogmble      89 109
Transformation basis      38 275
Transformation gradient      168 ff
Transformation group      32
Transformation infinitesimal point      71 136 233
Transformation of coordinates      31
Transformation point      1
Transformation similarity      167 181
Translation      2
Transvection      6 7
Triplet, ordinary      433 436
Trivector      13
Uniqueness theorem of, for $\mathfrak{S}_d^m$ -fields      I 453 II 454 III 454
Uniqueness theorem of, for Goursat systems      I 359 II 371 III 372
Unity afflnor      7
Unwesentlicher Randpunkt      516
v. Dantzig, D.      19 20 51 54 67 81
v. Kampen, E.R.      1 20 61 70
v. Weber, E.      vi 35 42 82 88 91 92 94 104 107 109 113 115 126 128 136 148 151 152 153 156 160 172 199 210 224 229 233 241 246 251 253 255 262 273 306 316 318 319
v. Weyssenhoff, J.      81
v.d. Kulk, W.      273 275 278 286 296 320 327 331 332 418 425 428 429 431 437 440 446 449 452 453 454 457 460
Variables, principal and parametrical      398 405 407
Veblen, O.      1 29 31 32
Vector      4 5
Vector coefficients      475
Vector density      19
Vector, element of       207
Vector, manifold $\mathfrak{N}_m$ ,       208
Vector, pseudo-      4 6
Weight      19
Weyl-density      20
Whitehead, J.H.G.      1 29 31 32
Whittaker, E.T.      199 210 224 229 246
Zorawski, K.      129

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