Thomas J.M. — Differential systems :: Электронная библиотека попечительского совета мехмата МГУ

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Thomas J.M. — Differential systems

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Название: Differential systems

Автор: Thomas J.M.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1937

Количество страниц: 64

Добавлена в каталог: 25.11.2012

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Предметный указатель

$A_{1}$ , $A_{2}$ , $A_{3}$ , $A_{4}$       10
$A_{5}$       11
$A_{6}$       22
$A_{7}$       47
$A_{8}$       56
$d_{1}$       34
$D_{2}$       35
$D_{3}$       37
$E_{0}$       69
$I_{1}$       36
$I_{2}$       37
$I_{3}$       41
$\delta^{i}_{j}$       8
$\Delta_{i}$       34 37
$\mathfrak{A}$       3
$\mathfrak{A}^{i}_{j}$       19
$\mathfrak{B}$       3
$\mathfrak{N}$       1
$\mathfrak{O}$       1
$\mathfrak{R}$       1 92 95
$\mathfrak{R}[u]=\mathfrak{R}[u^{1},...,u^{n}]$       11
$\mathfrak{R}^{''}$       35 92 95
$\mathfrak{R}^{'}$       34 92 95
$\mathfrak{R}^{*}$       2
$\mathfrak{R}^{N}$       37
$\mathfrak{R}_{C}$       54 94 95
$\sum_{k}$       59
$\theta$ -monomial      9
$\xi$ -monomial      9
Addition      1
Addition of systems      4
Adjoint      23 27
Adjunction      67 68
Algebraic complement      18
Associate of Grassmann form      22
Associate of prime system      65
Associate of symbol in $\mathfrak{R}$       47
Associated set      25 25
Assumptions, algebraic      10 11 22 47 56
Assumptions, differential      34 35 37
Assumptions, existence      69 76
Assumptions, inequation      76
Assumptions, integral      36 37 41
Assumptions, Weierstrass      75
Auxiliary system      80 81
Auxiliary system, non-singular      82
Basis of Grassmann ring      11
Basis of pfaffian system      41
Basis of polynomial      49
Basis of set of linear forms      18
Basis, canonical      45
Basis, differential      41
Basis, normalized      21
Bibliography      114
Blichfeldt, H.F.      114
Bocher, M.      114
Burstin, C.      85
Canonical basis      45
Canonical factor      61
Canonical form of pfaffian      45—46 104—106
Canonical form of pfaffian equation      45—46 104—105
Canonical ordering      8
Cartan, E.      v 10 25 79 83 114
Cauchy, A.      73 91 100
Cerf, G.      79 86 114
Characteristic system of pfaffian system      42
Characteristic system of set of forms      41
Characteristic variables for pfaffian system      43
Characteristic variables for set of forms      42
Characters of linear pfaffian equation      88
Characters of numerical determination      81
Characters of pfaffian system      82
Characters, calculation of      86—87
Class of pfaffian system      42
Class of set of forms      41
Coefficient, literal      13
Coefficient, parametric      96
Coefficient, principal      96
Coefficient, skew-symmetric      13
COMMON      48
Common, determination for two polynomials      51—53
Complement of function      33
Complement, algebraic      18
Complementary set, absolute      57 106
Complementary set, relative      587 107
Complete set, absolute      56 106
Complete set, relative      58 107
Composite      47
Compound symbol      1
Consistency, $A_{1}$ to $A_{6}$       22
Consistency, $A_{7}$ , $A_{8}$       94
Consistency, $D_{1}$ , $D_{2}$ , $D_{3}$       92
Consistency, $I_{1}$ , $I_{2}$       92
Consistency, $I_{3}$       92—94
Consistency, E      95—100
Consistency, W      94—95
Consistency, Z      95
Consistent system      5
Constant      35
Content      4
Content of pfaffian system      79
Contragredient      23
Cote      7 70 98
Degree, algebraic system      61
Degree, commutative monomial      48
Degree, commutative polynomial      48
Degree, Grassmann monomial      11
Degree, Grassmann polynomial      13
Degree, pfaffian system      79
Derivative, Grassmann monomial      15
Derivative, Grassmann polynomial      15
Derivative, parametric      66
Derivative, partial      37
Derivative, principal      66
Determinable system      75
Determinant      17
Determinant, bordered      33
Determinant, principal      32
Determinant, skew-symmetric      33
Determined system, algebraic      69
Determined system, differential      69
Differential      34
Differential coefficient      34
Differential ring      41
Differential system      5 77
Differential system, ordinary algebraic      110
Differential system, partial algebraic      110—112
Differential system, total      77
Differentiation, Grassmann polynomials      16
Differentiation, indirect      38
Differentiation, ordinary polynomials      49
Dimension, Grassmann ring      12
Dimension, integral variety      79
Dimension, polynomial ring      49
Discriminant      54 67 75
Dissimilar monomials      12
Dominant function      97
Dominant system      97
e      69 77
Eisenhart, L.P.      114
equation      4
Equation, linear, homogeneous      28
Equivalence of systems      4
Equivalence of systems, algebraic      67
Equivalence of systems, differential      67
Equivalence of systems, pfaffian      79
Euler's theorem      17
Extended substitution      5
Extension      77
Factor in $\mathfrak{R}$       47

Factor of Grassmann form      27
Factor of system      4
Factor Theorem      54
Factor, canonical      61 76
Factor, improper      47
Factor, proper      47
Factor, simple      61
Follower      7
Form, Grassmann      13
Form, linear      17
Form, monomial      43—44
Form, quadratic      29—32 103—104
Function      3
Function system      75 85
Function, analytic      78
Function, class l      91
Function, dominant      97
Function, proper      37
Function, same nature      4
Function, single-valued      3
Function, type k      3
Gauss, K.F.      49 102
General solution      78
Generator      57
Genus      82
Goursat, E.      vi 79 91 114
Grade in indeterminate      49
Grade, Grassmann monomial      11
Grade, Grassmann polynomial      13
Grade, ordinary monomial      48
Grade, ordinary polynomial      48
Grassmann ring      11
Grassmann, H.      v 10
Green, G.      102
Hadamard, J.      102
Identification      1
Imbedding      81
Implies      4
Inconsistent system      5 66
Indeterminate      2
Indeterminate, conditioned      61
Indeterminate, parametric      61
Indeterminate, principal      61
Indeterminate, unconditioned      61
Index of differential coefficient      34
Index of monomial      56
Index of system      63
Inequation      4
Initial      48 50 67
Initial determination for algebraic system      69
Initial determination, absolute      57
Initial determination, relative      58
Integral variety      79
Integral variety, non-singular      82 88 89
Integral variety, singular      vi 113
Integrity domain      1
Invariance, Grassmann monomial      11
Invariance, Grassmann polynomial      13
Inverse      47
Inverse of matrix      19
Janet, M.      vi 91 114
Kernel      48
Kronecker, L.      vi 8
Laplace’s expansion of determinant      18
Leader      50 67
Linear dependence      24
Lipschitz, R.      93 94
Literal coefficient      13
Lower ring      22
Makarov, A.G.      vi
Mark      10
Matrix      17
Matrix, inverse      19
Matrix, skew-symmetric      32
Meray, C.      102
Monomial, $\theta$ -      9
Monomial, $\xi$ -      9
Monomial, dissimilar      12
Monomial, Grassmann      11
Monomial, ordinary      48
Monomial, similar      12
Monomial, trivial      11
Monomial, unit      11 56—58 106—108
Multiplication      1
Multiplication of systems      4
Multiplication of variables      8 99
Multiplicity      47 54
Multiplier      56
Nature of function      4
Non-multiplier      56
Non-zero      4
Normal ring      77
Normal system      68 112—113
Numerical determination for algebraic system      69
Numerical determination for function system      75
Numerical determination, non-singular      82
Numerical determination, non-singular, pfaffian system      81
Order, standard      12
Ordering by cotes      7
Ordering of $i_{1}...i_{n}$       5
Ordering, canonical      8
Ordering, complete      8
Ordering, lexicographical      6
Ordinal      6
Ordinal of algebraic system      59
Ordinal of derivative      8
Ordinal of function      75
Ordinal of polynomial      49 50
Ordinal of polynomial in algebraic differential system      66
Osgood, W.F.      94 114
Ostrogradsky, M.      102
Parametric coefficient      96
Parametric derivative      66
Parametric indeterminate      61
Parametric unknown      66
Passive differential system      68 70—71
Passive pfaffian system      41 43 46 89 90
Permutation, signed      11
Pfaffian      44 45—46
Pfaffian equation      45—46
Pfaffian system      41 79 80
Picard, E.      91 114
Polynomial ring      2
Polynomial, Grassmann      11
Polynomial, ordinary      48
Polynomial, simple      55
Polynomial, unit      48
Prime      47 48
Prime system      65
Principal coefficient      96
Principal derivative      66
Principal determinant      32
Principal indeterminate      61
Principal unknown      66
Product of forms      14
Prolonged systems      66 79
Proper function      37
Quotient field      2 91
Rank      6
Rank in subring      21
Rank of derivative      7
Rank of Grassmann form      25
Rank of matrix      18
Rank of ordinary polynomial      49
Rank of pfaffian system      41
Rank of quadratic form      31
Rank of set of Grassmann forms      25
Rank of set of linear forms      18
Rank of skew-symmetric matrix      32
Rank of unit monomials (absolute)      57

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