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/Алгебра/Дифференциальная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1937

Количество страниц: 119

Добавлена в каталог: 15.03.2005

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Предметный указатель

, , ,       10
      22
      47
      50
      11
      34
      35
      37
      69
      36
      37
      41
$\Delta_i$       34 37
$\delta_i^j$       8
$\Re$       11
$\Re'$       34 92 95
$\Re''$       35
$\Re[u]=\Re[u^1,...,u^n]$       11
$\Re^N$       37
$\Re^{\ast}$       2
$\Re_C$       54 94 95
$\Sigma_k$       59
$\theta$ -monomial      9
$\xi$ -monomial      9
Addition      18
Addition of systems      4
Adjoint      23 27
Adjunction      67 68
Algebraic complement      18
Associate of Grassmann form      22
Associate of Grassmann form, prime system      65
Associate of Grassmann form, symbol in $\Re$       47
Associated set      25 25
Assumptions, algebraic      10 11 22 47 50
Assumptions, algebraic, differential      34 35 37
Assumptions, algebraic, existence      9 70
Assumptions, algebraic, inequation      70
Assumptions, algebraic, integral      30 37 41
Assumptions, algebraic, Weierstrass      75
Auxiliary system      80 81
Auxiliary system, non-singular      82
Basis, canonical      45
Basis, canonical of Grassmann ring      11
Basis, canonical of Grassmann ring, pfaffian system      41
Basis, canonical of Grassmann ring, polynomial      49
Basis, canonical of Grassmann ring, set of linear forms      18
Basis, canonical, differential      41
Basis, canonicalnormalized      21
Bibliography      114
Blichfeldt, H. F.      114
Bocher, M.      114
Burstin, C      85
Canonical basis      45
Canonical basis, factor      61
Canonical basis, form of pfaffian      45—40 104—106
Canonical basis, form of pfaffian, equation      45—46 104—105
Canonical basis, ordering      8
Cartan, K.      v 10 25 79 83 114
Cauchy, A.      73 91 100
Cerf, G.      79 80 114
Characteristic system of pfaffian system      42
Characteristic system of pfaffian system, set of forms      41
Characteristic variables for pfaffian system      43
Characteristic variables for pfaffian system, set of forms      42
Characters, calculation of      86—87
Characters, calculation of linear pfaffian equation      88
Characters, calculation of linear pfaffian equation, numerical determination      81
Characters, calculation of linear pfaffian equation, pfaffian system      82
Class of pfaffian system      42
Class of pfaffian system, set of forms      41
Coefficient, literal      13
Coefficient, literal, parametric      90
Coefficient, literal, principal      90
Coefficient, literal, skew-symmetric      13
COMMON      48
Common, determination for two polynomials      51—53
Complement, algebraic      18
Complement, algebraic, of function      3
Complementary set, absolute      57 106
Complementary set, relative      58 107
Complete set, absolute      56 106
Complete set, relative      58 107
Composite      47
Compound symbol      1
Consistency, ,       94
Consistency, to       22
Consistency, , ,       92
Consistency, ,       92
Consistency,       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, algebraic system, commutative monomial      48
Degree, algebraic system, commutative polynomial      48
Degree, algebraic system, Grassmann monomial      11
Degree, algebraic system, Grassmann polynomial      13
Degree, algebraic system, pfaffian system      79
Derivative, Grassmann monomial      15
Derivative, Grassmann monomial, Grassmann polynomial      15
Derivative, Grassmann monomial, parametric      66
Derivative, Grassmann monomial, partial      37
Derivative, Grassmann monomial, principal      66
Determinable system      75
Determinant      17
Determinant, bordered      33
Determinant, principal      32
Determinant, skew-symmetric      33
Determined system, algebraic      69
Determined system, algebraic, 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, Grassmann polynomials , indirect      38
Differentiation, Grassmann polynomials, ordinary polynomials      49
Dimension, Grassmann ring      12
Dimension, Grassmann ring, integral variety      79
Dimension, Grassmann ring, polynomial ring      49
Discriminant      54 67 75
Dissimilar monomials      12
Dominant function      97
Dominant function, system      97
e      69 77
Eisenbart, I.. P.      111
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
Extended substitution      5
Extension      77
Factor, canonical      61 70
Factor, canonical, improper      47
Factor, proper      47
Factor, proper in SR      47
Factor, proper of Grassmann form      27
Factor, proper of Grassmann form, system      4
Factor, proper, simple      61

Factor, proper, theorem      54
Follower      7
Form, Grassmann      13
Form, Grassmann, linear      17
Form, Grassmann, monomial      43—44
Form, Grassmann, 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 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 differential coefficient, monomial      56
Index of differential coefficient, 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
Kuler’s theorem      17
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, 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 systems 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, non-singular      82
Numerical determination, non-singular for algebraic system      69
Numerical determination, non-singular for algebraic system, function system      75".
Numerical determination, non-singular, pfaffian system      81
o      1
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 algebraic system, derivative      8
Ordinal of algebraic system, function      75
Ordinal of algebraic system, polynomial      49 50
Ordinal of algebraic system, polynomial in algebraic differential system      66
Osgood, W. F.,94,      114
Ostrogradsky, M.      102
Parametric coefficient      96
Parametric coefficient, derivative      66
Parametric coefficient, indeterminate      61
Parametric coefficient, unknown      66
Passive differential system      68 70—71
Passive differential system, pfaffian system      41 43 46 89 90
Permutation, signed      11
Pfaffian      44 45—46
Pfaffian, equation      45—46
Pfaffian, system      41 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 coefficient, derivative      66
Principal coefficient, determinant      32
Principal coefficient, indeterminate      61
Principal coefficient, 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 derivative, Grassmann form      25
Rank of derivative, matrix      18
Rank of derivative, ordinary ])o)ynomial      49
Rank of derivative, pfafHan system      41
Rank of derivative, quadratic form      31
Rank of derivative, set of Grassmann forms      25
Rank of derivative, set of Grassmann forms, linear forms      18
Rank of derivative, skew-symmetric matrix      32
Rank of derivative, unit monomials (absolute)      57
Raudenbush, H. W.      35
Reduced      62
Reduction algorithm      6
Reduction of function system      75—76
Regular system      84

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