Bruno A.D., Fen L.S. — Power geometry in algebraic and differential equations :: Электронная библиотека попечительского совета мехмата МГУ

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Bruno A.D., Fen L.S. — Power geometry in algebraic and differential equations

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Название: Power geometry in algebraic and differential equations

Авторы: Bruno A.D., Fen L.S.

Аннотация:

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.
The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.
The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 386

Добавлена в каталог: 07.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolutely convergent series      57
Affine hull      9 10
Analytical hypersurface      55
Analytical set      55 217
Asymptotic support      298 299
Asymptotics      105
Basic subsystem      146
Basis      11
Belitskii normal form      265
Blow-up solution      320
Boundary layer      308
Boundary subset      10 196
Class $\mathcal{C}(T)$       58
Closure      10
Coherent boundary subsets      43
Complexity of reduced problem      85
Complexity of truncated system      85
Cone of normals      14
Cone of problem      32 73 196
Cone of truncation      73
Conic hull      9 10
Conjugate space      49
Convergent Series      57 58
Convex cone      10
Convex hull      9
Convex set      10
Critical point      55
Curve      60
Degenerate case      82 84
Dehn — Sammerville equations      13
Differential logarithmic monomial      325
Differential monomial      277 316 336
Differential polynomial      277 298 317 336
DIMENSION      11 53 203 315 336
Dimension of aggregate      77 336
Dimension of function      316
Dimension of polynomial      65
Dimension of system      113
Dimension of truncation      63 122
Dimension of truncation of aggregate      73 290
Dominant Newton polyhedron      87
Dual cone      12
Dual descriptions      316
Dual space      49
EDGE      12
Elementary stationary point      106
Equation admitting Lie operator      317
Euler equation      303
Euler formula      13
Exponent of the monomial      60
Face      11 12 196
Finite-      11
Folium of Descartes      2
Formal set      217
Forward cone      12 39
Forward convex cone      39
Fundamental problem      81
Fundamental system of solutions      20
g-asymptotical curve      125
Generalized power transformation      117
Groebner's bases      101
h-asymptotical curve      107
Inner hull      9
Integer convex cone      39
Integral curve      105
Integral set      217
Intermediate truncated system      135
Intermediate truncation      139
k-multiple resonance      273
Lie operator      317 337
Linear hull      9 10
Linear manifold      10
Linear subspace      10
Logarithmic form      326
Logarithmic transformation      5 136 290 329
Manifold      217
Maximal positive minor      24
Method of Groebner's bases      101
Method of Newton polyhedra      101
Method of Newton's open polygons      101
Method of successive elimination      101
Minimal dominant subset      39
Minor      24
Monomial transformations      356
Multi-      11
Negative half space      10
Newton polyhedron      2 4 61 103 122 196 356
Newton's open polygon      100 235

Nonelementary stationary point      106
Nonresonant case      224
Nontrivial integral curve      105
Normal cone      14 196
Normal cone of aggregate of subsets      43
Normal form      195
Normal subspace      316 336
Normal subspace of aggregate      336
Number of degrees of freedom of mechanism      88
Order of scalar function      107
Order of system      339
Order of vector function      59 107
Order with respect to coordinate      339
Outer hull      10
Poly tope      12
Poly-      11
Polyhedral cone      12
Polyhedral set      12
Polyhedron      12
Polyhedron hull      10
Positional function of mechanism      88
Positive minor      24
Power change of time      112
Power of the monomial      60
Power transformation      5 63 111 286 325
Prandtl equation      303
Proper face      13
Proper subsum      319
Pseudo-homogeneous function      299
Rank      116
Reduced fundamental problem      81
Regular solution      1
Resonant normal form      215
Self-similar function      299
Self-similar solution      318 337
Simple point      55 88 105
Simple polyhedron      13
Simple position of mechanism      89
simplex      14
Simplex system      145
Simplicial cone      14 125
Singular point      55 89
Singular point of first type      89
Singular point of second type      89
Singular position of mechanism      89
Singular solution      1
Skeleton      12 197
Solution to equation      318
Solution to ODE system      105
Solution to system of equations      337
Standard transformation      212
Stationary point      105
Stokes equation      303
Subset dominant with respect to forward cone      39
Subspace of coefficients      116 122
Super-support      315
Super-support of function      315
Super-support of polynomial      317 336
Supernormal form      273
Support      2 103 277 317 336 356
Support of expansion      57 58
Support of polynomial      298
Support of sum      162 315
Support of system      111 162 196
Supporting halfspace      10
Supporting hyperplane      10
System admitting Lie operator      337
Table of boundary subsets      27
Table of correspondence      23
Table of projections      169
Tangent cone of aggregate of boundary subsets      43
Tangent cone of face      15
Trivial integral curve      105
Truncated polynomial      278
Truncated problem      300
Truncated system      73 122 162 196 278
Truncation      2
Truncation of aggregate      73 278
Truncation of sum      162
Truncation of sum with respect to order      61
Truncation of system with respect to order      278
Uniformization      99
Unimodular matrix      50 111
Vector coefficients      112
Vector exponents      112
Vector power      277 298
Vertices      12
Zero invariant manifold      140

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