| Edition |
1st ed. |
| Description |
1 online resource (ix, 385 pages) : illustrations |
|
text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematical library ; v. 57 |
|
North-Holland mathematical library ; v. 57.
|
| Summary |
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. |
| Contents |
Preface. Introduction. The linear inequalitites. Singularities of algebraic equations. Hamiltonian truncations. Local analysis of an ODE system. Systems of arbitrary equations. Self-similar solutions. On complexity of problems of Power Geometry. Bibliography. Subject index. |
| Bibliography |
Includes bibliographical references (pages 359-381) and index. |
| Note |
Print version record. |
| Language |
English. |
| Subject |
Geometry, Plane.
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Differential-algebraic equations.
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Géométrie plane.
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Équations différentielles algébriques.
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MATHEMATICS -- Geometry -- General.
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Differential-algebraic equations
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Geometry, Plane
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| Other Form: |
Print version: Briuno, Aleksandr Dmitrievich. Stepennaia geometriia v algebraicheskikh i differentsialnykh uravneniiakh. English. Power geometry in algebraic and differential equations. 1st ed. Amsterdam ; New York : Elsevier, 2000 0444502971 9780444502971 (DLC) 00041723 (OCoLC)45029927 |
| ISBN |
9780444502971 |
|
0444502971 |
|
9780080539331 (electronic bk.) |
|
0080539335 (electronic bk.) |
|
1281038725 |
|
9781281038722 |
|
9786611038724 |
|
6611038728 |
| Standard No. |
AU@ 000048130345 |
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CHNEW 001005953 |
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DEBBG BV036962275 |
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DEBBG BV039830143 |
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DEBBG BV042317289 |
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DEBSZ 276237366 |
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DEBSZ 482353600 |
|
NZ1 12433124 |
|
NZ1 15192849 |
|
AU@ 000075311110 |
|
