Ramified integrals, singularities and lacunas:
This volume contains an introduction to the Picard-Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1995
|
| Schriftenreihe: | Mathematics and its applications
315 |
| Schlagworte: | |
| Zusammenfassung: | This volume contains an introduction to the Picard-Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given This book will be valuable to those who are interested in integral transforms, operational calculus, algebraic geometry, PDEs, manifolds and cell complexes and potential theory |
| Beschreibung: | XVII, 289 S. |
| ISBN: | 0792331931 |
Internformat
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| 100 | 1 | |a Vasilev, Vladislav A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ramified integrals, singularities and lacunas |c by V. A. Vassiliev |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1995 | |
| 300 | |a XVII, 289 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 315 | |
| 520 | 3 | |a This volume contains an introduction to the Picard-Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory | |
| 520 | |a Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given | ||
| 520 | |a This book will be valuable to those who are interested in integral transforms, operational calculus, algebraic geometry, PDEs, manifolds and cell complexes and potential theory | ||
| 650 | 4 | |a Differential geometry | |
| 650 | 7 | |a Géométrie intégrale |2 ram | |
| 650 | 7 | |a Transformations intégrales |2 ram | |
| 650 | 4 | |a Integral geometry | |
| 650 | 4 | |a Integral transforms | |
| 830 | 0 | |a Mathematics and its applications |v 315 |w (DE-604)BV008163334 |9 315 | |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006786607 | ||
Datensatz im Suchindex
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| author_facet | Vasilev, Vladislav A. |
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| building | Verbundindex |
| bvnumber | BV010213356 |
| callnumber-first | Q - Science |
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| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)31242848 (DE-599)BVBBV010213356 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010213356 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:34Z |
| institution | BVB |
| isbn | 0792331931 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006786607 |
| oclc_num | 31242848 |
| open_access_boolean | |
| owner | DE-12 DE-11 DE-188 |
| owner_facet | DE-12 DE-11 DE-188 |
| physical | XVII, 289 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Vasilev, Vladislav A. Verfasser aut Ramified integrals, singularities and lacunas by V. A. Vassiliev Dordrecht u.a. Kluwer 1995 XVII, 289 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 315 This volume contains an introduction to the Picard-Lefschetz theory, which controls the ramification and qualitative behaviour of many important functions of PDEs and integral geometry, and its foundations in singularity theory Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given This book will be valuable to those who are interested in integral transforms, operational calculus, algebraic geometry, PDEs, manifolds and cell complexes and potential theory Differential geometry Géométrie intégrale ram Transformations intégrales ram Integral geometry Integral transforms Mathematics and its applications 315 (DE-604)BV008163334 315 |
| spellingShingle | Vasilev, Vladislav A. Ramified integrals, singularities and lacunas Mathematics and its applications Differential geometry Géométrie intégrale ram Transformations intégrales ram Integral geometry Integral transforms |
| title | Ramified integrals, singularities and lacunas |
| title_auth | Ramified integrals, singularities and lacunas |
| title_exact_search | Ramified integrals, singularities and lacunas |
| title_full | Ramified integrals, singularities and lacunas by V. A. Vassiliev |
| title_fullStr | Ramified integrals, singularities and lacunas by V. A. Vassiliev |
| title_full_unstemmed | Ramified integrals, singularities and lacunas by V. A. Vassiliev |
| title_short | Ramified integrals, singularities and lacunas |
| title_sort | ramified integrals singularities and lacunas |
| topic | Differential geometry Géométrie intégrale ram Transformations intégrales ram Integral geometry Integral transforms |
| topic_facet | Differential geometry Géométrie intégrale Transformations intégrales Integral geometry Integral transforms |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT vasilevvladislava ramifiedintegralssingularitiesandlacunas |