Branching solutions to one-dimensional variational problems /:
This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. |
| Beschreibung: | 1 online resource (xxi, 342 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 323-329) and index. |
| ISBN: | 9789812810717 9812810714 9810240600 9789810240608 1281956368 9781281956361 9786611956363 6611956360 |
Internformat
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| 100 | 1 | |a Ivanov, A. O. |q (Alexander O.) |1 https://id.oclc.org/worldcat/entity/E39PCjJJ8XBcpkhYmM7P3wftTd |0 http://id.loc.gov/authorities/names/n93070462 | |
| 245 | 1 | 0 | |a Branching solutions to one-dimensional variational problems / |c A.O. Ivanov & A.A. Tuzhilin. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (xxi, 342 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 323-329) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. | ||
| 505 | 0 | |a Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem -- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces -- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem -- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees -- ch. 5. Extremals of the length functional: the case of networks -- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks -- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. Manhattan local minimal and extreme networks. | |
| 546 | |a English. | ||
| 650 | 0 | |a Extremal problems (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85046597 | |
| 650 | 0 | |a Steiner systems. |0 http://id.loc.gov/authorities/subjects/sh85127898 | |
| 650 | 6 | |a Problèmes extrémaux (Mathématiques) | |
| 650 | 6 | |a Systèmes de Steiner. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Extremal problems (Mathematics) |2 fast | |
| 650 | 7 | |a Steiner systems |2 fast | |
| 700 | 1 | |a Tuzhilin, A. A. |1 https://id.oclc.org/worldcat/entity/E39PCjqQ6jhV49QGbRQ8XyqJDq |0 http://id.loc.gov/authorities/names/n91050904 | |
| 758 | |i has work: |a Branching solutions to one-dimensional variational problems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG4864q3y7FPBb4g3DMbMP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Ivanov, A.O. (Alexander O.). |t Branching solutions to one-dimensional variational problems. |d Singapore ; River Edge, NJ : World Scientific, ©2001 |z 9789810240608 |w (DLC) 00063439 |w (OCoLC)44811646 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn269468852 |
|---|---|
| _version_ | 1816881679804923904 |
| adam_text | |
| any_adam_object | |
| author | Ivanov, A. O. (Alexander O.) |
| author2 | Tuzhilin, A. A. |
| author2_role | |
| author2_variant | a a t aa aat |
| author_GND | http://id.loc.gov/authorities/names/n93070462 http://id.loc.gov/authorities/names/n91050904 |
| author_facet | Ivanov, A. O. (Alexander O.) Tuzhilin, A. A. |
| author_role | |
| author_sort | Ivanov, A. O. |
| author_variant | a o i ao aoi |
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| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331 .I935 2001eb |
| callnumber-search | QA331 .I935 2001eb |
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| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem -- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces -- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem -- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees -- ch. 5. Extremals of the length functional: the case of networks -- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks -- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. Manhattan local minimal and extreme networks. |
| ctrlnum | (OCoLC)269468852 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem -- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces -- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem -- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees -- ch. 5. Extremals of the length functional: the case of networks -- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks -- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. 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| id | ZDB-4-EBA-ocn269468852 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:33Z |
| institution | BVB |
| isbn | 9789812810717 9812810714 9810240600 9789810240608 1281956368 9781281956361 9786611956363 6611956360 |
| language | English |
| oclc_num | 269468852 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 342 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Ivanov, A. O. (Alexander O.) https://id.oclc.org/worldcat/entity/E39PCjJJ8XBcpkhYmM7P3wftTd http://id.loc.gov/authorities/names/n93070462 Branching solutions to one-dimensional variational problems / A.O. Ivanov & A.A. Tuzhilin. Singapore ; River Edge, NJ : World Scientific, ©2001. 1 online resource (xxi, 342 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 323-329) and index. Print version record. This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem -- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces -- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem -- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees -- ch. 5. Extremals of the length functional: the case of networks -- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks -- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. Manhattan local minimal and extreme networks. English. Extremal problems (Mathematics) http://id.loc.gov/authorities/subjects/sh85046597 Steiner systems. http://id.loc.gov/authorities/subjects/sh85127898 Problèmes extrémaux (Mathématiques) Systèmes de Steiner. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Extremal problems (Mathematics) fast Steiner systems fast Tuzhilin, A. A. https://id.oclc.org/worldcat/entity/E39PCjqQ6jhV49QGbRQ8XyqJDq http://id.loc.gov/authorities/names/n91050904 has work: Branching solutions to one-dimensional variational problems (Text) https://id.oclc.org/worldcat/entity/E39PCG4864q3y7FPBb4g3DMbMP https://id.oclc.org/worldcat/ontology/hasWork Print version: Ivanov, A.O. (Alexander O.). Branching solutions to one-dimensional variational problems. Singapore ; River Edge, NJ : World Scientific, ©2001 9789810240608 (DLC) 00063439 (OCoLC)44811646 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235934 Volltext |
| spellingShingle | Ivanov, A. O. (Alexander O.) Branching solutions to one-dimensional variational problems / Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem -- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces -- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem -- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees -- ch. 5. Extremals of the length functional: the case of networks -- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks -- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. Manhattan local minimal and extreme networks. Extremal problems (Mathematics) http://id.loc.gov/authorities/subjects/sh85046597 Steiner systems. http://id.loc.gov/authorities/subjects/sh85127898 Problèmes extrémaux (Mathématiques) Systèmes de Steiner. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Extremal problems (Mathematics) fast Steiner systems fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85046597 http://id.loc.gov/authorities/subjects/sh85127898 |
| title | Branching solutions to one-dimensional variational problems / |
| title_auth | Branching solutions to one-dimensional variational problems / |
| title_exact_search | Branching solutions to one-dimensional variational problems / |
| title_full | Branching solutions to one-dimensional variational problems / A.O. Ivanov & A.A. Tuzhilin. |
| title_fullStr | Branching solutions to one-dimensional variational problems / A.O. Ivanov & A.A. Tuzhilin. |
| title_full_unstemmed | Branching solutions to one-dimensional variational problems / A.O. Ivanov & A.A. Tuzhilin. |
| title_short | Branching solutions to one-dimensional variational problems / |
| title_sort | branching solutions to one dimensional variational problems |
| topic | Extremal problems (Mathematics) http://id.loc.gov/authorities/subjects/sh85046597 Steiner systems. http://id.loc.gov/authorities/subjects/sh85127898 Problèmes extrémaux (Mathématiques) Systèmes de Steiner. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Extremal problems (Mathematics) fast Steiner systems fast |
| topic_facet | Extremal problems (Mathematics) Steiner systems. Problèmes extrémaux (Mathématiques) Systèmes de Steiner. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Steiner systems |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235934 |
| work_keys_str_mv | AT ivanovao branchingsolutionstoonedimensionalvariationalproblems AT tuzhilinaa branchingsolutionstoonedimensionalvariationalproblems |