000 | 04110nam a22005895i 4500 | ||
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001 | 978-3-540-69315-4 | ||
003 | DE-He213 | ||
005 | 20190213151628.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2009 gw | s |||| 0|eng d | ||
020 |
_a9783540693154 _9978-3-540-69315-4 |
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024 | 7 |
_a10.1007/978-3-540-69315-4 _2doi |
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050 | 4 | _aQA315-316 | |
050 | 4 | _aQA402.3 | |
050 | 4 | _aQA402.5-QA402.6 | |
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_aPBKQ _2bicssc |
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_aMAT005000 _2bisacsh |
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_aPBKQ _2thema |
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_aPBU _2thema |
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082 | 0 | 4 |
_a515.64 _223 |
100 | 1 |
_aBernot, Marc. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aOptimal Transportation Networks _h[electronic resource] : _bModels and Theory / _cby Marc Bernot, Vicent Caselles, Jean-Michel Morel. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2009. |
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300 |
_aX, 200 p. 58 illus., 5 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1955 |
|
505 | 0 | _aIntroduction: The Models -- The Mathematical Models -- Traffic Plans -- The Structure of Optimal Traffic Plans -- Operations on Traffic Plans -- Traffic Plans and Distances between Measures -- The Tree Structure of Optimal Traffic Plans and their Approximation -- Interior and Boundary Regularity -- The Equivalence of Various Models -- Irrigability and Dimension -- The Landscape of an Optimal Pattern -- The Gilbert-Steiner Problem -- Dirac to Lebesgue Segment: A Case Study -- Application: Embedded Irrigation Networks -- Open Problems. | |
520 | _aThe transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume. | ||
650 | 0 | _aMathematical optimization. | |
650 | 0 | _aEngineering economy. | |
650 | 0 | _aOperations research. | |
650 | 0 | _aMathematics. | |
650 | 1 | 4 |
_aCalculus of Variations and Optimal Control; Optimization. _0http://scigraph.springernature.com/things/product-market-codes/M26016 |
650 | 2 | 4 |
_aOperations Research, Management Science. _0http://scigraph.springernature.com/things/product-market-codes/M26024 |
650 | 2 | 4 |
_aEngineering Economics, Organization, Logistics, Marketing. _0http://scigraph.springernature.com/things/product-market-codes/T22016 |
650 | 2 | 4 |
_aOperations Research/Decision Theory. _0http://scigraph.springernature.com/things/product-market-codes/521000 |
650 | 2 | 4 |
_aApplications of Mathematics. _0http://scigraph.springernature.com/things/product-market-codes/M13003 |
700 | 1 |
_aCaselles, Vicent. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
700 | 1 |
_aMorel, Jean-Michel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540865308 |
776 | 0 | 8 |
_iPrinted edition: _z9783540693147 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1955 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-540-69315-4 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c11335 _d11335 |