See symplectic on Wiktionary
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I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99:", "text": "There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.", "type": "quote" }, { "text": "1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser)." }, { "text": "2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938." }, { "ref": "2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:", "type": "quote" }, { "ref": "2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72:", "text": "In symplectic geometry, there is a notion of fibrations #x5C;pi#x3A;P#x5C;rightarrowM with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,#x5C;omega#x5F;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.", "type": "quote" } ], "glosses": [ "Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form." ], "id": "en-symplectic-en-adj-LLPk~MI~", "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "differentiable", "differentiable" ], [ "manifold", "manifold" ], [ "closed", "closed" ], [ "nondegenerate", "nondegenerate" ], [ "bilinear form", "bilinear form" ] ], "raw_glosses": [ "(mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ { "_dis": "7 6 8 14 12 17 9 16 11", "kind": "other", "name": "English terms prefixed with sym-", "parents": [], "source": "w+disamb" } ], "glosses": [ "That moves in the same direction as a system of synchronized waves." ], "id": "en-symplectic-en-adj-SbTp1iKg", "links": [ [ "synchronized", "synchronized" ], [ "wave", "wave" ] ], "tags": [ "not-comparable" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mineralogy", "orig": "en:Mineralogy", "parents": [ "Geology", "Earth sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Petrology", "orig": "en:Petrology", "parents": [ "Geology", "Earth sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Of or pertaining to a symplectite; symplectitic." ], "id": "en-symplectic-en-adj-qTRFkZNB", "links": [ [ "petrology", "petrology" ], [ "mineralogy", "mineralogy" ], [ "symplectite", "symplectite" ], [ "symplectitic", "symplectitic#English" ] ], "raw_glosses": [ "(petrology, mineralogy) Of or pertaining to a symplectite; symplectitic." ], "tags": [ "not-comparable" ], "topics": [ "chemistry", "geography", "geology", "mineralogy", "natural-sciences", "petrology", "physical-sciences" ] } ], "sounds": [ { "ipa": "/sɪmˈplɛktɪk/" }, { "rhymes": "-ɛktɪk" } ], "wikipedia": [ "Hermann Weyl", "The Classical Groups" ], "word": "symplectic" } { "etymology_templates": [ { "args": { "1": "en", "2": "grc", "3": "συμπλεκτικός" }, "expansion": "Ancient Greek συμπλεκτικός (sumplektikós)", "name": "der" } ], "etymology_text": "A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations. From Ancient Greek συμπλεκτικός (sumplektikós), from συμ (sum) (variant of σύν (sún)), + πλεκτικός (plektikós) (from πλέκω (plékō)); modelled on complex (from Latin complexus (“braided together”), from com- (“together”) + plectere (“to weave, braid”)).\nThe symplectic group has previously been called the line complex group.", "forms": [ { "form": "symplectics", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "symplectic (plural symplectics)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "6 6 3 17 13 15 8 23 10", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "7 6 8 14 12 17 9 16 11", "kind": "other", "name": "English terms prefixed with sym-", "parents": [], "source": "w+disamb" }, { "_dis": "5 6 5 16 13 15 8 22 10", "kind": "other", "name": "English terms with non-redundant non-automated sortkeys", "parents": [ "Terms with non-redundant non-automated sortkeys", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "3 6 2 18 14 16 7 25 10", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "6 6 1 17 14 17 7 23 10", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339:", "text": "The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.", "type": "quote" } ], "glosses": [ "A symplectic bilinear form, manifold, geometry, etc." ], "id": "en-symplectic-en-noun-nVxKaLV4", "links": [ [ "mathematics", "mathematics" ] ], "raw_glosses": [ "(mathematics) A symplectic bilinear form, manifold, geometry, etc." ], "topics": [ "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Ichthyology", "orig": "en:Ichthyology", "parents": [ "Zoology", "Biology", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "7 6 8 14 12 17 9 16 11", "kind": "other", "name": "English terms prefixed with sym-", "parents": [], "source": "w+disamb" } ], "examples": [ { "ref": "1914, The Philippine Journal of Science, Volume 9, page 27:", "text": "The symplectics (9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.", "type": "quote" }, { "ref": "1965, Agra University Journal of Research: Science, Volume 14, page 71:", "text": "The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.", "type": "quote" }, { "ref": "1967, Tyson R. Roberts, Studies on the Osteology and Phylogeny of Characoid Fishes, page 59:", "text": "In many teleosts, on the other hand, including the catfishes, the symplectics have been entirely lost.", "type": "quote" } ], "glosses": [ "A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held." ], "id": "en-symplectic-en-noun-o57D2z7X", "links": [ [ "ichthyology", "ichthyology" ], [ "bone", "bone" ], [ "teleostean", "teleostean" ], [ "fish", "fish" ], [ "ossification", "ossification" ], [ "suspensorium", "suspensorium" ], [ "articulate", "articulate" ], [ "quadrate bone", "quadrate bone" ] ], "raw_glosses": [ "(ichthyology) A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held." ], "topics": [ "biology", "ichthyology", "natural-sciences", "zoology" ] } ], "sounds": [ { "ipa": "/sɪmˈplɛktɪk/" }, { "rhymes": "-ɛktɪk" } ], "wikipedia": [ "Hermann Weyl", "The Classical Groups" ], "word": "symplectic" }
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I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99:", "text": "There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.", "type": "quote" }, { "text": "1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser)." }, { "text": "2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938." }, { "ref": "2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:", "type": "quote" }, { "ref": "2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72:", "text": "In symplectic geometry, there is a notion of fibrations #x5C;pi#x3A;P#x5C;rightarrowM with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,#x5C;omega#x5F;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.", "type": "quote" } ], "glosses": [ "Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form." ], "links": [ [ "mathematics", "mathematics" ], [ "geometry", "geometry" ], [ "differentiable", "differentiable" ], [ "manifold", "manifold" ], [ "closed", "closed" ], [ "nondegenerate", "nondegenerate" ], [ "bilinear form", "bilinear form" ] ], "raw_glosses": [ "(mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] }, { "glosses": [ "That moves in the same direction as a system of synchronized waves." ], "links": [ [ "synchronized", "synchronized" ], [ "wave", "wave" ] ], "tags": [ "not-comparable" ] }, { "categories": [ "en:Mineralogy", "en:Petrology" ], "glosses": [ "Of or pertaining to a symplectite; symplectitic." ], "links": [ [ "petrology", "petrology" ], [ "mineralogy", "mineralogy" ], [ "symplectite", "symplectite" ], [ "symplectitic", "symplectitic#English" ] ], "raw_glosses": [ "(petrology, mineralogy) Of or pertaining to a symplectite; symplectitic." ], "tags": [ "not-comparable" ], "topics": [ "chemistry", "geography", "geology", "mineralogy", "natural-sciences", "petrology", "physical-sciences" ] } ], "sounds": [ { "ipa": "/sɪmˈplɛktɪk/" }, { "rhymes": "-ɛktɪk" } ], "wikipedia": [ "Hermann Weyl", "The Classical Groups" ], "word": "symplectic" } { "categories": [ "English adjectives", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms derived from Ancient Greek", "English terms prefixed with sym-", "English terms with non-redundant non-automated sortkeys", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries", "Rhymes:English/ɛktɪk", "Rhymes:English/ɛktɪk/3 syllables" ], "etymology_templates": [ { "args": { "1": "en", "2": "grc", "3": "συμπλεκτικός" }, "expansion": "Ancient Greek συμπλεκτικός (sumplektikós)", "name": "der" } ], "etymology_text": "A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations. 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